From 05229053e7280f82f69b6d076037a98dd8ff2e28 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Cl=C3=A9ment=20Lejeune?= <54889281+Clej@users.noreply.github.com> Date: Wed, 12 Jan 2022 19:44:38 +0100 Subject: [PATCH 01/21] add soft-DTW divergence to metrics --- skfda/misc/_math.py | 35 + skfda/misc/metrics/__init__.py | 2 + skfda/misc/metrics/_sdtw_distances.py | 383 ++ skfda/misc/metrics/sdtw_fast.c | 6487 +++++++++++++++++++++++++ skfda/misc/metrics/sdtw_fast.pyx | 88 + skfda/misc/metrics/setup.py | 13 + 6 files changed, 7008 insertions(+) create mode 100644 skfda/misc/metrics/_sdtw_distances.py create mode 100644 skfda/misc/metrics/sdtw_fast.c create mode 100644 skfda/misc/metrics/sdtw_fast.pyx create mode 100644 skfda/misc/metrics/setup.py diff --git a/skfda/misc/_math.py b/skfda/misc/_math.py index b0f8a482d..722aff759 100644 --- a/skfda/misc/_math.py +++ b/skfda/misc/_math.py @@ -679,3 +679,38 @@ def cosine_similarity_matrix( return _clip_cosine( inner_matrix / norm1[:, np.newaxis] / norm2[np.newaxis, :], ) + +def half_sq_euclidean( + arg1: NDArrayFloat, + arg2: Optional[NDArrayFloat] = None, +) -> NDArrayFloat: + """ + Return the half squared Euclidean row distance between + two matrices. + + Args: + arg1: First sample (n_samples_1, n_features). + arg2: Second sample (n_samples_2, n_features). + If it is ``None`` returns the half squared Euclidean distance + between the rows of ``arg1``. + + The distance is taken w.r.t matrix rows. + """ + if arg2 is not None: + # np.dot(X, Y.T)=inner_product_matrix(X, Y) but np ~1.6 faster + cost_12 = -1 * np.dot(arg1, arg2.T) + + # np.sum(arg1 ** 2, axis=1)=diag(inner_product_matrix(X, X)) + cost_12 += (0.5 * np.sum(arg1 ** 2, axis=1))[:, np.newaxis] + cost_12 += 0.5 * np.sum(arg2 ** 2, axis=1) + + return cost_12 + else: + cost_11 = -1 * np.dot(arg1, arg1.T) + # half sum of squares on each row + sos_row = 0.5 * np.sum(arg1 ** 2, axis=1) + cost_11 += sos_row[:, np.newaxis] + cost_11 += sos_row + + return cost_11 + \ No newline at end of file diff --git a/skfda/misc/metrics/__init__.py b/skfda/misc/metrics/__init__.py index b2fc981f2..07e19089f 100644 --- a/skfda/misc/metrics/__init__.py +++ b/skfda/misc/metrics/__init__.py @@ -22,3 +22,5 @@ TransformationMetric, pairwise_metric_optimization, ) + +from ._sdtw_distances import sdtwDivergence, sdtw_divergence \ No newline at end of file diff --git a/skfda/misc/metrics/_sdtw_distances.py b/skfda/misc/metrics/_sdtw_distances.py new file mode 100644 index 000000000..a705feab1 --- /dev/null +++ b/skfda/misc/metrics/_sdtw_distances.py @@ -0,0 +1,383 @@ +"""" +Implementation of soft Dynamic-Time-Warping (sDTW) divergence. +""" +from __future__ import annotations + +from typing import Optional, TypeVar, Union, Callable, List, Tuple +from numba.core.types.scalars import Boolean, Float + +import numpy as np +from typing_extensions import Final + +from ...representation import FData, FDataGrid, FDataBasis +from ...representation._typing import NDArrayFloat, GridPointsLike, ArrayLike +from ._utils import pairwise_metric_optimization + +from skfda._utils._utils import _check_compatible_fdata +from skfda.misc.metrics import sdtw_fast as sdtw_fast +from skfda.misc._math import half_sq_euclidean + +def _check_shape_postive_cost_mat(cost, expected_shape, shape_only=False): + """check that matrix 'cost' is nonnegative and has expected shape""" + n1, n2 = expected_shape + # must have shape fdata1.grid_points[0], fdata1.grid_points[0] + if not cost.shape == (n1, n2): + raise ValueError( + "Cost matrix must have shape" + " ({}, {})".format(n1, n2) + ) + # non-negativity + if not(shape_only): + if not np.all(cost >= 0): + raise ValueError( + "Cost matrix must contain non-negative entries" + ) + +def _check_indiscernable_sym(cost, X, Y): + """check cost returns a symmetric matrix with zero diag""" + # indiscernability: cost(x_t, x_t) = 0 for any t + if ( + np.all(np.diag(cost(X, X)) != 0) + or np.all(np.diag(cost(Y, Y)) != 0) + ): + raise ValueError( + "The cost between two identical objects " + " must be identically (null diagonal)" + ) + + # symmetry: cost(X1, X2) = cost(X2, X1).T + if not np.allclose(cost(X, Y), cost(Y, X).T): + raise ValueError( + "The cost function does not return a symmetric matrix" + ) + +def _check_input_evalpoints(eval_points): + """check eval_points contains one or two one-dim array""" + if isinstance(eval_points, Tuple) or isinstance(eval_points, List): + if not len(eval_points) <= 2: + raise ValueError( + "eval_points must be a tuple or a list containing one or" + " two elements, each one being a one-dimensional numpy array" + ) + + for idx, ep_i in enumerate(eval_points): + if ( + not (isinstance(ep_i, NDArrayFloat) + and ep_i.ndim == 1) + ): + raise ValueError( + "{}-th element of the tuple must be a one-dimensional" + " numpy array.".format(idx) + ) + + if not np.all(np.diff(ep_i) > 0): + raise ValueError( + "Values in eval_points must be arranged increasingly" + ) + + else: + raise ValueError( + "eval_points must be a tuple containing either one" + " or two one-dimensional numpy array(s)." + ) + +def _check_input_fdata(fdata1, fdata2): + """check compatible and one sample per object""" + _check_compatible_fdata(fdata1, fdata2) + + same_fdata_format = type(fdata1) == type(fdata2) + + if not same_fdata_format: + raise ValueError( + "fdata1 and fdata2 should be either two FDataBasis objects," + " either two FDataGrid objects" + ) + + # if not (fdata1.n_samples == 1 and fdata2.n_samples == 1): + # raise ValueError( + # "Both fdata1 and fdata2 must contain a single sample" + # ) + +def _sdtw_divergence( + fdata1: FData, + fdata2: FData, + *, + gamma: 1.0, + cost: None, + check_cost: False, + eval_points: None +) -> NDArrayFloat: + + # For developers and PR: + # final format of fdata1 and fdata2 is required to be FDataGrid, + # sharing the same domain and codomain dimensions. + # No need for _check_compatible and _cast_to_grid: + # => would raise an error in the following situation: + # if fdata1.domain_range[0] != fdata1.grid_points[0].domain_range[0] + # (sdtw_divergence can deal with different domain_range and grid_points) + + # check whether fdata1 and fdata2 are equivalent + # and have one sample + _check_input_fdata(fdata1, fdata2) + + if not isinstance(fdata1, FDataGrid): + # check eval_points + # must be a tuple of one or two one-dim grid + # maybe an existing skfda function does the job ? + _check_input_evalpoints(eval_points) + + if len(eval_points) == 1: + fdata1 = fdata1.to_grid(eval_points[0]) + fdata2 = fdata2.to_grid(eval_points[0]) + + elif len(eval_points) == 2: + fdata1 = fdata1.to_grid(eval_points[0]) + fdata2 = fdata2.to_grid(eval_points[1]) + + n1, n2 = fdata1.grid_points[0].size, fdata2.grid_points[0].size + d = fdata1.dim_codomain + + if gamma <= 0: + raise ValueError( + "gamma was set to {} but must be positive".format(gamma) + ) + + # cost must satisfy: + # shape=(n1, n2), + # nonnegativity, + # indiscernability and symmetry + if cost is not None: + if isinstance(cost, List): + if not len(cost) == 3: + raise ValueError( + "When the alignment cost matrices are pre-computed," + " then 'cost' must be a list of three two-dimensional" + " numpy arrays" + ) + else: + # shape of cost_12, cost_11 and cost_22 + expected_shapes = [(n1, n2), (n1, n1), (n2, n2)] + for idx, c in enumerate(cost): + if ( + not (isinstance(c, NDArrayFloat) + and c.ndim == 2) + ): + raise ValueError( + "The elements of cost must all be two-dimensional numpy arrays." + " The {}-th element does not satisfy the expected format".format(idx) + ) + + if not c.shape == (n1, n2): + raise ValueError( + "Cost matrix must have shape" + " ({}, {})".format(n1, n2) + ) + + _check_shape_postive_cost_mat( + cost=c, + expected_shape=expected_shapes[idx], + shape_only=not(check_cost) + ) + + cost_12, cost_11, cost_22 = cost[0], cost[1], cost[2] + + elif isinstance(cost, Callable): + cost_12 = cost( + fdata1.data_matrix[0, :, :], + fdata2.data_matrix[0, :, :] + ) + + # check nonnegativity and/or shape + _check_shape_postive_cost_mat( + cost_12, + expected_shape=(n1, n2), + shape_only=not(check_cost) + ) + + if check_cost: + # check indiscernability and symmetry + _check_indiscernable_sym( + cost, + fdata1.data_matrix[0, :, :], + fdata2.data_matrix[0, :, :] + ) + + cost_11 = cost( + fdata1.data_matrix[0, :, :], + fdata1.data_matrix[0, :, :] + ) + cost_22 = cost( + fdata2.data_matrix[0, :, :], + fdata2.data_matrix[0, :, :] + ) + + else: + raise ValueError( + "Cost must be either " + " a list of three numpy arrays" + " or a callable that returns a numpy array" + ) + + else: # default cost: 0.5 * squared Euclidean + + # => 0.5 * squared euclidean or global kernel alignment (depends on gamma !=0) + # half squared euclidean norm on each dimension + # sq_euclidean = DotProduct(sigma_0_bounds=(10**-10, 10**10)) + + # sq_euclidean(X, Y) = diag(np.dot(X, X.T)) + diag(np.dot(Y, Y.T)) - 2*np.dot(X, Y.T) + ## X @ X.T + # cost_11 = sq_euclidean( + # fdata1.data_matrix[0, :, :], + # fdata1.data_matrix[0, :, :] + # ) + # fdata1_vecnorms = 0.5 * np.diag(cost_11) + # cost_11 *= -1 + # cost_11 += fdata1_vecnorms[:, np.newaxis] + # cost_11 += fdata1_vecnorms + + # sq_euclidean(X, Y) = diag(np.dot(X, X.T)) + diag(np.dot(Y, Y.T)) - 2*np.dot(X, Y.T) + ## X @ X.T + cost_11 = half_sq_euclidean(fdata1.data_matrix[0, :, :]) + + ## Y @ Y.T + # cost_22 = sq_euclidean( + # fdata2.data_matrix[0, :, :], + # fdata2.data_matrix[0, :, :] + # ) + # fdata2_vecnorms = 0.5 * np.diag(cost_22) + # cost_22 *= -1 + # cost_22 += fdata2_vecnorms[:, np.newaxis] + # cost_22 += fdata2_vecnorms + + ## Y @ Y.T + cost_22 = half_sq_euclidean(fdata2.data_matrix[0, :, :]) + + # fdata1_vecnorms = 0.5 * sq_euclidean.diag(fdata1.data_matrix[0, :, :]) + # fdata2_vecnorms = 0.5 * sq_euclidean.diag(fdata2.data_matrix[0, :, :]) + + ## X @ Y.T * -1 + # cost_12 = -1 * sq_euclidean( + # fdata1.data_matrix[0, :, :], + # fdata2.data_matrix[0, :, :] + # ) + # cost_12 += fdata1_vecnorms[:, np.newaxis] + # cost_12 += fdata2_vecnorms + + ## X @ Y.T * -1 + cost_12 = half_sq_euclidean( + fdata1.data_matrix[0, :, :], + fdata2.data_matrix[0, :, :] + ) + + # for nonnegativity, symmetry, unicity of div(X,Y)=0 at X=Y + # for other cost, generalize code with Covariance or SKLEARN.kernel + return( + sdtw_fast._sdtw_C_cy(cost_12, gamma) - \ + 0.5 * sdtw_fast._sdtw_C_cy(cost_11, gamma) - \ + 0.5 * sdtw_fast._sdtw_C_cy(cost_22, gamma) + ) + +class sdtwDivergence(): + r""" + Compute the soft Dynamic-Time-Warping (DTW) divergence between + two multivariate functional data whose domain is one-dimensional. + The soft Dynamic-Time-Warping is defined as (:footcite:`Cuturi_2017_sdtw`): + + .. math:: + \text{SDTW}_{\gamma}(x, y) = - \gamma \log + \sum_{A \in \mathcal{A}_{n_x,n_y}} + \exp \big(- \text{Tr}(C^{\top} A) / \gamma \big) + + and the divergence is derived as: + + .. math:: + \text{SDTW}_{div, \gamma}(x, y) = + \text{SDTW}_{\gamma}(x, y) + - \frac{1}{2} \text{SDTW}_{\gamma}(x, x) + - \frac{1}{2} \text{SDTW}_{\gamma}(y, y) + + with :math:`\gamma > 0, C \in \mathbf{R}^{n_x \times n_y}` is the cost matrix + and :math:`\mathcal{A}_{n_x, n_y} \subset \{0, 1\}^{n_x \times n_y}` is an + alignment matrix. If the cost is the half squared Euclidean distance, + :math:`c_{ij} = \frac{1}{2} \lVert x({t_i}) - y({t_j}) \rVert^2_2`. + This a smooth version where the min operator has been replaced by + the soft-min one, whose smoothness is controlled by :math:`\gamma` + (the higher the smoother). + + Dynamic-Time-Warping is a distance metric defined as the minimal cost + to align two time series X and Y. Typically, the cost is chosen as the + squared Euclidean distance. However the classical DTW is not uniquely + minimized and not differentiable w.r.t one argument given the other. + Soft-DTW divergence is a differentiable version of DTW with unique minimizer, + meaning that :math:`sdtw_div(X,Y)=0` if and only if :math:`X=Y`. + It is symmetric and nonnegative but does not satisfy the triangle + inequality. See :footcite:`Blondel_2021_sdtw_div`. + + Args: + fdata1: First FData object. + fdata2: Second FData object. + gamma: smoothing parameter, must be positive. + cost: Either a two-dimensional array or a callable. + If it is an array, then it must have shape ``(n1, n2)`` + where ``n1`` is the grid size of fdata1 and equivalently for ``n2``. + If fdata1 and fdata2 are FDataBasis, then ``cost`` + must be shaped according to the grid size(s) of ``eval_points``. + If it is a callable, then it must take two two-dimensional numpy + arrays (equivalent to the ``data_matirx`` attribute of an FDataGrid + object) as inputs and return a single value. + check_cost: Wheter to check the mathematical properties of ``cost`` + (function or matrix). + eval_points: Tuple of two one-dimensional arrays with points of + evaluation if fdata1 and fdata2 are FDataBasis. + If the tuple contains a single array, it is used both to convert + fdata1 and fdata2 into FDataGrid objects. + + Returns: + soft Dynamic-Time-Warping divergence value. + + References: + .. footbibliography:: + + """ + def __init__( + self, + gamma: float = 1.0, + cost: Optional[Union[List, ArrayLike]] = None, + ) -> None: + + self.gamma = gamma + self.cost = cost + + def __call__( + self, + fdata1: FData, + fdata2: FData, + *, + eval_points: Optional[Union[Tuple, GridPointsLike]] = None, + check_cost: Optional[Boolean] = False + ) -> NDArrayFloat: + """Compute the soft-DTW divergence.""" + return _sdtw_divergence( + fdata1, + fdata2, + gamma=self.gamma, + cost=self.cost, + check_cost=check_cost, + eval_points=eval_points + ) + + def __repr__(self) -> str: + return ( + f"{type(self).__name__}()" + ) + +sdtw_divergence: Final = sdtwDivergence() + +# @pairwise_metric_optimization.register +# def _pairwise_metric_optimization_sdtw( +# metric: sdtwDivergence, +# elem1: FData, +# elem2: FData, +# ) -> NDArrayFloat: + +# return metric(elem1, elem2) diff --git a/skfda/misc/metrics/sdtw_fast.c b/skfda/misc/metrics/sdtw_fast.c new file mode 100644 index 000000000..e26e8b7b8 --- /dev/null +++ b/skfda/misc/metrics/sdtw_fast.c @@ -0,0 +1,6487 @@ +/* Generated by Cython 0.29.24 */ + +#ifndef PY_SSIZE_T_CLEAN +#define PY_SSIZE_T_CLEAN +#endif /* PY_SSIZE_T_CLEAN */ +#include "Python.h" +#ifndef Py_PYTHON_H + #error Python headers needed to compile C extensions, please install development version of Python. +#elif PY_VERSION_HEX < 0x02060000 || (0x03000000 <= PY_VERSION_HEX && PY_VERSION_HEX < 0x03030000) + #error Cython requires Python 2.6+ or Python 3.3+. +#else +#define CYTHON_ABI "0_29_24" +#define CYTHON_HEX_VERSION 0x001D18F0 +#define CYTHON_FUTURE_DIVISION 0 +#include +#ifndef offsetof + #define offsetof(type, member) ( (size_t) & ((type*)0) -> member ) +#endif +#if !defined(WIN32) && !defined(MS_WINDOWS) + #ifndef __stdcall + #define __stdcall + #endif + #ifndef __cdecl + #define __cdecl + #endif + #ifndef __fastcall + #define __fastcall + #endif +#endif +#ifndef DL_IMPORT + #define DL_IMPORT(t) t +#endif +#ifndef DL_EXPORT + #define DL_EXPORT(t) t +#endif +#define __PYX_COMMA , +#ifndef HAVE_LONG_LONG + #if PY_VERSION_HEX >= 0x02070000 + #define HAVE_LONG_LONG + #endif +#endif +#ifndef PY_LONG_LONG + #define PY_LONG_LONG LONG_LONG +#endif +#ifndef Py_HUGE_VAL + #define Py_HUGE_VAL HUGE_VAL +#endif +#ifdef PYPY_VERSION + #define CYTHON_COMPILING_IN_PYPY 1 + #define CYTHON_COMPILING_IN_PYSTON 0 + #define CYTHON_COMPILING_IN_CPYTHON 0 + #undef CYTHON_USE_TYPE_SLOTS + #define CYTHON_USE_TYPE_SLOTS 0 + #undef CYTHON_USE_PYTYPE_LOOKUP + #define CYTHON_USE_PYTYPE_LOOKUP 0 + #if PY_VERSION_HEX < 0x03050000 + #undef CYTHON_USE_ASYNC_SLOTS + #define CYTHON_USE_ASYNC_SLOTS 0 + #elif !defined(CYTHON_USE_ASYNC_SLOTS) + #define CYTHON_USE_ASYNC_SLOTS 1 + #endif + #undef CYTHON_USE_PYLIST_INTERNALS + #define CYTHON_USE_PYLIST_INTERNALS 0 + #undef CYTHON_USE_UNICODE_INTERNALS + #define CYTHON_USE_UNICODE_INTERNALS 0 + #undef CYTHON_USE_UNICODE_WRITER + #define 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#define CYTHON_USE_PYTYPE_LOOKUP 0 + #undef CYTHON_USE_ASYNC_SLOTS + #define CYTHON_USE_ASYNC_SLOTS 0 + #undef CYTHON_USE_PYLIST_INTERNALS + #define CYTHON_USE_PYLIST_INTERNALS 0 + #ifndef CYTHON_USE_UNICODE_INTERNALS + #define CYTHON_USE_UNICODE_INTERNALS 1 + #endif + #undef CYTHON_USE_UNICODE_WRITER + #define CYTHON_USE_UNICODE_WRITER 0 + #undef CYTHON_USE_PYLONG_INTERNALS + #define CYTHON_USE_PYLONG_INTERNALS 0 + #ifndef CYTHON_AVOID_BORROWED_REFS + #define CYTHON_AVOID_BORROWED_REFS 0 + #endif + #ifndef CYTHON_ASSUME_SAFE_MACROS + #define CYTHON_ASSUME_SAFE_MACROS 1 + #endif + #ifndef CYTHON_UNPACK_METHODS + #define CYTHON_UNPACK_METHODS 1 + #endif + #undef CYTHON_FAST_THREAD_STATE + #define CYTHON_FAST_THREAD_STATE 0 + #undef CYTHON_FAST_PYCALL + #define CYTHON_FAST_PYCALL 0 + #undef CYTHON_PEP489_MULTI_PHASE_INIT + #define CYTHON_PEP489_MULTI_PHASE_INIT 0 + #undef CYTHON_USE_TP_FINALIZE + #define CYTHON_USE_TP_FINALIZE 0 + #undef CYTHON_USE_DICT_VERSIONS + #define CYTHON_USE_DICT_VERSIONS 0 + #undef CYTHON_USE_EXC_INFO_STACK + #define CYTHON_USE_EXC_INFO_STACK 0 +#else + #define CYTHON_COMPILING_IN_PYPY 0 + #define CYTHON_COMPILING_IN_PYSTON 0 + #define CYTHON_COMPILING_IN_CPYTHON 1 + #ifndef CYTHON_USE_TYPE_SLOTS + #define CYTHON_USE_TYPE_SLOTS 1 + #endif + #if PY_VERSION_HEX < 0x02070000 + #undef CYTHON_USE_PYTYPE_LOOKUP + #define CYTHON_USE_PYTYPE_LOOKUP 0 + #elif !defined(CYTHON_USE_PYTYPE_LOOKUP) + #define CYTHON_USE_PYTYPE_LOOKUP 1 + #endif + #if PY_MAJOR_VERSION < 3 + #undef CYTHON_USE_ASYNC_SLOTS + #define CYTHON_USE_ASYNC_SLOTS 0 + #elif !defined(CYTHON_USE_ASYNC_SLOTS) + #define CYTHON_USE_ASYNC_SLOTS 1 + #endif + #if PY_VERSION_HEX < 0x02070000 + #undef CYTHON_USE_PYLONG_INTERNALS + #define CYTHON_USE_PYLONG_INTERNALS 0 + #elif !defined(CYTHON_USE_PYLONG_INTERNALS) + #define CYTHON_USE_PYLONG_INTERNALS 1 + #endif + #ifndef CYTHON_USE_PYLIST_INTERNALS + #define CYTHON_USE_PYLIST_INTERNALS 1 + #endif + #ifndef CYTHON_USE_UNICODE_INTERNALS + #define CYTHON_USE_UNICODE_INTERNALS 1 + #endif + #if PY_VERSION_HEX < 0x030300F0 + #undef CYTHON_USE_UNICODE_WRITER + #define CYTHON_USE_UNICODE_WRITER 0 + #elif !defined(CYTHON_USE_UNICODE_WRITER) + #define CYTHON_USE_UNICODE_WRITER 1 + #endif + #ifndef CYTHON_AVOID_BORROWED_REFS + #define CYTHON_AVOID_BORROWED_REFS 0 + #endif + #ifndef CYTHON_ASSUME_SAFE_MACROS + #define CYTHON_ASSUME_SAFE_MACROS 1 + #endif + #ifndef CYTHON_UNPACK_METHODS + #define CYTHON_UNPACK_METHODS 1 + #endif + #ifndef CYTHON_FAST_THREAD_STATE + #define CYTHON_FAST_THREAD_STATE 1 + #endif + #ifndef CYTHON_FAST_PYCALL + #define CYTHON_FAST_PYCALL 1 + #endif + #ifndef CYTHON_PEP489_MULTI_PHASE_INIT + #define CYTHON_PEP489_MULTI_PHASE_INIT (PY_VERSION_HEX >= 0x03050000) + #endif + #ifndef CYTHON_USE_TP_FINALIZE + #define CYTHON_USE_TP_FINALIZE (PY_VERSION_HEX >= 0x030400a1) + #endif + #ifndef CYTHON_USE_DICT_VERSIONS + #define CYTHON_USE_DICT_VERSIONS (PY_VERSION_HEX >= 0x030600B1) + #endif + #ifndef CYTHON_USE_EXC_INFO_STACK + #define CYTHON_USE_EXC_INFO_STACK (PY_VERSION_HEX >= 0x030700A3) + #endif +#endif +#if !defined(CYTHON_FAST_PYCCALL) +#define CYTHON_FAST_PYCCALL (CYTHON_FAST_PYCALL && PY_VERSION_HEX >= 0x030600B1) +#endif +#if CYTHON_USE_PYLONG_INTERNALS + #include "longintrepr.h" + #undef SHIFT + #undef BASE + #undef MASK + #ifdef SIZEOF_VOID_P + enum { __pyx_check_sizeof_voidp = 1 / (int)(SIZEOF_VOID_P == sizeof(void*)) }; + #endif +#endif +#ifndef __has_attribute + #define __has_attribute(x) 0 +#endif +#ifndef __has_cpp_attribute + #define __has_cpp_attribute(x) 0 +#endif +#ifndef CYTHON_RESTRICT + #if defined(__GNUC__) + #define CYTHON_RESTRICT __restrict__ + #elif defined(_MSC_VER) && _MSC_VER >= 1400 + #define CYTHON_RESTRICT __restrict + #elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L + #define CYTHON_RESTRICT restrict + #else + #define CYTHON_RESTRICT + #endif +#endif +#ifndef CYTHON_UNUSED +# if defined(__GNUC__) +# if !(defined(__cplusplus)) || (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 4)) +# define CYTHON_UNUSED __attribute__ ((__unused__)) +# else +# define CYTHON_UNUSED +# endif +# elif defined(__ICC) || (defined(__INTEL_COMPILER) && !defined(_MSC_VER)) +# define CYTHON_UNUSED __attribute__ ((__unused__)) +# else +# define CYTHON_UNUSED +# endif +#endif +#ifndef CYTHON_MAYBE_UNUSED_VAR +# if defined(__cplusplus) + template void CYTHON_MAYBE_UNUSED_VAR( const T& ) { } +# else +# define CYTHON_MAYBE_UNUSED_VAR(x) (void)(x) +# endif +#endif +#ifndef CYTHON_NCP_UNUSED +# if CYTHON_COMPILING_IN_CPYTHON +# define CYTHON_NCP_UNUSED +# else +# define CYTHON_NCP_UNUSED CYTHON_UNUSED +# endif +#endif +#define __Pyx_void_to_None(void_result) ((void)(void_result), Py_INCREF(Py_None), Py_None) +#ifdef _MSC_VER + #ifndef _MSC_STDINT_H_ + #if _MSC_VER < 1300 + typedef unsigned char uint8_t; + typedef unsigned int uint32_t; + #else + typedef unsigned __int8 uint8_t; + typedef unsigned __int32 uint32_t; + #endif + #endif +#else + #include +#endif +#ifndef CYTHON_FALLTHROUGH + #if defined(__cplusplus) && __cplusplus >= 201103L + #if __has_cpp_attribute(fallthrough) + #define CYTHON_FALLTHROUGH [[fallthrough]] + #elif __has_cpp_attribute(clang::fallthrough) + #define CYTHON_FALLTHROUGH [[clang::fallthrough]] + #elif __has_cpp_attribute(gnu::fallthrough) + #define CYTHON_FALLTHROUGH [[gnu::fallthrough]] + #endif + #endif + #ifndef CYTHON_FALLTHROUGH + #if __has_attribute(fallthrough) + #define CYTHON_FALLTHROUGH __attribute__((fallthrough)) + #else + #define CYTHON_FALLTHROUGH + #endif + #endif + #if defined(__clang__ ) && defined(__apple_build_version__) + #if __apple_build_version__ < 7000000 + #undef CYTHON_FALLTHROUGH + #define CYTHON_FALLTHROUGH + #endif + #endif +#endif + +#ifndef CYTHON_INLINE + #if defined(__clang__) + #define CYTHON_INLINE __inline__ __attribute__ ((__unused__)) + #elif defined(__GNUC__) + #define CYTHON_INLINE __inline__ + #elif defined(_MSC_VER) + #define CYTHON_INLINE __inline + #elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L + #define CYTHON_INLINE inline + #else + #define CYTHON_INLINE + #endif +#endif + +#if CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x02070600 && !defined(Py_OptimizeFlag) + #define Py_OptimizeFlag 0 +#endif +#define __PYX_BUILD_PY_SSIZE_T "n" +#define CYTHON_FORMAT_SSIZE_T "z" +#if PY_MAJOR_VERSION < 3 + #define __Pyx_BUILTIN_MODULE_NAME "__builtin__" + #define __Pyx_PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\ + PyCode_New(a+k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos) + #define __Pyx_DefaultClassType PyClass_Type +#else + #define __Pyx_BUILTIN_MODULE_NAME "builtins" +#if PY_VERSION_HEX >= 0x030800A4 && PY_VERSION_HEX < 0x030800B2 + #define __Pyx_PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\ + PyCode_New(a, 0, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos) +#else + #define __Pyx_PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\ + PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos) +#endif + #define __Pyx_DefaultClassType PyType_Type +#endif +#ifndef Py_TPFLAGS_CHECKTYPES + #define Py_TPFLAGS_CHECKTYPES 0 +#endif +#ifndef Py_TPFLAGS_HAVE_INDEX + #define Py_TPFLAGS_HAVE_INDEX 0 +#endif +#ifndef Py_TPFLAGS_HAVE_NEWBUFFER + #define Py_TPFLAGS_HAVE_NEWBUFFER 0 +#endif +#ifndef Py_TPFLAGS_HAVE_FINALIZE + #define Py_TPFLAGS_HAVE_FINALIZE 0 +#endif +#ifndef METH_STACKLESS + #define METH_STACKLESS 0 +#endif +#if PY_VERSION_HEX <= 0x030700A3 || !defined(METH_FASTCALL) + #ifndef METH_FASTCALL + #define METH_FASTCALL 0x80 + #endif + typedef PyObject *(*__Pyx_PyCFunctionFast) (PyObject *self, PyObject *const *args, Py_ssize_t nargs); + typedef PyObject *(*__Pyx_PyCFunctionFastWithKeywords) (PyObject *self, PyObject *const *args, + Py_ssize_t nargs, PyObject *kwnames); +#else + #define __Pyx_PyCFunctionFast _PyCFunctionFast + #define __Pyx_PyCFunctionFastWithKeywords _PyCFunctionFastWithKeywords +#endif +#if CYTHON_FAST_PYCCALL +#define __Pyx_PyFastCFunction_Check(func)\ + ((PyCFunction_Check(func) && (METH_FASTCALL == (PyCFunction_GET_FLAGS(func) & ~(METH_CLASS | METH_STATIC | METH_COEXIST | METH_KEYWORDS | METH_STACKLESS))))) +#else +#define __Pyx_PyFastCFunction_Check(func) 0 +#endif +#if CYTHON_COMPILING_IN_PYPY && !defined(PyObject_Malloc) + #define PyObject_Malloc(s) PyMem_Malloc(s) + #define PyObject_Free(p) PyMem_Free(p) + #define PyObject_Realloc(p) PyMem_Realloc(p) +#endif +#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX < 0x030400A1 + #define PyMem_RawMalloc(n) PyMem_Malloc(n) + #define PyMem_RawRealloc(p, n) PyMem_Realloc(p, n) + #define PyMem_RawFree(p) PyMem_Free(p) +#endif +#if CYTHON_COMPILING_IN_PYSTON + #define __Pyx_PyCode_HasFreeVars(co) PyCode_HasFreeVars(co) + #define __Pyx_PyFrame_SetLineNumber(frame, lineno) PyFrame_SetLineNumber(frame, lineno) +#else + #define __Pyx_PyCode_HasFreeVars(co) (PyCode_GetNumFree(co) > 0) + #define __Pyx_PyFrame_SetLineNumber(frame, lineno) (frame)->f_lineno = (lineno) +#endif +#if !CYTHON_FAST_THREAD_STATE || PY_VERSION_HEX < 0x02070000 + #define __Pyx_PyThreadState_Current PyThreadState_GET() +#elif PY_VERSION_HEX >= 0x03060000 + #define __Pyx_PyThreadState_Current _PyThreadState_UncheckedGet() +#elif PY_VERSION_HEX >= 0x03000000 + #define __Pyx_PyThreadState_Current PyThreadState_GET() +#else + #define __Pyx_PyThreadState_Current _PyThreadState_Current +#endif +#if PY_VERSION_HEX < 0x030700A2 && !defined(PyThread_tss_create) && !defined(Py_tss_NEEDS_INIT) +#include "pythread.h" +#define Py_tss_NEEDS_INIT 0 +typedef int Py_tss_t; +static CYTHON_INLINE int PyThread_tss_create(Py_tss_t *key) { + *key = PyThread_create_key(); + return 0; +} +static CYTHON_INLINE Py_tss_t * PyThread_tss_alloc(void) { + Py_tss_t *key = (Py_tss_t *)PyObject_Malloc(sizeof(Py_tss_t)); + *key = Py_tss_NEEDS_INIT; + return key; +} +static CYTHON_INLINE void PyThread_tss_free(Py_tss_t *key) { + PyObject_Free(key); +} +static CYTHON_INLINE int PyThread_tss_is_created(Py_tss_t *key) { + return *key != Py_tss_NEEDS_INIT; +} +static CYTHON_INLINE void PyThread_tss_delete(Py_tss_t *key) { + PyThread_delete_key(*key); + *key = Py_tss_NEEDS_INIT; +} +static CYTHON_INLINE int PyThread_tss_set(Py_tss_t *key, void *value) { + return PyThread_set_key_value(*key, value); +} +static CYTHON_INLINE void * PyThread_tss_get(Py_tss_t *key) { + return PyThread_get_key_value(*key); +} +#endif +#if CYTHON_COMPILING_IN_CPYTHON || defined(_PyDict_NewPresized) +#define __Pyx_PyDict_NewPresized(n) ((n <= 8) ? PyDict_New() : _PyDict_NewPresized(n)) +#else +#define __Pyx_PyDict_NewPresized(n) PyDict_New() +#endif +#if PY_MAJOR_VERSION >= 3 || CYTHON_FUTURE_DIVISION + #define __Pyx_PyNumber_Divide(x,y) PyNumber_TrueDivide(x,y) + #define __Pyx_PyNumber_InPlaceDivide(x,y) PyNumber_InPlaceTrueDivide(x,y) +#else + #define __Pyx_PyNumber_Divide(x,y) PyNumber_Divide(x,y) + #define __Pyx_PyNumber_InPlaceDivide(x,y) PyNumber_InPlaceDivide(x,y) +#endif +#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x030500A1 && CYTHON_USE_UNICODE_INTERNALS +#define __Pyx_PyDict_GetItemStr(dict, name) _PyDict_GetItem_KnownHash(dict, name, ((PyASCIIObject *) name)->hash) +#else +#define __Pyx_PyDict_GetItemStr(dict, name) PyDict_GetItem(dict, name) +#endif +#if PY_VERSION_HEX > 0x03030000 && defined(PyUnicode_KIND) + #define CYTHON_PEP393_ENABLED 1 + #if defined(PyUnicode_IS_READY) + #define __Pyx_PyUnicode_READY(op) (likely(PyUnicode_IS_READY(op)) ?\ + 0 : _PyUnicode_Ready((PyObject *)(op))) + #else + #define __Pyx_PyUnicode_READY(op) (0) + #endif + #define __Pyx_PyUnicode_GET_LENGTH(u) PyUnicode_GET_LENGTH(u) + #define __Pyx_PyUnicode_READ_CHAR(u, i) PyUnicode_READ_CHAR(u, i) + #define __Pyx_PyUnicode_MAX_CHAR_VALUE(u) PyUnicode_MAX_CHAR_VALUE(u) + #define __Pyx_PyUnicode_KIND(u) PyUnicode_KIND(u) + #define __Pyx_PyUnicode_DATA(u) PyUnicode_DATA(u) + #define __Pyx_PyUnicode_READ(k, d, i) PyUnicode_READ(k, d, i) + #define __Pyx_PyUnicode_WRITE(k, d, i, ch) PyUnicode_WRITE(k, d, i, ch) + #if defined(PyUnicode_IS_READY) && defined(PyUnicode_GET_SIZE) + #if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x03090000 + #define __Pyx_PyUnicode_IS_TRUE(u) (0 != (likely(PyUnicode_IS_READY(u)) ? PyUnicode_GET_LENGTH(u) : ((PyCompactUnicodeObject *)(u))->wstr_length)) + #else + #define __Pyx_PyUnicode_IS_TRUE(u) (0 != (likely(PyUnicode_IS_READY(u)) ? PyUnicode_GET_LENGTH(u) : PyUnicode_GET_SIZE(u))) + #endif + #else + #define __Pyx_PyUnicode_IS_TRUE(u) (0 != PyUnicode_GET_LENGTH(u)) + #endif +#else + #define CYTHON_PEP393_ENABLED 0 + #define PyUnicode_1BYTE_KIND 1 + #define PyUnicode_2BYTE_KIND 2 + #define PyUnicode_4BYTE_KIND 4 + #define __Pyx_PyUnicode_READY(op) (0) + #define __Pyx_PyUnicode_GET_LENGTH(u) PyUnicode_GET_SIZE(u) + #define __Pyx_PyUnicode_READ_CHAR(u, i) ((Py_UCS4)(PyUnicode_AS_UNICODE(u)[i])) + #define __Pyx_PyUnicode_MAX_CHAR_VALUE(u) ((sizeof(Py_UNICODE) == 2) ? 65535 : 1114111) + #define __Pyx_PyUnicode_KIND(u) (sizeof(Py_UNICODE)) + #define __Pyx_PyUnicode_DATA(u) ((void*)PyUnicode_AS_UNICODE(u)) + #define __Pyx_PyUnicode_READ(k, d, i) ((void)(k), (Py_UCS4)(((Py_UNICODE*)d)[i])) + #define __Pyx_PyUnicode_WRITE(k, d, i, ch) (((void)(k)), ((Py_UNICODE*)d)[i] = ch) + #define __Pyx_PyUnicode_IS_TRUE(u) (0 != PyUnicode_GET_SIZE(u)) +#endif +#if CYTHON_COMPILING_IN_PYPY + #define __Pyx_PyUnicode_Concat(a, b) PyNumber_Add(a, b) + #define __Pyx_PyUnicode_ConcatSafe(a, b) PyNumber_Add(a, b) +#else + #define __Pyx_PyUnicode_Concat(a, b) PyUnicode_Concat(a, b) + #define __Pyx_PyUnicode_ConcatSafe(a, b) ((unlikely((a) == Py_None) || unlikely((b) == Py_None)) ?\ + PyNumber_Add(a, b) : __Pyx_PyUnicode_Concat(a, b)) +#endif +#if CYTHON_COMPILING_IN_PYPY && !defined(PyUnicode_Contains) + #define PyUnicode_Contains(u, s) PySequence_Contains(u, s) +#endif +#if CYTHON_COMPILING_IN_PYPY && !defined(PyByteArray_Check) + #define PyByteArray_Check(obj) PyObject_TypeCheck(obj, &PyByteArray_Type) +#endif +#if CYTHON_COMPILING_IN_PYPY && !defined(PyObject_Format) + #define PyObject_Format(obj, fmt) PyObject_CallMethod(obj, "__format__", "O", fmt) +#endif +#define __Pyx_PyString_FormatSafe(a, b) ((unlikely((a) == Py_None || (PyString_Check(b) && !PyString_CheckExact(b)))) ? PyNumber_Remainder(a, b) : __Pyx_PyString_Format(a, b)) +#define __Pyx_PyUnicode_FormatSafe(a, b) ((unlikely((a) == Py_None || (PyUnicode_Check(b) && !PyUnicode_CheckExact(b)))) ? PyNumber_Remainder(a, b) : PyUnicode_Format(a, b)) +#if PY_MAJOR_VERSION >= 3 + #define __Pyx_PyString_Format(a, b) PyUnicode_Format(a, b) +#else + #define __Pyx_PyString_Format(a, b) PyString_Format(a, b) +#endif +#if PY_MAJOR_VERSION < 3 && !defined(PyObject_ASCII) + #define PyObject_ASCII(o) PyObject_Repr(o) +#endif +#if PY_MAJOR_VERSION >= 3 + #define PyBaseString_Type PyUnicode_Type + #define PyStringObject PyUnicodeObject + #define PyString_Type PyUnicode_Type + #define PyString_Check PyUnicode_Check + #define PyString_CheckExact PyUnicode_CheckExact +#ifndef PyObject_Unicode + #define PyObject_Unicode PyObject_Str +#endif +#endif +#if PY_MAJOR_VERSION >= 3 + #define __Pyx_PyBaseString_Check(obj) PyUnicode_Check(obj) + #define __Pyx_PyBaseString_CheckExact(obj) PyUnicode_CheckExact(obj) +#else + #define __Pyx_PyBaseString_Check(obj) (PyString_Check(obj) || PyUnicode_Check(obj)) + #define __Pyx_PyBaseString_CheckExact(obj) (PyString_CheckExact(obj) || PyUnicode_CheckExact(obj)) +#endif +#ifndef PySet_CheckExact + #define PySet_CheckExact(obj) (Py_TYPE(obj) == &PySet_Type) +#endif +#if PY_VERSION_HEX >= 0x030900A4 + #define __Pyx_SET_REFCNT(obj, refcnt) Py_SET_REFCNT(obj, refcnt) + #define __Pyx_SET_SIZE(obj, size) Py_SET_SIZE(obj, size) +#else + #define __Pyx_SET_REFCNT(obj, refcnt) Py_REFCNT(obj) = (refcnt) + #define __Pyx_SET_SIZE(obj, size) Py_SIZE(obj) = (size) +#endif +#if CYTHON_ASSUME_SAFE_MACROS + #define __Pyx_PySequence_SIZE(seq) Py_SIZE(seq) +#else + #define __Pyx_PySequence_SIZE(seq) PySequence_Size(seq) +#endif +#if PY_MAJOR_VERSION >= 3 + #define PyIntObject PyLongObject + #define PyInt_Type PyLong_Type + #define PyInt_Check(op) PyLong_Check(op) + #define PyInt_CheckExact(op) PyLong_CheckExact(op) + #define PyInt_FromString PyLong_FromString + #define PyInt_FromUnicode PyLong_FromUnicode + #define PyInt_FromLong PyLong_FromLong + #define PyInt_FromSize_t PyLong_FromSize_t + #define PyInt_FromSsize_t PyLong_FromSsize_t + #define PyInt_AsLong PyLong_AsLong + #define PyInt_AS_LONG PyLong_AS_LONG + #define PyInt_AsSsize_t PyLong_AsSsize_t + #define PyInt_AsUnsignedLongMask PyLong_AsUnsignedLongMask + #define PyInt_AsUnsignedLongLongMask PyLong_AsUnsignedLongLongMask + #define PyNumber_Int PyNumber_Long +#endif +#if PY_MAJOR_VERSION >= 3 + #define PyBoolObject PyLongObject +#endif +#if PY_MAJOR_VERSION >= 3 && CYTHON_COMPILING_IN_PYPY + #ifndef PyUnicode_InternFromString + #define PyUnicode_InternFromString(s) PyUnicode_FromString(s) + #endif +#endif +#if PY_VERSION_HEX < 0x030200A4 + typedef long Py_hash_t; + #define __Pyx_PyInt_FromHash_t PyInt_FromLong + #define __Pyx_PyInt_AsHash_t PyInt_AsLong +#else + #define __Pyx_PyInt_FromHash_t PyInt_FromSsize_t + #define __Pyx_PyInt_AsHash_t PyInt_AsSsize_t +#endif +#if PY_MAJOR_VERSION >= 3 + #define __Pyx_PyMethod_New(func, self, klass) ((self) ? ((void)(klass), PyMethod_New(func, self)) : __Pyx_NewRef(func)) +#else + #define __Pyx_PyMethod_New(func, self, klass) PyMethod_New(func, self, klass) +#endif +#if CYTHON_USE_ASYNC_SLOTS + #if PY_VERSION_HEX >= 0x030500B1 + #define __Pyx_PyAsyncMethodsStruct PyAsyncMethods + #define __Pyx_PyType_AsAsync(obj) (Py_TYPE(obj)->tp_as_async) + #else + #define __Pyx_PyType_AsAsync(obj) ((__Pyx_PyAsyncMethodsStruct*) (Py_TYPE(obj)->tp_reserved)) + #endif +#else + #define __Pyx_PyType_AsAsync(obj) NULL +#endif +#ifndef __Pyx_PyAsyncMethodsStruct + typedef struct { + unaryfunc am_await; + unaryfunc am_aiter; + unaryfunc am_anext; + } __Pyx_PyAsyncMethodsStruct; +#endif + +#if defined(WIN32) || defined(MS_WINDOWS) + #define _USE_MATH_DEFINES +#endif +#include +#ifdef NAN +#define __PYX_NAN() ((float) NAN) +#else +static CYTHON_INLINE float __PYX_NAN() { + float value; + memset(&value, 0xFF, sizeof(value)); + return value; +} +#endif +#if defined(__CYGWIN__) && defined(_LDBL_EQ_DBL) +#define __Pyx_truncl trunc +#else +#define __Pyx_truncl truncl +#endif + +#define __PYX_MARK_ERR_POS(f_index, lineno) \ + { __pyx_filename = __pyx_f[f_index]; (void)__pyx_filename; __pyx_lineno = lineno; (void)__pyx_lineno; __pyx_clineno = __LINE__; (void)__pyx_clineno; } +#define __PYX_ERR(f_index, lineno, Ln_error) \ + { __PYX_MARK_ERR_POS(f_index, lineno) goto Ln_error; } + +#ifndef __PYX_EXTERN_C + #ifdef __cplusplus + #define __PYX_EXTERN_C extern "C" + #else + #define __PYX_EXTERN_C extern + #endif +#endif + +#define __PYX_HAVE__sdtw_fast +#define __PYX_HAVE_API__sdtw_fast +/* Early includes */ +#include +#include +#include "numpy/arrayobject.h" +#include "numpy/ndarrayobject.h" +#include "numpy/ndarraytypes.h" +#include "numpy/arrayscalars.h" +#include "numpy/ufuncobject.h" + + /* NumPy API declarations from "numpy/__init__.pxd" */ + +#include +#include +#ifdef _OPENMP +#include +#endif /* _OPENMP */ + +#if defined(PYREX_WITHOUT_ASSERTIONS) && !defined(CYTHON_WITHOUT_ASSERTIONS) +#define CYTHON_WITHOUT_ASSERTIONS +#endif + +typedef struct {PyObject **p; const char *s; const Py_ssize_t n; const char* encoding; + const char is_unicode; const char is_str; const char intern; } __Pyx_StringTabEntry; + +#define __PYX_DEFAULT_STRING_ENCODING_IS_ASCII 0 +#define __PYX_DEFAULT_STRING_ENCODING_IS_UTF8 0 +#define __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT (PY_MAJOR_VERSION >= 3 && __PYX_DEFAULT_STRING_ENCODING_IS_UTF8) +#define __PYX_DEFAULT_STRING_ENCODING "" +#define __Pyx_PyObject_FromString __Pyx_PyBytes_FromString +#define __Pyx_PyObject_FromStringAndSize __Pyx_PyBytes_FromStringAndSize +#define __Pyx_uchar_cast(c) ((unsigned char)c) +#define __Pyx_long_cast(x) ((long)x) +#define __Pyx_fits_Py_ssize_t(v, type, is_signed) (\ + (sizeof(type) < sizeof(Py_ssize_t)) ||\ + (sizeof(type) > sizeof(Py_ssize_t) &&\ + likely(v < (type)PY_SSIZE_T_MAX ||\ + v == (type)PY_SSIZE_T_MAX) &&\ + (!is_signed || likely(v > (type)PY_SSIZE_T_MIN ||\ + v == (type)PY_SSIZE_T_MIN))) ||\ + (sizeof(type) == sizeof(Py_ssize_t) &&\ + (is_signed || likely(v < (type)PY_SSIZE_T_MAX ||\ + v == (type)PY_SSIZE_T_MAX))) ) +static CYTHON_INLINE int __Pyx_is_valid_index(Py_ssize_t i, Py_ssize_t limit) { + return (size_t) i < (size_t) limit; +} +#if defined (__cplusplus) && __cplusplus >= 201103L + #include + #define __Pyx_sst_abs(value) std::abs(value) +#elif SIZEOF_INT >= SIZEOF_SIZE_T + #define __Pyx_sst_abs(value) abs(value) +#elif SIZEOF_LONG >= SIZEOF_SIZE_T + #define __Pyx_sst_abs(value) labs(value) +#elif defined (_MSC_VER) + #define __Pyx_sst_abs(value) ((Py_ssize_t)_abs64(value)) +#elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L + #define __Pyx_sst_abs(value) llabs(value) +#elif defined (__GNUC__) + #define __Pyx_sst_abs(value) __builtin_llabs(value) +#else + #define __Pyx_sst_abs(value) ((value<0) ? -value : value) +#endif +static CYTHON_INLINE const char* __Pyx_PyObject_AsString(PyObject*); +static CYTHON_INLINE const char* __Pyx_PyObject_AsStringAndSize(PyObject*, Py_ssize_t* length); +#define __Pyx_PyByteArray_FromString(s) PyByteArray_FromStringAndSize((const char*)s, strlen((const char*)s)) +#define __Pyx_PyByteArray_FromStringAndSize(s, l) PyByteArray_FromStringAndSize((const char*)s, l) +#define __Pyx_PyBytes_FromString PyBytes_FromString +#define __Pyx_PyBytes_FromStringAndSize PyBytes_FromStringAndSize +static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char*); +#if PY_MAJOR_VERSION < 3 + #define __Pyx_PyStr_FromString __Pyx_PyBytes_FromString + #define __Pyx_PyStr_FromStringAndSize __Pyx_PyBytes_FromStringAndSize +#else + #define __Pyx_PyStr_FromString __Pyx_PyUnicode_FromString + #define __Pyx_PyStr_FromStringAndSize __Pyx_PyUnicode_FromStringAndSize +#endif +#define __Pyx_PyBytes_AsWritableString(s) ((char*) PyBytes_AS_STRING(s)) +#define __Pyx_PyBytes_AsWritableSString(s) ((signed char*) PyBytes_AS_STRING(s)) +#define __Pyx_PyBytes_AsWritableUString(s) ((unsigned char*) PyBytes_AS_STRING(s)) +#define __Pyx_PyBytes_AsString(s) ((const char*) PyBytes_AS_STRING(s)) +#define __Pyx_PyBytes_AsSString(s) ((const signed char*) PyBytes_AS_STRING(s)) +#define __Pyx_PyBytes_AsUString(s) ((const unsigned char*) PyBytes_AS_STRING(s)) +#define __Pyx_PyObject_AsWritableString(s) ((char*) __Pyx_PyObject_AsString(s)) +#define __Pyx_PyObject_AsWritableSString(s) ((signed char*) __Pyx_PyObject_AsString(s)) +#define __Pyx_PyObject_AsWritableUString(s) ((unsigned char*) __Pyx_PyObject_AsString(s)) +#define __Pyx_PyObject_AsSString(s) ((const signed char*) __Pyx_PyObject_AsString(s)) +#define __Pyx_PyObject_AsUString(s) ((const unsigned char*) __Pyx_PyObject_AsString(s)) +#define __Pyx_PyObject_FromCString(s) __Pyx_PyObject_FromString((const char*)s) +#define __Pyx_PyBytes_FromCString(s) __Pyx_PyBytes_FromString((const char*)s) +#define __Pyx_PyByteArray_FromCString(s) __Pyx_PyByteArray_FromString((const char*)s) +#define __Pyx_PyStr_FromCString(s) __Pyx_PyStr_FromString((const char*)s) +#define __Pyx_PyUnicode_FromCString(s) __Pyx_PyUnicode_FromString((const char*)s) +static CYTHON_INLINE size_t __Pyx_Py_UNICODE_strlen(const Py_UNICODE *u) { + const Py_UNICODE *u_end = u; + while (*u_end++) ; + return (size_t)(u_end - u - 1); +} +#define __Pyx_PyUnicode_FromUnicode(u) PyUnicode_FromUnicode(u, __Pyx_Py_UNICODE_strlen(u)) +#define __Pyx_PyUnicode_FromUnicodeAndLength PyUnicode_FromUnicode +#define __Pyx_PyUnicode_AsUnicode PyUnicode_AsUnicode +#define __Pyx_NewRef(obj) (Py_INCREF(obj), obj) +#define __Pyx_Owned_Py_None(b) __Pyx_NewRef(Py_None) +static CYTHON_INLINE PyObject * __Pyx_PyBool_FromLong(long b); +static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject*); +static CYTHON_INLINE int __Pyx_PyObject_IsTrueAndDecref(PyObject*); +static CYTHON_INLINE PyObject* __Pyx_PyNumber_IntOrLong(PyObject* x); +#define __Pyx_PySequence_Tuple(obj)\ + (likely(PyTuple_CheckExact(obj)) ? __Pyx_NewRef(obj) : PySequence_Tuple(obj)) +static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject*); +static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t); +#if CYTHON_ASSUME_SAFE_MACROS +#define __pyx_PyFloat_AsDouble(x) (PyFloat_CheckExact(x) ? PyFloat_AS_DOUBLE(x) : PyFloat_AsDouble(x)) +#else +#define __pyx_PyFloat_AsDouble(x) PyFloat_AsDouble(x) +#endif +#define __pyx_PyFloat_AsFloat(x) ((float) __pyx_PyFloat_AsDouble(x)) +#if PY_MAJOR_VERSION >= 3 +#define __Pyx_PyNumber_Int(x) (PyLong_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Long(x)) +#else +#define __Pyx_PyNumber_Int(x) (PyInt_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Int(x)) +#endif +#define __Pyx_PyNumber_Float(x) (PyFloat_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Float(x)) +#if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII +static int __Pyx_sys_getdefaultencoding_not_ascii; +static int __Pyx_init_sys_getdefaultencoding_params(void) { + PyObject* sys; + PyObject* default_encoding = NULL; + PyObject* ascii_chars_u = NULL; + PyObject* ascii_chars_b = NULL; + const char* default_encoding_c; + sys = PyImport_ImportModule("sys"); + if (!sys) goto bad; + default_encoding = PyObject_CallMethod(sys, (char*) "getdefaultencoding", NULL); + Py_DECREF(sys); + if (!default_encoding) goto bad; + default_encoding_c = PyBytes_AsString(default_encoding); + if (!default_encoding_c) goto bad; + if (strcmp(default_encoding_c, "ascii") == 0) { + __Pyx_sys_getdefaultencoding_not_ascii = 0; + } else { + char ascii_chars[128]; + int c; + for (c = 0; c < 128; c++) { + ascii_chars[c] = c; + } + __Pyx_sys_getdefaultencoding_not_ascii = 1; + ascii_chars_u = PyUnicode_DecodeASCII(ascii_chars, 128, NULL); + if (!ascii_chars_u) goto bad; + ascii_chars_b = PyUnicode_AsEncodedString(ascii_chars_u, default_encoding_c, NULL); + if (!ascii_chars_b || !PyBytes_Check(ascii_chars_b) || memcmp(ascii_chars, PyBytes_AS_STRING(ascii_chars_b), 128) != 0) { + PyErr_Format( + PyExc_ValueError, + "This module compiled with c_string_encoding=ascii, but default encoding '%.200s' is not a superset of ascii.", + default_encoding_c); + goto bad; + } + Py_DECREF(ascii_chars_u); + Py_DECREF(ascii_chars_b); + } + Py_DECREF(default_encoding); + return 0; +bad: + Py_XDECREF(default_encoding); + Py_XDECREF(ascii_chars_u); + Py_XDECREF(ascii_chars_b); + return -1; +} +#endif +#if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT && PY_MAJOR_VERSION >= 3 +#define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_DecodeUTF8(c_str, size, NULL) +#else +#define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_Decode(c_str, size, __PYX_DEFAULT_STRING_ENCODING, NULL) +#if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT +static char* __PYX_DEFAULT_STRING_ENCODING; +static int __Pyx_init_sys_getdefaultencoding_params(void) { + PyObject* sys; + PyObject* default_encoding = NULL; + char* default_encoding_c; + sys = PyImport_ImportModule("sys"); + if (!sys) goto bad; + default_encoding = PyObject_CallMethod(sys, (char*) (const char*) "getdefaultencoding", NULL); + Py_DECREF(sys); + if (!default_encoding) goto bad; + default_encoding_c = PyBytes_AsString(default_encoding); + if (!default_encoding_c) goto bad; + __PYX_DEFAULT_STRING_ENCODING = (char*) malloc(strlen(default_encoding_c) + 1); + if (!