from sympy.core import (S, symbols, Eq, pi, Catalan, EulerGamma, Lambda,
                        Dummy, Function)
from sympy.core.compatibility import StringIO
from sympy import erf, Integral, Piecewise
from sympy import Equality
from sympy.matrices import Matrix, MatrixSymbol
from sympy.utilities.codegen import OctaveCodeGen, codegen, make_routine
from sympy.utilities.pytest import raises
from sympy.utilities.lambdify import implemented_function
from sympy.utilities.pytest import XFAIL
import sympy


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


def test_empty_m_code():
    code_gen = OctaveCodeGen()
    output = StringIO()
    code_gen.dump_m([], output, "file", header=False, empty=False)
    source = output.getvalue()
    assert source == ""


def test_m_simple_code():
    name_expr = ("test", (x + y)*z)
    result, = codegen(name_expr, "Octave", header=False, empty=False)
    assert result[0] == "test.m"
    source = result[1]
    expected = (
        "function out1 = test(x, y, z)\n"
        "  out1 = z.*(x + y);\n"
        "end\n"
    )
    assert source == expected


def test_m_simple_code_with_header():
    name_expr = ("test", (x + y)*z)
    result, = codegen(name_expr, "Octave", header=True, empty=False)
    assert result[0] == "test.m"
    source = result[1]
    expected = (
        "function out1 = test(x, y, z)\n"
        "  %TEST  Autogenerated by sympy\n"
        "  %   Code generated with sympy " + sympy.__version__ + "\n"
        "  %\n"
        "  %   See http://www.sympy.org/ for more information.\n"
        "  %\n"
        "  %   This file is part of 'project'\n"
        "  out1 = z.*(x + y);\n"
        "end\n"
    )
    assert source == expected


def test_m_simple_code_nameout():
    expr = Equality(z, (x + y))
    name_expr = ("test", expr)
    result, = codegen(name_expr, "Octave", header=False, empty=False)
    source = result[1]
    expected = (
        "function z = test(x, y)\n"
        "  z = x + y;\n"
        "end\n"
    )
    assert source == expected


def test_m_numbersymbol():
    name_expr = ("test", pi**Catalan)
    result, = codegen(name_expr, "Octave", header=False, empty=False)
    source = result[1]
    expected = (
        "function out1 = test()\n"
        "  out1 = pi^0.915965594177219;\n"
        "end\n"
    )
    assert source == expected


@XFAIL
def test_m_numbersymbol_no_inline():
    # FIXME: how to pass inline=False to the OctaveCodePrinter?
    name_expr = ("test", [pi**Catalan, EulerGamma])
    result, = codegen(name_expr, "Octave", header=False,
                      empty=False, inline=False)
    source = result[1]
    expected = (
        "function [out1, out2] = test()\n"
        "  Catalan = 0.915965594177219;  % constant\n"
        "  EulerGamma = 0.5772156649015329;  % constant\n"
        "  out1 = pi^Catalan;\n"
        "  out2 = EulerGamma;\n"
        "end\n"
    )
    assert source == expected


def test_m_code_argument_order():
    expr = x + y
    routine = make_routine("test", expr, argument_sequence=[z, x, y], language="octave")
    code_gen = OctaveCodeGen()
    output = StringIO()
    code_gen.dump_m([routine], output, "test", header=False, empty=False)
    source = output.getvalue()
    expected = (
        "function out1 = test(z, x, y)\n"
        "  out1 = x + y;\n"
        "end\n"
    )
    assert source == expected


def test_multiple_results_m():
    # Here the output order is the input order
    expr1 = (x + y)*z
    expr2 = (x - y)*z
    name_expr = ("test", [expr1, expr2])
    result, = codegen(name_expr, "Octave", header=False, empty=False)
    source = result[1]
    expected = (
        "function [out1, out2] = test(x, y, z)\n"
        "  out1 = z.*(x + y);\n"
        "  out2 = z.*(x - y);\n"
        "end\n"
    )
    assert source == expected


