def test_Pow():
assert octave_code(x**3) == 'x.^3'
assert octave_code(x**(y**3)) == 'x.^(y.^3)'
assert octave_code(x**Rational(2, 3)) == 'x.^(2/3)'
g = implemented_function('g', Lambda(x, 2 * x))
assert octave_code(1/(g(x)*3.5)**(x - y**x)/(x**2 + y)) == \
'(3.5*2*x).^(-x + y.^x)./(x.^2 + y)'
def test_octave_piecewise_times_const():
pw = Piecewise((x, x < 1), (x**2, True))
assert octave_code(2 * pw) == '2*((x < 1).*(x) + (~(x < 1)).*(x.^2))'
assert octave_code(pw / x) == '((x < 1).*(x) + (~(x < 1)).*(x.^2))./x'
assert octave_code(
pw / (x * y)) == '((x < 1).*(x) + (~(x < 1)).*(x.^2))./(x.*y)'
assert octave_code(pw / 3) == '((x < 1).*(x) + (~(x < 1)).*(x.^2))/3'
def test_octave_matrix_1x1():
A = Matrix([[3]])
B = MatrixSymbol('B', 1, 1)
C = MatrixSymbol('C', 1, 2)
assert octave_code(A, assign_to=B) == 'B = 3;'
# FIXME?
# assert octave_code(A, assign_to=x) == 'x = 3;'
pytest.raises(ValueError, lambda: octave_code(A, assign_to=C))
def test_octave_matrix_elements():
A = Matrix([[x, 2, x * y]])
assert octave_code(A[0, 0]**2 + A[0, 1] + A[0, 2]) == 'x.^2 + x.*y + 2'
A = MatrixSymbol('AA', 1, 3)
assert octave_code(A) == 'AA'
assert octave_code(A[0, 0]**2 + sin(A[0, 1]) + A[0, 2]) == \
'sin(AA(1, 2)) + AA(1, 1).^2 + AA(1, 3)'
assert octave_code(sum(A)) == 'AA(1, 1) + AA(1, 2) + AA(1, 3)'
def test_octave_not_supported():
assert octave_code(zoo) == ('% Not supported in Octave:\n'
'% ComplexInfinity\n'
'zoo')
f = Function('f')
assert octave_code(f(x).diff(x)) == ('% Not supported in Octave:\n'
'% Derivative\n'
'Derivative(f(x), x)')
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 octave_code(A, assign_to=B) == 'B = [1 2 3];'
pytest.raises(ValueError, lambda: octave_code(A, assign_to=x))
pytest.raises(ValueError, lambda: octave_code(A, assign_to=C))
def test_haramard():
A = MatrixSymbol('A', 3, 3)
B = MatrixSymbol('B', 3, 3)
v = MatrixSymbol('v', 3, 1)
h = MatrixSymbol('h', 1, 3)
C = HadamardProduct(A, B)
assert octave_code(C) == 'A.*B'
assert octave_code(C * v) == '(A.*B)*v'
assert octave_code(h * C * v) == 'h*(A.*B)*v'
assert octave_code(C * A) == '(A.*B)*A'
# mixing Hadamard and scalar strange b/c we vectorize scalars
assert octave_code(C * x * y) == '(x.*y)*(A.*B)'
def test_boolean():
assert octave_code(True) == 'true'
assert octave_code(False) == 'false'
assert octave_code(x & y) == 'x & y'
assert octave_code(x | y) == 'x | y'
assert octave_code(~x) == '~x'
assert octave_code(x & y & z) == 'x & y & z'
assert octave_code(x | y | z) == 'x | y | z'
assert octave_code((x & y) | z) == 'z | x & y'
assert octave_code((x | y) & z) == 'z & (x | y)'
def test_specfun():
n = Symbol('n')
for f in [besselj, bessely, besseli, besselk]:
assert octave_code(f(n, x)) == f.__name__ + '(n, 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(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'
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(x*y, order="none") == "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 octave_code(x*y**-2) == "x./y.^2"
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(Rational(3, 5)) == "3/5"
assert mcode(Rational(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)/0.5772156649015329"
assert mcode(x/3/pi) == "x/(3*pi)"
assert mcode(Rational(3, 5)*x*y/pi) == "3*x.*y/(5*pi)"
def test_constants():
assert octave_code(pi) == 'pi'
assert octave_code(oo) == 'inf'
assert octave_code(-oo) == '-inf'
assert octave_code(nan) == 'NaN'
assert octave_code(E) == 'exp(1)'
assert octave_code(exp(1)) == 'exp(1)'
assert octave_code(true) == 'true'
assert octave_code(false) == 'false'
