from numpy.testing import assert_raises
from numpy.f2py.symbolic import (
    Expr, Op, ArithOp, Language,
    as_symbol, as_number, as_string, as_array, as_complex,
    as_terms, as_factors, eliminate_quotes, insert_quotes,
    fromstring, as_expr, as_apply,
    as_numer_denom, as_ternary, as_ref, as_deref,
    normalize, as_eq, as_ne, as_lt, as_gt, as_le, as_ge
    )
from . import util


class TestSymbolic(util.F2PyTest):

    def test_eliminate_quotes(self):
        def worker(s):
            r, d = eliminate_quotes(s)
            s1 = insert_quotes(r, d)
            assert s1 == s

        for kind in ['', 'mykind_']:
            worker(kind + '"1234" // "ABCD"')
            worker(kind + '"1234" // ' + kind + '"ABCD"')
            worker(kind + '"1234" // \'ABCD\'')
            worker(kind + '"1234" // ' + kind + '\'ABCD\'')
            worker(kind + '"1\\"2\'AB\'34"')
            worker('a = ' + kind + "'1\\'2\"AB\"34'")

    def test_sanity(self):
        x = as_symbol('x')
        y = as_symbol('y')
        z = as_symbol('z')

        assert x.op == Op.SYMBOL
        assert repr(x) == "Expr(Op.SYMBOL, 'x')"
        assert x == x
        assert x != y
        assert hash(x) is not None

        n = as_number(123)
        m = as_number(456)
        assert n.op == Op.INTEGER
        assert repr(n) == "Expr(Op.INTEGER, (123, 4))"
        assert n == n
        assert n != m
        assert hash(n) is not None

        fn = as_number(12.3)
        fm = as_number(45.6)
        assert fn.op == Op.REAL
        assert repr(fn) == "Expr(Op.REAL, (12.3, 4))"
        assert fn == fn
        assert fn != fm
        assert hash(fn) is not None

        c = as_complex(1, 2)
        c2 = as_complex(3, 4)
        assert c.op == Op.COMPLEX
        assert repr(c) == ("Expr(Op.COMPLEX, (Expr(Op.INTEGER, (1, 4)),"
                           " Expr(Op.INTEGER, (2, 4))))")
        assert c == c
        assert c != c2
        assert hash(c) is not None

        s = as_string("'123'")
        s2 = as_string('"ABC"')
        assert s.op == Op.STRING
        assert repr(s) == "Expr(Op.STRING, (\"'123'\", 1))", repr(s)
        assert s == s
        assert s != s2

        a = as_array((n, m))
        b = as_array((n,))
        assert a.op == Op.ARRAY
        assert repr(a) == ("Expr(Op.ARRAY, (Expr(Op.INTEGER, (123, 4)),"
                           " Expr(Op.INTEGER, (456, 4))))")
        assert a == a
        assert a != b

        t = as_terms(x)
        u = as_terms(y)
        assert t.op == Op.TERMS
        assert repr(t) == "Expr(Op.TERMS, {Expr(Op.SYMBOL, 'x'): 1})"
        assert t == t
        assert t != u
        assert hash(t) is not None

        v = as_factors(x)
        w = as_factors(y)
        assert v.op == Op.FACTORS
        assert repr(v) == "Expr(Op.FACTORS, {Expr(Op.SYMBOL, 'x'): 1})"
        assert v == v
        assert w != v
        assert hash(v) is not None

        t = as_ternary(x, y, z)
        u = as_ternary(x, z, y)
        assert t.op == Op.TERNARY
        assert t == t
        assert t != u
        assert hash(t) is not None

        e = as_eq(x, y)
        f = as_lt(x, y)
        assert e.op == Op.RELATIONAL
        assert e == e
        assert e != f
        assert hash(e) is not None

    def test_tostring_fortran(self):
        x = as_symbol('x')
        y = as_symbol('y')
        z = as_symbol('z')
        n = as_number(123)
        m = as_number(456)
        a = as_array((n, m))
        c = as_complex(n, m)

        assert str(x) == 'x'
        assert str(n) == '123'
        assert str(a) == '[123, 456]'
        assert str(c) == '(123, 456)'

