def test_matrix_derivative_non_matrix_result():
# This is a 4-dimensional array:
assert A.diff(A) == Derivative(A, A)
assert A.T.diff(A) == Derivative(A.T, A)
assert (2 * A).diff(A) == Derivative(2 * A, A)
assert MatAdd(A, A).diff(A) == Derivative(MatAdd(A, A), A)
assert (A + B).diff(A) == Derivative(A + B, A) # TODO: `B` can be removed.
def test_MatMul_MatAdd():
X, Y = MatrixSymbol("X", 2, 2), MatrixSymbol("Y", 2, 2)
assert str(2*(X + Y)) == "2*X + 2*Y"
assert str(I*X) == "I*X"
assert str(-I*X) == "-I*X"
assert str((1 + I)*X) == '(1 + I)*X'
assert str(-(1 + I)*X) == '(-1 - I)*X'
assert str(MatAdd(MatAdd(X, Y), MatAdd(X, Y))) == '(X + Y) + (X + Y)'
def test_lm_sym_expanded():
m = Matrix([[0, x], [3.4 * y, 3 * x - 4.5 * y + z]])
c = Matrix([[1.2, 0], [0, 1.2]])
cx = MatMul(Matrix([[0.0, 1.0], [0.0, 3.0]]), x)
cy = MatMul(Matrix([[0.0, 0.0], [3.4, -4.5]]), y)
cz = MatMul(Matrix([[0.0, 0.0], [0.0, 1.0]]), z)
cc = Matrix([[1.2, 0.0], [0.0, 1.2]])
assert MatAdd(cx, cy, cz, cc) == lm_sym_expanded(m + c, [x, y, z])
assert MatAdd(cx, cy, cz) == lm_sym_expanded(m, [x, y, z])
assert cc == lm_sym_expanded(c, [x, y, z])
def test_hadamard():
m, n, p = symbols('m, n, p', integer=True)
A = MatrixSymbol('A', m, n)
B = MatrixSymbol('B', m, n)
C = MatrixSymbol('C', m, p)
X = MatrixSymbol('X', m, m)
I = Identity(m)
with raises(TypeError):
hadamard_product()
assert hadamard_product(A) == A
assert isinstance(hadamard_product(A, B), HadamardProduct)
assert hadamard_product(A, B).doit() == hadamard_product(A, B)
with raises(ShapeError):
hadamard_product(A, C)
hadamard_product(A, I)
assert hadamard_product(X, I) == X
assert isinstance(hadamard_product(X, I), MatrixSymbol)
a = MatrixSymbol("a", k, 1)
expr = MatAdd(ZeroMatrix(k, 1), OneMatrix(k, 1))
expr = HadamardProduct(expr, a)
assert expr.doit() == a
def lm_sym_expanded(linear_matrix, variables):
"""Return matrix in the form of sum of coefficent matrices times varibles.
"""
if S(linear_matrix).free_symbols & set(variables):
coeffs, const = lm_sym_to_coeffs(linear_matrix, variables)
terms = []
for i, v in enumerate(variables):
terms.append(MatMul(ImmutableMatrix(coeffs[i]), v))
if const.any():
terms.append(ImmutableMatrix(const))
return MatAdd(*terms)
else:
return linear_matrix
def repl(x):
pre, post = [], []
sawAdd = False
for arg in x.args:
if arg.is_MatAdd:
sawAdd = True
add = arg
continue
if not sawAdd:
pre.append(arg)
else:
post.append(arg)
# ugly hack here because I can't figure out how to not end up
# with nested parens that break other things
addends = [[*addend.args] if addend.is_MatMul else [addend]
for addend in add.args]
return MatAdd(*[MatMul(*[*pre, *addend, *post]) for addend in addends])
class TestAllGood(object):
# These latex strings should parse to the corresponding SymPy expression
GOOD_PAIRS = [
("0", Rational(0)),
