def test_matrix():
    A = Matrix([[x, y], [y*x, z**2]])
    assert lambdarepr(A) == "ImmutableDenseMatrix([[x, y], [x*y, z**2]])"

    # Test printing a Matrix that has an element that is printed differently
    # with the LambdaPrinter than in the StrPrinter.
    p = Piecewise((x, True), evaluate=False)
    A = Matrix([p])
    assert lambdarepr(A) == "ImmutableDenseMatrix([[((x) if (True) else None)]])"

def lambdastr(args, expr):
    """
    Returns a string that can be evaluated to a lambda function.

    >>> from sympy import symbols
    >>> x,y,z = symbols('xyz')
    >>> lambdastr(x, x**2)
    'lambda x: (x**2)'
    >>> lambdastr((x,y,z), [z,y,x])
    'lambda x,y,z: ([z, y, x])'
    """

    #XXX: This has to be done here because of circular imports
    from sympy.printing.lambdarepr import lambdarepr

    # Transform everything to strings.
    expr = lambdarepr(expr)
    if isinstance(args, str):
        pass
    elif hasattr(args, "__iter__"):
        args = ",".join(str(a) for a in args)
    else:
        args = str(args)

    return "lambda %s: (%s)" % (args, expr)

def test_piecewise():
    p = Piecewise(
        (x, x < 1),
        (x**2, Interval(3, 4, True, False)),
        (0, True)
    )
    assert lambdarepr(p) == 'iff(x < 1,x,iff(((x <= 4) and (3 < x)),x**2,iff(True,0,0)))'

 def lambdarepr(self):
     """
     """
     from sympy.printing.lambdarepr import lambdarepr
     temp_arr=numpy.empty(self.getShape(), dtype=object)
     for idx,el in numpy.ndenumerate(self._arr):
         atoms=el.atoms(sympy.Symbol) if isinstance(el,sympy.Basic) else []
         # create a dictionary to convert names like [x]_0_0 to x[0,0]
         symdict={}
         for a in atoms:
             n,c=Symbol._symComp(a)
             if len(c)>0:
                 c=[str(i) for i in c]
                 symstr=n+'['+','.join(c)+']'
             else:
                 symstr=n
             symdict[a.name]=symstr
         s=lambdarepr(el)
         for key in symdict:
             s=s.replace(key, symdict[key])
         temp_arr[idx]=s
     if self.getRank()==0:
         return temp_arr.item()
     else:
         return 'combineData(%s,%s)'%(str(temp_arr.tolist()).replace("'",""),str(self.getShape()))

def lambdastr(args, expr, printer=None):
    """
    Returns a string that can be evaluated to a lambda function.

    >>> from sympy.abc import x, y, z
    >>> from sympy.utilities.lambdify import lambdastr
    >>> lambdastr(x, x**2)
    'lambda x: (x**2)'
    >>> lambdastr((x,y,z), [z,y,x])
    'lambda x,y,z: ([z, y, x])'

    """
    if printer is not None:
        if inspect.isfunction(printer):
            lambdarepr = printer
        else:
            if inspect.isclass(printer):
                lambdarepr = lambda expr: printer().doprint(expr)
            else:
                lambdarepr = lambda expr: printer.doprint(expr)
    else:
        #XXX: This has to be done here because of circular imports
        from sympy.printing.lambdarepr import lambdarepr

    # Transform everything to strings.
    expr = lambdarepr(expr)
    if isinstance(args, str):
        pass
    elif hasattr(args, "__iter__"):
        args = ",".join(str(a) for a in args)
    else:
        args = str(args)

    return "lambda %s: (%s)" % (args, expr)

def test_multiple_sums():
    s = Sum(i * x + j, (i, a, b), (j, c, d))

    l = lambdarepr(s)
    assert l == "(builtins.sum(i*x + j for i in range(a, b+1) for j in range(c, d+1)))"

