119 lines
3.4 KiB
Python
119 lines
3.4 KiB
Python
from sympy.core.symbol import symbols, Dummy
|
|
from sympy.matrices.expressions.applyfunc import ElementwiseApplyFunction
|
|
from sympy.core.function import Lambda
|
|
from sympy.functions.elementary.exponential import exp
|
|
from sympy.functions.elementary.trigonometric import sin
|
|
from sympy.matrices.dense import Matrix
|
|
from sympy.matrices.expressions.matexpr import MatrixSymbol
|
|
from sympy.matrices.expressions.matmul import MatMul
|
|
from sympy.simplify.simplify import simplify
|
|
|
|
|
|
X = MatrixSymbol("X", 3, 3)
|
|
Y = MatrixSymbol("Y", 3, 3)
|
|
|
|
k = symbols("k")
|
|
Xk = MatrixSymbol("X", k, k)
|
|
|
|
Xd = X.as_explicit()
|
|
|
|
x, y, z, t = symbols("x y z t")
|
|
|
|
|
|
def test_applyfunc_matrix():
|
|
x = Dummy('x')
|
|
double = Lambda(x, x**2)
|
|
|
|
expr = ElementwiseApplyFunction(double, Xd)
|
|
assert isinstance(expr, ElementwiseApplyFunction)
|
|
assert expr.doit() == Xd.applyfunc(lambda x: x**2)
|
|
assert expr.shape == (3, 3)
|
|
assert expr.func(*expr.args) == expr
|
|
assert simplify(expr) == expr
|
|
assert expr[0, 0] == double(Xd[0, 0])
|
|
|
|
expr = ElementwiseApplyFunction(double, X)
|
|
assert isinstance(expr, ElementwiseApplyFunction)
|
|
assert isinstance(expr.doit(), ElementwiseApplyFunction)
|
|
assert expr == X.applyfunc(double)
|
|
assert expr.func(*expr.args) == expr
|
|
|
|
expr = ElementwiseApplyFunction(exp, X*Y)
|
|
assert expr.expr == X*Y
|
|
assert expr.function.dummy_eq(Lambda(x, exp(x)))
|
|
assert expr.dummy_eq((X*Y).applyfunc(exp))
|
|
assert expr.func(*expr.args) == expr
|
|
|
|
assert isinstance(X*expr, MatMul)
|
|
assert (X*expr).shape == (3, 3)
|
|
Z = MatrixSymbol("Z", 2, 3)
|
|
assert (Z*expr).shape == (2, 3)
|
|
|
|
expr = ElementwiseApplyFunction(exp, Z.T)*ElementwiseApplyFunction(exp, Z)
|
|
assert expr.shape == (3, 3)
|
|
expr = ElementwiseApplyFunction(exp, Z)*ElementwiseApplyFunction(exp, Z.T)
|
|
assert expr.shape == (2, 2)
|
|
|
|
M = Matrix([[x, y], [z, t]])
|
|
expr = ElementwiseApplyFunction(sin, M)
|
|
assert isinstance(expr, ElementwiseApplyFunction)
|
|
assert expr.function.dummy_eq(Lambda(x, sin(x)))
|
|
assert expr.expr == M
|
|
assert expr.doit() == M.applyfunc(sin)
|
|
assert expr.doit() == Matrix([[sin(x), sin(y)], [sin(z), sin(t)]])
|
|
assert expr.func(*expr.args) == expr
|
|
|
|
expr = ElementwiseApplyFunction(double, Xk)
|
|
assert expr.doit() == expr
|
|
assert expr.subs(k, 2).shape == (2, 2)
|
|
assert (expr*expr).shape == (k, k)
|
|
M = MatrixSymbol("M", k, t)
|
|
expr2 = M.T*expr*M
|
|
assert isinstance(expr2, MatMul)
|
|
assert expr2.args[1] == expr
|
|
assert expr2.shape == (t, t)
|
|
expr3 = expr*M
|
|
assert expr3.shape == (k, t)
|
|
|
|
expr1 = ElementwiseApplyFunction(lambda x: x+1, Xk)
|
|
expr2 = ElementwiseApplyFunction(lambda x: x, Xk)
|
|
assert expr1 != expr2
|
|
|
|
|
|
def test_applyfunc_entry():
|
|
|
|
af = X.applyfunc(sin)
|
|
assert af[0, 0] == sin(X[0, 0])
|
|
|
|
af = Xd.applyfunc(sin)
|
|
assert af[0, 0] == sin(X[0, 0])
|
|
|
|
|
|
def test_applyfunc_as_explicit():
|
|
|
|
af = X.applyfunc(sin)
|
|
assert af.as_explicit() == Matrix([
|
|
[sin(X[0, 0]), sin(X[0, 1]), sin(X[0, 2])],
|
|
[sin(X[1, 0]), sin(X[1, 1]), sin(X[1, 2])],
|
|
[sin(X[2, 0]), sin(X[2, 1]), sin(X[2, 2])],
|
|
])
|
|
|
|
|
|
def test_applyfunc_transpose():
|
|
|
|
af = Xk.applyfunc(sin)
|
|
assert af.T.dummy_eq(Xk.T.applyfunc(sin))
|
|
|
|
|
|
def test_applyfunc_shape_11_matrices():
|
|
M = MatrixSymbol("M", 1, 1)
|
|
|
|
double = Lambda(x, x*2)
|
|
|
|
expr = M.applyfunc(sin)
|
|
assert isinstance(expr, ElementwiseApplyFunction)
|
|
|
|
expr = M.applyfunc(double)
|
|
assert isinstance(expr, MatMul)
|
|
assert expr == 2*M
|