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from sympy.core import (S, pi, oo, symbols, Function, Rational, Integer, |
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Tuple, Symbol, Eq, Ne, Le, Lt, Gt, Ge) |
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from sympy.core import EulerGamma, GoldenRatio, Catalan, Lambda, Mul, Pow |
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from sympy.functions import Piecewise, sqrt, ceiling, exp, sin, cos, sinc |
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from sympy.testing.pytest import raises |
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from sympy.utilities.lambdify import implemented_function |
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from sympy.matrices import (eye, Matrix, MatrixSymbol, Identity, |
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HadamardProduct, SparseMatrix) |
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from sympy.functions.special.bessel import (jn, yn, besselj, bessely, besseli, |
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besselk, hankel1, hankel2, airyai, |
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airybi, airyaiprime, airybiprime) |
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from sympy.testing.pytest import XFAIL |
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from sympy.printing.julia import julia_code |
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x, y, z = symbols('x,y,z') |
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def test_Integer(): |
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assert julia_code(Integer(67)) == "67" |
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assert julia_code(Integer(-1)) == "-1" |
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def test_Rational(): |
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assert julia_code(Rational(3, 7)) == "3 // 7" |
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assert julia_code(Rational(18, 9)) == "2" |
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assert julia_code(Rational(3, -7)) == "-3 // 7" |
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assert julia_code(Rational(-3, -7)) == "3 // 7" |
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assert julia_code(x + Rational(3, 7)) == "x + 3 // 7" |
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assert julia_code(Rational(3, 7)*x) == "(3 // 7) * x" |
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def test_Relational(): |
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assert julia_code(Eq(x, y)) == "x == y" |
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assert julia_code(Ne(x, y)) == "x != y" |
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assert julia_code(Le(x, y)) == "x <= y" |
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assert julia_code(Lt(x, y)) == "x < y" |
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assert julia_code(Gt(x, y)) == "x > y" |
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assert julia_code(Ge(x, y)) == "x >= y" |
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def test_Function(): |
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assert julia_code(sin(x) ** cos(x)) == "sin(x) .^ cos(x)" |
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assert julia_code(abs(x)) == "abs(x)" |
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assert julia_code(ceiling(x)) == "ceil(x)" |
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def test_Pow(): |
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assert julia_code(x**3) == "x .^ 3" |
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assert julia_code(x**(y**3)) == "x .^ (y .^ 3)" |
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assert julia_code(x**Rational(2, 3)) == 'x .^ (2 // 3)' |
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g = implemented_function('g', Lambda(x, 2*x)) |
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assert julia_code(1/(g(x)*3.5)**(x - y**x)/(x**2 + y)) == \ |
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"(3.5 * 2 * x) .^ (-x + y .^ x) ./ (x .^ 2 + y)" |
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assert julia_code(Mul(-2, x, Pow(Mul(y,y,evaluate=False), -1, evaluate=False), |
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evaluate=False)) == '-2 * x ./ (y .* y)' |
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def test_basic_ops(): |
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assert julia_code(x*y) == "x .* y" |
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assert julia_code(x + y) == "x + y" |
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assert julia_code(x - y) == "x - y" |
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assert julia_code(-x) == "-x" |
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def test_1_over_x_and_sqrt(): |
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assert julia_code(1/x) == '1 ./ x' |
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assert julia_code(x**-1) == julia_code(x**-1.0) == '1 ./ x' |
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assert julia_code(1/sqrt(x)) == '1 ./ sqrt(x)' |
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assert julia_code(x**-S.Half) == julia_code(x**-0.5) == '1 ./ sqrt(x)' |
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assert julia_code(sqrt(x)) == 'sqrt(x)' |
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assert julia_code(x**S.Half) == julia_code(x**0.5) == 'sqrt(x)' |
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assert julia_code(1/pi) == '1 / pi' |
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assert julia_code(pi**-1) == julia_code(pi**-1.0) == '1 / pi' |
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assert julia_code(pi**-0.5) == '1 / sqrt(pi)' |
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def test_mix_number_mult_symbols(): |
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assert julia_code(3*x) == "3 * x" |
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assert julia_code(pi*x) == "pi * x" |
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assert julia_code(3/x) == "3 ./ x" |
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assert julia_code(pi/x) == "pi ./ x" |
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assert julia_code(x/3) == "x / 3" |
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assert julia_code(x/pi) == "x / pi" |
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assert julia_code(x*y) == "x .* y" |
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assert julia_code(3*x*y) == "3 * x .* y" |
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assert julia_code(3*pi*x*y) == "3 * pi * x .* y" |
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assert julia_code(x/y) == "x ./ y" |
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assert julia_code(3*x/y) == "3 * x ./ y" |
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assert julia_code(x*y/z) == "x .* y ./ z" |
