Add northness and eastness functions (#1039)

README.md

@@ -279,6 +279,8 @@ In the GIS world, rasters are used for representing continuous phenomena (e.g. e
 | Name | Description | Source | NumPy xr.DataArray | Dask xr.DataArray | CuPy GPU xr.DataArray | Dask GPU xr.DataArray |
 |:----------:|:------------|:------:|:----------------------:|:--------------------:|:-------------------:|:------:|
 | [Aspect](xrspatial/aspect.py) | Computes downslope direction of each cell in degrees | Horn 1981 | ✅️ | ✅️ | ✅️ | ✅️ |
+| [Northness](xrspatial/aspect.py) | North-south component of aspect: cos(aspect) for linear models | Stage 1976 | ✅️ | ✅️ | ✅️ | ✅️ |
+| [Eastness](xrspatial/aspect.py) | East-west component of aspect: sin(aspect) for linear models | Stage 1976 | ✅️ | ✅️ | ✅️ | ✅️ |
 | [Curvature](xrspatial/curvature.py) | Measures rate of slope change (concavity/convexity) at each cell | Zevenbergen & Thorne 1987 | ✅️ |✅️ |✅️ | ✅️  |
 | [Hillshade](xrspatial/hillshade.py) | Simulates terrain illumination from a given sun angle and azimuth | GDAL gdaldem | ✅️ | ✅️ | ✅️ | ✅️ |
 | [Roughness](xrspatial/terrain_metrics.py) | Computes local relief as max minus min elevation in a 3×3 window | GDAL gdaldem | ✅️ | ✅️ | ✅️ | ✅️ |

docs/source/reference/surface.rst

@@ -11,6 +11,20 @@ Aspect
 
     xrspatial.aspect.aspect
 
+Northness
+=========
+.. autosummary::
+    :toctree: _autosummary
+
+    xrspatial.aspect.northness
+
+Eastness
+========
+.. autosummary::
+    :toctree: _autosummary
+
+    xrspatial.aspect.eastness
+
 Curvature
 =========
 .. autosummary::

xrspatial/__init__.py

@@ -1,4 +1,6 @@
 from xrspatial.aspect import aspect  # noqa
+from xrspatial.aspect import eastness  # noqa
+from xrspatial.aspect import northness  # noqa
 from xrspatial.balanced_allocation import balanced_allocation  # noqa
 from xrspatial.bilateral import bilateral  # noqa
 from xrspatial.contour import contours  # noqa