__PYX_DEFAULT_STRING_ENCODING) goto bad; + strcpy(__PYX_DEFAULT_STRING_ENCODING, default_encoding_c); + Py_DECREF(default_encoding); + return 0; +bad: + Py_XDECREF(default_encoding); + return -1; +} +#endif +#endif + + +/* Test for GCC > 2.95 */ +#if defined(__GNUC__) && (__GNUC__ > 2 || (__GNUC__ == 2 && (__GNUC_MINOR__ > 95))) + #define likely(x) __builtin_expect(!!(x), 1) + #define unlikely(x) __builtin_expect(!!(x), 0) +#else /* !__GNUC__ or GCC < 2.95 */ + #define likely(x) (x) + #define unlikely(x) (x) +#endif /* __GNUC__ */ +static CYTHON_INLINE void __Pyx_pretend_to_initialize(void* ptr) { (void)ptr; } + +static PyObject *__pyx_m = NULL; +static PyObject *__pyx_d; +static PyObject *__pyx_b; +static PyObject *__pyx_cython_runtime = NULL; +static PyObject *__pyx_empty_tuple; +static PyObject *__pyx_empty_bytes; +static PyObject *__pyx_empty_unicode; +static int __pyx_lineno; +static int __pyx_clineno = 0; +static const char * __pyx_cfilenm= __FILE__; +static const char *__pyx_filename; + +/* Header.proto */ +#if !defined(CYTHON_CCOMPLEX) + #if defined(__cplusplus) + #define CYTHON_CCOMPLEX 1 + #elif defined(_Complex_I) + #define CYTHON_CCOMPLEX 1 + #else + #define CYTHON_CCOMPLEX 0 + #endif +#endif +#if CYTHON_CCOMPLEX + #ifdef __cplusplus + #include + #else + #include + #endif +#endif +#if CYTHON_CCOMPLEX && !defined(__cplusplus) && defined(__sun__) && defined(__GNUC__) + #undef _Complex_I + #define _Complex_I 1.0fj +#endif + + +static const char *__pyx_f[] = { + "sdtw_fast.pyx", + "__init__.pxd", + "type.pxd", +}; +/* BufferFormatStructs.proto */ +#define IS_UNSIGNED(type) (((type) -1) > 0) +struct __Pyx_StructField_; +#define __PYX_BUF_FLAGS_PACKED_STRUCT (1 << 0) +typedef struct { + const char* name; + struct __Pyx_StructField_* fields; + size_t size; + size_t arraysize[8]; + int ndim; + char typegroup; + char is_unsigned; + int flags; +} __Pyx_TypeInfo; +typedef struct __Pyx_StructField_ { + __Pyx_TypeInfo* type; + const char* name; + size_t offset; +} __Pyx_StructField; +typedef struct { + __Pyx_StructField* field; + size_t parent_offset; +} __Pyx_BufFmt_StackElem; +typedef struct { + __Pyx_StructField root; + __Pyx_BufFmt_StackElem* head; + size_t fmt_offset; + size_t new_count, enc_count; + size_t struct_alignment; + int is_complex; + char enc_type; + char new_packmode; + char enc_packmode; + char is_valid_array; +} __Pyx_BufFmt_Context; + +/* NoFastGil.proto */ +#define __Pyx_PyGILState_Ensure PyGILState_Ensure +#define __Pyx_PyGILState_Release PyGILState_Release +#define __Pyx_FastGIL_Remember() +#define __Pyx_FastGIL_Forget() +#define __Pyx_FastGilFuncInit() + +/* ForceInitThreads.proto */ +#ifndef __PYX_FORCE_INIT_THREADS + #define __PYX_FORCE_INIT_THREADS 0 +#endif + + +/* "../../../../numpy/__init__.pxd":690 + * # in Cython to enable them only on the right systems. + * + * ctypedef npy_int8 int8_t # <<<<<<<<<<<<<< + * ctypedef npy_int16 int16_t + * ctypedef npy_int32 int32_t + */ +typedef npy_int8 __pyx_t_5numpy_int8_t; + +/* "../../../../numpy/__init__.pxd":691 + * + * ctypedef npy_int8 int8_t + * ctypedef npy_int16 int16_t # <<<<<<<<<<<<<< + * ctypedef npy_int32 int32_t + * ctypedef npy_int64 int64_t + */ +typedef npy_int16 __pyx_t_5numpy_int16_t; + +/* "../../../../numpy/__init__.pxd":692 + * ctypedef npy_int8 int8_t + * ctypedef npy_int16 int16_t + * ctypedef npy_int32 int32_t # <<<<<<<<<<<<<< + * ctypedef npy_int64 int64_t + * #ctypedef npy_int96 int96_t + */ +typedef npy_int32 __pyx_t_5numpy_int32_t; + +/* "../../../../numpy/__init__.pxd":693 + * ctypedef npy_int16 int16_t + * ctypedef npy_int32 int32_t + * ctypedef npy_int64 int64_t # <<<<<<<<<<<<<< + * #ctypedef npy_int96 int96_t + * #ctypedef npy_int128 int128_t + */ +typedef npy_int64 __pyx_t_5numpy_int64_t; + +/* "../../../../numpy/__init__.pxd":697 + * #ctypedef npy_int128 int128_t + * + * ctypedef npy_uint8 uint8_t # <<<<<<<<<<<<<< + * ctypedef npy_uint16 uint16_t + * ctypedef npy_uint32 uint32_t + */ +typedef npy_uint8 __pyx_t_5numpy_uint8_t; + +/* "../../../../numpy/__init__.pxd":698 + * + * ctypedef npy_uint8 uint8_t + * ctypedef npy_uint16 uint16_t # <<<<<<<<<<<<<< + * ctypedef npy_uint32 uint32_t + * ctypedef npy_uint64 uint64_t + */ +typedef npy_uint16 __pyx_t_5numpy_uint16_t; + +/* "../../../../numpy/__init__.pxd":699 + * ctypedef npy_uint8 uint8_t + * ctypedef npy_uint16 uint16_t + * ctypedef npy_uint32 uint32_t # <<<<<<<<<<<<<< + * ctypedef npy_uint64 uint64_t + * #ctypedef npy_uint96 uint96_t + */ +typedef npy_uint32 __pyx_t_5numpy_uint32_t; + +/* "../../../../numpy/__init__.pxd":700 + * ctypedef npy_uint16 uint16_t + * ctypedef npy_uint32 uint32_t + * ctypedef npy_uint64 uint64_t # <<<<<<<<<<<<<< + * #ctypedef npy_uint96 uint96_t + * #ctypedef npy_uint128 uint128_t + */ +typedef npy_uint64 __pyx_t_5numpy_uint64_t; + +/* "../../../../numpy/__init__.pxd":704 + * #ctypedef npy_uint128 uint128_t + * + * ctypedef npy_float32 float32_t # <<<<<<<<<<<<<< + * ctypedef npy_float64 float64_t + * #ctypedef npy_float80 float80_t + */ +typedef npy_float32 __pyx_t_5numpy_float32_t; + +/* "../../../../numpy/__init__.pxd":705 + * + * ctypedef npy_float32 float32_t + * ctypedef npy_float64 float64_t # <<<<<<<<<<<<<< + * #ctypedef npy_float80 float80_t + * #ctypedef npy_float128 float128_t + */ +typedef npy_float64 __pyx_t_5numpy_float64_t; + +/* "../../../../numpy/__init__.pxd":714 + * # The int types are mapped a bit surprising -- + * # numpy.int corresponds to 'l' and numpy.long to 'q' + * ctypedef npy_long int_t # <<<<<<<<<<<<<< + * ctypedef npy_longlong long_t + * ctypedef npy_longlong longlong_t + */ +typedef npy_long __pyx_t_5numpy_int_t; + +/* "../../../../numpy/__init__.pxd":715 + * # numpy.int corresponds to 'l' and numpy.long to 'q' + * ctypedef npy_long int_t + * ctypedef npy_longlong long_t # <<<<<<<<<<<<<< + * ctypedef npy_longlong longlong_t + * + */ +typedef npy_longlong __pyx_t_5numpy_long_t; + +/* "../../../../numpy/__init__.pxd":716 + * ctypedef npy_long int_t + * ctypedef npy_longlong long_t + * ctypedef npy_longlong longlong_t # <<<<<<<<<<<<<< + * + * ctypedef npy_ulong uint_t + */ +typedef npy_longlong __pyx_t_5numpy_longlong_t; + +/* "../../../../numpy/__init__.pxd":718 + * ctypedef npy_longlong longlong_t + * + * ctypedef npy_ulong uint_t # <<<<<<<<<<<<<< + * ctypedef npy_ulonglong ulong_t + * ctypedef npy_ulonglong ulonglong_t + */ +typedef npy_ulong __pyx_t_5numpy_uint_t; + +/* "../../../../numpy/__init__.pxd":719 + * + * ctypedef npy_ulong uint_t + * ctypedef npy_ulonglong ulong_t # <<<<<<<<<<<<<< + * ctypedef npy_ulonglong ulonglong_t + * + */ +typedef npy_ulonglong __pyx_t_5numpy_ulong_t; + +/* "../../../../numpy/__init__.pxd":720 + * ctypedef npy_ulong uint_t + * ctypedef npy_ulonglong ulong_t + * ctypedef npy_ulonglong ulonglong_t # <<<<<<<<<<<<<< + * + * ctypedef npy_intp intp_t + */ +typedef npy_ulonglong __pyx_t_5numpy_ulonglong_t; + +/* "../../../../numpy/__init__.pxd":722 + * ctypedef npy_ulonglong ulonglong_t + * + * ctypedef npy_intp intp_t # <<<<<<<<<<<<<< + * ctypedef npy_uintp uintp_t + * + */ +typedef npy_intp __pyx_t_5numpy_intp_t; + +/* "../../../../numpy/__init__.pxd":723 + * + * ctypedef npy_intp intp_t + * ctypedef npy_uintp uintp_t # <<<<<<<<<<<<<< + * + * ctypedef npy_double float_t + */ +typedef npy_uintp __pyx_t_5numpy_uintp_t; + +/* "../../../../numpy/__init__.pxd":725 + * ctypedef npy_uintp uintp_t + * + * ctypedef npy_double float_t # <<<<<<<<<<<<<< + * ctypedef npy_double double_t + * ctypedef npy_longdouble longdouble_t + */ +typedef npy_double __pyx_t_5numpy_float_t; + +/* "../../../../numpy/__init__.pxd":726 + * + * ctypedef npy_double float_t + * ctypedef npy_double double_t # <<<<<<<<<<<<<< + * ctypedef npy_longdouble longdouble_t + * + */ +typedef npy_double __pyx_t_5numpy_double_t; + +/* "../../../../numpy/__init__.pxd":727 + * ctypedef npy_double float_t + * ctypedef npy_double double_t + * ctypedef npy_longdouble longdouble_t # <<<<<<<<<<<<<< + * + * ctypedef npy_cfloat cfloat_t + */ +typedef npy_longdouble __pyx_t_5numpy_longdouble_t; + +/* "sdtw_fast.pyx":18 + * + * DTYPE = np.float64 + * ctypedef np.float64_t DTYPE_t # <<<<<<<<<<<<<< + * + * @cdivision(True) + */ +typedef __pyx_t_5numpy_float64_t __pyx_t_9sdtw_fast_DTYPE_t; +/* Declarations.proto */ +#if CYTHON_CCOMPLEX + #ifdef __cplusplus + typedef ::std::complex< float > __pyx_t_float_complex; + #else + typedef float _Complex __pyx_t_float_complex; + #endif +#else + typedef struct { float real, imag; } __pyx_t_float_complex; +#endif +static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float, float); + +/* Declarations.proto */ +#if CYTHON_CCOMPLEX + #ifdef __cplusplus + typedef ::std::complex< double > __pyx_t_double_complex; + #else + typedef double _Complex __pyx_t_double_complex; + #endif +#else + typedef struct { double real, imag; } __pyx_t_double_complex; +#endif +static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double, double); + + +/*--- Type declarations ---*/ + +/* "../../../../numpy/__init__.pxd":729 + * ctypedef npy_longdouble longdouble_t + * + * ctypedef npy_cfloat cfloat_t # <<<<<<<<<<<<<< + * ctypedef npy_cdouble cdouble_t + * ctypedef npy_clongdouble clongdouble_t + */ +typedef npy_cfloat __pyx_t_5numpy_cfloat_t; + +/* "../../../../numpy/__init__.pxd":730 + * + * ctypedef npy_cfloat cfloat_t + * ctypedef npy_cdouble cdouble_t # <<<<<<<<<<<<<< + * ctypedef npy_clongdouble clongdouble_t + * + */ +typedef npy_cdouble __pyx_t_5numpy_cdouble_t; 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r = NULL; __Pyx_DECREF(tmp);}} while(0) + +/* PyObjectGetAttrStr.proto */ +#if CYTHON_USE_TYPE_SLOTS +static CYTHON_INLINE PyObject* __Pyx_PyObject_GetAttrStr(PyObject* obj, PyObject* attr_name); +#else +#define __Pyx_PyObject_GetAttrStr(o,n) PyObject_GetAttr(o,n) +#endif + +/* GetBuiltinName.proto */ +static PyObject *__Pyx_GetBuiltinName(PyObject *name); + +/* RaiseArgTupleInvalid.proto */ +static void __Pyx_RaiseArgtupleInvalid(const char* func_name, int exact, + Py_ssize_t num_min, Py_ssize_t num_max, Py_ssize_t num_found); + +/* RaiseDoubleKeywords.proto */ +static void __Pyx_RaiseDoubleKeywordsError(const char* func_name, PyObject* kw_name); + +/* ParseKeywords.proto */ +static int __Pyx_ParseOptionalKeywords(PyObject *kwds, PyObject **argnames[],\ + PyObject *kwds2, PyObject *values[], Py_ssize_t num_pos_args,\ + const char* function_name); + +/* ArgTypeTest.proto */ +#define __Pyx_ArgTypeTest(obj, type, none_allowed, name, exact)\ + ((likely((Py_TYPE(obj) == type) | (none_allowed && (obj == Py_None)))) ? 1 :\ + __Pyx__ArgTypeTest(obj, type, name, exact)) +static int __Pyx__ArgTypeTest(PyObject *obj, PyTypeObject *type, const char *name, int exact); + +/* IsLittleEndian.proto */ +static CYTHON_INLINE int __Pyx_Is_Little_Endian(void); + +/* BufferFormatCheck.proto */ +static const char* __Pyx_BufFmt_CheckString(__Pyx_BufFmt_Context* ctx, const char* ts); +static void __Pyx_BufFmt_Init(__Pyx_BufFmt_Context* ctx, + __Pyx_BufFmt_StackElem* stack, + __Pyx_TypeInfo* type); + +/* BufferGetAndValidate.proto */ +#define __Pyx_GetBufferAndValidate(buf, obj, dtype, flags, nd, cast, stack)\ + ((obj == Py_None || obj == NULL) ?\ + (__Pyx_ZeroBuffer(buf), 0) :\ + __Pyx__GetBufferAndValidate(buf, obj, dtype, flags, nd, cast, stack)) +static int __Pyx__GetBufferAndValidate(Py_buffer* buf, PyObject* obj, + __Pyx_TypeInfo* dtype, int flags, int nd, int cast, __Pyx_BufFmt_StackElem* stack); +static void __Pyx_ZeroBuffer(Py_buffer* buf); +static CYTHON_INLINE void __Pyx_SafeReleaseBuffer(Py_buffer* info); +static Py_ssize_t __Pyx_minusones[] = { -1, -1, -1, -1, -1, -1, -1, -1 }; +static Py_ssize_t __Pyx_zeros[] = { 0, 0, 0, 0, 0, 0, 0, 0 }; + +/* PyDictVersioning.proto */ +#if CYTHON_USE_DICT_VERSIONS && CYTHON_USE_TYPE_SLOTS +#define __PYX_DICT_VERSION_INIT ((PY_UINT64_T) -1) +#define __PYX_GET_DICT_VERSION(dict) (((PyDictObject*)(dict))->ma_version_tag) +#define __PYX_UPDATE_DICT_CACHE(dict, value, cache_var, version_var)\ + (version_var) = __PYX_GET_DICT_VERSION(dict);\ + (cache_var) = (value); +#define __PYX_PY_DICT_LOOKUP_IF_MODIFIED(VAR, DICT, LOOKUP) {\ + static PY_UINT64_T __pyx_dict_version = 0;\ + static PyObject *__pyx_dict_cached_value = NULL;\ + if (likely(__PYX_GET_DICT_VERSION(DICT) == __pyx_dict_version)) {\ + (VAR) = __pyx_dict_cached_value;\ + } else {\ + (VAR) = __pyx_dict_cached_value = (LOOKUP);\ + __pyx_dict_version = __PYX_GET_DICT_VERSION(DICT);\ + }\ +} +static CYTHON_INLINE PY_UINT64_T __Pyx_get_tp_dict_version(PyObject *obj); +static CYTHON_INLINE PY_UINT64_T __Pyx_get_object_dict_version(PyObject *obj); +static CYTHON_INLINE int __Pyx_object_dict_version_matches(PyObject* obj, PY_UINT64_T tp_dict_version, PY_UINT64_T obj_dict_version); +#else +#define __PYX_GET_DICT_VERSION(dict) (0) +#define __PYX_UPDATE_DICT_CACHE(dict, value, cache_var, version_var) +#define __PYX_PY_DICT_LOOKUP_IF_MODIFIED(VAR, DICT, LOOKUP) (VAR) = (LOOKUP); +#endif + +/* GetModuleGlobalName.proto */ +#if CYTHON_USE_DICT_VERSIONS +#define __Pyx_GetModuleGlobalName(var, name) {\ + static PY_UINT64_T __pyx_dict_version = 0;\ + static PyObject *__pyx_dict_cached_value = NULL;\ + (var) = (likely(__pyx_dict_version == __PYX_GET_DICT_VERSION(__pyx_d))) ?\ + (likely(__pyx_dict_cached_value) ? __Pyx_NewRef(__pyx_dict_cached_value) : __Pyx_GetBuiltinName(name)) :\ + __Pyx__GetModuleGlobalName(name, &__pyx_dict_version, &__pyx_dict_cached_value);\ +} +#define __Pyx_GetModuleGlobalNameUncached(var, name) {\ + PY_UINT64_T __pyx_dict_version;\ + PyObject *__pyx_dict_cached_value;\ + (var) = __Pyx__GetModuleGlobalName(name, &__pyx_dict_version, &__pyx_dict_cached_value);\ +} +static PyObject *__Pyx__GetModuleGlobalName(PyObject *name, PY_UINT64_T *dict_version, PyObject **dict_cached_value); +#else +#define __Pyx_GetModuleGlobalName(var, name) (var) = __Pyx__GetModuleGlobalName(name) +#define __Pyx_GetModuleGlobalNameUncached(var, name) (var) = __Pyx__GetModuleGlobalName(name) +static CYTHON_INLINE PyObject *__Pyx__GetModuleGlobalName(PyObject *name); +#endif + +/* PyObjectCall.proto */ +#if CYTHON_COMPILING_IN_CPYTHON +static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw); +#else +#define __Pyx_PyObject_Call(func, arg, kw) PyObject_Call(func, arg, kw) +#endif + +/* ExtTypeTest.proto */ +static CYTHON_INLINE int __Pyx_TypeTest(PyObject *obj, PyTypeObject *type); + +#define __Pyx_BufPtrStrided2d(type, buf, i0, s0, i1, s1) (type)((char*)buf + i0 * s0 + i1 * s1) +/* PyThreadStateGet.proto */ +#if CYTHON_FAST_THREAD_STATE +#define __Pyx_PyThreadState_declare PyThreadState *__pyx_tstate; +#define __Pyx_PyThreadState_assign __pyx_tstate = __Pyx_PyThreadState_Current; +#define __Pyx_PyErr_Occurred() __pyx_tstate->curexc_type +#else +#define __Pyx_PyThreadState_declare +#define __Pyx_PyThreadState_assign +#define __Pyx_PyErr_Occurred() PyErr_Occurred() +#endif + +/* PyErrFetchRestore.proto */ +#if CYTHON_FAST_THREAD_STATE +#define __Pyx_PyErr_Clear() __Pyx_ErrRestore(NULL, NULL, NULL) +#define __Pyx_ErrRestoreWithState(type, value, tb) __Pyx_ErrRestoreInState(PyThreadState_GET(), type, value, tb) +#define __Pyx_ErrFetchWithState(type, value, tb) __Pyx_ErrFetchInState(PyThreadState_GET(), type, value, tb) +#define __Pyx_ErrRestore(type, value, tb) __Pyx_ErrRestoreInState(__pyx_tstate, type, value, tb) +#define __Pyx_ErrFetch(type, value, tb) __Pyx_ErrFetchInState(__pyx_tstate, type, value, tb) +static CYTHON_INLINE void __Pyx_ErrRestoreInState(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb); +static CYTHON_INLINE void __Pyx_ErrFetchInState(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb); +#if CYTHON_COMPILING_IN_CPYTHON +#define __Pyx_PyErr_SetNone(exc) (Py_INCREF(exc), __Pyx_ErrRestore((exc), NULL, NULL)) +#else +#define __Pyx_PyErr_SetNone(exc) PyErr_SetNone(exc) +#endif +#else +#define __Pyx_PyErr_Clear() PyErr_Clear() +#define __Pyx_PyErr_SetNone(exc) PyErr_SetNone(exc) +#define __Pyx_ErrRestoreWithState(type, value, tb) PyErr_Restore(type, value, tb) +#define __Pyx_ErrFetchWithState(type, value, tb) PyErr_Fetch(type, value, tb) +#define __Pyx_ErrRestoreInState(tstate, type, value, tb) PyErr_Restore(type, value, tb) +#define __Pyx_ErrFetchInState(tstate, type, value, tb) PyErr_Fetch(type, value, tb) +#define __Pyx_ErrRestore(type, value, tb) PyErr_Restore(type, value, tb) +#define __Pyx_ErrFetch(type, value, tb) PyErr_Fetch(type, value, tb) +#endif + +/* GetTopmostException.proto */ +#if CYTHON_USE_EXC_INFO_STACK +static _PyErr_StackItem * __Pyx_PyErr_GetTopmostException(PyThreadState *tstate); +#endif + +/* SaveResetException.proto */ +#if CYTHON_FAST_THREAD_STATE +#define __Pyx_ExceptionSave(type, value, tb) __Pyx__ExceptionSave(__pyx_tstate, type, value, tb) +static CYTHON_INLINE void __Pyx__ExceptionSave(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb); +#define __Pyx_ExceptionReset(type, value, tb) __Pyx__ExceptionReset(__pyx_tstate, type, value, tb) +static CYTHON_INLINE void __Pyx__ExceptionReset(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb); +#else +#define __Pyx_ExceptionSave(type, value, tb) PyErr_GetExcInfo(type, value, tb) +#define __Pyx_ExceptionReset(type, value, tb) PyErr_SetExcInfo(type, value, tb) +#endif + +/* PyErrExceptionMatches.proto */ +#if CYTHON_FAST_THREAD_STATE +#define __Pyx_PyErr_ExceptionMatches(err) __Pyx_PyErr_ExceptionMatchesInState(__pyx_tstate, err) +static CYTHON_INLINE int __Pyx_PyErr_ExceptionMatchesInState(PyThreadState* tstate, PyObject* err); +#else +#define __Pyx_PyErr_ExceptionMatches(err) PyErr_ExceptionMatches(err) +#endif + +/* GetException.proto */ +#if CYTHON_FAST_THREAD_STATE +#define __Pyx_GetException(type, value, tb) __Pyx__GetException(__pyx_tstate, type, value, tb) +static int __Pyx__GetException(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb); +#else +static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb); +#endif + +/* RaiseException.proto */ +static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause); + +/* TypeImport.proto */ +#ifndef __PYX_HAVE_RT_ImportType_proto +#define __PYX_HAVE_RT_ImportType_proto +enum __Pyx_ImportType_CheckSize { + __Pyx_ImportType_CheckSize_Error = 0, + __Pyx_ImportType_CheckSize_Warn = 1, + __Pyx_ImportType_CheckSize_Ignore = 2 +}; +static PyTypeObject *__Pyx_ImportType(PyObject* module, const char *module_name, const char *class_name, size_t size, enum __Pyx_ImportType_CheckSize check_size); +#endif + +/* Import.proto */ +static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level); + +/* CLineInTraceback.proto */ +#ifdef CYTHON_CLINE_IN_TRACEBACK +#define __Pyx_CLineForTraceback(tstate, c_line) (((CYTHON_CLINE_IN_TRACEBACK)) ? c_line : 0) +#else +static int __Pyx_CLineForTraceback(PyThreadState *tstate, int c_line); +#endif + +/* CodeObjectCache.proto */ +typedef struct { + PyCodeObject* code_object; + int code_line; +} __Pyx_CodeObjectCacheEntry; +struct __Pyx_CodeObjectCache { + int count; + int max_count; + __Pyx_CodeObjectCacheEntry* entries; +}; +static struct __Pyx_CodeObjectCache __pyx_code_cache = {0,0,NULL}; +static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line); +static PyCodeObject *__pyx_find_code_object(int code_line); +static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object); + +/* AddTraceback.proto */ +static void __Pyx_AddTraceback(const char *funcname, int c_line, + int py_line, const char *filename); + +/* BufferStructDeclare.proto */ +typedef struct { + Py_ssize_t shape, strides, suboffsets; +} __Pyx_Buf_DimInfo; +typedef struct { + size_t refcount; + Py_buffer pybuffer; +} __Pyx_Buffer; +typedef struct { + __Pyx_Buffer *rcbuffer; + char *data; + __Pyx_Buf_DimInfo diminfo[8]; +} __Pyx_LocalBuf_ND; + +#if PY_MAJOR_VERSION < 3 + static int __Pyx_GetBuffer(PyObject *obj, Py_buffer *view, int flags); + static void __Pyx_ReleaseBuffer(Py_buffer *view); +#else + #define __Pyx_GetBuffer PyObject_GetBuffer + #define __Pyx_ReleaseBuffer PyBuffer_Release +#endif + + +/* RealImag.proto */ +#if CYTHON_CCOMPLEX + #ifdef __cplusplus + #define __Pyx_CREAL(z) ((z).real()) + #define __Pyx_CIMAG(z) ((z).imag()) + #else + #define __Pyx_CREAL(z) (__real__(z)) + #define __Pyx_CIMAG(z) (__imag__(z)) + #endif +#else + #define __Pyx_CREAL(z) ((z).real) + #define __Pyx_CIMAG(z) ((z).imag) +#endif +#if defined(__cplusplus) && CYTHON_CCOMPLEX\ + && (defined(_WIN32) || defined(__clang__) || (defined(__GNUC__) && (__GNUC__ >= 5 || __GNUC__ == 4 && __GNUC_MINOR__ >= 4 )) || __cplusplus >= 201103) + #define __Pyx_SET_CREAL(z,x) ((z).real(x)) + #define __Pyx_SET_CIMAG(z,y) ((z).imag(y)) +#else + #define __Pyx_SET_CREAL(z,x) __Pyx_CREAL(z) = (x) + #define __Pyx_SET_CIMAG(z,y) __Pyx_CIMAG(z) = (y) +#endif + +/* Arithmetic.proto */ +#if CYTHON_CCOMPLEX + #define __Pyx_c_eq_float(a, b) ((a)==(b)) + #define __Pyx_c_sum_float(a, b) ((a)+(b)) + #define __Pyx_c_diff_float(a, b) ((a)-(b)) + #define __Pyx_c_prod_float(a, b) ((a)*(b)) + #define __Pyx_c_quot_float(a, b) ((a)/(b)) + #define __Pyx_c_neg_float(a) (-(a)) + #ifdef __cplusplus + #define __Pyx_c_is_zero_float(z) ((z)==(float)0) + #define __Pyx_c_conj_float(z) (::std::conj(z)) + #if 1 + #define __Pyx_c_abs_float(z) (::std::abs(z)) + #define __Pyx_c_pow_float(a, b) (::std::pow(a, b)) + #endif + #else + #define __Pyx_c_is_zero_float(z) ((z)==0) + #define __Pyx_c_conj_float(z) (conjf(z)) + #if 1 + #define __Pyx_c_abs_float(z) (cabsf(z)) + #define __Pyx_c_pow_float(a, b) (cpowf(a, b)) + #endif + #endif +#else + static CYTHON_INLINE int __Pyx_c_eq_float(__pyx_t_float_complex, __pyx_t_float_complex); + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_sum_float(__pyx_t_float_complex, __pyx_t_float_complex); + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_diff_float(__pyx_t_float_complex, __pyx_t_float_complex); + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_prod_float(__pyx_t_float_complex, __pyx_t_float_complex); + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quot_float(__pyx_t_float_complex, __pyx_t_float_complex); + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_neg_float(__pyx_t_float_complex); + static CYTHON_INLINE int __Pyx_c_is_zero_float(__pyx_t_float_complex); + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_conj_float(__pyx_t_float_complex); + #if 1 + static CYTHON_INLINE float __Pyx_c_abs_float(__pyx_t_float_complex); + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_pow_float(__pyx_t_float_complex, __pyx_t_float_complex); + #endif +#endif + +/* Arithmetic.proto */ +#if CYTHON_CCOMPLEX + #define __Pyx_c_eq_double(a, b) ((a)==(b)) + #define __Pyx_c_sum_double(a, b) ((a)+(b)) + #define __Pyx_c_diff_double(a, b) ((a)-(b)) + #define __Pyx_c_prod_double(a, b) ((a)*(b)) + #define __Pyx_c_quot_double(a, b) ((a)/(b)) + #define __Pyx_c_neg_double(a) (-(a)) + #ifdef __cplusplus + #define __Pyx_c_is_zero_double(z) ((z)==(double)0) + #define __Pyx_c_conj_double(z) (::std::conj(z)) + #if 1 + #define __Pyx_c_abs_double(z) (::std::abs(z)) + #define __Pyx_c_pow_double(a, b) (::std::pow(a, b)) + #endif + #else + #define __Pyx_c_is_zero_double(z) ((z)==0) + #define __Pyx_c_conj_double(z) (conj(z)) + #if 1 + #define __Pyx_c_abs_double(z) (cabs(z)) + #define __Pyx_c_pow_double(a, b) (cpow(a, b)) + #endif + #endif +#else + static CYTHON_INLINE int __Pyx_c_eq_double(__pyx_t_double_complex, __pyx_t_double_complex); + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_sum_double(__pyx_t_double_complex, __pyx_t_double_complex); + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_diff_double(__pyx_t_double_complex, __pyx_t_double_complex); + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_prod_double(__pyx_t_double_complex, __pyx_t_double_complex); + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex, __pyx_t_double_complex); + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_neg_double(__pyx_t_double_complex); + static CYTHON_INLINE int __Pyx_c_is_zero_double(__pyx_t_double_complex); + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_conj_double(__pyx_t_double_complex); + #if 1 + static CYTHON_INLINE double __Pyx_c_abs_double(__pyx_t_double_complex); + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_pow_double(__pyx_t_double_complex, __pyx_t_double_complex); + #endif +#endif + +/* GCCDiagnostics.proto */ +#if defined(__GNUC__) && (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6)) +#define __Pyx_HAS_GCC_DIAGNOSTIC +#endif + +/* CIntToPy.proto */ +static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value); + +/* CIntFromPy.proto */ +static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *); + +/* CIntFromPy.proto */ +static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *); + +/* FastTypeChecks.proto */ +#if CYTHON_COMPILING_IN_CPYTHON +#define __Pyx_TypeCheck(obj, type) __Pyx_IsSubtype(Py_TYPE(obj), (PyTypeObject *)type) +static CYTHON_INLINE int __Pyx_IsSubtype(PyTypeObject *a, PyTypeObject *b); +static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches(PyObject *err, PyObject *type); +static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches2(PyObject *err, PyObject *type1, PyObject *type2); +#else +#define __Pyx_TypeCheck(obj, type) PyObject_TypeCheck(obj, (PyTypeObject *)type) +#define __Pyx_PyErr_GivenExceptionMatches(err, type) PyErr_GivenExceptionMatches(err, type) +#define __Pyx_PyErr_GivenExceptionMatches2(err, type1, type2) (PyErr_GivenExceptionMatches(err, type1) || PyErr_GivenExceptionMatches(err, type2)) +#endif +#define __Pyx_PyException_Check(obj) __Pyx_TypeCheck(obj, PyExc_Exception) + +/* CheckBinaryVersion.proto */ +static int __Pyx_check_binary_version(void); + +/* InitStrings.proto */ +static int __Pyx_InitStrings(__Pyx_StringTabEntry *t); + + +/* Module declarations from 'cpython.buffer' */ + +/* Module declarations from 'libc.string' */ + +/* Module declarations from 'libc.stdio' */ + +/* Module declarations from '__builtin__' */ + +/* Module declarations from 'cpython.type' */ +static PyTypeObject *__pyx_ptype_7cpython_4type_type = 0; + +/* Module declarations from 'cpython' */ + +/* Module declarations from 'cpython.object' */ + +/* Module declarations from 'cpython.ref' */ + +/* Module declarations from 'cpython.mem' */ + +/* Module declarations from 'numpy' */ + +/* Module declarations from 'numpy' */ +static PyTypeObject *__pyx_ptype_5numpy_dtype = 0; +static PyTypeObject *__pyx_ptype_5numpy_flatiter = 0; +static PyTypeObject *__pyx_ptype_5numpy_broadcast = 0; +static PyTypeObject *__pyx_ptype_5numpy_ndarray = 0; +static PyTypeObject *__pyx_ptype_5numpy_generic = 0; +static PyTypeObject *__pyx_ptype_5numpy_number = 0; +static PyTypeObject *__pyx_ptype_5numpy_integer = 0; +static PyTypeObject *__pyx_ptype_5numpy_signedinteger = 0; +static PyTypeObject *__pyx_ptype_5numpy_unsignedinteger = 0; +static PyTypeObject *__pyx_ptype_5numpy_inexact = 0; +static PyTypeObject *__pyx_ptype_5numpy_floating = 0; +static PyTypeObject *__pyx_ptype_5numpy_complexfloating = 0; +static PyTypeObject *__pyx_ptype_5numpy_flexible = 0; +static PyTypeObject *__pyx_ptype_5numpy_character = 0; +static PyTypeObject *__pyx_ptype_5numpy_ufunc = 0; + +/* Module declarations from 'libc.math' */ + +/* Module declarations from 'libc.float' */ + +/* Module declarations from 'sdtw_fast' */ +static CYTHON_INLINE __pyx_t_9sdtw_fast_DTYPE_t __pyx_f_9sdtw_fast__soft_min_argmin(__pyx_t_9sdtw_fast_DTYPE_t, __pyx_t_9sdtw_fast_DTYPE_t, __pyx_t_9sdtw_fast_DTYPE_t); /*proto*/ +static __Pyx_TypeInfo __Pyx_TypeInfo_nn___pyx_t_9sdtw_fast_DTYPE_t = { "DTYPE_t", NULL, sizeof(__pyx_t_9sdtw_fast_DTYPE_t), { 0 }, 0, 'R', 0, 0 }; +#define __Pyx_MODULE_NAME "sdtw_fast" +extern int __pyx_module_is_main_sdtw_fast; +int __pyx_module_is_main_sdtw_fast = 0; + +/* Implementation of 'sdtw_fast' */ +static PyObject *__pyx_builtin_range; +static PyObject *__pyx_builtin_ImportError; +static const char __pyx_k_C[] = "C"; +static const char __pyx_k_V[] = "V"; +static const char __pyx_k_i[] = "i"; +static const char __pyx_k_j[] = "j"; +static const char __pyx_k_np[] = "np"; +static const char __pyx_k_main[] = "__main__"; +static const char __pyx_k_name[] = "__name__"; +static const char __pyx_k_test[] = "__test__"; +static const char __pyx_k_DTYPE[] = "DTYPE"; +static const char __pyx_k_dtype[] = "dtype"; +static const char __pyx_k_gamma[] = "gamma"; +static const char __pyx_k_len_X[] = "len_X"; +static const char __pyx_k_len_Y[] = "len_Y"; +static const char __pyx_k_numpy[] = "numpy"; +static const char __pyx_k_range[] = "range"; +static const char __pyx_k_zeros[] = "zeros"; +static const char __pyx_k_import[] = "__import__"; +static const char __pyx_k_float64[] = "float64"; +static const char __pyx_k_soft_min[] = "soft_min"; +static const char __pyx_k_sdtw_C_cy[] = "_sdtw_C_cy"; +static const char __pyx_k_sdtw_fast[] = "sdtw_fast"; +static const char __pyx_k_ImportError[] = "ImportError"; +static const char __pyx_k_sdtw_fast_pyx[] = "sdtw_fast.pyx"; +static const char __pyx_k_cline_in_traceback[] = "cline_in_traceback"; +static const char __pyx_k_cython_implementation_of_soft_D[] = "\ncython implementation of soft-DTW recursion.\nRefs:\n - Blondel, M., Mensch, A., & Vert, J.-P. (2021).\n Differentiable Divergences Between Time Series. AISTATS. http://arxiv.org/abs/2010.08354\n - Mensch, A., Blondel, M. (2018).\n Differentiable Dynamic Programming for Structured Prediction and Attention. ICML. https://proceedings.mlr.press/v80/mensch18a.html\n\n@author: Cl\303\251ment Lejeune \n"; +static const char __pyx_k_numpy_core_multiarray_failed_to[] = "numpy.core.multiarray failed to import"; +static const char __pyx_k_numpy_core_umath_failed_to_impor[] = "numpy.core.umath failed to import"; +static PyObject *__pyx_n_s_C; +static PyObject *__pyx_n_s_DTYPE; +static PyObject *__pyx_n_s_ImportError; +static PyObject *__pyx_n_s_V; +static PyObject *__pyx_n_s_cline_in_traceback; +static PyObject *__pyx_n_s_dtype; +static PyObject *__pyx_n_s_float64; +static PyObject *__pyx_n_s_gamma; +static PyObject *__pyx_n_s_i; +static PyObject *__pyx_n_s_import; +static PyObject *__pyx_n_s_j; +static PyObject *__pyx_n_s_len_X; +static PyObject *__pyx_n_s_len_Y; +static PyObject *__pyx_n_s_main; +static PyObject *__pyx_n_s_name; +static PyObject *__pyx_n_s_np; +static PyObject *__pyx_n_s_numpy; +static PyObject *__pyx_kp_s_numpy_core_multiarray_failed_to; +static PyObject *__pyx_kp_s_numpy_core_umath_failed_to_impor; +static PyObject *__pyx_n_s_range; +static PyObject *__pyx_n_s_sdtw_C_cy; +static PyObject *__pyx_n_s_sdtw_fast; +static PyObject *__pyx_kp_s_sdtw_fast_pyx; +static PyObject *__pyx_n_s_soft_min; +static PyObject *__pyx_n_s_test; +static PyObject *__pyx_n_s_zeros; +static PyObject *__pyx_pf_9sdtw_fast__sdtw_C_cy(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_C, __pyx_t_9sdtw_fast_DTYPE_t __pyx_v_gamma); /* proto */ +static PyObject *__pyx_tuple_; +static PyObject *__pyx_tuple__2; +static PyObject *__pyx_tuple__3; +static PyObject *__pyx_codeobj__4; +/* Late includes */ + +/* "sdtw_fast.pyx":23 + * @boundscheck(False) + * @wraparound(False) + * cdef inline DTYPE_t _soft_min_argmin( # <<<<<<<<<<<<<< + * DTYPE_t x, DTYPE_t y, DTYPE_t z) nogil: + * + */ + +static CYTHON_INLINE __pyx_t_9sdtw_fast_DTYPE_t __pyx_f_9sdtw_fast__soft_min_argmin(__pyx_t_9sdtw_fast_DTYPE_t __pyx_v_x, __pyx_t_9sdtw_fast_DTYPE_t __pyx_v_y, __pyx_t_9sdtw_fast_DTYPE_t __pyx_v_z) { + __pyx_t_9sdtw_fast_DTYPE_t __pyx_v_min_xyz; + __pyx_t_9sdtw_fast_DTYPE_t __pyx_v_nn; + __pyx_t_9sdtw_fast_DTYPE_t __pyx_r; + __pyx_t_9sdtw_fast_DTYPE_t __pyx_t_1; + __pyx_t_9sdtw_fast_DTYPE_t __pyx_t_2; + __pyx_t_9sdtw_fast_DTYPE_t __pyx_t_3; + + /* "sdtw_fast.pyx":26 + * DTYPE_t x, DTYPE_t y, DTYPE_t z) nogil: + * + * cdef DTYPE_t min_xyz = min(x, min(y, z)) # <<<<<<<<<<<<<< + * # cdef double e_x + * # cdef double e_y + */ + __pyx_t_1 = __pyx_v_z; + __pyx_t_2 = __pyx_v_y; + if (((__pyx_t_1 < __pyx_t_2) != 0)) { + __pyx_t_3 = __pyx_t_1; + } else { + __pyx_t_3 = __pyx_t_2; + } + __pyx_t_1 = __pyx_t_3; + __pyx_t_3 = __pyx_v_x; + if (((__pyx_t_1 < __pyx_t_3) != 0)) { + __pyx_t_2 = __pyx_t_1; + } else { + __pyx_t_2 = __pyx_t_3; + } + __pyx_v_min_xyz = __pyx_t_2; + + /* "sdtw_fast.pyx":38 + * # nn = e_x + e_y + e_z # normalizing constant + * + * nn = exp(min_xyz - x) # <<<<<<<<<<<<<< + * nn += exp(min_xyz - y) + * nn += exp(min_xyz - z) + */ + __pyx_v_nn = exp((__pyx_v_min_xyz - __pyx_v_x)); + + /* "sdtw_fast.pyx":39 + * + * nn = exp(min_xyz - x) + * nn += exp(min_xyz - y) # <<<<<<<<<<<<<< + * nn += exp(min_xyz - z) + * # soft_min = min_xyz - log(nn) # smoothed_min operator value + */ + __pyx_v_nn = (__pyx_v_nn + exp((__pyx_v_min_xyz - __pyx_v_y))); + + /* "sdtw_fast.pyx":40 + * nn = exp(min_xyz - x) + * nn += exp(min_xyz - y) + * nn += exp(min_xyz - z) # <<<<<<<<<<<<<< + * # soft_min = min_xyz - log(nn) # smoothed_min operator value + * + */ + __pyx_v_nn = (__pyx_v_nn + exp((__pyx_v_min_xyz - __pyx_v_z))); + + /* "sdtw_fast.pyx":43 + * # soft_min = min_xyz - log(nn) # smoothed_min operator value + * + * return min_xyz - log(nn)# soft_min#, e_x/nn, e_y/nn, e_z/nn # <<<<<<<<<<<<<< + * + * @cdivision(True) + */ + __pyx_r = (__pyx_v_min_xyz - log(__pyx_v_nn)); + goto __pyx_L0; + + /* "sdtw_fast.pyx":23 + * @boundscheck(False) + * @wraparound(False) + * cdef inline DTYPE_t _soft_min_argmin( # <<<<<<<<<<<<<< + * DTYPE_t x, DTYPE_t y, DTYPE_t z) nogil: + * + */ + + /* function exit code */ + __pyx_L0:; + return __pyx_r; +} + +/* "sdtw_fast.pyx":48 + * @boundscheck(False) + * @wraparound(False) + * def _sdtw_C_cy( # <<<<<<<<<<<<<< + * np.ndarray[DTYPE_t, ndim=2] C, + * DTYPE_t gamma): + */ + +/* Python wrapper */ +static PyObject *__pyx_pw_9sdtw_fast_1_sdtw_C_cy(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/ +static PyMethodDef __pyx_mdef_9sdtw_fast_1_sdtw_C_cy = {"_sdtw_C_cy", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_9sdtw_fast_1_sdtw_C_cy, METH_VARARGS|METH_KEYWORDS, 0}; +static PyObject *__pyx_pw_9sdtw_fast_1_sdtw_C_cy(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds) { + PyArrayObject *__pyx_v_C = 0; + __pyx_t_9sdtw_fast_DTYPE_t __pyx_v_gamma; + int __pyx_lineno = 0; + const char *__pyx_filename = NULL; + int __pyx_clineno = 0; + PyObject *__pyx_r = 0; + __Pyx_RefNannyDeclarations + __Pyx_RefNannySetupContext("_sdtw_C_cy (wrapper)", 0); + { + static PyObject **__pyx_pyargnames[] = {&__pyx_n_s_C,&__pyx_n_s_gamma,0}; + PyObject* values[2] = {0,0}; + if (unlikely(__pyx_kwds)) { + Py_ssize_t kw_args; + const Py_ssize_t pos_args = PyTuple_GET_SIZE(__pyx_args); + switch (pos_args) { + case 2: values[1] = PyTuple_GET_ITEM(__pyx_args, 1); + CYTHON_FALLTHROUGH; + case 1: values[0] = PyTuple_GET_ITEM(__pyx_args, 0); + CYTHON_FALLTHROUGH; + case 0: break; + default: goto __pyx_L5_argtuple_error; 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"" : "s", num_found); +} + +/* RaiseDoubleKeywords */ +static void __Pyx_RaiseDoubleKeywordsError( + const char* func_name, + PyObject* kw_name) +{ + PyErr_Format(PyExc_TypeError, + #if PY_MAJOR_VERSION >= 3 + "%s() got multiple values for keyword argument '%U'", func_name, kw_name); + #else + "%s() got multiple values for keyword argument '%s'", func_name, + PyString_AsString(kw_name)); + #endif +} + +/* ParseKeywords */ +static int __Pyx_ParseOptionalKeywords( + PyObject *kwds, + PyObject **argnames[], + PyObject *kwds2, + PyObject *values[], + Py_ssize_t num_pos_args, + const char* function_name) +{ + PyObject *key = 0, *value = 0; + Py_ssize_t pos = 0; + PyObject*** name; + PyObject*** first_kw_arg = argnames + num_pos_args; + while (PyDict_Next(kwds, &pos, &key, &value)) { + name = first_kw_arg; + while (*name && (**name != key)) name++; + if (*name) { + values[name-argnames] = value; + continue; + } + name = first_kw_arg; + #if PY_MAJOR_VERSION < 3 + if (likely(PyString_Check(key))) { + while (*name) { + if ((CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**name) == PyString_GET_SIZE(key)) + && _PyString_Eq(**name, key)) { + values[name-argnames] = value; + break; + } + name++; + } + if (*name) continue; + else { + PyObject*** argname = argnames; + while (argname != first_kw_arg) { + if ((**argname == key) || ( + (CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**argname) == PyString_GET_SIZE(key)) + && _PyString_Eq(**argname, key))) { + goto arg_passed_twice; + } + argname++; + } + } + } else + #endif + if (likely(PyUnicode_Check(key))) { + while (*name) { + int cmp = (**name == key) ? 