def test_matrices(): from sympy.matrices import MutableDenseMatrix, MutableSparseMatrix, \ ImmutableDenseMatrix, ImmutableSparseMatrix A = MutableDenseMatrix( [[1, -1, 0, 0], [0, 1, -1, 0], [0, 0, 1, -1], [0, 0, 0, 1]] ) B = MutableSparseMatrix(A) C = ImmutableDenseMatrix(A) D = ImmutableSparseMatrix(A) assert mcode(C) == mcode(A) == \ "{{1, -1, 0, 0}, " \ "{0, 1, -1, 0}, " \ "{0, 0, 1, -1}, " \ "{0, 0, 0, 1}}" assert mcode(D) == mcode(B) == \ "SparseArray[{" \ "{1, 1} -> 1, {1, 2} -> -1, {2, 2} -> 1, {2, 3} -> -1, " \ "{3, 3} -> 1, {3, 4} -> -1, {4, 4} -> 1" \ "}, {4, 4}]" # Trivial cases of matrices assert mcode(MutableDenseMatrix(0, 0, [])) == '{}' assert mcode(MutableSparseMatrix(0, 0, [])) == 'SparseArray[{}, {0, 0}]' assert mcode(MutableDenseMatrix(0, 3, [])) == '{}' assert mcode(MutableSparseMatrix(0, 3, [])) == 'SparseArray[{}, {0, 3}]' assert mcode(MutableDenseMatrix(3, 0, [])) == '{{}, {}, {}}' assert mcode(MutableSparseMatrix(3, 0, [])) == 'SparseArray[{}, {3, 0}]'
def test_Mul(): A, B, C, D = symbols('A B C D', commutative=False) assert mcode(x*y*z) == "x*y*z" assert mcode(x*y*A) == "x*y*A" assert mcode(x*y*A*B) == "x*y*A**B" assert mcode(x*y*A*B*C) == "x*y*A**B**C" assert mcode(x*A*B*(C + D)*A*y) == "x*y*A**B**(C + D)**A"
def test_Pow(): assert mcode(x**3) == "x^3" assert mcode(x**(y**3)) == "x^(y^3)" assert mcode(1/(f(x)*3.5)**(x - y**x)/(x**2 + y)) == \ "(3.5*f[x])^(-x + y^x)/(x^2 + y)" assert mcode(x**-1.0) == 'x^(-1.0)' assert mcode(x**Rational(2, 3)) == 'x^(2/3)'
def test_Integral(): assert mcode(Integral(sin(sin(x)), x)) == "Hold[Integrate[Sin[Sin[x]], x]]" assert mcode(Integral(exp(-x**2 - y**2), (x, -oo, oo), (y, -oo, oo))) == \ "Hold[Integrate[Exp[-x^2 - y^2], {x, -Infinity, Infinity}, " \ "{y, -Infinity, Infinity}]]"
def test_Sum(): assert mcode(Sum(sin(x), (x, 0, 10))) == "Hold[Sum[Sin[x], {x, 0, 10}]]" assert mcode(Sum(exp(-x**2 - y**2), (x, -oo, oo), (y, -oo, oo))) == \ "Hold[Sum[Exp[-x^2 - y^2], {x, -Infinity, Infinity}, " \ "{y, -Infinity, Infinity}]]"
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)"
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_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}"
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_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_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) == "(-B + A)(1, 1)"
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_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 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)"
def test_NDArray(): from sympy.tensor.array import ( MutableDenseNDimArray, ImmutableDenseNDimArray, MutableSparseNDimArray, ImmutableSparseNDimArray) example = MutableDenseNDimArray( [[[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]], [[13, 14, 15, 16], [17, 18, 19, 20], [21, 22, 23, 24]]] ) assert mcode(example) == \ "{{{1, 2, 3, 4}, {5, 6, 7, 8}, {9, 10, 11, 12}}, " \ "{{13, 14, 15, 16}, {17, 18, 19, 20}, {21, 22, 23, 24}}}" example = ImmutableDenseNDimArray(example) assert mcode(example) == \ "{{{1, 2, 3, 4}, {5, 6, 7, 8}, {9, 10, 11, 12}}, " \ "{{13, 14, 15, 16}, {17, 18, 19, 20}, {21, 22, 23, 24}}}" example = MutableSparseNDimArray(example) assert mcode(example) == \ "SparseArray[{" \ "{1, 1, 1} -> 1, {1, 1, 2} -> 2, {1, 1, 3} -> 3, " \ "{1, 1, 4} -> 4, {1, 2, 1} -> 5, {1, 2, 2} -> 6, " \ "{1, 2, 3} -> 7, {1, 2, 4} -> 8, {1, 3, 1} -> 9, " \ "{1, 3, 2} -> 10, {1, 3, 3} -> 11, {1, 3, 4} -> 12, " \ "{2, 1, 1} -> 13, {2, 1, 2} -> 14, {2, 1, 3} -> 15, " \ "{2, 1, 4} -> 16, {2, 2, 1} -> 17, {2, 2, 2} -> 18, " \ "{2, 2, 3} -> 19, {2, 2, 4} -> 20, {2, 3, 1} -> 21, " \ "{2, 3, 2} -> 22, {2, 3, 3} -> 23, {2, 3, 4} -> 24" \ "}, {2, 3, 4}]" example = ImmutableSparseNDimArray(example) assert mcode(example) == \ "SparseArray[{" \ "{1, 1, 1} -> 1, {1, 1, 2} -> 2, {1, 1, 3} -> 3, " \ "{1, 1, 4} -> 4, {1, 2, 1} -> 5, {1, 2, 2} -> 6, " \ "{1, 2, 3} -> 7, {1, 2, 4} -> 8, {1, 3, 1} -> 9, " \ "{1, 3, 2} -> 10, {1, 3, 3} -> 11, {1, 3, 4} -> 12, " \ "{2, 1, 1} -> 13, {2, 1, 2} -> 14, {2, 1, 3} -> 15, " \ "{2, 1, 4} -> 16, {2, 2, 1} -> 17, {2, 2, 2} -> 18, " \ "{2, 2, 3} -> 19, {2, 2, 4} -> 20, {2, 3, 1} -> 21, " \ "{2, 3, 2} -> 22, {2, 3, 3} -> 23, {2, 3, 4} -> 24" \ "}, {2, 3, 4}]"
