MLPY/Lib/site-packages/sympy/printing/tests/test_octave.py

from sympy.core import (S, pi, oo, symbols, Function, Rational, Integer,
                        Tuple, Symbol, EulerGamma, GoldenRatio, Catalan,
                        Lambda, Mul, Pow, Mod, Eq, Ne, Le, Lt, Gt, Ge)
from sympy.codegen.matrix_nodes import MatrixSolve
from sympy.functions import (arg, atan2, bernoulli, beta, ceiling, chebyshevu,
                             chebyshevt, conjugate, DiracDelta, exp, expint,
                             factorial, floor, harmonic, Heaviside, im,
                             laguerre, LambertW, log, Max, Min, Piecewise,
                             polylog, re, RisingFactorial, sign, sinc, sqrt,
                             zeta, binomial, legendre, dirichlet_eta,
                             riemann_xi)
from sympy.functions import (sin, cos, tan, cot, sec, csc, asin, acos, acot,
                             atan, asec, acsc, sinh, cosh, tanh, coth, csch,
                             sech, asinh, acosh, atanh, acoth, asech, acsch)
from sympy.testing.pytest import raises, XFAIL
from sympy.utilities.lambdify import implemented_function
from sympy.matrices import (eye, Matrix, MatrixSymbol, Identity,
                            HadamardProduct, SparseMatrix, HadamardPower)
from sympy.functions.special.bessel import (jn, yn, besselj, bessely, besseli,
                                            besselk, hankel1, hankel2, airyai,
                                            airybi, airyaiprime, airybiprime)
from sympy.functions.special.gamma_functions import (gamma, lowergamma,
                                                     uppergamma, loggamma,
                                                     polygamma)
from sympy.functions.special.error_functions import (Chi, Ci, erf, erfc, erfi,
                                                     erfcinv, erfinv, fresnelc,
                                                     fresnels, li, Shi, Si, Li,
                                                     erf2, Ei)
from sympy.printing.octave import octave_code, octave_code as mcode

x, y, z = symbols('x,y,z')


def test_Integer():
    assert mcode(Integer(67)) == "67"
    assert mcode(Integer(-1)) == "-1"


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_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_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_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_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_basic_ops():
    assert mcode(x*y) == "x.*y"
    assert mcode(x + y) == "x + y"
    assert mcode(x - y) == "x - y"
    assert mcode(-x) == "-x"


def test_1_over_x_and_sqrt():
    # 1.0 and 0.5 would do something different in regular StrPrinter,
    # but these are exact in IEEE floating point so no different here.
    assert mcode(1/x) == '1./x'
    assert mcode(x**-1) == mcode(x**-1.0) == '1./x'
    assert mcode(1/sqrt(x)) == '1./sqrt(x)'
    assert mcode(x**-S.Half) == mcode(x**-0.5) == '1./sqrt(x)'
    assert mcode(sqrt(x)) == 'sqrt(x)'
    assert mcode(x**S.Half) == mcode(x**0.5) == 'sqrt(x)'
    assert mcode(1/pi) == '1/pi'
    assert mcode(pi**-1) == mcode(pi**-1.0) == '1/pi'
    assert mcode(pi**-0.5) == '1/sqrt(pi)'


def test_mix_number_mult_symbols():
    assert mcode(3*x) == "3*x"
    assert mcode(pi*x) == "pi*x"
    assert mcode(3/x) == "3./x"
    assert mcode(pi/x) == "pi./x"
    assert mcode(x/3) == "x/3"
    assert mcode(x/pi) == "x/pi"
    assert mcode(x*y) == "x.*y"
    assert mcode(3*x*y) == "3*x.*y"
    assert mcode(3*pi*x*y) == "3*pi*x.*y"
    assert mcode(x/y) == "x./y"
    assert mcode(3*x/y) == "3*x./y"
    assert mcode(x*y/z) == "x.*y./z"
    assert mcode(x/y*z) == "x.*z./y"
    assert mcode(1/x/y) == "1./(x.*y)"
    assert mcode(2*pi*x/y/z) == "2*pi*x./(y.*z)"
    assert mcode(3*pi/x) == "3*pi./x"
    assert mcode(S(3)/5) == "3/5"
    assert mcode(S(3)/5*x) == "3*x/5"
    assert mcode(x/y/z) == "x./(y.*z)"
    assert mcode((x+y)/z) == "(x + y)./z"
    assert mcode((x+y)/(z+x)) == "(x + y)./(x + z)"
    assert mcode((x+y)/EulerGamma) == "(x + y)/%s" % EulerGamma.evalf(17)
    assert mcode(x/3/pi) == "x/(3*pi)"
    assert mcode(S(3)/5*x*y/pi) == "3*x.*y/(5*pi)"


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_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_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_constants_other():
    assert mcode(2*GoldenRatio) == "2*(1+sqrt(5))/2"
    assert mcode(2*Catalan) == "2*%s" % Catalan.evalf(17)
    assert mcode(2*EulerGamma) == "2*%s" % EulerGamma.evalf(17)