0 : + #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3 + (__Pyx_PyUnicode_GET_LENGTH(**name) != __Pyx_PyUnicode_GET_LENGTH(key)) ? 1 : + #endif + PyUnicode_Compare(**name, key); + if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad; + if (cmp == 0) { + values[name-argnames] = value; + break; + } + name++; + } + if (*name) continue; + else { + PyObject*** argname = argnames; + while (argname != first_kw_arg) { + int cmp = (**argname == key) ? 0 : + #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3 + (__Pyx_PyUnicode_GET_LENGTH(**argname) != __Pyx_PyUnicode_GET_LENGTH(key)) ? 1 : + #endif + PyUnicode_Compare(**argname, key); + if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad; + if (cmp == 0) goto arg_passed_twice; + argname++; + } + } + } else + goto invalid_keyword_type; + if (kwds2) { + if (unlikely(PyDict_SetItem(kwds2, key, value))) goto bad; + } else { + goto invalid_keyword; + } + } + return 0; +arg_passed_twice: + __Pyx_RaiseDoubleKeywordsError(function_name, key); + goto bad; +invalid_keyword_type: + PyErr_Format(PyExc_TypeError, + "%.200s() keywords must be strings", function_name); + goto bad; +invalid_keyword: + PyErr_Format(PyExc_TypeError, + #if PY_MAJOR_VERSION < 3 + "%.200s() got an unexpected keyword argument '%.200s'", + function_name, PyString_AsString(key)); + #else + "%s() got an unexpected keyword argument '%U'", + function_name, key); + #endif +bad: + return -1; +} + +/* ArgTypeTest */ +static int __Pyx__ArgTypeTest(PyObject *obj, PyTypeObject *type, const char *name, int exact) +{ + if (unlikely(!type)) { + PyErr_SetString(PyExc_SystemError, "Missing type object"); + return 0; + } + else if (exact) { + #if PY_MAJOR_VERSION == 2 + if ((type == &PyBaseString_Type) && likely(__Pyx_PyBaseString_CheckExact(obj))) return 1; + #endif + } + else { + if (likely(__Pyx_TypeCheck(obj, type))) return 1; + } + PyErr_Format(PyExc_TypeError, + "Argument '%.200s' has incorrect type (expected %.200s, got %.200s)", + name, type->tp_name, Py_TYPE(obj)->tp_name); + return 0; +} + +/* IsLittleEndian */ +static CYTHON_INLINE int __Pyx_Is_Little_Endian(void) +{ + union { + uint32_t u32; + uint8_t u8[4]; + } S; + S.u32 = 0x01020304; + return S.u8[0] == 4; +} + +/* BufferFormatCheck */ +static void __Pyx_BufFmt_Init(__Pyx_BufFmt_Context* ctx, + __Pyx_BufFmt_StackElem* stack, + __Pyx_TypeInfo* type) { + stack[0].field = &ctx->root; + stack[0].parent_offset = 0; + ctx->root.type = type; + ctx->root.name = "buffer dtype"; + ctx->root.offset = 0; + ctx->head = stack; + ctx->head->field = &ctx->root; + ctx->fmt_offset = 0; + ctx->head->parent_offset = 0; + ctx->new_packmode = '@'; + ctx->enc_packmode = '@'; + ctx->new_count = 1; + ctx->enc_count = 0; + ctx->enc_type = 0; + ctx->is_complex = 0; + ctx->is_valid_array = 0; + ctx->struct_alignment = 0; + while (type->typegroup == 'S') { + ++ctx->head; + ctx->head->field = type->fields; + ctx->head->parent_offset = 0; + type = type->fields->type; + } +} +static int __Pyx_BufFmt_ParseNumber(const char** ts) { + int count; + const char* t = *ts; + if (*t < '0' || *t > '9') { + return -1; + } else { + count = *t++ - '0'; + while (*t >= '0' && *t <= '9') { + count *= 10; + count += *t++ - '0'; + } + } + *ts = t; + return count; +} +static int __Pyx_BufFmt_ExpectNumber(const char **ts) { + int number = __Pyx_BufFmt_ParseNumber(ts); + if (number == -1) + PyErr_Format(PyExc_ValueError,\ + "Does not understand character buffer dtype format string ('%c')", **ts); + return number; +} +static void __Pyx_BufFmt_RaiseUnexpectedChar(char ch) { + PyErr_Format(PyExc_ValueError, + "Unexpected format string character: '%c'", ch); +} +static const char* __Pyx_BufFmt_DescribeTypeChar(char ch, int is_complex) { + switch (ch) { + case '?': return "'bool'"; + case 'c': return "'char'"; + case 'b': return "'signed char'"; + case 'B': return "'unsigned char'"; + case 'h': return "'short'"; + case 'H': return "'unsigned short'"; + case 'i': return "'int'"; + case 'I': return "'unsigned int'"; + case 'l': return "'long'"; + case 'L': return "'unsigned long'"; + case 'q': return "'long long'"; + case 'Q': return "'unsigned long long'"; + case 'f': return (is_complex ? "'complex float'" : "'float'"); + case 'd': return (is_complex ? "'complex double'" : "'double'"); + case 'g': return (is_complex ? "'complex long double'" : "'long double'"); + case 'T': return "a struct"; + case 'O': return "Python object"; + case 'P': return "a pointer"; + case 's': case 'p': return "a string"; + case 0: return "end"; + default: return "unparseable format string"; + } +} +static size_t __Pyx_BufFmt_TypeCharToStandardSize(char ch, int is_complex) { + switch (ch) { + case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1; + case 'h': case 'H': return 2; + case 'i': case 'I': case 'l': case 'L': return 4; + case 'q': case 'Q': return 8; + case 'f': return (is_complex ? 8 : 4); + case 'd': return (is_complex ? 16 : 8); + case 'g': { + PyErr_SetString(PyExc_ValueError, "Python does not define a standard format string size for long double ('g').."); + return 0; + } + case 'O': case 'P': return sizeof(void*); + default: + __Pyx_BufFmt_RaiseUnexpectedChar(ch); + return 0; + } +} +static size_t __Pyx_BufFmt_TypeCharToNativeSize(char ch, int is_complex) { + switch (ch) { + case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1; + case 'h': case 'H': return sizeof(short); + case 'i': case 'I': return sizeof(int); + case 'l': case 'L': return sizeof(long); + #ifdef HAVE_LONG_LONG + case 'q': case 'Q': return sizeof(PY_LONG_LONG); + #endif + case 'f': return sizeof(float) * (is_complex ? 2 : 1); + case 'd': return sizeof(double) * (is_complex ? 2 : 1); + case 'g': return sizeof(long double) * (is_complex ? 2 : 1); + case 'O': case 'P': return sizeof(void*); + default: { + __Pyx_BufFmt_RaiseUnexpectedChar(ch); + return 0; + } + } +} +typedef struct { char c; short x; } __Pyx_st_short; +typedef struct { char c; int x; } __Pyx_st_int; +typedef struct { char c; long x; } __Pyx_st_long; +typedef struct { char c; float x; } __Pyx_st_float; +typedef struct { char c; double x; } __Pyx_st_double; +typedef struct { char c; long double x; } __Pyx_st_longdouble; +typedef struct { char c; void *x; } __Pyx_st_void_p; +#ifdef HAVE_LONG_LONG +typedef struct { char c; PY_LONG_LONG x; } __Pyx_st_longlong; +#endif +static size_t __Pyx_BufFmt_TypeCharToAlignment(char ch, CYTHON_UNUSED int is_complex) { + switch (ch) { + case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1; + case 'h': case 'H': return sizeof(__Pyx_st_short) - sizeof(short); + case 'i': case 'I': return sizeof(__Pyx_st_int) - sizeof(int); + case 'l': case 'L': return sizeof(__Pyx_st_long) - sizeof(long); +#ifdef HAVE_LONG_LONG + case 'q': case 'Q': return sizeof(__Pyx_st_longlong) - sizeof(PY_LONG_LONG); +#endif + case 'f': return sizeof(__Pyx_st_float) - sizeof(float); + case 'd': return sizeof(__Pyx_st_double) - sizeof(double); + case 'g': return sizeof(__Pyx_st_longdouble) - sizeof(long double); + case 'P': case 'O': return sizeof(__Pyx_st_void_p) - sizeof(void*); + default: + __Pyx_BufFmt_RaiseUnexpectedChar(ch); + return 0; + } +} +/* These are for computing the padding at the end of the struct to align + on the first member of the struct. This will probably the same as above, + but we don't have any guarantees. + */ +typedef struct { short x; char c; } __Pyx_pad_short; +typedef struct { int x; char c; } __Pyx_pad_int; +typedef struct { long x; char c; } __Pyx_pad_long; +typedef struct { float x; char c; } __Pyx_pad_float; +typedef struct { double x; char c; } __Pyx_pad_double; +typedef struct { long double x; char c; } __Pyx_pad_longdouble; +typedef struct { void *x; char c; } __Pyx_pad_void_p; +#ifdef HAVE_LONG_LONG +typedef struct { PY_LONG_LONG x; char c; } __Pyx_pad_longlong; +#endif +static size_t __Pyx_BufFmt_TypeCharToPadding(char ch, CYTHON_UNUSED int is_complex) { + switch (ch) { + case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1; + case 'h': case 'H': return sizeof(__Pyx_pad_short) - sizeof(short); + case 'i': case 'I': return sizeof(__Pyx_pad_int) - sizeof(int); + case 'l': case 'L': return sizeof(__Pyx_pad_long) - sizeof(long); +#ifdef HAVE_LONG_LONG + case 'q': case 'Q': return sizeof(__Pyx_pad_longlong) - sizeof(PY_LONG_LONG); +#endif + case 'f': return sizeof(__Pyx_pad_float) - sizeof(float); + case 'd': return sizeof(__Pyx_pad_double) - sizeof(double); + case 'g': return sizeof(__Pyx_pad_longdouble) - sizeof(long double); + case 'P': case 'O': return sizeof(__Pyx_pad_void_p) - sizeof(void*); + default: + __Pyx_BufFmt_RaiseUnexpectedChar(ch); + return 0; + } +} +static char __Pyx_BufFmt_TypeCharToGroup(char ch, int is_complex) { + switch (ch) { + case 'c': + return 'H'; + case 'b': case 'h': case 'i': + case 'l': case 'q': case 's': case 'p': + return 'I'; + case '?': case 'B': case 'H': case 'I': case 'L': case 'Q': + return 'U'; + case 'f': case 'd': case 'g': + return (is_complex ? 'C' : 'R'); + case 'O': + return 'O'; + case 'P': + return 'P'; + default: { + __Pyx_BufFmt_RaiseUnexpectedChar(ch); + return 0; + } + } +} +static void __Pyx_BufFmt_RaiseExpected(__Pyx_BufFmt_Context* ctx) { + if (ctx->head == NULL || ctx->head->field == &ctx->root) { + const char* expected; + const char* quote; + if (ctx->head == NULL) { + expected = "end"; + quote = ""; + } else { + expected = ctx->head->field->type->name; + quote = "'"; + } + PyErr_Format(PyExc_ValueError, + "Buffer dtype mismatch, expected %s%s%s but got %s", + quote, expected, quote, + __Pyx_BufFmt_DescribeTypeChar(ctx->enc_type, ctx->is_complex)); + } else { + __Pyx_StructField* field = ctx->head->field; + __Pyx_StructField* parent = (ctx->head - 1)->field; + PyErr_Format(PyExc_ValueError, + "Buffer dtype mismatch, expected '%s' but got %s in '%s.%s'", + field->type->name, __Pyx_BufFmt_DescribeTypeChar(ctx->enc_type, ctx->is_complex), + parent->type->name, field->name); + } +} +static int __Pyx_BufFmt_ProcessTypeChunk(__Pyx_BufFmt_Context* ctx) { + char group; + size_t size, offset, arraysize = 1; + if (ctx->enc_type == 0) return 0; + if (ctx->head->field->type->arraysize[0]) { + int i, ndim = 0; + if (ctx->enc_type == 's' || ctx->enc_type == 'p') { + ctx->is_valid_array = ctx->head->field->type->ndim == 1; + ndim = 1; + if (ctx->enc_count != ctx->head->field->type->arraysize[0]) { + PyErr_Format(PyExc_ValueError, + "Expected a dimension of size %zu, got %zu", + ctx->head->field->type->arraysize[0], ctx->enc_count); + return -1; + } + } + if (!ctx->is_valid_array) { + PyErr_Format(PyExc_ValueError, "Expected %d dimensions, got %d", + ctx->head->field->type->ndim, ndim); + return -1; + } + for (i = 0; i < ctx->head->field->type->ndim; i++) { + arraysize *= ctx->head->field->type->arraysize[i]; + } + ctx->is_valid_array = 0; + ctx->enc_count = 1; + } + group = __Pyx_BufFmt_TypeCharToGroup(ctx->enc_type, ctx->is_complex); + do { + __Pyx_StructField* field = ctx->head->field; + __Pyx_TypeInfo* type = field->type; + if (ctx->enc_packmode == '@' || ctx->enc_packmode == '^') { + size = __Pyx_BufFmt_TypeCharToNativeSize(ctx->enc_type, ctx->is_complex); + } else { + size = __Pyx_BufFmt_TypeCharToStandardSize(ctx->enc_type, ctx->is_complex); + } + if (ctx->enc_packmode == '@') { + size_t align_at = __Pyx_BufFmt_TypeCharToAlignment(ctx->enc_type, ctx->is_complex); + size_t align_mod_offset; + if (align_at == 0) return -1; + align_mod_offset = ctx->fmt_offset % align_at; + if (align_mod_offset > 0) ctx->fmt_offset += align_at - align_mod_offset; + if (ctx->struct_alignment == 0) + ctx->struct_alignment = __Pyx_BufFmt_TypeCharToPadding(ctx->enc_type, + ctx->is_complex); + } + if (type->size != size || type->typegroup != group) { + if (type->typegroup == 'C' && type->fields != NULL) { + size_t parent_offset = ctx->head->parent_offset + field->offset; + ++ctx->head; + ctx->head->field = type->fields; + ctx->head->parent_offset = parent_offset; + continue; + } + if ((type->typegroup == 'H' || group == 'H') && type->size == size) { + } else { + __Pyx_BufFmt_RaiseExpected(ctx); + return -1; + } + } + offset = ctx->head->parent_offset + field->offset; + if (ctx->fmt_offset != offset) { + PyErr_Format(PyExc_ValueError, + "Buffer dtype mismatch; next field is at offset %" CYTHON_FORMAT_SSIZE_T "d but %" CYTHON_FORMAT_SSIZE_T "d expected", + (Py_ssize_t)ctx->fmt_offset, (Py_ssize_t)offset); + return -1; + } + ctx->fmt_offset += size; + if (arraysize) + ctx->fmt_offset += (arraysize - 1) * size; + --ctx->enc_count; + while (1) { + if (field == &ctx->root) { + ctx->head = NULL; + if (ctx->enc_count != 0) { + __Pyx_BufFmt_RaiseExpected(ctx); + return -1; + } + break; + } + ctx->head->field = ++field; + if (field->type == NULL) { + --ctx->head; + field = ctx->head->field; + continue; + } else if (field->type->typegroup == 'S') { + size_t parent_offset = ctx->head->parent_offset + field->offset; + if (field->type->fields->type == NULL) continue; + field = field->type->fields; + ++ctx->head; + ctx->head->field = field; + ctx->head->parent_offset = parent_offset; + break; + } else { + break; + } + } + } while (ctx->enc_count); + ctx->enc_type = 0; + ctx->is_complex = 0; + return 0; +} +static PyObject * +__pyx_buffmt_parse_array(__Pyx_BufFmt_Context* ctx, const char** tsp) +{ + const char *ts = *tsp; + int i = 0, number, ndim; + ++ts; + if (ctx->new_count != 1) { + PyErr_SetString(PyExc_ValueError, + "Cannot handle repeated arrays in format string"); + return NULL; + } + if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL; + ndim = ctx->head->field->type->ndim; + while (*ts && *ts != ')') { + switch (*ts) { + case ' ': case '\f': case '\r': case '\n': case '\t': case '\v': continue; + default: break; + } + number = __Pyx_BufFmt_ExpectNumber(&ts); + if (number == -1) return NULL; + if (i < ndim && (size_t) number != ctx->head->field->type->arraysize[i]) + return PyErr_Format(PyExc_ValueError, + "Expected a dimension of size %zu, got %d", + ctx->head->field->type->arraysize[i], number); + if (*ts != ',' && *ts != ')') + return PyErr_Format(PyExc_ValueError, + "Expected a comma in format string, got '%c'", *ts); + if (*ts == ',') ts++; + i++; + } + if (i != ndim) + return PyErr_Format(PyExc_ValueError, "Expected %d dimension(s), got %d", + ctx->head->field->type->ndim, i); + if (!*ts) { + PyErr_SetString(PyExc_ValueError, + "Unexpected end of format string, expected ')'"); + return NULL; + } + ctx->is_valid_array = 1; + ctx->new_count = 1; + *tsp = ++ts; + return Py_None; +} +static const char* __Pyx_BufFmt_CheckString(__Pyx_BufFmt_Context* ctx, const char* ts) { + int got_Z = 0; + while (1) { + switch(*ts) { + case 0: + if (ctx->enc_type != 0 && ctx->head == NULL) { + __Pyx_BufFmt_RaiseExpected(ctx); + return NULL; + } + if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL; + if (ctx->head != NULL) { + __Pyx_BufFmt_RaiseExpected(ctx); + return NULL; + } + return ts; + case ' ': + case '\r': + case '\n': + ++ts; + break; + case '<': + if (!__Pyx_Is_Little_Endian()) { + PyErr_SetString(PyExc_ValueError, "Little-endian buffer not supported on big-endian compiler"); + return NULL; + } + ctx->new_packmode = '='; + ++ts; + break; + case '>': + case '!': + if (__Pyx_Is_Little_Endian()) { + PyErr_SetString(PyExc_ValueError, "Big-endian buffer not supported on little-endian compiler"); + return NULL; + } + ctx->new_packmode = '='; + ++ts; + break; + case '=': + case '@': + case '^': + ctx->new_packmode = *ts++; + break; + case 'T': + { + const char* ts_after_sub; + size_t i, struct_count = ctx->new_count; + size_t struct_alignment = ctx->struct_alignment; + ctx->new_count = 1; + ++ts; + if (*ts != '{') { + PyErr_SetString(PyExc_ValueError, "Buffer acquisition: Expected '{' after 'T'"); + return NULL; + } + if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL; + ctx->enc_type = 0; + ctx->enc_count = 0; + ctx->struct_alignment = 0; + ++ts; + ts_after_sub = ts; + for (i = 0; i != struct_count; ++i) { + ts_after_sub = __Pyx_BufFmt_CheckString(ctx, ts); + if (!ts_after_sub) return NULL; + } + ts = ts_after_sub; + if (struct_alignment) ctx->struct_alignment = struct_alignment; + } + break; + case '}': + { + size_t alignment = ctx->struct_alignment; + ++ts; + if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL; + ctx->enc_type = 0; + if (alignment && ctx->fmt_offset % alignment) { + ctx->fmt_offset += alignment - (ctx->fmt_offset % alignment); + } + } + return ts; + case 'x': + if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL; + ctx->fmt_offset += ctx->new_count; + ctx->new_count = 1; + ctx->enc_count = 0; + ctx->enc_type = 0; + ctx->enc_packmode = ctx->new_packmode; + ++ts; + break; + case 'Z': + got_Z = 1; + ++ts; + if (*ts != 'f' && *ts != 'd' && *ts != 'g') { + __Pyx_BufFmt_RaiseUnexpectedChar('Z'); + return NULL; + } + CYTHON_FALLTHROUGH; + case '?': case 'c': case 'b': case 'B': case 'h': case 'H': case 'i': case 'I': + case 'l': case 'L': case 'q': case 'Q': + case 'f': case 'd': case 'g': + case 'O': case 'p': + if ((ctx->enc_type == *ts) && (got_Z == ctx->is_complex) && + (ctx->enc_packmode == ctx->new_packmode) && (!ctx->is_valid_array)) { + ctx->enc_count += ctx->new_count; + ctx->new_count = 1; + got_Z = 0; + ++ts; + break; + } + CYTHON_FALLTHROUGH; + case 's': + if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL; + ctx->enc_count = ctx->new_count; + ctx->enc_packmode = ctx->new_packmode; + ctx->enc_type = *ts; + ctx->is_complex = got_Z; + ++ts; + ctx->new_count = 1; + got_Z = 0; + break; + case ':': + ++ts; + while(*ts != ':') ++ts; + ++ts; + break; + case '(': + if (!__pyx_buffmt_parse_array(ctx, &ts)) return NULL; + break; + default: + { + int number = __Pyx_BufFmt_ExpectNumber(&ts); + if (number == -1) return NULL; + ctx->new_count = (size_t)number; + } + } + } +} + +/* BufferGetAndValidate */ + static CYTHON_INLINE void __Pyx_SafeReleaseBuffer(Py_buffer* info) { + if (unlikely(info->buf == NULL)) return; + if (info->suboffsets == __Pyx_minusones) info->suboffsets = NULL; + __Pyx_ReleaseBuffer(info); +} +static void __Pyx_ZeroBuffer(Py_buffer* buf) { + buf->buf = NULL; + buf->obj = NULL; + buf->strides = __Pyx_zeros; + buf->shape = __Pyx_zeros; + buf->suboffsets = __Pyx_minusones; +} +static int __Pyx__GetBufferAndValidate( + Py_buffer* buf, PyObject* obj, __Pyx_TypeInfo* dtype, int flags, + int nd, int cast, __Pyx_BufFmt_StackElem* stack) +{ + buf->buf = NULL; + if (unlikely(__Pyx_GetBuffer(obj, buf, flags) == -1)) { + __Pyx_ZeroBuffer(buf); + return -1; + } + if (unlikely(buf->ndim != nd)) { + PyErr_Format(PyExc_ValueError, + "Buffer has wrong number of dimensions (expected %d, got %d)", + nd, buf->ndim); + goto fail; + } + if (!cast) { + __Pyx_BufFmt_Context ctx; + __Pyx_BufFmt_Init(&ctx, stack, dtype); + if (!__Pyx_BufFmt_CheckString(&ctx, buf->format)) goto fail; + } + if (unlikely((size_t)buf->itemsize != dtype->size)) { + PyErr_Format(PyExc_ValueError, + "Item size of buffer (%" CYTHON_FORMAT_SSIZE_T "d byte%s) does not match size of '%s' (%" CYTHON_FORMAT_SSIZE_T "d byte%s)", + buf->itemsize, (buf->itemsize > 1) ? "s" : "", + dtype->name, (Py_ssize_t)dtype->size, (dtype->size > 1) ? "s" : ""); + goto fail; + } + if (buf->suboffsets == NULL) buf->suboffsets = __Pyx_minusones; + return 0; +fail:; + __Pyx_SafeReleaseBuffer(buf); + return -1; +} + +/* PyDictVersioning */ + #if CYTHON_USE_DICT_VERSIONS && CYTHON_USE_TYPE_SLOTS +static CYTHON_INLINE PY_UINT64_T __Pyx_get_tp_dict_version(PyObject *obj) { + PyObject *dict = Py_TYPE(obj)->tp_dict; + return likely(dict) ? __PYX_GET_DICT_VERSION(dict) : 0; +} +static CYTHON_INLINE PY_UINT64_T __Pyx_get_object_dict_version(PyObject *obj) { + PyObject **dictptr = NULL; + Py_ssize_t offset = Py_TYPE(obj)->tp_dictoffset; + if (offset) { +#if CYTHON_COMPILING_IN_CPYTHON + dictptr = (likely(offset > 0)) ? (PyObject **) ((char *)obj + offset) : _PyObject_GetDictPtr(obj); +#else + dictptr = _PyObject_GetDictPtr(obj); +#endif + } + return (dictptr && *dictptr) ? __PYX_GET_DICT_VERSION(*dictptr) : 0; +} +static CYTHON_INLINE int __Pyx_object_dict_version_matches(PyObject* obj, PY_UINT64_T tp_dict_version, PY_UINT64_T obj_dict_version) { + PyObject *dict = Py_TYPE(obj)->tp_dict; + if (unlikely(!dict) || unlikely(tp_dict_version != __PYX_GET_DICT_VERSION(dict))) + return 0; + return obj_dict_version == __Pyx_get_object_dict_version(obj); +} +#endif + +/* GetModuleGlobalName */ + #if CYTHON_USE_DICT_VERSIONS +static PyObject *__Pyx__GetModuleGlobalName(PyObject *name, PY_UINT64_T *dict_version, PyObject **dict_cached_value) +#else +static CYTHON_INLINE PyObject *__Pyx__GetModuleGlobalName(PyObject *name) +#endif +{ + PyObject *result; +#if !CYTHON_AVOID_BORROWED_REFS +#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x030500A1 + result = _PyDict_GetItem_KnownHash(__pyx_d, name, ((PyASCIIObject *) name)->hash); + __PYX_UPDATE_DICT_CACHE(__pyx_d, result, *dict_cached_value, *dict_version) + if (likely(result)) { + return __Pyx_NewRef(result); + } else if (unlikely(PyErr_Occurred())) { + return NULL; + } +#else + result = PyDict_GetItem(__pyx_d, name); + __PYX_UPDATE_DICT_CACHE(__pyx_d, result, *dict_cached_value, *dict_version) + if (likely(result)) { + return __Pyx_NewRef(result); + } +#endif +#else + result = PyObject_GetItem(__pyx_d, name); + __PYX_UPDATE_DICT_CACHE(__pyx_d, result, *dict_cached_value, *dict_version) + if (likely(result)) { + return __Pyx_NewRef(result); + } + PyErr_Clear(); +#endif + return __Pyx_GetBuiltinName(name); +} + +/* PyObjectCall */ + #if CYTHON_COMPILING_IN_CPYTHON +static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw) { + PyObject *result; + ternaryfunc call = Py_TYPE(func)->tp_call; + if (unlikely(!call)) + return PyObject_Call(func, arg, kw); + if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object"))) + return NULL; + result = (*call)(func, arg, kw); + Py_LeaveRecursiveCall(); + if (unlikely(!result) && unlikely(!PyErr_Occurred())) { + PyErr_SetString( + PyExc_SystemError, + "NULL result without error in PyObject_Call"); + } + return result; +} +#endif + +/* ExtTypeTest */ + static CYTHON_INLINE int __Pyx_TypeTest(PyObject *obj, PyTypeObject *type) { + if (unlikely(!type)) { + PyErr_SetString(PyExc_SystemError, "Missing type object"); + return 0; + } + if (likely(__Pyx_TypeCheck(obj, type))) + return 1; + PyErr_Format(PyExc_TypeError, "Cannot convert %.200s to %.200s", + Py_TYPE(obj)->tp_name, type->tp_name); + return 0; +} + +/* PyErrFetchRestore */ + #if CYTHON_FAST_THREAD_STATE +static CYTHON_INLINE void __Pyx_ErrRestoreInState(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb) { + PyObject *tmp_type, *tmp_value, *tmp_tb; + tmp_type = tstate->curexc_type; + tmp_value = tstate->curexc_value; + tmp_tb = tstate->curexc_traceback; + tstate->curexc_type = type; + tstate->curexc_value = value; + tstate->curexc_traceback = tb; + Py_XDECREF(tmp_type); + Py_XDECREF(tmp_value); + Py_XDECREF(tmp_tb); +} +static CYTHON_INLINE void __Pyx_ErrFetchInState(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) { + *type = tstate->curexc_type; + *value = tstate->curexc_value; + *tb = tstate->curexc_traceback; + tstate->curexc_type = 0; + tstate->curexc_value = 0; + tstate->curexc_traceback = 0; +} +#endif + +/* GetTopmostException */ + #if CYTHON_USE_EXC_INFO_STACK +static _PyErr_StackItem * +__Pyx_PyErr_GetTopmostException(PyThreadState *tstate) +{ + _PyErr_StackItem *exc_info = tstate->exc_info; + while ((exc_info->exc_type == NULL || exc_info->exc_type == Py_None) && + exc_info->previous_item != NULL) + { + exc_info = exc_info->previous_item; + } + return exc_info; +} +#endif + +/* SaveResetException */ + #if CYTHON_FAST_THREAD_STATE +static CYTHON_INLINE void __Pyx__ExceptionSave(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) { + #if CYTHON_USE_EXC_INFO_STACK + _PyErr_StackItem *exc_info = __Pyx_PyErr_GetTopmostException(tstate); + *type = exc_info->exc_type; + *value = exc_info->exc_value; + *tb = exc_info->exc_traceback; + #else + *type = tstate->exc_type; + *value = tstate->exc_value; + *tb = tstate->exc_traceback; + #endif + Py_XINCREF(*type); + Py_XINCREF(*value); + Py_XINCREF(*tb); +} +static CYTHON_INLINE void __Pyx__ExceptionReset(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb) { + PyObject *tmp_type, *tmp_value, *tmp_tb; + #if CYTHON_USE_EXC_INFO_STACK + _PyErr_StackItem *exc_info = tstate->exc_info; + tmp_type = exc_info->exc_type; + tmp_value = exc_info->exc_value; + tmp_tb = exc_info->exc_traceback; + exc_info->exc_type = type; + exc_info->exc_value = value; + exc_info->exc_traceback = tb; + #else + tmp_type = tstate->exc_type; + tmp_value = tstate->exc_value; + tmp_tb = tstate->exc_traceback; + tstate->exc_type = type; + tstate->exc_value = value; + tstate->exc_traceback = tb; + #endif + Py_XDECREF(tmp_type); + Py_XDECREF(tmp_value); + Py_XDECREF(tmp_tb); +} +#endif + +/* PyErrExceptionMatches */ + #if CYTHON_FAST_THREAD_STATE +static int __Pyx_PyErr_ExceptionMatchesTuple(PyObject *exc_type, PyObject *tuple) { + Py_ssize_t i, n; + n = PyTuple_GET_SIZE(tuple); +#if PY_MAJOR_VERSION >= 3 + for (i=0; icurexc_type; + if (exc_type == err) return 1; + if (unlikely(!exc_type)) return 0; + if (unlikely(PyTuple_Check(err))) + return __Pyx_PyErr_ExceptionMatchesTuple(exc_type, err); + return __Pyx_PyErr_GivenExceptionMatches(exc_type, err); +} +#endif + +/* GetException */ + #if CYTHON_FAST_THREAD_STATE +static int __Pyx__GetException(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) +#else +static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb) +#endif +{ + PyObject *local_type, *local_value, *local_tb; +#if CYTHON_FAST_THREAD_STATE + PyObject *tmp_type, *tmp_value, *tmp_tb; + local_type = tstate->curexc_type; + local_value = tstate->curexc_value; + local_tb = tstate->curexc_traceback; + tstate->curexc_type = 0; + tstate->curexc_value = 0; + tstate->curexc_traceback = 0; +#else + PyErr_Fetch(&local_type, &local_value, &local_tb); +#endif + PyErr_NormalizeException(&local_type, &local_value, &local_tb); +#if CYTHON_FAST_THREAD_STATE + if (unlikely(tstate->curexc_type)) +#else + if (unlikely(PyErr_Occurred())) +#endif + goto bad; + #if PY_MAJOR_VERSION >= 3 + if (local_tb) { + if (unlikely(PyException_SetTraceback(local_value, local_tb) < 0)) + goto bad; + } + #endif + Py_XINCREF(local_tb); + Py_XINCREF(local_type); + Py_XINCREF(local_value); + *type = local_type; + *value = local_value; + *tb = local_tb; +#if CYTHON_FAST_THREAD_STATE + #if CYTHON_USE_EXC_INFO_STACK + { + _PyErr_StackItem *exc_info = tstate->exc_info; + tmp_type = exc_info->exc_type; + tmp_value = exc_info->exc_value; + tmp_tb = exc_info->exc_traceback; + exc_info->exc_type = local_type; + exc_info->exc_value = local_value; + exc_info->exc_traceback = local_tb; + } + #else + tmp_type = tstate->exc_type; + tmp_value = tstate->exc_value; + tmp_tb = tstate->exc_traceback; + tstate->exc_type = local_type; + tstate->exc_value = local_value; + tstate->exc_traceback = local_tb; + #endif + Py_XDECREF(tmp_type); + Py_XDECREF(tmp_value); + Py_XDECREF(tmp_tb); +#else + PyErr_SetExcInfo(local_type, local_value, local_tb); +#endif + return 0; +bad: + *type = 0; + *value = 0; + *tb = 0; + Py_XDECREF(local_type); + Py_XDECREF(local_value); + Py_XDECREF(local_tb); + return -1; +} + +/* RaiseException */ + #if PY_MAJOR_VERSION < 3 +static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, + CYTHON_UNUSED PyObject *cause) { + __Pyx_PyThreadState_declare + Py_XINCREF(type); + if (!value || value == Py_None) + value = NULL; + else + Py_INCREF(value); + if (!tb || tb == Py_None) + tb = NULL; + else { + Py_INCREF(tb); + if (!PyTraceBack_Check(tb)) { + PyErr_SetString(PyExc_TypeError, + "raise: arg 3 must be a traceback or None"); + goto raise_error; + } + } + if (PyType_Check(type)) { +#if CYTHON_COMPILING_IN_PYPY + if (!value) { + Py_INCREF(Py_None); + value = Py_None; + } +#endif + PyErr_NormalizeException(&type, &value, &tb); + } else { + if (value) { + PyErr_SetString(PyExc_TypeError, + "instance exception may not have a separate value"); + goto raise_error; + } + value = type; + type = (PyObject*) Py_TYPE(type); + Py_INCREF(type); + if (!PyType_IsSubtype((PyTypeObject *)type, (PyTypeObject *)PyExc_BaseException)) { + PyErr_SetString(PyExc_TypeError, + "raise: exception class must be a subclass of BaseException"); + goto raise_error; + } + } + __Pyx_PyThreadState_assign + __Pyx_ErrRestore(type, value, tb); + return; +raise_error: + Py_XDECREF(value); + Py_XDECREF(type); + Py_XDECREF(tb); + return; +} +#else +static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause) { + PyObject* owned_instance = NULL; + if (tb == Py_None) { + tb = 0; + } else if (tb && !PyTraceBack_Check(tb)) { + PyErr_SetString(PyExc_TypeError, + "raise: arg 3 must be a traceback or None"); + goto bad; + } + if (value == Py_None) + value = 0; + if (PyExceptionInstance_Check(type)) { + if (value) { + PyErr_SetString(PyExc_TypeError, + "instance exception may not have a separate value"); + goto bad; + } + value = type; + type = (PyObject*) Py_TYPE(value); + } else if (PyExceptionClass_Check(type)) { + PyObject *instance_class = NULL; + if (value && PyExceptionInstance_Check(value)) { + instance_class = (PyObject*) Py_TYPE(value); + if (instance_class != type) { + int is_subclass = PyObject_IsSubclass(instance_class, type); + if (!is_subclass) { + instance_class = NULL; + } else if (unlikely(is_subclass == -1)) { + goto bad; + } else { + type = instance_class; + } + } + } + if (!instance_class) { + PyObject *args; + if (!value) + args = PyTuple_New(0); + else if (PyTuple_Check(value)) { + Py_INCREF(value); + args = value; + } else + args = PyTuple_Pack(1, value); + if (!args) + goto bad; + owned_instance = PyObject_Call(type, args, NULL); + Py_DECREF(args); + if (!owned_instance) + goto bad; + value = owned_instance; + if (!PyExceptionInstance_Check(value)) { + PyErr_Format(PyExc_TypeError, + "calling %R should have returned an instance of " + "BaseException, not %R", + type, Py_TYPE(value)); + goto bad; + } + } + } else { + PyErr_SetString(PyExc_TypeError, + "raise: exception class must be a subclass of BaseException"); + goto bad; + } + if (cause) { + PyObject *fixed_cause; + if (cause == Py_None) { + fixed_cause = NULL; + } else if (PyExceptionClass_Check(cause)) { + fixed_cause = PyObject_CallObject(cause, NULL); + if (fixed_cause == NULL) + goto bad; + } else if (PyExceptionInstance_Check(cause)) { + fixed_cause = cause; + Py_INCREF(fixed_cause); + } else { + PyErr_SetString(PyExc_TypeError, + "exception causes must derive from " + "BaseException"); + goto bad; + } + PyException_SetCause(value, fixed_cause); + } + PyErr_SetObject(type, value); + if (tb) { +#if CYTHON_COMPILING_IN_PYPY + PyObject *tmp_type, *tmp_value, *tmp_tb; + PyErr_Fetch(&tmp_type, &tmp_value, &tmp_tb); + Py_INCREF(tb); + PyErr_Restore(tmp_type, tmp_value, tb); + Py_XDECREF(tmp_tb); +#else + PyThreadState *tstate = __Pyx_PyThreadState_Current; + PyObject* tmp_tb = tstate->curexc_traceback; + if (tb != tmp_tb) { + Py_INCREF(tb); + tstate->curexc_traceback = tb; + Py_XDECREF(tmp_tb); + } +#endif + } +bad: + Py_XDECREF(owned_instance); + return; +} +#endif + +/* TypeImport */ + #ifndef __PYX_HAVE_RT_ImportType +#define __PYX_HAVE_RT_ImportType +static PyTypeObject *__Pyx_ImportType(PyObject *module, const char *module_name, const char *class_name, + size_t size, enum __Pyx_ImportType_CheckSize check_size) +{ + PyObject *result = 0; + char warning[200]; + Py_ssize_t basicsize; +#ifdef Py_LIMITED_API + PyObject *py_basicsize; +#endif + result = PyObject_GetAttrString(module, class_name); + if (!result) + goto bad; + if (!PyType_Check(result)) { + PyErr_Format(PyExc_TypeError, + "%.200s.%.200s is not a type object", + module_name, class_name); + goto bad; + } +#ifndef Py_LIMITED_API + basicsize = ((PyTypeObject *)result)->tp_basicsize; +#else + py_basicsize = PyObject_GetAttrString(result, "__basicsize__"); + if (!py_basicsize) + goto bad; + basicsize = PyLong_AsSsize_t(py_basicsize); + Py_DECREF(py_basicsize); + py_basicsize = 0; + if (basicsize == (Py_ssize_t)-1 && PyErr_Occurred()) + goto bad; +#endif + if ((size_t)basicsize < size) { + PyErr_Format(PyExc_ValueError, + "%.200s.%.200s size changed, may indicate binary incompatibility. " + "Expected %zd from C header, got %zd from PyObject", + module_name, class_name, size, basicsize); + goto bad; + } + if (check_size == __Pyx_ImportType_CheckSize_Error && (size_t)basicsize != size) { + PyErr_Format(PyExc_ValueError, + "%.200s.%.200s size changed, may indicate binary incompatibility. " + "Expected %zd from C header, got %zd from PyObject", + module_name, class_name, size, basicsize); + goto bad; + } + else if (check_size == __Pyx_ImportType_CheckSize_Warn && (size_t)basicsize > size) { + PyOS_snprintf(warning, sizeof(warning), + "%s.%s size changed, may indicate binary incompatibility. " + "Expected %zd from C header, got %zd from PyObject", + module_name, class_name, size, basicsize); + if (PyErr_WarnEx(NULL, warning, 0) < 0) goto bad; + } + return (PyTypeObject *)result; +bad: + Py_XDECREF(result); + return NULL; +} +#endif + +/* Import */ + static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level) { + PyObject *empty_list = 0; + PyObject *module = 0; + PyObject *global_dict = 0; + PyObject *empty_dict = 0; + PyObject *list; + #if PY_MAJOR_VERSION < 3 + PyObject *py_import; + py_import = __Pyx_PyObject_GetAttrStr(__pyx_b, __pyx_n_s_import); + if (!py_import) + goto bad; + #endif + if (from_list) + list = from_list; + else { + empty_list = PyList_New(0); + if (!empty_list) + goto bad; + list = empty_list; + } + global_dict = PyModule_GetDict(__pyx_m); + if (!global_dict) + goto bad; + empty_dict = PyDict_New(); + if (!empty_dict) + goto bad; + { + #if PY_MAJOR_VERSION >= 3 + if (level == -1) { + if ((1) && (strchr(__Pyx_MODULE_NAME, '.'))) { + module = PyImport_ImportModuleLevelObject( + name, global_dict, empty_dict, list, 1); + if (!module) { + if (!PyErr_ExceptionMatches(PyExc_ImportError)) + goto bad; + PyErr_Clear(); + } + } + level = 0; + } + #endif + if (!module) { + #if PY_MAJOR_VERSION < 3 + PyObject *py_level = PyInt_FromLong(level); + if (!py_level) + goto bad; + module = PyObject_CallFunctionObjArgs(py_import, + name, global_dict, empty_dict, list, py_level, (PyObject *)NULL); + Py_DECREF(py_level); + #else + module = PyImport_ImportModuleLevelObject( + name, global_dict, empty_dict, list, level); + #endif + } + } +bad: + #if PY_MAJOR_VERSION < 3 + Py_XDECREF(py_import); + #endif + Py_XDECREF(empty_list); + Py_XDECREF(empty_dict); + return module; +} + +/* CLineInTraceback */ + #ifndef CYTHON_CLINE_IN_TRACEBACK +static int __Pyx_CLineForTraceback(CYTHON_NCP_UNUSED PyThreadState *tstate, int c_line) { + PyObject *use_cline; + PyObject *ptype, *pvalue, *ptraceback; +#if CYTHON_COMPILING_IN_CPYTHON + PyObject **cython_runtime_dict; +#endif + if (unlikely(!__pyx_cython_runtime)) { + return c_line; + } + __Pyx_ErrFetchInState(tstate, &ptype, &pvalue, &ptraceback); +#if CYTHON_COMPILING_IN_CPYTHON + cython_runtime_dict = _PyObject_GetDictPtr(__pyx_cython_runtime); + if (likely(cython_runtime_dict)) { + __PYX_PY_DICT_LOOKUP_IF_MODIFIED( + use_cline, *cython_runtime_dict, + __Pyx_PyDict_GetItemStr(*cython_runtime_dict, __pyx_n_s_cline_in_traceback)) + } else +#endif + { + PyObject *use_cline_obj = __Pyx_PyObject_GetAttrStr(__pyx_cython_runtime, __pyx_n_s_cline_in_traceback); + if (use_cline_obj) { + use_cline = PyObject_Not(use_cline_obj) ? Py_False : Py_True; + Py_DECREF(use_cline_obj); + } else { + PyErr_Clear(); + use_cline = NULL; + } + } + if (!use_cline) { + c_line = 0; + PyObject_SetAttr(__pyx_cython_runtime, __pyx_n_s_cline_in_traceback, Py_False); + } + else if (use_cline == Py_False || (use_cline != Py_True && PyObject_Not(use_cline) != 0)) { + c_line = 0; + } + __Pyx_ErrRestoreInState(tstate, ptype, pvalue, ptraceback); + return c_line; +} +#endif + +/* CodeObjectCache */ + static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line) { + int start = 0, mid = 0, end = count - 1; + if (end >= 0 && code_line > entries[end].code_line) { + return count; + } + while (start < end) { + mid = start + (end - start) / 2; + if (code_line < entries[mid].code_line) { + end = mid; + } else if (code_line > entries[mid].code_line) { + start = mid + 1; + } else { + return mid; + } + } + if (code_line <= entries[mid].code_line) { + return mid; + } else { + return mid + 1; + } +} +static PyCodeObject *__pyx_find_code_object(int code_line) { + PyCodeObject* code_object; + int pos; + if (unlikely(!code_line) || unlikely(!