def test_Function(): assert mcode(sin(x) ** cos(x)) == "sin(x).^cos(x)" 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(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_matrices(): from sympy.matrices import MutableDenseMatrix, MutableSparseMatrix A = MutableDenseMatrix( [[1, -1, 0, 0], [0, 1, -1, 0], [0, 0, 1, -1], [0, 0, 0, 1]] ) B = MutableSparseMatrix( [[1, -1, 0, 0], [0, 1, -1, 0], [0, 0, 1, -1], [0, 0, 0, 1]] ) assert mcode(A) == """\ {{1, -1, 0, 0}, \ {0, 1, -1, 0}, \ {0, 0, 1, -1}, \ {0, 0, 0, 1}}\ """ assert mcode(B) == """\ SparseArray[\ {{1, 1} -> 1, {1, 2} -> -1, {2, 2} -> 1, {2, 3} -> -1, \ {3, 3} -> 1, {3, 4} -> -1, {4, 4} -> 1}, {4, 4}]\ """ # Trivial cases of matrices assert mcode(MutableDenseMatrix(0, 0, [])) == '{}' assert mcode(MutableSparseMatrix(0, 0, [])) == 'SparseArray[{}, {0, 0}]' assert mcode(MutableDenseMatrix(0, 3, [])) == '{}' assert mcode(MutableSparseMatrix(0, 3, [])) == 'SparseArray[{}, {0, 3}]' assert mcode(MutableDenseMatrix(3, 0, [])) == '{{}, {}, {}}' assert mcode(MutableSparseMatrix(3, 0, [])) == 'SparseArray[{}, {3, 0}]'
def test_octave_noninline(): source = mcode((x+y)/Catalan, assign_to='me', inline=False) expected = ( "Catalan = 0.915965594177219;\n" "me = (x + y)/Catalan;" ) assert source == expected
def test_octave_not_supported_not_on_whitelist(): from sympy 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_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_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_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_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_userfuncs(): # Dictionary mutation test some_function = symbols("some_function", cls=Function) my_user_functions = {"some_function": "SomeFunction"} assert mcode( some_function(z), user_functions=my_user_functions) == \ 'SomeFunction[z]' assert mcode( some_function(z), user_functions=my_user_functions) == \ 'SomeFunction[z]' # List argument test my_user_functions = \ {"some_function": [(lambda x: True, "SomeOtherFunction")]} assert mcode( some_function(z), user_functions=my_user_functions) == \ 'SomeOtherFunction[z]'
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;\n0 1 0;\n0 0 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_Function(): assert mcode(sin(x)**cos(x)) == "sin(x).^cos(x)" assert mcode(abs(x)) == "abs(x)" assert mcode(ceiling(x)) == "ceil(x)" 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_constants(): assert mcode(pi) == "Pi" assert mcode(oo) == "Infinity" assert mcode(S.NegativeInfinity) == "-Infinity" assert mcode(S.EulerGamma) == "EulerGamma" assert mcode(S.Catalan) == "Catalan" assert mcode(S.Exp1) == "E"
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_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_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_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 parse_to_print(to_print): if isinstance(to_print, RuleSet): return str(to_print) elif isinstance(to_print, list): out = '{' for item in to_print: out += parse_to_print(item) out += ',' out = out[:-1] return out + '}' elif not isinstance(to_print, str): return mcode(to_print) return to_print