("1", Rational(1)),
("-3.14", Rational(-314, 100)),
("5-3", _Add(5, _Mul(-1, 3))),
("(-7.13)(1.5)", _Mul(Rational('-7.13'), Rational('1.5'))),
("\\left(-7.13\\right)\\left(1.5\\right)", _Mul(Rational('-7.13'), Rational('1.5'))),
("x", x),
("2x", 2 * x),
("x^2", x**2),
("x^{3 + 1}", x**_Add(3, 1)),
("x^{\\left\\{3 + 1\\right\\}}", x**_Add(3, 1)),
("-3y + 2x", _Add(_Mul(2, x), Mul(-1, 3, y, evaluate=False))),
("-c", -c),
("a \\cdot b", a * b),
("a / b", a / b),
("a \\div b", a / b),
("a + b", a + b),
("a + b - a", Add(a, b, _Mul(-1, a), evaluate=False)),
("a^2 + b^2 = c^2", Eq(a**2 + b**2, c**2)),
("a^2 + b^2 != 2c^2", Ne(a**2 + b**2, 2 * c**2)),
("a\\mod b", Mod(a, b)),
("\\sin \\theta", sin(theta)),
("\\sin(\\theta)", sin(theta)),
("\\sin\\left(\\theta\\right)", sin(theta)),
("\\sin^{-1} a", asin(a)),
("\\sin a \\cos b", _Mul(sin(a), cos(b))),
("\\sin \\cos \\theta", sin(cos(theta))),
("\\sin(\\cos \\theta)", sin(cos(theta))),
("\\arcsin(a)", asin(a)),
("\\arccos(a)", acos(a)),
("\\arctan(a)", atan(a)),
("\\sinh(a)", sinh(a)),
("\\cosh(a)", cosh(a)),
("\\tanh(a)", tanh(a)),
("\\sinh^{-1}(a)", asinh(a)),
("\\cosh^{-1}(a)", acosh(a)),
("\\tanh^{-1}(a)", atanh(a)),
("\\arcsinh(a)", asinh(a)),
("\\arccosh(a)", acosh(a)),
("\\arctanh(a)", atanh(a)),
("\\arsinh(a)", asinh(a)),
("\\arcosh(a)", acosh(a)),
("\\artanh(a)", atanh(a)),
("\\operatorname{arcsinh}(a)", asinh(a)),
("\\operatorname{arccosh}(a)", acosh(a)),
("\\operatorname{arctanh}(a)", atanh(a)),
("\\operatorname{arsinh}(a)", asinh(a)),
("\\operatorname{arcosh}(a)", acosh(a)),
("\\operatorname{artanh}(a)", atanh(a)),
("\\operatorname{gcd}(a, b)", UnevaluatedExpr(gcd(a, b))),
("\\operatorname{lcm}(a, b)", UnevaluatedExpr(lcm(a, b))),
("\\operatorname{gcd}(a,b)", UnevaluatedExpr(gcd(a, b))),
("\\operatorname{lcm}(a,b)", UnevaluatedExpr(lcm(a, b))),
("\\operatorname{floor}(a)", floor(a)),
("\\operatorname{ceil}(b)", ceiling(b)),
("\\cos^2(x)", cos(x)**2),
("\\cos(x)^2", cos(x)**2),
("\\gcd(a, b)", UnevaluatedExpr(gcd(a, b))),
("\\lcm(a, b)", UnevaluatedExpr(lcm(a, b))),
("\\gcd(a,b)", UnevaluatedExpr(gcd(a, b))),
("\\lcm(a,b)", UnevaluatedExpr(lcm(a, b))),
("\\floor(a)", floor(a)),
("\\ceil(b)", ceiling(b)),
("\\max(a, b)", Max(a, b)),
("\\min(a, b)", Min(a, b)),
("\\frac{a}{b}", a / b),
("\\frac{a + b}{c}", _Mul(a + b, _Pow(c, -1))),
("\\frac{7}{3}", Rational(7, 3)),
("(\\csc x)(\\sec y)", csc(x) * sec(y)),
("\\lim_{x \\to 3} a", Limit(a, x, 3)),
("\\lim_{x \\rightarrow 3} a", Limit(a, x, 3)),
("\\lim_{x \\Rightarrow 3} a", Limit(a, x, 3)),
("\\lim_{x \\longrightarrow 3} a", Limit(a, x, 3)),
("\\lim_{x \\Longrightarrow 3} a", Limit(a, x, 3)),
("\\lim_{x \\to 3^{+}} a", Limit(a, x, 3, dir='+')),
("\\lim_{x \\to 3^{-}} a", Limit(a, x, 3, dir='-')),
("\\infty", oo),
("\\infty\\%", oo),
("\\$\\infty", oo),
("-\\infty", -oo),
