def test_imag():
I = S('I')
assert mcode(I) == "1i"
assert mcode(5 * I) == "5i"
assert mcode((S(3) / 2) * I) == "3*1i/2"
assert mcode(3 + 4 * I) == "3 + 4i"
assert mcode(sqrt(3) * I) == "sqrt(3)*1i"
def test_octave_matrix_1x1():
A = Matrix([[3]])
B = MatrixSymbol('B', 1, 1)
C = MatrixSymbol('C', 1, 2)
assert mcode(A, assign_to=B) == "B = 3;"
# FIXME?
#assert mcode(A, assign_to=x) == "x = 3;"
raises(ValueError, lambda: mcode(A, assign_to=C))
def test_octave_matrix_assign_to_more():
# assigning to Symbol or MatrixSymbol requires lhs/rhs match
A = Matrix([[1, 2, 3]])
B = MatrixSymbol('B', 1, 3)
C = MatrixSymbol('C', 2, 3)
assert mcode(A, assign_to=B) == "B = [1 2 3];"
raises(ValueError, lambda: mcode(A, assign_to=x))
raises(ValueError, lambda: mcode(A, assign_to=C))
def test_octave_not_supported():
assert mcode(S.ComplexInfinity) == ("% Not supported in Octave:\n"
"% ComplexInfinity\n"
"zoo")
f = Function('f')
assert mcode(f(x).diff(x)) == ("% Not supported in Octave:\n"
"% Derivative\n"
"Derivative(f(x), x)")
def test_octave_expint():
assert mcode(expint(1, x)) == "expint(x)"
assert mcode(expint(2, x)) == ("% Not supported in Octave:\n"
"% expint\n"
"expint(2, x)")
assert mcode(expint(y, x)) == ("% Not supported in Octave:\n"
"% expint\n"
"expint(y, x)")
def test_octave_matrix_elements():
A = Matrix([[x, 2, x * y]])
assert mcode(A[0, 0]**2 + A[0, 1] + A[0, 2]) == "x.^2 + x.*y + 2"
A = MatrixSymbol('AA', 1, 3)
assert mcode(A) == "AA"
assert mcode(A[0, 0]**2 + sin(A[0,1]) + A[0,2]) == \
"sin(AA(1, 2)) + AA(1, 1).^2 + AA(1, 3)"
assert mcode(sum(A)) == "AA(1, 1) + AA(1, 2) + AA(1, 3)"
def test_MatrixElement_printing():
# test cases for issue #11821
A = MatrixSymbol("A", 1, 3)
B = MatrixSymbol("B", 1, 3)
C = MatrixSymbol("C", 1, 3)
assert mcode(A[0, 0]) == "A(1, 1)"
assert mcode(3 * A[0, 0]) == "3*A(1, 1)"
F = C[0, 0].subs(C, A - B)
assert mcode(F) == "(A - B)(1, 1)"
def test_Pow():
assert mcode(x**3) == "x.^3"
assert mcode(x**(y**3)) == "x.^(y.^3)"
assert mcode(x**Rational(2, 3)) == 'x.^(2/3)'
g = implemented_function('g', Lambda(x, 2 * x))
assert mcode(1/(g(x)*3.5)**(x - y**x)/(x**2 + y)) == \
"(3.5*2*x).^(-x + y.^x)./(x.^2 + y)"
# For issue 14160
assert mcode(
Mul(-2,
x,
Pow(Mul(y, y, evaluate=False), -1, evaluate=False),
evaluate=False)) == '-2*x./(y.*y)'
def test_Matrices_entries_not_hadamard():
