def test_Trace(): assert isinstance(Trace(A), Trace) assert not isinstance(Trace(A), MatrixExpr) pytest.raises(ShapeError, lambda: Trace(C)) assert trace(eye(3)) == 3 assert trace(Matrix(3, 3, [1, 2, 3, 4, 5, 6, 7, 8, 9])) == 15 assert adjoint(Trace(A)) == trace(Adjoint(A)) assert conjugate(Trace(A)) == trace(Adjoint(A)) assert transpose(Trace(A)) == Trace(A) A / Trace(A) # Make sure this is possible # Some easy simplifications assert trace(Identity(5)) == 5 assert trace(ZeroMatrix(5, 5)) == 0 assert trace(2*A*B) == 2*Trace(A*B) assert trace(A.T) == trace(A) i, j = symbols('i j') F = FunctionMatrix(3, 3, Lambda((i, j), i + j)) assert trace(F) == (0 + 0) + (1 + 1) + (2 + 2) pytest.raises(TypeError, lambda: Trace(1)) assert Trace(A).arg is A assert str(trace(A)) == str(Trace(A).doit())
def test_Trace(): assert isinstance(Trace(A), Trace) assert not isinstance(Trace(A), MatrixExpr) pytest.raises(ShapeError, lambda: Trace(C)) assert trace(eye(3)) == 3 assert trace(Matrix(3, 3, [1, 2, 3, 4, 5, 6, 7, 8, 9])) == 15 assert adjoint(Trace(A)) == trace(Adjoint(A)) assert conjugate(Trace(A)) == trace(Adjoint(A)) assert transpose(Trace(A)) == Trace(A) A / Trace(A) # Make sure this is possible # Some easy simplifications assert trace(Identity(5)) == 5 assert trace(ZeroMatrix(5, 5)) == 0 assert trace(2 * A * B) == 2 * Trace(A * B) assert trace(A.T) == trace(A) i, j = symbols('i j') F = FunctionMatrix(3, 3, Lambda((i, j), i + j)) assert trace(F) == (0 + 0) + (1 + 1) + (2 + 2) pytest.raises(TypeError, lambda: Trace(S.One)) assert Trace(A).arg is A assert str(trace(A)) == str(Trace(A).doit())
def test_transpose(): Sq = MatrixSymbol('Sq', n, n) assert transpose(A) == Transpose(A) assert Transpose(A).shape == (m, n) assert Transpose(A*B).shape == (l, n) assert transpose(Transpose(A)) == A assert isinstance(Transpose(Transpose(A)), Transpose) assert adjoint(Transpose(A)) == Adjoint(Transpose(A)) assert conjugate(Transpose(A)) == Adjoint(A) assert Transpose(eye(3)).doit() == eye(3) assert Transpose(eye(3)).doit(deep=False) == eye(3) assert Transpose(Integer(5)).doit() == Integer(5) assert Transpose(Matrix([[1, 2], [3, 4]])).doit() == Matrix([[1, 3], [2, 4]]) assert transpose(trace(Sq)) == trace(Sq) assert trace(Transpose(Sq)) == trace(Sq) assert Transpose(Sq)[0, 1] == Sq[1, 0] assert Transpose(A*B).doit() == Transpose(B) * Transpose(A)
def test_Function(): assert mcode(f(x, y, z)) == "f[x, y, z]" assert mcode(sin(x)**cos(x)) == "Sin[x]^Cos[x]" assert mcode(sign(x)) == "Sign[x]" assert mcode(atanh(x), user_functions={"atanh": "ArcTanh"}) == "ArcTanh[x]" assert (mcode(meijerg(((1, 1), (3, 4)), ((1, ), ()), x)) == "MeijerG[{{1, 1}, {3, 4}}, {{1}, {}}, x]") assert (mcode(hyper((1, 2, 3), (3, 4), x)) == "HypergeometricPFQ[{1, 2, 3}, {3, 4}, x]") assert mcode(Min(x, y)) == "Min[x, y]" assert mcode(Max(x, y)) == "Max[x, y]" assert mcode(Max(x, 2)) == "Max[2, x]" # issue sympy/sympy#15344 assert mcode(binomial(x, y)) == "Binomial[x, y]" assert mcode(log(x)) == "Log[x]" assert mcode(tan(x)) == "Tan[x]" assert mcode(cot(x)) == "Cot[x]" assert mcode(asin(x)) == "ArcSin[x]" assert mcode(acos(x)) == "ArcCos[x]" assert mcode(atan(x)) == "ArcTan[x]" assert mcode(sinh(x)) == "Sinh[x]" assert mcode(cosh(x)) == "Cosh[x]" assert mcode(tanh(x)) == "Tanh[x]" assert mcode(coth(x)) == "Coth[x]" assert mcode(sech(x)) == "Sech[x]" assert mcode(csch(x)) == "Csch[x]" assert mcode(erfc(x)) == "Erfc[x]" assert mcode(conjugate(x)) == "Conjugate[x]" assert mcode(re(x)) == "Re[x]" assert mcode(im(x)) == "Im[x]" assert mcode(polygamma(x, y)) == "PolyGamma[x, y]" class myfunc1(Function): @classmethod def eval(cls, x): pass class myfunc2(Function): @classmethod def eval(cls, x, y): pass pytest.raises( ValueError, lambda: mcode(myfunc1(x), user_functions={"myfunc1": ["Myfunc1"]})) assert mcode(myfunc1(x), user_functions={"myfunc1": "Myfunc1"}) == "Myfunc1[x]" assert mcode(myfunc2(x, y), user_functions={"myfunc2": [(lambda *x: False, "Myfunc2")] }) == "myfunc2[x, y]"