def test_results_named_unordered():
    # Here output order is based on name_expr
    A, B, C = symbols('A,B,C')
    expr1 = Equality(C, (x + y)*z)
    expr2 = Equality(A, (x - y)*z)
    expr3 = Equality(B, 2*x)
    name_expr = ("test", [expr1, expr2, expr3])
    result, = codegen(name_expr, "Octave", header=False, empty=False)
    source = result[1]
    expected = (
        "function [C, A, B] = test(x, y, z)\n"
        "  C = z.*(x + y);\n"
        "  A = z.*(x - y);\n"
        "  B = 2*x;\n"
        "end\n"
    )
    assert source == expected


def test_results_named_ordered():
    A, B, C = symbols('A,B,C')
    expr1 = Equality(C, (x + y)*z)
    expr2 = Equality(A, (x - y)*z)
    expr3 = Equality(B, 2*x)
    name_expr = ("test", [expr1, expr2, expr3])
    result = codegen(name_expr, "Octave", header=False, empty=False,
                     argument_sequence=(x, z, y))
    assert result[0][0] == "test.m"
    source = result[0][1]
    expected = (
        "function [C, A, B] = test(x, z, y)\n"
        "  C = z.*(x + y);\n"
        "  A = z.*(x - y);\n"
        "  B = 2*x;\n"
        "end\n"
    )
    assert source == expected


def test_complicated_m_codegen():
    from sympy import sin, cos, tan
    name_expr = ("testlong",
            [ ((sin(x) + cos(y) + tan(z))**3).expand(),
            cos(cos(cos(cos(cos(cos(cos(cos(x + y + z))))))))
    ])
    result = codegen(name_expr, "Octave", header=False, empty=False)
    assert result[0][0] == "testlong.m"
    source = result[0][1]
    expected = (
        "function [out1, out2] = testlong(x, y, z)\n"
        "  out1 = sin(x).^3 + 3*sin(x).^2.*cos(y) + 3*sin(x).^2.*tan(z)"
        " + 3*sin(x).*cos(y).^2 + 6*sin(x).*cos(y).*tan(z) + 3*sin(x).*tan(z).^2"
        " + cos(y).^3 + 3*cos(y).^2.*tan(z) + 3*cos(y).*tan(z).^2 + tan(z).^3;\n"
        "  out2 = cos(cos(cos(cos(cos(cos(cos(cos(x + y + z))))))));\n"
        "end\n"
    )
    assert source == expected


def test_m_output_arg_mixed_unordered():
    # named outputs are alphabetical, unnamed output appear in the given order
    from sympy import sin, cos, tan
    a = symbols("a")
    name_expr = ("foo", [cos(2*x), Equality(y, sin(x)), cos(x), Equality(a, sin(2*x))])
    result, = codegen(name_expr, "Octave", header=False, empty=False)
    assert result[0] == "foo.m"
    source = result[1];
    expected = (
        'function [out1, y, out3, a] = foo(x)\n'
        '  out1 = cos(2*x);\n'
        '  y = sin(x);\n'
        '  out3 = cos(x);\n'
        '  a = sin(2*x);\n'
        'end\n'
    )
    assert source == expected


def test_m_piecewise_():
    pw = Piecewise((0, x < -1), (x**2, x <= 1), (-x+2, x > 1), (1, True))
    name_expr = ("pwtest", pw)
    result, = codegen(name_expr, "Octave", header=False, empty=False)
    source = result[1]
    expected = (
        "function out1 = pwtest(x)\n"
        "  out1 = ((x < -1).*(0) + (~(x < -1)).*( ...\n"
        "  (x <= 1).*(x.^2) + (~(x <= 1)).*( ...\n"
        "  (x > 1).*(-x + 2) + (~(x > 1)).*(1))));\n"
        "end\n"
    )
    assert source == expected