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assert julia_code(x/y*z) == "x .* z ./ y" |
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assert julia_code(1/x/y) == "1 ./ (x .* y)" |
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assert julia_code(2*pi*x/y/z) == "2 * pi * x ./ (y .* z)" |
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assert julia_code(3*pi/x) == "3 * pi ./ x" |
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assert julia_code(S(3)/5) == "3 // 5" |
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assert julia_code(S(3)/5*x) == "(3 // 5) * x" |
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assert julia_code(x/y/z) == "x ./ (y .* z)" |
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assert julia_code((x+y)/z) == "(x + y) ./ z" |
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assert julia_code((x+y)/(z+x)) == "(x + y) ./ (x + z)" |
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assert julia_code((x+y)/EulerGamma) == "(x + y) / eulergamma" |
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assert julia_code(x/3/pi) == "x / (3 * pi)" |
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assert julia_code(S(3)/5*x*y/pi) == "(3 // 5) * x .* y / pi" |
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def test_mix_number_pow_symbols(): |
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assert julia_code(pi**3) == 'pi ^ 3' |
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assert julia_code(x**2) == 'x .^ 2' |
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assert julia_code(x**(pi**3)) == 'x .^ (pi ^ 3)' |
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assert julia_code(x**y) == 'x .^ y' |
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assert julia_code(x**(y**z)) == 'x .^ (y .^ z)' |
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assert julia_code((x**y)**z) == '(x .^ y) .^ z' |
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def test_imag(): |
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I = S('I') |
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assert julia_code(I) == "im" |
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assert julia_code(5*I) == "5im" |
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assert julia_code((S(3)/2)*I) == "(3 // 2) * im" |
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assert julia_code(3+4*I) == "3 + 4im" |
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def test_constants(): |
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assert julia_code(pi) == "pi" |
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assert julia_code(oo) == "Inf" |
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assert julia_code(-oo) == "-Inf" |
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assert julia_code(S.NegativeInfinity) == "-Inf" |
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assert julia_code(S.NaN) == "NaN" |
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assert julia_code(S.Exp1) == "e" |
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assert julia_code(exp(1)) == "e" |
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def test_constants_other(): |
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assert julia_code(2*GoldenRatio) == "2 * golden" |
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assert julia_code(2*Catalan) == "2 * catalan" |
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assert julia_code(2*EulerGamma) == "2 * eulergamma" |
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def test_boolean(): |
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assert julia_code(x & y) == "x && y" |
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assert julia_code(x | y) == "x || y" |
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assert julia_code(~x) == "!x" |
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assert julia_code(x & y & z) == "x && y && z" |
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assert julia_code(x | y | z) == "x || y || z" |
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assert julia_code((x & y) | z) == "z || x && y" |
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assert julia_code((x | y) & z) == "z && (x || y)" |
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def test_sinc(): |
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assert julia_code(sinc(x)) == 'sinc(x / pi)' |
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assert julia_code(sinc(x + 3)) == 'sinc((x + 3) / pi)' |
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assert julia_code(sinc(pi * (x + 3))) == 'sinc(x + 3)' |
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def test_Matrices(): |
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assert julia_code(Matrix(1, 1, [10])) == "[10]" |
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A = Matrix([[1, sin(x/2), abs(x)], |
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[0, 1, pi], |
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[0, exp(1), ceiling(x)]]) |
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expected = ("[1 sin(x / 2) abs(x);\n" |
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"0 1 pi;\n" |
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"0 e ceil(x)]") |
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assert julia_code(A) == expected |
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assert julia_code(A[:,0]) == "[1, 0, 0]" |
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assert julia_code(A[0,:]) == "[1 sin(x / 2) abs(x)]" |
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assert julia_code(Matrix(0, 0, [])) == 'zeros(0, 0)' |
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assert julia_code(Matrix(0, 3, [])) == 'zeros(0, 3)' |
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assert julia_code(Matrix([[x, x - y, -y]])) == "[x x - y -y]" |
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def test_vector_entries_hadamard(): |
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A = Matrix([[1, sin(2/x), 3*pi/x/5]]) |
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assert julia_code(A) == "[1 sin(2 ./ x) (3 // 5) * pi ./ x]" |
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assert julia_code(A.T) == "[1, sin(2 ./ x), (3 // 5) * pi ./ x]" |
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@XFAIL |
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def test_Matrices_entries_not_hadamard(): |
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A = Matrix([[1, sin(2/x), 3*pi/x/5], [1, 2, x*y]]) |
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expected = ("[1 sin(2/x) 3*pi/(5*x);\n" |
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"1 2 x*y]") |
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assert julia_code(A) == expected |
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def test_MatrixSymbol(): |