    assert (lambdify((x, a, b, c, d), s)(2, 3, 4, 5, 6) ==
            s.subs([(x, 2), (a, 3), (b, 4), (c, 5), (d, 6)]).doit())

def test_sum__2():
    s = Sum(i * x, (i, a, b))
    l = lambdarepr(s)
    assert l == "(builtins.sum(i*x for i in range(a, b+1)))"

    args = x, a, b
    f = lambdify(args, s)
    v = 2, 3, 8
    assert f(*v) == s.subs(zip(args, v)).doit()

def test_piecewise():
    # In each case, test eval() the lambdarepr() to make sure there are a
    # correct number of parentheses. It will give a SyntaxError if there aren't.

    h = "lambda x: "

    p = Piecewise((x, True), evaluate=False)
    l = lambdarepr(p)
    eval(h + l)
    assert l == "((x) if (True) else None)"

    p = Piecewise((x, x < 0))
    l = lambdarepr(p)
    eval(h + l)
    assert l == "((x) if (x < 0) else None)"

    p = Piecewise((1, x < 1), (2, x < 2), (0, True))
    l = lambdarepr(p)
    eval(h + l)
    assert l == "((1) if (x < 1) else (((2) if (x < 2) else (((0) if (True) " "else None)))))"

    p = Piecewise((1, x < 1), (2, x < 2))
    l = lambdarepr(p)
    eval(h + l)
    assert l == "((1) if (x < 1) else (((2) if (x < 2) else None)))"

    p = Piecewise((x, x < 1), (x ** 2, Interval(3, 4, True, False)), (0, True))
    l = lambdarepr(p)
    eval(h + l)
    assert l == "((x) if (x < 1) else (((x**2) if (((x <= 4) " "and (3 < x))) else (((0) if (True) else None)))))"

    p = Piecewise((x ** 2, x < 0), (x, Interval(0, 1, False, True)), (2 - x, x >= 1), (0, True))
    l = lambdarepr(p)
    eval(h + l)
    assert (
        l == "((x**2) if (x < 0) else (((x) if (((x < 1) and (0 <= x))) "
        "else (((-x + 2) if (1 <= x) else (((0) if (True) else None)))))))"
    )

    p = Piecewise((x ** 2, x < 0), (x, Interval(0, 1, False, True)), (2 - x, x >= 1))
    l = lambdarepr(p)
    eval(h + l)
    assert (
        l == "((x**2) if (x < 0) else (((x) if (((x < 1) and " "(0 <= x))) else (((-x + 2) if (1 <= x) else None)))))"
    )

    p = Piecewise((1, x < 1), (2, x < 2), (3, x < 3), (4, x < 4), (5, x < 5), (6, True))
    l = lambdarepr(p)
    eval(h + l)
    assert (
        l == "((1) if (x < 1) else (((2) if (x < 2) else (((3) if "
        "(x < 3) else (((4) if (x < 4) else (((5) if (x < 5) else (((6) if "
        "(True) else None)))))))))))"
    )

def test_sum():
    # In each case, test eval() the lambdarepr() to make sure that
    # it evaluates to the same results as the symbolic expression

    s = Sum(x ** i, (i, a, b))

    l = lambdarepr(s)
    assert l == "(builtins.sum(x**i for i in range(a, b+1)))"

    assert (lambdify((x, a, b), s)(2, 3, 8) ==
            s.subs([(x, 2), (a, 3), (b, 8)]).doit())

    s = Sum(i * x, (i, a, b))

    l = lambdarepr(s)
    assert l == "(builtins.sum(i*x for i in range(a, b+1)))"

    assert (lambdify((x, a, b), s)(2, 3, 8) ==
            s.subs([(x, 2), (a, 3), (b, 8)]).doit())

def test_sum__1():
    # In each case, test eval() the lambdarepr() to make sure that
    # it evaluates to the same results as the symbolic expression
    s = Sum(x ** i, (i, a, b))
    l = lambdarepr(s)
    assert l == "(builtins.sum(x**i for i in range(a, b+1)))"