@XFAIL
def test_m_piecewise_no_inline():
    # FIXME: how to pass inline=False to the OctaveCodePrinter?
    pw = Piecewise((0, x < -1), (x**2, x <= 1), (-x+2, x > 1), (1, True))
    name_expr = ("pwtest", pw)
    result, = codegen(name_expr, "Octave", header=False, empty=False,
                      inline=False)
    source = result[1]
    expected = (
        "function out1 = pwtest(x)\n"
        "  if (x < -1)\n"
        "    out1 = 0;\n"
        "  elseif (x <= 1)\n"
        "    out1 = x.^2;\n"
        "  elseif (x > 1)\n"
        "    out1 = -x + 2;\n"
        "  else\n"
        "    out1 = 1;\n"
        "  end\n"
        "end\n"
    )
    assert source == expected


def test_m_multifcns_per_file():
    name_expr = [ ("foo", [2*x, 3*y]), ("bar", [y**2, 4*y]) ]
    result = codegen(name_expr, "Octave", header=False, empty=False)
    assert result[0][0] == "foo.m"
    source = result[0][1];
    expected = (
        "function [out1, out2] = foo(x, y)\n"
        "  out1 = 2*x;\n"
        "  out2 = 3*y;\n"
        "end\n"
        "function [out1, out2] = bar(y)\n"
        "  out1 = y.^2;\n"
        "  out2 = 4*y;\n"
        "end\n"
    )
    assert source == expected


def test_m_multifcns_per_file_w_header():
    name_expr = [ ("foo", [2*x, 3*y]), ("bar", [y**2, 4*y]) ]
    result = codegen(name_expr, "Octave", header=True, empty=False)
    assert result[0][0] == "foo.m"
    source = result[0][1];
    expected = (
        "function [out1, out2] = foo(x, y)\n"
        "  %FOO  Autogenerated by sympy\n"
        "  %   Code generated with sympy " + sympy.__version__ + "\n"
        "  %\n"
        "  %   See http://www.sympy.org/ for more information.\n"
        "  %\n"
        "  %   This file is part of 'project'\n"
        "  out1 = 2*x;\n"
        "  out2 = 3*y;\n"
        "end\n"
        "function [out1, out2] = bar(y)\n"
        "  out1 = y.^2;\n"
        "  out2 = 4*y;\n"
        "end\n"
    )
    assert source == expected


def test_m_filename_match_first_fcn():
    name_expr = [ ("foo", [2*x, 3*y]), ("bar", [y**2, 4*y]) ]
    raises(ValueError, lambda: codegen(name_expr,
                        "Octave", prefix="bar", header=False, empty=False))


def test_m_matrix_named():
    e2 = Matrix([[x, 2*y, pi*z]])
    name_expr = ("test", Equality(MatrixSymbol('myout1', 1, 3), e2))
    result = codegen(name_expr, "Octave", header=False, empty=False)
    assert result[0][0] == "test.m"
    source = result[0][1]
    expected = (
        "function myout1 = test(x, y, z)\n"
        "  myout1 = [x 2*y pi*z];\n"
        "end\n"
    )
    assert source == expected


def test_m_matrix_named_matsym():
    myout1 = MatrixSymbol('myout1', 1, 3)
    e2 = Matrix([[x, 2*y, pi*z]])
    name_expr = ("test", Equality(myout1, e2, evaluate=False))
    result, = codegen(name_expr, "Octave", header=False, empty=False)
    source = result[1]
    expected = (
        "function myout1 = test(x, y, z)\n"
        "  myout1 = [x 2*y pi*z];\n"
        "end\n"
    )
    assert source == expected


def test_m_matrix_output_autoname():
    expr = Matrix([[x, x+y, 3]])
    name_expr = ("test", expr)
    result, = codegen(name_expr, "Octave", header=False, empty=False)
    source = result[1]
    expected = (
        "function out1 = test(x, y)\n"
        "  out1 = [x x + y 3];\n"
        "end\n"
    )
    assert source == expected


def test_m_matrix_output_autoname_2():
    e1 = (x + y)
    e2 = Matrix([[2*x, 2*y, 2*z]])
    e3 = Matrix([[x], [y], [z]])
    e4 = Matrix([[x, y], [z, 16]])
    name_expr = ("test", (e1, e2, e3, e4))
    result, = codegen(name_expr, "Octave", header=False, empty=False)
    source = result[1]
    expected = (
        "function [out1, out2, out3, out4] = test(x, y, z)\n"
        "  out1 = x + y;\n"
        "  out2 = [2*x 2*y 2*z];\n"
        "  out3 = [x; y; z];\n"
        "  out4 = [x y; z 16];\n"
        "end\n"
    )
    assert source == expected


