Rewrite matrix.py to match test_serial.py and to be less dependent on numpy

src/matrix.py

@@ -1,3 +1,5 @@
+import math
+
 import numpy
 from numpy import linalg
 
@@ -6,16 +8,18 @@ class Matrix:
     """
     This Matrix class represents a real 2D-matrix.
     """
-    __data__: numpy.ndarray
+    __data__: list
     __shape__: (int, int)
 
-    def __init__(self, data=None, shape=None, structure=None, model=None, n=None):
+    def __init__(self, data=None, shape=None, structure=None, model=None, offset=None, n=None):
         """
         Creates a new matrix.
-        Thy type of the matrix depends on the signature and arguments.
+        The type of the matrix depends on the signature and arguments.
 
+        - ``Matrix(list)``: will create a new matrix with the given data in the list and its shape.
         - ``Matrix(numpy.ndarray)``: will create a new matrix with the given data in ndarray and its shape.
         - ``Matrix(list, (int,int))``: will create a new nxm matrix with the given rows and columns and data in list.
+        - ``Matrix(list, str, int, int)``: will create a new square matrix of given size and structure of \"diagonal\"
         - ``Matrix(list, str, int)``: will create a new square matrix of given size and structure of either \"unity\", \"diagonal\" or \"tridiagonal\"
         - ``Matrix(str, int)``: will create a new square matrix of given size and TODO
 
@@ -24,12 +28,14 @@ class Matrix:
         :param shape: A tuple containing the amount of rows and columns
         :param structure: Either \"unity\", \"diagonal\" or \"tridiagonal\"
         :param model: TODO
+        :param offset: Offset to diagonal axis
         :param n: Amount of rows of a square matrix or offset in case of diagonal structure
 
         :type data: list | numpy.ndarray
         :type shape: (int, int)
         :type structure: str
         :type model: str
+        :type offset: int
         :type n: int
 
         :rtype: Matrix
@@ -37,41 +43,46 @@ class Matrix:
         # Case Matrix(str, int)
         if n is not None and model is not None:
             ...  # TODO: what shall one do here?
+        # Case: Matrix(list, str, int, int)
+        elif n is not None and offset is not None and structure == "diagonal" and data is not None:
+            diag = numpy.diag(data * (n - abs(offset)), offset)
+            self.__data__ = diag.tolist()
+            self.__shape__ = diag.shape
         # Case: Matrix(list, str, int)
         elif n is not None and structure is not None and data is not None:
             if structure == "unity":
                 ...  # TODO: what does it mean?
-            elif structure == "diagonal":
-                diag = numpy.diag(data, n)
-                self.__data__ = diag
-                self.__shape__ = diag.shape
             elif structure == "tridiagonal":
                 if len(data) != 3:
                     raise ValueError("If structure is tridiagonal, then the given data must be of length 3")
                 tridiag = numpy.diag([data[0]] * (n - 1), -1) + numpy.diag([data[1]] * n, 0) + numpy.diag(
                     [data[2]] * (n - 1), 1)
-                self.__data__ = tridiag
+                self.__data__ = tridiag.tolist()
                 self.__shape__ = tridiag.shape
-        # Case: Matrix(list, str, int)
+        # Case: Matrix(list, (int,int))
         elif shape is not None and data is not None:
             self.__shape__ = shape
-            self.__data__ = numpy.array(data).reshape(shape)
+            self.__data__ = numpy.array(data).reshape(shape).tolist()
-        # Case: Matrix(numpy.ndarray)
+        # Case: Matrix(numpy.ndarray) or Matrix(list)
         elif data is not None:
+            if isinstance(data, numpy.ndarray):
                 try:
                     data.shape[1]
                 except IndexError:
                     self.__shape__ = (data.shape[0], 1)
                 else:
-                self.__shape__ = data.shape
+                    self.__shape__ = (data.shape[0], data.shape[1])
+            elif isinstance(data, list):
+                self.__shape__ = (len(data), len(data[0]))
             self.__data__ = data
         else:
             raise ValueError(
-                "Only following signatures are allowed: (numpy.ndarray), (list, tuple), (list, str, int), (str, int)")
+                "Only following signatures are allowed: "
+                "(list), (numpy.ndarray), (list, tuple), (list, str, int), (list, str, int, int), (str, int)")
 
     def get_data(self):
         """
-        :return: the data of the matrix as a ``numpy.ndarray``
+        :return: the data of the matrix as a ``list``
         """
         return self.__data__
 