    args = x, a, b
    f = lambdify(args, s)
    v = 2, 3, 8
    assert f(*v) == s.subs(zip(args, v)).doit()

def test_multiple_sums():
    s = Sum(i * x + j, (i, a, b), (j, c, d))

    l = lambdarepr(s)
    assert l == "(builtins.sum(i*x + j for i in range(a, b+1) for j in range(c, d+1)))"

    args = x, a, b, c, d
    f = lambdify(args, s)
    vals = 2, 3, 4, 5, 6
    f_ref = s.subs(zip(args, vals)).doit()
    f_res = f(*vals)
    assert f_res == f_ref

def callback_factory(args, expr, module, use_numba=False):
    if module == 'numpy':
        from sympy.utilities.lambdify import NUMPY_TRANSLATIONS as TRANSLATIONS
        from sympy.printing.lambdarepr import NumPyPrinter as Printer

        def lambdarepr(_x):
            return Printer().doprint(_x)
    else:
        from sympy.printing.lambdarepr import lambdarepr
        if module == 'mpmath':
            from sympy.utilities.lambdify import MPMATH_TRANSLATIONS as TRANSLATIONS
        elif module == 'sympy':
            TRANSLATIONS = {}
        else:
            raise NotImplementedError("Lambdify does not yet support %s" % module)

    mod = __import__(module)
    from sympy import IndexedBase, Symbol
    x = IndexedBase('x')
    indices = [Symbol('..., %d' % i) for i in range(len(args))]
    dummy_subs = dict(zip(args, [x[i] for i in indices]))
    dummified = expr.xreplace(dummy_subs)
    estr = lambdarepr(dummified)

    namespace = mod.__dict__.copy()

    # e.g. NumPyPrinter incomplete: https://github.com/sympy/sympy/issues/11023
    # we need to read translations from lambdify
    for k, v in TRANSLATIONS.items():
        namespace[k] = namespace[v]

    if module != 'mpmath':
        namespace['Abs'] = abs

    func = eval('lambda x: %s' % estr, namespace)
    if use_numba:
        from numba import njit
        func = njit(func)
    if module == 'numpy':
        def wrapper(x):
            return func(mod.asarray(x, dtype=mod.float64))
    else:
        wrapper = func
    wrapper.__doc__ = estr

    return wrapper

def lambdastr(args, expr, printer=None, dummify=False):
    """
    Returns a string that can be evaluated to a lambda function.

    >>> from sympy.abc import x, y, z
    >>> from sympy.utilities.lambdify import lambdastr
    >>> lambdastr(x, x**2)
    'lambda x: (x**2)'
    >>> lambdastr((x,y,z), [z,y,x])
    'lambda x,y,z: ([z, y, x])'

    """
    # Transforming everything to strings.
    from sympy.matrices import DeferredVector
    from sympy import Dummy, sympify, Symbol, Function

    if printer is not None:
        if inspect.isfunction(printer):
            lambdarepr = printer
        else:
            if inspect.isclass(printer):
                lambdarepr = lambda expr: printer().doprint(expr)
            else:
                lambdarepr = lambda expr: printer.doprint(expr)
    else:
        #XXX: This has to be done here because of circular imports
        from sympy.printing.lambdarepr import lambdarepr

    def sub_args(args, dummies_dict):
        if isinstance(args, str):
            return args
        elif isinstance(args, DeferredVector):
            return str(args)
        elif iterable(args):
            flatten = lambda *n: (e for a in n for e in
                                  (flatten(*a) if iterable(a) else (a,)))
            dummies = flatten([sub_args(a, dummies_dict) for a in args])
            return ",".join(str(a) for a in dummies)
        else:
            if isinstance(args, Function):
                dummies = Dummy()
                dummies_dict.update({args : dummies})
                return str(dummies)
            else:
                return str(args)

    def sub_expr(expr, dummies_dict):
        try:
            expr = sympify(expr).xreplace(dummies_dict)
        except:
            if isinstance(expr, DeferredVector):
                pass
            elif isinstance(expr, dict):
                k = [sub_expr(sympify(a), dummies_dict) for a in expr.keys()]
                v = [sub_expr(sympify(a), dummies_dict) for a in expr.values()]
                expr = dict(zip(k, v))
            elif isinstance(expr, tuple):
                expr = tuple(sub_expr(sympify(a), dummies_dict) for a in expr)
            elif isinstance(expr, list):
                expr = [sub_expr(sympify(a), dummies_dict) for a in expr]
        return expr