__pyx_code_cache.entries)) { + return NULL; + } + pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line); + if (unlikely(pos >= __pyx_code_cache.count) || unlikely(__pyx_code_cache.entries[pos].code_line != code_line)) { + return NULL; + } + code_object = __pyx_code_cache.entries[pos].code_object; + Py_INCREF(code_object); + return code_object; +} +static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object) { + int pos, i; + __Pyx_CodeObjectCacheEntry* entries = __pyx_code_cache.entries; + if (unlikely(!code_line)) { + return; + } + if (unlikely(!entries)) { + entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Malloc(64*sizeof(__Pyx_CodeObjectCacheEntry)); + if (likely(entries)) { + __pyx_code_cache.entries = entries; + __pyx_code_cache.max_count = 64; + __pyx_code_cache.count = 1; + entries[0].code_line = code_line; + entries[0].code_object = code_object; + Py_INCREF(code_object); + } + return; + } + pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line); + if ((pos < __pyx_code_cache.count) && unlikely(__pyx_code_cache.entries[pos].code_line == code_line)) { + PyCodeObject* tmp = entries[pos].code_object; + entries[pos].code_object = code_object; + Py_DECREF(tmp); + return; + } + if (__pyx_code_cache.count == __pyx_code_cache.max_count) { + int new_max = __pyx_code_cache.max_count + 64; + entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Realloc( + __pyx_code_cache.entries, ((size_t)new_max) * sizeof(__Pyx_CodeObjectCacheEntry)); + if (unlikely(!entries)) { + return; + } + __pyx_code_cache.entries = entries; + __pyx_code_cache.max_count = new_max; + } + for (i=__pyx_code_cache.count; i>pos; i--) { + entries[i] = entries[i-1]; + } + entries[pos].code_line = code_line; + entries[pos].code_object = code_object; + __pyx_code_cache.count++; + Py_INCREF(code_object); +} + +/* AddTraceback */ + #include "compile.h" +#include "frameobject.h" +#include "traceback.h" +static PyCodeObject* __Pyx_CreateCodeObjectForTraceback( + const char *funcname, int c_line, + int py_line, const char *filename) { + PyCodeObject *py_code = 0; + PyObject *py_srcfile = 0; + PyObject *py_funcname = 0; + #if PY_MAJOR_VERSION < 3 + py_srcfile = PyString_FromString(filename); + #else + py_srcfile = PyUnicode_FromString(filename); + #endif + if (!py_srcfile) goto bad; + if (c_line) { + #if PY_MAJOR_VERSION < 3 + py_funcname = PyString_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line); + #else + py_funcname = PyUnicode_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line); + #endif + } + else { + #if PY_MAJOR_VERSION < 3 + py_funcname = PyString_FromString(funcname); + #else + py_funcname = PyUnicode_FromString(funcname); + #endif + } + if (!py_funcname) goto bad; + py_code = __Pyx_PyCode_New( + 0, + 0, + 0, + 0, + 0, + __pyx_empty_bytes, /*PyObject *code,*/ + __pyx_empty_tuple, /*PyObject *consts,*/ + __pyx_empty_tuple, /*PyObject *names,*/ + __pyx_empty_tuple, /*PyObject *varnames,*/ + __pyx_empty_tuple, /*PyObject *freevars,*/ + __pyx_empty_tuple, /*PyObject *cellvars,*/ + py_srcfile, /*PyObject *filename,*/ + py_funcname, /*PyObject *name,*/ + py_line, + __pyx_empty_bytes /*PyObject *lnotab*/ + ); + Py_DECREF(py_srcfile); + Py_DECREF(py_funcname); + return py_code; +bad: + Py_XDECREF(py_srcfile); + Py_XDECREF(py_funcname); + return NULL; +} +static void __Pyx_AddTraceback(const char *funcname, int c_line, + int py_line, const char *filename) { + PyCodeObject *py_code = 0; + PyFrameObject *py_frame = 0; + PyThreadState *tstate = __Pyx_PyThreadState_Current; + if (c_line) { + c_line = __Pyx_CLineForTraceback(tstate, c_line); + } + py_code = __pyx_find_code_object(c_line ? -c_line : py_line); + if (!py_code) { + py_code = __Pyx_CreateCodeObjectForTraceback( + funcname, c_line, py_line, filename); + if (!py_code) goto bad; + __pyx_insert_code_object(c_line ? -c_line : py_line, py_code); + } + py_frame = PyFrame_New( + tstate, /*PyThreadState *tstate,*/ + py_code, /*PyCodeObject *code,*/ + __pyx_d, /*PyObject *globals,*/ + 0 /*PyObject *locals*/ + ); + if (!py_frame) goto bad; + __Pyx_PyFrame_SetLineNumber(py_frame, py_line); + PyTraceBack_Here(py_frame); +bad: + Py_XDECREF(py_code); + Py_XDECREF(py_frame); +} + +#if PY_MAJOR_VERSION < 3 +static int __Pyx_GetBuffer(PyObject *obj, Py_buffer *view, int flags) { + if (PyObject_CheckBuffer(obj)) return PyObject_GetBuffer(obj, view, flags); + PyErr_Format(PyExc_TypeError, "'%.200s' does not have the buffer interface", Py_TYPE(obj)->tp_name); + return -1; +} +static void __Pyx_ReleaseBuffer(Py_buffer *view) { + PyObject *obj = view->obj; + if (!obj) return; + if (PyObject_CheckBuffer(obj)) { + PyBuffer_Release(view); + return; + } + if ((0)) {} + view->obj = NULL; + Py_DECREF(obj); +} +#endif + + + /* Declarations */ + #if CYTHON_CCOMPLEX + #ifdef __cplusplus + static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) { + return ::std::complex< float >(x, y); + } + #else + static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) { + return x + y*(__pyx_t_float_complex)_Complex_I; + } + #endif +#else + static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) { + __pyx_t_float_complex z; + z.real = x; + z.imag = y; + return z; + } +#endif + +/* Arithmetic */ + #if CYTHON_CCOMPLEX +#else + static CYTHON_INLINE int __Pyx_c_eq_float(__pyx_t_float_complex a, __pyx_t_float_complex b) { + return (a.real == b.real) && (a.imag == b.imag); + } + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_sum_float(__pyx_t_float_complex a, __pyx_t_float_complex b) { + __pyx_t_float_complex z; + z.real = a.real + b.real; + z.imag = a.imag + b.imag; + return z; + } + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_diff_float(__pyx_t_float_complex a, __pyx_t_float_complex b) { + __pyx_t_float_complex z; + z.real = a.real - b.real; + z.imag = a.imag - b.imag; + return z; + } + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_prod_float(__pyx_t_float_complex a, __pyx_t_float_complex b) { + __pyx_t_float_complex z; + z.real = a.real * b.real - a.imag * b.imag; + z.imag = a.real * b.imag + a.imag * b.real; + return z; + } + #if 1 + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quot_float(__pyx_t_float_complex a, __pyx_t_float_complex b) { + if (b.imag == 0) { + return __pyx_t_float_complex_from_parts(a.real / b.real, a.imag / b.real); + } else if (fabsf(b.real) >= fabsf(b.imag)) { + if (b.real == 0 && b.imag == 0) { + return __pyx_t_float_complex_from_parts(a.real / b.real, a.imag / b.imag); + } else { + float r = b.imag / b.real; + float s = (float)(1.0) / (b.real + b.imag * r); + return __pyx_t_float_complex_from_parts( + (a.real + a.imag * r) * s, (a.imag - a.real * r) * s); + } + } else { + float r = b.real / b.imag; + float s = (float)(1.0) / (b.imag + b.real * r); + return __pyx_t_float_complex_from_parts( + (a.real * r + a.imag) * s, (a.imag * r - a.real) * s); + } + } + #else + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quot_float(__pyx_t_float_complex a, __pyx_t_float_complex b) { + if (b.imag == 0) { + return __pyx_t_float_complex_from_parts(a.real / b.real, a.imag / b.real); + } else { + float denom = b.real * b.real + b.imag * b.imag; + return __pyx_t_float_complex_from_parts( + (a.real * b.real + a.imag * b.imag) / denom, + (a.imag * b.real - a.real * b.imag) / denom); + } + } + #endif + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_neg_float(__pyx_t_float_complex a) { + __pyx_t_float_complex z; + z.real = -a.real; + z.imag = -a.imag; + return z; + } + static CYTHON_INLINE int __Pyx_c_is_zero_float(__pyx_t_float_complex a) { + return (a.real == 0) && (a.imag == 0); + } + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_conj_float(__pyx_t_float_complex a) { + __pyx_t_float_complex z; + z.real = a.real; + z.imag = -a.imag; + return z; + } + #if 1 + static CYTHON_INLINE float __Pyx_c_abs_float(__pyx_t_float_complex z) { + #if !defined(HAVE_HYPOT) || defined(_MSC_VER) + return sqrtf(z.real*z.real + z.imag*z.imag); + #else + return hypotf(z.real, z.imag); + #endif + } + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_pow_float(__pyx_t_float_complex a, __pyx_t_float_complex b) { + __pyx_t_float_complex z; + float r, lnr, theta, z_r, z_theta; + if (b.imag == 0 && b.real == (int)b.real) { + if (b.real < 0) { + float denom = a.real * a.real + a.imag * a.imag; + a.real = a.real / denom; + a.imag = -a.imag / denom; + b.real = -b.real; + } + switch ((int)b.real) { + case 0: + z.real = 1; + z.imag = 0; + return z; + case 1: + return a; + case 2: + return __Pyx_c_prod_float(a, a); + case 3: + z = __Pyx_c_prod_float(a, a); + return __Pyx_c_prod_float(z, a); + case 4: + z = __Pyx_c_prod_float(a, a); + return __Pyx_c_prod_float(z, z); + } + } + if (a.imag == 0) { + if (a.real == 0) { + return a; + } else if (b.imag == 0) { + z.real = powf(a.real, b.real); + z.imag = 0; + return z; + } else if (a.real > 0) { + r = a.real; + theta = 0; + } else { + r = -a.real; + theta = atan2f(0.0, -1.0); + } + } else { + r = __Pyx_c_abs_float(a); + theta = atan2f(a.imag, a.real); + } + lnr = logf(r); + z_r = expf(lnr * b.real - theta * b.imag); + z_theta = theta * b.real + lnr * b.imag; + z.real = z_r * cosf(z_theta); + z.imag = z_r * sinf(z_theta); + return z; + } + #endif +#endif + +/* Declarations */ + #if CYTHON_CCOMPLEX + #ifdef __cplusplus + static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) { + return ::std::complex< double >(x, y); + } + #else + static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) { + return x + y*(__pyx_t_double_complex)_Complex_I; + } + #endif +#else + static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) { + __pyx_t_double_complex z; + z.real = x; + z.imag = y; + return z; + } +#endif + +/* Arithmetic */ + #if CYTHON_CCOMPLEX +#else + static CYTHON_INLINE int __Pyx_c_eq_double(__pyx_t_double_complex a, __pyx_t_double_complex b) { + return (a.real == b.real) && (a.imag == b.imag); + } + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_sum_double(__pyx_t_double_complex a, __pyx_t_double_complex b) { + __pyx_t_double_complex z; + z.real = a.real + b.real; + z.imag = a.imag + b.imag; + return z; + } + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_diff_double(__pyx_t_double_complex a, __pyx_t_double_complex b) { + __pyx_t_double_complex z; + z.real = a.real - b.real; + z.imag = a.imag - b.imag; + return z; + } + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_prod_double(__pyx_t_double_complex a, __pyx_t_double_complex b) { + __pyx_t_double_complex z; + z.real = a.real * b.real - a.imag * b.imag; + z.imag = a.real * b.imag + a.imag * b.real; + return z; + } + #if 1 + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex a, __pyx_t_double_complex b) { + if (b.imag == 0) { + return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.real); + } else if (fabs(b.real) >= fabs(b.imag)) { + if (b.real == 0 && b.imag == 0) { + return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.imag); + } else { + double r = b.imag / b.real; + double s = (double)(1.0) / (b.real + b.imag * r); + return __pyx_t_double_complex_from_parts( + (a.real + a.imag * r) * s, (a.imag - a.real * r) * s); + } + } else { + double r = b.real / b.imag; + double s = (double)(1.0) / (b.imag + b.real * r); + return __pyx_t_double_complex_from_parts( + (a.real * r + a.imag) * s, (a.imag * r - a.real) * s); + } + } + #else + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex a, __pyx_t_double_complex b) { + if (b.imag == 0) { + return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.real); + } else { + double denom = b.real * b.real + b.imag * b.imag; + return __pyx_t_double_complex_from_parts( + (a.real * b.real + a.imag * b.imag) / denom, + (a.imag * b.real - a.real * b.imag) / denom); + } + } + #endif + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_neg_double(__pyx_t_double_complex a) { + __pyx_t_double_complex z; + z.real = -a.real; + z.imag = -a.imag; + return z; + } + static CYTHON_INLINE int __Pyx_c_is_zero_double(__pyx_t_double_complex a) { + return (a.real == 0) && (a.imag == 0); + } + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_conj_double(__pyx_t_double_complex a) { + __pyx_t_double_complex z; + z.real = a.real; + z.imag = -a.imag; + return z; + } + #if 1 + static CYTHON_INLINE double __Pyx_c_abs_double(__pyx_t_double_complex z) { + #if !defined(HAVE_HYPOT) || defined(_MSC_VER) + return sqrt(z.real*z.real + z.imag*z.imag); + #else + return hypot(z.real, z.imag); + #endif + } + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_pow_double(__pyx_t_double_complex a, __pyx_t_double_complex b) { + __pyx_t_double_complex z; + double r, lnr, theta, z_r, z_theta; + if (b.imag == 0 && b.real == (int)b.real) { + if (b.real < 0) { + double denom = a.real * a.real + a.imag * a.imag; + a.real = a.real / denom; + a.imag = -a.imag / denom; + b.real = -b.real; + } + switch ((int)b.real) { + case 0: + z.real = 1; + z.imag = 0; + return z; + case 1: + return a; + case 2: + return __Pyx_c_prod_double(a, a); + case 3: + z = __Pyx_c_prod_double(a, a); + return __Pyx_c_prod_double(z, a); + case 4: + z = __Pyx_c_prod_double(a, a); + return __Pyx_c_prod_double(z, z); + } + } + if (a.imag == 0) { + if (a.real == 0) { + return a; + } else if (b.imag == 0) { + z.real = pow(a.real, b.real); + z.imag = 0; + return z; + } else if (a.real > 0) { + r = a.real; + theta = 0; + } else { + r = -a.real; + theta = atan2(0.0, -1.0); + } + } else { + r = __Pyx_c_abs_double(a); + theta = atan2(a.imag, a.real); + } + lnr = log(r); + z_r = exp(lnr * b.real - theta * b.imag); + z_theta = theta * b.real + lnr * b.imag; + z.real = z_r * cos(z_theta); + z.imag = z_r * sin(z_theta); + return z; + } + #endif +#endif + +/* CIntToPy */ + static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value) { +#ifdef __Pyx_HAS_GCC_DIAGNOSTIC +#pragma GCC diagnostic push +#pragma GCC diagnostic ignored "-Wconversion" +#endif + const long neg_one = (long) -1, const_zero = (long) 0; +#ifdef __Pyx_HAS_GCC_DIAGNOSTIC +#pragma GCC diagnostic pop +#endif + const int is_unsigned = neg_one > const_zero; + if (is_unsigned) { + if (sizeof(long) < sizeof(long)) { + return PyInt_FromLong((long) value); + } else if (sizeof(long) <= sizeof(unsigned long)) { + return PyLong_FromUnsignedLong((unsigned long) value); +#ifdef HAVE_LONG_LONG + } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) { + return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value); +#endif + } + } else { + if (sizeof(long) <= sizeof(long)) { + return PyInt_FromLong((long) value); +#ifdef HAVE_LONG_LONG + } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) { + return PyLong_FromLongLong((PY_LONG_LONG) value); +#endif + } + } + { + int one = 1; int little = (int)*(unsigned char *)&one; + unsigned char *bytes = (unsigned char *)&value; + return _PyLong_FromByteArray(bytes, sizeof(long), + little, !is_unsigned); + } +} + +/* CIntFromPyVerify */ + #define __PYX_VERIFY_RETURN_INT(target_type, func_type, func_value)\ + __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 0) +#define __PYX_VERIFY_RETURN_INT_EXC(target_type, func_type, func_value)\ + __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 1) +#define __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, exc)\ + {\ + func_type value = func_value;\ + if (sizeof(target_type) < sizeof(func_type)) {\ + if (unlikely(value != (func_type) (target_type) value)) {\ + func_type zero = 0;\ + if (exc && unlikely(value == (func_type)-1 && PyErr_Occurred()))\ + return (target_type) -1;\ + if (is_unsigned && unlikely(value < zero))\ + goto raise_neg_overflow;\ + else\ + goto raise_overflow;\ + }\ + }\ + return (target_type) value;\ + } + +/* CIntFromPy */ + static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *x) { +#ifdef __Pyx_HAS_GCC_DIAGNOSTIC +#pragma GCC diagnostic push +#pragma GCC diagnostic ignored "-Wconversion" +#endif + const long neg_one = (long) -1, const_zero = (long) 0; +#ifdef __Pyx_HAS_GCC_DIAGNOSTIC +#pragma GCC diagnostic pop +#endif + const int is_unsigned = neg_one > const_zero; +#if PY_MAJOR_VERSION < 3 + if (likely(PyInt_Check(x))) { + if (sizeof(long) < sizeof(long)) { + __PYX_VERIFY_RETURN_INT(long, long, PyInt_AS_LONG(x)) + } else { + long val = PyInt_AS_LONG(x); + if (is_unsigned && unlikely(val < 0)) { + goto raise_neg_overflow; + } + return (long) val; + } + } else +#endif + if (likely(PyLong_Check(x))) { + if (is_unsigned) { +#if CYTHON_USE_PYLONG_INTERNALS + const digit* digits = ((PyLongObject*)x)->ob_digit; + switch (Py_SIZE(x)) { + case 0: return (long) 0; + case 1: __PYX_VERIFY_RETURN_INT(long, digit, digits[0]) + case 2: + if (8 * sizeof(long) > 1 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(long) >= 2 * PyLong_SHIFT) { + return (long) (((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])); + } + } + break; + case 3: + if (8 * sizeof(long) > 2 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(long) >= 3 * PyLong_SHIFT) { + return (long) (((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])); + } + } + break; + case 4: + if (8 * sizeof(long) > 3 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(long) >= 4 * PyLong_SHIFT) { + return (long) (((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])); + } + } + break; + } +#endif +#if CYTHON_COMPILING_IN_CPYTHON + if (unlikely(Py_SIZE(x) < 0)) { + goto raise_neg_overflow; + } +#else + { + int result = PyObject_RichCompareBool(x, Py_False, Py_LT); + if (unlikely(result < 0)) + return (long) -1; + if (unlikely(result == 1)) + goto raise_neg_overflow; + } +#endif + if (sizeof(long) <= sizeof(unsigned long)) { + __PYX_VERIFY_RETURN_INT_EXC(long, unsigned long, PyLong_AsUnsignedLong(x)) +#ifdef HAVE_LONG_LONG + } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) { + __PYX_VERIFY_RETURN_INT_EXC(long, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x)) +#endif + } + } else { +#if CYTHON_USE_PYLONG_INTERNALS + const digit* digits = ((PyLongObject*)x)->ob_digit; + switch (Py_SIZE(x)) { + case 0: return (long) 0; + case -1: __PYX_VERIFY_RETURN_INT(long, sdigit, (sdigit) (-(sdigit)digits[0])) + case 1: __PYX_VERIFY_RETURN_INT(long, digit, +digits[0]) + case -2: + if (8 * sizeof(long) - 1 > 1 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) { + return (long) (((long)-1)*(((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0]))); + } + } + break; + case 2: + if (8 * sizeof(long) > 1 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) { + return (long) ((((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0]))); + } + } + break; + case -3: + if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) { + return (long) (((long)-1)*(((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]))); + } + } + break; + case 3: + if (8 * sizeof(long) > 2 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) { + return (long) ((((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]))); + } + } + break; + case -4: + if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) { + return (long) (((long)-1)*(((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]))); + } + } + break; + case 4: + if (8 * sizeof(long) > 3 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) { + return (long) ((((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]))); + } + } + break; + } +#endif + if (sizeof(long) <= sizeof(long)) { + __PYX_VERIFY_RETURN_INT_EXC(long, long, PyLong_AsLong(x)) +#ifdef HAVE_LONG_LONG + } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) { + __PYX_VERIFY_RETURN_INT_EXC(long, PY_LONG_LONG, PyLong_AsLongLong(x)) +#endif + } + } + { +#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray) + PyErr_SetString(PyExc_RuntimeError, + "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers"); +#else + long val; + PyObject *v = __Pyx_PyNumber_IntOrLong(x); + #if PY_MAJOR_VERSION < 3 + if (likely(v) && !PyLong_Check(v)) { + PyObject *tmp = v; + v = PyNumber_Long(tmp); + Py_DECREF(tmp); + } + #endif + if (likely(v)) { + int one = 1; int is_little = (int)*(unsigned char *)&one; + unsigned char *bytes = (unsigned char *)&val; + int ret = _PyLong_AsByteArray((PyLongObject *)v, + bytes, sizeof(val), + is_little, !is_unsigned); + Py_DECREF(v); + if (likely(!ret)) + return val; + } +#endif + return (long) -1; + } + } else { + long val; + PyObject *tmp = __Pyx_PyNumber_IntOrLong(x); + if (!tmp) return (long) -1; + val = __Pyx_PyInt_As_long(tmp); + Py_DECREF(tmp); + return val; + } +raise_overflow: + PyErr_SetString(PyExc_OverflowError, + "value too large to convert to long"); + return (long) -1; +raise_neg_overflow: + PyErr_SetString(PyExc_OverflowError, + "can't convert negative value to long"); + return (long) -1; +} + +/* CIntFromPy */ + static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *x) { +#ifdef __Pyx_HAS_GCC_DIAGNOSTIC +#pragma GCC diagnostic push +#pragma GCC diagnostic ignored "-Wconversion" +#endif + const int neg_one = (int) -1, const_zero = (int) 0; +#ifdef __Pyx_HAS_GCC_DIAGNOSTIC +#pragma GCC diagnostic pop +#endif + const int is_unsigned = neg_one > const_zero; +#if PY_MAJOR_VERSION < 3 + if (likely(PyInt_Check(x))) { + if (sizeof(int) < sizeof(long)) { + __PYX_VERIFY_RETURN_INT(int, long, PyInt_AS_LONG(x)) + } else { + long val = PyInt_AS_LONG(x); + if (is_unsigned && unlikely(val < 0)) { + goto raise_neg_overflow; + } + return (int) val; + } + } else +#endif + if (likely(PyLong_Check(x))) { + if (is_unsigned) { +#if CYTHON_USE_PYLONG_INTERNALS + const digit* digits = ((PyLongObject*)x)->ob_digit; + switch (Py_SIZE(x)) { + case 0: return (int) 0; + case 1: __PYX_VERIFY_RETURN_INT(int, digit, digits[0]) + case 2: + if (8 * sizeof(int) > 1 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(int) >= 2 * PyLong_SHIFT) { + return (int) (((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])); + } + } + break; + case 3: + if (8 * sizeof(int) > 2 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(int) >= 3 * PyLong_SHIFT) { + return (int) (((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])); + } + } + break; + case 4: + if (8 * sizeof(int) > 3 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(int) >= 4 * PyLong_SHIFT) { + return (int) (((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])); + } + } + break; + } +#endif +#if CYTHON_COMPILING_IN_CPYTHON + if (unlikely(Py_SIZE(x) < 0)) { + goto raise_neg_overflow; + } +#else + { + int result = PyObject_RichCompareBool(x, Py_False, Py_LT); + if (unlikely(result < 0)) + return (int) -1; + if (unlikely(result == 1)) + goto raise_neg_overflow; + } +#endif + if (sizeof(int) <= sizeof(unsigned long)) { + __PYX_VERIFY_RETURN_INT_EXC(int, unsigned long, PyLong_AsUnsignedLong(x)) +#ifdef HAVE_LONG_LONG + } else if (sizeof(int) <= sizeof(unsigned PY_LONG_LONG)) { + __PYX_VERIFY_RETURN_INT_EXC(int, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x)) +#endif + } + } else { +#if CYTHON_USE_PYLONG_INTERNALS + const digit* digits = ((PyLongObject*)x)->ob_digit; + switch (Py_SIZE(x)) { + case 0: return (int) 0; + case -1: __PYX_VERIFY_RETURN_INT(int, sdigit, (sdigit) (-(sdigit)digits[0])) + case 1: __PYX_VERIFY_RETURN_INT(int, digit, +digits[0]) + case -2: + if (8 * sizeof(int) - 1 > 1 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) { + return (int) (((int)-1)*(((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0]))); + } + } + break; + case 2: + if (8 * sizeof(int) > 1 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) { + return (int) ((((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0]))); + } + } + break; + case -3: + if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) { + return (int) (((int)-1)*(((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]))); + } + } + break; + case 3: + if (8 * sizeof(int) > 2 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) { + return (int) ((((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]))); + } + } + break; + case -4: + if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(int) - 1 > 4 * PyLong_SHIFT) { + return (int) (((int)-1)*(((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]))); + } + } + break; + case 4: + if (8 * sizeof(int) > 3 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(int) - 1 > 4 * PyLong_SHIFT) { + return (int) ((((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]))); + } + } + break; + } +#endif + if (sizeof(int) <= sizeof(long)) { + __PYX_VERIFY_RETURN_INT_EXC(int, long, PyLong_AsLong(x)) +#ifdef HAVE_LONG_LONG + } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) { + __PYX_VERIFY_RETURN_INT_EXC(int, PY_LONG_LONG, PyLong_AsLongLong(x)) +#endif + } + } + { +#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray) + PyErr_SetString(PyExc_RuntimeError, + "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers"); +#else + int val; + PyObject *v = __Pyx_PyNumber_IntOrLong(x); + #if PY_MAJOR_VERSION < 3 + if (likely(v) && !PyLong_Check(v)) { + PyObject *tmp = v; + v = PyNumber_Long(tmp); + Py_DECREF(tmp); + } + #endif + if (likely(v)) { + int one = 1; int is_little = (int)*(unsigned char *)&one; + unsigned char *bytes = (unsigned char *)&val; + int ret = _PyLong_AsByteArray((PyLongObject *)v, + bytes, sizeof(val), + is_little, !is_unsigned); + Py_DECREF(v); + if (likely(!ret)) + return val; + } +#endif + return (int) -1; + } + } else { + int val; + PyObject *tmp = __Pyx_PyNumber_IntOrLong(x); + if (!tmp) return (int) -1; + val = __Pyx_PyInt_As_int(tmp); + Py_DECREF(tmp); + return val; + } +raise_overflow: + PyErr_SetString(PyExc_OverflowError, + "value too large to convert to int"); + return (int) -1; +raise_neg_overflow: + PyErr_SetString(PyExc_OverflowError, + "can't convert negative value to int"); + return (int) -1; +} + +/* FastTypeChecks */ + #if CYTHON_COMPILING_IN_CPYTHON +static int __Pyx_InBases(PyTypeObject *a, PyTypeObject *b) { + while (a) { + a = a->tp_base; + if (a == b) + return 1; + } + return b == &PyBaseObject_Type; +} +static CYTHON_INLINE int __Pyx_IsSubtype(PyTypeObject *a, PyTypeObject *b) { + PyObject *mro; + if (a == b) return 1; + mro = a->tp_mro; + if (likely(mro)) { + Py_ssize_t i, n; + n = PyTuple_GET_SIZE(mro); + for (i = 0; i < n; i++) { + if (PyTuple_GET_ITEM(mro, i) == (PyObject *)b) + return 1; + } + return 0; + } + return __Pyx_InBases(a, b); +} +#if PY_MAJOR_VERSION == 2 +static int __Pyx_inner_PyErr_GivenExceptionMatches2(PyObject *err, PyObject* exc_type1, PyObject* exc_type2) { + PyObject *exception, *value, *tb; + int res; + __Pyx_PyThreadState_declare + __Pyx_PyThreadState_assign + __Pyx_ErrFetch(&exception, &value, &tb); + res = exc_type1 ? PyObject_IsSubclass(err, exc_type1) : 0; + if (unlikely(res == -1)) { + PyErr_WriteUnraisable(err); + res = 0; + } + if (!res) { + res = PyObject_IsSubclass(err, exc_type2); + if (unlikely(res == -1)) { + PyErr_WriteUnraisable(err); + res = 0; + } + } + __Pyx_ErrRestore(exception, value, tb); + return res; +} +#else +static CYTHON_INLINE int __Pyx_inner_PyErr_GivenExceptionMatches2(PyObject *err, PyObject* exc_type1, PyObject *exc_type2) { + int res = exc_type1 ? __Pyx_IsSubtype((PyTypeObject*)err, (PyTypeObject*)exc_type1) : 0; + if (!res) { + res = __Pyx_IsSubtype((PyTypeObject*)err, (PyTypeObject*)exc_type2); + } + return res; +} +#endif +static int __Pyx_PyErr_GivenExceptionMatchesTuple(PyObject *exc_type, PyObject *tuple) { + Py_ssize_t i, n; + assert(PyExceptionClass_Check(exc_type)); + n = PyTuple_GET_SIZE(tuple); +#if PY_MAJOR_VERSION >= 3 + for (i=0; ip) { + #if PY_MAJOR_VERSION < 3 + if (t->is_unicode) { + *t->p = PyUnicode_DecodeUTF8(t->s, t->n - 1, NULL); + } else if (t->intern) { + *t->p = PyString_InternFromString(t->s); + } else { + *t->p = PyString_FromStringAndSize(t->s, t->n - 1); + } + #else + if (t->is_unicode | t->is_str) { + if (t->intern) { + *t->p = PyUnicode_InternFromString(t->s); + } else if (t->encoding) { + *t->p = PyUnicode_Decode(t->s, t->n - 1, t->encoding, NULL); + } else { + *t->p = PyUnicode_FromStringAndSize(t->s, t->n - 1); + } + } else { + *t->p = PyBytes_FromStringAndSize(t->s, t->n - 1); + } + #endif + if (!*t->p) + return -1; + if (PyObject_Hash(*t->p) == -1) + return -1; + ++t; + } + return 0; +} + +static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char* c_str) { + return __Pyx_PyUnicode_FromStringAndSize(c_str, (Py_ssize_t)strlen(c_str)); +} +static CYTHON_INLINE const char* __Pyx_PyObject_AsString(PyObject* o) { + Py_ssize_t ignore; + return __Pyx_PyObject_AsStringAndSize(o, &ignore); +} +#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT +#if !CYTHON_PEP393_ENABLED +static const char* __Pyx_PyUnicode_AsStringAndSize(PyObject* o, Py_ssize_t *length) { + char* defenc_c; + PyObject* defenc = _PyUnicode_AsDefaultEncodedString(o, NULL); + if (!defenc) return NULL; + defenc_c = PyBytes_AS_STRING(defenc); +#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII + { + char* end = defenc_c + PyBytes_GET_SIZE(defenc); + char* c; + for (c = defenc_c; c < end; c++) { + if ((unsigned char) (*c) >= 128) { + PyUnicode_AsASCIIString(o); + return NULL; + } + } + } +#endif + *length = PyBytes_GET_SIZE(defenc); + return defenc_c; +} +#else +static CYTHON_INLINE const char* __Pyx_PyUnicode_AsStringAndSize(PyObject* o, Py_ssize_t *length) { + if (unlikely(__Pyx_PyUnicode_READY(o) == -1)) return NULL; +#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII + if (likely(PyUnicode_IS_ASCII(o))) { + *length = PyUnicode_GET_LENGTH(o); + return PyUnicode_AsUTF8(o); + } else { + PyUnicode_AsASCIIString(o); + return NULL; + } +#else + return PyUnicode_AsUTF8AndSize(o, length); +#endif +} +#endif +#endif +static CYTHON_INLINE const char* __Pyx_PyObject_AsStringAndSize(PyObject* o, Py_ssize_t *length) { +#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT + if ( +#if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII + __Pyx_sys_getdefaultencoding_not_ascii && +#endif + PyUnicode_Check(o)) { + return __Pyx_PyUnicode_AsStringAndSize(o, length); + } else +#endif +#if (!CYTHON_COMPILING_IN_PYPY) || (defined(PyByteArray_AS_STRING) && defined(PyByteArray_GET_SIZE)) + if (PyByteArray_Check(o)) { + *length = PyByteArray_GET_SIZE(o); + return PyByteArray_AS_STRING(o); + } else +#endif + { + char* result; + int r = PyBytes_AsStringAndSize(o, &result, length); + if (unlikely(r < 0)) { + return NULL; + } else { + return result; + } + } +} +static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject* x) { + int is_true = x == Py_True; + if (is_true | (x == Py_False) | (x == Py_None)) return is_true; + else return PyObject_IsTrue(x); +} +static CYTHON_INLINE int __Pyx_PyObject_IsTrueAndDecref(PyObject* x) { + int retval; + if (unlikely(!x)) return -1; + retval = __Pyx_PyObject_IsTrue(x); + Py_DECREF(x); + return retval; +} +static PyObject* __Pyx_PyNumber_IntOrLongWrongResultType(PyObject* result, const char* type_name) { +#if PY_MAJOR_VERSION >= 3 + if (PyLong_Check(result)) { + if (PyErr_WarnFormat(PyExc_DeprecationWarning, 1, + "__int__ returned non-int (type %.200s). " + "The ability to return an instance of a strict subclass of int " + "is deprecated, and may be removed in a future version of Python.", + Py_TYPE(result)->tp_name)) { + Py_DECREF(result); + return NULL; + } + return result; + } +#endif + PyErr_Format(PyExc_TypeError, + "__%.4s__ returned non-%.4s (type %.200s)", + type_name, type_name, Py_TYPE(result)->tp_name); + Py_DECREF(result); + return NULL; +} +static CYTHON_INLINE PyObject* __Pyx_PyNumber_IntOrLong(PyObject* x) { +#if CYTHON_USE_TYPE_SLOTS + PyNumberMethods *m; +#endif + const char *name = NULL; + PyObject *res = NULL; +#if PY_MAJOR_VERSION < 3 + if (likely(PyInt_Check(x) || PyLong_Check(x))) +#else + if (likely(PyLong_Check(x))) +#endif + return __Pyx_NewRef(x); +#if CYTHON_USE_TYPE_SLOTS + m = Py_TYPE(x)->tp_as_number; + #if PY_MAJOR_VERSION < 3 + if (m && m->nb_int) { + name = "int"; + res = m->nb_int(x); + } + else if (m && m->nb_long) { + name = "long"; + res = m->nb_long(x); + } + #else + if (likely(m && m->nb_int)) { + name = "int"; + res = m->nb_int(x); + } + #endif +#else + if (!PyBytes_CheckExact(x) && !PyUnicode_CheckExact(x)) { + res = PyNumber_Int(x); + } +#endif + if (likely(res)) { +#if PY_MAJOR_VERSION < 3 + if (unlikely(!PyInt_Check(res) && !PyLong_Check(res))) { +#else + if (unlikely(!PyLong_CheckExact(res))) { +#endif + return __Pyx_PyNumber_IntOrLongWrongResultType(res, name); + } + } + else if (!PyErr_Occurred()) { + PyErr_SetString(PyExc_TypeError, + "an integer is required"); + } + return res; +} +static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject* b) { + Py_ssize_t ival; + PyObject *x; +#if PY_MAJOR_VERSION < 3 + if (likely(PyInt_CheckExact(b))) { + if (sizeof(Py_ssize_t) >= sizeof(long)) + return PyInt_AS_LONG(b); + else + return PyInt_AsSsize_t(b); + } +#endif + if (likely(PyLong_CheckExact(b))) { + #if CYTHON_USE_PYLONG_INTERNALS + const digit* digits = ((PyLongObject*)b)->ob_digit; + const Py_ssize_t size = Py_SIZE(b); + if (likely(__Pyx_sst_abs(size) <= 1)) { + ival = likely(size) ? digits[0] : 0; + if (size == -1) ival = -ival; + return ival; + } else { + switch (size) { + case 2: + if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) { + return (Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); + } + break; + case -2: + if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) { + return -(Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); + } + break; + case 3: + if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) { + return (Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); + } + break; + case -3: + if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) { + return -(Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); + } + break; + case 4: + if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) { + return (Py_ssize_t) (((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); + } + break; + case -4: + if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) { + return -(Py_ssize_t) (((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); + } + break; + } + } + #endif + return PyLong_AsSsize_t(b); + } + x = PyNumber_Index(b); + if (!x) return -1; + ival = PyInt_AsSsize_t(x); + Py_DECREF(x); + return ival; +} +static CYTHON_INLINE PyObject * __Pyx_PyBool_FromLong(long b) { + return b ? __Pyx_NewRef(Py_True) : __Pyx_NewRef(Py_False); +} +static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t ival) { + return PyInt_FromSize_t(ival); +} + + +#endif /* Py_PYTHON_H */ diff --git a/skfda/misc/metrics/sdtw_fast.pyx b/skfda/misc/metrics/sdtw_fast.pyx new file mode 100644 index 000000000..db670fb6f --- /dev/null +++ b/skfda/misc/metrics/sdtw_fast.pyx @@ -0,0 +1,88 @@ +""" +cython implementation of soft-DTW recursion. +Refs: + - Blondel, M., Mensch, A., & Vert, J.-P. (2021). + Differentiable Divergences Between Time Series. AISTATS. http://arxiv.org/abs/2010.08354 + - Mensch, A., Blondel, M. (2018). + Differentiable Dynamic Programming for Structured Prediction and Attention. ICML. https://proceedings.mlr.press/v80/mensch18a.html + +@author: Clément Lejeune +""" +cimport numpy as np +import numpy as np +from cython cimport boundscheck, wraparound, cdivision +from libc.math cimport exp, log +from libc.float cimport DBL_MAX + +DTYPE = np.float64 +ctypedef np.float64_t DTYPE_t + +@cdivision(True) +@boundscheck(False) +@wraparound(False) +cdef inline DTYPE_t _soft_min_argmin( + DTYPE_t x, DTYPE_t y, DTYPE_t z) nogil: + + cdef DTYPE_t min_xyz = min(x, min(y, z)) + # cdef double e_x + # cdef double e_y + # cdef double e_z + cdef DTYPE_t nn + # cdef DTYPE_t soft_min + + # e_x = exp(min_xyz - x) + # e_y = exp(min_xyz - y) + # e_z = exp(min_xyz - z) + # nn = e_x + e_y + e_z # normalizing constant + + nn = exp(min_xyz - x) + nn += exp(min_xyz - y) + nn += exp(min_xyz - z) + # soft_min = min_xyz - log(nn) # smoothed_min operator value + + return min_xyz - log(nn)# soft_min#, e_x/nn, e_y/nn, e_z/nn + +@cdivision(True) +@boundscheck(False) +@wraparound(False) +def _sdtw_C_cy( + np.ndarray[DTYPE_t, ndim=2] C, + DTYPE_t gamma): + + dtype = DTYPE + + cdef Py_ssize_t i, j + cdef Py_ssize_t len_X = C.shape[0] + cdef Py_ssize_t len_Y = C.shape[0] + + cdef np.ndarray[DTYPE_t, ndim=2] V = np.zeros((len_X + 1, len_Y + 1), dtype=dtype) + + # this is useless: + # cdef double[:, :, :] P = np.zeros((len_X + 2, len_Y + 2, 3), dtype=dtype) + + cdef DTYPE_t soft_min = 0.0 + + with nogil: + + # initialize firt row to a large value + for j in range(1, len_Y + 1): + V[0, j] = DBL_MAX + + # initilize first column to a large value + for i in range(1, len_X + 1): + V[i, 0] = DBL_MAX + + for i in range(1, len_X + 1): + for j in range(1, len_Y + 1): + # P_ij are useless (unless need for gradient computation) + ## soft_min, P[i, j, 0], P[i, j, 1], P[i, j, 2] = _soft_min_argmin( + ## V[i, j-1], + ## V[i-1, j-1], + ## V[i-1, j]) + soft_min = _soft_min_argmin(V[i, j-1], V[i-1, j-1], V[i-1, j]) + if gamma != 1.0: + V[i, j] = (C[i-1, j-1] / gamma) + soft_min + else: + V[i, j] = C[i-1, j-1] + soft_min + + return gamma * V[len_X, len_Y] diff --git a/skfda/misc/metrics/setup.py b/skfda/misc/metrics/setup.py new file mode 100644 index 000000000..12fa0931c --- /dev/null +++ b/skfda/misc/metrics/setup.py @@ -0,0 +1,13 @@ +from setuptools import setup +from setuptools import Extension +import numpy as np + +setup( + ext_modules=[ + Extension('sdtw_fast', + sources=['sdtw_fast.pyx'], + language='c', + include_dirs=[np.get_include()] + )], + zip_safe=False +) \ No newline at end of file From 44863e3823f200be9ac7ed1efe69056511200599 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Cl=C3=A9ment=20Lejeune?