("-\\infty\\%", -oo),
("-\\$\\infty", -oo),
("\\lim_{x \\to \\infty} \\frac{1}{x}", Limit(_Mul(1, _Pow(x, -1)), x, oo)),
("\\frac{d}{dx} x", Derivative(x, x)),
("\\frac{d}{dt} x", Derivative(x, t)),
# ("f(x)", f(x)),
# ("f(x, y)", f(x, y)),
# ("f(x, y, z)", f(x, y, z)),
# ("\\frac{d f(x)}{dx}", Derivative(f(x), x)),
# ("\\frac{d\\theta(x)}{dx}", Derivative(theta(x), x)),
("|x|", _Abs(x)),
("\\left|x\\right|", _Abs(x)),
("||x||", _Abs(_Abs(x))),
("|x||y|", _Abs(x) * _Abs(y)),
("||x||y||", _Abs(_Abs(x) * _Abs(y))),
("\\lfloor x\\rfloor", floor(x)),
("\\lceil y\\rceil", ceiling(y)),
("\\pi^{|xy|}", pi**_Abs(x * y)),
("\\frac{\\pi}{3}", _Mul(pi, _Pow(3, -1))),
("\\sin{\\frac{\\pi}{2}}", sin(_Mul(pi, _Pow(2, -1)), evaluate=False)),
("a+bI", a + I * b),
("e^{I\\pi}", Integer(-1)),
("\\int x dx", Integral(x, x)),
("\\int x d\\theta", Integral(x, theta)),
("\\int (x^2 - y)dx", Integral(x**2 - y, x)),
("\\int x + a dx", Integral(_Add(x, a), x)),
("\\int da", Integral(1, a)),
("\\int_0^7 dx", Integral(1, (x, 0, 7))),
("\\int_a^b x dx", Integral(x, (x, a, b))),
("\\int^b_a x dx", Integral(x, (x, a, b))),
("\\int_{a}^b x dx", Integral(x, (x, a, b))),
("\\int^{b}_a x dx", Integral(x, (x, a, b))),
("\\int_{a}^{b} x dx", Integral(x, (x, a, b))),
("\\int_{ }^{}x dx", Integral(x, x)),
("\\int^{ }_{ }x dx", Integral(x, x)),
("\\int^{b}_{a} x dx", Integral(x, (x, a, b))),
# ("\\int_{f(a)}^{f(b)} f(z) dz", Integral(f(z), (z, f(a), f(b)))),
("\\int (x+a)", Integral(_Add(x, a), x)),
("\\int a + b + c dx", Integral(Add(a, b, c, evaluate=False), x)),
("\\int \\frac{dz}{z}", Integral(Pow(z, -1), z)),
("\\int \\frac{3 dz}{z}", Integral(3 * Pow(z, -1), z)),
("\\int \\frac{1}{x} dx", Integral(Pow(x, -1), x)),
("\\int \\frac{1}{a} + \\frac{1}{b} dx", Integral(_Add(_Pow(a, -1), Pow(b, -1)), x)),
("\\int \\frac{3 \\cdot d\\theta}{\\theta}", Integral(3 * _Pow(theta, -1), theta)),
("\\int \\frac{1}{x} + 1 dx", Integral(_Add(_Pow(x, -1), 1), x)),
("x_0", Symbol('x_0', real=True, positive=True)),
("x_{1}", Symbol('x_1', real=True, positive=True)),
("x_a", Symbol('x_a', real=True, positive=True)),
("x_{b}", Symbol('x_b', real=True, positive=True)),
("h_\\theta", Symbol('h_{\\theta}', real=True, positive=True)),
("h_\\theta ", Symbol('h_{\\theta}', real=True, positive=True)),
("h_{\\theta}", Symbol('h_{\\theta}', real=True, positive=True)),
# ("h_{\\theta}(x_0, x_1)", Symbol('h_{theta}', real=True)(Symbol('x_{0}', real=True), Symbol('x_{1}', real=True))),
("x!", _factorial(x)),
("100!", _factorial(100)),
("\\theta!", _factorial(theta)),
("(x + 1)!", _factorial(_Add(x, 1))),
("\\left(x + 1\\right)!", _factorial(_Add(x, 1))),
("(x!)!", _factorial(_factorial(x))),
("x!!!", _factorial(_factorial(_factorial(x)))),
("5!7!", _Mul(_factorial(5), _factorial(7))),
("\\sqrt{x}", sqrt(x)),
("\\sqrt{x + b}", sqrt(_Add(x, b))),