def test_adjoint(): Sq = MatrixSymbol('Sq', n, n) assert Adjoint(A).shape == (m, n) assert Adjoint(A * B).shape == (l, n) assert adjoint(Adjoint(A)) == A assert isinstance(Adjoint(Adjoint(A)), Adjoint) assert conjugate(Adjoint(A)) == Transpose(A) assert transpose(Adjoint(A)) == Adjoint(Transpose(A)) assert Adjoint(eye(3)).doit() == eye(3) assert Adjoint(Integer(5)).doit() == Integer(5) assert Adjoint(Matrix([[1, 2], [3, 4]])).doit() == Matrix([[1, 3], [2, 4]]) assert adjoint(trace(Sq)) == conjugate(trace(Sq)) assert trace(adjoint(Sq)) == conjugate(trace(Sq)) assert Adjoint(Sq)[0, 1] == conjugate(Sq[1, 0]) assert Adjoint(A * B).doit() == Adjoint(B) * Adjoint(A)
def test_adjoint(): Sq = MatrixSymbol('Sq', n, n) assert Adjoint(A).shape == (m, n) assert Adjoint(A*B).shape == (l, n) assert adjoint(Adjoint(A)) == A assert isinstance(Adjoint(Adjoint(A)), Adjoint) assert conjugate(Adjoint(A)) == Transpose(A) == Adjoint(A).conjugate() assert transpose(Adjoint(A)) == Adjoint(Transpose(A)) == Transpose(A).adjoint() assert Adjoint(eye(3)).doit() == Adjoint(eye(3)).doit(deep=False) == eye(3) assert Adjoint(Integer(5)).doit() == Integer(5) assert Adjoint(Matrix([[1, 2], [3, 4]])).doit() == Matrix([[1, 3], [2, 4]]) assert adjoint(trace(Sq)) == conjugate(trace(Sq)) assert trace(adjoint(Sq)) == conjugate(trace(Sq)) assert Adjoint(Sq)[0, 1] == conjugate(Sq[1, 0]) assert Adjoint(A*B).doit() == Adjoint(B) * Adjoint(A) assert Adjoint(C + D).doit() == Adjoint(C) + Adjoint(D)
def _eval_adjoint(self): return conjugate(self.arg)
def _eval_transpose(self): return conjugate(self.arg)
def _eval_trace(self): from diofant.matrices.expressions.trace import Trace return conjugate(Trace(self.arg))
def _entry(self, i, j): return conjugate(self.arg._entry(j, i))
def test_Function(): assert mcode(f(x, y, z)) == "f[x, y, z]" assert mcode(sin(x) ** cos(x)) == "Sin[x]^Cos[x]" assert mcode(sign(x)) == "Sign[x]" assert mcode(atanh(x), user_functions={"atanh": "ArcTanh"}) == "ArcTanh[x]" assert (mcode(meijerg(((1, 1), (3, 4)), ((1,), ()), x)) == "MeijerG[{{1, 1}, {3, 4}}, {{1}, {}}, x]") assert (mcode(hyper((1, 2, 3), (3, 4), x)) == "HypergeometricPFQ[{1, 2, 3}, {3, 4}, x]") assert mcode(Min(x, y)) == "Min[x, y]" assert mcode(Max(x, y)) == "Max[x, y]" assert mcode(Max(x, 2)) == "Max[2, x]" # issue sympy/sympy#15344 assert mcode(binomial(x, y)) == "Binomial[x, y]" assert mcode(log(x)) == "Log[x]" assert mcode(tan(x)) == "Tan[x]" assert mcode(cot(x)) == "Cot[x]" assert mcode(asin(x)) == "ArcSin[x]" assert mcode(acos(x)) == "ArcCos[x]" assert mcode(atan(x)) == "ArcTan[x]" assert mcode(sinh(x)) == "Sinh[x]" assert mcode(cosh(x)) == "Cosh[x]" assert mcode(tanh(x)) == "Tanh[x]" assert mcode(coth(x)) == "Coth[x]" assert mcode(sech(x)) == "Sech[x]" assert mcode(csch(x)) == "Csch[x]" assert mcode(erfc(x)) == "Erfc[x]" assert mcode(conjugate(x)) == "Conjugate[x]" assert mcode(re(x)) == "Re[x]" assert mcode(im(x)) == "Im[x]" assert mcode(polygamma(x, y)) == "PolyGamma[x, y]" assert mcode(factorial(x)) == "Factorial[x]" assert mcode(factorial2(x)) == "Factorial2[x]" assert mcode(rf(x, y)) == "Pochhammer[x, y]" assert mcode(gamma(x)) == "Gamma[x]" assert mcode(zeta(x)) == "Zeta[x]" assert mcode(asinh(x)) == "ArcSinh[x]" assert mcode(Heaviside(x)) == "UnitStep[x]" assert mcode(fibonacci(x)) == "Fibonacci[x]" assert mcode(polylog(x, y)) == "PolyLog[x, y]" assert mcode(atanh(x)) == "ArcTanh[x]" class myfunc1(Function): @classmethod def eval(cls, x): pass class myfunc2(Function): @classmethod def eval(cls, x, y): pass pytest.raises(ValueError, lambda: mcode(myfunc1(x), user_functions={"myfunc1": ["Myfunc1"]})) assert mcode(myfunc1(x), user_functions={"myfunc1": "Myfunc1"}) == "Myfunc1[x]" assert mcode(myfunc2(x, y), user_functions={"myfunc2": [(lambda *x: False, "Myfunc2")]}) == "myfunc2[x, y]"
def conjugate(self): return conjugate(self)