        assert str(Expr(Op.TERMS, {x: 1})) == 'x'
        assert str(Expr(Op.TERMS, {x: 2})) == '2 * x'
        assert str(Expr(Op.TERMS, {x: -1})) == '-x'
        assert str(Expr(Op.TERMS, {x: -2})) == '-2 * x'
        assert str(Expr(Op.TERMS, {x: 1, y: 1})) == 'x + y'
        assert str(Expr(Op.TERMS, {x: -1, y: -1})) == '-x - y'
        assert str(Expr(Op.TERMS, {x: 2, y: 3})) == '2 * x + 3 * y'
        assert str(Expr(Op.TERMS, {x: -2, y: 3})) == '-2 * x + 3 * y'
        assert str(Expr(Op.TERMS, {x: 2, y: -3})) == '2 * x - 3 * y'

        assert str(Expr(Op.FACTORS, {x: 1})) == 'x'
        assert str(Expr(Op.FACTORS, {x: 2})) == 'x ** 2'
        assert str(Expr(Op.FACTORS, {x: -1})) == 'x ** -1'
        assert str(Expr(Op.FACTORS, {x: -2})) == 'x ** -2'
        assert str(Expr(Op.FACTORS, {x: 1, y: 1})) == 'x * y'
        assert str(Expr(Op.FACTORS, {x: 2, y: 3})) == 'x ** 2 * y ** 3'

        v = Expr(Op.FACTORS, {x: 2, Expr(Op.TERMS, {x: 1, y: 1}): 3})
        assert str(v) == 'x ** 2 * (x + y) ** 3', str(v)
        v = Expr(Op.FACTORS, {x: 2, Expr(Op.FACTORS, {x: 1, y: 1}): 3})
        assert str(v) == 'x ** 2 * (x * y) ** 3', str(v)

        assert str(Expr(Op.APPLY, ('f', (), {}))) == 'f()'
        assert str(Expr(Op.APPLY, ('f', (x,), {}))) == 'f(x)'
        assert str(Expr(Op.APPLY, ('f', (x, y), {}))) == 'f(x, y)'
        assert str(Expr(Op.INDEXING, ('f', x))) == 'f[x]'

        assert str(as_ternary(x, y, z)) == 'merge(y, z, x)'
        assert str(as_eq(x, y)) == 'x .eq. y'
        assert str(as_ne(x, y)) == 'x .ne. y'
        assert str(as_lt(x, y)) == 'x .lt. y'
        assert str(as_le(x, y)) == 'x .le. y'
        assert str(as_gt(x, y)) == 'x .gt. y'
        assert str(as_ge(x, y)) == 'x .ge. y'

    def test_tostring_c(self):
        language = Language.C
        x = as_symbol('x')
        y = as_symbol('y')
        z = as_symbol('z')
        n = as_number(123)

        assert Expr(Op.FACTORS, {x: 2}).tostring(language=language) == 'x * x'
        assert Expr(Op.FACTORS, {x + y: 2}).tostring(
            language=language) == '(x + y) * (x + y)'
        assert Expr(Op.FACTORS, {x: 12}).tostring(
            language=language) == 'pow(x, 12)'

        assert as_apply(ArithOp.DIV, x, y).tostring(
            language=language) == 'x / y'
        assert as_apply(ArithOp.DIV, x, x + y).tostring(
            language=language) == 'x / (x + y)'
        assert as_apply(ArithOp.DIV, x - y, x + y).tostring(
            language=language) == '(x - y) / (x + y)'
        assert (x + (x - y) / (x + y) + n).tostring(
            language=language) == '123 + x + (x - y) / (x + y)'

        assert as_ternary(x, y, z).tostring(language=language) == '(x ? y : z)'
        assert as_eq(x, y).tostring(language=language) == 'x == y'
        assert as_ne(x, y).tostring(language=language) == 'x != y'
        assert as_lt(x, y).tostring(language=language) == 'x < y'
        assert as_le(x, y).tostring(language=language) == 'x <= y'
        assert as_gt(x, y).tostring(language=language) == 'x > y'
        assert as_ge(x, y).tostring(language=language) == 'x >= y'

    def test_operations(self):
        x = as_symbol('x')
        y = as_symbol('y')
        z = as_symbol('z')

