Adding memModel Trees and some code correction (#161)

* Adding memModel Trees and some code correction

 - memModel Trees (Unit Tests to do)
 - Adding matrix rotation for PCA (tests available)
 - simplifying code for vModel

TO DO (to complete 0.7.0):
 - tests for trees
 - memModel for Naive Bayes (+ tests)

* Adding tests for trees

TO DO:
test for the SQL syntax in vDataFrame

* copyedits

* reword

* Update memmodel.py

Co-authored-by: kxu <[email protected]>

verticapy/learn/tools.py

@@ -54,6 +54,8 @@
 
 # Standard Python Modules
 import numpy as np
+from numpy import eye, asarray, dot, sum, diag
+from numpy.linalg import svd
 from typing import Union
 
 #
@@ -635,4 +637,52 @@ def load_model(name: str, cursor=None, input_relation: str = "", test_relation:
             model.classes_ = [0, 1]
         if model_type in ("svm_classifier", "svm_regressor", "logistic_reg", "linear_reg",):
             model.coef_ = model.get_attr("details")
-    return model
+    return model
+
+# ---#
+# This piece of code was taken from
+# https://en.wikipedia.org/wiki/Talk:Varimax_rotation
+def matrix_rotation(Phi: list, 
+					gamma: float = 1.0, 
+					q: int = 20, 
+					tol: float = 1e-6):
+    """
+---------------------------------------------------------------------------
+Performs a Oblimin (Varimax, Quartimax) rotation on the the model's 
+PCA matrix.
+
+Parameters
+----------
+Phi: list / numpy.array
+	input matrix.
+gamma: float, optional
+    Oblimin rotation factor, determines the type of rotation.
+    It must be between 0.0 and 1.0.
+        gamma = 0.0 results in a Quartimax rotation.
+        gamma = 1.0 results in a Varimax rotation.
+q: int, optional
+	Maximum number of iterations.
+tol: float, optional
+    The algorithm stops when the Frobenius norm of gradient is less than tol.
+
+Returns
+-------
+model
+    The model.
+    """
+    check_types([("Phi", Phi, [list,],),
+    			 ("gamma", gamma, [int, float,],),
+    			 ("q", q, [int, float,],),
+    			 ("tol", tol, [int, float,],),])
+    Phi = np.array(Phi)
+    p,k = Phi.shape
+    R = eye(k)
+    d=0
+    for i in range(q):
+        d_old = d
+        Lambda = dot(Phi, R)
+        u,s,vh = svd(dot(Phi.T,asarray(Lambda)**3 - (gamma/p) * dot(Lambda, diag(diag(dot(Lambda.T,Lambda))))))
+        R = dot(u,vh)
+        d = sum(s)
+        if d_old!=0 and d/d_old < 1 + tol: break
+    return dot(Phi, R)

verticapy/learn/vmodel.py

@@ -51,7 +51,6 @@
 # Standard Python Modules
 import os, warnings
 import numpy as np
-from collections.abc import Iterable
 from typing import Union
 
 # VerticaPy Modules
@@ -2387,10 +2386,8 @@ def to_python(self, name: str = "predict", return_proba: bool = False, return_di
         func = "def {}(X):\n\timport numpy as np\n\t".format(name)
         if self.type in ("LinearRegression", "LinearSVR", "LogisticRegression", "LinearSVC",):
             result = "{} + np.sum(np.array({}) * np.array(X), axis=1)".format(self.coef_["coefficient"][0], self.coef_["coefficient"][1:])
-            if self.type in ("LogisticRegression",):
+            if self.type in ("LogisticRegression", "LinearSVC",):
                 func += f"result = 1 / (1 + np.exp(- ({result})))"
-            elif self.type in ("LinearSVC",):
-                func += f"result =  1 - 1 / (1 + np.exp({result}))"
             else:
                 func += "result =  " + result
             if return_proba and self.type in ("LogisticRegression", "LinearSVC",):

verticapy/stats/tools.py

@@ -635,16 +635,16 @@ def het_breuschpagan(
 ):
     """
 ---------------------------------------------------------------------------
-Breusch-Pagan test for heteroscedasticity.
+Uses the Breusch-Pagan to test a model for heteroskedasticity.
 
 Parameters
 ----------
 vdf: vDataFrame
     Input vDataFrame.
 eps: str
-    Input residual vcolumn.
+    Input residual vColumn.
 X: list
-    Exogenous Variables to test the heteroscedasticity on.
+    The exogenous variables to test.
 
 Returns
 -------