= <54889281+Clej@users.noreply.github.com> Date: Wed, 12 Jan 2022 19:52:20 +0100 Subject: [PATCH 02/21] add soft-dtw divergence paper references --- docs/refs.bib | 24 +++++++++++++++++++++++- 1 file changed, 23 insertions(+), 1 deletion(-) diff --git a/docs/refs.bib b/docs/refs.bib index 50e64219d..78fbc971a 100644 --- a/docs/refs.bib +++ b/docs/refs.bib @@ -365,7 +365,7 @@ @inbook{wasserman_2006_nonparametric_nw } @inbook{wasserman_2006_nonparametric_llr, - author = {Larry Wasserman}, + author = {Larry Wasserman}, title = {All of Nonparametric Statistics}, chapter = {Nonparametric Regression}, pages = {77}, @@ -373,4 +373,26 @@ @inbook{wasserman_2006_nonparametric_llr year = {2006}, isbn = {978-0-387-25145-5}, doi = {10.1007/0-387-30623-4} +} + +@pnproceedings{Cuturi_2017_sdtw, + title = {Soft-{DTW}: a Differentiable Loss Function for Time-Series}, + author = {Marco Cuturi and Mathieu Blondel}, + booktitle = {Proceedings of the 34th International Conference on Machine Learning}, + pages = {894 -- 903}, + year = {2017}, + volume = {70}, + series = {Proceedings of Machine Learning Research}, + publisher = {PMLR}, +} + +@inproceedings{Blondel_2021_sdtw_div, + author = {Blondel, Mathieu and Mensch, Arthur and Vert, Jean-Philippe}, + title = {Differentiable Divergences Between Time Series}, + booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics}, + pages = {3853 -- 3861}, + year = {2021}, + volume = {130}, + series = {Proceedings of Machine Learning Research}, + publisher = {PMLR}, } \ No newline at end of file From f6c6254f7b57cfe2e32d20ed6351012fb6fbe334 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Cl=C3=A9ment=20Lejeune?= <54889281+Clej@users.noreply.github.com> Date: Thu, 13 Jan 2022 15:18:25 +0100 Subject: [PATCH 03/21] code style correction --- skfda/misc/metrics/__init__.py | 2 +- skfda/misc/metrics/_sdtw_distances.py | 157 ++++++++++---------------- skfda/misc/metrics/setup.py | 13 ++- 3 files changed, 70 insertions(+), 102 deletions(-) diff --git a/skfda/misc/metrics/__init__.py b/skfda/misc/metrics/__init__.py index 07e19089f..fcae547c6 100644 --- a/skfda/misc/metrics/__init__.py +++ b/skfda/misc/metrics/__init__.py @@ -23,4 +23,4 @@ pairwise_metric_optimization, ) -from ._sdtw_distances import sdtwDivergence, sdtw_divergence \ No newline at end of file +from ._sdtw_distances import sdtwDivergence, sdtw_divergence diff --git a/skfda/misc/metrics/_sdtw_distances.py b/skfda/misc/metrics/_sdtw_distances.py index a705feab1..b995096a9 100644 --- a/skfda/misc/metrics/_sdtw_distances.py +++ b/skfda/misc/metrics/_sdtw_distances.py @@ -3,20 +3,21 @@ """ from __future__ import annotations -from typing import Optional, TypeVar, Union, Callable, List, Tuple -from numba.core.types.scalars import Boolean, Float +from typing import Optional, Union, Callable, List, Tuple +from numba.core.types.scalars import Boolean import numpy as np from typing_extensions import Final -from ...representation import FData, FDataGrid, FDataBasis +from ...representation import FData, FDataBasis from ...representation._typing import NDArrayFloat, GridPointsLike, ArrayLike -from ._utils import pairwise_metric_optimization +# from ._utils import pairwise_metric_optimization from skfda._utils._utils import _check_compatible_fdata from skfda.misc.metrics import sdtw_fast as sdtw_fast from skfda.misc._math import half_sq_euclidean + def _check_shape_postive_cost_mat(cost, expected_shape, shape_only=False): """check that matrix 'cost' is nonnegative and has expected shape""" n1, n2 = expected_shape @@ -25,7 +26,7 @@ def _check_shape_postive_cost_mat(cost, expected_shape, shape_only=False): raise ValueError( "Cost matrix must have shape" " ({}, {})".format(n1, n2) - ) + ) # non-negativity if not(shape_only): if not np.all(cost >= 0): @@ -33,11 +34,12 @@ def _check_shape_postive_cost_mat(cost, expected_shape, shape_only=False): "Cost matrix must contain non-negative entries" ) + def _check_indiscernable_sym(cost, X, Y): """check cost returns a symmetric matrix with zero diag""" # indiscernability: cost(x_t, x_t) = 0 for any t if ( - np.all(np.diag(cost(X, X)) != 0) + np.all(np.diag(cost(X, X)) != 0) or np.all(np.diag(cost(Y, Y)) != 0) ): raise ValueError( @@ -51,6 +53,7 @@ def _check_indiscernable_sym(cost, X, Y): "The cost function does not return a symmetric matrix" ) + def _check_input_evalpoints(eval_points): """check eval_points contains one or two one-dim array""" if isinstance(eval_points, Tuple) or isinstance(eval_points, List): @@ -62,8 +65,7 @@ def _check_input_evalpoints(eval_points): for idx, ep_i in enumerate(eval_points): if ( - not (isinstance(ep_i, NDArrayFloat) - and ep_i.ndim == 1) + not (isinstance(ep_i, NDArrayFloat) and ep_i.ndim == 1) ): raise ValueError( "{}-th element of the tuple must be a one-dimensional" @@ -81,6 +83,7 @@ def _check_input_evalpoints(eval_points): " or two one-dimensional numpy array(s)." ) + def _check_input_fdata(fdata1, fdata2): """check compatible and one sample per object""" _check_compatible_fdata(fdata1, fdata2) @@ -98,6 +101,7 @@ def _check_input_fdata(fdata1, fdata2): # "Both fdata1 and fdata2 must contain a single sample" # ) + def _sdtw_divergence( fdata1: FData, fdata2: FData, @@ -117,10 +121,9 @@ def _sdtw_divergence( # (sdtw_divergence can deal with different domain_range and grid_points) # check whether fdata1 and fdata2 are equivalent - # and have one sample _check_input_fdata(fdata1, fdata2) - if not isinstance(fdata1, FDataGrid): + if isinstance(fdata1, FDataBasis): # check eval_points # must be a tuple of one or two one-dim grid # maybe an existing skfda function does the job ? @@ -135,7 +138,6 @@ def _sdtw_divergence( fdata2 = fdata2.to_grid(eval_points[1]) n1, n2 = fdata1.grid_points[0].size, fdata2.grid_points[0].size - d = fdata1.dim_codomain if gamma <= 0: raise ValueError( @@ -158,26 +160,25 @@ def _sdtw_divergence( # shape of cost_12, cost_11 and cost_22 expected_shapes = [(n1, n2), (n1, n1), (n2, n2)] for idx, c in enumerate(cost): - if ( - not (isinstance(c, NDArrayFloat) - and c.ndim == 2) - ): + if not (isinstance(c, NDArrayFloat) and c.ndim == 2): raise ValueError( - "The elements of cost must all be two-dimensional numpy arrays." - " The {}-th element does not satisfy the expected format".format(idx) + "The elements of cost must all be " + "two-dimensional numpy arrays. " + "The {}-th element does not satisfy the expected " + "format".format(idx) ) - if not c.shape == (n1, n2): + if not c.shape == (n1, n2): raise ValueError( "Cost matrix must have shape" " ({}, {})".format(n1, n2) - ) + ) _check_shape_postive_cost_mat( cost=c, expected_shape=expected_shapes[idx], shape_only=not(check_cost) - ) + ) cost_12, cost_11, cost_22 = cost[0], cost[1], cost[2] @@ -192,24 +193,24 @@ def _sdtw_divergence( cost_12, expected_shape=(n1, n2), shape_only=not(check_cost) - ) - + ) + if check_cost: # check indiscernability and symmetry _check_indiscernable_sym( cost, fdata1.data_matrix[0, :, :], fdata2.data_matrix[0, :, :] - ) + ) cost_11 = cost( fdata1.data_matrix[0, :, :], fdata1.data_matrix[0, :, :] - ) + ) cost_22 = cost( fdata2.data_matrix[0, :, :], fdata2.data_matrix[0, :, :] - ) + ) else: raise ValueError( @@ -218,65 +219,28 @@ def _sdtw_divergence( " or a callable that returns a numpy array" ) - else: # default cost: 0.5 * squared Euclidean - - # => 0.5 * squared euclidean or global kernel alignment (depends on gamma !=0) - # half squared euclidean norm on each dimension - # sq_euclidean = DotProduct(sigma_0_bounds=(10**-10, 10**10)) - - # sq_euclidean(X, Y) = diag(np.dot(X, X.T)) + diag(np.dot(Y, Y.T)) - 2*np.dot(X, Y.T) - ## X @ X.T - # cost_11 = sq_euclidean( - # fdata1.data_matrix[0, :, :], - # fdata1.data_matrix[0, :, :] - # ) - # fdata1_vecnorms = 0.5 * np.diag(cost_11) - # cost_11 *= -1 - # cost_11 += fdata1_vecnorms[:, np.newaxis] - # cost_11 += fdata1_vecnorms - - # sq_euclidean(X, Y) = diag(np.dot(X, X.T)) + diag(np.dot(Y, Y.T)) - 2*np.dot(X, Y.T) - ## X @ X.T - cost_11 = half_sq_euclidean(fdata1.data_matrix[0, :, :]) + else: # default cost: 0.5 * squared Euclidean - ## Y @ Y.T - # cost_22 = sq_euclidean( - # fdata2.data_matrix[0, :, :], - # fdata2.data_matrix[0, :, :] - # ) - # fdata2_vecnorms = 0.5 * np.diag(cost_22) - # cost_22 *= -1 - # cost_22 += fdata2_vecnorms[:, np.newaxis] - # cost_22 += fdata2_vecnorms - - ## Y @ Y.T + # 0.5 * squared euclidean + # or global kernel alignment (depends on gamma !=0) + # 0.5 * diag(X@X.T) + 0.5 * diag(Y@Y.T) - X@Y.T + # <=> sq_euclidean = DotProduct(sigma_0_bounds=(10**-10, 10**10)) + # <=> diag(np.dot(X, X.T)) + diag(np.dot(Y, Y.T)) - 2*np.dot(X, Y.T) + cost_11 = half_sq_euclidean(fdata1.data_matrix[0, :, :]) cost_22 = half_sq_euclidean(fdata2.data_matrix[0, :, :]) - - # fdata1_vecnorms = 0.5 * sq_euclidean.diag(fdata1.data_matrix[0, :, :]) - # fdata2_vecnorms = 0.5 * sq_euclidean.diag(fdata2.data_matrix[0, :, :]) - - ## X @ Y.T * -1 - # cost_12 = -1 * sq_euclidean( - # fdata1.data_matrix[0, :, :], - # fdata2.data_matrix[0, :, :] - # ) - # cost_12 += fdata1_vecnorms[:, np.newaxis] - # cost_12 += fdata2_vecnorms - - ## X @ Y.T * -1 cost_12 = half_sq_euclidean( fdata1.data_matrix[0, :, :], fdata2.data_matrix[0, :, :] ) # for nonnegativity, symmetry, unicity of div(X,Y)=0 at X=Y - # for other cost, generalize code with Covariance or SKLEARN.kernel return( - sdtw_fast._sdtw_C_cy(cost_12, gamma) - \ - 0.5 * sdtw_fast._sdtw_C_cy(cost_11, gamma) - \ - 0.5 * sdtw_fast._sdtw_C_cy(cost_22, gamma) + sdtw_fast._sdtw_C_cy(cost_12, gamma) + - 0.5 * sdtw_fast._sdtw_C_cy(cost_11, gamma) + - 0.5 * sdtw_fast._sdtw_C_cy(cost_22, gamma) ) + class sdtwDivergence(): r""" Compute the soft Dynamic-Time-Warping (DTW) divergence between @@ -296,41 +260,43 @@ class sdtwDivergence(): - \frac{1}{2} \text{SDTW}_{\gamma}(x, x) - \frac{1}{2} \text{SDTW}_{\gamma}(y, y) - with :math:`\gamma > 0, C \in \mathbf{R}^{n_x \times n_y}` is the cost matrix - and :math:`\mathcal{A}_{n_x, n_y} \subset \{0, 1\}^{n_x \times n_y}` is an - alignment matrix. If the cost is the half squared Euclidean distance, + with :math:`\gamma > 0, C \in \mathbf{R}^{n_x \times n_y}` is the cost + matrix and + :math:`\mathcal{A}_{n_x, n_y} \subset \{0, 1\}^{n_x \times n_y}` + is an alignment matrix. If the cost is the half squared Euclidean + distance, :math:`c_{ij} = \frac{1}{2} \lVert x({t_i}) - y({t_j}) \rVert^2_2`. This a smooth version where the min operator has been replaced by the soft-min one, whose smoothness is controlled by :math:`\gamma` (the higher the smoother). - + Dynamic-Time-Warping is a distance metric defined as the minimal cost to align two time series X and Y. Typically, the cost is chosen as the squared Euclidean distance. However the classical DTW is not uniquely minimized and not differentiable w.r.t one argument given the other. - Soft-DTW divergence is a differentiable version of DTW with unique minimizer, - meaning that :math:`sdtw_div(X,Y)=0` if and only if :math:`X=Y`. - It is symmetric and nonnegative but does not satisfy the triangle - inequality. See :footcite:`Blondel_2021_sdtw_div`. + Soft-DTW divergence is a differentiable version of DTW with unique + minimizer, meaning that :math:`sdtw_div(X,Y)=0` if and only if + :math:`X=Y`. It is symmetric and nonnegative but does not satisfy the + triangle inequality. See :footcite:`Blondel_2021_sdtw_div`. Args: fdata1: First FData object. fdata2: Second FData object. gamma: smoothing parameter, must be positive. - cost: Either a two-dimensional array or a callable. + cost: Either a two-dimensional numpy array or a callable. If it is an array, then it must have shape ``(n1, n2)`` - where ``n1`` is the grid size of fdata1 and equivalently for ``n2``. - If fdata1 and fdata2 are FDataBasis, then ``cost`` + where ``n1`` is the grid size of fdata1 and equivalently for + ``n2``. When fdata1 and fdata2 are FDataBasis, then ``cost`` must be shaped according to the grid size(s) of ``eval_points``. If it is a callable, then it must take two two-dimensional numpy - arrays (equivalent to the ``data_matirx`` attribute of an FDataGrid - object) as inputs and return a single value. - check_cost: Wheter to check the mathematical properties of ``cost`` - (function or matrix). - eval_points: Tuple of two one-dimensional arrays with points of + arrays (equivalent to the ``data_matirx`` attribute of an + FDataGrid object) as inputs and return a ``(n1, n2)`` numpy array. + check_cost: Wheter to check the mathematical properties of + ``cost`` (function or matrix). + eval_points: Tuple of two one-dimensional numpy arrays with points of evaluation if fdata1 and fdata2 are FDataBasis. - If the tuple contains a single array, it is used both to convert - fdata1 and fdata2 into FDataGrid objects. + If the tuple contains a single array, it is used to convert + both fdata1 and fdata2 into FDataGrid objects. Returns: soft Dynamic-Time-Warping divergence value. @@ -358,19 +324,20 @@ def __call__( ) -> NDArrayFloat: """Compute the soft-DTW divergence.""" return _sdtw_divergence( - fdata1, - fdata2, - gamma=self.gamma, + fdata1, + fdata2, + gamma=self.gamma, cost=self.cost, check_cost=check_cost, eval_points=eval_points - ) + ) def __repr__(self) -> str: return ( f"{type(self).__name__}()" ) + sdtw_divergence: Final = sdtwDivergence() # @pairwise_metric_optimization.register diff --git a/skfda/misc/metrics/setup.py b/skfda/misc/metrics/setup.py index 12fa0931c..c2895edc8 100644 --- a/skfda/misc/metrics/setup.py +++ b/skfda/misc/metrics/setup.py @@ -4,10 +4,11 @@ setup( ext_modules=[ - Extension('sdtw_fast', - sources=['sdtw_fast.pyx'], - language='c', - include_dirs=[np.get_include()] - )], + Extension( + 'sdtw_fast', + sources=['sdtw_fast.pyx'], + language='c', + include_dirs=[np.get_include()] + )], zip_safe=False -) \ No newline at end of file +) From 37b5b16aff1721cfd0c301192d717589d4814c0b Mon Sep 17 00:00:00 2001 From: Lejeune Date: Mon, 7 Feb 2022 12:33:56 +0100 Subject: [PATCH 04/21] conversion of sdtw in cython to python@numba --- skfda/misc/metrics/_sdtw_numba.py | 34 +++++++++++++++++++++++++++++++ 1 file changed, 34 insertions(+) create mode 100644 skfda/misc/metrics/_sdtw_numba.py diff --git a/skfda/misc/metrics/_sdtw_numba.py b/skfda/misc/metrics/_sdtw_numba.py new file mode 100644 index 000000000..9934faa04 --- /dev/null +++ b/skfda/misc/metrics/_sdtw_numba.py @@ -0,0 +1,34 @@ +import numpy as np +from numba import njit + + +@njit(cache=True, fastmath=True) +def _soft_min_argmin(x, y, z): + """soft-min of three real numbers""" + + min_xyz = np.minimum(x, np.minimum(y, z)) + nn = np.exp(min_xyz - x) + nn += np.exp(min_xyz - y) + nn += np.exp(min_xyz - z) + + return min_xyz - np.log(nn) + + +@njit(cache=True, fastmath=True) +def _sdtw(cost_mat, gamma=1.0): + """soft-dtw divergence with dynamic recursion""" + + len_x = cost_mat.shape[0] + len_y = cost_mat.shape[1] + + V = np.zeros(shape=(len_x + 1, len_y + 1)) + V[0, 1:] = np.inf + V[1:, 0] = np.inf + + for i in range(1, len_x + 1): + for j in range(1, len_y + 1): + + V[i, j] = (cost_mat[i - 1, j - 1] / gamma) \ + + _soft_min_argmin(V[i, j - 1], V[i - 1, j - 1], V[i - 1, j]) + + return gamma * V[len_x, len_y] From 10de3d659490e9a278545587f954dfa8e79d09fa Mon Sep 17 00:00:00 2001 From: Lejeune Date: Mon, 7 Feb 2022 12:38:39 +0100 Subject: [PATCH 05/21] sdtw cython version replaced by numba version --- skfda/misc/metrics/_sdtw_distances.py | 14 +- skfda/misc/metrics/sdtw_fast.c | 6487 ------------------------- skfda/misc/metrics/sdtw_fast.pyx | 88 - skfda/misc/metrics/setup.py | 14 - 4 files changed, 7 insertions(+), 6596 deletions(-) delete mode 100644 skfda/misc/metrics/sdtw_fast.c delete mode 100644 skfda/misc/metrics/sdtw_fast.pyx delete mode 100644 skfda/misc/metrics/setup.py diff --git a/skfda/misc/metrics/_sdtw_distances.py b/skfda/misc/metrics/_sdtw_distances.py index b995096a9..51e11f83c 100644 --- a/skfda/misc/metrics/_sdtw_distances.py +++ b/skfda/misc/metrics/_sdtw_distances.py @@ -14,7 +14,7 @@ # from ._utils import pairwise_metric_optimization from skfda._utils._utils import _check_compatible_fdata -from skfda.misc.metrics import sdtw_fast as sdtw_fast +from skfda.misc.metrics import _sdtw_numba from skfda.misc._math import half_sq_euclidean @@ -114,7 +114,7 @@ def _sdtw_divergence( # For developers and PR: # final format of fdata1 and fdata2 is required to be FDataGrid, - # sharing the same domain and codomain dimensions. + # sharing the same domain(1D) and codomain dimensions(1D...nD). # No need for _check_compatible and _cast_to_grid: # => would raise an error in the following situation: # if fdata1.domain_range[0] != fdata1.grid_points[0].domain_range[0] @@ -152,7 +152,7 @@ def _sdtw_divergence( if isinstance(cost, List): if not len(cost) == 3: raise ValueError( - "When the alignment cost matrices are pre-computed," + "If the alignment cost matrices are pre-computed," " then 'cost' must be a list of three two-dimensional" " numpy arrays" ) @@ -162,7 +162,7 @@ def _sdtw_divergence( for idx, c in enumerate(cost): if not (isinstance(c, NDArrayFloat) and c.ndim == 2): raise ValueError( - "The elements of cost must all be " + "The elements of 'cost' must all be " "two-dimensional numpy arrays. " "The {}-th element does not satisfy the expected " "format".format(idx) @@ -235,9 +235,9 @@ def _sdtw_divergence( # for nonnegativity, symmetry, unicity of div(X,Y)=0 at X=Y return( - sdtw_fast._sdtw_C_cy(cost_12, gamma) - - 0.5 * sdtw_fast._sdtw_C_cy(cost_11, gamma) - - 0.5 * sdtw_fast._sdtw_C_cy(cost_22, gamma) + _sdtw_numba._sdtw(cost_12, gamma) + - 0.5 * _sdtw_numba._sdtw(cost_11, gamma) + - 0.5 * _sdtw_numba._sdtw(cost_22, gamma) ) diff --git a/skfda/misc/metrics/sdtw_fast.c b/skfda/misc/metrics/sdtw_fast.c deleted file mode 100644 index e26e8b7b8..000000000 --- a/skfda/misc/metrics/sdtw_fast.c +++ /dev/null @@ -1,6487 +0,0 @@ -/* Generated by Cython 0.29.24 */ - -#ifndef PY_SSIZE_T_CLEAN -#define PY_SSIZE_T_CLEAN -#endif /* PY_SSIZE_T_CLEAN */ -#include "Python.h" -#ifndef Py_PYTHON_H - #error Python headers needed to compile C extensions, please install development version of Python. -#elif PY_VERSION_HEX < 0x02060000 || (0x03000000 <= PY_VERSION_HEX && PY_VERSION_HEX < 0x03030000) - 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-value : value) -#endif -static CYTHON_INLINE const char* __Pyx_PyObject_AsString(PyObject*); -static CYTHON_INLINE const char* __Pyx_PyObject_AsStringAndSize(PyObject*, Py_ssize_t* length); -#define __Pyx_PyByteArray_FromString(s) PyByteArray_FromStringAndSize((const char*)s, strlen((const char*)s)) -#define __Pyx_PyByteArray_FromStringAndSize(s, l) PyByteArray_FromStringAndSize((const char*)s, l) -#define __Pyx_PyBytes_FromString PyBytes_FromString -#define __Pyx_PyBytes_FromStringAndSize PyBytes_FromStringAndSize -static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char*); -#if PY_MAJOR_VERSION < 3 - #define __Pyx_PyStr_FromString __Pyx_PyBytes_FromString - #define __Pyx_PyStr_FromStringAndSize __Pyx_PyBytes_FromStringAndSize -#else - #define __Pyx_PyStr_FromString __Pyx_PyUnicode_FromString - #define __Pyx_PyStr_FromStringAndSize __Pyx_PyUnicode_FromStringAndSize -#endif -#define __Pyx_PyBytes_AsWritableString(s) ((char*) PyBytes_AS_STRING(s)) -#define __Pyx_PyBytes_AsWritableSString(s) ((signed char*) PyBytes_AS_STRING(s)) -#define __Pyx_PyBytes_AsWritableUString(s) ((unsigned char*) PyBytes_AS_STRING(s)) -#define __Pyx_PyBytes_AsString(s) ((const char*) PyBytes_AS_STRING(s)) -#define __Pyx_PyBytes_AsSString(s) ((const signed char*) PyBytes_AS_STRING(s)) -#define __Pyx_PyBytes_AsUString(s) ((const unsigned char*) PyBytes_AS_STRING(s)) -#define __Pyx_PyObject_AsWritableString(s) ((char*) __Pyx_PyObject_AsString(s)) -#define __Pyx_PyObject_AsWritableSString(s) ((signed char*) __Pyx_PyObject_AsString(s)) -#define __Pyx_PyObject_AsWritableUString(s) ((unsigned char*) __Pyx_PyObject_AsString(s)) -#define __Pyx_PyObject_AsSString(s) ((const signed char*) __Pyx_PyObject_AsString(s)) -#define __Pyx_PyObject_AsUString(s) ((const unsigned char*) __Pyx_PyObject_AsString(s)) -#define __Pyx_PyObject_FromCString(s) __Pyx_PyObject_FromString((const char*)s) -#define __Pyx_PyBytes_FromCString(s) __Pyx_PyBytes_FromString((const char*)s) -#define __Pyx_PyByteArray_FromCString(s) __Pyx_PyByteArray_FromString((const char*)s) -#define __Pyx_PyStr_FromCString(s) __Pyx_PyStr_FromString((const char*)s) -#define __Pyx_PyUnicode_FromCString(s) __Pyx_PyUnicode_FromString((const char*)s) -static CYTHON_INLINE size_t __Pyx_Py_UNICODE_strlen(const Py_UNICODE *u) { - const Py_UNICODE *u_end = u; - while (*u_end++) ; - return (size_t)(u_end - u - 1); -} -#define __Pyx_PyUnicode_FromUnicode(u) PyUnicode_FromUnicode(u, __Pyx_Py_UNICODE_strlen(u)) -#define __Pyx_PyUnicode_FromUnicodeAndLength PyUnicode_FromUnicode -#define __Pyx_PyUnicode_AsUnicode PyUnicode_AsUnicode -#define __Pyx_NewRef(obj) (Py_INCREF(obj), obj) -#define __Pyx_Owned_Py_None(b) __Pyx_NewRef(Py_None) -static CYTHON_INLINE PyObject * __Pyx_PyBool_FromLong(long b); -static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject*); -static CYTHON_INLINE int __Pyx_PyObject_IsTrueAndDecref(PyObject*); -static CYTHON_INLINE PyObject* __Pyx_PyNumber_IntOrLong(PyObject* x); -#define __Pyx_PySequence_Tuple(obj)\ - (likely(PyTuple_CheckExact(obj)) ? __Pyx_NewRef(obj) : PySequence_Tuple(obj)) -static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject*); -static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t); -#if CYTHON_ASSUME_SAFE_MACROS -#define __pyx_PyFloat_AsDouble(x) (PyFloat_CheckExact(x) ? PyFloat_AS_DOUBLE(x) : PyFloat_AsDouble(x)) -#else -#define __pyx_PyFloat_AsDouble(x) PyFloat_AsDouble(x) -#endif -#define __pyx_PyFloat_AsFloat(x) ((float) __pyx_PyFloat_AsDouble(x)) -#if PY_MAJOR_VERSION >= 3 -#define __Pyx_PyNumber_Int(x) (PyLong_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Long(x)) -#else -#define __Pyx_PyNumber_Int(x) (PyInt_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Int(x)) -#endif -#define __Pyx_PyNumber_Float(x) (PyFloat_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Float(x)) -#if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII -static int __Pyx_sys_getdefaultencoding_not_ascii; -static int __Pyx_init_sys_getdefaultencoding_params(void) { - PyObject* sys; - PyObject* default_encoding = NULL; - PyObject* ascii_chars_u = NULL; - PyObject* ascii_chars_b = NULL; - const char* default_encoding_c; - sys = PyImport_ImportModule("sys"); - if (!sys) goto bad; - default_encoding = PyObject_CallMethod(sys, (char*) "getdefaultencoding", NULL); - Py_DECREF(sys); - if (!default_encoding) goto bad; - default_encoding_c = PyBytes_AsString(default_encoding); - if (!default_encoding_c) goto bad; - if (strcmp(default_encoding_c, "ascii") == 0) { - __Pyx_sys_getdefaultencoding_not_ascii = 0; - } else { - char ascii_chars[128]; - int c; - for (c = 0; c < 128; c++) { - ascii_chars[c] = c; - } - __Pyx_sys_getdefaultencoding_not_ascii = 1; - ascii_chars_u = PyUnicode_DecodeASCII(ascii_chars, 128, NULL); - if (!ascii_chars_u) goto bad; - ascii_chars_b = PyUnicode_AsEncodedString(ascii_chars_u, default_encoding_c, NULL); - if (!ascii_chars_b || !PyBytes_Check(ascii_chars_b) || memcmp(ascii_chars, PyBytes_AS_STRING(ascii_chars_b), 128) != 0) { - PyErr_Format( - PyExc_ValueError, - "This module compiled with c_string_encoding=ascii, but default encoding '%.200s' is not a superset of ascii.", - default_encoding_c); - goto bad; - } - Py_DECREF(ascii_chars_u); - Py_DECREF(ascii_chars_b); - } - Py_DECREF(default_encoding); - return 0; -bad: - Py_XDECREF(default_encoding); - Py_XDECREF(ascii_chars_u); 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-#endif - -/* SaveResetException.proto */ -#if CYTHON_FAST_THREAD_STATE -#define __Pyx_ExceptionSave(type, value, tb) __Pyx__ExceptionSave(__pyx_tstate, type, value, tb) -static CYTHON_INLINE void __Pyx__ExceptionSave(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb); -#define __Pyx_ExceptionReset(type, value, tb) __Pyx__ExceptionReset(__pyx_tstate, type, value, tb) -static CYTHON_INLINE void __Pyx__ExceptionReset(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb); -#else -#define __Pyx_ExceptionSave(type, value, tb) PyErr_GetExcInfo(type, value, tb) -#define __Pyx_ExceptionReset(type, value, tb) PyErr_SetExcInfo(type, value, tb) -#endif - -/* PyErrExceptionMatches.proto */ -#if CYTHON_FAST_THREAD_STATE -#define __Pyx_PyErr_ExceptionMatches(err) __Pyx_PyErr_ExceptionMatchesInState(__pyx_tstate, err) -static CYTHON_INLINE int __Pyx_PyErr_ExceptionMatchesInState(PyThreadState* tstate, PyObject* err); -#else -#define __Pyx_PyErr_ExceptionMatches(err) PyErr_ExceptionMatches(err) -#endif - -/* GetException.proto */ -#if CYTHON_FAST_THREAD_STATE -#define __Pyx_GetException(type, value, tb) __Pyx__GetException(__pyx_tstate, type, value, tb) -static int __Pyx__GetException(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb); -#else -static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb); -#endif - -/* RaiseException.proto */ -static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause); - -/* TypeImport.proto */ -#ifndef __PYX_HAVE_RT_ImportType_proto -#define __PYX_HAVE_RT_ImportType_proto -enum __Pyx_ImportType_CheckSize { - __Pyx_ImportType_CheckSize_Error = 0, - __Pyx_ImportType_CheckSize_Warn = 1, - __Pyx_ImportType_CheckSize_Ignore = 2 -}; -static PyTypeObject *__Pyx_ImportType(PyObject* module, const char *module_name, const char *class_name, size_t size, enum __Pyx_ImportType_CheckSize check_size); -#endif - -/* Import.proto */ -static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level); - -/* CLineInTraceback.proto */ -#ifdef CYTHON_CLINE_IN_TRACEBACK -#define __Pyx_CLineForTraceback(tstate, c_line) (((CYTHON_CLINE_IN_TRACEBACK)) ? c_line : 0) -#else -static int __Pyx_CLineForTraceback(PyThreadState *tstate, int c_line); -#endif - -/* CodeObjectCache.proto */ -typedef struct { - PyCodeObject* code_object; - int code_line; -} __Pyx_CodeObjectCacheEntry; -struct __Pyx_CodeObjectCache { - int count; - int max_count; - __Pyx_CodeObjectCacheEntry* entries; -}; -static struct __Pyx_CodeObjectCache __pyx_code_cache = {0,0,NULL}; -static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line); -static PyCodeObject *__pyx_find_code_object(int code_line); -static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object); - -/* AddTraceback.proto */ -static void __Pyx_AddTraceback(const char *funcname, int c_line, - int py_line, const char *filename); - -/* BufferStructDeclare.proto */ -typedef struct { - Py_ssize_t shape, strides, suboffsets; -} __Pyx_Buf_DimInfo; -typedef struct { - size_t refcount; - Py_buffer pybuffer; -} __Pyx_Buffer; -typedef struct { - __Pyx_Buffer *rcbuffer; - char *data; - __Pyx_Buf_DimInfo diminfo[8]; -} __Pyx_LocalBuf_ND; - -#if PY_MAJOR_VERSION < 3 - static int __Pyx_GetBuffer(PyObject *obj, Py_buffer *view, int flags); - static void __Pyx_ReleaseBuffer(Py_buffer *view); -#else - #define __Pyx_GetBuffer PyObject_GetBuffer - #define __Pyx_ReleaseBuffer PyBuffer_Release -#endif - - -/* RealImag.proto */ -#if CYTHON_CCOMPLEX - #ifdef __cplusplus - #define __Pyx_CREAL(z) ((z).real()) - #define __Pyx_CIMAG(z) ((z).imag()) - #else - #define __Pyx_CREAL(z) (__real__(z)) - #define __Pyx_CIMAG(z) (__imag__(z)) - #endif -#else - #define __Pyx_CREAL(z) ((z).real) - #define __Pyx_CIMAG(z) ((z).imag) -#endif -#if defined(__cplusplus) && CYTHON_CCOMPLEX\ - && (defined(_WIN32) || defined(__clang__) || (defined(__GNUC__) && (__GNUC__ >= 5 || __GNUC__ == 4 && __GNUC_MINOR__ >= 4 )) || __cplusplus >= 201103) - #define __Pyx_SET_CREAL(z,x) ((z).real(x)) - #define __Pyx_SET_CIMAG(z,y) ((z).imag(y)) -#else - #define __Pyx_SET_CREAL(z,x) __Pyx_CREAL(z) = (x) - #define __Pyx_SET_CIMAG(z,y) __Pyx_CIMAG(z) = (y) -#endif - -/* Arithmetic.proto */ -#if CYTHON_CCOMPLEX - #define __Pyx_c_eq_float(a, b) ((a)==(b)) - #define __Pyx_c_sum_float(a, b) ((a)+(b)) - #define __Pyx_c_diff_float(a, b) ((a)-(b)) - #define __Pyx_c_prod_float(a, b) ((a)*(b)) - #define __Pyx_c_quot_float(a, b) ((a)/(b)) - #define __Pyx_c_neg_float(a) (-(a)) - #ifdef __cplusplus - #define __Pyx_c_is_zero_float(z) ((z)==(float)0) - #define __Pyx_c_conj_float(z) (::std::conj(z)) - #if 1 - #define __Pyx_c_abs_float(z) (::std::abs(z)) - #define __Pyx_c_pow_float(a, b) (::std::pow(a, b)) - #endif - #else - #define __Pyx_c_is_zero_float(z) ((z)==0) - #define __Pyx_c_conj_float(z) (conjf(z)) - #if 1 - #define __Pyx_c_abs_float(z) (cabsf(z)) - #define __Pyx_c_pow_float(a, b) (cpowf(a, b)) - #endif - #endif -#else - static CYTHON_INLINE int __Pyx_c_eq_float(__pyx_t_float_complex, __pyx_t_float_complex); - static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_sum_float(__pyx_t_float_complex, __pyx_t_float_complex); - static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_diff_float(__pyx_t_float_complex, __pyx_t_float_complex); - static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_prod_float(__pyx_t_float_complex, __pyx_t_float_complex); - static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quot_float(__pyx_t_float_complex, __pyx_t_float_complex); - static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_neg_float(__pyx_t_float_complex); - static CYTHON_INLINE int __Pyx_c_is_zero_float(__pyx_t_float_complex); - static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_conj_float(__pyx_t_float_complex); - #if 1 - static CYTHON_INLINE float __Pyx_c_abs_float(__pyx_t_float_complex); - static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_pow_float(__pyx_t_float_complex, __pyx_t_float_complex); - #endif -#endif - -/* Arithmetic.proto */ -#if CYTHON_CCOMPLEX - #define __Pyx_c_eq_double(a, b) ((a)==(b)) - #define __Pyx_c_sum_double(a, b) ((a)+(b)) - #define __Pyx_c_diff_double(a, b) ((a)-(b)) - #define __Pyx_c_prod_double(a, b) ((a)*(b)) - #define __Pyx_c_quot_double(a, b) ((a)/(b)) - #define __Pyx_c_neg_double(a) (-(a)) - #ifdef __cplusplus - #define __Pyx_c_is_zero_double(z) ((z)==(double)0) - #define __Pyx_c_conj_double(z) (::std::conj(z)) - #if 1 - #define __Pyx_c_abs_double(z) (::std::abs(z)) - #define __Pyx_c_pow_double(a, b) (::std::pow(a, b)) - #endif - #else - #define __Pyx_c_is_zero_double(z) ((z)==0) - #define __Pyx_c_conj_double(z) (conj(z)) - #if 1 - #define __Pyx_c_abs_double(z) (cabs(z)) - #define __Pyx_c_pow_double(a, b) (cpow(a, b)) - #endif - #endif -#else - static CYTHON_INLINE int __Pyx_c_eq_double(__pyx_t_double_complex, __pyx_t_double_complex); - static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_sum_double(__pyx_t_double_complex, __pyx_t_double_complex); - static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_diff_double(__pyx_t_double_complex, __pyx_t_double_complex); - static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_prod_double(__pyx_t_double_complex, __pyx_t_double_complex); - static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex, __pyx_t_double_complex); - static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_neg_double(__pyx_t_double_complex); - static CYTHON_INLINE int __Pyx_c_is_zero_double(__pyx_t_double_complex); - static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_conj_double(__pyx_t_double_complex); - #if 1 - static CYTHON_INLINE double __Pyx_c_abs_double(__pyx_t_double_complex); - static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_pow_double(__pyx_t_double_complex, __pyx_t_double_complex); - #endif -#endif - -/* GCCDiagnostics.proto */ -#if defined(__GNUC__) && (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6)) -#define __Pyx_HAS_GCC_DIAGNOSTIC -#endif - -/* CIntToPy.proto */ -static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value); - -/* CIntFromPy.proto */ -static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *); - -/* CIntFromPy.proto */ -static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *); - -/* FastTypeChecks.proto */ -#if CYTHON_COMPILING_IN_CPYTHON -#define __Pyx_TypeCheck(obj, type) __Pyx_IsSubtype(Py_TYPE(obj), (PyTypeObject *)type) -static CYTHON_INLINE int __Pyx_IsSubtype(PyTypeObject *a, PyTypeObject *b); -static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches(PyObject *err, PyObject *type); -static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches2(PyObject *err, PyObject *type1, PyObject *type2); -#else -#define __Pyx_TypeCheck(obj, type) PyObject_TypeCheck(obj, (PyTypeObject *)type) -#define __Pyx_PyErr_GivenExceptionMatches(err, type) PyErr_GivenExceptionMatches(err, type) -#define __Pyx_PyErr_GivenExceptionMatches2(err, type1, type2) (PyErr_GivenExceptionMatches(err, type1) || PyErr_GivenExceptionMatches(err, type2)) -#endif -#define __Pyx_PyException_Check(obj) __Pyx_TypeCheck(obj, PyExc_Exception) - -/* CheckBinaryVersion.proto */ -static int __Pyx_check_binary_version(void); - -/* InitStrings.proto */ -static int __Pyx_InitStrings(__Pyx_StringTabEntry *t); - - -/* Module declarations from 'cpython.buffer' */ - -/* Module declarations from 'libc.string' */ - -/* Module declarations from 'libc.stdio' */ - -/* Module declarations from '__builtin__' */ - -/* Module declarations from 'cpython.type' */ -static PyTypeObject *__pyx_ptype_7cpython_4type_type = 0; - -/* Module declarations from 'cpython' */ - -/* Module declarations from 'cpython.object' */ - -/* Module declarations from 'cpython.ref' */ - -/* Module declarations from 'cpython.mem' */ - -/* Module declarations from 'numpy' */ - -/* Module declarations from 'numpy' */ -static PyTypeObject *__pyx_ptype_5numpy_dtype = 0; -static PyTypeObject *__pyx_ptype_5numpy_flatiter = 0; -static PyTypeObject *__pyx_ptype_5numpy_broadcast = 0; -static PyTypeObject *__pyx_ptype_5numpy_ndarray = 0; -static PyTypeObject *__pyx_ptype_5numpy_generic = 0; -static PyTypeObject *__pyx_ptype_5numpy_number = 0; -static PyTypeObject *__pyx_ptype_5numpy_integer = 0; -static PyTypeObject *__pyx_ptype_5numpy_signedinteger = 0; -static PyTypeObject *__pyx_ptype_5numpy_unsignedinteger = 0; -static PyTypeObject *__pyx_ptype_5numpy_inexact = 0; -static PyTypeObject *__pyx_ptype_5numpy_floating = 0; -static PyTypeObject *__pyx_ptype_5numpy_complexfloating = 0; -static PyTypeObject *__pyx_ptype_5numpy_flexible = 0; -static PyTypeObject *__pyx_ptype_5numpy_character = 0; -static PyTypeObject *__pyx_ptype_5numpy_ufunc = 0; - -/* Module declarations from 'libc.math' */ - -/* Module declarations from 'libc.float' */ - -/* Module declarations from 'sdtw_fast' */ -static CYTHON_INLINE __pyx_t_9sdtw_fast_DTYPE_t __pyx_f_9sdtw_fast__soft_min_argmin(__pyx_t_9sdtw_fast_DTYPE_t, __pyx_t_9sdtw_fast_DTYPE_t, __pyx_t_9sdtw_fast_DTYPE_t); /*proto*/ -static __Pyx_TypeInfo __Pyx_TypeInfo_nn___pyx_t_9sdtw_fast_DTYPE_t = { "DTYPE_t", NULL, sizeof(__pyx_t_9sdtw_fast_DTYPE_t), { 0 }, 0, 'R', 0, 0 }; -#define __Pyx_MODULE_NAME "sdtw_fast" -extern int __pyx_module_is_main_sdtw_fast; -int __pyx_module_is_main_sdtw_fast = 0; - -/* Implementation of 'sdtw_fast' */ -static PyObject *__pyx_builtin_range; -static PyObject *__pyx_builtin_ImportError; -static const char __pyx_k_C[] = "C"; -static const char __pyx_k_V[] = "V"; -static const char __pyx_k_i[] = "i"; -static const char __pyx_k_j[] = "j"; -static const char __pyx_k_np[] = "np"; -static const char __pyx_k_main[] = "__main__"; -static const char __pyx_k_name[] = "__name__"; -static const char __pyx_k_test[] = "__test__"; -static const char __pyx_k_DTYPE[] = "DTYPE"; -static const char __pyx_k_dtype[] = "dtype"; -static const char __pyx_k_gamma[] = "gamma"; -static const char __pyx_k_len_X[] = "len_X"; -static const char __pyx_k_len_Y[] = "len_Y"; -static const char __pyx_k_numpy[] = "numpy"; -static const char __pyx_k_range[] = "range"; -static const char __pyx_k_zeros[] = "zeros"; -static const char __pyx_k_import[] = "__import__"; -static const char __pyx_k_float64[] = "float64"; -static const char __pyx_k_soft_min[] = "soft_min"; -static const char __pyx_k_sdtw_C_cy[] = "_sdtw_C_cy"; -static const char __pyx_k_sdtw_fast[] = "sdtw_fast"; -static const char __pyx_k_ImportError[] = "ImportError"; -static const char __pyx_k_sdtw_fast_pyx[] = "sdtw_fast.pyx"; -static const char __pyx_k_cline_in_traceback[] = "cline_in_traceback"; -static const char __pyx_k_cython_implementation_of_soft_D[] = "\ncython implementation of soft-DTW recursion.\nRefs:\n - Blondel, M., Mensch, A., & Vert, J.-P. (2021).\n Differentiable Divergences Between Time Series. AISTATS. http://arxiv.org/abs/2010.08354\n - Mensch, A., Blondel, M. (2018).\n Differentiable Dynamic Programming for Structured Prediction and Attention. ICML. https://proceedings.mlr.press/v80/mensch18a.html\n\n@author: Cl\303\251ment Lejeune \n"; -static const char __pyx_k_numpy_core_multiarray_failed_to[] = "numpy.core.multiarray failed to import"; -static const char __pyx_k_numpy_core_umath_failed_to_impor[] = "numpy.core.umath failed to import"; -static PyObject *__pyx_n_s_C; -static PyObject *__pyx_n_s_DTYPE; -static PyObject *__pyx_n_s_ImportError; -static PyObject *__pyx_n_s_V; -static PyObject *__pyx_n_s_cline_in_traceback; -static PyObject *__pyx_n_s_dtype; -static PyObject *__pyx_n_s_float64; -static PyObject *__pyx_n_s_gamma; -static PyObject *__pyx_n_s_i; -static PyObject *__pyx_n_s_import; -static PyObject *__pyx_n_s_j; -static PyObject *__pyx_n_s_len_X; -static PyObject *__pyx_n_s_len_Y; -static PyObject *__pyx_n_s_main; -static PyObject *__pyx_n_s_name; -static PyObject *__pyx_n_s_np; -static PyObject *__pyx_n_s_numpy; -static PyObject *__pyx_kp_s_numpy_core_multiarray_failed_to; -static PyObject *__pyx_kp_s_numpy_core_umath_failed_to_impor; -static PyObject *__pyx_n_s_range; -static PyObject *__pyx_n_s_sdtw_C_cy; -static PyObject *__pyx_n_s_sdtw_fast; -static PyObject *__pyx_kp_s_sdtw_fast_pyx; -static PyObject *__pyx_n_s_soft_min; -static PyObject *__pyx_n_s_test; -static PyObject *__pyx_n_s_zeros; -static PyObject *__pyx_pf_9sdtw_fast__sdtw_C_cy(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_C, __pyx_t_9sdtw_fast_DTYPE_t __pyx_v_gamma); /* proto */ -static PyObject *__pyx_tuple_; -static PyObject *__pyx_tuple__2; -static PyObject *__pyx_tuple__3; -static PyObject *__pyx_codeobj__4; -/* Late includes */ - -/* "sdtw_fast.pyx":23 - * @boundscheck(False) - * @wraparound(False) - * cdef inline DTYPE_t _soft_min_argmin( # <<<<<<<<<<<<<< - * DTYPE_t x, DTYPE_t y, DTYPE_t z) nogil: - * - */ - -static CYTHON_INLINE __pyx_t_9sdtw_fast_DTYPE_t __pyx_f_9sdtw_fast__soft_min_argmin(__pyx_t_9sdtw_fast_DTYPE_t __pyx_v_x, __pyx_t_9sdtw_fast_DTYPE_t __pyx_v_y, __pyx_t_9sdtw_fast_DTYPE_t __pyx_v_z) { - __pyx_t_9sdtw_fast_DTYPE_t __pyx_v_min_xyz; 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This will probably the same as above, - but we don't have any guarantees. - */ -typedef struct { short x; char c; } __Pyx_pad_short; -typedef struct { int x; char c; } __Pyx_pad_int; -typedef struct { long x; char c; } __Pyx_pad_long; -typedef struct { float x; char c; } __Pyx_pad_float; -typedef struct { double x; char c; } __Pyx_pad_double; -typedef struct { long double x; char c; } __Pyx_pad_longdouble; -typedef struct { void *x; char c; } __Pyx_pad_void_p; -#ifdef HAVE_LONG_LONG -typedef struct { PY_LONG_LONG x; char c; } __Pyx_pad_longlong; -#endif -static size_t __Pyx_BufFmt_TypeCharToPadding(char ch, CYTHON_UNUSED int is_complex) { - switch (ch) { - case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1; - case 'h': case 'H': return sizeof(__Pyx_pad_short) - sizeof(short); - case 'i': case 'I': return sizeof(__Pyx_pad_int) - sizeof(int); - case 'l': case 'L': return sizeof(__Pyx_pad_long) - sizeof(long); -#ifdef HAVE_LONG_LONG - case 'q': case 'Q': return sizeof(__Pyx_pad_longlong) - sizeof(PY_LONG_LONG); -#endif - case 'f': return sizeof(__Pyx_pad_float) - sizeof(float); - case 'd': return sizeof(__Pyx_pad_double) - sizeof(double); - case 'g': return sizeof(__Pyx_pad_longdouble) - sizeof(long double); - case 'P': case 'O': return sizeof(__Pyx_pad_void_p) - sizeof(void*); - default: - __Pyx_BufFmt_RaiseUnexpectedChar(ch); - return 0; - } -} -static char __Pyx_BufFmt_TypeCharToGroup(char ch, int is_complex) { - switch (ch) { - case 'c': - return 'H'; - case 'b': case 'h': case 'i': - case 'l': case 'q': case 's': case 'p': - return 'I'; - case '?': case 'B': case 'H': case 'I': case 'L': case 'Q': - return 'U'; - case 'f': case 'd': case 'g': - return (is_complex ? 