        assert x + x == Expr(Op.TERMS, {x: 2})
        assert x - x == Expr(Op.INTEGER, (0, 4))
        assert x + y == Expr(Op.TERMS, {x: 1, y: 1})
        assert x - y == Expr(Op.TERMS, {x: 1, y: -1})
        assert x * x == Expr(Op.FACTORS, {x: 2})
        assert x * y == Expr(Op.FACTORS, {x: 1, y: 1})

        assert +x == x
        assert -x == Expr(Op.TERMS, {x: -1}), repr(-x)
        assert 2 * x == Expr(Op.TERMS, {x: 2})
        assert 2 + x == Expr(Op.TERMS, {x: 1, as_number(1): 2})
        assert 2 * x + 3 * y == Expr(Op.TERMS, {x: 2, y: 3})
        assert (x + y) * 2 == Expr(Op.TERMS, {x: 2, y: 2})

        assert x ** 2 == Expr(Op.FACTORS, {x: 2})
        assert (x + y) ** 2 == Expr(Op.TERMS,
                                    {Expr(Op.FACTORS, {x: 2}): 1,
                                     Expr(Op.FACTORS, {y: 2}): 1,
                                     Expr(Op.FACTORS, {x: 1, y: 1}): 2})
        assert (x + y) * x == x ** 2 + x * y
        assert (x + y) ** 2 == x ** 2 + 2 * x * y + y ** 2
        assert (x + y) ** 2 + (x - y) ** 2 == 2 * x ** 2 + 2 * y ** 2
        assert (x + y) * z == x * z + y * z
        assert z * (x + y) == x * z + y * z

        assert (x / 2) == as_apply(ArithOp.DIV, x, as_number(2))
        assert (2 * x / 2) == x
        assert (3 * x / 2) == as_apply(ArithOp.DIV, 3*x, as_number(2))
        assert (4 * x / 2) == 2 * x
        assert (5 * x / 2) == as_apply(ArithOp.DIV, 5*x, as_number(2))
        assert (6 * x / 2) == 3 * x
        assert ((3*5) * x / 6) == as_apply(ArithOp.DIV, 5*x, as_number(2))
        assert (30*x**2*y**4 / (24*x**3*y**3)) == as_apply(ArithOp.DIV,
                                                           5*y, 4*x)
        assert ((15 * x / 6) / 5) == as_apply(
            ArithOp.DIV, x, as_number(2)), ((15 * x / 6) / 5)
        assert (x / (5 / x)) == as_apply(ArithOp.DIV, x**2, as_number(5))

        assert (x / 2.0) == Expr(Op.TERMS, {x: 0.5})

        s = as_string('"ABC"')
        t = as_string('"123"')

        assert s // t == Expr(Op.STRING, ('"ABC123"', 1))
        assert s // x == Expr(Op.CONCAT, (s, x))
        assert x // s == Expr(Op.CONCAT, (x, s))

        c = as_complex(1., 2.)
        assert -c == as_complex(-1., -2.)
        assert c + c == as_expr((1+2j)*2)
        assert c * c == as_expr((1+2j)**2)

    def test_substitute(self):
        x = as_symbol('x')
        y = as_symbol('y')
        z = as_symbol('z')
        a = as_array((x, y))

        assert x.substitute({x: y}) == y
        assert (x + y).substitute({x: z}) == y + z
        assert (x * y).substitute({x: z}) == y * z
        assert (x ** 4).substitute({x: z}) == z ** 4
        assert (x / y).substitute({x: z}) == z / y
        assert x.substitute({x: y + z}) == y + z
        assert a.substitute({x: y + z}) == as_array((y + z, y))

        assert as_ternary(x, y, z).substitute(
            {x: y + z}) == as_ternary(y + z, y, z)
        assert as_eq(x, y).substitute(
            {x: y + z}) == as_eq(y + z, y)

    def test_fromstring(self):

        x = as_symbol('x')
        y = as_symbol('y')
        z = as_symbol('z')
        f = as_symbol('f')
        s = as_string('"ABC"')
        t = as_string('"123"')
        a = as_array((x, y))