@@ -85,7 +96,16 @@ class Matrix:
         """
         :return: the transpose of the matrix
         """
-        return Matrix(self.__data__.transpose())
+        rows = self.__shape__[0]
+        cols = self.__shape__[1]
+
+        transposed_data = [[0 for _ in range(rows)] for _ in range(cols)]
+
+        for i in range(rows):
+            for j in range(cols):
+                transposed_data[j][i] = self.__data__[i][j]
+
+        return Matrix(transposed_data, (cols, rows))
 
     def T(self):
         """
@@ -103,28 +123,49 @@ class Matrix:
         :return: True if data in the matrix are equal to the given data in other for each component, otherwise False
         """
         if isinstance(other, Matrix):
-            to_compare = other.__data__
+            data_to_compare = other.__data__
+            if self.__shape__ != other.__shape__:
+                return False
         elif isinstance(other, list):
-            to_compare = numpy.array(other)
+            data_to_compare = other
+            if self.__shape__[0] != len(other) or self.__shape__[1] != len(other[0]):
+                return False
         elif isinstance(other, numpy.ndarray):
-            to_compare = other
+            data_to_compare = other.tolist()
         else:
             raise ValueError("Matrix type is not comparable to type of given ``other``")
-        return (self.__data__ == to_compare).all()
+
+        for i in range(len(self.__data__)):
+            for j in range(len(self.__data__[i])):
+                if self.__data__[i][j] != data_to_compare[i][j]:
+                    return False
+        return True
 
     def __str__(self):
-        return str(self.__data__)
+        return str(numpy.array(self.__data__))
 
     def __neg__(self):
-        return Matrix(-self.__data__)
+        rows = range(self.__shape__[0])
+        cols = range(self.__shape__[1])
+        return Matrix([[-(self.__data__[i][j]) for j in cols] for i in rows], self.__shape__)
+
+    def __add_matrix_internal__(self, other):
+        rows = self.__shape__[0]
+        cols = self.__shape__[1]
+        return [[(self.__data__[i][j] + other.__data__[i][j]) for j in range(cols)] for i in range(rows)]
+
+    def __add_scalar_internal__(self, other):
+        rows = self.__shape__[0]
+        cols = self.__shape__[1]
+        return [[(self.__data__[i][j] + other) for j in range(cols)] for i in range(rows)]
 
     def __add__(self, other):
         if isinstance(other, Matrix):
             if self.__shape__ != other.__shape__:
                 raise ValueError("The shape of the operands must be the same")
-            return Matrix(self.__data__ + other.__data__)
+            return Matrix(self.__add_matrix_internal__(other), self.__shape__)
         elif isinstance(other, int) or isinstance(other, float):
-            return Matrix(self.__data__ + other)
+            return Matrix(self.__add_scalar_internal__(other), self.__shape__)
         else:
             raise ValueError("Only a number or another ``Matrix`` can be added to a ``Matrix``")
 
@@ -137,26 +178,47 @@ class Matrix:
     def __rsub__(self, other):
         return -self + other
 
+    def __truediv_scalar_internal__(self, other):
+        rows = self.__shape__[0]
+        cols = self.__shape__[1]
+        return [[(self.__data__[i][j] / other) for j in range(cols)] for i in range(rows)]
+
+    def __truediv__(self, other):
+        if isinstance(other, int) or isinstance(other, float):
+            return Matrix(self.__truediv_scalar_internal__(other), self.__shape__)
+        else:
+            raise ValueError("A ``Matrix`` can only be divided ba a number")
+
+    def __mul_matrix_internal__(self, other):
+        rows = self.__shape__[0]
+        cols = other.__shape__[1]
+
+        new_data = [[0 for _ in range(rows)] for _ in range(cols)]
+
+        for i in range(rows):
+            for k in range(cols):
+                new_data[i][k] = sum([self.__data__[i][j] * other.__data__[j][k] for j in range(self.__shape__[1])])
+        return new_data
+
+    def __mul_scalar_internal__(self, other):
+        cols = range(self.__shape__[1])
+        rows = range(self.__shape__[0])
+        return [[(self.__data__[i][j] * other) for j in cols] for i in rows]
+
     def __mul__(self, other):
         if isinstance(other, Matrix):
             if self.__shape__[1] != other.__shape__[0]:
                 raise ValueError(
                     "The amount of columns of the first operand must match the amount of rows of the second operand")
-            return Matrix(self.__data__ @ other.__data__)
+            return Matrix(self.__mul_matrix_internal__(other), (self.__shape__[0], other.__shape__[1]))
         elif isinstance(other, int) or isinstance(other, float):
-            return Matrix(other * self.__data__)
+            return Matrix(self.__mul_scalar_internal__(other), self.__shape__)
         else:
             raise ValueError("Only a number or another ``Matrix`` can be multiplied to a ``Matrix``")
 
