def test_matsolve():
n = Symbol('n', integer=True)
A = MatrixSymbol('A', n, n)
x = MatrixSymbol('x', n, 1)
with assuming(Q.fullrank(A)):
assert optimize(A**(-1) * x, [matinv_opt]) == MatrixSolve(A, x)
assert optimize(A**(-1) * x + x, [matinv_opt]) == MatrixSolve(A, x) + x
def test_NumPyPrinter():
from sympy import (
Lambda,
ZeroMatrix,
OneMatrix,
FunctionMatrix,
HadamardProduct,
KroneckerProduct,
Adjoint,
DiagonalOf,
DiagMatrix,
DiagonalMatrix,
)
from sympy.abc import a, b
p = NumPyPrinter()
assert p.doprint(sign(x)) == "numpy.sign(x)"
A = MatrixSymbol("A", 2, 2)
B = MatrixSymbol("B", 2, 2)
C = MatrixSymbol("C", 1, 5)
D = MatrixSymbol("D", 3, 4)
assert p.doprint(A**(-1)) == "numpy.linalg.inv(A)"
assert p.doprint(A**5) == "numpy.linalg.matrix_power(A, 5)"
assert p.doprint(Identity(3)) == "numpy.eye(3)"
u = MatrixSymbol("x", 2, 1)
v = MatrixSymbol("y", 2, 1)
assert p.doprint(MatrixSolve(A, u)) == "numpy.linalg.solve(A, x)"
assert p.doprint(MatrixSolve(A, u) + v) == "numpy.linalg.solve(A, x) + y"
assert p.doprint(ZeroMatrix(2, 3)) == "numpy.zeros((2, 3))"
assert p.doprint(OneMatrix(2, 3)) == "numpy.ones((2, 3))"
assert (p.doprint(FunctionMatrix(4, 5, Lambda(
(a, b), a + b))) == "numpy.fromfunction(lambda a, b: a + b, (4, 5))")
assert p.doprint(HadamardProduct(A, B)) == "numpy.multiply(A, B)"
assert p.doprint(KroneckerProduct(A, B)) == "numpy.kron(A, B)"
assert p.doprint(Adjoint(A)) == "numpy.conjugate(numpy.transpose(A))"
assert p.doprint(DiagonalOf(A)) == "numpy.reshape(numpy.diag(A), (-1, 1))"
assert p.doprint(DiagMatrix(C)) == "numpy.diagflat(C)"
assert p.doprint(DiagonalMatrix(D)) == "numpy.multiply(D, numpy.eye(3, 4))"
# Workaround for numpy negative integer power errors
assert p.doprint(x**-1) == "x**(-1.0)"
assert p.doprint(x**-2) == "x**(-2.0)"
assert p.doprint(S.Exp1) == "numpy.e"
assert p.doprint(S.Pi) == "numpy.pi"
assert p.doprint(S.EulerGamma) == "numpy.euler_gamma"
assert p.doprint(S.NaN) == "numpy.nan"
assert p.doprint(S.Infinity) == "numpy.PINF"
assert p.doprint(S.NegativeInfinity) == "numpy.NINF"
def test_NumPyPrinter():
from sympy.core.function import Lambda
from sympy.matrices.expressions.adjoint import Adjoint
from sympy.matrices.expressions.diagonal import (DiagMatrix,
DiagonalMatrix,
DiagonalOf)
from sympy.matrices.expressions.funcmatrix import FunctionMatrix
from sympy.matrices.expressions.hadamard import HadamardProduct
from sympy.matrices.expressions.kronecker import KroneckerProduct
from sympy.matrices.expressions.special import (OneMatrix, ZeroMatrix)
from sympy.abc import a, b
p = NumPyPrinter()
assert p.doprint(sign(x)) == 'numpy.sign(x)'
A = MatrixSymbol("A", 2, 2)
B = MatrixSymbol("B", 2, 2)
C = MatrixSymbol("C", 1, 5)
D = MatrixSymbol("D", 3, 4)
assert p.doprint(A**(-1)) == "numpy.linalg.inv(A)"
assert p.doprint(A**5) == "numpy.linalg.matrix_power(A, 5)"
assert p.doprint(Identity(3)) == "numpy.eye(3)"
u = MatrixSymbol('x', 2, 1)
v = MatrixSymbol('y', 2, 1)
assert p.doprint(MatrixSolve(A, u)) == 'numpy.linalg.solve(A, x)'
assert p.doprint(MatrixSolve(A, u) + v) == 'numpy.linalg.solve(A, x) + y'
assert p.doprint(ZeroMatrix(2, 3)) == "numpy.zeros((2, 3))"
assert p.doprint(OneMatrix(2, 3)) == "numpy.ones((2, 3))"