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_KroneckerDelta():
    from sympy.functions import KroneckerDelta
    assert mcode(KroneckerDelta(x, y)) == "double(x == y)"
    assert mcode(KroneckerDelta(x, y + 1)) == "double(x == (y + 1))"
    assert mcode(KroneckerDelta(2**x, y)) == "double((2.^x) == y)"


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_vector_entries_hadamard():
    # For a row or column, user might to use the other dimension
    A = Matrix([[1, sin(2/x), 3*pi/x/5]])
    assert mcode(A) == "[1 sin(2./x) 3*pi./(5*x)]"
    assert mcode(A.T) == "[1; sin(2./x); 3*pi./(5*x)]"


@XFAIL
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_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_MatrixSolve():
    n = Symbol('n', integer=True)
    A = MatrixSymbol('A', n, n)
    x = MatrixSymbol('x', n, 1)
    assert mcode(MatrixSolve(A, x)) == "A \\ x"

def test_special_matrices():
    assert mcode(6*Identity(3)) == "6*eye(3)"


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_octave_noninline():
    source = mcode((x+y)/Catalan, assign_to='me', inline=False)
    expected = (
        "Catalan = %s;\n"
        "me = (x + y)/Catalan;"
    ) % Catalan.evalf(17)
    assert source == 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_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_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_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_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_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_octave_boolean():
    assert mcode(True) == "true"
    assert mcode(S.true) == "true"
    assert mcode(False) == "false"
    assert mcode(S.false) == "false"


def test_octave_not_supported():
    with raises(NotImplementedError):
        mcode(S.ComplexInfinity)
    f = Function('f')
    assert mcode(f(x).diff(x), strict=False) == (
        "% Not supported in Octave:\n"
        "% Derivative\n"
        "Derivative(f(x), x)"
    )


def test_octave_not_supported_not_on_whitelist():
    from sympy.functions.special.polynomials import assoc_laguerre
    with raises(NotImplementedError):
        mcode(assoc_laguerre(x, y, z))


def test_octave_expint():
    assert mcode(expint(1, x)) == "expint(x)"
    with raises(NotImplementedError):
        mcode(expint(2, x))
    assert mcode(expint(y, x), strict=False) == (
        "% Not supported in Octave:\n"
        "% expint\n"
        "expint(y, x)"
    )


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_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_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_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_trigfun():
    for f in (sin, cos, tan, cot, sec, csc, asin, acos, acot, atan, asec, acsc,
              sinh, cosh, tanh, coth, csch, sech, asinh, acosh, atanh, acoth,
              asech, acsch):
        assert octave_code(f(x) == f.__name__ + '(x)')


def test_specfun():
    n = Symbol('n')
    for f in [besselj, bessely, besseli, besselk]:
        assert octave_code(f(n, x)) == f.__name__ + '(n, x)'
    for f in (erfc, erfi, erf, erfinv, erfcinv, fresnelc, fresnels, gamma):
        assert octave_code(f(x)) == f.__name__ + '(x)'
    assert octave_code(hankel1(n, x)) == 'besselh(n, 1, x)'
    assert octave_code(hankel2(n, x)) == 'besselh(n, 2, x)'
    assert octave_code(airyai(x)) == 'airy(0, x)'
    assert octave_code(airyaiprime(x)) == 'airy(1, x)'
    assert octave_code(airybi(x)) == 'airy(2, x)'
    assert octave_code(airybiprime(x)) == 'airy(3, x)'
    assert octave_code(uppergamma(n, x)) == '(gammainc(x, n, \'upper\').*gamma(n))'
    assert octave_code(lowergamma(n, x)) == '(gammainc(x, n).*gamma(n))'
    assert octave_code(z**lowergamma(n, x)) == 'z.^(gammainc(x, n).*gamma(n))'
    assert octave_code(jn(n, x)) == 'sqrt(2)*sqrt(pi)*sqrt(1./x).*besselj(n + 1/2, x)/2'
    assert octave_code(yn(n, x)) == 'sqrt(2)*sqrt(pi)*sqrt(1./x).*bessely(n + 1/2, x)/2'
    assert octave_code(LambertW(x)) == 'lambertw(x)'
    assert octave_code(LambertW(x, n)) == 'lambertw(n, x)'

    # Automatic rewrite
    assert octave_code(Ei(x)) == '(logint(exp(x)))'
    assert octave_code(dirichlet_eta(x)) == '(((x == 1).*(log(2)) + (~(x == 1)).*((1 - 2.^(1 - x)).*zeta(x))))'
    assert octave_code(riemann_xi(x)) == '(pi.^(-x/2).*x.*(x - 1).*gamma(x/2).*zeta(x)/2)'


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_zeta_printing_issue_14820():
    assert octave_code(zeta(x)) == 'zeta(x)'
    with raises(NotImplementedError):
        octave_code(zeta(x, y))


def test_automatic_rewrite():
    assert octave_code(Li(x)) == '(logint(x) - logint(2))'
    assert octave_code(erf2(x, y)) == '(-erf(x) + erf(y))'