Initialisation du repository de Beta

venv/lib/python3.12/site-packages/sympy/matrices/tests/test_interactions.py

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+"""
+We have a few different kind of Matrices
+Matrix, ImmutableMatrix, MatrixExpr
+
+Here we test the extent to which they cooperate
+"""
+
+from sympy.core.symbol import symbols
+from sympy.matrices import (Matrix, MatrixSymbol, eye, Identity,
+        ImmutableMatrix)
+from sympy.matrices.expressions import MatrixExpr, MatAdd
+from sympy.matrices.matrixbase import classof
+from sympy.testing.pytest import raises
+
+SM = MatrixSymbol('X', 3, 3)
+SV = MatrixSymbol('v', 3, 1)
+MM = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
+IM = ImmutableMatrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
+meye = eye(3)
+imeye = ImmutableMatrix(eye(3))
+ideye = Identity(3)
+a, b, c = symbols('a,b,c')
+
+
+def test_IM_MM():
+    assert isinstance(MM + IM, ImmutableMatrix)
+    assert isinstance(IM + MM, ImmutableMatrix)
+    assert isinstance(2*IM + MM, ImmutableMatrix)
+    assert MM.equals(IM)
+
+
+def test_ME_MM():
+    assert isinstance(Identity(3) + MM, MatrixExpr)
+    assert isinstance(SM + MM, MatAdd)
+    assert isinstance(MM + SM, MatAdd)
+    assert (Identity(3) + MM)[1, 1] == 6
+
+
+def test_equality():
+    a, b, c = Identity(3), eye(3), ImmutableMatrix(eye(3))
+    for x in [a, b, c]:
+        for y in [a, b, c]:
+            assert x.equals(y)
+
+
+def test_matrix_symbol_MM():
+    X = MatrixSymbol('X', 3, 3)
+    Y = eye(3) + X
+    assert Y[1, 1] == 1 + X[1, 1]
+
+
+def test_matrix_symbol_vector_matrix_multiplication():
+    A = MM * SV
+    B = IM * SV
+    assert A == B
+    C = (SV.T * MM.T).T
+    assert B == C
+    D = (SV.T * IM.T).T
+    assert C == D
+
+
+def test_indexing_interactions():
+    assert (a * IM)[1, 1] == 5*a
+    assert (SM + IM)[1, 1] == SM[1, 1] + IM[1, 1]
+    assert (SM * IM)[1, 1] == SM[1, 0]*IM[0, 1] + SM[1, 1]*IM[1, 1] + \
+        SM[1, 2]*IM[2, 1]
+
+
+def test_classof():
+    A = Matrix(3, 3, range(9))
+    B = ImmutableMatrix(3, 3, range(9))
+    C = MatrixSymbol('C', 3, 3)
+    assert classof(A, A) == Matrix
+    assert classof(B, B) == ImmutableMatrix
+    assert classof(A, B) == ImmutableMatrix
+    assert classof(B, A) == ImmutableMatrix
+    raises(TypeError, lambda: classof(A, C))