67 lines
2.0 KiB
Python
67 lines
2.0 KiB
Python
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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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@property
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def shape(self):
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return self.vector.shape
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