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n = Symbol('n', integer=True) |
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A = MatrixSymbol('A', n, n) |
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B = MatrixSymbol('B', n, n) |
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assert julia_code(A*B) == "A * B" |
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assert julia_code(B*A) == "B * A" |
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assert julia_code(2*A*B) == "2 * A * B" |
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assert julia_code(B*2*A) == "2 * B * A" |
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assert julia_code(A*(B + 3*Identity(n))) == "A * (3 * eye(n) + B)" |
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assert julia_code(A**(x**2)) == "A ^ (x .^ 2)" |
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assert julia_code(A**3) == "A ^ 3" |
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assert julia_code(A**S.Half) == "A ^ (1 // 2)" |
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def test_special_matrices(): |
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assert julia_code(6*Identity(3)) == "6 * eye(3)" |
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def test_containers(): |
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assert julia_code([1, 2, 3, [4, 5, [6, 7]], 8, [9, 10], 11]) == \ |
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"Any[1, 2, 3, Any[4, 5, Any[6, 7]], 8, Any[9, 10], 11]" |
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assert julia_code((1, 2, (3, 4))) == "(1, 2, (3, 4))" |
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assert julia_code([1]) == "Any[1]" |
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assert julia_code((1,)) == "(1,)" |
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assert julia_code(Tuple(*[1, 2, 3])) == "(1, 2, 3)" |
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assert julia_code((1, x*y, (3, x**2))) == "(1, x .* y, (3, x .^ 2))" |
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assert julia_code((1, eye(3), Matrix(0, 0, []), [])) == "(1, [1 0 0;\n0 1 0;\n0 0 1], zeros(0, 0), Any[])" |
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def test_julia_noninline(): |
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source = julia_code((x+y)/Catalan, assign_to='me', inline=False) |
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expected = ( |
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"const Catalan = %s\n" |
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"me = (x + y) / Catalan" |
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) % Catalan.evalf(17) |
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assert source == expected |
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def test_julia_piecewise(): |
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expr = Piecewise((x, x < 1), (x**2, True)) |
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assert julia_code(expr) == "((x < 1) ? (x) : (x .^ 2))" |
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assert julia_code(expr, assign_to="r") == ( |
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"r = ((x < 1) ? (x) : (x .^ 2))") |
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assert julia_code(expr, assign_to="r", inline=False) == ( |
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"if (x < 1)\n" |
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" r = x\n" |
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"else\n" |
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" r = x .^ 2\n" |
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"end") |
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expr = Piecewise((x**2, x < 1), (x**3, x < 2), (x**4, x < 3), (x**5, True)) |
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expected = ("((x < 1) ? (x .^ 2) :\n" |
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"(x < 2) ? (x .^ 3) :\n" |
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"(x < 3) ? (x .^ 4) : (x .^ 5))") |
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assert julia_code(expr) == expected |
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assert julia_code(expr, assign_to="r") == "r = " + expected |
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assert julia_code(expr, assign_to="r", inline=False) == ( |
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"if (x < 1)\n" |
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" r = x .^ 2\n" |
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"elseif (x < 2)\n" |
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" r = x .^ 3\n" |
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"elseif (x < 3)\n" |
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" r = x .^ 4\n" |
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"else\n" |
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" r = x .^ 5\n" |
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"end") |
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expr = Piecewise((x, x < 1), (x**2, x > 1), (sin(x), x > 0)) |
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raises(ValueError, lambda: julia_code(expr)) |
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def test_julia_piecewise_times_const(): |
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pw = Piecewise((x, x < 1), (x**2, True)) |
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assert julia_code(2*pw) == "2 * ((x < 1) ? (x) : (x .^ 2))" |
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assert julia_code(pw/x) == "((x < 1) ? (x) : (x .^ 2)) ./ x" |
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assert julia_code(pw/(x*y)) == "((x < 1) ? (x) : (x .^ 2)) ./ (x .* y)" |
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assert julia_code(pw/3) == "((x < 1) ? (x) : (x .^ 2)) / 3" |
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def test_julia_matrix_assign_to(): |
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A = Matrix([[1, 2, 3]]) |
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assert julia_code(A, assign_to='a') == "a = [1 2 3]" |
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A = Matrix([[1, 2], [3, 4]]) |
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assert julia_code(A, assign_to='A') == "A = [1 2;\n3 4]" |
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def test_julia_matrix_assign_to_more(): |
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A = Matrix([[1, 2, 3]]) |
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B = MatrixSymbol('B', 1, 3) |
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C = MatrixSymbol('C', 2, 3) |
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assert julia_code(A, assign_to=B) == "B = [1 2 3]" |
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raises(ValueError, lambda: julia_code(A, assign_to=x)) |
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raises(ValueError, lambda: julia_code(A, assign_to=C)) |