def test_m_results_matrix_named_ordered():
    B, C = symbols('B,C')
    A = MatrixSymbol('A', 1, 3)
    expr1 = Equality(C, (x + y)*z)
    expr2 = Equality(A, Matrix([[1, 2, x]]))
    expr3 = Equality(B, 2*x)
    name_expr = ("test", [expr1, expr2, expr3])
    result, = codegen(name_expr, "Octave", header=False, empty=False,
                     argument_sequence=(x, z, y))
    source = result[1]
    expected = (
        "function [C, A, B] = test(x, z, y)\n"
        "  C = z.*(x + y);\n"
        "  A = [1 2 x];\n"
        "  B = 2*x;\n"
        "end\n"
    )
    assert source == expected


def test_m_matrixsymbol_slice():
    A = MatrixSymbol('A', 2, 3)
    B = MatrixSymbol('B', 1, 3)
    C = MatrixSymbol('C', 1, 3)
    D = MatrixSymbol('D', 2, 1)
    name_expr = ("test", [Equality(B, A[0, :]),
                          Equality(C, A[1, :]),
                          Equality(D, A[:, 2])])
    result, = codegen(name_expr, "Octave", header=False, empty=False)
    source = result[1]
    expected = (
        "function [B, C, D] = test(A)\n"
        "  B = A(1, :);\n"
        "  C = A(2, :);\n"
        "  D = A(:, 3);\n"
        "end\n"
    )
    assert source == expected


def test_m_matrixsymbol_slice2():
    A = MatrixSymbol('A', 3, 4)
    B = MatrixSymbol('B', 2, 2)
    C = MatrixSymbol('C', 2, 2)
    name_expr = ("test", [Equality(B, A[0:2, 0:2]),
                          Equality(C, A[0:2, 1:3])])
    result, = codegen(name_expr, "Octave", header=False, empty=False)
    source = result[1]
    expected = (
        "function [B, C] = test(A)\n"
        "  B = A(1:2, 1:2);\n"
        "  C = A(1:2, 2:3);\n"
        "end\n"
    )
    assert source == expected


def test_m_matrixsymbol_slice3():
    A = MatrixSymbol('A', 8, 7)
    B = MatrixSymbol('B', 2, 2)
    C = MatrixSymbol('C', 4, 2)
    name_expr = ("test", [Equality(B, A[6:, 1::3]),
                          Equality(C, A[::2, ::3])])
    result, = codegen(name_expr, "Octave", header=False, empty=False)
    source = result[1]
    expected = (
        "function [B, C] = test(A)\n"
        "  B = A(7:end, 2:3:end);\n"
        "  C = A(1:2:end, 1:3:end);\n"
        "end\n"
    )
    assert source == expected


def test_m_matrixsymbol_slice_autoname():
    A = MatrixSymbol('A', 2, 3)
    B = MatrixSymbol('B', 1, 3)
    name_expr = ("test", [Equality(B, A[0,:]), A[1,:], A[:,0], A[:,1]])
    result, = codegen(name_expr, "Octave", header=False, empty=False)
    source = result[1]
    expected = (
        "function [B, out2, out3, out4] = test(A)\n"
        "  B = A(1, :);\n"
        "  out2 = A(2, :);\n"
        "  out3 = A(:, 1);\n"
        "  out4 = A(:, 2);\n"
        "end\n"
    )
    assert source == expected


def test_m_loops():
    # Note: an Octave programmer would probably vectorize this across one or
    # more dimensions.  Also, size(A) would be used rather than passing in m
    # and n.  Perhaps users would expect us to vectorize automatically here?
    # Or is it possible to represent such things using IndexedBase?
    from sympy.tensor import IndexedBase, Idx
    from sympy import symbols
    n, m = symbols('n m', integer=True)
    A = IndexedBase('A')
    x = IndexedBase('x')
    y = IndexedBase('y')
    i = Idx('i', m)
    j = Idx('j', n)
    result, = codegen(('mat_vec_mult', Eq(y[i], A[i, j]*x[j])), "Octave",
                      header=False, empty=False)
    source = result[1]
    expected = (
        'function y = mat_vec_mult(A, m, n, x)\n'
        '  for i = 1:m\n'
        '    y(i) = 0;\n'
        '  end\n'
        '  for i = 1:m\n'
        '    for j = 1:n\n'
        '      y(i) = %(rhs)s + y(i);\n'
        '    end\n'
        '  end\n'
        'end\n'
    )
    assert (source == expected % {'rhs': 'A(%s, %s).*x(j)' % (i, j)} or
            source == expected % {'rhs': 'x(j).*A(%s, %s)' % (i, j)})


