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from sympy.core import Lambda, S, symbols |
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from sympy.concrete import Sum |
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from sympy.functions import adjoint, conjugate, transpose |
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from sympy.matrices import eye, Matrix, ShapeError, ImmutableMatrix |
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from sympy.matrices.expressions import ( |
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Adjoint, Identity, FunctionMatrix, MatrixExpr, MatrixSymbol, Trace, |
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ZeroMatrix, trace, MatPow, MatAdd, MatMul |
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) |
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from sympy.matrices.expressions.special import OneMatrix |
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from sympy.testing.pytest import raises |
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from sympy.abc import i |
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n = symbols('n', integer=True) |
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A = MatrixSymbol('A', n, n) |
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B = MatrixSymbol('B', n, n) |
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C = MatrixSymbol('C', 3, 4) |
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def test_Trace(): |
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assert isinstance(Trace(A), Trace) |
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assert not isinstance(Trace(A), MatrixExpr) |
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raises(ShapeError, lambda: Trace(C)) |
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assert trace(eye(3)) == 3 |
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assert trace(Matrix(3, 3, [1, 2, 3, 4, 5, 6, 7, 8, 9])) == 15 |
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assert adjoint(Trace(A)) == trace(Adjoint(A)) |
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assert conjugate(Trace(A)) == trace(Adjoint(A)) |
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assert transpose(Trace(A)) == Trace(A) |
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_ = A / Trace(A) |
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assert trace(Identity(5)) == 5 |
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assert trace(ZeroMatrix(5, 5)) == 0 |
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assert trace(OneMatrix(1, 1)) == 1 |
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assert trace(OneMatrix(2, 2)) == 2 |
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assert trace(OneMatrix(n, n)) == n |
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assert trace(2*A*B) == 2*Trace(A*B) |
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assert trace(A.T) == trace(A) |
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i, j = symbols('i j') |
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F = FunctionMatrix(3, 3, Lambda((i, j), i + j)) |
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assert trace(F) == (0 + 0) + (1 + 1) + (2 + 2) |
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raises(TypeError, lambda: Trace(S.One)) |
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assert Trace(A).arg is A |
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assert str(trace(A)) == str(Trace(A).doit()) |
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assert Trace(A).is_commutative is True |
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def test_Trace_A_plus_B(): |
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assert trace(A + B) == Trace(A) + Trace(B) |
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assert Trace(A + B).arg == MatAdd(A, B) |
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assert Trace(A + B).doit() == Trace(A) + Trace(B) |
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def test_Trace_MatAdd_doit(): |
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X = ImmutableMatrix([[1, 2, 3]]*3) |
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Y = MatrixSymbol('Y', 3, 3) |
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q = MatAdd(X, 2*X, Y, -3*Y) |
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assert Trace(q).arg == q |
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assert Trace(q).doit() == 18 - 2*Trace(Y) |
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def test_Trace_MatPow_doit(): |
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X = Matrix([[1, 2], [3, 4]]) |
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assert Trace(X).doit() == 5 |
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q = MatPow(X, 2) |
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assert Trace(q).arg == q |
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assert Trace(q).doit() == 29 |
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def test_Trace_MutableMatrix_plus(): |
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X = Matrix([[1, 2], [3, 4]]) |
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assert Trace(X) + Trace(X) == 2*Trace(X) |
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def test_Trace_doit_deep_False(): |
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X = Matrix([[1, 2], [3, 4]]) |
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q = MatPow(X, 2) |
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assert Trace(q).doit(deep=False).arg == q |
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q = MatAdd(X, 2*X) |
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assert Trace(q).doit(deep=False).arg == q |
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q = MatMul(X, 2*X) |
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assert Trace(q).doit(deep=False).arg == q |
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def test_trace_constant_factor(): |
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assert trace(2*A) == 2*Trace(A) |
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X = ImmutableMatrix([[1, 2], [3, 4]]) |
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assert trace(MatMul(2, X)) == 10 |
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def test_trace_rewrite(): |
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assert trace(A).rewrite(Sum) == Sum(A[i, i], (i, 0, n - 1)) |
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assert trace(eye(3)).rewrite(Sum) == 3 |
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def test_trace_normalize(): |
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assert Trace(B*A) != Trace(A*B) |
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assert Trace(B*A)._normalize() == Trace(A*B) |
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assert Trace(B*A.T)._normalize() == Trace(A*B.T) |
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def test_trace_as_explicit(): |
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raises(ValueError, lambda: Trace(A).as_explicit()) |
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X = MatrixSymbol("X", 3, 3) |
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assert Trace(X).as_explicit() == X[0, 0] + X[1, 1] + X[2, 2] |
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assert Trace(eye(3)).as_explicit() == 3 |
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