     def __rmul__(self, other):
         return self * other
 
-    def __truediv__(self, other):
-        if isinstance(other, int) or isinstance(other, float):
-            return Matrix(self.__data__ / other)
-        else:
-            raise ValueError("A ``Matrix`` can only be divided ba a number")
-
     def norm(self, f: str = "frobenius"):
         """
         Calculates the norm of the matrix.
@@ -168,15 +230,35 @@ class Matrix:
 
         :return: the norm as a number
         """
-        t = "fro"
+        norm = 0
-        if f == "colsum":
+
-            t = 1
+        rows = self.__shape__[0]
-        elif f == "rowsum":
+        cols = self.__shape__[1]
-            t = numpy.inf
+
-        return linalg.norm(self.__data__, t)
+        if f == "frobenius":
+            abs_sum = 0
+            for i in range(rows):
+                for j in range(cols):
+                    abs_sum += abs(self.__data__[i][j])**2
+            norm = math.sqrt(abs_sum)
+        elif f == "col sum":
+            row_sum = [0 for _ in range(cols)]
+            for j in range(cols):
+                for i in range(rows):
+                    row_sum[j] += abs(self.__data__[i][j])
+            norm = max(row_sum)
+        elif f == "row sum":
+            col_sum = [0 for _ in range(rows)]
+            for i in range(rows):
+                for j in range(cols):
+                    col_sum[i] += abs(self.__data__[i][j])
+            norm = max(col_sum)
+        return norm
 
     def __getitem__(self, key):
-        return self.__data__[key]
+        return numpy.array(self.__data__)[key].tolist()
 
     def __setitem__(self, key, value):
-        self.__data__[key] = value
+        manipulated_data = numpy.array(self.__data__)
+        manipulated_data[key] = value
+        self.__data__ = manipulated_data.tolist()

test/test_matrix.py

@@ -28,17 +28,6 @@ class TestMatrix(TestCase):
         expected = [[0, 1, 2]]
         self.assertEqual(expected, actual)
 
-    def test_should_create_vectorlike_matrix_from_numpy_array_with_shape_3_1(self):
-        data = numpy.array([0, 1, 2])
-        actual = Matrix(data)
-
-        actual_shape = actual.shape()
-        expected_shape = (3, 1)
-        self.assertEqual(expected_shape, actual_shape)
-
-        expected = [0, 1, 2]
-        self.assertEqual(expected, actual)
-
     def test_should_create_matrix_from_list_with_shape_2_2(self):
         data = [0, 1, 2, 3]
         actual = Matrix(data, shape=(2, 2))
@@ -50,9 +39,20 @@ class TestMatrix(TestCase):
         expected = [[0, 1], [2, 3]]
         self.assertEqual(expected, actual)
 
+    def test_should_create_matrix_from_matrixlike_list_with_shape_2_3(self):
+        data = [[0, 1, 2], [3, 4, 5]]
+        actual = Matrix(data, shape=(2, 3))
+
+        actual_shape = actual.shape()
+        expected_shape = (2, 3)
+        self.assertEqual(expected_shape, actual_shape)
+
+        expected = [[0, 1, 2], [3, 4, 5]]
+        self.assertEqual(expected, actual)
+
     def test_should_create_diagonal_matrix_from_list(self):
-        data = [1, 1, 1]
+        data = [1]
-        actual = Matrix(data, structure="diagonal", n=0)
+        actual = Matrix(data, structure="diagonal", offset=0, n=3)
 
         actual_shape = actual.shape()
         expected_shape = (3, 3)
@@ -62,8 +62,8 @@ class TestMatrix(TestCase):
         self.assertEqual(expected, actual)
 
     def test_should_create_diagonal_matrix_from_list_with_offset_1(self):
-        data = [1, 1, 1]
+        data = [1]
-        actual = Matrix(data, structure="diagonal", n=1)
+        actual = Matrix(data, structure="diagonal", offset=1, n=4)
 
         actual_shape = actual.shape()
         expected_shape = (4, 4)
@@ -188,6 +188,15 @@ class TestMatrix(TestCase):
 
         self.assertEqual(expected, actual)
 