("\\sqrt[3]{\\sin x}", root(sin(x), 3)),
("\\sqrt[y]{\\sin x}", root(sin(x), y)),
("\\sqrt[\\theta]{\\sin x}", root(sin(x), theta)),
("x < y", StrictLessThan(x, y)),
("x \\leq y", LessThan(x, y)),
("x > y", StrictGreaterThan(x, y)),
("x \\geq y", GreaterThan(x, y)),
("\\sum_{k = 1}^{3} c", Sum(c, (k, 1, 3))),
("\\sum_{k = 1}^3 c", Sum(c, (k, 1, 3))),
("\\sum^{3}_{k = 1} c", Sum(c, (k, 1, 3))),
("\\sum^3_{k = 1} c", Sum(c, (k, 1, 3))),
("\\sum_{k = 1}^{10} k^2", Sum(k**2, (k, 1, 10))),
("\\sum_{n = 0}^{\\infty} \\frac{1}{n!}", Sum(_Pow(_factorial(n), -1), (n, 0, oo))),
("\\prod_{a = b}^{c} x", Product(x, (a, b, c))),
("\\prod_{a = b}^c x", Product(x, (a, b, c))),
("\\prod^{c}_{a = b} x", Product(x, (a, b, c))),
("\\prod^c_{a = b} x", Product(x, (a, b, c))),
("\\ln x", _log(x, E)),
("\\ln xy", _log(x * y, E)),
("\\log x", _log(x, 10)),
("\\log xy", _log(x * y, 10)),
# ("\\log_2 x", _log(x, 2)),
("\\log_{2} x", _log(x, 2)),
# ("\\log_a x", _log(x, a)),
("\\log_{a} x", _log(x, a)),
("\\log_{11} x", _log(x, 11)),
("\\log_{a^2} x", _log(x, _Pow(a, 2))),
("[x]", x),
("[a + b]", _Add(a, b)),
("\\frac{d}{dx} [ \\tan x ]", Derivative(tan(x), x)),
("2\\overline{x}", 2 * Symbol('xbar', real=True, positive=True)),
("2\\overline{x}_n", 2 * Symbol('xbar_n', real=True, positive=True)),
("\\frac{x}{\\overline{x}_n}", x / Symbol('xbar_n', real=True, positive=True)),
("\\frac{\\sin(x)}{\\overline{x}_n}", sin(x) / Symbol('xbar_n', real=True, positive=True)),
("2\\bar{x}", 2 * Symbol('xbar', real=True, positive=True)),
("2\\bar{x}_n", 2 * Symbol('xbar_n', real=True, positive=True)),
("\\sin\\left(\\theta\\right) \\cdot4", sin(theta) * 4),
("\\ln\\left(\\theta\\right)", _log(theta, E)),
("\\ln\\left(x-\\theta\\right)", _log(x - theta, E)),
("\\ln\\left(\\left(x-\\theta\\right)\\right)", _log(x - theta, E)),
("\\ln\\left(\\left[x-\\theta\\right]\\right)", _log(x - theta, E)),
("\\ln\\left(\\left\\{x-\\theta\\right\\}\\right)", _log(x - theta, E)),
("\\ln\\left(\\left|x-\\theta\\right|\\right)", _log(_Abs(x - theta), E)),
("\\frac{1}{2}xy(x+y)", Mul(Rational(1, 2), x, y, (x + y), evaluate=False)),
("\\frac{1}{2}\\theta(x+y)", Mul(Rational(1, 2), theta, (x + y), evaluate=False)),
("1-f(x)", 1 - f * x),
("\\begin{matrix}1&2\\\\3&4\\end{matrix}", Matrix([[1, 2], [3, 4]])),
("\\begin{matrix}x&x^2\\\\\\sqrt{x}&x\\end{matrix}", Matrix([[x, x**2], [_Pow(x, S.Half), x]])),
("\\begin{matrix}\\sqrt{x}\\\\\\sin(\\theta)\\end{matrix}", Matrix([_Pow(x, S.Half), sin(theta)])),
("\\begin{pmatrix}1&2\\\\3&4\\end{pmatrix}", Matrix([[1, 2], [3, 4]])),
("\\begin{bmatrix}1&2\\\\3&4\\end{bmatrix}", Matrix([[1, 2], [3, 4]])),
# scientific notation
("2.5\\times 10^2", Rational(250)),
("1,500\\times 10^{-1}", Rational(150)),
# e notation
("2.5E2", Rational(250)),
("1,500E-1", Rational(150)),