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 parse_output(to_print): if isinstance(to_print, RuleSet): return str(to_print) elif isinstance(to_print, list): out = '{' for item in to_print: out += parse_output(item) out += ',' out = out[:-1] return out + '}' elif not isinstance(to_print, str) and not ( isinstance(to_print, Plot) or isinstance(to_print, PlotArray) or isinstance(to_print, Manipulate) ): return mcode(to_print) return to_print
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_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_octave_boolean(): assert mcode(True) == "true" assert mcode(S.true) == "true" assert mcode(False) == "false" assert mcode(S.false) == "false"
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_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)" 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_Derivative(): assert mcode(Derivative(sin(x), x)) == "Hold[D[Sin[x], x]]" assert mcode(Derivative(x, x)) == "Hold[D[x, x]]" assert mcode(Derivative(sin(x)*y**4, x, 2)) == "Hold[D[y^4*Sin[x], {x, 2}]]" assert mcode(Derivative(sin(x)*y**4, x, y, x)) == "Hold[D[y^4*Sin[x], x, y, x]]" assert mcode(Derivative(sin(x)*y**4, x, y, 3, x)) == "Hold[D[y^4*Sin[x], x, {y, 3}, x]]"
def test_constants(): assert mcode(S.Zero) == "0" assert mcode(S.One) == "1" assert mcode(S.NegativeOne) == "-1" assert mcode(S.Half) == "1/2" assert mcode(S.ImaginaryUnit) == "I" assert mcode(oo) == "Infinity" assert mcode(S.NegativeInfinity) == "-Infinity" assert mcode(S.ComplexInfinity) == "ComplexInfinity" assert mcode(S.NaN) == "Indeterminate" assert mcode(S.Exp1) == "E" assert mcode(pi) == "Pi" assert mcode(S.GoldenRatio) == "GoldenRatio" assert mcode(S.TribonacciConstant) == \ "1/3 + (1/3)*(19 - 3*33^(1/2))^(1/3) + " \ "(1/3)*(3*33^(1/2) + 19)^(1/3)" assert mcode(S.EulerGamma) == "EulerGamma" assert mcode(S.Catalan) == "Catalan"
def test_special_matrices(): assert mcode(6 * Identity(3)) == "6*eye(3)"
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)]"
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_Function(): assert mcode(f(x, y, z)) == "f[x, y, z]" assert mcode(sin(x)**cos(x)) == "Sin[x]^Cos[x]" assert mcode(conjugate(x)) == "Conjugate[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_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_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_Function(): assert mcode(f(x, y, z)) == "f[x, y, z]" assert mcode(sin(x) ** cos(x)) == "Sin[x]^Cos[x]" assert mcode(sec(x) * acsc(x)) == "ArcCsc[x]*Sec[x]" assert mcode(atan2(x, y)) == "ArcTan[x, y]" assert mcode(conjugate(x)) == "Conjugate[x]" assert mcode(Max(x, y, z)*Min(y, z)) == "Max[x, y, z]*Min[y, z]" assert mcode(fresnelc(x)) == "FresnelC[x]" assert mcode(fresnels(x)) == "FresnelS[x]" assert mcode(gamma(x)) == "Gamma[x]" assert mcode(uppergamma(x, y)) == "Gamma[x, y]" assert mcode(polygamma(x, y)) == "PolyGamma[x, y]" assert mcode(loggamma(x)) == "LogGamma[x]" assert mcode(erf(x)) == "Erf[x]" assert mcode(erfc(x)) == "Erfc[x]" assert mcode(erfi(x)) == "Erfi[x]" assert mcode(erf2(x, y)) == "Erf[x, y]" assert mcode(expint(x, y)) == "ExpIntegralE[x, y]" assert mcode(erfcinv(x)) == "InverseErfc[x]" assert mcode(erfinv(x)) == "InverseErf[x]" assert mcode(erf2inv(x, y)) == "InverseErf[x, y]" assert mcode(Ei(x)) == "ExpIntegralEi[x]" assert mcode(Ci(x)) == "CosIntegral[x]" assert mcode(li(x)) == "LogIntegral[x]" assert mcode(Si(x)) == "SinIntegral[x]" assert mcode(Shi(x)) == "SinhIntegral[x]" assert mcode(Chi(x)) == "CoshIntegral[x]" assert mcode(beta(x, y)) == "Beta[x, y]" assert mcode(factorial(x)) == "Factorial[x]" assert mcode(factorial2(x)) == "Factorial2[x]" assert mcode(subfactorial(x)) == "Subfactorial[x]" assert mcode(FallingFactorial(x, y)) == "FactorialPower[x, y]" assert mcode(RisingFactorial(x, y)) == "Pochhammer[x, y]" assert mcode(catalan(x)) == "CatalanNumber[x]" assert mcode(harmonic(x)) == "HarmonicNumber[x]" assert mcode(harmonic(x, y)) == "HarmonicNumber[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))"