    # Transform args
    dummies_dict = {}
    if dummify:
        args = sub_args(args, dummies_dict)
    else:
        if isinstance(args, str):
            pass
        elif iterable(args, exclude=DeferredVector):
            args = ",".join(str(a) for a in args)

    # Transform expr
    if dummify:
        if isinstance(expr, str):
            pass
        else:
            expr = sub_expr(expr, dummies_dict)
    expr = lambdarepr(expr)

    return "lambda %s: (%s)" % (args, expr)

def test_basic():
    assert lambdarepr(x*y) == "x*y"
    assert lambdarepr(x + y) in ["y + x", "x + y"]
    assert lambdarepr(x**y) == "x**y"

def test_piecewise():
    # In each case, test eval() the lambdarepr() to make sure there are a
    # correct number of parentheses. It will give a SyntaxError if there aren't.

    h = "lambda x: "

    p = Piecewise((x, True), evaluate=False)
    l = lambdarepr(p)
    eval(h + l)
    assert l == "((x))"

    p = Piecewise((x, x < 0))
    l = lambdarepr(p)
    eval(h + l)
    assert l == "((x) if (x < 0) else None)"

    p = Piecewise(
        (1, x < 1),
        (2, x < 2),
        (0, True)
    )
    l = lambdarepr(p)
    eval(h + l)
    assert l == "((1) if (x < 1) else (2) if (x < 2) else (0))"

    p = Piecewise(
        (1, x < 1),
        (2, x < 2),
    )
    l = lambdarepr(p)
    eval(h + l)
    assert l == "((1) if (x < 1) else (2) if (x < 2) else None)"

    p = Piecewise(
        (x, x < 1),
        (x**2, Interval(3, 4, True, False).contains(x)),
        (0, True),
    )
    l = lambdarepr(p)
    eval(h + l)
    assert l == "((x) if (x < 1) else (x**2) if (((x <= 4)) and ((x > 3))) else (0))"

    p = Piecewise(
        (x**2, x < 0),
        (x, x < 1),
        (2 - x, x >= 1),
        (0, True), evaluate=False
    )
    l = lambdarepr(p)
    eval(h + l)
    assert l == "((x**2) if (x < 0) else (x) if (x < 1)"\
                                " else (-x + 2) if (x >= 1) else (0))"

    p = Piecewise(
        (x**2, x < 0),
        (x, x < 1),
        (2 - x, x >= 1), evaluate=False
    )
    l = lambdarepr(p)
    eval(h + l)
    assert l == "((x**2) if (x < 0) else (x) if (x < 1)"\
                    " else (-x + 2) if (x >= 1) else None)"

    p = Piecewise(
        (1, x >= 1),
        (2, x >= 2),
        (3, x >= 3),
        (4, x >= 4),
        (5, x >= 5),
        (6, True)
    )
    l = lambdarepr(p)
    eval(h + l)
    assert l == "((1) if (x >= 1) else (2) if (x >= 2) else (3) if (x >= 3)"\
                        " else (4) if (x >= 4) else (5) if (x >= 5) else (6))"

    p = Piecewise(
        (1, x <= 1),
        (2, x <= 2),
        (3, x <= 3),
        (4, x <= 4),
        (5, x <= 5),
        (6, True)
    )
    l = lambdarepr(p)
    eval(h + l)
    assert l == "((1) if (x <= 1) else (2) if (x <= 2) else (3) if (x <= 3)"\
                            " else (4) if (x <= 4) else (5) if (x <= 5) else (6))"

    p = Piecewise(
        (1, x > 1),
        (2, x > 2),
        (3, x > 3),
        (4, x > 4),
        (5, x > 5),
        (6, True)
    )
    l = lambdarepr(p)
    eval(h + l)
    assert l =="((1) if (x > 1) else (2) if (x > 2) else (3) if (x > 3)"\
#.........这里部分代码省略.........