def test_octave_piecewise():
expr = Piecewise((x, x < 1), (x**2, True))
assert octave_code(expr) == '((x < 1).*(x) + (~(x < 1)).*(x.^2))'
assert octave_code(
expr, assign_to='r') == ('r = ((x < 1).*(x) + (~(x < 1)).*(x.^2));')
assert octave_code(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 octave_code(expr) == expected
assert octave_code(expr, assign_to='r') == 'r = ' + expected + ';'
assert octave_code(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))
pytest.raises(ValueError, lambda: octave_code(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 octave_code(M) == (
'sparse([4 2 3 1 2], [1 3 3 4 4], [x.*y 20 10 30 22], 5, 6)')
def test_MatrixSymbol():
n = Symbol('n', integer=True)
A = MatrixSymbol('A', n, n)
B = MatrixSymbol('B', n, n)
assert octave_code(A * B) == 'A*B'
assert octave_code(B * A) == 'B*A'
assert octave_code(2 * A * B) == '2*A*B'
assert octave_code(B * 2 * A) == '2*B*A'
assert octave_code(A * (B + 3 * Identity(n))) == 'A*(B + 3*eye(n))'
assert octave_code(A**(x**2)) == 'A^(x.^2)'
assert octave_code(A**3) == 'A^3'
assert octave_code(A**Rational(1, 2)) == 'A^(1/2)'
def test_trick_indent_with_end_else_words():
# words starting with 'end' or 'else' do not confuse the indenter
t1 = Symbol('endless')
t2 = Symbol('elsewhere')
pw = Piecewise((t1, x < 0), (t2, x <= 1), (1, True))
assert octave_code(pw, inline=False) == ('if (x < 0)\n'
' endless\n'
'elseif (x <= 1)\n'
' elsewhere\n'
'else\n'
' 1\n'
'end')
def test_octave_piecewise():
expr = Piecewise((x, x < 1), (x**2, True))
assert octave_code(expr) == '((x < 1).*(x) + (~(x < 1)).*(x.^2))'
assert octave_code(
expr, assign_to='r') == ('r = ((x < 1).*(x) + (~(x < 1)).*(x.^2));')
assert octave_code(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 octave_code(expr) == expected
assert octave_code(expr, assign_to='r') == 'r = ' + expected + ';'
assert octave_code(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')
def test_Rational():
assert octave_code(Rational(3, 7)) == '3/7'
assert octave_code(Rational(18, 9)) == '2'
assert octave_code(Rational(3, -7)) == '-3/7'
assert octave_code(Rational(-3, -7)) == '3/7'
assert octave_code(x + Rational(3, 7)) == 'x + 3/7'
assert octave_code(Rational(3, 7) * x) == '3*x/7'
def test_mix_number_pow_symbols():
assert octave_code(pi**3) == 'pi^3'
assert octave_code(x**2) == 'x.^2'
assert octave_code(x**(pi**3)) == 'x.^(pi^3)'
assert octave_code(x**y) == 'x.^y'
assert octave_code(x**(y**z)) == 'x.^(y.^z)'
assert octave_code((x**y)**z) == '(x.^y).^z'
def test_containers():
assert octave_code([1, 2, 3, [4, 5, [6, 7]], 8, [9, 10], 11]) == \
'{1, 2, 3, {4, 5, {6, 7}}, 8, {9, 10}, 11}'
assert octave_code((1, 2, (3, 4))) == '{1, 2, {3, 4}}'
assert octave_code([1]) == '{1}'
assert octave_code((1, )) == '{1}'
assert octave_code(Tuple(*[1, 2, 3])) == '{1, 2, 3}'
assert octave_code((1, x * y, (3, x**2))) == '{1, x.*y, {3, x.^2}}'
# scalar, matrix, empty matrix and empty list
assert octave_code(
(1, eye(3), Matrix(0, 0,
[]), [])) == '{1, [1 0 0;\n0 1 0;\n0 0 1], [], {}}'
def test_Matrices():
assert octave_code(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);\n'
'0 1 pi;\n'
'0 exp(1) ceil(x)]')
assert octave_code(A) == expected
# row and columns
assert octave_code(A[:, 0]) == '[1; 0; 0]'
assert octave_code(A[0, :]) == '[1 sin(x/2) abs(x)]'
# empty matrices
assert octave_code(Matrix(0, 0, [])) == '[]'
assert octave_code(Matrix(0, 3, [])) == 'zeros(0, 3)'
# annoying to read but correct
assert octave_code(Matrix([[x, x - y, -y]])) == '[x x - y -y]'
def test_mix_number_mult_symbols():
assert octave_code(3 * x) == '3*x'