xrspatial/aspect.py

@@ -437,3 +437,155 @@ def aspect(agg: xr.DataArray,
                         coords=agg.coords,
                         dims=agg.dims,
                         attrs=agg.attrs)
+
+
+@supports_dataset
+def northness(agg: xr.DataArray,
+              name: Optional[str] = 'northness',
+              method: str = 'planar',
+              z_unit: str = 'meter',
+              boundary: str = 'nan') -> xr.DataArray:
+    """
+    Computes the north-south component of aspect.
+
+    Returns ``cos(aspect)`` for each cell, ranging from +1 (due north)
+    to -1 (due south).  Flat cells (where ``aspect()`` returns -1) are
+    set to NaN.
+
+    This is the standard way to encode aspect for use in regression,
+    clustering, and other models that assume linear inputs.  Raw aspect
+    in degrees is circular (0 and 360 are the same direction), so
+    feeding it directly into a linear model gives wrong results.
+
+    Parameters
+    ----------
+    agg : xarray.DataArray or xr.Dataset
+        2D elevation raster (NumPy, CuPy, Dask, or Dask+CuPy backed).
+        If a Dataset is passed, the operation is applied to each
+        data variable independently.
+    name : str, default='northness'
+        Name of output DataArray.
+    method : str, default='planar'
+        Passed to :func:`aspect`.  ``'planar'`` or ``'geodesic'``.
+    z_unit : str, default='meter'
+        Passed to :func:`aspect`.  Only used when ``method='geodesic'``.
+    boundary : str, default='nan'
+        Passed to :func:`aspect`.  ``'nan'``, ``'nearest'``,
+        ``'reflect'``, or ``'wrap'``.
+
+    Returns
+    -------
+    northness_agg : xarray.DataArray or xr.Dataset
+        Values in [-1, +1].  NaN where the input has NaN or where
+        the surface is flat.
+
+    References
+    ----------
+    Stage, A.R. (1976). "An Expression for the Effect of Aspect, Slope,
+    and Habitat Type on Tree Growth." *Forest Science* 22(4): 457-460.
+
+    Examples
+    --------
+    .. sourcecode:: python
+
+        >>> import numpy as np
+        >>> import xarray as xr
+        >>> from xrspatial import northness
+
+        >>> data = np.array([
+            [1, 1, 1, 1, 1],
+            [1, 1, 1, 2, 0],
+            [1, 1, 1, 0, 0],
+            [4, 4, 9, 2, 4],
+            [1, 5, 0, 1, 4],
+            [1, 5, 0, 5, 5]
+        ], dtype=np.float32)
+        >>> raster = xr.DataArray(data, dims=['y', 'x'])
+        >>> north = northness(raster)
+    """
+    asp = aspect(agg, name='_aspect', method=method, z_unit=z_unit,
+                 boundary=boundary)
+    asp_data = asp.data
+    trig = np.cos(np.deg2rad(asp_data))
+    out = np.where(asp_data == -1, np.nan, trig)
+    return xr.DataArray(out,
+                        name=name,
+                        coords=agg.coords,
+                        dims=agg.dims,
+                        attrs=agg.attrs)
+
+
+@supports_dataset
+def eastness(agg: xr.DataArray,
+             name: Optional[str] = 'eastness',
+             method: str = 'planar',
+             z_unit: str = 'meter',
+             boundary: str = 'nan') -> xr.DataArray:
+    """
+    Computes the east-west component of aspect.
+
+    Returns ``sin(aspect)`` for each cell, ranging from +1 (due east)
+    to -1 (due west).  Flat cells (where ``aspect()`` returns -1) are
+    set to NaN.
+
+    This is the standard way to encode aspect for use in regression,
+    clustering, and other models that assume linear inputs.  Raw aspect
+    in degrees is circular (0 and 360 are the same direction), so
+    feeding it directly into a linear model gives wrong results.
+
+    Parameters
+    ----------
+    agg : xarray.DataArray or xr.Dataset
+        2D elevation raster (NumPy, CuPy, Dask, or Dask+CuPy backed).
+        If a Dataset is passed, the operation is applied to each
+        data variable independently.
+    name : str, default='eastness'
+        Name of output DataArray.
+    method : str, default='planar'
+        Passed to :func:`aspect`.  ``'planar'`` or ``'geodesic'``.
+    z_unit : str, default='meter'
+        Passed to :func:`aspect`.  Only used when ``method='geodesic'``.
+    boundary : str, default='nan'
+        Passed to :func:`aspect`.  ``'nan'``, ``'nearest'``,
+        ``'reflect'``, or ``'wrap'``.
+
+    Returns
+    -------
+    eastness_agg : xarray.DataArray or xr.Dataset
+        Values in [-1, +1].  NaN where the input has NaN or where
+        the surface is flat.
+
+    References
+    ----------
+    Stage, A.R. (1976). "An Expression for the Effect of Aspect, Slope,
+    and Habitat Type on Tree Growth." *Forest Science* 22(4): 457-460.
+
+    Examples
+    --------
+    .. sourcecode:: python
+
+        >>> import numpy as np
+        >>> import xarray as xr
+        >>> from xrspatial import eastness
+
+        >>> data = np.array([
+            [1, 1, 1, 1, 1],
+            [1, 1, 1, 2, 0],
+            [1, 1, 1, 0, 0],
+            [4, 4, 9, 2, 4],
+            [1, 5, 0, 1, 4],
+            [1, 5, 0, 5, 5]
+        ], dtype=np.float32)
+        >>> raster = xr.DataArray(data, dims=['y', 'x'])
+        >>> east = eastness(raster)
+    """
+    asp = aspect(agg, name='_aspect', method=method, z_unit=z_unit,
+                 boundary=boundary)
+    asp_data = asp.data
+    trig = np.sin(np.deg2rad(asp_data))
+    out = np.where(asp_data == -1, np.nan, trig)
+    return xr.DataArray(out,
+                        name=name,
+                        coords=agg.coords,
+                        dims=agg.dims,
+                        attrs=agg.attrs)