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def test_julia_matrix_1x1(): |
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A = Matrix([[3]]) |
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B = MatrixSymbol('B', 1, 1) |
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C = MatrixSymbol('C', 1, 2) |
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assert julia_code(A, assign_to=B) == "B = [3]" |
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raises(ValueError, lambda: julia_code(A, assign_to=C)) |
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def test_julia_matrix_elements(): |
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A = Matrix([[x, 2, x*y]]) |
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assert julia_code(A[0, 0]**2 + A[0, 1] + A[0, 2]) == "x .^ 2 + x .* y + 2" |
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A = MatrixSymbol('AA', 1, 3) |
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assert julia_code(A) == "AA" |
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assert julia_code(A[0, 0]**2 + sin(A[0,1]) + A[0,2]) == \ |
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"sin(AA[1,2]) + AA[1,1] .^ 2 + AA[1,3]" |
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assert julia_code(sum(A)) == "AA[1,1] + AA[1,2] + AA[1,3]" |
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def test_julia_boolean(): |
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assert julia_code(True) == "true" |
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assert julia_code(S.true) == "true" |
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assert julia_code(False) == "false" |
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assert julia_code(S.false) == "false" |
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def test_julia_not_supported(): |
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with raises(NotImplementedError): |
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julia_code(S.ComplexInfinity) |
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f = Function('f') |
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assert julia_code(f(x).diff(x), strict=False) == ( |
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"# Not supported in Julia:\n" |
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"# Derivative\n" |
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"Derivative(f(x), x)" |
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) |
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def test_trick_indent_with_end_else_words(): |
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t1 = S('endless') |
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t2 = S('elsewhere') |
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pw = Piecewise((t1, x < 0), (t2, x <= 1), (1, True)) |
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assert julia_code(pw, inline=False) == ( |
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"if (x < 0)\n" |
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" endless\n" |
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"elseif (x <= 1)\n" |
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" elsewhere\n" |
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"else\n" |
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" 1\n" |
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"end") |
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def test_haramard(): |
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A = MatrixSymbol('A', 3, 3) |
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B = MatrixSymbol('B', 3, 3) |
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v = MatrixSymbol('v', 3, 1) |
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h = MatrixSymbol('h', 1, 3) |
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C = HadamardProduct(A, B) |
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assert julia_code(C) == "A .* B" |
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assert julia_code(C*v) == "(A .* B) * v" |
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assert julia_code(h*C*v) == "h * (A .* B) * v" |
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assert julia_code(C*A) == "(A .* B) * A" |
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assert julia_code(C*x*y) == "(x .* y) * (A .* B)" |
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def test_sparse(): |
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M = SparseMatrix(5, 6, {}) |
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M[2, 2] = 10 |
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M[1, 2] = 20 |
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M[1, 3] = 22 |
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M[0, 3] = 30 |
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M[3, 0] = x*y |
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assert julia_code(M) == ( |
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"sparse([4, 2, 3, 1, 2], [1, 3, 3, 4, 4], [x .* y, 20, 10, 30, 22], 5, 6)" |
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) |
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def test_specfun(): |
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n = Symbol('n') |
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for f in [besselj, bessely, besseli, besselk]: |
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assert julia_code(f(n, x)) == f.__name__ + '(n, x)' |
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for f in [airyai, airyaiprime, airybi, airybiprime]: |
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assert julia_code(f(x)) == f.__name__ + '(x)' |
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assert julia_code(hankel1(n, x)) == 'hankelh1(n, x)' |
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assert julia_code(hankel2(n, x)) == 'hankelh2(n, x)' |
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assert julia_code(jn(n, x)) == 'sqrt(2) * sqrt(pi) * sqrt(1 ./ x) .* besselj(n + 1 // 2, x) / 2' |
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assert julia_code(yn(n, x)) == 'sqrt(2) * sqrt(pi) * sqrt(1 ./ x) .* bessely(n + 1 // 2, x) / 2' |
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def test_MatrixElement_printing(): |
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A = MatrixSymbol("A", 1, 3) |
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B = MatrixSymbol("B", 1, 3) |
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C = MatrixSymbol("C", 1, 3) |
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assert(julia_code(A[0, 0]) == "A[1,1]") |
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assert(julia_code(3 * A[0, 0]) == "3 * A[1,1]") |
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F = C[0, 0].subs(C, A - B) |
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assert(julia_code(F) == "(A - B)[1,1]") |
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