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""" |
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Additional AST nodes for operations on matrices. The nodes in this module |
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are meant to represent optimization of matrix expressions within codegen's |
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target languages that cannot be represented by SymPy expressions. |
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As an example, we can use :meth:`sympy.codegen.rewriting.optimize` and the |
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``matin_opt`` optimization provided in :mod:`sympy.codegen.rewriting` to |
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transform matrix multiplication under certain assumptions: |
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>>> from sympy import symbols, MatrixSymbol |
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>>> n = symbols('n', integer=True) |
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>>> A = MatrixSymbol('A', n, n) |
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>>> x = MatrixSymbol('x', n, 1) |
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>>> expr = A**(-1) * x |
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>>> from sympy import assuming, Q |
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>>> from sympy.codegen.rewriting import matinv_opt, optimize |
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>>> with assuming(Q.fullrank(A)): |
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... optimize(expr, [matinv_opt]) |
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MatrixSolve(A, vector=x) |
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""" |
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from .ast import Token |
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from sympy.matrices import MatrixExpr |
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from sympy.core.sympify import sympify |
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class MatrixSolve(Token, MatrixExpr): |
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"""Represents an operation to solve a linear matrix equation. |
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Parameters |
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========== |
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matrix : MatrixSymbol |
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Matrix representing the coefficients of variables in the linear |
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equation. This matrix must be square and full-rank (i.e. all columns must |
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be linearly independent) for the solving operation to be valid. |
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vector : MatrixSymbol |
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One-column matrix representing the solutions to the equations |
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represented in ``matrix``. |
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Examples |
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======== |
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>>> from sympy import symbols, MatrixSymbol |
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>>> from sympy.codegen.matrix_nodes import MatrixSolve |
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>>> n = symbols('n', integer=True) |
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>>> A = MatrixSymbol('A', n, n) |
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>>> x = MatrixSymbol('x', n, 1) |
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>>> from sympy.printing.numpy import NumPyPrinter |
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>>> NumPyPrinter().doprint(MatrixSolve(A, x)) |
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'numpy.linalg.solve(A, x)' |
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>>> from sympy import octave_code |
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>>> octave_code(MatrixSolve(A, x)) |
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'A \\\\ x' |
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""" |
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__slots__ = _fields = ('matrix', 'vector') |
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_construct_matrix = staticmethod(sympify) |
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_construct_vector = staticmethod(sympify) |
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@property |
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def shape(self): |
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return self.vector.shape |
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def _eval_derivative(self, x): |
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A, b = self.matrix, self.vector |
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return MatrixSolve(A, b.diff(x) - A.diff(x) * MatrixSolve(A, b)) |
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