assert octave_code(pi * x) == 'pi*x'
assert octave_code(3 / x) == '3./x'
assert octave_code(pi / x) == 'pi./x'
assert octave_code(x / 3) == 'x/3'
assert octave_code(x / pi) == 'x/pi'
assert octave_code(x * y) == 'x.*y'
assert octave_code(x * y, order='none') == 'x.*y'
assert octave_code(3 * x * y) == '3*x.*y'
assert octave_code(3 * pi * x * y) == '3*pi*x.*y'
assert octave_code(x / y) == 'x./y'
assert octave_code(x * y**-2) == 'x./y.^2'
assert octave_code(3 * x / y) == '3*x./y'
assert octave_code(x * y / z) == 'x.*y./z'
assert octave_code(x / y * z) == 'x.*z./y'
assert octave_code(1 / x / y) == '1./(x.*y)'
assert octave_code(2 * pi * x / y / z) == '2*pi*x./(y.*z)'
assert octave_code(3 * pi / x) == '3*pi./x'
assert octave_code(Rational(3, 5)) == '3/5'
assert octave_code(Rational(3, 5) * x) == '3*x/5'
assert octave_code(x / y / z) == 'x./(y.*z)'
assert octave_code((x + y) / z) == '(x + y)./z'
assert octave_code((x + y) / (z + x)) == '(x + y)./(x + z)'
assert octave_code((x + y) / EulerGamma) == '(x + y)/0.5772156649015329'
assert octave_code(x / 3 / pi) == 'x/(3*pi)'
assert octave_code(Rational(3, 5) * x * y / pi) == '3*x.*y/(5*pi)'
def test_basic_ops():
assert octave_code(x * y) == 'x.*y'
assert octave_code(x + y) == 'x + y'
assert octave_code(x - y) == 'x - y'
assert octave_code(-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 octave_code(1 / x) == '1./x'
assert octave_code(x**-1) == octave_code(x**-1.0) == '1./x'
assert octave_code(1 / sqrt(x)) == '1./sqrt(x)'
assert octave_code(x**Rational(-1, 2)) == octave_code(x**
-0.5) == '1./sqrt(x)'
assert octave_code(sqrt(x)) == octave_code(x**0.5) == 'sqrt(x)'
assert octave_code(1 / pi) == '1/pi'
assert octave_code(pi**-1) == octave_code(pi**-1.0) == '1/pi'
assert octave_code(pi**-0.5) == '1/sqrt(pi)'
def test_specfun():
for f in [besselj, bessely, besseli, besselk]:
assert octave_code(f(n, x)) == f.__name__ + '(n, 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')"
assert octave_code(lowergamma(n, x)) == "gammainc(x, n, 'lower')"
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(Chi(x)) == 'coshint(x)'
assert octave_code(Ci(x)) == 'cosint(x)'
assert octave_code(laguerre(n, x)) == 'laguerreL(n, x)'
assert octave_code(li(x)) == 'logint(x)'
assert octave_code(loggamma(x)) == 'gammaln(x)'
assert octave_code(polygamma(n, x)) == 'psi(n, x)'
assert octave_code(Shi(x)) == 'sinhint(x)'
assert octave_code(Si(x)) == 'sinint(x)'
assert octave_code(LambertW(x)) == 'lambertw(x)'
assert octave_code(LambertW(x, n)) == 'lambertw(n, x)'
assert octave_code(zeta(x)) == 'zeta(x)'
assert octave_code(zeta(
x, y)) == '% Not supported in Octave:\n% zeta\nzeta(x, y)'
def test_special_matrices():
assert octave_code(6 * Identity(3)) == '6*eye(3)'
def test_octave_matrix_assign_to():
A = Matrix([[1, 2, 3]])
assert octave_code(A, assign_to='a') == 'a = [1 2 3];'
A = Matrix([[1, 2], [3, 4]])
assert octave_code(A, assign_to='A') == 'A = [1 2;\n3 4];'
def test_Function():
assert octave_code(sin(x)**cos(x)) == 'sin(x).^cos(x)'
assert octave_code(abs(x)) == 'abs(x)'
assert octave_code(ceiling(x)) == 'ceil(x)'
def test_Integer():
assert octave_code(Integer(67)) == '67'
assert octave_code(Integer(-1)) == '-1'
def test_octave_boolean():
assert octave_code(True) == 'true'
assert octave_code(true) == 'true'
assert octave_code(False) == 'false'
assert octave_code(false) == 'false'
def test_octave_noninline():
source = octave_code((x + y) / Catalan, assign_to='me', inline=False)
expected = ('Catalan = 0.915965594177219;\n' 'me = (x + y)/Catalan;')
assert source == expected