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