# For Matrix with col >= 2, row >= 2, they need to be scalars
# FIXME: is it worth worrying about this? Its not wrong, just
# leave it user's responsibility to put scalar data for x.
A = Matrix([[1, sin(2 / x), 3 * pi / x / 5], [1, 2, x * y]])
expected = ("[1 sin(2/x) 3*pi/(5*x);\n"
"1 2 x*y]") # <- we give x.*y
assert mcode(A) == expected
def test_octave_piecewise():
expr = Piecewise((x, x < 1), (x**2, True))
assert mcode(expr) == "((x < 1).*(x) + (~(x < 1)).*(x.^2))"
assert mcode(expr,
assign_to="r") == ("r = ((x < 1).*(x) + (~(x < 1)).*(x.^2));")
assert mcode(expr, assign_to="r", inline=False) == ("if (x < 1)\n"
" r = x;\n"
"else\n"
" r = x.^2;\n"
"end")
expr = Piecewise((x**2, x < 1), (x**3, x < 2), (x**4, x < 3), (x**5, True))
expected = ("((x < 1).*(x.^2) + (~(x < 1)).*( ...\n"
"(x < 2).*(x.^3) + (~(x < 2)).*( ...\n"
"(x < 3).*(x.^4) + (~(x < 3)).*(x.^5))))")
assert mcode(expr) == expected
assert mcode(expr, assign_to="r") == "r = " + expected + ";"
assert mcode(expr, assign_to="r", inline=False) == ("if (x < 1)\n"
" r = x.^2;\n"
"elseif (x < 2)\n"
" r = x.^3;\n"
"elseif (x < 3)\n"
" r = x.^4;\n"
"else\n"
" r = x.^5;\n"
"end")
# Check that Piecewise without a True (default) condition error
expr = Piecewise((x, x < 1), (x**2, x > 1), (sin(x), x > 0))
raises(ValueError, lambda: mcode(expr))
def test_sparse():
M = SparseMatrix(5, 6, {})
M[2, 2] = 10
M[1, 2] = 20
M[1, 3] = 22
M[0, 3] = 30
M[3, 0] = x * y
assert mcode(M) == (
"sparse([4 2 3 1 2], [1 3 3 4 4], [x.*y 20 10 30 22], 5, 6)")
def test_boolean():
assert mcode(x & y) == "x & y"
assert mcode(x | y) == "x | y"
assert mcode(~x) == "~x"
assert mcode(x & y & z) == "x & y & z"
assert mcode(x | y | z) == "x | y | z"
assert mcode((x & y) | z) == "z | x & y"
assert mcode((x | y) & z) == "z & (x | y)"
def test_constants():
assert mcode(pi) == "pi"
assert mcode(oo) == "inf"
assert mcode(-oo) == "-inf"
assert mcode(S.NegativeInfinity) == "-inf"
assert mcode(S.NaN) == "NaN"
assert mcode(S.Exp1) == "exp(1)"
assert mcode(exp(1)) == "exp(1)"
def test_MatrixSymbol():
n = Symbol('n', integer=True)
A = MatrixSymbol('A', n, n)
B = MatrixSymbol('B', n, n)
assert mcode(A * B) == "A*B"
assert mcode(B * A) == "B*A"
assert mcode(2 * A * B) == "2*A*B"
assert mcode(B * 2 * A) == "2*B*A"
assert mcode(A * (B + 3 * Identity(n))) == "A*(3*eye(n) + B)"
assert mcode(A**(x**2)) == "A^(x.^2)"
assert mcode(A**3) == "A^3"
assert mcode(A**S.Half) == "A^(1/2)"
def test_trick_indent_with_end_else_words():
# words starting with "end" or "else" do not confuse the indenter
t1 = S('endless')
t2 = S('elsewhere')
pw = Piecewise((t1, x < 0), (t2, x <= 1), (1, True))
assert mcode(pw, inline=False) == ("if (x < 0)\n"
