Vehicle-cpp/hkpc/software/sympy/printing/pycode.py

"""
Python code printers

This module contains Python code printers for plain Python as well as NumPy & SciPy enabled code.
"""
from collections import defaultdict
from itertools import chain
from sympy.core import S
from sympy.core.mod import Mod
from .precedence import precedence
from .codeprinter import CodePrinter

_kw = {
    'and', 'as', 'assert', 'break', 'class', 'continue', 'def', 'del', 'elif',
    'else', 'except', 'finally', 'for', 'from', 'global', 'if', 'import', 'in',
    'is', 'lambda', 'not', 'or', 'pass', 'raise', 'return', 'try', 'while',
    'with', 'yield', 'None', 'False', 'nonlocal', 'True'
}

_known_functions = {
    'Abs': 'abs',
    'Min': 'min',
    'Max': 'max',
}
_known_functions_math = {
    'acos': 'acos',
    'acosh': 'acosh',
    'asin': 'asin',
    'asinh': 'asinh',
    'atan': 'atan',
    'atan2': 'atan2',
    'atanh': 'atanh',
    'ceiling': 'ceil',
    'cos': 'cos',
    'cosh': 'cosh',
    'erf': 'erf',
    'erfc': 'erfc',
    'exp': 'exp',
    'expm1': 'expm1',
    'factorial': 'factorial',
    'floor': 'floor',
    'gamma': 'gamma',
    'hypot': 'hypot',
    'loggamma': 'lgamma',
    'log': 'log',
    'ln': 'log',
    'log10': 'log10',
    'log1p': 'log1p',
    'log2': 'log2',
    'sin': 'sin',
    'sinh': 'sinh',
    'Sqrt': 'sqrt',
    'tan': 'tan',
    'tanh': 'tanh'
}  # Not used from ``math``: [copysign isclose isfinite isinf isnan ldexp frexp pow modf
# radians trunc fmod fsum gcd degrees fabs]
_known_constants_math = {
    'Exp1': 'e',
    'Pi': 'pi',
    'E': 'e',
    'Infinity': 'inf',
    'NaN': 'nan',
    'ComplexInfinity': 'nan'
}

def _print_known_func(self, expr):
    known = self.known_functions[expr.__class__.__name__]
    return '{name}({args})'.format(name=self._module_format(known),
                                   args=', '.join((self._print(arg) for arg in expr.args)))


def _print_known_const(self, expr):
    known = self.known_constants[expr.__class__.__name__]
    return self._module_format(known)


class AbstractPythonCodePrinter(CodePrinter):
    printmethod = "_pythoncode"
    language = "Python"
    reserved_words = _kw
    modules = None  # initialized to a set in __init__
    tab = '    '
    _kf = dict(chain(
        _known_functions.items(),
        [(k, 'math.' + v) for k, v in _known_functions_math.items()]
    ))
    _kc = {k: 'math.'+v for k, v in _known_constants_math.items()}
    _operators = {'and': 'and', 'or': 'or', 'not': 'not'}
    _default_settings = dict(
        CodePrinter._default_settings,
        user_functions={},
        precision=17,
        inline=True,
        fully_qualified_modules=True,
        contract=False,
        standard='python3',
    )

    def __init__(self, settings=None):
        super().__init__(settings)

        # Python standard handler
        std = self._settings['standard']
        if std is None:
            import sys
            std = 'python{}'.format(sys.version_info.major)
        if std != 'python3':
            raise ValueError('Only Python 3 is supported.')
        self.standard = std

        self.module_imports = defaultdict(set)

        # Known functions and constants handler
        self.known_functions = dict(self._kf, **(settings or {}).get(
            'user_functions', {}))
        self.known_constants = dict(self._kc, **(settings or {}).get(
            'user_constants', {}))

    def _declare_number_const(self, name, value):
        return "%s = %s" % (name, value)

    def _module_format(self, fqn, register=True):
        parts = fqn.split('.')
        if register and len(parts) > 1:
            self.module_imports['.'.join(parts[:-1])].add(parts[-1])

        if self._settings['fully_qualified_modules']:
            return fqn
        else:
            return fqn.split('(')[0].split('[')[0].split('.')[-1]

    def _format_code(self, lines):
        return lines

    def _get_statement(self, codestring):
        return "{}".format(codestring)

    def _get_comment(self, text):
        return "  # {}".format(text)

    def _expand_fold_binary_op(self, op, args):
        """
        This method expands a fold on binary operations.

        ``functools.reduce`` is an example of a folded operation.

        For example, the expression

        `A + B + C + D`

        is folded into

        `((A + B) + C) + D`
        """
        if len(args) == 1:
            return self._print(args[0])
        else:
            return "%s(%s, %s)" % (
                self._module_format(op),
                self._expand_fold_binary_op(op, args[:-1]),
                self._print(args[-1]),
            )

    def _expand_reduce_binary_op(self, op, args):
        """
        This method expands a reductin on binary operations.

        Notice: this is NOT the same as ``functools.reduce``.