# multiplication without cmd
("2x2y", Mul(2, x, 2, y, evaluate=False)),
("2x2", Mul(2, x, 2, evaluate=False)),
("x2", x * 2),
# lin alg processing
("\\theta\\begin{matrix}1&2\\\\3&4\\end{matrix}", MatMul(theta, Matrix([[1, 2], [3, 4]]), evaluate=False)),
("\\theta\\begin{matrix}1\\\\3\\end{matrix} - \\begin{matrix}-1\\\\2\\end{matrix}", MatAdd(MatMul(theta, Matrix([[1], [3]]), evaluate=False), MatMul(-1, Matrix([[-1], [2]]), evaluate=False), evaluate=False)),
("\\theta\\begin{matrix}1&0\\\\0&1\\end{matrix}*\\begin{matrix}3\\\\-2\\end{matrix}", MatMul(theta, Matrix([[1, 0], [0, 1]]), Matrix([3, -2]), evaluate=False)),
("\\frac{1}{9}\\theta\\begin{matrix}1&2\\\\3&4\\end{matrix}", MatMul(Rational(1, 9), theta, Matrix([[1, 2], [3, 4]]), evaluate=False)),
("\\begin{pmatrix}1\\\\2\\\\3\\end{pmatrix},\\begin{pmatrix}4\\\\3\\\\1\\end{pmatrix}", [Matrix([1, 2, 3]), Matrix([4, 3, 1])]),
("\\begin{pmatrix}1\\\\2\\\\3\\end{pmatrix};\\begin{pmatrix}4\\\\3\\\\1\\end{pmatrix}", [Matrix([1, 2, 3]), Matrix([4, 3, 1])]),
("\\left\\{\\begin{pmatrix}1\\\\2\\\\3\\end{pmatrix},\\begin{pmatrix}4\\\\3\\\\1\\end{pmatrix}\\right\\}", [Matrix([1, 2, 3]), Matrix([4, 3, 1])]),
("\\left\\{\\begin{pmatrix}1\\\\2\\\\3\\end{pmatrix},\\begin{pmatrix}4\\\\3\\\\1\\end{pmatrix},\\begin{pmatrix}1\\\\1\\\\1\\end{pmatrix}\\right\\}", [Matrix([1, 2, 3]), Matrix([4, 3, 1]), Matrix([1, 1, 1])]),
("\\left\\{\\begin{pmatrix}1\\\\2\\\\3\\end{pmatrix}\\right\\}", Matrix([1, 2, 3])),
("\\left{\\begin{pmatrix}1\\\\2\\\\3\\end{pmatrix}\\right}", Matrix([1, 2, 3])),
("{\\begin{pmatrix}1\\\\2\\\\3\\end{pmatrix}}", Matrix([1, 2, 3])),
# us dollars
("\\$1,000.00", Rational(1000)),
("\\$543.21", Rational(54321, 100)),
("\\$0.009", Rational(9, 1000)),
# percentages
("100\\%", Rational(1)),
("1.5\\%", Rational(15, 1000)),
("0.05\\%", Rational(5, 10000)),
# empty set
("\\emptyset", S.EmptySet),
# divide by zero
("\\frac{1}{0}", _Pow(0, -1)),
("1+\\frac{5}{0}", _Add(1, _Mul(5, _Pow(0, -1)))),
# adjacent single char sub sup
("4^26^2", _Mul(_Pow(4, 2), _Pow(6, 2))),
("x_22^2", _Mul(Symbol('x_2', real=True, positive=True), _Pow(2, 2)))
]
def test_good_pair(self, s, eq):
assert_equal(s, eq)
from sympy import (Symbol, MatrixSymbol, ZeroMatrix, Add, Mul, MatAdd, MatMul,
Determinant, Inverse, Trace, Transpose)
from .symbols import d, Kron, SymmetricMatrixSymbol
from .simplifications import simplify_matdiff
MATRIX_DIFF_RULES = {
# e =expression, s = a list of symbols respsect to which
# we want to differentiate
Symbol: lambda e, s: d(e) if (e in s) else 0,
MatrixSymbol: lambda e, s: d(e) if (e in s) else ZeroMatrix(*e.shape),
SymmetricMatrixSymbol: lambda e, s: d(e) if (e in s) else ZeroMatrix(*e.shape),
Add: lambda e, s: Add(*[_matDiff_apply(arg, s) for arg in e.args]),
Mul: lambda e, s: _matDiff_apply(e.args[0], s) if len(e.args)==1 else Mul(_matDiff_apply(e.args[0],s),Mul(*e.args[1:])) + Mul(e.args[0], _matDiff_apply(Mul(*e.args[1:]),s)),