" endless\n"
"elseif (x <= 1)\n"
" elsewhere\n"
"else\n"
" 1\n"
"end")
def test_mix_number_pow_symbols():
assert mcode(pi**3) == 'pi^3'
assert mcode(x**2) == 'x.^2'
assert mcode(x**(pi**3)) == 'x.^(pi^3)'
assert mcode(x**y) == 'x.^y'
assert mcode(x**(y**z)) == 'x.^(y.^z)'
assert mcode((x**y)**z) == '(x.^y).^z'
def test_Rational():
assert mcode(Rational(3, 7)) == "3/7"
assert mcode(Rational(18, 9)) == "2"
assert mcode(Rational(3, -7)) == "-3/7"
assert mcode(Rational(-3, -7)) == "3/7"
assert mcode(x + Rational(3, 7)) == "x + 3/7"
assert mcode(Rational(3, 7) * x) == "3*x/7"
def test_Relational():
assert mcode(Eq(x, y)) == "x == y"
assert mcode(Ne(x, y)) == "x != y"
assert mcode(Le(x, y)) == "x <= y"
assert mcode(Lt(x, y)) == "x < y"
assert mcode(Gt(x, y)) == "x > y"
assert mcode(Ge(x, y)) == "x >= y"
def test_containers():
assert mcode([1, 2, 3, [4, 5, [6, 7]], 8, [9, 10], 11]) == \
"{1, 2, 3, {4, 5, {6, 7}}, 8, {9, 10}, 11}"
assert mcode((1, 2, (3, 4))) == "{1, 2, {3, 4}}"
assert mcode([1]) == "{1}"
assert mcode((1, )) == "{1}"
assert mcode(Tuple(*[1, 2, 3])) == "{1, 2, 3}"
assert mcode((1, x * y, (3, x**2))) == "{1, x.*y, {3, x.^2}}"
# scalar, matrix, empty matrix and empty list
assert mcode(
(1, eye(3), Matrix(0, 0,
[]), [])) == "{1, [1 0 0; 0 1 0; 0 0 1], [], {}}"
def test_Matrices():
assert mcode(Matrix(1, 1, [10])) == "10"
A = Matrix([[1, sin(x / 2), abs(x)], [0, 1, pi], [0, exp(1),
ceiling(x)]])
expected = "[1 sin(x/2) abs(x); 0 1 pi; 0 exp(1) ceil(x)]"
assert mcode(A) == expected
# row and columns
assert mcode(A[:, 0]) == "[1; 0; 0]"
assert mcode(A[0, :]) == "[1 sin(x/2) abs(x)]"
# empty matrices
assert mcode(Matrix(0, 0, [])) == '[]'
assert mcode(Matrix(0, 3, [])) == 'zeros(0, 3)'
# annoying to read but correct
assert mcode(Matrix([[x, x - y, -y]])) == "[x x - y -y]"
def test_hadamard():
A = MatrixSymbol('A', 3, 3)
B = MatrixSymbol('B', 3, 3)
v = MatrixSymbol('v', 3, 1)
h = MatrixSymbol('h', 1, 3)
C = HadamardProduct(A, B)
n = Symbol('n')
assert mcode(C) == "A.*B"
assert mcode(C * v) == "(A.*B)*v"
assert mcode(h * C * v) == "h*(A.*B)*v"
assert mcode(C * A) == "(A.*B)*A"
# mixing Hadamard and scalar strange b/c we vectorize scalars
assert mcode(C * x * y) == "(x.*y)*(A.*B)"
# Testing HadamardPower:
assert mcode(HadamardPower(A, n)) == "A.**n"
assert mcode(HadamardPower(A, 1 + n)) == "A.**(n + 1)"
assert mcode(HadamardPower(A * B.T, 1 + n)) == "(A*B.T).**(n + 1)"
def test_minmax():
assert mcode(Max(x, y) + Min(x, y)) == "max(x, y) + min(x, y)"
assert mcode(Max(x, y, z)) == "max(x, max(y, z))"
assert mcode(Min(x, y, z)) == "min(x, min(y, z))"
def test_Function_change_name():
assert mcode(abs(x)) == "abs(x)"
