Small improvements to Matrix and regression

matrix.py:
- defined power operator for Matrix to perform elementwise raise to power
- added method for entry-wise p-norm

regression.py:
- improved iteratively reweighted LS method

main.py

@@ -174,6 +174,6 @@
 # define the measurements
 y = Matrix([[0],[1],[2]])
 
-theta = regression.irls(H, y, threshold = 1e-12)
+theta = regression.fit_irls(H, y, p=2, threshold = 1e-12)
 
 print(theta)

mola/matrix.py

@@ -87,6 +87,16 @@ def __iter__(self):
         else:
             return iter(self.data)
 
+    def __pow__(self,exponent):
+        n = self.get_height()
+        m = self.get_width()
+        mat = Matrix(n,m,0)
+
+        for i in range(n):
+            for j in range(m):
+                mat[i,j] = self.data[i][j]**exponent
+        return mat
+
     def __abs__(self):
         """
         Return the absolute value of a 1x1 matrix (i.e., a matrix with just one element).
@@ -980,6 +990,22 @@ def norm_Euclidean(self) -> float:
             for j in range(self.n_cols):
                 norm = norm + pow(self.data[i][j],2)
         return math.sqrt(norm)
+
+    def norm_entrywise(self,p=2) -> float:
+        """
+        Return the entry-wise norm of the matrix with a given p.
+        
+        Arguments:
+        p -- float: the exponential of the norm (default 2, where the norm is the Frobenius norm)
+        """
+        n = self.get_height()
+        m = self.get_width()
+        s = 0
+
+        for i in range(n):
+            for j in range(m):
+                s += (abs(self.data[i][j])**p)**(1/p)
+        return s
 
     # doesn't seem to work
     def get_dominant_eigenvector(self):

mola/regression.py

@@ -1,5 +1,5 @@
 from mola.matrix import Matrix
-from mola.utils import identity, ones, zeros, randoms, covmat, diag
+from mola.utils import identity, ones, zeros, randoms, diag
 from copy import deepcopy
 
 def linear_least_squares(H: Matrix, z: Matrix, W=None):
@@ -23,35 +23,40 @@ def linear_least_squares(H: Matrix, z: Matrix, W=None):
     th_tuple = (th.get(0,0), th.get(1,0))
     return th_tuple
 
-def irls(H: Matrix, z: Matrix, threshold = 1e-6):
+def fit_irls(H: Matrix, z: Matrix, p: int = 2, threshold: float = 1e-6):
     """
     Return the iteratively reweighted least squares (IRLS) estimate of the parameters of a model defined by observation matrix H and dependent values z.
     
     Arguments:
     H -- Matrix: the observation matrix of the linear system of equations
     z -- Matrix: the observed or dependent values depicting the right side of the linear system of equations
+    p -- float: norm exponential (default 2)
+    threshold -- float: the maximum difference between two consecutive estimate sets to break from iteration
     """
 
     # estimate the parameters using ordinary least squares
     th = ((H.get_transpose())*H).get_inverse() * H.get_transpose() * z
 
 
     difference = float('inf')
+    delta = 1e-5
 
     while difference > threshold:
 
+        th_previous = th
+
         # calculate absolute values of residuals
-        residuals = (H*th-z).get_absolute_matrix()
-
-        # estimate sample variance-covariance matrix V using the OLS residuals
-        #V = covmat(residuals)
+        residuals = ((H*th-z).get_absolute_matrix())**(p-2)
+
+        # formulate weighting matrix W as the diagonal of the residuals
         W = diag(residuals)
         print("W: ", W)
 
         # re-estimate the parameters using generalized least squares
         th = ((H.get_transpose())*W*H).get_inverse() * H.get_transpose() * W * z
 
-        difference = residuals.norm_Euclidean()
+        difference = (th-th_previous).norm_entrywise(p)
+        print("diff: ", difference)
 
     th_tuple = tuple(th.get_column(0))
     return th_tuple