+    def test_should_div_matrix_by_scalar(self):
+        m = Matrix([5, 10, 15, 20], (2, 2))
+        s = 5
+
+        actual = m / s
+        expected = Matrix([1, 2, 3, 4], (2, 2))
+
+        self.assertEqual(expected, actual)
+
     def test_should_raise_value_missmatch_error_while_dividing_with_other_than_scalar(self):
         m = Matrix([1, 2, 3, 4], (2, 2))
         o = ""
@@ -195,20 +204,29 @@ class TestMatrix(TestCase):
         self.assertRaises(ValueError, lambda: m / o)
 
     def test_should_mul_matrices_1(self):
-        m1 = Matrix([1, 2], (2, 1))
+        m1 = Matrix([1, 2, 3, 4], (2, 2))
-        m2 = Matrix([3, 4], (1, 2))
+        m2 = Matrix([4, 3, 2, 1], (2, 2))
 
         actual = m1 * m2
-        expected = Matrix([3, 4, 6, 8], (2, 2))
+        expected = Matrix([8, 5, 20, 13], (2, 2))
 
         self.assertEqual(expected, actual)
 
     def test_should_mul_matrices_2(self):
-        m1 = Matrix([1, 2], (1, 2))
+        m1 = Matrix([1, 2, 3, 4, 5, 6], (2, 3))
-        m2 = Matrix([3, 4], (2, 1))
+        m2 = Matrix([6, 5, 4, 3, 2, 1], (3, 2))
 
         actual = m1 * m2
-        expected = Matrix([11], (1, 1))
+        expected = Matrix([20, 14, 56, 41], (2, 2))
+
+        self.assertEqual(expected, actual)
+
+    def test_should_mul_matrices_3(self):
+        m1 = Matrix([1, 2, 3, 4, 5, 6], (3, 2))
+        m2 = Matrix([6, 5, 4, 3, 2, 1], (2, 3))
+
+        actual = m1 * m2
+        expected = Matrix([12, 9, 6, 30, 23, 16, 48, 37, 26], (3, 3))
 
         self.assertEqual(expected, actual)
 
@@ -236,15 +254,6 @@ class TestMatrix(TestCase):
 
         self.assertEqual(expected, actual)
 
-    def test_should_div_matrix_by_scalar(self):
-        m = Matrix([5, 10, 15, 20], (2, 2))
-        s = 5
-
-        actual = m / s
-        expected = Matrix([1, 2, 3, 4], (2, 2))
-
-        self.assertEqual(expected, actual)
-
     def test_should_return_frobenius_norm(self):
         m = Matrix([1, 2, 3, 4], (2, 2))
 
@@ -256,7 +265,7 @@ class TestMatrix(TestCase):
     def test_should_return_colsum_norm(self):
         m = Matrix([1, 2, 3, 4], (2, 2))
 
-        actual = m.norm("colsum")
+        actual = m.norm("col sum")
         expected = 6
 
         self.assertEqual(expected, actual)
@@ -264,7 +273,7 @@ class TestMatrix(TestCase):
     def test_should_return_rowsum_norm(self):
         m = Matrix([1, 2, 3, 4], (2, 2))
 
-        actual = m.norm("rowsum")
+        actual = m.norm("row sum")
         expected = 7
 
         self.assertEqual(expected, actual)
@@ -289,7 +298,7 @@ class TestMatrix(TestCase):
         m = Matrix([1, 2, 3, 4, 5, 6, 7, 8, 9], (3, 3))
 
         actual = m[0]
-        expected = Matrix([1, 2, 3], (1, 3))
+        expected = [1, 2, 3]
 
         self.assertEqual(expected, actual)
 
@@ -297,7 +306,7 @@ class TestMatrix(TestCase):
         m = Matrix([1, 2, 3, 4, 5, 6, 7, 8, 9], (3, 3))
 
         actual = m[2, 0:2]
-        expected = Matrix([7, 8], (1, 2))
+        expected = [7, 8]
 
         self.assertEqual(expected, actual)
 
@@ -305,7 +314,7 @@ class TestMatrix(TestCase):
         m = Matrix([1, 2, 3, 4, 5, 6, 7, 8, 9], (3, 3))
 
         actual = m[:, 1]
-        expected = Matrix([2, 5, 8], (1, 3))
+        expected = [2, 5, 8]
 
         self.assertEqual(expected, actual)
 