assert mcode(ceiling(x)) == "ceil(x)"
assert mcode(arg(x)) == "angle(x)"
assert mcode(im(x)) == "imag(x)"
assert mcode(re(x)) == "real(x)"
assert mcode(conjugate(x)) == "conj(x)"
assert mcode(chebyshevt(y, x)) == "chebyshevT(y, x)"
assert mcode(chebyshevu(y, x)) == "chebyshevU(y, x)"
assert mcode(laguerre(x, y)) == "laguerreL(x, y)"
assert mcode(Chi(x)) == "coshint(x)"
assert mcode(Shi(x)) == "sinhint(x)"
assert mcode(Ci(x)) == "cosint(x)"
assert mcode(Si(x)) == "sinint(x)"
assert mcode(li(x)) == "logint(x)"
assert mcode(loggamma(x)) == "gammaln(x)"
assert mcode(polygamma(x, y)) == "psi(x, y)"
assert mcode(RisingFactorial(x, y)) == "pochhammer(x, y)"
assert mcode(DiracDelta(x)) == "dirac(x)"
assert mcode(DiracDelta(x, 3)) == "dirac(3, x)"
assert mcode(Heaviside(x)) == "heaviside(x, 1/2)"
assert mcode(Heaviside(x, y)) == "heaviside(x, y)"
assert mcode(binomial(x, y)) == "bincoeff(x, y)"
assert mcode(Mod(x, y)) == "mod(x, y)"
def test_Function():
assert mcode(sin(x)**cos(x)) == "sin(x).^cos(x)"
assert mcode(sign(x)) == "sign(x)"
assert mcode(exp(x)) == "exp(x)"
assert mcode(log(x)) == "log(x)"
assert mcode(factorial(x)) == "factorial(x)"
assert mcode(floor(x)) == "floor(x)"
assert mcode(atan2(y, x)) == "atan2(y, x)"
assert mcode(beta(x, y)) == 'beta(x, y)'
assert mcode(polylog(x, y)) == 'polylog(x, y)'
assert mcode(harmonic(x)) == 'harmonic(x)'
assert mcode(bernoulli(x)) == "bernoulli(x)"
assert mcode(bernoulli(x, y)) == "bernoulli(x, y)"
assert mcode(legendre(x, y)) == "legendre(x, y)"
def test_sinc():
assert mcode(sinc(x)) == 'sinc(x/pi)'
assert mcode(sinc(x + 3)) == 'sinc((x + 3)/pi)'
assert mcode(sinc(pi * (x + 3))) == 'sinc(x + 3)'
def test_Integer():
assert mcode(Integer(67)) == "67"
assert mcode(Integer(-1)) == "-1"
def test_octave_piecewise_times_const():
pw = Piecewise((x, x < 1), (x**2, True))
assert mcode(2 * pw) == "2*((x < 1).*(x) + (~(x < 1)).*(x.^2))"
assert mcode(pw / x) == "((x < 1).*(x) + (~(x < 1)).*(x.^2))./x"
assert mcode(pw / (x * y)) == "((x < 1).*(x) + (~(x < 1)).*(x.^2))./(x.*y)"
assert mcode(pw / 3) == "((x < 1).*(x) + (~(x < 1)).*(x.^2))/3"
def test_octave_not_supported_not_on_whitelist():
from sympy.functions.special.polynomials import assoc_laguerre
assert mcode(assoc_laguerre(x, y, z)) == ("% Not supported in Octave:\n"
"% assoc_laguerre\n"
"assoc_laguerre(x, y, z)")
def test_octave_matrix_assign_to():
A = Matrix([[1, 2, 3]])
assert mcode(A, assign_to='a') == "a = [1 2 3];"
A = Matrix([[1, 2], [3, 4]])
assert mcode(A, assign_to='A') == "A = [1 2; 3 4];"
def test_octave_boolean():
assert mcode(True) == "true"
assert mcode(S.true) == "true"
assert mcode(False) == "false"
assert mcode(S.false) == "false"