'C' : 'R'); - case 'O': - return 'O'; - case 'P': - return 'P'; - default: { - __Pyx_BufFmt_RaiseUnexpectedChar(ch); - return 0; - } - } -} -static void __Pyx_BufFmt_RaiseExpected(__Pyx_BufFmt_Context* ctx) { - if (ctx->head == NULL || ctx->head->field == &ctx->root) { - const char* expected; - const char* quote; - if (ctx->head == NULL) { - expected = "end"; - quote = ""; - } else { - expected = ctx->head->field->type->name; - quote = "'"; - } - PyErr_Format(PyExc_ValueError, - "Buffer dtype mismatch, expected %s%s%s but got %s", - quote, expected, quote, - __Pyx_BufFmt_DescribeTypeChar(ctx->enc_type, ctx->is_complex)); - } else { - __Pyx_StructField* field = ctx->head->field; - __Pyx_StructField* parent = (ctx->head - 1)->field; - PyErr_Format(PyExc_ValueError, - "Buffer dtype mismatch, expected '%s' but got %s in '%s.%s'", - field->type->name, __Pyx_BufFmt_DescribeTypeChar(ctx->enc_type, ctx->is_complex), - parent->type->name, field->name); - } -} -static int __Pyx_BufFmt_ProcessTypeChunk(__Pyx_BufFmt_Context* ctx) { - char group; - size_t size, offset, arraysize = 1; - if (ctx->enc_type == 0) return 0; - if (ctx->head->field->type->arraysize[0]) { - int i, ndim = 0; - if (ctx->enc_type == 's' || ctx->enc_type == 'p') { - ctx->is_valid_array = ctx->head->field->type->ndim == 1; - ndim = 1; - if (ctx->enc_count != ctx->head->field->type->arraysize[0]) { - PyErr_Format(PyExc_ValueError, - "Expected a dimension of size %zu, got %zu", - ctx->head->field->type->arraysize[0], ctx->enc_count); - return -1; - } - } - if (!ctx->is_valid_array) { - PyErr_Format(PyExc_ValueError, "Expected %d dimensions, got %d", - ctx->head->field->type->ndim, ndim); - return -1; - } - for (i = 0; i < ctx->head->field->type->ndim; i++) { - arraysize *= ctx->head->field->type->arraysize[i]; - } - ctx->is_valid_array = 0; - ctx->enc_count = 1; - } - group = __Pyx_BufFmt_TypeCharToGroup(ctx->enc_type, ctx->is_complex); - do { - __Pyx_StructField* field = ctx->head->field; - __Pyx_TypeInfo* type = field->type; - if (ctx->enc_packmode == '@' || ctx->enc_packmode == '^') { - size = __Pyx_BufFmt_TypeCharToNativeSize(ctx->enc_type, ctx->is_complex); - } else { - size = __Pyx_BufFmt_TypeCharToStandardSize(ctx->enc_type, ctx->is_complex); - } - if (ctx->enc_packmode == '@') { - size_t align_at = __Pyx_BufFmt_TypeCharToAlignment(ctx->enc_type, ctx->is_complex); - size_t align_mod_offset; - if (align_at == 0) return -1; - align_mod_offset = ctx->fmt_offset % align_at; - if (align_mod_offset > 0) ctx->fmt_offset += align_at - align_mod_offset; - if (ctx->struct_alignment == 0) - ctx->struct_alignment = __Pyx_BufFmt_TypeCharToPadding(ctx->enc_type, - ctx->is_complex); - } - if (type->size != size || type->typegroup != group) { - if (type->typegroup == 'C' && type->fields != NULL) { - size_t parent_offset = ctx->head->parent_offset + field->offset; - ++ctx->head; - ctx->head->field = type->fields; - ctx->head->parent_offset = parent_offset; - continue; - } - if ((type->typegroup == 'H' || group == 'H') && type->size == size) { - } else { - __Pyx_BufFmt_RaiseExpected(ctx); - return -1; - } - } - offset = ctx->head->parent_offset + field->offset; - if (ctx->fmt_offset != offset) { - PyErr_Format(PyExc_ValueError, - "Buffer dtype mismatch; next field is at offset %" CYTHON_FORMAT_SSIZE_T "d but %" CYTHON_FORMAT_SSIZE_T "d expected", - (Py_ssize_t)ctx->fmt_offset, (Py_ssize_t)offset); - return -1; - } - ctx->fmt_offset += size; - if (arraysize) - ctx->fmt_offset += (arraysize - 1) * size; - --ctx->enc_count; - while (1) { - if (field == &ctx->root) { - ctx->head = NULL; - if (ctx->enc_count != 0) { - __Pyx_BufFmt_RaiseExpected(ctx); - return -1; - } - break; - } - ctx->head->field = ++field; - if (field->type == NULL) { - --ctx->head; - field = ctx->head->field; - continue; - } else if (field->type->typegroup == 'S') { - size_t parent_offset = ctx->head->parent_offset + field->offset; - if (field->type->fields->type == NULL) continue; - field = field->type->fields; - ++ctx->head; - ctx->head->field = field; - ctx->head->parent_offset = parent_offset; - break; - } else { - break; - } - } - } while (ctx->enc_count); - ctx->enc_type = 0; - ctx->is_complex = 0; - return 0; -} -static PyObject * -__pyx_buffmt_parse_array(__Pyx_BufFmt_Context* ctx, const char** tsp) -{ - const char *ts = *tsp; - int i = 0, number, ndim; - ++ts; - if (ctx->new_count != 1) { - PyErr_SetString(PyExc_ValueError, - "Cannot handle repeated arrays in format string"); - return NULL; - } - if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL; - ndim = ctx->head->field->type->ndim; - while (*ts && *ts != ')') { - switch (*ts) { - case ' ': case '\f': case '\r': case '\n': case '\t': case '\v': continue; - default: break; - } - number = __Pyx_BufFmt_ExpectNumber(&ts); - if (number == -1) return NULL; - if (i < ndim && (size_t) number != ctx->head->field->type->arraysize[i]) - return PyErr_Format(PyExc_ValueError, - "Expected a dimension of size %zu, got %d", - ctx->head->field->type->arraysize[i], number); - if (*ts != ',' && *ts != ')') - return PyErr_Format(PyExc_ValueError, - "Expected a comma in format string, got '%c'", *ts); - if (*ts == ',') ts++; - i++; - } - if (i != ndim) - return PyErr_Format(PyExc_ValueError, "Expected %d dimension(s), got %d", - ctx->head->field->type->ndim, i); - if (!*ts) { - PyErr_SetString(PyExc_ValueError, - "Unexpected end of format string, expected ')'"); - return NULL; - } - ctx->is_valid_array = 1; - ctx->new_count = 1; - *tsp = ++ts; - return Py_None; -} -static const char* __Pyx_BufFmt_CheckString(__Pyx_BufFmt_Context* ctx, const char* ts) { - int got_Z = 0; - while (1) { - switch(*ts) { - case 0: - if (ctx->enc_type != 0 && ctx->head == NULL) { - __Pyx_BufFmt_RaiseExpected(ctx); - return NULL; - } - if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL; - if (ctx->head != NULL) { - __Pyx_BufFmt_RaiseExpected(ctx); - return NULL; - } - return ts; - case ' ': - case '\r': - case '\n': - ++ts; - break; - case '<': - if (!__Pyx_Is_Little_Endian()) { - PyErr_SetString(PyExc_ValueError, "Little-endian buffer not supported on big-endian compiler"); - return NULL; - } - ctx->new_packmode = '='; - ++ts; - break; - case '>': - case '!': - if (__Pyx_Is_Little_Endian()) { - PyErr_SetString(PyExc_ValueError, "Big-endian buffer not supported on little-endian compiler"); - return NULL; - } - ctx->new_packmode = '='; - ++ts; - break; - case '=': - case '@': - case '^': - ctx->new_packmode = *ts++; - break; - case 'T': - { - const char* ts_after_sub; - size_t i, struct_count = ctx->new_count; - size_t struct_alignment = ctx->struct_alignment; - ctx->new_count = 1; - ++ts; - if (*ts != '{') { - PyErr_SetString(PyExc_ValueError, "Buffer acquisition: Expected '{' after 'T'"); - return NULL; - } - if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL; - ctx->enc_type = 0; - ctx->enc_count = 0; - ctx->struct_alignment = 0; - ++ts; - ts_after_sub = ts; - for (i = 0; i != struct_count; ++i) { - ts_after_sub = __Pyx_BufFmt_CheckString(ctx, ts); - if (!ts_after_sub) return NULL; - } - ts = ts_after_sub; - if (struct_alignment) ctx->struct_alignment = struct_alignment; - } - break; - case '}': - { - size_t alignment = ctx->struct_alignment; - ++ts; - if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL; - ctx->enc_type = 0; - if (alignment && ctx->fmt_offset % alignment) { - ctx->fmt_offset += alignment - (ctx->fmt_offset % alignment); - } - } - return ts; - case 'x': - if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL; - ctx->fmt_offset += ctx->new_count; - ctx->new_count = 1; - ctx->enc_count = 0; - ctx->enc_type = 0; - ctx->enc_packmode = ctx->new_packmode; - ++ts; - break; - case 'Z': - got_Z = 1; - ++ts; - if (*ts != 'f' && *ts != 'd' && *ts != 'g') { - __Pyx_BufFmt_RaiseUnexpectedChar('Z'); - return NULL; - } - CYTHON_FALLTHROUGH; - case '?': case 'c': case 'b': case 'B': case 'h': case 'H': case 'i': case 'I': - case 'l': case 'L': case 'q': case 'Q': - case 'f': case 'd': case 'g': - case 'O': case 'p': - if ((ctx->enc_type == *ts) && (got_Z == ctx->is_complex) && - (ctx->enc_packmode == ctx->new_packmode) && (!ctx->is_valid_array)) { - ctx->enc_count += ctx->new_count; - ctx->new_count = 1; - got_Z = 0; - ++ts; - break; - } - CYTHON_FALLTHROUGH; - case 's': - if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL; - ctx->enc_count = ctx->new_count; - ctx->enc_packmode = ctx->new_packmode; - ctx->enc_type = *ts; - ctx->is_complex = got_Z; - ++ts; - ctx->new_count = 1; - got_Z = 0; - break; - case ':': - ++ts; - while(*ts != ':') ++ts; - ++ts; - break; - case '(': - if (!__pyx_buffmt_parse_array(ctx, &ts)) return NULL; - break; - default: - { - int number = __Pyx_BufFmt_ExpectNumber(&ts); - if (number == -1) return NULL; - ctx->new_count = (size_t)number; - } - } - } -} - -/* BufferGetAndValidate */ - static CYTHON_INLINE void __Pyx_SafeReleaseBuffer(Py_buffer* info) { - if (unlikely(info->buf == NULL)) return; - if (info->suboffsets == __Pyx_minusones) info->suboffsets = NULL; - __Pyx_ReleaseBuffer(info); -} -static void __Pyx_ZeroBuffer(Py_buffer* buf) { - buf->buf = NULL; - buf->obj = NULL; - buf->strides = __Pyx_zeros; - buf->shape = __Pyx_zeros; - buf->suboffsets = __Pyx_minusones; -} -static int __Pyx__GetBufferAndValidate( - Py_buffer* buf, PyObject* obj, __Pyx_TypeInfo* dtype, int flags, - int nd, int cast, __Pyx_BufFmt_StackElem* stack) -{ - buf->buf = NULL; - if (unlikely(__Pyx_GetBuffer(obj, buf, flags) == -1)) { - __Pyx_ZeroBuffer(buf); - return -1; - } - if (unlikely(buf->ndim != nd)) { - PyErr_Format(PyExc_ValueError, - "Buffer has wrong number of dimensions (expected %d, got %d)", - nd, buf->ndim); - goto fail; - } - if (!cast) { - __Pyx_BufFmt_Context ctx; - __Pyx_BufFmt_Init(&ctx, stack, dtype); - if (!__Pyx_BufFmt_CheckString(&ctx, buf->format)) goto fail; - } - if (unlikely((size_t)buf->itemsize != dtype->size)) { - PyErr_Format(PyExc_ValueError, - "Item size of buffer (%" CYTHON_FORMAT_SSIZE_T "d byte%s) does not match size of '%s' (%" CYTHON_FORMAT_SSIZE_T "d byte%s)", - buf->itemsize, (buf->itemsize > 1) ? "s" : "", - dtype->name, (Py_ssize_t)dtype->size, (dtype->size > 1) ? "s" : ""); - goto fail; - } - if (buf->suboffsets == NULL) buf->suboffsets = __Pyx_minusones; - return 0; -fail:; - __Pyx_SafeReleaseBuffer(buf); - return -1; -} - -/* PyDictVersioning */ - #if CYTHON_USE_DICT_VERSIONS && CYTHON_USE_TYPE_SLOTS -static CYTHON_INLINE PY_UINT64_T __Pyx_get_tp_dict_version(PyObject *obj) { - PyObject *dict = Py_TYPE(obj)->tp_dict; - return likely(dict) ? __PYX_GET_DICT_VERSION(dict) : 0; -} -static CYTHON_INLINE PY_UINT64_T __Pyx_get_object_dict_version(PyObject *obj) { - PyObject **dictptr = NULL; - Py_ssize_t offset = Py_TYPE(obj)->tp_dictoffset; - if (offset) { -#if CYTHON_COMPILING_IN_CPYTHON - dictptr = (likely(offset > 0)) ? (PyObject **) ((char *)obj + offset) : _PyObject_GetDictPtr(obj); -#else - dictptr = _PyObject_GetDictPtr(obj); -#endif - } - return (dictptr && *dictptr) ? __PYX_GET_DICT_VERSION(*dictptr) : 0; -} -static CYTHON_INLINE int __Pyx_object_dict_version_matches(PyObject* obj, PY_UINT64_T tp_dict_version, PY_UINT64_T obj_dict_version) { - PyObject *dict = Py_TYPE(obj)->tp_dict; - if (unlikely(!dict) || unlikely(tp_dict_version != __PYX_GET_DICT_VERSION(dict))) - return 0; - return obj_dict_version == __Pyx_get_object_dict_version(obj); -} -#endif - -/* GetModuleGlobalName */ - #if CYTHON_USE_DICT_VERSIONS -static PyObject *__Pyx__GetModuleGlobalName(PyObject *name, PY_UINT64_T *dict_version, PyObject **dict_cached_value) -#else -static CYTHON_INLINE PyObject *__Pyx__GetModuleGlobalName(PyObject *name) -#endif -{ - PyObject *result; -#if !CYTHON_AVOID_BORROWED_REFS -#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x030500A1 - result = _PyDict_GetItem_KnownHash(__pyx_d, name, ((PyASCIIObject *) name)->hash); - __PYX_UPDATE_DICT_CACHE(__pyx_d, result, *dict_cached_value, *dict_version) - if (likely(result)) { - return __Pyx_NewRef(result); - } else if (unlikely(PyErr_Occurred())) { - return NULL; - } -#else - result = PyDict_GetItem(__pyx_d, name); - __PYX_UPDATE_DICT_CACHE(__pyx_d, result, *dict_cached_value, *dict_version) - if (likely(result)) { - return __Pyx_NewRef(result); - } -#endif -#else - result = PyObject_GetItem(__pyx_d, name); - __PYX_UPDATE_DICT_CACHE(__pyx_d, result, *dict_cached_value, *dict_version) - if (likely(result)) { - return __Pyx_NewRef(result); - } - PyErr_Clear(); -#endif - return __Pyx_GetBuiltinName(name); -} - -/* PyObjectCall */ - #if CYTHON_COMPILING_IN_CPYTHON -static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw) { - PyObject *result; - ternaryfunc call = Py_TYPE(func)->tp_call; - if (unlikely(!call)) - return PyObject_Call(func, arg, kw); - if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object"))) - return NULL; - result = (*call)(func, arg, kw); - Py_LeaveRecursiveCall(); - if (unlikely(!result) && unlikely(!PyErr_Occurred())) { - PyErr_SetString( - PyExc_SystemError, - "NULL result without error in PyObject_Call"); - } - return result; -} -#endif - -/* ExtTypeTest */ - static CYTHON_INLINE int __Pyx_TypeTest(PyObject *obj, PyTypeObject *type) { - if (unlikely(!type)) { - PyErr_SetString(PyExc_SystemError, "Missing type object"); - return 0; - } - if (likely(__Pyx_TypeCheck(obj, type))) - return 1; - PyErr_Format(PyExc_TypeError, "Cannot convert %.200s to %.200s", - Py_TYPE(obj)->tp_name, type->tp_name); - return 0; -} - -/* PyErrFetchRestore */ - #if CYTHON_FAST_THREAD_STATE -static CYTHON_INLINE void __Pyx_ErrRestoreInState(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb) { - PyObject *tmp_type, *tmp_value, *tmp_tb; - tmp_type = tstate->curexc_type; - tmp_value = tstate->curexc_value; - tmp_tb = tstate->curexc_traceback; - tstate->curexc_type = type; - tstate->curexc_value = value; - tstate->curexc_traceback = tb; - Py_XDECREF(tmp_type); - Py_XDECREF(tmp_value); - Py_XDECREF(tmp_tb); -} -static CYTHON_INLINE void __Pyx_ErrFetchInState(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) { - *type = tstate->curexc_type; - *value = tstate->curexc_value; - *tb = tstate->curexc_traceback; - tstate->curexc_type = 0; - tstate->curexc_value = 0; - tstate->curexc_traceback = 0; -} -#endif - -/* GetTopmostException */ - #if CYTHON_USE_EXC_INFO_STACK -static _PyErr_StackItem * -__Pyx_PyErr_GetTopmostException(PyThreadState *tstate) -{ - _PyErr_StackItem *exc_info = tstate->exc_info; - while ((exc_info->exc_type == NULL || exc_info->exc_type == Py_None) && - exc_info->previous_item != NULL) - { - exc_info = exc_info->previous_item; - } - return exc_info; -} -#endif - -/* SaveResetException */ - #if CYTHON_FAST_THREAD_STATE -static CYTHON_INLINE void __Pyx__ExceptionSave(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) { - #if CYTHON_USE_EXC_INFO_STACK - _PyErr_StackItem *exc_info = __Pyx_PyErr_GetTopmostException(tstate); - *type = exc_info->exc_type; - *value = exc_info->exc_value; - *tb = exc_info->exc_traceback; - #else - *type = tstate->exc_type; - *value = tstate->exc_value; - *tb = tstate->exc_traceback; - #endif - Py_XINCREF(*type); - Py_XINCREF(*value); - Py_XINCREF(*tb); -} -static CYTHON_INLINE void __Pyx__ExceptionReset(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb) { - PyObject *tmp_type, *tmp_value, *tmp_tb; - #if CYTHON_USE_EXC_INFO_STACK - _PyErr_StackItem *exc_info = tstate->exc_info; - tmp_type = exc_info->exc_type; - tmp_value = exc_info->exc_value; - tmp_tb = exc_info->exc_traceback; - exc_info->exc_type = type; - exc_info->exc_value = value; - exc_info->exc_traceback = tb; - #else - tmp_type = tstate->exc_type; - tmp_value = tstate->exc_value; - tmp_tb = tstate->exc_traceback; - tstate->exc_type = type; - tstate->exc_value = value; - tstate->exc_traceback = tb; - #endif - Py_XDECREF(tmp_type); - Py_XDECREF(tmp_value); - Py_XDECREF(tmp_tb); -} -#endif - -/* PyErrExceptionMatches */ - #if CYTHON_FAST_THREAD_STATE -static int __Pyx_PyErr_ExceptionMatchesTuple(PyObject *exc_type, PyObject *tuple) { - Py_ssize_t i, n; - n = PyTuple_GET_SIZE(tuple); -#if PY_MAJOR_VERSION >= 3 - for (i=0; icurexc_type; - if (exc_type == err) return 1; - if (unlikely(!exc_type)) return 0; - if (unlikely(PyTuple_Check(err))) - return __Pyx_PyErr_ExceptionMatchesTuple(exc_type, err); - return __Pyx_PyErr_GivenExceptionMatches(exc_type, err); -} -#endif - -/* GetException */ - #if CYTHON_FAST_THREAD_STATE -static int __Pyx__GetException(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) -#else -static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb) -#endif -{ - PyObject *local_type, *local_value, *local_tb; -#if CYTHON_FAST_THREAD_STATE - PyObject *tmp_type, *tmp_value, *tmp_tb; - local_type = tstate->curexc_type; - local_value = tstate->curexc_value; - local_tb = tstate->curexc_traceback; - tstate->curexc_type = 0; - tstate->curexc_value = 0; - tstate->curexc_traceback = 0; -#else - PyErr_Fetch(&local_type, &local_value, &local_tb); -#endif - PyErr_NormalizeException(&local_type, &local_value, &local_tb); -#if CYTHON_FAST_THREAD_STATE - if (unlikely(tstate->curexc_type)) -#else - if (unlikely(PyErr_Occurred())) -#endif - goto bad; - #if PY_MAJOR_VERSION >= 3 - if (local_tb) { - if (unlikely(PyException_SetTraceback(local_value, local_tb) < 0)) - goto bad; - } - #endif - Py_XINCREF(local_tb); - Py_XINCREF(local_type); - Py_XINCREF(local_value); - *type = local_type; - *value = local_value; - *tb = local_tb; -#if CYTHON_FAST_THREAD_STATE - #if CYTHON_USE_EXC_INFO_STACK - { - _PyErr_StackItem *exc_info = tstate->exc_info; - tmp_type = exc_info->exc_type; - tmp_value = exc_info->exc_value; - tmp_tb = exc_info->exc_traceback; - exc_info->exc_type = local_type; - exc_info->exc_value = local_value; - exc_info->exc_traceback = local_tb; - } - #else - tmp_type = tstate->exc_type; - tmp_value = tstate->exc_value; - tmp_tb = tstate->exc_traceback; - tstate->exc_type = local_type; - tstate->exc_value = local_value; - tstate->exc_traceback = local_tb; - #endif - Py_XDECREF(tmp_type); - Py_XDECREF(tmp_value); - Py_XDECREF(tmp_tb); -#else - PyErr_SetExcInfo(local_type, local_value, local_tb); -#endif - return 0; -bad: - *type = 0; - *value = 0; - *tb = 0; - Py_XDECREF(local_type); - Py_XDECREF(local_value); - Py_XDECREF(local_tb); - return -1; -} - -/* RaiseException */ - #if PY_MAJOR_VERSION < 3 -static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, - CYTHON_UNUSED PyObject *cause) { - __Pyx_PyThreadState_declare - Py_XINCREF(type); - if (!value || value == Py_None) - value = NULL; - else - Py_INCREF(value); - if (!tb || tb == Py_None) - tb = NULL; - else { - Py_INCREF(tb); - if (!PyTraceBack_Check(tb)) { - PyErr_SetString(PyExc_TypeError, - "raise: arg 3 must be a traceback or None"); - goto raise_error; - } - } - if (PyType_Check(type)) { -#if CYTHON_COMPILING_IN_PYPY - if (!value) { - Py_INCREF(Py_None); - value = Py_None; - } -#endif - PyErr_NormalizeException(&type, &value, &tb); - } else { - if (value) { - PyErr_SetString(PyExc_TypeError, - "instance exception may not have a separate value"); - goto raise_error; - } - value = type; - type = (PyObject*) Py_TYPE(type); - Py_INCREF(type); - if (!PyType_IsSubtype((PyTypeObject *)type, (PyTypeObject *)PyExc_BaseException)) { - PyErr_SetString(PyExc_TypeError, - "raise: exception class must be a subclass of BaseException"); - goto raise_error; - } - } - __Pyx_PyThreadState_assign - __Pyx_ErrRestore(type, value, tb); - return; -raise_error: - Py_XDECREF(value); - Py_XDECREF(type); - Py_XDECREF(tb); - return; -} -#else -static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause) { - PyObject* owned_instance = NULL; - if (tb == Py_None) { - tb = 0; - } else if (tb && !PyTraceBack_Check(tb)) { - PyErr_SetString(PyExc_TypeError, - "raise: arg 3 must be a traceback or None"); - goto bad; - } - if (value == Py_None) - value = 0; - if (PyExceptionInstance_Check(type)) { - if (value) { - PyErr_SetString(PyExc_TypeError, - "instance exception may not have a separate value"); - goto bad; - } - value = type; - type = (PyObject*) Py_TYPE(value); - } else if (PyExceptionClass_Check(type)) { - PyObject *instance_class = NULL; - if (value && PyExceptionInstance_Check(value)) { - instance_class = (PyObject*) Py_TYPE(value); - if (instance_class != type) { - int is_subclass = PyObject_IsSubclass(instance_class, type); - if (!is_subclass) { - instance_class = NULL; - } else if (unlikely(is_subclass == -1)) { - goto bad; - } else { - type = instance_class; - } - } - } - if (!instance_class) { - PyObject *args; - if (!value) - args = PyTuple_New(0); - else if (PyTuple_Check(value)) { - Py_INCREF(value); - args = value; - } else - args = PyTuple_Pack(1, value); - if (!args) - goto bad; - owned_instance = PyObject_Call(type, args, NULL); - Py_DECREF(args); - if (!owned_instance) - goto bad; - value = owned_instance; - if (!PyExceptionInstance_Check(value)) { - PyErr_Format(PyExc_TypeError, - "calling %R should have returned an instance of " - "BaseException, not %R", - type, Py_TYPE(value)); - goto bad; - } - } - } else { - PyErr_SetString(PyExc_TypeError, - "raise: exception class must be a subclass of BaseException"); - goto bad; - } - if (cause) { - PyObject *fixed_cause; - if (cause == Py_None) { - fixed_cause = NULL; - } else if (PyExceptionClass_Check(cause)) { - fixed_cause = PyObject_CallObject(cause, NULL); - if (fixed_cause == NULL) - goto bad; - } else if (PyExceptionInstance_Check(cause)) { - fixed_cause = cause; - Py_INCREF(fixed_cause); - } else { - PyErr_SetString(PyExc_TypeError, - "exception causes must derive from " - "BaseException"); - goto bad; - } - PyException_SetCause(value, fixed_cause); - } - PyErr_SetObject(type, value); - if (tb) { -#if CYTHON_COMPILING_IN_PYPY - PyObject *tmp_type, *tmp_value, *tmp_tb; - PyErr_Fetch(&tmp_type, &tmp_value, &tmp_tb); - Py_INCREF(tb); - PyErr_Restore(tmp_type, tmp_value, tb); - Py_XDECREF(tmp_tb); -#else - PyThreadState *tstate = __Pyx_PyThreadState_Current; - PyObject* tmp_tb = tstate->curexc_traceback; - if (tb != tmp_tb) { - Py_INCREF(tb); - tstate->curexc_traceback = tb; - Py_XDECREF(tmp_tb); - } -#endif - } -bad: - Py_XDECREF(owned_instance); - return; -} -#endif - -/* TypeImport */ - #ifndef __PYX_HAVE_RT_ImportType -#define __PYX_HAVE_RT_ImportType -static PyTypeObject *__Pyx_ImportType(PyObject *module, const char *module_name, const char *class_name, - size_t size, enum __Pyx_ImportType_CheckSize check_size) -{ - PyObject *result = 0; - char warning[200]; - Py_ssize_t basicsize; -#ifdef Py_LIMITED_API - PyObject *py_basicsize; -#endif - result = PyObject_GetAttrString(module, class_name); - if (!result) - goto bad; - if (!PyType_Check(result)) { - PyErr_Format(PyExc_TypeError, - "%.200s.%.200s is not a type object", - module_name, class_name); - goto bad; - } -#ifndef Py_LIMITED_API - basicsize = ((PyTypeObject *)result)->tp_basicsize; -#else - py_basicsize = PyObject_GetAttrString(result, "__basicsize__"); - if (!py_basicsize) - goto bad; - basicsize = PyLong_AsSsize_t(py_basicsize); - Py_DECREF(py_basicsize); - py_basicsize = 0; - if (basicsize == (Py_ssize_t)-1 && PyErr_Occurred()) - goto bad; -#endif - if ((size_t)basicsize < size) { - PyErr_Format(PyExc_ValueError, - "%.200s.%.200s size changed, may indicate binary incompatibility. " - "Expected %zd from C header, got %zd from PyObject", - module_name, class_name, size, basicsize); - goto bad; - } - if (check_size == __Pyx_ImportType_CheckSize_Error && (size_t)basicsize != size) { - PyErr_Format(PyExc_ValueError, - "%.200s.%.200s size changed, may indicate binary incompatibility. " - "Expected %zd from C header, got %zd from PyObject", - module_name, class_name, size, basicsize); - goto bad; - } - else if (check_size == __Pyx_ImportType_CheckSize_Warn && (size_t)basicsize > size) { - PyOS_snprintf(warning, sizeof(warning), - "%s.%s size changed, may indicate binary incompatibility. " - "Expected %zd from C header, got %zd from PyObject", - module_name, class_name, size, basicsize); - if (PyErr_WarnEx(NULL, warning, 0) < 0) goto bad; - } - return (PyTypeObject *)result; -bad: - Py_XDECREF(result); - return NULL; -} -#endif - -/* Import */ - static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level) { - PyObject *empty_list = 0; - PyObject *module = 0; - PyObject *global_dict = 0; - PyObject *empty_dict = 0; - PyObject *list; - #if PY_MAJOR_VERSION < 3 - PyObject *py_import; - py_import = __Pyx_PyObject_GetAttrStr(__pyx_b, __pyx_n_s_import); - if (!py_import) - goto bad; - #endif - if (from_list) - list = from_list; - else { - empty_list = PyList_New(0); - if (!empty_list) - goto bad; - list = empty_list; - } - global_dict = PyModule_GetDict(__pyx_m); - if (!global_dict) - goto bad; - empty_dict = PyDict_New(); - if (!empty_dict) - goto bad; - { - #if PY_MAJOR_VERSION >= 3 - if (level == -1) { - if ((1) && (strchr(__Pyx_MODULE_NAME, '.'))) { - module = PyImport_ImportModuleLevelObject( - name, global_dict, empty_dict, list, 1); - if (!module) { - if (!PyErr_ExceptionMatches(PyExc_ImportError)) - goto bad; - PyErr_Clear(); - } - } - level = 0; - } - #endif - if (!module) { - #if PY_MAJOR_VERSION < 3 - PyObject *py_level = PyInt_FromLong(level); - if (!py_level) - goto bad; - module = PyObject_CallFunctionObjArgs(py_import, - name, global_dict, empty_dict, list, py_level, (PyObject *)NULL); - Py_DECREF(py_level); - #else - module = PyImport_ImportModuleLevelObject( - name, global_dict, empty_dict, list, level); - #endif - } - } -bad: - #if PY_MAJOR_VERSION < 3 - Py_XDECREF(py_import); - #endif - Py_XDECREF(empty_list); - Py_XDECREF(empty_dict); - return module; -} - -/* CLineInTraceback */ - #ifndef CYTHON_CLINE_IN_TRACEBACK -static int __Pyx_CLineForTraceback(CYTHON_NCP_UNUSED PyThreadState *tstate, int c_line) { - PyObject *use_cline; - PyObject *ptype, *pvalue, *ptraceback; -#if CYTHON_COMPILING_IN_CPYTHON - PyObject **cython_runtime_dict; -#endif - if (unlikely(!__pyx_cython_runtime)) { - return c_line; - } - __Pyx_ErrFetchInState(tstate, &ptype, &pvalue, &ptraceback); -#if CYTHON_COMPILING_IN_CPYTHON - cython_runtime_dict = _PyObject_GetDictPtr(__pyx_cython_runtime); - if (likely(cython_runtime_dict)) { - __PYX_PY_DICT_LOOKUP_IF_MODIFIED( - use_cline, *cython_runtime_dict, - __Pyx_PyDict_GetItemStr(*cython_runtime_dict, __pyx_n_s_cline_in_traceback)) - } else -#endif - { - PyObject *use_cline_obj = __Pyx_PyObject_GetAttrStr(__pyx_cython_runtime, __pyx_n_s_cline_in_traceback); - if (use_cline_obj) { - use_cline = PyObject_Not(use_cline_obj) ? Py_False : Py_True; - Py_DECREF(use_cline_obj); - } else { - PyErr_Clear(); - use_cline = NULL; - } - } - if (!use_cline) { - c_line = 0; - PyObject_SetAttr(__pyx_cython_runtime, __pyx_n_s_cline_in_traceback, Py_False); - } - else if (use_cline == Py_False || (use_cline != Py_True && PyObject_Not(use_cline) != 0)) { - c_line = 0; - } - __Pyx_ErrRestoreInState(tstate, ptype, pvalue, ptraceback); - return c_line; -} -#endif - -/* CodeObjectCache */ - static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line) { - int start = 0, mid = 0, end = count - 1; - if (end >= 0 && code_line > entries[end].code_line) { - return count; - } - while (start < end) { - mid = start + (end - start) / 2; - if (code_line < entries[mid].code_line) { - end = mid; - } else if (code_line > entries[mid].code_line) { - start = mid + 1; - } else { - return mid; - } - } - if (code_line <= entries[mid].code_line) { - return mid; - } else { - return mid + 1; - } -} -static PyCodeObject *__pyx_find_code_object(int code_line) { - PyCodeObject* code_object; - int pos; - if (unlikely(!code_line) || unlikely(!__pyx_code_cache.entries)) { - return NULL; - } - pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line); - if (unlikely(pos >= __pyx_code_cache.count) || unlikely(__pyx_code_cache.entries[pos].code_line != code_line)) { - return NULL; - } - code_object = __pyx_code_cache.entries[pos].code_object; - Py_INCREF(code_object); - return code_object; -} -static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object) { - int pos, i; - __Pyx_CodeObjectCacheEntry* entries = __pyx_code_cache.entries; - if (unlikely(!code_line)) { - return; - } - if (unlikely(!entries)) { - entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Malloc(64*sizeof(__Pyx_CodeObjectCacheEntry)); - if (likely(entries)) { - __pyx_code_cache.entries = entries; - __pyx_code_cache.max_count = 64; - __pyx_code_cache.count = 1; - entries[0].code_line = code_line; - entries[0].code_object = code_object; - Py_INCREF(code_object); - } - return; - } - pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line); - if ((pos < __pyx_code_cache.count) && unlikely(__pyx_code_cache.entries[pos].code_line == code_line)) { - PyCodeObject* tmp = entries[pos].code_object; - entries[pos].code_object = code_object; - Py_DECREF(tmp); - return; - } - if (__pyx_code_cache.count == __pyx_code_cache.max_count) { - int new_max = __pyx_code_cache.max_count + 64; - entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Realloc( - __pyx_code_cache.entries, ((size_t)new_max) * sizeof(__Pyx_CodeObjectCacheEntry)); - if (unlikely(!entries)) { - return; - } - __pyx_code_cache.entries = entries; - __pyx_code_cache.max_count = new_max; - } - for (i=__pyx_code_cache.count; i>pos; i--) { - entries[i] = entries[i-1]; - } - entries[pos].code_line = code_line; - entries[pos].code_object = code_object; - __pyx_code_cache.count++; - Py_INCREF(code_object); -} - -/* AddTraceback */ - #include "compile.h" -#include "frameobject.h" -#include "traceback.h" -static PyCodeObject* __Pyx_CreateCodeObjectForTraceback( - const char *funcname, int c_line, - int py_line, const char *filename) { - PyCodeObject *py_code = 0; - PyObject *py_srcfile = 0; - PyObject *py_funcname = 0; - #if PY_MAJOR_VERSION < 3 - py_srcfile = PyString_FromString(filename); - #else - py_srcfile = PyUnicode_FromString(filename); - #endif - if (!py_srcfile) goto bad; - if (c_line) { - #if PY_MAJOR_VERSION < 3 - py_funcname = PyString_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line); - #else - py_funcname = PyUnicode_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line); - #endif - } - else { - #if PY_MAJOR_VERSION < 3 - py_funcname = PyString_FromString(funcname); - #else - py_funcname = PyUnicode_FromString(funcname); - #endif - } - if (!py_funcname) goto bad; - py_code = __Pyx_PyCode_New( - 0, - 0, - 0, - 0, - 0, - __pyx_empty_bytes, /*PyObject *code,*/ - __pyx_empty_tuple, /*PyObject *consts,*/ - __pyx_empty_tuple, /*PyObject *names,*/ - __pyx_empty_tuple, /*PyObject *varnames,*/ - __pyx_empty_tuple, /*PyObject *freevars,*/ - __pyx_empty_tuple, /*PyObject *cellvars,*/ - py_srcfile, /*PyObject *filename,*/ - py_funcname, /*PyObject *name,*/ - py_line, - __pyx_empty_bytes /*PyObject *lnotab*/ - ); - Py_DECREF(py_srcfile); - Py_DECREF(py_funcname); - return py_code; -bad: - Py_XDECREF(py_srcfile); - Py_XDECREF(py_funcname); - return NULL; -} -static void __Pyx_AddTraceback(const char *funcname, int c_line, - int py_line, const char *filename) { - PyCodeObject *py_code = 0; - PyFrameObject *py_frame = 0; - PyThreadState *tstate = __Pyx_PyThreadState_Current; - if (c_line) { - c_line = __Pyx_CLineForTraceback(tstate, c_line); - } - py_code = __pyx_find_code_object(c_line ? -c_line : py_line); - if (!py_code) { - py_code = __Pyx_CreateCodeObjectForTraceback( - funcname, c_line, py_line, filename); - if (!py_code) goto bad; - __pyx_insert_code_object(c_line ? -c_line : py_line, py_code); - } - py_frame = PyFrame_New( - tstate, /*PyThreadState *tstate,*/ - py_code, /*PyCodeObject *code,*/ - __pyx_d, /*PyObject *globals,*/ - 0 /*PyObject *locals*/ - ); - if (!py_frame) goto bad; - __Pyx_PyFrame_SetLineNumber(py_frame, py_line); - PyTraceBack_Here(py_frame); -bad: - Py_XDECREF(py_code); - Py_XDECREF(py_frame); -} - -#if PY_MAJOR_VERSION < 3 -static int __Pyx_GetBuffer(PyObject *obj, Py_buffer *view, int flags) { - if (PyObject_CheckBuffer(obj)) return PyObject_GetBuffer(obj, view, flags); - PyErr_Format(PyExc_TypeError, "'%.200s' does not have the buffer interface", Py_TYPE(obj)->tp_name); - return -1; -} -static void __Pyx_ReleaseBuffer(Py_buffer *view) { - PyObject *obj = view->obj; - if (!obj) return; - if (PyObject_CheckBuffer(obj)) { - PyBuffer_Release(view); - return; - } - if ((0)) {} - view->obj = NULL; - Py_DECREF(obj); -} -#endif - - - /* Declarations */ - #if CYTHON_CCOMPLEX - #ifdef __cplusplus - static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) { - return ::std::complex< float >(x, y); - } - #else - static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) { - return x + y*(__pyx_t_float_complex)_Complex_I; - } - #endif -#else - static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) { - __pyx_t_float_complex z; - z.real = x; - z.imag = y; - return z; - } -#endif - -/* Arithmetic */ - #if CYTHON_CCOMPLEX -#else - static CYTHON_INLINE int __Pyx_c_eq_float(__pyx_t_float_complex a, __pyx_t_float_complex b) { - return (a.real == b.real) && (a.imag == b.imag); - } - static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_sum_float(__pyx_t_float_complex a, __pyx_t_float_complex b) { - __pyx_t_float_complex z; - z.real = a.real + b.real; - z.imag = a.imag + b.imag; - return z; - } - static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_diff_float(__pyx_t_float_complex a, __pyx_t_float_complex b) { - __pyx_t_float_complex z; - z.real = a.real - b.real; - z.imag = a.imag - b.imag; - return z; - } - static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_prod_float(__pyx_t_float_complex a, __pyx_t_float_complex b) { - __pyx_t_float_complex z; - z.real = a.real * b.real - a.imag * b.imag; - z.imag = a.real * b.imag + a.imag * b.real; - return z; - } - #if 1 - static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quot_float(__pyx_t_float_complex a, __pyx_t_float_complex b) { - if (b.imag == 0) { - return __pyx_t_float_complex_from_parts(a.real / b.real, a.imag / b.real); - } else if (fabsf(b.real) >= fabsf(b.imag)) { - if (b.real == 0 && b.imag == 0) { - return __pyx_t_float_complex_from_parts(a.real / b.real, a.imag / b.imag); - } else { - float r = b.imag / b.real; - float s = (float)(1.0) / (b.real + b.imag * r); - return __pyx_t_float_complex_from_parts( - (a.real + a.imag * r) * s, (a.imag - a.real * r) * s); - } - } else { - float r = b.real / b.imag; - float s = (float)(1.0) / (b.imag + b.real * r); - return __pyx_t_float_complex_from_parts( - (a.real * r + a.imag) * s, (a.imag * r - a.real) * s); - } - } - #else - static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quot_float(__pyx_t_float_complex a, __pyx_t_float_complex b) { - if (b.imag == 0) { - return __pyx_t_float_complex_from_parts(a.real / b.real, a.imag / b.real); - } else { - float denom = b.real * b.real + b.imag * b.imag; - return __pyx_t_float_complex_from_parts( - (a.real * b.real + a.imag * b.imag) / denom, - (a.imag * b.real - a.real * b.imag) / denom); - } - } - #endif - static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_neg_float(__pyx_t_float_complex a) { - __pyx_t_float_complex z; - z.real = -a.real; - z.imag = -a.imag; - return z; - } - static CYTHON_INLINE int __Pyx_c_is_zero_float(__pyx_t_float_complex a) { - return (a.real == 0) && (a.imag == 0); - } - static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_conj_float(__pyx_t_float_complex a) { - __pyx_t_float_complex z; - z.real = a.real; - z.imag = -a.imag; - return z; - } - #if 1 - static CYTHON_INLINE float __Pyx_c_abs_float(__pyx_t_float_complex z) { - #if !defined(HAVE_HYPOT) || defined(_MSC_VER) - return sqrtf(z.real*z.real + z.imag*z.imag); - #else - return hypotf(z.real, z.imag); - #endif - } - static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_pow_float(__pyx_t_float_complex a, __pyx_t_float_complex b) { - __pyx_t_float_complex z; - float r, lnr, theta, z_r, z_theta; - if (b.imag == 0 && b.real == (int)b.real) { - if (b.real < 0) { - float denom = a.real * a.real + a.imag * a.imag; - a.real = a.real / denom; - a.imag = -a.imag / denom; - b.real = -b.real; - } - switch ((int)b.real) { - case 0: - z.real = 1; - z.imag = 0; - return z; - case 1: - return a; - case 2: - return __Pyx_c_prod_float(a, a); - case 3: - z = __Pyx_c_prod_float(a, a); - return __Pyx_c_prod_float(z, a); - case 4: - z = __Pyx_c_prod_float(a, a); - return __Pyx_c_prod_float(z, z); - } - } - if (a.imag == 0) { - if (a.real == 0) { - return a; - } else if (b.imag == 0) { - z.real = powf(a.real, b.real); - z.imag = 0; - return z; - } else if (a.real > 0) { - r = a.real; - theta = 0; - } else { - r = -a.real; - theta = atan2f(0.0, -1.0); - } - } else { - r = __Pyx_c_abs_float(a); - theta = atan2f(a.imag, a.real); - } - lnr = logf(r); - z_r = expf(lnr * b.real - theta * b.imag); - z_theta = theta * b.real + lnr * b.imag; - z.real = z_r * cosf(z_theta); - z.imag = z_r * sinf(z_theta); - return z; - } - #endif -#endif - -/* Declarations */ - #if CYTHON_CCOMPLEX - #ifdef __cplusplus - static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) { - return ::std::complex< double >(x, y); - } - #else - static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) { - return x + y*(__pyx_t_double_complex)_Complex_I; - } - #endif -#else - static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) { - __pyx_t_double_complex z; - z.real = x; - z.imag = y; - return z; - } -#endif - -/* Arithmetic */ - #if CYTHON_CCOMPLEX -#else - static CYTHON_INLINE int __Pyx_c_eq_double(__pyx_t_double_complex a, __pyx_t_double_complex b) { - return (a.real == b.real) && (a.imag == b.imag); - } - static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_sum_double(__pyx_t_double_complex a, __pyx_t_double_complex b) { - __pyx_t_double_complex z; - z.real = a.real + b.real; - z.imag = a.imag + b.imag; - return z; - } - static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_diff_double(__pyx_t_double_complex a, __pyx_t_double_complex b) { - __pyx_t_double_complex z; - z.real = a.real - b.real; - z.imag = a.imag - b.imag; - return z; - } - static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_prod_double(__pyx_t_double_complex a, __pyx_t_double_complex b) { - __pyx_t_double_complex z; - z.real = a.real * b.real - a.imag * b.imag; - z.imag = a.real * b.imag + a.imag * b.real; - return z; - } - #if 1 - static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex a, __pyx_t_double_complex b) { - if (b.imag == 0) { - return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.real); - } else if (fabs(b.real) >= fabs(b.imag)) { - if (b.real == 0 && b.imag == 0) { - return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.imag); - } else { - double r = b.imag / b.real; - double s = (double)(1.0) / (b.real + b.imag * r); - return __pyx_t_double_complex_from_parts( - (a.real + a.imag * r) * s, (a.imag - a.real * r) * s); - } - } else { - double r = b.real / b.imag; - double s = (double)(1.0) / (b.imag + b.real * r); - return __pyx_t_double_complex_from_parts( - (a.real * r + a.imag) * s, (a.imag * r - a.real) * s); - } - } - #else - static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex a, __pyx_t_double_complex b) { - if (b.imag == 0) { - return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.real); - } else { - double denom = b.real * b.real + b.imag * b.imag; - return __pyx_t_double_complex_from_parts( - (a.real * b.real + a.imag * b.imag) / denom, - (a.imag * b.real - a.real * b.imag) / denom); - } - } - #endif - static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_neg_double(__pyx_t_double_complex a) { - __pyx_t_double_complex z; - z.real = -a.real; - z.imag = -a.imag; - return z; - } - static CYTHON_INLINE int __Pyx_c_is_zero_double(__pyx_t_double_complex a) { - return (a.real == 0) && (a.imag == 0); - } - static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_conj_double(__pyx_t_double_complex a) { - __pyx_t_double_complex z; - z.real = a.real; - z.imag = -a.imag; - return z; - } - #if 1 - static CYTHON_INLINE double __Pyx_c_abs_double(__pyx_t_double_complex z) { - #if !defined(HAVE_HYPOT) || defined(_MSC_VER) - return sqrt(z.real*z.real + z.imag*z.imag); - #else - return hypot(z.real, z.imag); - #endif - } - static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_pow_double(__pyx_t_double_complex a, __pyx_t_double_complex b) { - __pyx_t_double_complex z; - double r, lnr, theta, z_r, z_theta; - if (b.imag == 0 && b.real == (int)b.real) { - if (b.real < 0) { - double denom = a.real * a.real + a.imag * a.imag; - a.real = a.real / denom; - a.imag = -a.imag / denom; - b.real = -b.real; - } - switch ((int)b.real) { - case 0: - z.real = 1; - z.imag = 0; - return z; - case 1: - return a; - case 2: - return __Pyx_c_prod_double(a, a); - case 3: - z = __Pyx_c_prod_double(a, a); - return __Pyx_c_prod_double(z, a); - case 4: - z = __Pyx_c_prod_double(a, a); - return __Pyx_c_prod_double(z, z); - } - } - if (a.imag == 0) { - if (a.real == 0) { - return a; - } else if (b.imag == 0) { - z.real = pow(a.real, b.real); - z.imag = 0; - return z; - } else if (a.real > 0) { - r = a.real; - theta = 0; - } else { - r = -a.real; - theta = atan2(0.0, -1.0); - } - } else { - r = __Pyx_c_abs_double(a); - theta = atan2(a.imag, a.real); - } - lnr = log(r); - z_r = exp(lnr * b.real - theta * b.imag); - z_theta = theta * b.real + lnr * b.imag; - z.real = z_r * cos(z_theta); - z.imag = z_r * sin(z_theta); - return z; - } - #endif -#endif - -/* CIntToPy */ - static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value) { -#ifdef __Pyx_HAS_GCC_DIAGNOSTIC -#pragma GCC diagnostic push -#pragma GCC diagnostic ignored "-Wconversion" -#endif - const long neg_one = (long) -1, const_zero = (long) 0; -#ifdef __Pyx_HAS_GCC_DIAGNOSTIC -#pragma GCC diagnostic pop -#endif - const int is_unsigned = neg_one > const_zero; - if (is_unsigned) { - if (sizeof(long) < sizeof(long)) { - return PyInt_FromLong((long) value); - } else if (sizeof(long) <= sizeof(unsigned long)) { - return PyLong_FromUnsignedLong((unsigned long) value); -#ifdef HAVE_LONG_LONG - } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) { - return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value); -#endif - } - } else { - if (sizeof(long) <= sizeof(long)) { - return PyInt_FromLong((long) value); -#ifdef HAVE_LONG_LONG - } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) { - return PyLong_FromLongLong((PY_LONG_LONG) value); -#endif - } - } - { - int one = 1; int little = (int)*(unsigned char *)&one; - unsigned char *bytes = (unsigned char *)&value; - return _PyLong_FromByteArray(bytes, sizeof(long), - little, !is_unsigned); - } -} - -/* CIntFromPyVerify */ - #define __PYX_VERIFY_RETURN_INT(target_type, func_type, func_value)\ - __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 0) -#define __PYX_VERIFY_RETURN_INT_EXC(target_type, func_type, func_value)\ - __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 1) -#define __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, exc)\ - {\ - func_type value = func_value;\ - if (sizeof(target_type) < sizeof(func_type)) {\ - if (unlikely(value != (func_type) (target_type) value)) {\ - func_type zero = 0;\ - if (exc && unlikely(value == (func_type)-1 && PyErr_Occurred()))\ - return (target_type) -1;\ - if (is_unsigned && unlikely(value < zero))\ - goto raise_neg_overflow;\ - else\ - goto raise_overflow;\ - }\ - }\ - return (target_type) value;\ - } - -/* CIntFromPy */ - static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *x) { -#ifdef __Pyx_HAS_GCC_DIAGNOSTIC -#pragma GCC diagnostic push -#pragma GCC diagnostic ignored "-Wconversion" -#endif - const long neg_one = (long) -1, const_zero = (long) 0; -#ifdef __Pyx_HAS_GCC_DIAGNOSTIC -#pragma GCC diagnostic pop -#endif - const int is_unsigned = neg_one > const_zero; -#if PY_MAJOR_VERSION < 3 - if (likely(PyInt_Check(x))) { - if (sizeof(long) < sizeof(long)) { - __PYX_VERIFY_RETURN_INT(long, long, PyInt_AS_LONG(x)) - } else { - long val = PyInt_AS_LONG(x); - if (is_unsigned && unlikely(val < 0)) { - goto raise_neg_overflow; - } - return (long) val; - } - } else -#endif - if (likely(PyLong_Check(x))) { - if (is_unsigned) { -#if CYTHON_USE_PYLONG_INTERNALS - const digit* digits = ((PyLongObject*)x)->ob_digit; - switch (Py_SIZE(x)) { - case 0: return (long) 0; - case 1: __PYX_VERIFY_RETURN_INT(long, digit, digits[0]) - case 2: - if (8 * sizeof(long) > 1 * PyLong_SHIFT) { - if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) { - __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) - } else if (8 * sizeof(long) >= 2 * PyLong_SHIFT) { - return (long) (((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])); - } - } - break; - case 3: - if (8 * sizeof(long) > 2 * PyLong_SHIFT) { - if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) { - __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) - } else if (8 * sizeof(long) >= 3 * PyLong_SHIFT) { - return (long) (((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])); - } - } - break; - case 4: - if (8 * sizeof(long) > 3 * PyLong_SHIFT) { - if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) { - __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) - } else if (8 * sizeof(long) >= 4 * PyLong_SHIFT) { - return (long) (((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])); - } - } - break; - } -#endif -#if CYTHON_COMPILING_IN_CPYTHON - if (unlikely(Py_SIZE(x) < 0)) { - goto raise_neg_overflow; - } -#else - { - int result = PyObject_RichCompareBool(x, Py_False, Py_LT); - if (unlikely(result < 0)) - return (long) -1; - if (unlikely(result == 1)) - goto raise_neg_overflow; - } -#endif - if (sizeof(long) <= sizeof(unsigned long)) { - __PYX_VERIFY_RETURN_INT_EXC(long, unsigned long, PyLong_AsUnsignedLong(x)) -#ifdef HAVE_LONG_LONG - } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) { - __PYX_VERIFY_RETURN_INT_EXC(long, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x)) -#endif - } - } else { -#if CYTHON_USE_PYLONG_INTERNALS - const digit* digits = ((PyLongObject*)x)->ob_digit; - switch (Py_SIZE(x)) { - case 0: return (long) 0; - case -1: __PYX_VERIFY_RETURN_INT(long, sdigit, (sdigit) (-(sdigit)digits[0])) - case 1: __PYX_VERIFY_RETURN_INT(long, digit, +digits[0]) - case -2: - if (8 * sizeof(long) - 1 > 1 * PyLong_SHIFT) { - if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) { - __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) - } else if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) { - return (long) (((long)-1)*(((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0]))); - } - } - break; - case 2: - if (8 * sizeof(long) > 1 * PyLong_SHIFT) { - if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) { - __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) - } else if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) { - return (long) ((((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0]))); - } - } - break; - case -3: - if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) { - if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) { - __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) - } else if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) { - return (long) (((long)-1)*(((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]))); - } - } - break; - case 3: - if (8 * sizeof(long) > 2 * PyLong_SHIFT) { - if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) { - __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) - } else if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) { - return (long) ((((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]))); - } - } - break; - case -4: - if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) { - if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) { - __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) - } else if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) { - return (long) (((long)-1)*(((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]))); - } - } - break; - case 4: - if (8 * sizeof(long) > 3 * PyLong_SHIFT) { - if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) { - __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) - } else if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) { - return (long) ((((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]))); - } - } - break; - } -#endif - if (sizeof(long) <= sizeof(long)) { - __PYX_VERIFY_RETURN_INT_EXC(long, long, PyLong_AsLong(x)) -#ifdef HAVE_LONG_LONG - } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) { - __PYX_VERIFY_RETURN_INT_EXC(long, PY_LONG_LONG, PyLong_AsLongLong(x)) -#endif - } - } - { -#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray) - PyErr_SetString(PyExc_RuntimeError, - "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers"); -#else - long val; - PyObject *v = __Pyx_PyNumber_IntOrLong(x); - #if PY_MAJOR_VERSION < 3 - if (likely(v) && !PyLong_Check(v)) { - PyObject *tmp = v; - v = PyNumber_Long(tmp); - Py_DECREF(tmp); - } - #endif - if (likely(v)) { - int one = 1; int is_little = (int)*(unsigned char *)&one; - unsigned char *bytes = (unsigned char *)&val; - int ret = _PyLong_AsByteArray((PyLongObject *)v, - bytes, sizeof(val), - is_little, !is_unsigned); - Py_DECREF(v); - if (likely(!ret)) - return val; - } -#endif - return (long) -1; - } - } else { - long val; - PyObject *tmp = __Pyx_PyNumber_IntOrLong(x); - if (!tmp) return (long) -1; - val = __Pyx_PyInt_As_long(tmp); - Py_DECREF(tmp); - return val; - } -raise_overflow: - PyErr_SetString(PyExc_OverflowError, - "value too large to convert to long"); - return (long) -1; -raise_neg_overflow: - PyErr_SetString(PyExc_OverflowError, - "can't convert negative value to long"); - return (long) -1; -} - -/* CIntFromPy */ - static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *x) { -#ifdef __Pyx_HAS_GCC_DIAGNOSTIC -#pragma GCC diagnostic push -#pragma GCC diagnostic ignored "-Wconversion" -#endif - const int neg_one = (int) -1, const_zero = (int) 0; -#ifdef __Pyx_HAS_GCC_DIAGNOSTIC -#pragma GCC diagnostic pop -#endif - const int is_unsigned = neg_one > const_zero; -#if PY_MAJOR_VERSION < 3 - if (likely(PyInt_Check(x))) { - if (sizeof(int) < sizeof(long)) { - __PYX_VERIFY_RETURN_INT(int, long, PyInt_AS_LONG(x)) - } else { - long val = PyInt_AS_LONG(x); - if (is_unsigned && unlikely(val < 0)) { - goto raise_neg_overflow; - } - return (int) val; - } - } else -#endif - if (likely(PyLong_Check(x))) { - if (is_unsigned) { -#if CYTHON_USE_PYLONG_INTERNALS - const digit* digits = ((PyLongObject*)x)->ob_digit; - switch (Py_SIZE(x)) { - case 0: return (int) 0; - case 1: __PYX_VERIFY_RETURN_INT(int, digit, digits[0]) - case 2: - if (8 * sizeof(int) > 1 * PyLong_SHIFT) { - if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) { - __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) - } else if (8 * sizeof(int) >= 2 * PyLong_SHIFT) { - return (int) (((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])); - } - } - break; - case 3: - if (8 * sizeof(int) > 2 * PyLong_SHIFT) { - if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) { - __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) - } else if (8 * sizeof(int) >= 3 * PyLong_SHIFT) { - return (int) (((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])); - } - } - break; - case 4: - if (8 * sizeof(int) > 3 * PyLong_SHIFT) { - if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) { - __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) - } else if (8 * sizeof(int) >= 4 * PyLong_SHIFT) { - return (int) (((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])); - } - } - break; - } -#endif -#if CYTHON_COMPILING_IN_CPYTHON - if (unlikely(Py_SIZE(x) < 0)) { - goto raise_neg_overflow; - } -#else - { - int result = PyObject_RichCompareBool(x, Py_False, Py_LT); - if (unlikely(result < 0)) - return (int) -1; - if (unlikely(result == 1)) - goto raise_neg_overflow; - } -#endif - if (sizeof(int) <= sizeof(unsigned long)) { - __PYX_VERIFY_RETURN_INT_EXC(int, unsigned long, PyLong_AsUnsignedLong(x)) -#ifdef HAVE_LONG_LONG - } else if (sizeof(int) <= sizeof(unsigned PY_LONG_LONG)) { - __PYX_VERIFY_RETURN_INT_EXC(int, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x)) -#endif - } - } else { -#if CYTHON_USE_PYLONG_INTERNALS - const digit* digits = ((PyLongObject*)x)->ob_digit; - switch (Py_SIZE(x)) { - case 0: return (int) 0; - case -1: __PYX_VERIFY_RETURN_INT(int, sdigit, (sdigit) (-(sdigit)digits[0])) - case 1: __PYX_VERIFY_RETURN_INT(int, digit, +digits[0]) - case -2: - if (8 * sizeof(int) - 1 > 1 * PyLong_SHIFT) { - if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) { - __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) - } else if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) { - return (int) (((int)-1)*(((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0]))); - } - } - break; - case 2: - if (8 * sizeof(int) > 1 * PyLong_SHIFT) { - if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) { - __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) - } else if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) { - return (int) ((((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0]))); - } - } - break; - case -3: - if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) { - if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) { - __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) - } else if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) { - return (int) (((int)-1)*(((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]))); - } - } - break; - case 3: - if (8 * sizeof(int) > 2 * PyLong_SHIFT) { - if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) { - __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) - } else if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) { - return (int) ((((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]))); - } - } - break; - case -4: - if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) { - if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) { - __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) - } else if (8 * sizeof(int) - 1 > 4 * PyLong_SHIFT) { - return (int) (((int)-1)*(((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]))); - } - } - break; - case 4: - if (8 * sizeof(int) > 3 * PyLong_SHIFT) { - if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) { - __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) - } else if (8 * sizeof(int) - 1 > 4 * PyLong_SHIFT) { - return (int) ((((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]))); - } - } - break; - } -#endif - if (sizeof(int) <= sizeof(long)) { - __PYX_VERIFY_RETURN_INT_EXC(int, long, PyLong_AsLong(x)) -#ifdef HAVE_LONG_LONG - } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) { - __PYX_VERIFY_RETURN_INT_EXC(int, PY_LONG_LONG, PyLong_AsLongLong(x)) -#endif - } - } - { -#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray) - PyErr_SetString(PyExc_RuntimeError, - "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers"); -#else - int val; - PyObject *v = __Pyx_PyNumber_IntOrLong(x); - #if PY_MAJOR_VERSION < 3 - if (likely(v) && !PyLong_Check(v)) { - PyObject *tmp = v; - v = PyNumber_Long(tmp); - Py_DECREF(tmp); - } - #endif - if (likely(v)) { - int one = 1; int is_little = (int)*(unsigned char *)&one; - unsigned char *bytes = (unsigned char *)&val; - int ret = _PyLong_AsByteArray((PyLongObject *)v, - bytes, sizeof(val), - is_little, !is_unsigned); - Py_DECREF(v); - if (likely(!ret)) - return val; - } -#endif - return (int) -1; - } - } else { - int val; - PyObject *tmp = __Pyx_PyNumber_IntOrLong(x); - if (!tmp) return (int) -1; - val = __Pyx_PyInt_As_int(tmp); - Py_DECREF(tmp); - return val; - } -raise_overflow: - PyErr_SetString(PyExc_OverflowError, - "value too large to convert to int"); - return (int) -1; -raise_neg_overflow: - PyErr_SetString(PyExc_OverflowError, - "can't convert negative value to int"); - return (int) -1; -} - -/* FastTypeChecks */ - #if CYTHON_COMPILING_IN_CPYTHON -static int __Pyx_InBases(PyTypeObject *a, PyTypeObject *b) { - while (a) { - a = a->tp_base; - if (a == b) - return 1; - } - return b == &PyBaseObject_Type; -} -static CYTHON_INLINE int __Pyx_IsSubtype(PyTypeObject *a, PyTypeObject *b) { - PyObject *mro; - if (a == b) return 1; - mro = a->tp_mro; - if (likely(mro)) { - Py_ssize_t i, n; - n = PyTuple_GET_SIZE(mro); - for (i = 0; i < n; i++) { - if (PyTuple_GET_ITEM(mro, i) == (PyObject *)b) - return 1; - } - return 0; - } - return __Pyx_InBases(a, b); -} -#if PY_MAJOR_VERSION == 2 -static int __Pyx_inner_PyErr_GivenExceptionMatches2(PyObject *err, PyObject* exc_type1, PyObject* exc_type2) { - PyObject *exception, *value, *tb; - int res; - __Pyx_PyThreadState_declare - __Pyx_PyThreadState_assign - __Pyx_ErrFetch(&exception, &value, &tb); - res = exc_type1 ? PyObject_IsSubclass(err, exc_type1) : 0; - if (unlikely(res == -1)) { - PyErr_WriteUnraisable(err); - res = 0; - } - if (!res) { - res = PyObject_IsSubclass(err, exc_type2); - if (unlikely(res == -1)) { - PyErr_WriteUnraisable(err); - res = 0; - } - } - __Pyx_ErrRestore(exception, value, tb); - return res; -} -#else -static CYTHON_INLINE int __Pyx_inner_PyErr_GivenExceptionMatches2(PyObject *err, PyObject* exc_type1, PyObject *exc_type2) { - int res = exc_type1 ? __Pyx_IsSubtype((PyTypeObject*)err, (PyTypeObject*)exc_type1) : 0; - if (!res) { - res = __Pyx_IsSubtype((PyTypeObject*)err, (PyTypeObject*)exc_type2); - } - return res; -} -#endif -static int __Pyx_PyErr_GivenExceptionMatchesTuple(PyObject *exc_type, PyObject *tuple) { - Py_ssize_t i, n; - assert(PyExceptionClass_Check(exc_type)); - n = PyTuple_GET_SIZE(tuple); -#if PY_MAJOR_VERSION >= 3 - for (i=0; ip) { - #if PY_MAJOR_VERSION < 3 - if (t->is_unicode) { - *t->p = PyUnicode_DecodeUTF8(t->s, t->n - 1, NULL); - } else if (t->intern) { - *t->p = PyString_InternFromString(t->s); - } else { - *t->p = PyString_FromStringAndSize(t->s, t->n - 1); - } - #else - if (t->is_unicode | t->is_str) { - if (t->intern) { - *t->p = PyUnicode_InternFromString(t->s); - } else if (t->encoding) { - *t->p = PyUnicode_Decode(t->s, t->n - 1, t->encoding, NULL); - } else { - *t->p = PyUnicode_FromStringAndSize(t->s, t->n - 1); - } - } else { - *t->p = PyBytes_FromStringAndSize(t->s, t->n - 1); - } - #endif - if (!*t->p) - return -1; - if (PyObject_Hash(*t->p) == -1) - return -1; - ++t; - } - return 0; -} - -static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char* c_str) { - return __Pyx_PyUnicode_FromStringAndSize(c_str, (Py_ssize_t)strlen(c_str)); -} -static CYTHON_INLINE const char* __Pyx_PyObject_AsString(PyObject* o) { - Py_ssize_t ignore; - return __Pyx_PyObject_AsStringAndSize(o, &ignore); -} -#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT -#if !CYTHON_PEP393_ENABLED -static const char* __Pyx_PyUnicode_AsStringAndSize(PyObject* o, Py_ssize_t *length) { - char* defenc_c; - PyObject* defenc = _PyUnicode_AsDefaultEncodedString(o, NULL); - if (!defenc) return NULL; - defenc_c = PyBytes_AS_STRING(defenc); -#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII - { - char* end = defenc_c + PyBytes_GET_SIZE(defenc); - char* c; - for (c = defenc_c; c < end; c++) { - if ((unsigned char) (*c) >= 128) { - PyUnicode_AsASCIIString(o); - return NULL; - } - } - } -#endif - *length = PyBytes_GET_SIZE(defenc); - return defenc_c; -} -#else -static CYTHON_INLINE const char* __Pyx_PyUnicode_AsStringAndSize(PyObject* o, Py_ssize_t *length) { - if (unlikely(__Pyx_PyUnicode_READY(o) == -1)) return NULL; -#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII - if (likely(PyUnicode_IS_ASCII(o))) { - *length = PyUnicode_GET_LENGTH(o); - return PyUnicode_AsUTF8(o); - } else { - PyUnicode_AsASCIIString(o); - return NULL; - } -#else - return PyUnicode_AsUTF8AndSize(o, length); -#endif -} -#endif -#endif -static CYTHON_INLINE const char* __Pyx_PyObject_AsStringAndSize(PyObject* o, Py_ssize_t *length) { -#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT - if ( -#if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII - __Pyx_sys_getdefaultencoding_not_ascii && -#endif - PyUnicode_Check(o)) { - return __Pyx_PyUnicode_AsStringAndSize(o, length); - } else -#endif -#if (!CYTHON_COMPILING_IN_PYPY) || (defined(PyByteArray_AS_STRING) && defined(PyByteArray_GET_SIZE)) - if (PyByteArray_Check(o)) { - *length = PyByteArray_GET_SIZE(o); - return PyByteArray_AS_STRING(o); - } else -#endif - { - char* result; - int r = PyBytes_AsStringAndSize(o, &result, length); - if (unlikely(r < 0)) { - return NULL; - } else { - return result; - } - } -} -static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject* x) { - int is_true = x == Py_True; - if (is_true | (x == Py_False) | (x == Py_None)) return is_true; - else return PyObject_IsTrue(x); -} -static CYTHON_INLINE int __Pyx_PyObject_IsTrueAndDecref(PyObject* x) { - int retval; - if (unlikely(!x)) return -1; - retval = __Pyx_PyObject_IsTrue(x); - Py_DECREF(x); - return retval; -} -static PyObject* __Pyx_PyNumber_IntOrLongWrongResultType(PyObject* result, const char* type_name) { -#if PY_MAJOR_VERSION >= 3 - if (PyLong_Check(result)) { - if (PyErr_WarnFormat(PyExc_DeprecationWarning, 1, - "__int__ returned non-int (type %.200s). " - "The ability to return an instance of a strict subclass of int " - "is deprecated, and may be removed in a future version of Python.", - Py_TYPE(result)->tp_name)) { - Py_DECREF(result); - return NULL; - } - return result; - } -#endif - PyErr_Format(PyExc_TypeError, - "__%.4s__ returned non-%.4s (type %.200s)", - type_name, type_name, Py_TYPE(result)->tp_name); - Py_DECREF(result); - return NULL; -} -static CYTHON_INLINE PyObject* __Pyx_PyNumber_IntOrLong(PyObject* x) { -#if CYTHON_USE_TYPE_SLOTS - PyNumberMethods *m; -#endif - const char *name = NULL; - PyObject *res = NULL; -#if PY_MAJOR_VERSION < 3 - if (likely(PyInt_Check(x) || PyLong_Check(x))) -#else - if (likely(PyLong_Check(x))) -#endif - return __Pyx_NewRef(x); -#if CYTHON_USE_TYPE_SLOTS - m = Py_TYPE(x)->tp_as_number; - #if PY_MAJOR_VERSION < 3 - if (m && m->nb_int) { - name = "int"; - res = m->nb_int(x); - } - else if (m && m->nb_long) { - name = "long"; - res = m->nb_long(x); - } - #else - if (likely(m && m->nb_int)) { - name = "int"; - res = m->nb_int(x); - } - #endif -#else - if (!PyBytes_CheckExact(x) && !PyUnicode_CheckExact(x)) { - res = PyNumber_Int(x); - } -#endif - if (likely(res)) { -#if PY_MAJOR_VERSION < 3 - if (unlikely(!PyInt_Check(res) && !PyLong_Check(res))) { -#else - if (unlikely(!PyLong_CheckExact(res))) { -#endif - return __Pyx_PyNumber_IntOrLongWrongResultType(res, name); - } - } - else if (!PyErr_Occurred()) { - PyErr_SetString(PyExc_TypeError, - "an integer is required"); - } - return res; -} -static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject* b) { - Py_ssize_t ival; - PyObject *x; -#if PY_MAJOR_VERSION < 3 - if (likely(PyInt_CheckExact(b))) { - if (sizeof(Py_ssize_t) >= sizeof(long)) - return PyInt_AS_LONG(b); - else - return PyInt_AsSsize_t(b); - } -#endif - if (likely(PyLong_CheckExact(b))) { - #if CYTHON_USE_PYLONG_INTERNALS - const digit* digits = ((PyLongObject*)b)->ob_digit; - const Py_ssize_t size = Py_SIZE(b); - if (likely(__Pyx_sst_abs(size) <= 1)) { - ival = likely(size) ? digits[0] : 0; - if (size == -1) ival = -ival; - return ival; - } else { - switch (size) { - case 2: - if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) { - return (Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); - } - break; - case -2: - if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) { - return -(Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); - } - break; - case 3: - if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) { - return (Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); - } - break; - case -3: - if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) { - return -(Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); - } - break; - case 4: - if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) { - return (Py_ssize_t) (((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); - } - break; - case -4: - if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) { - return -(Py_ssize_t) (((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); - } - break; - } - } - #endif - return PyLong_AsSsize_t(b); - } - x = PyNumber_Index(b); - if (!x) return -1; - ival = PyInt_AsSsize_t(x); - Py_DECREF(x); - return ival; -} -static CYTHON_INLINE PyObject * __Pyx_PyBool_FromLong(long b) { - return b ? __Pyx_NewRef(Py_True) : __Pyx_NewRef(Py_False); -} -static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t ival) { - return PyInt_FromSize_t(ival); -} - - -#endif /* Py_PYTHON_H */ diff --git a/skfda/misc/metrics/sdtw_fast.pyx b/skfda/misc/metrics/sdtw_fast.pyx deleted file mode 100644 index db670fb6f..000000000 --- a/skfda/misc/metrics/sdtw_fast.pyx +++ /dev/null @@ -1,88 +0,0 @@ -""" -cython implementation of soft-DTW recursion. -Refs: - - Blondel, M., Mensch, A., & Vert, J.-P. (2021). - Differentiable Divergences Between Time Series. AISTATS. http://arxiv.org/abs/2010.08354 - - Mensch, A., Blondel, M. (2018). - Differentiable Dynamic Programming for Structured Prediction and Attention. ICML. https://proceedings.mlr.press/v80/mensch18a.html - -@author: Clément Lejeune -""" -cimport numpy as np -import numpy as np -from cython cimport boundscheck, wraparound, cdivision -from libc.math cimport exp, log -from libc.float cimport DBL_MAX - -DTYPE = np.float64 -ctypedef np.float64_t DTYPE_t - -@cdivision(True) -@boundscheck(False) -@wraparound(False) -cdef inline DTYPE_t _soft_min_argmin( - DTYPE_t x, DTYPE_t y, DTYPE_t z) nogil: - - cdef DTYPE_t min_xyz = min(x, min(y, z)) - # cdef double e_x - # cdef double e_y - # cdef double e_z - cdef DTYPE_t nn - # cdef DTYPE_t soft_min - - # e_x = exp(min_xyz - x) - # e_y = exp(min_xyz - y) - # e_z = exp(min_xyz - z) - # nn = e_x + e_y + e_z # normalizing constant - - nn = exp(min_xyz - x) - nn += exp(min_xyz - y) - nn += exp(min_xyz - z) - # soft_min = min_xyz - log(nn) # smoothed_min operator value - - return min_xyz - log(nn)# soft_min#, e_x/nn, e_y/nn, e_z/nn - -@cdivision(True) -@boundscheck(False) -@wraparound(False) -def _sdtw_C_cy( - np.ndarray[DTYPE_t, ndim=2] C, - DTYPE_t gamma): - - dtype = DTYPE - - cdef Py_ssize_t i, j - cdef Py_ssize_t len_X = C.shape[0] - cdef Py_ssize_t len_Y = C.shape[0] - - cdef np.ndarray[DTYPE_t, ndim=2] V = np.zeros((len_X + 1, len_Y + 1), dtype=dtype) - - # this is useless: - # cdef double[:, :, :] P = np.zeros((len_X + 2, len_Y + 2, 3), dtype=dtype) - - cdef DTYPE_t soft_min = 0.0 - - with nogil: - - # initialize firt row to a large value - for j in range(1, len_Y + 1): - V[0, j] = DBL_MAX - - # initilize first column to a large value - for i in range(1, len_X + 1): - V[i, 0] = DBL_MAX - - for i in range(1, len_X + 1): - for j in range(1, len_Y + 1): - # P_ij are useless (unless need for gradient computation) - ## soft_min, P[i, j, 0], P[i, j, 1], P[i, j, 2] = _soft_min_argmin( - ## V[i, j-1], - ## V[i-1, j-1], - ## V[i-1, j]) - soft_min = _soft_min_argmin(V[i, j-1], V[i-1, j-1], V[i-1, j]) - if gamma != 1.0: - V[i, j] = (C[i-1, j-1] / gamma) + soft_min - else: - V[i, j] = C[i-1, j-1] + soft_min - - return gamma * V[len_X, len_Y] diff --git a/skfda/misc/metrics/setup.py b/skfda/misc/metrics/setup.py deleted file mode 100644 index c2895edc8..000000000 --- a/skfda/misc/metrics/setup.py +++ /dev/null @@ -1,14 +0,0 @@ -from setuptools import setup -from setuptools import Extension -import numpy as np - -setup( - ext_modules=[ - Extension( - 'sdtw_fast', - sources=['sdtw_fast.pyx'], - language='c', - include_dirs=[np.get_include()] - )], - zip_safe=False -) From 0079ce412278e44f67dde7682ec3ea6ead828e2c Mon Sep 17 00:00:00 2001 From: Lejeune Date: Tue, 15 Feb 2022 12:00:46 +0100 Subject: [PATCH 06/21] np.einsum in inner_product_matrix replaced by np.dot --- skfda/misc/_math.py | 37 ++----------------------------------- 1 file changed, 2 insertions(+), 35 deletions(-) diff --git a/skfda/misc/_math.py b/skfda/misc/_math.py index 722aff759..6d954e8e5 100644 --- a/skfda/misc/_math.py +++ b/skfda/misc/_math.py @@ -324,7 +324,8 @@ def inner_product( ) return ( - np.einsum('n...,m...->nm...', arg1, arg2).sum(axis=-1) + np.dot(arg1, arg2.T) + # np.einsum('n...,m...->nm...', arg1, arg2).sum(axis=-1) if _matrix else (arg1 * arg2).sum(axis=-1) ) @@ -679,38 +680,4 @@ def cosine_similarity_matrix( return _clip_cosine( inner_matrix / norm1[:, np.newaxis] / norm2[np.newaxis, :], ) - -def half_sq_euclidean( - arg1: NDArrayFloat, - arg2: Optional[NDArrayFloat] = None, -) -> NDArrayFloat: - """ - Return the half squared Euclidean row distance between - two matrices. - - Args: - arg1: First sample (n_samples_1, n_features). - arg2: Second sample (n_samples_2, n_features). - If it is ``None`` returns the half squared Euclidean distance - between the rows of ``arg1``. - - The distance is taken w.r.t matrix rows. - """ - if arg2 is not None: - # np.dot(X, Y.T)=inner_product_matrix(X, Y) but np ~1.6 faster - cost_12 = -1 * np.dot(arg1, arg2.T) - - # np.sum(arg1 ** 2, axis=1)=diag(inner_product_matrix(X, X)) - cost_12 += (0.5 * np.sum(arg1 ** 2, axis=1))[:, np.newaxis] - cost_12 += 0.5 * np.sum(arg2 ** 2, axis=1) - - return cost_12 - else: - cost_11 = -1 * np.dot(arg1, arg1.T) - # half sum of squares on each row - sos_row = 0.5 * np.sum(arg1 ** 2, axis=1) - cost_11 += sos_row[:, np.newaxis] - cost_11 += sos_row - - return cost_11 \ No newline at end of file From 7a0c5c9aea512c7fd9a55cbd67f3dfa741a2186b Mon Sep 17 00:00:00 2001 From: Lejeune Date: Tue, 15 Feb 2022 12:20:01 +0100 Subject: [PATCH 07/21] replaced np.sum(X**2, axis=1) by inner_product --- skfda/misc/metrics/_sdtw_distances.py | 38 ++++++++++++++++++++++++++- 1 file changed, 37 insertions(+), 1 deletion(-) diff --git a/skfda/misc/metrics/_sdtw_distances.py b/skfda/misc/metrics/_sdtw_distances.py index 51e11f83c..b75fa547a 100644 --- a/skfda/misc/metrics/_sdtw_distances.py +++ b/skfda/misc/metrics/_sdtw_distances.py @@ -15,7 +15,7 @@ from skfda._utils._utils import _check_compatible_fdata from skfda.misc.metrics import _sdtw_numba -from skfda.misc._math import half_sq_euclidean +from skfda.misc._math import inner_product_matrix, inner_product def _check_shape_postive_cost_mat(cost, expected_shape, shape_only=False): @@ -102,6 +102,42 @@ def _check_input_fdata(fdata1, fdata2): # ) +def half_sq_euclidean( + arg1: NDArrayFloat, + arg2: Optional[NDArrayFloat] = None, +) -> NDArrayFloat: + """ + Return the half squared Euclidean row distance between + two matrices of size (n1, d) and (n2, d). + + Args: + arg1: First sample (n_samples_1, n_features). + arg2: Second sample (n_samples_2, n_features). + If it is ``None`` returns the half squared Euclidean distance + between the rows of ``arg1``. + + The distance is taken w.r.t matrix rows. + """ + if arg2 is not None: + # np.dot(X, Y.T)=inner_product_matrix(X, Y) but np ~1.6 faster + # X.shape is (n_X, d) and Y.shape is (n_Y, d) + cost_12 = -1 * inner_product_matrix(arg1, arg2) + + # np.sum(X ** 2, axis=1)=inner_product(X, X) + cost_12 += (0.5 * inner_product(arg1, arg1))[:, np.newaxis] + cost_12 += 0.5 * inner_product(arg2, arg2) + + return cost_12 + else: + cost_11 = -1 * inner_product_matrix(arg1, arg2) + # half Sum Of Squares on each row + sos_row = 0.5 * inner_product(arg1, arg1) + cost_11 += sos_row[:, np.newaxis] + cost_11 += sos_row + + return cost_11 + + def _sdtw_divergence( fdata1: FData, fdata2: FData, From 1668b2026a685128a69e8af69df97241f5910c35 Mon Sep 17 00:00:00 2001 From: Lejeune Date: Tue, 15 Feb 2022 14:03:23 +0100 Subject: [PATCH 08/21] format, type hints --- skfda/misc/metrics/_sdtw_distances.py | 154 ++++++++++---------------- 1 file changed, 57 insertions(+), 97 deletions(-) diff --git a/skfda/misc/metrics/_sdtw_distances.py b/skfda/misc/metrics/_sdtw_distances.py index b75fa547a..4605dcd87 100644 --- a/skfda/misc/metrics/_sdtw_distances.py +++ b/skfda/misc/metrics/_sdtw_distances.py @@ -3,29 +3,31 @@ """ from __future__ import annotations -from typing import Optional, Union, Callable, List, Tuple +from typing import Optional, Union, Callable, Tuple from numba.core.types.scalars import Boolean import numpy as np from typing_extensions import Final -from ...representation import FData, FDataBasis -from ...representation._typing import NDArrayFloat, GridPointsLike, ArrayLike -# from ._utils import pairwise_metric_optimization +from ...representation import FDataGrid +from ...representation._typing import NDArrayFloat, GridPointsLike from skfda._utils._utils import _check_compatible_fdata from skfda.misc.metrics import _sdtw_numba from skfda.misc._math import inner_product_matrix, inner_product -def _check_shape_postive_cost_mat(cost, expected_shape, shape_only=False): +def _check_shape_postive_cost_mat( + cost: NDArrayFloat, + expected_shape: Tuple, + shape_only: Boolean = False +) -> None: """check that matrix 'cost' is nonnegative and has expected shape""" n1, n2 = expected_shape # must have shape fdata1.grid_points[0], fdata1.grid_points[0] if not cost.shape == (n1, n2): raise ValueError( - "Cost matrix must have shape" - " ({}, {})".format(n1, n2) + f"Cost matrix must have shape ({n1}, {n2})" ) # non-negativity if not(shape_only): @@ -35,8 +37,12 @@ def _check_shape_postive_cost_mat(cost, expected_shape, shape_only=False): ) -def _check_indiscernable_sym(cost, X, Y): - """check cost returns a symmetric matrix with zero diag""" +def _check_indiscernable_sym( + cost: NDArrayFloat, + X: NDArrayFloat, + Y: NDArrayFloat +) -> None: + """check that cost returns a symmetric matrix with zero diag""" # indiscernability: cost(x_t, x_t) = 0 for any t if ( np.all(np.diag(cost(X, X)) != 0) @@ -44,62 +50,39 @@ def _check_indiscernable_sym(cost, X, Y): ): raise ValueError( "The cost between two identical objects " - " must be identically (null diagonal)" + "must be zero (i.e cost(X, X) is zero diagonal)" ) - # symmetry: cost(X1, X2) = cost(X2, X1).T + # symmetry: cost(X, Y) = cost(y, X).T if not np.allclose(cost(X, Y), cost(Y, X).T): raise ValueError( "The cost function does not return a symmetric matrix" ) -def _check_input_evalpoints(eval_points): - """check eval_points contains one or two one-dim array""" - if isinstance(eval_points, Tuple) or isinstance(eval_points, List): - if not len(eval_points) <= 2: - raise ValueError( - "eval_points must be a tuple or a list containing one or" - " two elements, each one being a one-dimensional numpy array" - ) - - for idx, ep_i in enumerate(eval_points): - if ( - not (isinstance(ep_i, NDArrayFloat) and ep_i.ndim == 1) - ): - raise ValueError( - "{}-th element of the tuple must be a one-dimensional" - " numpy array.".format(idx) - ) - - if not np.all(np.diff(ep_i) > 0): - raise ValueError( - "Values in eval_points must be arranged increasingly" - ) +def _check_input_fdata( + fdata1, + fdata2 +) -> None: + """check compatible, one sample and one-dimensional""" + _check_compatible_fdata(fdata1, fdata2) - else: + if not isinstance(fdata1, FDataGrid): raise ValueError( - "eval_points must be a tuple containing either one" - " or two one-dimensional numpy array(s)." + "fdata1 and fdata2 must be FDataGrid objects" ) - -def _check_input_fdata(fdata1, fdata2): - """check compatible and one sample per object""" - _check_compatible_fdata(fdata1, fdata2) - - same_fdata_format = type(fdata1) == type(fdata2) - - if not same_fdata_format: + # dim_codomain can be higher than one, + # but dim_domain must be one + if not fdata1.dim_domain == 1: raise ValueError( - "fdata1 and fdata2 should be either two FDataBasis objects," - " either two FDataGrid objects" + "fdata1 and fdata2 must have their domain dimension equal to one" ) - # if not (fdata1.n_samples == 1 and fdata2.n_samples == 1): - # raise