Spaces:
Running
Running
| from sympy.core import Lambda, S, symbols | |
| from sympy.concrete import Sum | |
| from sympy.functions import adjoint, conjugate, transpose | |
| from sympy.matrices import eye, Matrix, ShapeError, ImmutableMatrix | |
| from sympy.matrices.expressions import ( | |
| Adjoint, Identity, FunctionMatrix, MatrixExpr, MatrixSymbol, Trace, | |
| ZeroMatrix, trace, MatPow, MatAdd, MatMul | |
| ) | |
| from sympy.matrices.expressions.special import OneMatrix | |
| from sympy.testing.pytest import raises | |
| from sympy.abc import i | |
| n = symbols('n', integer=True) | |
| A = MatrixSymbol('A', n, n) | |
| B = MatrixSymbol('B', n, n) | |
| C = MatrixSymbol('C', 3, 4) | |
| def test_Trace(): | |
| assert isinstance(Trace(A), Trace) | |
| assert not isinstance(Trace(A), MatrixExpr) | |
| raises(ShapeError, lambda: Trace(C)) | |
| assert trace(eye(3)) == 3 | |
| assert trace(Matrix(3, 3, [1, 2, 3, 4, 5, 6, 7, 8, 9])) == 15 | |
| assert adjoint(Trace(A)) == trace(Adjoint(A)) | |
| assert conjugate(Trace(A)) == trace(Adjoint(A)) | |
| assert transpose(Trace(A)) == Trace(A) | |
| _ = A / Trace(A) # Make sure this is possible | |
| # Some easy simplifications | |
| assert trace(Identity(5)) == 5 | |
| assert trace(ZeroMatrix(5, 5)) == 0 | |
| assert trace(OneMatrix(1, 1)) == 1 | |
| assert trace(OneMatrix(2, 2)) == 2 | |
| assert trace(OneMatrix(n, n)) == n | |
| assert trace(2*A*B) == 2*Trace(A*B) | |
| assert trace(A.T) == trace(A) | |
| i, j = symbols('i j') | |
| F = FunctionMatrix(3, 3, Lambda((i, j), i + j)) | |
| assert trace(F) == (0 + 0) + (1 + 1) + (2 + 2) | |
| raises(TypeError, lambda: Trace(S.One)) | |
| assert Trace(A).arg is A | |
| assert str(trace(A)) == str(Trace(A).doit()) | |
| assert Trace(A).is_commutative is True | |
| def test_Trace_A_plus_B(): | |
| assert trace(A + B) == Trace(A) + Trace(B) | |
| assert Trace(A + B).arg == MatAdd(A, B) | |
| assert Trace(A + B).doit() == Trace(A) + Trace(B) | |
| def test_Trace_MatAdd_doit(): | |
| # See issue #9028 | |
| X = ImmutableMatrix([[1, 2, 3]]*3) | |
| Y = MatrixSymbol('Y', 3, 3) | |
| q = MatAdd(X, 2*X, Y, -3*Y) | |
| assert Trace(q).arg == q | |
| assert Trace(q).doit() == 18 - 2*Trace(Y) | |
| def test_Trace_MatPow_doit(): | |
| X = Matrix([[1, 2], [3, 4]]) | |
| assert Trace(X).doit() == 5 | |
| q = MatPow(X, 2) | |
| assert Trace(q).arg == q | |
| assert Trace(q).doit() == 29 | |
| def test_Trace_MutableMatrix_plus(): | |
| # See issue #9043 | |
| X = Matrix([[1, 2], [3, 4]]) | |
| assert Trace(X) + Trace(X) == 2*Trace(X) | |
| def test_Trace_doit_deep_False(): | |
| X = Matrix([[1, 2], [3, 4]]) | |
| q = MatPow(X, 2) | |
| assert Trace(q).doit(deep=False).arg == q | |
| q = MatAdd(X, 2*X) | |
| assert Trace(q).doit(deep=False).arg == q | |
| q = MatMul(X, 2*X) | |
| assert Trace(q).doit(deep=False).arg == q | |
| def test_trace_constant_factor(): | |
| # Issue 9052: gave 2*Trace(MatMul(A)) instead of 2*Trace(A) | |
| assert trace(2*A) == 2*Trace(A) | |
| X = ImmutableMatrix([[1, 2], [3, 4]]) | |
| assert trace(MatMul(2, X)) == 10 | |
| def test_trace_rewrite(): | |
| assert trace(A).rewrite(Sum) == Sum(A[i, i], (i, 0, n - 1)) | |
| assert trace(eye(3)).rewrite(Sum) == 3 | |
| def test_trace_normalize(): | |
| assert Trace(B*A) != Trace(A*B) | |
| assert Trace(B*A)._normalize() == Trace(A*B) | |
| assert Trace(B*A.T)._normalize() == Trace(A*B.T) | |
| def test_trace_as_explicit(): | |
| raises(ValueError, lambda: Trace(A).as_explicit()) | |
| X = MatrixSymbol("X", 3, 3) | |
| assert Trace(X).as_explicit() == X[0, 0] + X[1, 1] + X[2, 2] | |
| assert Trace(eye(3)).as_explicit() == 3 | |