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