MatAdd: lambda e, s: MatAdd(*[_matDiff_apply(arg, s) for arg in e.args]),
MatMul: lambda e, s: _matDiff_apply(e.args[0], s) if len(e.args)==1 else MatMul(_matDiff_apply(e.args[0],s),MatMul(*e.args[1:])) + MatMul(e.args[0], _matDiff_apply(MatMul(*e.args[1:]),s)),
Kron: lambda e, s: _matDiff_apply(e.args[0],s) if len(e.args)==1 else Kron(_matDiff_apply(e.args[0],s),Kron(*e.args[1:]))
+ Kron(e.args[0],_matDiff_apply(Kron(*e.args[1:]),s)),
Determinant: lambda e, s: MatMul(Determinant(e.args[0]), Trace(e.args[0].I*_matDiff_apply(e.args[0], s))),
# inverse always has 1 arg, so we index
Inverse: lambda e, s: -Inverse(e.args[0]) * _matDiff_apply(e.args[0], s) * Inverse(e.args[0]),
# trace always has 1 arg
Trace: lambda e, s: Trace(_matDiff_apply(e.args[0], s)),
# transpose also always has 1 arg, index
Transpose: lambda e, s: Transpose(_matDiff_apply(e.args[0], s))
}
def _matDiff_apply(expr, syms):
if expr.__class__ in list(MATRIX_DIFF_RULES.keys()):
return MATRIX_DIFF_RULES[expr.__class__](expr, syms)
elif expr.is_constant():
def _a2m_add(*args):
if all(not isinstance(i, _CodegenArrayAbstract) for i in args):
from sympy import MatAdd
return MatAdd(*args).doit()
else:
return ArrayAdd(*args)
def expand(expr, factor=1, depth=0):
return sympyExpand(expr)
if depth == 0:
return flattenAdd(expand(expr, depth=depth + 1))
if not isinstance(expr, MatMul) and not isinstance(expr, MatAdd):
return sympyExpand(factor * expr, depth=depth + 1)
else:
if isinstance(expr, MatAdd):
ret = []
for arg in expr.args:
tmp = expand(arg, factor=factor, depth=depth + 1)
if not isZero(tmp):
ret.append(tmp)
return MatAdd(*ret)
scalar = factor
mat = []
for el in expr.args:
if not (hasattr(el, 'is_Matrix') and el.is_Matrix):
scalar *= el
else:
mat.append(el)
scalar = [
el for el in flatten(sympyExpand(scalar).as_coeff_add()) if el != 0
]
if len(scalar) == 0:
return 0
if len(scalar) > 1:
ret = []
for s in scalar:
tmp = expand(MatMul(*mat), factor=s, depth=depth + 1)
if not isZero(tmp):
ret.append(tmp)
return MatAdd(*ret)
add = []
toDistribute = False
for el in mat:
el = expand(el, depth=depth + 1)
if isinstance(el, MatAdd):
add.append(el.args)
toDistribute = True
else:
add.append([el])
if toDistribute == False:
ret = scalar[0]
for el in mat:
if not isinstance(el, MatMul):
ret *= el
else:
for ell in el.args:
ret *= ell
return ret
add = itertools.product(*add)
ret = []
for el in add:
if len(el) == 1:
tmp = expand(el[0], factor=scalar[0], depth=depth + 1)
else:
tmp = expand(MatMul(*el), factor=scalar[0], depth=depth + 1)
if tmp == 0:
continue
ret.append(tmp)
return MatAdd(*ret)
def time_MatAdd_doit(self):
MatAdd(*args).doit()
def time_MatAdd(self):
MatAdd(*args)
def __new__(cls, *args, **kwargs):
return MatAdd.__new__(cls, *args, **kwargs)