assert p.doprint(FunctionMatrix(4, 5, Lambda((a, b), a + b))) == \
"numpy.fromfunction(lambda a, b: a + b, (4, 5))"
assert p.doprint(HadamardProduct(A, B)) == "numpy.multiply(A, B)"
assert p.doprint(KroneckerProduct(A, B)) == "numpy.kron(A, B)"
assert p.doprint(Adjoint(A)) == "numpy.conjugate(numpy.transpose(A))"
assert p.doprint(DiagonalOf(A)) == "numpy.reshape(numpy.diag(A), (-1, 1))"
assert p.doprint(DiagMatrix(C)) == "numpy.diagflat(C)"
assert p.doprint(DiagonalMatrix(D)) == "numpy.multiply(D, numpy.eye(3, 4))"
# Workaround for numpy negative integer power errors
assert p.doprint(x**-1) == 'x**(-1.0)'
assert p.doprint(x**-2) == 'x**(-2.0)'
expr = Pow(2, -1, evaluate=False)
assert p.doprint(expr) == "2**(-1.0)"
assert p.doprint(S.Exp1) == 'numpy.e'
assert p.doprint(S.Pi) == 'numpy.pi'
assert p.doprint(S.EulerGamma) == 'numpy.euler_gamma'
assert p.doprint(S.NaN) == 'numpy.nan'
assert p.doprint(S.Infinity) == 'numpy.PINF'
assert p.doprint(S.NegativeInfinity) == 'numpy.NINF'
def test_NumPyPrinter():
p = NumPyPrinter()
assert p.doprint(sign(x)) == 'numpy.sign(x)'
A = MatrixSymbol("A", 2, 2)
assert p.doprint(A**(-1)) == "numpy.linalg.inv(A)"
assert p.doprint(A**5) == "numpy.linalg.matrix_power(A, 5)"
u = MatrixSymbol('x', 2, 1)
v = MatrixSymbol('y', 2, 1)
assert p.doprint(MatrixSolve(A, u)) == 'numpy.linalg.solve(A, x)'
assert p.doprint(MatrixSolve(A, u) + v) == 'numpy.linalg.solve(A, x) + y'
# Workaround for numpy negative integer power errors
assert p.doprint(x**-1) == 'x**(-1.0)'
assert p.doprint(x**-2) == 'x**(-2.0)'
def test_NumPyPrinter():
p = NumPyPrinter()
assert p.doprint(sign(x)) == 'numpy.sign(x)'
A = MatrixSymbol("A", 2, 2)
assert p.doprint(A**(-1)) == "numpy.linalg.inv(A)"
assert p.doprint(A**5) == "numpy.linalg.matrix_power(A, 5)"
assert p.doprint(Identity(3)) == "numpy.eye(3)"
u = MatrixSymbol('x', 2, 1)
v = MatrixSymbol('y', 2, 1)
assert p.doprint(MatrixSolve(A, u)) == 'numpy.linalg.solve(A, x)'
assert p.doprint(MatrixSolve(A, u) + v) == 'numpy.linalg.solve(A, x) + y'
# Workaround for numpy negative integer power errors
assert p.doprint(x**-1) == 'x**(-1.0)'
assert p.doprint(x**-2) == 'x**(-2.0)'
assert p.doprint(S.Exp1) == 'numpy.e'
assert p.doprint(S.Pi) == 'numpy.pi'
assert p.doprint(S.EulerGamma) == 'numpy.euler_gamma'
assert p.doprint(S.NaN) == 'numpy.nan'
assert p.doprint(S.Infinity) == 'numpy.PINF'
assert p.doprint(S.NegativeInfinity) == 'numpy.NINF'
def test_matsolve():
if not np:
skip("NumPy not installed")
M = MatrixSymbol("M", 3, 3)
x = MatrixSymbol("x", 3, 1)
expr = M**(-1) * x + x
matsolve_expr = MatrixSolve(M, x) + x
f = lambdify((M, x), expr)
f_matsolve = lambdify((M, x), matsolve_expr)
m0 = np.array([[1, 2, 3], [3, 2, 5], [5, 6, 7]])
assert np.linalg.matrix_rank(m0) == 3
x0 = np.array([3, 4, 5])
assert np.allclose(f_matsolve(m0, x0), f(m0, x0))
def test_MatrixSolve():
n = Symbol('n', integer=True)
A = MatrixSymbol('A', n, n)
x = MatrixSymbol('x', n, 1)
assert mcode(MatrixSolve(A, x)) == "A \\ x"
def _matinv_transform(expr):
left, right = expr.args
inv_arg = left.arg
return MatrixSolve(inv_arg, right)
def test_MatrixSolve():
n = Symbol("n", integer=True)
A = MatrixSymbol("A", n, n)
x = MatrixSymbol("x", n, 1)
assert mcode(MatrixSolve(A, x)) == "A \\ x"