def lambdastr(args, expr, printer=None, dummify=None):
    """
    Returns a string that can be evaluated to a lambda function.

    Examples
    ========

    >>> from sympy.abc import x, y, z
    >>> from sympy.utilities.lambdify import lambdastr
    >>> lambdastr(x, x**2)
    'lambda x: (x**2)'
    >>> lambdastr((x,y,z), [z,y,x])
    'lambda x,y,z: ([z, y, x])'

    Although tuples may not appear as arguments to lambda in Python 3,
    lambdastr will create a lambda function that will unpack the original
    arguments so that nested arguments can be handled:

    >>> lambdastr((x, (y, z)), x + y)
    'lambda _0,_1: (lambda x,y,z: (x + y))(_0,_1[0],_1[1])'
    """
    # Transforming everything to strings.
    from sympy.matrices import DeferredVector
    from sympy import Dummy, sympify, Symbol, Function, flatten, Derivative, Basic

    if printer is not None:
        if inspect.isfunction(printer):
            lambdarepr = printer
        else:
            if inspect.isclass(printer):
                lambdarepr = lambda expr: printer().doprint(expr)
            else:
                lambdarepr = lambda expr: printer.doprint(expr)
    else:
        #XXX: This has to be done here because of circular imports
        from sympy.printing.lambdarepr import lambdarepr

    def sub_args(args, dummies_dict):
        if isinstance(args, str):
            return args
        elif isinstance(args, DeferredVector):
            return str(args)
        elif iterable(args):
            dummies = flatten([sub_args(a, dummies_dict) for a in args])
            return ",".join(str(a) for a in dummies)
        else:
            # replace these with Dummy symbols
            if isinstance(args, (Function, Symbol, Derivative)):
                dummies = Dummy()
                dummies_dict.update({args : dummies})
                return str(dummies)
            else:
                return str(args)

    def sub_expr(expr, dummies_dict):
        try:
            expr = sympify(expr).xreplace(dummies_dict)
        except Exception:
            if isinstance(expr, DeferredVector):
                pass
            elif isinstance(expr, dict):
                k = [sub_expr(sympify(a), dummies_dict) for a in expr.keys()]
                v = [sub_expr(sympify(a), dummies_dict) for a in expr.values()]
                expr = dict(zip(k, v))
            elif isinstance(expr, tuple):
                expr = tuple(sub_expr(sympify(a), dummies_dict) for a in expr)
            elif isinstance(expr, list):
                expr = [sub_expr(sympify(a), dummies_dict) for a in expr]
        return expr

    # Transform args
    def isiter(l):
        return iterable(l, exclude=(str, DeferredVector, NotIterable))

    def flat_indexes(iterable):
        n = 0

        for el in iterable:
            if isiter(el):
                for ndeep in flat_indexes(el):
                    yield (n,) + ndeep
            else:
                yield (n,)

            n += 1

    if dummify is None:
        dummify = any(isinstance(a, Basic) and
            a.atoms(Function, Derivative) for a in (
            args if isiter(args) else [args]))

    if isiter(args) and any(isiter(i) for i in args):
        dum_args = [str(Dummy(str(i))) for i in range(len(args))]

        indexed_args = ','.join([
            dum_args[ind[0]] + ''.join(["[%s]" % k for k in ind[1:]])
                    for ind in flat_indexes(args)])

        lstr = lambdastr(flatten(args), expr, printer=printer, dummify=dummify)

#.........这里部分代码省略.........

def test_settings():
    raises(TypeError, lambda: lambdarepr(sin(x), method="garbage"))

def lambdastr(args, expr, printer=None, dummify=False):
    """
    Returns a string that can be evaluated to a lambda function.

