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from sympy.core import Basic |
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from sympy.functions import adjoint, conjugate |
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from sympy.matrices.expressions.matexpr import MatrixExpr |
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class Adjoint(MatrixExpr): |
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""" |
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The Hermitian adjoint of a matrix expression. |
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This is a symbolic object that simply stores its argument without |
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evaluating it. To actually compute the adjoint, use the ``adjoint()`` |
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function. |
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Examples |
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======== |
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>>> from sympy import MatrixSymbol, Adjoint, adjoint |
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>>> A = MatrixSymbol('A', 3, 5) |
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>>> B = MatrixSymbol('B', 5, 3) |
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>>> Adjoint(A*B) |
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Adjoint(A*B) |
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>>> adjoint(A*B) |
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Adjoint(B)*Adjoint(A) |
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>>> adjoint(A*B) == Adjoint(A*B) |
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False |
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>>> adjoint(A*B) == Adjoint(A*B).doit() |
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True |
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""" |
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is_Adjoint = True |
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def doit(self, **hints): |
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arg = self.arg |
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if hints.get('deep', True) and isinstance(arg, Basic): |
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return adjoint(arg.doit(**hints)) |
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else: |
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return adjoint(self.arg) |
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@property |
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def arg(self): |
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return self.args[0] |
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@property |
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def shape(self): |
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return self.arg.shape[::-1] |
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def _entry(self, i, j, **kwargs): |
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return conjugate(self.arg._entry(j, i, **kwargs)) |
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def _eval_adjoint(self): |
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return self.arg |
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def _eval_transpose(self): |
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return self.arg.conjugate() |
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def _eval_conjugate(self): |
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return self.arg.transpose() |
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def _eval_trace(self): |
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from sympy.matrices.expressions.trace import Trace |
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return conjugate(Trace(self.arg)) |
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