        assert fromstring('x') == x
        assert fromstring('+ x') == x
        assert fromstring('-  x') == -x
        assert fromstring('x + y') == x + y
        assert fromstring('x + 1') == x + 1
        assert fromstring('x * y') == x * y
        assert fromstring('x * 2') == x * 2
        assert fromstring('x / y') == x / y
        assert fromstring('x ** 2',
                          language=Language.Python) == x ** 2
        assert fromstring('x ** 2 ** 3',
                          language=Language.Python) == x ** 2 ** 3
        assert fromstring('(x + y) * z') == (x + y) * z

        assert fromstring('f(x)') == f(x)
        assert fromstring('f(x,y)') == f(x, y)
        assert fromstring('f[x]') == f[x]
        assert fromstring('f[x][y]') == f[x][y]

        assert fromstring('"ABC"') == s
        assert normalize(fromstring('"ABC" // "123" ',
                                    language=Language.Fortran)) == s // t
        assert fromstring('f("ABC")') == f(s)
        assert fromstring('MYSTRKIND_"ABC"') == as_string('"ABC"', 'MYSTRKIND')

        assert fromstring('(/x, y/)') == a, fromstring('(/x, y/)')
        assert fromstring('f((/x, y/))') == f(a)
        assert fromstring('(/(x+y)*z/)') == as_array(((x+y)*z,))

        assert fromstring('123') == as_number(123)
        assert fromstring('123_2') == as_number(123, 2)
        assert fromstring('123_myintkind') == as_number(123, 'myintkind')

        assert fromstring('123.0') == as_number(123.0, 4)
        assert fromstring('123.0_4') == as_number(123.0, 4)
        assert fromstring('123.0_8') == as_number(123.0, 8)
        assert fromstring('123.0e0') == as_number(123.0, 4)
        assert fromstring('123.0d0') == as_number(123.0, 8)
        assert fromstring('123d0') == as_number(123.0, 8)
        assert fromstring('123e-0') == as_number(123.0, 4)
        assert fromstring('123d+0') == as_number(123.0, 8)
        assert fromstring('123.0_myrealkind') == as_number(123.0, 'myrealkind')
        assert fromstring('3E4') == as_number(30000.0, 4)

        assert fromstring('(1, 2)') == as_complex(1, 2)
        assert fromstring('(1e2, PI)') == as_complex(
            as_number(100.0), as_symbol('PI'))

        assert fromstring('[1, 2]') == as_array((as_number(1), as_number(2)))

        assert fromstring('POINT(x, y=1)') == as_apply(
            as_symbol('POINT'), x, y=as_number(1))
        assert (fromstring('PERSON(name="John", age=50, shape=(/34, 23/))')
                == as_apply(as_symbol('PERSON'),
                            name=as_string('"John"'),
                            age=as_number(50),
                            shape=as_array((as_number(34), as_number(23)))))

        assert fromstring('x?y:z') == as_ternary(x, y, z)

        assert fromstring('*x') == as_deref(x)
        assert fromstring('**x') == as_deref(as_deref(x))
        assert fromstring('&x') == as_ref(x)
        assert fromstring('(*x) * (*y)') == as_deref(x) * as_deref(y)
        assert fromstring('(*x) * *y') == as_deref(x) * as_deref(y)
        assert fromstring('*x * *y') == as_deref(x) * as_deref(y)
        assert fromstring('*x**y') == as_deref(x) * as_deref(y)

        assert fromstring('x == y') == as_eq(x, y)
        assert fromstring('x != y') == as_ne(x, y)
        assert fromstring('x < y') == as_lt(x, y)
        assert fromstring('x > y') == as_gt(x, y)
        assert fromstring('x <= y') == as_le(x, y)
        assert fromstring('x >= y') == as_ge(x, y)

        assert fromstring('x .eq. y', language=Language.Fortran) == as_eq(x, y)
        assert fromstring('x .ne. y', language=Language.Fortran) == as_ne(x, y)
        assert fromstring('x .lt. y', language=Language.Fortran) == as_lt(x, y)
        assert fromstring('x .gt. y', language=Language.Fortran) == as_gt(x, y)
        assert fromstring('x .le. y', language=Language.Fortran) == as_le(x, y)
        assert fromstring('x .ge. y', language=Language.Fortran) == as_ge(x, y)

    def test_traverse(self):
        x = as_symbol('x')
        y = as_symbol('y')
        z = as_symbol('z')
        f = as_symbol('f')

