#62 matrix_multiply_by_squaring

src/solutions/chapter4/section2/exercise6.py

@@ -0,0 +1,34 @@
+from typing import Callable
+
+from book.data_structures import Matrix
+from solutions.chapter4.section2.exercise2 import matrix_add
+from util import range_of
+
+
+def matrix_multiply_by_squaring(A: Matrix, B: Matrix, C: Matrix, matrix_square: Callable[[Matrix, Matrix, int], None],
+                                n: int) -> None:
+    """Multiplies two square matrices and adds the result to the third square matrix, using a function for squaring
+    matrices.
+
+    Args:
+        A: the first square matrix to multiply
+        B: the second square matrix to multiply
+        C: the matrix to add the result of the matrix multiplication
+        matrix_square: a function for squaring matrices.
+            The first argument is the square matrix to square, the second argument is the matrix to accumulate the
+            result, and the third argument is the dimension of the input matrix.
+        n: the dimension of matrices A and B
+    """
+    D = __create_padded_input_matrix(A, B, n)
+    E = Matrix(2 * n, 2 * n)
+    matrix_square(D, E, 2 * n)
+    matrix_add(C, E.submatrix((n + 1, 2 * n), (1, n)), C, n)
+
+
+def __create_padded_input_matrix(A, B, n):
+    M = Matrix(2 * n, 2 * n)
+    for i in range_of(1, to=n):
+        for j in range_of(1, to=n):
+            M[i, j] = B[i, j]
+            M[n + i, j] = A[i, j]
+    return M

test/test_solutions/test_chapter4.py

@@ -5,12 +5,14 @@
 from hypothesis.strategies import integers
 from hypothesis.strategies import lists
 
+from book.chapter4.section1 import matrix_multiply
 from book.data_structures import Matrix
 from solutions.chapter4.section1.exercise1 import matrix_multiply_recursive_general
 from solutions.chapter4.section1.exercise3 import matrix_multiply_recursive_by_copying
 from solutions.chapter4.section1.exercise4 import matrix_add_recursive
 from solutions.chapter4.section2.exercise2 import strassen
 from solutions.chapter4.section2.exercise5 import complex_multiply
+from solutions.chapter4.section2.exercise6 import matrix_multiply_by_squaring
 from test_case import ClrsTestCase
 from test_util import create_matrix
 
@@ -102,3 +104,24 @@ def test_complex_multiply(self, data):
         actual_product = complex(real, imag)
         expected_product = z1 * z2
         self.assertAlmostEqual(actual_product, expected_product, places=7)
+
+    @given(st.data())
+    def test_matrix_multiply_by_squaring(self, data):
+        n = data.draw(integers(min_value=1, max_value=15), label="Matrices dimension")
+        elements1 = data.draw(
+            lists(lists(integers(min_value=-1000, max_value=1000), min_size=n, max_size=n), min_size=n, max_size=n),
+            label="First matrix elements")
+        elements2 = data.draw(
+            lists(lists(integers(min_value=-1000, max_value=1000), min_size=n, max_size=n), min_size=n, max_size=n),
+            label="Second matrix elements")
+        A = create_matrix(elements1)
+        B = create_matrix(elements2)
+        C = Matrix(n, n)
+
+        def matrix_square_function(D, E, m):
+            matrix_multiply(D, D, E, m)
+
+        matrix_multiply_by_squaring(A, B, C, matrix_square_function, n)
+
+        expected_product = create_matrix(numpy.matmul(elements1, elements2))
+        self.assertEqual(C, expected_product)