def test_m_tensor_loops_multiple_contractions():
    # see comments in previous test about vectorizing
    from sympy.tensor import IndexedBase, Idx
    from sympy import symbols
    n, m, o, p = symbols('n m o p', integer=True)
    A = IndexedBase('A')
    B = IndexedBase('B')
    y = IndexedBase('y')
    i = Idx('i', m)
    j = Idx('j', n)
    k = Idx('k', o)
    l = Idx('l', p)
    result, = codegen(('tensorthing', Eq(y[i], B[j, k, l]*A[i, j, k, l])),
                      "Octave", header=False, empty=False)
    source = result[1]
    expected = (
        'function y = tensorthing(A, B, m, n, o, p)\n'
        '  for i = 1:m\n'
        '    y(i) = 0;\n'
        '  end\n'
        '  for i = 1:m\n'
        '    for j = 1:n\n'
        '      for k = 1:o\n'
        '        for l = 1:p\n'
        '          y(i) = A(i, j, k, l).*B(j, k, l) + y(i);\n'
        '        end\n'
        '      end\n'
        '    end\n'
        '  end\n'
        'end\n'
    )
    assert source == expected


def test_m_InOutArgument():
    expr = Equality(x, x**2)
    name_expr = ("mysqr", expr)
    result, = codegen(name_expr, "Octave", header=False, empty=False)
    source = result[1]
    expected = (
        "function x = mysqr(x)\n"
        "  x = x.^2;\n"
        "end\n"
    )
    assert source == expected


def test_m_InOutArgument_order():
    # can specify the order as (x, y)
    expr = Equality(x, x**2 + y)
    name_expr = ("test", expr)
    result, = codegen(name_expr, "Octave", header=False,
                      empty=False, argument_sequence=(x,y))
    source = result[1]
    expected = (
        "function x = test(x, y)\n"
        "  x = x.^2 + y;\n"
        "end\n"
    )
    assert source == expected
    # make sure it gives (x, y) not (y, x)
    expr = Equality(x, x**2 + y)
    name_expr = ("test", expr)
    result, = codegen(name_expr, "Octave", header=False, empty=False)
    source = result[1]
    expected = (
        "function x = test(x, y)\n"
        "  x = x.^2 + y;\n"
        "end\n"
    )
    assert source == expected


def test_m_not_supported():
    f = Function('f')
    name_expr = ("test", [f(x).diff(x), S.ComplexInfinity])
    result, = codegen(name_expr, "Octave", header=False, empty=False)
    source = result[1]
    expected = (
        "function [out1, out2] = test(x)\n"
        "  % unsupported: Derivative(f(x), x)\n"
        "  % unsupported: zoo\n"
        "  out1 = Derivative(f(x), x);\n"
        "  out2 = zoo;\n"
        "end\n"
    )
    assert source == expected


def test_global_vars_octave():
    x, y, z, t = symbols("x y z t")
    result = codegen(('f', x*y), "Octave", header=False, empty=False,
                     global_vars=(y,))
    source = result[0][1]
    expected = (
        "function out1 = f(x)\n"
        "  global y\n"
        "  out1 = x.*y;\n"
        "end\n"
        )
    assert source == expected

    result = codegen(('f', x*y+z), "Octave", header=False, empty=False,
                     argument_sequence=(x, y), global_vars=(z, t))
    source = result[0][1]
    expected = (
        "function out1 = f(x, y)\n"
        "  global t z\n"
        "  out1 = x.*y + z;\n"
        "end\n"
    )
    assert source == expected