        # Use traverse to substitute a symbol
        def replace_visit(s, r=z):
            if s == x:
                return r

        assert x.traverse(replace_visit) == z
        assert y.traverse(replace_visit) == y
        assert z.traverse(replace_visit) == z
        assert (f(y)).traverse(replace_visit) == f(y)
        assert (f(x)).traverse(replace_visit) == f(z)
        assert (f[y]).traverse(replace_visit) == f[y]
        assert (f[z]).traverse(replace_visit) == f[z]
        assert (x + y + z).traverse(replace_visit) == (2 * z + y)
        assert (x + f(y, x - z)).traverse(
            replace_visit) == (z + f(y, as_number(0)))
        assert as_eq(x, y).traverse(replace_visit) == as_eq(z, y)

        # Use traverse to collect symbols, method 1
        function_symbols = set()
        symbols = set()

        def collect_symbols(s):
            if s.op is Op.APPLY:
                oper = s.data[0]
                function_symbols.add(oper)
                if oper in symbols:
                    symbols.remove(oper)
            elif s.op is Op.SYMBOL and s not in function_symbols:
                symbols.add(s)

        (x + f(y, x - z)).traverse(collect_symbols)
        assert function_symbols == {f}
        assert symbols == {x, y, z}

        # Use traverse to collect symbols, method 2
        def collect_symbols2(expr, symbols):
            if expr.op is Op.SYMBOL:
                symbols.add(expr)

        symbols = set()
        (x + f(y, x - z)).traverse(collect_symbols2, symbols)
        assert symbols == {x, y, z, f}

        # Use traverse to partially collect symbols
        def collect_symbols3(expr, symbols):
            if expr.op is Op.APPLY:
                # skip traversing function calls
                return expr
            if expr.op is Op.SYMBOL:
                symbols.add(expr)

        symbols = set()
        (x + f(y, x - z)).traverse(collect_symbols3, symbols)
        assert symbols == {x}

    def test_linear_solve(self):
        x = as_symbol('x')
        y = as_symbol('y')
        z = as_symbol('z')

        assert x.linear_solve(x) == (as_number(1), as_number(0))
        assert (x+1).linear_solve(x) == (as_number(1), as_number(1))
        assert (2*x).linear_solve(x) == (as_number(2), as_number(0))
        assert (2*x+3).linear_solve(x) == (as_number(2), as_number(3))
        assert as_number(3).linear_solve(x) == (as_number(0), as_number(3))
        assert y.linear_solve(x) == (as_number(0), y)
        assert (y*z).linear_solve(x) == (as_number(0), y * z)

        assert (x+y).linear_solve(x) == (as_number(1), y)
        assert (z*x+y).linear_solve(x) == (z, y)
        assert ((z+y)*x+y).linear_solve(x) == (z + y, y)
        assert (z*y*x+y).linear_solve(x) == (z * y, y)

        assert_raises(RuntimeError, lambda: (x*x).linear_solve(x))

    def test_as_numer_denom(self):
        x = as_symbol('x')
        y = as_symbol('y')
        n = as_number(123)

        assert as_numer_denom(x) == (x, as_number(1))
        assert as_numer_denom(x / n) == (x, n)
        assert as_numer_denom(n / x) == (n, x)
        assert as_numer_denom(x / y) == (x, y)
        assert as_numer_denom(x * y) == (x * y, as_number(1))
        assert as_numer_denom(n + x / y) == (x + n * y, y)
        assert as_numer_denom(n + x / (y - x / n)) == (y * n ** 2, y * n - x)

    def test_polynomial_atoms(self):
        x = as_symbol('x')
        y = as_symbol('y')
        n = as_number(123)

        assert x.polynomial_atoms() == {x}
        assert n.polynomial_atoms() == set()
        assert (y[x]).polynomial_atoms() == {y[x]}
        assert (y(x)).polynomial_atoms() == {y(x)}
        assert (y(x) + x).polynomial_atoms() == {y(x), x}
        assert (y(x) * x[y]).polynomial_atoms() == {y(x), x[y]}
        assert (y(x) ** x).polynomial_atoms() == {y(x)}