ValueError( - # "Both fdata1 and fdata2 must contain a single sample" - # ) + if not (fdata1.n_samples == 1 & fdata2.n_samples == 1): + raise ValueError( + "Both fdata1 and fdata2 must each contain a single sample" + ) def half_sq_euclidean( @@ -139,58 +122,36 @@ def half_sq_euclidean( def _sdtw_divergence( - fdata1: FData, - fdata2: FData, + fdata1: FDataGrid, + fdata2: FDataGrid, *, - gamma: 1.0, - cost: None, - check_cost: False, - eval_points: None -) -> NDArrayFloat: + gamma: float = 1.0, + cost: Union[Tuple[NDArrayFloat], Callable] = None, + check_cost: Boolean = False, +) -> float: - # For developers and PR: - # final format of fdata1 and fdata2 is required to be FDataGrid, - # sharing the same domain(1D) and codomain dimensions(1D...nD). - # No need for _check_compatible and _cast_to_grid: - # => would raise an error in the following situation: - # if fdata1.domain_range[0] != fdata1.grid_points[0].domain_range[0] - # (sdtw_divergence can deal with different domain_range and grid_points) + # fdata1 and fdata2 are only required to be one-dimensional. + # They can have different (one-dimensional) domain ranges and + # different grid points size - # check whether fdata1 and fdata2 are equivalent _check_input_fdata(fdata1, fdata2) - if isinstance(fdata1, FDataBasis): - # check eval_points - # must be a tuple of one or two one-dim grid - # maybe an existing skfda function does the job ? - _check_input_evalpoints(eval_points) - - if len(eval_points) == 1: - fdata1 = fdata1.to_grid(eval_points[0]) - fdata2 = fdata2.to_grid(eval_points[0]) - - elif len(eval_points) == 2: - fdata1 = fdata1.to_grid(eval_points[0]) - fdata2 = fdata2.to_grid(eval_points[1]) - n1, n2 = fdata1.grid_points[0].size, fdata2.grid_points[0].size if gamma <= 0: raise ValueError( - "gamma was set to {} but must be positive".format(gamma) + f"gamma was set to {gamma} but must be positive" ) - # cost must satisfy: - # shape=(n1, n2), - # nonnegativity, - # indiscernability and symmetry + # cost must satisfy:shape=(n1, n2),nonnegativity,indiscernability + # and symmetry if cost is not None: - if isinstance(cost, List): + if isinstance(cost, tuple): if not len(cost) == 3: raise ValueError( - "If the alignment cost matrices are pre-computed," - " then 'cost' must be a list of three two-dimensional" - " numpy arrays" + "When the alignment cost matrices are pre-computed, " + "then 'cost' must be a list of three two-dimensional " + "numpy arrays" ) else: # shape of cost_12, cost_11 and cost_22 @@ -200,14 +161,13 @@ def _sdtw_divergence( raise ValueError( "The elements of 'cost' must all be " "two-dimensional numpy arrays. " - "The {}-th element does not satisfy the expected " - "format".format(idx) + f"The {idx}-th element does not satisfy the " + "expected format" ) if not c.shape == (n1, n2): raise ValueError( - "Cost matrix must have shape" - " ({}, {})".format(n1, n2) + f"Cost matrix must have shape ({n1}, {n2})" ) _check_shape_postive_cost_mat( @@ -251,8 +211,8 @@ def _sdtw_divergence( else: raise ValueError( "Cost must be either " - " a list of three numpy arrays" - " or a callable that returns a numpy array" + "a list of three numpy arrays " + "or a callable that returns a numpy array" ) else: # default cost: 0.5 * squared Euclidean @@ -344,7 +304,7 @@ class sdtwDivergence(): def __init__( self, gamma: float = 1.0, - cost: Optional[Union[List, ArrayLike]] = None, + cost: Union[Tuple[NDArrayFloat], Callable] = None, ) -> None: self.gamma = gamma @@ -352,8 +312,8 @@ def __init__( def __call__( self, - fdata1: FData, - fdata2: FData, + fdata1: FDataGrid, + fdata2: FDataGrid, *, eval_points: Optional[Union[Tuple, GridPointsLike]] = None, check_cost: Optional[Boolean] = False From 81af9e34f4bd602a2368b1772433699d5d2a144f Mon Sep 17 00:00:00 2001 From: Lejeune Date: Tue, 31 May 2022 16:37:46 +0200 Subject: [PATCH 09/21] corrections asked by mantainers --- docs/refs.bib | 6 +- skfda/misc/metrics/__init__.py | 2 +- skfda/misc/metrics/_sdtw_distances.py | 252 ++++++++++++++------------ skfda/misc/metrics/_sdtw_numba.py | 2 +- 4 files changed, 142 insertions(+), 120 deletions(-) diff --git a/docs/refs.bib b/docs/refs.bib index 24a62a10b..b81791df3 100644 --- a/docs/refs.bib +++ b/docs/refs.bib @@ -397,7 +397,7 @@ @inbook{wasserman_2006_nonparametric_nw } @inbook{wasserman_2006_nonparametric_llr, - author = {Larry Wasserman}, + author = {Larry Wasserman}, title = {All of Nonparametric Statistics}, chapter = {Nonparametric Regression}, pages = {77}, @@ -407,7 +407,7 @@ @inbook{wasserman_2006_nonparametric_llr doi = {10.1007/0-387-30623-4} } -@pnproceedings{Cuturi_2017_sdtw, +@inproceedings{Cuturi_2017_sdtw, title = {Soft-{DTW}: a Differentiable Loss Function for Time-Series}, author = {Marco Cuturi and Mathieu Blondel}, booktitle = {Proceedings of the 34th International Conference on Machine Learning}, @@ -420,7 +420,7 @@ @pnproceedings{Cuturi_2017_sdtw @inproceedings{Blondel_2021_sdtw_div, author = {Blondel, Mathieu and Mensch, Arthur and Vert, Jean-Philippe}, - title = {Differentiable Divergences Between Time Series}, + title = {Differentiable Divergences Between Time Series}, booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics}, pages = {3853 -- 3861}, year = {2021}, diff --git a/skfda/misc/metrics/__init__.py b/skfda/misc/metrics/__init__.py index fcae547c6..5cee75931 100644 --- a/skfda/misc/metrics/__init__.py +++ b/skfda/misc/metrics/__init__.py @@ -23,4 +23,4 @@ pairwise_metric_optimization, ) -from ._sdtw_distances import sdtwDivergence, sdtw_divergence +from ._sdtw_distances import sdtwDivergence diff --git a/skfda/misc/metrics/_sdtw_distances.py b/skfda/misc/metrics/_sdtw_distances.py index 4605dcd87..938043ad1 100644 --- a/skfda/misc/metrics/_sdtw_distances.py +++ b/skfda/misc/metrics/_sdtw_distances.py @@ -3,14 +3,12 @@ """ from __future__ import annotations -from typing import Optional, Union, Callable, Tuple -from numba.core.types.scalars import Boolean +from typing import Dict, Optional, Union, Callable, Tuple import numpy as np -from typing_extensions import Final from ...representation import FDataGrid -from ...representation._typing import NDArrayFloat, GridPointsLike +from ...representation._typing import NDArrayFloat from skfda._utils._utils import _check_compatible_fdata from skfda.misc.metrics import _sdtw_numba @@ -19,8 +17,8 @@ def _check_shape_postive_cost_mat( cost: NDArrayFloat, - expected_shape: Tuple, - shape_only: Boolean = False + expected_shape: Tuple[int, int], + shape_only: bool = False ) -> None: """check that matrix 'cost' is nonnegative and has expected shape""" n1, n2 = expected_shape @@ -37,24 +35,30 @@ def _check_shape_postive_cost_mat( ) -def _check_indiscernable_sym( - cost: NDArrayFloat, - X: NDArrayFloat, - Y: NDArrayFloat +def _check_indiscernable( + cost_XX: NDArrayFloat, + cost_YY: NDArrayFloat, + cost_was_callable: bool = False, ) -> None: """check that cost returns a symmetric matrix with zero diag""" # indiscernability: cost(x_t, x_t) = 0 for any t if ( - np.all(np.diag(cost(X, X)) != 0) - or np.all(np.diag(cost(Y, Y)) != 0) + np.all(np.diag(cost_XX) != 0) + or np.all(np.diag(cost_YY) != 0) ): raise ValueError( "The cost between two identical objects " - "must be zero (i.e cost(X, X) is zero diagonal)" + "must be zero (i.e cost(X, X) must be zero-diagonal)" ) - # symmetry: cost(X, Y) = cost(y, X).T - if not np.allclose(cost(X, Y), cost(Y, X).T): + +def _check_symmetry( + cost_XY: NDArrayFloat, + cost_YX: NDArrayFloat, +) -> None: + """check that cost_XY==cost_YX.T""" + + if not np.allclose(cost_XY, cost_YX.T): raise ValueError( "The cost function does not return a symmetric matrix" ) @@ -79,7 +83,7 @@ def _check_input_fdata( "fdata1 and fdata2 must have their domain dimension equal to one" ) - if not (fdata1.n_samples == 1 & fdata2.n_samples == 1): + if not (fdata1.n_samples == 1 and fdata2.n_samples == 1): raise ValueError( "Both fdata1 and fdata2 must each contain a single sample" ) @@ -102,8 +106,10 @@ def half_sq_euclidean( The distance is taken w.r.t matrix rows. """ if arg2 is not None: - # np.dot(X, Y.T)=inner_product_matrix(X, Y) but np ~1.6 faster - # X.shape is (n_X, d) and Y.shape is (n_Y, d) + # sq_euclidean(X, Y) = + # DotProduct(sigma_0_bounds=(10**-10, 10**10)) = + # diag(np.dot(X, X.T)) + diag(np.dot(Y, Y.T)) - 2*np.dot(X, Y.T) + # np.dot(X, Y.T)=inner_product_matrix(X, Y) cost_12 = -1 * inner_product_matrix(arg1, arg2) # np.sum(X ** 2, axis=1)=inner_product(X, X) @@ -126,8 +132,10 @@ def _sdtw_divergence( fdata2: FDataGrid, *, gamma: float = 1.0, - cost: Union[Tuple[NDArrayFloat], Callable] = None, - check_cost: Boolean = False, + cost: Union[Tuple[NDArrayFloat], Callable[[ + NDArrayFloat, NDArrayFloat, NDArrayFloat]]] = None, + check_cost: bool = False, + **kwargs_cost: Dict ) -> float: # fdata1 and fdata2 are only required to be one-dimensional. @@ -136,104 +144,126 @@ def _sdtw_divergence( _check_input_fdata(fdata1, fdata2) - n1, n2 = fdata1.grid_points[0].size, fdata2.grid_points[0].size + n1, n2 = len(fdata1.grid_points[0]), len(fdata2.grid_points[0]) if gamma <= 0: raise ValueError( f"gamma was set to {gamma} but must be positive" ) - # cost must satisfy:shape=(n1, n2),nonnegativity,indiscernability - # and symmetry - if cost is not None: - if isinstance(cost, tuple): - if not len(cost) == 3: - raise ValueError( - "When the alignment cost matrices are pre-computed, " - "then 'cost' must be a list of three two-dimensional " - "numpy arrays" - ) - else: - # shape of cost_12, cost_11 and cost_22 - expected_shapes = [(n1, n2), (n1, n1), (n2, n2)] - for idx, c in enumerate(cost): - if not (isinstance(c, NDArrayFloat) and c.ndim == 2): - raise ValueError( - "The elements of 'cost' must all be " - "two-dimensional numpy arrays. " - f"The {idx}-th element does not satisfy the " - "expected format" - ) - - if not c.shape == (n1, n2): - raise ValueError( - f"Cost matrix must have shape ({n1}, {n2})" - ) - - _check_shape_postive_cost_mat( - cost=c, - expected_shape=expected_shapes[idx], - shape_only=not(check_cost) - ) - - cost_12, cost_11, cost_22 = cost[0], cost[1], cost[2] - - elif isinstance(cost, Callable): - cost_12 = cost( - fdata1.data_matrix[0, :, :], - fdata2.data_matrix[0, :, :] - ) + # booleans to remember the input format of cost if given + cost_was_tuple = isinstance(cost, tuple) + cost_was_callable = isinstance(cost, Callable) - # check nonnegativity and/or shape - _check_shape_postive_cost_mat( - cost_12, - expected_shape=(n1, n2), - shape_only=not(check_cost) + if cost_was_tuple: + if len(cost) != 3: + raise ValueError( + "When the alignment cost matrices are pre-computed, " + "then 'cost' must be a tuple of three two-dimensional " + "numpy arrays." ) - if check_cost: - # check indiscernability and symmetry - _check_indiscernable_sym( - cost, - fdata1.data_matrix[0, :, :], - fdata2.data_matrix[0, :, :] - ) - - cost_11 = cost( - fdata1.data_matrix[0, :, :], - fdata1.data_matrix[0, :, :] - ) - cost_22 = cost( - fdata2.data_matrix[0, :, :], - fdata2.data_matrix[0, :, :] + elif cost_was_callable: + # pre-computation for the symmetry check + # of the cross-product part of the cost + if check_cost: + cost_21 = cost( + fdata2.data_matrix[0], + fdata1.data_matrix[0], + **kwargs_cost ) - else: - raise ValueError( - "Cost must be either " - "a list of three numpy arrays " - "or a callable that returns a numpy array" + # compute the cost matrices + cost = ( + cost( + fdata1.data_matrix[0], + fdata2.data_matrix[0], + **kwargs_cost + ), + cost( + fdata1.data_matrix[0], + fdata1.data_matrix[0], + **kwargs_cost + ), + cost( + fdata2.data_matrix[0], + fdata2.data_matrix[0], + **kwargs_cost ) + ) - else: # default cost: 0.5 * squared Euclidean - + # cost_12 = cost( + # fdata1.data_matrix[0], + # fdata2.data_matrix[0], + # **kwargs_cost + # ) + # cost_11 = cost( + # fdata1.data_matrix[0], + # fdata1.data_matrix[0], + # **kwargs_cost + # ) + # cost_22 = cost( + # fdata2.data_matrix[0], + # fdata2.data_matrix[0], + # **kwargs_cost + # ) + + # cost = (cost_12, cost_11, cost_22) + + elif cost is None: + # default cost: 0.5 * squared Euclidean: # 0.5 * squared euclidean # or global kernel alignment (depends on gamma !=0) # 0.5 * diag(X@X.T) + 0.5 * diag(Y@Y.T) - X@Y.T - # <=> sq_euclidean = DotProduct(sigma_0_bounds=(10**-10, 10**10)) - # <=> diag(np.dot(X, X.T)) + diag(np.dot(Y, Y.T)) - 2*np.dot(X, Y.T) - cost_11 = half_sq_euclidean(fdata1.data_matrix[0, :, :]) - cost_22 = half_sq_euclidean(fdata2.data_matrix[0, :, :]) - cost_12 = half_sq_euclidean( - fdata1.data_matrix[0, :, :], - fdata2.data_matrix[0, :, :] + + cost = ( + half_sq_euclidean( + fdata1.data_matrix[0], + fdata2.data_matrix[0] + ), + half_sq_euclidean( + fdata1.data_matrix[0], + fdata1.data_matrix[0] + ), + half_sq_euclidean( + fdata2.data_matrix[0], + fdata2.data_matrix[0] + ) ) + else: + raise ValueError( + "Cost must be a tuple containing three numpy arrays " + "or a Callable that returns a numpy array." + ) + + # now for any initial input format of cost, cost has become a 3-tuple + if check_cost and (cost_was_callable or cost_was_tuple): + + expected_shapes = [(n1, n2), (n1, n1), (n2, n2)] + for idx, c in enumerate(cost): + _check_shape_postive_cost_mat( + cost=c, + expected_shape=expected_shapes[idx], + shape_only=False + ) + + _check_indiscernable( + cost_XX=cost[1], + cost_YY=cost[2] + ) + + if cost_was_callable: + _check_symmetry( + cost_XY=cost[0], + cost_YX=cost_21 + ) + # for nonnegativity, symmetry, unicity of div(X,Y)=0 at X=Y return( - _sdtw_numba._sdtw(cost_12, gamma) - - 0.5 * _sdtw_numba._sdtw(cost_11, gamma) - - 0.5 * _sdtw_numba._sdtw(cost_22, gamma) + _sdtw_numba._sdtw(cost[0], gamma) + - 0.5 * _sdtw_numba._sdtw(cost[1], gamma) + - 0.5 * _sdtw_numba._sdtw(cost[2], gamma) ) @@ -276,23 +306,18 @@ class sdtwDivergence(): triangle inequality. See :footcite:`Blondel_2021_sdtw_div`. Args: - fdata1: First FData object. - fdata2: Second FData object. + fdata1: First FDataGrid object. + fdata2: Second FDataGrid object. gamma: smoothing parameter, must be positive. cost: Either a two-dimensional numpy array or a callable. If it is an array, then it must have shape ``(n1, n2)`` where ``n1`` is the grid size of fdata1 and equivalently for - ``n2``. When fdata1 and fdata2 are FDataBasis, then ``cost`` - must be shaped according to the grid size(s) of ``eval_points``. - If it is a callable, then it must take two two-dimensional numpy - arrays (equivalent to the ``data_matirx`` attribute of an - FDataGrid object) as inputs and return a ``(n1, n2)`` numpy array. + ``n2``. If it is a callable, then it must take two + two-dimensional numpy arrays (equivalent to the ``data_matirx`` + attribute of an FDataGrid object) as inputs and return a + ``(n1, n2)`` numpy array. check_cost: Wheter to check the mathematical properties of ``cost`` (function or matrix). - eval_points: Tuple of two one-dimensional numpy arrays with points of - evaluation if fdata1 and fdata2 are FDataBasis. - If the tuple contains a single array, it is used to convert - both fdata1 and fdata2 into FDataGrid objects. Returns: soft Dynamic-Time-Warping divergence value. @@ -304,7 +329,8 @@ class sdtwDivergence(): def __init__( self, gamma: float = 1.0, - cost: Union[Tuple[NDArrayFloat], Callable] = None, + cost: Union[Tuple[NDArrayFloat], Callable[[ + NDArrayFloat, NDArrayFloat, NDArrayFloat]]] = None, ) -> None: self.gamma = gamma @@ -315,8 +341,7 @@ def __call__( fdata1: FDataGrid, fdata2: FDataGrid, *, - eval_points: Optional[Union[Tuple, GridPointsLike]] = None, - check_cost: Optional[Boolean] = False + check_cost: Optional[bool] = False ) -> NDArrayFloat: """Compute the soft-DTW divergence.""" return _sdtw_divergence( @@ -325,7 +350,6 @@ def __call__( gamma=self.gamma, cost=self.cost, check_cost=check_cost, - eval_points=eval_points ) def __repr__(self) -> str: @@ -334,8 +358,6 @@ def __repr__(self) -> str: ) -sdtw_divergence: Final = sdtwDivergence() - # @pairwise_metric_optimization.register # def _pairwise_metric_optimization_sdtw( # metric: sdtwDivergence, diff --git a/skfda/misc/metrics/_sdtw_numba.py b/skfda/misc/metrics/_sdtw_numba.py index 9934faa04..b7dd8a09f 100644 --- a/skfda/misc/metrics/_sdtw_numba.py +++ b/skfda/misc/metrics/_sdtw_numba.py @@ -14,7 +14,7 @@ def _soft_min_argmin(x, y, z): return min_xyz - np.log(nn) -@njit(cache=True, fastmath=True) +@njit(cache=True, fastmath=False) def _sdtw(cost_mat, gamma=1.0): """soft-dtw divergence with dynamic recursion""" From 1881d208f1005982b0749fe5f5d38e00e08cf92b Mon Sep 17 00:00:00 2001 From: Lejeune Date: Wed, 19 Oct 2022 11:32:11 +0200 Subject: [PATCH 10/21] tabs replaced by spaces --- docs/refs.bib | 30 +++++++++++++++--------------- 1 file changed, 15 insertions(+), 15 deletions(-) diff --git a/docs/refs.bib b/docs/refs.bib index b81791df3..7bbd65181 100644 --- a/docs/refs.bib +++ b/docs/refs.bib @@ -408,23 +408,23 @@ @inbook{wasserman_2006_nonparametric_llr } @inproceedings{Cuturi_2017_sdtw, - title = {Soft-{DTW}: a Differentiable Loss Function for Time-Series}, - author = {Marco Cuturi and Mathieu Blondel}, - booktitle = {Proceedings of the 34th International Conference on Machine Learning}, - pages = {894 -- 903}, - year = {2017}, - volume = {70}, - series = {Proceedings of Machine Learning Research}, - publisher = {PMLR}, + title = {Soft-{DTW}: a Differentiable Loss Function for Time-Series}, + author = {Marco Cuturi and Mathieu Blondel}, + booktitle = {Proceedings of the 34th International Conference on Machine Learning}, + pages = {894 -- 903}, + year = {2017}, + volume = {70}, + series = {Proceedings of Machine Learning Research}, + publisher = {PMLR}, } @inproceedings{Blondel_2021_sdtw_div, - author = {Blondel, Mathieu and Mensch, Arthur and Vert, Jean-Philippe}, + author = {Blondel, Mathieu and Mensch, Arthur and Vert, Jean-Philippe}, title = {Differentiable Divergences Between Time Series}, - booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics}, - pages = {3853 -- 3861}, - year = {2021}, - volume = {130}, - series = {Proceedings of Machine Learning Research}, - publisher = {PMLR}, + booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics}, + pages = {3853 -- 3861}, + year = {2021}, + volume = {130}, + series = {Proceedings of Machine Learning Research}, + publisher = {PMLR}, } \ No newline at end of file From bca838490392f9875e2496e0316183ae7513cb9d Mon Sep 17 00:00:00 2001 From: Lejeune Date: Wed, 19 Oct 2022 11:51:53 +0200 Subject: [PATCH 11/21] shape_only parameter removed --- skfda/misc/metrics/_sdtw_distances.py | 17 +++++++---------- 1 file changed, 7 insertions(+), 10 deletions(-) diff --git a/skfda/misc/metrics/_sdtw_distances.py b/skfda/misc/metrics/_sdtw_distances.py index 938043ad1..1bb6ae707 100644 --- a/skfda/misc/metrics/_sdtw_distances.py +++ b/skfda/misc/metrics/_sdtw_distances.py @@ -17,8 +17,7 @@ def _check_shape_postive_cost_mat( cost: NDArrayFloat, - expected_shape: Tuple[int, int], - shape_only: bool = False + expected_shape: Tuple[int, int] ) -> None: """check that matrix 'cost' is nonnegative and has expected shape""" n1, n2 = expected_shape @@ -27,12 +26,11 @@ def _check_shape_postive_cost_mat( raise ValueError( f"Cost matrix must have shape ({n1}, {n2})" ) - # non-negativity - if not(shape_only): - if not np.all(cost >= 0): - raise ValueError( - "Cost matrix must contain non-negative entries" - ) + # non-negativity check + if not np.all(cost >= 0): + raise ValueError( + "Cost matrix must contain non-negative entries" + ) def _check_indiscernable( @@ -244,8 +242,7 @@ def _sdtw_divergence( for idx, c in enumerate(cost): _check_shape_postive_cost_mat( cost=c, - expected_shape=expected_shapes[idx], - shape_only=False + expected_shape=expected_shapes[idx] ) _check_indiscernable( From 2cad642a94975358a6d80abd98f0f4ca53558146 Mon Sep 17 00:00:00 2001 From: Lejeune Date: Wed, 19 Oct 2022 12:28:45 +0200 Subject: [PATCH 12/21] np.all corrected by np.any in indiscernability check --- skfda/misc/metrics/_sdtw_distances.py | 7 +++---- 1 file changed, 3 insertions(+), 4 deletions(-) diff --git a/skfda/misc/metrics/_sdtw_distances.py b/skfda/misc/metrics/_sdtw_distances.py index 1bb6ae707..f93cd1ba6 100644 --- a/skfda/misc/metrics/_sdtw_distances.py +++ b/skfda/misc/metrics/_sdtw_distances.py @@ -35,14 +35,13 @@ def _check_shape_postive_cost_mat( def _check_indiscernable( cost_XX: NDArrayFloat, - cost_YY: NDArrayFloat, - cost_was_callable: bool = False, + cost_YY: NDArrayFloat ) -> None: """check that cost returns a symmetric matrix with zero diag""" # indiscernability: cost(x_t, x_t) = 0 for any t if ( - np.all(np.diag(cost_XX) != 0) - or np.all(np.diag(cost_YY) != 0) + np.any(np.diag(cost_XX) != 0) + or np.any(np.diag(cost_YY) != 0) ): raise ValueError( "The cost between two identical objects " From c4e1af3ca988c2290e5c74eeab264a37aeab21d3 Mon Sep 17 00:00:00 2001 From: Lejeune Date: Wed, 19 Oct 2022 15:03:55 +0200 Subject: [PATCH 13/21] isinstance in if's and new variable for evaluated cost --- skfda/misc/metrics/_sdtw_distances.py | 43 ++++++++++++++------------- 1 file changed, 22 insertions(+), 21 deletions(-) diff --git a/skfda/misc/metrics/_sdtw_distances.py b/skfda/misc/metrics/_sdtw_distances.py index f93cd1ba6..9168bd92f 100644 --- a/skfda/misc/metrics/_sdtw_distances.py +++ b/skfda/misc/metrics/_sdtw_distances.py @@ -3,7 +3,7 @@ """ from __future__ import annotations -from typing import Dict, Optional, Union, Callable, Tuple +from typing import Dict, Optional, Union, Callable, Tuple, Any import numpy as np @@ -132,7 +132,7 @@ def _sdtw_divergence( cost: Union[Tuple[NDArrayFloat], Callable[[ NDArrayFloat, NDArrayFloat, NDArrayFloat]]] = None, check_cost: bool = False, - **kwargs_cost: Dict + **kwargs_cost: Any ) -> float: # fdata1 and fdata2 are only required to be one-dimensional. @@ -148,30 +148,28 @@ def _sdtw_divergence( f"gamma was set to {gamma} but must be positive" ) - # booleans to remember the input format of cost if given - cost_was_tuple = isinstance(cost, tuple) - cost_was_callable = isinstance(cost, Callable) - - if cost_was_tuple: + if isinstance(cost, tuple): if len(cost) != 3: raise ValueError( "When the alignment cost matrices are pre-computed, " "then 'cost' must be a tuple of three two-dimensional " "numpy arrays." ) + + cost_evaluated = cost - elif cost_was_callable: + elif isinstance(cost, callable): # pre-computation for the symmetry check # of the cross-product part of the cost if check_cost: - cost_21 = cost( + cost_evaluated_21 = cost( fdata2.data_matrix[0], fdata1.data_matrix[0], **kwargs_cost ) # compute the cost matrices - cost = ( + cost_evaluated = ( cost( fdata1.data_matrix[0], fdata2.data_matrix[0], @@ -213,7 +211,7 @@ def _sdtw_divergence( # or global kernel alignment (depends on gamma !=0) # 0.5 * diag(X@X.T) + 0.5 * diag(Y@Y.T) - X@Y.T - cost = ( + cost_evaluated = ( half_sq_euclidean( fdata1.data_matrix[0], fdata2.data_matrix[0] @@ -235,31 +233,34 @@ def _sdtw_divergence( ) # now for any initial input format of cost, cost has become a 3-tuple - if check_cost and (cost_was_callable or cost_was_tuple): + if ( + check_cost + and (isinstance(cost, callable) or isinstance(cost, tuple)) + ): expected_shapes = [(n1, n2), (n1, n1), (n2, n2)] - for idx, c in enumerate(cost): + for idx, c in enumerate(cost_evaluated): _check_shape_postive_cost_mat( cost=c, expected_shape=expected_shapes[idx] ) _check_indiscernable( - cost_XX=cost[1], - cost_YY=cost[2] + cost_XX=cost_evaluated[1], + cost_YY=cost_evaluated[2] ) - if cost_was_callable: + if isinstance(cost, callable): _check_symmetry( - cost_XY=cost[0], - cost_YX=cost_21 + cost_XY=cost_evaluated[0], + cost_YX=cost_evaluated_21 ) # for nonnegativity, symmetry, unicity of div(X,Y)=0 at X=Y return( - _sdtw_numba._sdtw(cost[0], gamma) - - 0.5 * _sdtw_numba._sdtw(cost[1], gamma) - - 0.5 * _sdtw_numba._sdtw(cost[2], gamma) + _sdtw_numba._sdtw(cost_evaluated[0], gamma) + - 0.5 * _sdtw_numba._sdtw(cost_evaluated[1], gamma) + - 0.5 * _sdtw_numba._sdtw(cost_evaluated[2], gamma) ) From 24fddea590621b276acf014006166ce48c10ec91 Mon Sep 17 00:00:00 2001 From: Lejeune Date: Wed, 19 Oct 2022 15:20:45 +0200 Subject: [PATCH 14/21] isinstance in if's and new variable for evaluated cost --- skfda/misc/metrics/_sdtw_distances.py | 9 +++++---- 1 file changed, 5 insertions(+), 4 deletions(-) diff --git a/skfda/misc/metrics/_sdtw_distances.py b/skfda/misc/metrics/_sdtw_distances.py index 9168bd92f..519931b89 100644 --- a/skfda/misc/metrics/_sdtw_distances.py +++ b/skfda/misc/metrics/_sdtw_distances.py @@ -158,7 +158,7 @@ def _sdtw_divergence( cost_evaluated = cost - elif isinstance(cost, callable): + elif callable(cost): # pre-computation for the symmetry check # of the cross-product part of the cost if check_cost: @@ -232,10 +232,11 @@ def _sdtw_divergence( "or a Callable that returns a numpy array." ) - # now for any initial input format of cost, cost has become a 3-tuple + # now for any initial input format of cost, cost_evaluated + # is a tuple of three array if ( check_cost - and (isinstance(cost, callable) or isinstance(cost, tuple)) + and (callable(cost) or isinstance(cost, tuple)) ): expected_shapes = [(n1, n2), (n1, n1), (n2, n2)] @@ -250,7 +251,7 @@ def _sdtw_divergence( cost_YY=cost_evaluated[2] ) - if isinstance(cost, callable): + if callable(cost): _check_symmetry( cost_XY=cost_evaluated[0], cost_YX=cost_evaluated_21 From 7d42906570fb27171c4a78cf9c19f31439b7a812 Mon Sep 17 00:00:00 2001 From: Lejeune Date: Wed, 19 Oct 2022 18:14:43 +0200 Subject: [PATCH 15/21] set hse cost as default and constrain callable cost to be computed fdatagrid --- skfda/misc/metrics/_sdtw_distances.py | 122 +++++++++++--------------- 1 file changed, 51 insertions(+), 71 deletions(-) diff --git a/skfda/misc/metrics/_sdtw_distances.py b/skfda/misc/metrics/_sdtw_distances.py index 519931b89..00c6c5ac0 100644 --- a/skfda/misc/metrics/_sdtw_distances.py +++ b/skfda/misc/metrics/_sdtw_distances.py @@ -62,8 +62,8 @@ def _check_symmetry( def _check_input_fdata( - fdata1, - fdata2 + fdata1: FDataGrid, + fdata2: FDataGrid ) -> None: """check compatible, one sample and one-dimensional""" _check_compatible_fdata(fdata1, fdata2) @@ -87,37 +87,56 @@ def _check_input_fdata( def half_sq_euclidean( - arg1: NDArrayFloat, - arg2: Optional[NDArrayFloat] = None, + arg1: FDataGrid, + arg2: Optional[FDataGrid] = None, ) -> NDArrayFloat: """ - Return the half squared Euclidean row distance between - two matrices of size (n1, d) and (n2, d). + Return the half squared distance between sample points of two + FDataGrid objects with possibly different one dimensional grid sizes. Args: - arg1: First sample (n_samples_1, n_features). - arg2: Second sample (n_samples_2, n_features). + arg1: First FDataGrid object. + arg2: Second FDataGrid object. If it is ``None`` returns the half squared Euclidean distance between the rows of ``arg1``. - The distance is taken w.r.t matrix rows. + The distance is only taken w.r.t the data_matrix rows and thus does + not depend on the grid points. """ + if arg2 is not None: - # sq_euclidean(X, Y) = - # DotProduct(sigma_0_bounds=(10**-10, 10**10)) = - # diag(np.dot(X, X.T)) + diag(np.dot(Y, Y.T)) - 2*np.dot(X, Y.T) - # np.dot(X, Y.T)=inner_product_matrix(X, Y) - cost_12 = -1 * inner_product_matrix(arg1, arg2) + # 0.5 * sq_euclidean(X, Y) = + # 0.5 * diag(np.dot(X, X.T)) + # + 0.5 * diag(np.dot(Y, Y.T)) + # - np.dot(X, Y.T) + # where here np.dot(X, Y.T) = inner_product_matrix(X, Y) + cost_12 = -1 * inner_product_matrix( + arg1.data_matrix[0], + arg2.data_matrix[0] + ) # np.sum(X ** 2, axis=1)=inner_product(X, X) - cost_12 += (0.5 * inner_product(arg1, arg1))[:, np.newaxis] - cost_12 += 0.5 * inner_product(arg2, arg2) + cost_12 += (0.5 * inner_product( + arg1.data_matrix[0], + arg1.data_matrix[0] + ))[:, np.newaxis] + cost_12 += 0.5 * inner_product( + arg2.data_matrix[0], + arg2.data_matrix[0] + ) return cost_12 + else: - cost_11 = -1 * inner_product_matrix(arg1, arg2) + cost_11 = -1 * inner_product_matrix( + arg1.data_matrix[0], + arg1.data_matrix[0] + ) # half Sum Of Squares on each row - sos_row = 0.5 * inner_product(arg1, arg1) + sos_row = 0.5 * inner_product( + arg1.data_matrix[0], + arg1.data_matrix[0] + ) cost_11 += sos_row[:, np.newaxis] cost_11 += sos_row @@ -163,69 +182,30 @@ def _sdtw_divergence( # of the cross-product part of the cost if check_cost: cost_evaluated_21 = cost( - fdata2.data_matrix[0], - fdata1.data_matrix[0], + fdata2, + fdata1, **kwargs_cost ) # compute the cost matrices cost_evaluated = ( cost( - fdata1.data_matrix[0], - fdata2.data_matrix[0], + fdata1, + fdata2, **kwargs_cost ), cost( - fdata1.data_matrix[0], - fdata1.data_matrix[0], + fdata1, + fdata1, **kwargs_cost ), cost( - fdata2.data_matrix[0], - fdata2.data_matrix[0], + fdata2, + fdata2, **kwargs_cost ) ) - # cost_12 = cost( - # fdata1.data_matrix[0], - # fdata2.data_matrix[0], - # **kwargs_cost - # ) - # cost_11 = cost( - # fdata1.data_matrix[0], - # fdata1.data_matrix[0], - # **kwargs_cost - # ) - # cost_22 = cost( - # fdata2.data_matrix[0], - # fdata2.data_matrix[0], - # **kwargs_cost - # ) - - # cost = (cost_12, cost_11, cost_22) - - elif cost is None: - # default cost: 0.5 * squared Euclidean: - # 0.5 * squared euclidean - # or global kernel alignment (depends on gamma !=0) - # 0.5 * diag(X@X.T) + 0.5 * diag(Y@Y.T) - X@Y.T - - cost_evaluated = ( - half_sq_euclidean( - fdata1.data_matrix[0], - fdata2.data_matrix[0] - ), - half_sq_euclidean( - fdata1.data_matrix[0], - fdata1.data_matrix[0] - ), - half_sq_euclidean( - fdata2.data_matrix[0], - fdata2.data_matrix[0] - ) - ) - else: raise ValueError( "Cost must be a tuple containing three numpy arrays " @@ -257,7 +237,7 @@ def _sdtw_divergence( cost_YX=cost_evaluated_21 ) - # for nonnegativity, symmetry, unicity of div(X,Y)=0 at X=Y + # for nonnegativity, symmetry, unicity of sdtw_div(X,Y)=0 at X=Y return( _sdtw_numba._sdtw(cost_evaluated[0], gamma) - 0.5 * _sdtw_numba._sdtw(cost_evaluated[1], gamma) @@ -328,18 +308,18 @@ def __init__( self, gamma: float = 1.0, cost: Union[Tuple[NDArrayFloat], Callable[[ - NDArrayFloat, NDArrayFloat, NDArrayFloat]]] = None, + NDArrayFloat, NDArrayFloat, NDArrayFloat]]] = half_sq_euclidean, + check_cost: Optional[bool] = False ) -> None: self.gamma = gamma self.cost = cost + self.check_cost = check_cost def __call__( self, fdata1: FDataGrid, - fdata2: FDataGrid, - *, - check_cost: Optional[bool] = False + fdata2: FDataGrid ) -> NDArrayFloat: """Compute the soft-DTW divergence.""" return _sdtw_divergence( @@ -347,7 +327,7 @@ def __call__( fdata2, gamma=self.gamma, cost=self.cost, - check_cost=check_cost, + check_cost=self.check_cost, ) def __repr__(self) -> str: From 6c9ed49739921c7e9d44b30dab8857c91f43f283 Mon Sep 17 00:00:00 2001 From: Lejeune Date: Thu, 20 Oct 2022 12:33:35 +0200 Subject: [PATCH 16/21] remove fastmath --- skfda/misc/metrics/_sdtw_numba.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/skfda/misc/metrics/_sdtw_numba.py b/skfda/misc/metrics/_sdtw_numba.py index b7dd8a09f..b48c7998c 100644 --- a/skfda/misc/metrics/_sdtw_numba.py +++ b/skfda/misc/metrics/_sdtw_numba.py @@ -14,7 +14,7 @@ def _soft_min_argmin(x, y, z): return min_xyz - np.log(nn) -@njit(cache=True, fastmath=False) +@njit(cache=True) def _sdtw(cost_mat, gamma=1.0): """soft-dtw divergence with dynamic recursion""" From 07bc96626a82e73f7dd6c35729c2b5023a9a2d3f Mon Sep 17 00:00:00 2001 From: Lejeune Date: Thu, 20 Oct 2022 16:04:14 +0200 Subject: [PATCH 17/21] make hse cost function more concise --- skfda/misc/metrics/_sdtw_distances.py | 70 ++++++++++++++------------- 1 file changed, 37 insertions(+), 33 deletions(-) diff --git a/skfda/misc/metrics/_sdtw_distances.py b/skfda/misc/metrics/_sdtw_distances.py index 00c6c5ac0..053bf8b50 100644 --- a/skfda/misc/metrics/_sdtw_distances.py +++ b/skfda/misc/metrics/_sdtw_distances.py @@ -3,14 +3,13 @@ """ from __future__ import annotations -from typing import Dict, Optional, Union, Callable, Tuple, Any +from typing import Optional, Union, Callable, Tuple, Any +from ...typing._numpy import NDArrayFloat import numpy as np from ...representation import FDataGrid -from ...representation._typing import NDArrayFloat -from skfda._utils._utils import _check_compatible_fdata from skfda.misc.metrics import _sdtw_numba from skfda.misc._math import inner_product_matrix, inner_product @@ -66,11 +65,22 @@ def _check_input_fdata( fdata2: FDataGrid ) -> None: """check compatible, one sample and one-dimensional""" - _check_compatible_fdata(fdata1, fdata2) + + if (fdata1.dim_domain != fdata2.dim_domain): + raise ValueError( + f"Functional data has incompatible domain dimensions: " + f"{fdata1.dim_domain} != {fdata2.dim_domain}", + ) + + if (fdata1.dim_codomain != fdata2.dim_codomain): + raise ValueError( + f"Functional data has incompatible codomain dimensions: " + f"{fdata1.dim_codomain} != {fdata2.dim_codomain}", + ) if not isinstance(fdata1, FDataGrid): raise ValueError( - "fdata1 and fdata2 must be FDataGrid objects" + "fdata1 and fdata2 must be FDataGrid objects." ) # dim_codomain can be higher than one, @@ -104,43 +114,37 @@ def half_sq_euclidean( not depend on the grid points. """ + # np.sum(X ** 2, axis=1)=inner_product(X, X) + cost_11 = 0.5 * inner_product( + arg1.data_matrix[0], + arg1.data_matrix[0] + ) + + # 0.5 * sq_euclidean(X, Y)= + # 0.5 * diag(np.dot(X, X.T)) + # + 0.5 * diag(np.dot(Y, Y.T)) + # - np.dot(X, Y.T) + # where np.dot(X, Y.T)=inner_product_matrix(X, Y) if arg2 is not None: - # 0.5 * sq_euclidean(X, Y) = - # 0.5 * diag(np.dot(X, X.T)) - # + 0.5 * diag(np.dot(Y, Y.T)) - # - np.dot(X, Y.T) - # where here np.dot(X, Y.T) = inner_product_matrix(X, Y) - cost_12 = -1 * inner_product_matrix( - arg1.data_matrix[0], - arg2.data_matrix[0] - ) - # np.sum(X ** 2, axis=1)=inner_product(X, X) - cost_12 += (0.5 * inner_product( - arg1.data_matrix[0], - arg1.data_matrix[0] - ))[:, np.newaxis] - cost_12 += 0.5 * inner_product( + cost = -1 * inner_product_matrix( arg2.data_matrix[0], - arg2.data_matrix[0] + arg1.data_matrix[0] ) - return cost_12 + cost += (0.5 * inner_product( + arg2.data_matrix[0], + arg2.data_matrix[0] + ))[:, np.newaxis] else: - cost_11 = -1 * inner_product_matrix( + cost = -1 * inner_product_matrix( arg1.data_matrix[0], arg1.data_matrix[0] ) - # half Sum Of Squares on each row - sos_row = 0.5 * inner_product( - arg1.data_matrix[0], - arg1.data_matrix[0] - ) - cost_11 += sos_row[:, np.newaxis] - cost_11 += sos_row + cost += cost_11[:, np.newaxis] - return cost_11 + return cost + cost_11 def _sdtw_divergence( @@ -174,7 +178,7 @@ def _sdtw_divergence( "then 'cost' must be a tuple of three two-dimensional " "numpy arrays." ) - + cost_evaluated = cost elif callable(cost): @@ -212,7 +216,7 @@ def _sdtw_divergence( "or a Callable that returns a numpy array." ) - # now for any initial input format of cost, cost_evaluated + # now for any initial input format of cost, cost_evaluated # is a tuple of three array if ( check_cost From a54d0cf11951a2d6fb3c18fc6859ffd344b572c7 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Carlos=20Ramos=20Carre=C3=B1o?= Date: Thu, 3 Nov 2022 13:12:35 +0100 Subject: [PATCH 18/21] Remove extra quotation mark --- skfda/misc/metrics/_sdtw_distances.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/skfda/misc/metrics/_sdtw_distances.py b/skfda/misc/metrics/_sdtw_distances.py index 053bf8b50..880b60835 100644 --- a/skfda/misc/metrics/_sdtw_distances.py +++ b/skfda/misc/metrics/_sdtw_distances.py @@ -1,4 +1,4 @@ -"""" +""" Implementation of soft Dynamic-Time-Warping (sDTW) divergence. """ from __future__ import annotations From 98e7dbb50ebe7d895da594869bd0bb0c55843691 Mon Sep 17 00:00:00 2001 From: Lejeune Date: Thu, 19 Jan 2023 13:49:17 +0100 Subject: [PATCH 19/21] add comment --- skfda/misc/_math.py | 1 - skfda/misc/metrics/_sdtw_distances.py | 6 +----- 2 files changed, 1 insertion(+), 6 deletions(-) diff --git a/skfda/misc/_math.py b/skfda/misc/_math.py index 8f3460980..59ce58f72 100644 --- a/skfda/misc/_math.py +++ b/skfda/misc/_math.py @@ -328,7 +328,6 @@ def inner_product( elif isinstance(arg1, np.ndarray) and isinstance(arg2, np.ndarray): return ( # type: ignore[no-any-return] np.dot(arg1, arg2.T) - # np.einsum('n...,m...->nm...', arg1, arg2).sum(axis=-1) if _matrix else (arg1 * arg2).sum(axis=-1) ) diff --git a/skfda/misc/metrics/_sdtw_distances.py b/skfda/misc/metrics/_sdtw_distances.py index 880b60835..40b7e78ae 100644 --- a/skfda/misc/metrics/_sdtw_distances.py +++ b/skfda/misc/metrics/_sdtw_distances.py @@ -1,6 +1,4 @@ -""" -Implementation of soft Dynamic-Time-Warping (sDTW) divergence. -""" +""" Implementation ofsoft Dynamic-Time-Warping (sDTW) divergence.""" from __future__ import annotations from typing import Optional, Union, Callable, Tuple, Any @@ -83,8 +81,6 @@ def _check_input_fdata( "fdata1 and fdata2 must be FDataGrid objects." ) - # dim_codomain can be higher than one, - # but dim_domain must be one if not fdata1.dim_domain == 1: raise ValueError( "fdata1 and fdata2 must have their domain dimension equal to one" From 9ca71d1bd7d554a3cd09fa846267bb523f36e8b8 Mon Sep 17 00:00:00 2001 From: Lejeune Date: Mon, 6 Feb 2023 13:08:36 +0100 Subject: [PATCH 20/21] add type annotations --- skfda/misc/metrics/_sdtw_numba.py | 12 ++++++++++-- 1 file changed, 10 insertions(+), 2 deletions(-) diff --git a/skfda/misc/metrics/_sdtw_numba.py b/skfda/misc/metrics/_sdtw_numba.py index b48c7998c..0633bc7e0 100644 --- a/skfda/misc/metrics/_sdtw_numba.py +++ b/skfda/misc/metrics/_sdtw_numba.py @@ -1,9 +1,14 @@ import numpy as np from numba import njit +from ...typing._numpy import NDArrayFloat @njit(cache=True, fastmath=True) -def _soft_min_argmin(x, y, z): +def _soft_min_argmin( + x: float, + y: float, + z: float +) -> float: """soft-min of three real numbers""" min_xyz = np.minimum(x, np.minimum(y, z)) @@ -15,7 +20,10 @@ def _soft_min_argmin(x, y, z): @njit(cache=True) -def _sdtw(cost_mat, gamma=1.0): +def _sdtw( + cost_mat: NDArrayFloat, + gamma: float = 1.0 +) -> float: """soft-dtw divergence with dynamic recursion""" len_x = cost_mat.shape[0] From f43c73bfc3cb130e3316ae352269f0971affd532 Mon Sep 17 00:00:00 2001 From: Lejeune Date: Mon, 6 Feb 2023 15:28:53 +0100 Subject: [PATCH 21/21] pep8 corrections --- skfda/misc/_math.py | 1 - 1 file changed, 1 deletion(-) diff --git a/skfda/misc/_math.py b/skfda/misc/_math.py index 6380de40e..59deb318b 100644 --- a/skfda/misc/_math.py +++ b/skfda/misc/_math.py @@ -675,4 +675,3 @@ def cosine_similarity_matrix( return _clip_cosine( inner_matrix / norm1[:, np.newaxis] / norm2[np.newaxis, :], ) - \ No newline at end of file