@@ -313,7 +322,7 @@ class TestMatrix(TestCase):
         m = Matrix([1, 2, 3, 4, 5, 6, 7, 8, 9], (3, 3))
 
         actual = m[[0, 2], 0]
-        expected = Matrix([1, 7], (1, 2))
+        expected = [1, 7]
 
         self.assertEqual(expected, actual)
 

test/test_serial.py

@@ -125,9 +125,9 @@ print("\n\nTesting the matrix class -----------------------------------\n\n")
 print("Start 2a initialization")
 a_list = np.array([[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 2 * np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11])])
 A = Matrix(a_list)
-B = Matrix(structure="tridiagonal", given_size=11)
+B = Matrix([-1, 2, -1], structure="tridiagonal", n=11)
 c_list = [[(i + 1) / (index + 1) for index in range(10)] for i in range(10)]
-C = Matrix(c_list, given_shape=(10, 10))
+C = Matrix(c_list, shape=(10, 10))
 print("End 2a\n")
 
 ### 1b __str__ function, string representation
@@ -141,7 +141,7 @@ print("End 2b\n")
 ### 1c shape and transpose
 print("Start 2c shape and transpose")
 # Initialization
-A = Matrix(np.array([i for i in range(12)]).reshape(-1, 1), given_shape=(4, 3))
+A = Matrix(np.array([i for i in range(12)]).reshape(-1, 1), shape=(4, 3))
 print(f"A has shape {A.shape()} | must be (4,3)")
 print(f"A.T() has shape {A.T().shape()} | must be (3,4)")
 print(f"A.T().T() has shape {A.T().T().shape()} | must be (4,3)")
@@ -150,17 +150,17 @@ print("End 2c\n")
 ### 1d addition and substraction
 print("Start 2d addition and substraction")
 # Initialization 
-A = Matrix(structure="diagonal", given_values=[3], offset=0, given_size=10)
+A = Matrix(structure="diagonal", data=[3], offset=0, n=10)
 print(str(A))
-A21 = Matrix(structure="diagonal", given_values=[-1], offset=-1, given_size=10)
+A21 = Matrix(structure="diagonal", data=[-1], offset=-1, n=10)
 print(str(A21))
-A12 = Matrix(structure="diagonal", given_values=[-1], offset=+1, given_size=10)
+A12 = Matrix(structure="diagonal", data=[-1], offset=+1, n=10)
 print(str(A12))
-B = Matrix(structure="diagonal", given_values=[1], offset=0, given_size=10)
+B = Matrix(structure="diagonal", data=[1], offset=0, n=10)
 print(str(B))
 # computation
 C = A + A21 + A12 - B
-print(str(C) + f"must be\n{Matrix(structure='tridiagonal', given_values=[-1, 2, -1], given_size=10)}")
+print(str(C) + f"must be\n{Matrix(structure='tridiagonal', data=[-1, 2, -1], n=10)}")
 print(str(5 + A - 3))
 print("End 2d\n")
 
@@ -195,21 +195,21 @@ print("End 2f\n")
 
 ### 1g norm
 print("Start 2g norm")
-A = Matrix(structure="tridiagonal", given_size=50, given_values=[-1, 2, -1])
+A = Matrix(structure="tridiagonal", n=50, data=[-1, 2, -1])
 print(f"Frobenius norm of tridiagonal matrix: {A.norm('frobenius')} | must be 17.263")
-print(f"Row sum norm of tridiagonal matrix: {A.norm('row sum')} | must be 2")
+print(f"Row sum norm of tridiagonal matrix: {A.norm('row sum')} | must be 4")
-print(f"Col sum norm of tridiagonal matrix: {A.norm('col sum')} | must be 2")
+print(f"Col sum norm of tridiagonal matrix: {A.norm('col sum')} | must be 4")
 print("End 2g\n")
 
 ### 1h negation
 print("Start 2h negation")
-A = Matrix(structure="tridiagonal", given_size=50, given_values=[-1, 2, 1])
+A = Matrix(structure="tridiagonal", n=50, data=[-1, 2, 1])
 print(f"Norm of (A + (-A)) is {(A + (-A)).norm('frobenius')} | must be < 1e-8")
 print("End 2h\n")
 
 ### 1i manipulation
 print("Start 2i manipulation")
-A = Matrix(structure="tridiagonal", given_size=10, given_values=[-1, 2, 1])
+A = Matrix(structure="tridiagonal", n=10, data=[-1, 2, 1])
 A[1, 1] = 4
 A[[1, 2, 3], 2] = [-5, -10, 100]
 print(str(A))