    Examples
    ========

    >>> from sympy.abc import x, y, z
    >>> from sympy.utilities.lambdify import lambdastr
    >>> lambdastr(x, x**2)
    'lambda x: (x**2)'
    >>> lambdastr((x,y,z), [z,y,x])
    'lambda x,y,z: ([z, y, x])'

    Although tuples may not appear as arguments to lambda in Python 3,
    lambdastr will create a lambda function that will unpack the original
    arguments so that nested arguments can be handled:

    >>> lambdastr((x, (y, z)), x + y)
    'lambda _0,_1: (lambda x,y,z: (x + y))(*list(__flatten_args__([_0,_1])))'
    """
    # Transforming everything to strings.
    from sympy.matrices import DeferredVector
    from sympy import Dummy, sympify, Symbol, Function, flatten

    if printer is not None:
        if inspect.isfunction(printer):
            lambdarepr = printer
        else:
            if inspect.isclass(printer):
                lambdarepr = lambda expr: printer().doprint(expr)
            else:
                lambdarepr = lambda expr: printer.doprint(expr)
    else:
        #XXX: This has to be done here because of circular imports
        from sympy.printing.lambdarepr import lambdarepr

    def sub_args(args, dummies_dict):
        if isinstance(args, str):
            return args
        elif isinstance(args, DeferredVector):
            return str(args)
        elif iterable(args):
            dummies = flatten([sub_args(a, dummies_dict) for a in args])
            return ",".join(str(a) for a in dummies)
        else:
            #Sub in dummy variables for functions or symbols
            if isinstance(args, (Function, Symbol)):
                dummies = Dummy()
                dummies_dict.update({args : dummies})
                return str(dummies)
            else:
                return str(args)

    def sub_expr(expr, dummies_dict):
        try:
            expr = sympify(expr).xreplace(dummies_dict)
        except Exception:
            if isinstance(expr, DeferredVector):
                pass
            elif isinstance(expr, dict):
                k = [sub_expr(sympify(a), dummies_dict) for a in expr.keys()]
                v = [sub_expr(sympify(a), dummies_dict) for a in expr.values()]
                expr = dict(zip(k, v))
            elif isinstance(expr, tuple):
                expr = tuple(sub_expr(sympify(a), dummies_dict) for a in expr)
            elif isinstance(expr, list):
                expr = [sub_expr(sympify(a), dummies_dict) for a in expr]
        return expr

    # Transform args
    def isiter(l):
        return iterable(l, exclude=(str, DeferredVector))

    if isiter(args) and any(isiter(i) for i in args):
        from sympy.utilities.iterables import flatten
        import re
        dum_args = [str(Dummy(str(i))) for i in range(len(args))]
        iter_args = ','.join([i if isiter(a) else i
            for i, a in zip(dum_args, args)])
        lstr = lambdastr(flatten(args), expr, printer=printer, dummify=dummify)
        flat = '__flatten_args__'
        rv = 'lambda %s: (%s)(*list(%s([%s])))' % (
            ','.join(dum_args), lstr, flat, iter_args)
        if len(re.findall(r'\b%s\b' % flat, rv)) > 1:
            raise ValueError('the name %s is reserved by lambdastr' % flat)
        return rv

    dummies_dict = {}
    if dummify:
        args = sub_args(args, dummies_dict)
    else:
        if isinstance(args, str):
            pass
        elif iterable(args, exclude=DeferredVector):
            args = ",".join(str(a) for a in args)

    # Transform expr
    if dummify:
        if isinstance(expr, str):
#.........这里部分代码省略.........

def test_matrix():
    A = Matrix([[x,y],[y*x,z**2]])
    assert lambdarepr(A)=="Matrix([[  x,    y],[x*y, z**2]])"