        For example, the expression

        `A + B + C + D`

        is reduced into:

        `(A + B) + (C + D)`
        """
        if len(args) == 1:
            return self._print(args[0])
        else:
            N = len(args)
            Nhalf = N // 2
            return "%s(%s, %s)" % (
                self._module_format(op),
                self._expand_reduce_binary_op(args[:Nhalf]),
                self._expand_reduce_binary_op(args[Nhalf:]),
            )

    def _print_NaN(self, expr):
        return "float('nan')"

    def _print_Infinity(self, expr):
        return "float('inf')"

    def _print_NegativeInfinity(self, expr):
        return "float('-inf')"

    def _print_ComplexInfinity(self, expr):
        return self._print_NaN(expr)

    def _print_Mod(self, expr):
        PREC = precedence(expr)
        return ('{} % {}'.format(*(self.parenthesize(x, PREC) for x in expr.args)))

    def _print_Piecewise(self, expr):
        result = []
        i = 0
        for arg in expr.args:
            e = arg.expr
            c = arg.cond
            if i == 0:
                result.append('(')
            result.append('(')
            result.append(self._print(e))
            result.append(')')
            result.append(' if ')
            result.append(self._print(c))
            result.append(' else ')
            i += 1
        result = result[:-1]
        if result[-1] == 'True':
            result = result[:-2]
            result.append(')')
        else:
            result.append(' else None)')
        return ''.join(result)

    def _print_Relational(self, expr):
        "Relational printer for Equality and Unequality"
        op = {
            '==' :'equal',
            '!=' :'not_equal',
            '<'  :'less',
            '<=' :'less_equal',
            '>'  :'greater',
            '>=' :'greater_equal',
        }
        if expr.rel_op in op:
            lhs = self._print(expr.lhs)
            rhs = self._print(expr.rhs)
            return '({lhs} {op} {rhs})'.format(op=expr.rel_op, lhs=lhs, rhs=rhs)
        return super()._print_Relational(expr)

    def _print_ITE(self, expr):
        from sympy.functions.elementary.piecewise import Piecewise
        return self._print(expr.rewrite(Piecewise))

    def _print_Sum(self, expr):
        loops = (
            'for {i} in range({a}, {b}+1)'.format(
                i=self._print(i),
                a=self._print(a),
                b=self._print(b))
            for i, a, b in expr.limits)
        return '(builtins.sum({function} {loops}))'.format(
            function=self._print(expr.function),
            loops=' '.join(loops))

    def _print_ImaginaryUnit(self, expr):
        return '1j'

    def _print_KroneckerDelta(self, expr):
        a, b = expr.args

        return '(1 if {a} == {b} else 0)'.format(
            a = self._print(a),
            b = self._print(b)
        )

    def _print_MatrixBase(self, expr):
        name = expr.__class__.__name__
        func = self.known_functions.get(name, name)
        return "%s(%s)" % (func, self._print(expr.tolist()))

    _print_SparseRepMatrix = \
        _print_MutableSparseMatrix = \
        _print_ImmutableSparseMatrix = \
        _print_Matrix = \
        _print_DenseMatrix = \
        _print_MutableDenseMatrix = \
        _print_ImmutableMatrix = \
        _print_ImmutableDenseMatrix = \
        lambda self, expr: self._print_MatrixBase(expr)

    def _indent_codestring(self, codestring):
        return '\n'.join([self.tab + line for line in codestring.split('\n')])

    def _print_FunctionDefinition(self, fd):
        body = '\n'.join((self._print(arg) for arg in fd.body))
        return "def {name}({parameters}):\n{body}".format(
            name=self._print(fd.name),
            parameters=', '.join([self._print(var.symbol) for var in fd.parameters]),
            body=self._indent_codestring(body)
        )

    def _print_While(self, whl):
        body = '\n'.join((self._print(arg) for arg in whl.body))
        return "while {cond}:\n{body}".format(
            cond=self._print(whl.condition),
            body=self._indent_codestring(body)
        )

    def _print_Declaration(self, decl):
        return '%s = %s' % (
            self._print(decl.variable.symbol),
            self._print(decl.variable.value)
        )

    def _print_Return(self, ret):
        arg, = ret.args
        return 'return %s' % self._print(arg)

    def _print_Print(self, prnt):
        print_args = ', '.join((self._print(arg) for arg in prnt.print_args))
        if prnt.format_string != None: # Must be '!= None', cannot be 'is not None'
            print_args = '{} % ({})'.format(
                self._print(prnt.format_string), print_args)
        if prnt.file != None: # Must be '!= None', cannot be 'is not None'
            print_args += ', file=%s' % self._print(prnt.file)

        return 'print(%s)' % print_args

    def _print_Stream(self, strm):
        if str(strm.name) == 'stdout':
            return self._module_format('sys.stdout')
        elif str(strm.name) == 'stderr':
            return self._module_format('sys.stderr')
        else:
            return self._print(strm.name)

    def _print_NoneToken(self, arg):
        return 'None'

    def _hprint_Pow(self, expr, rational=False, sqrt='math.sqrt'):
        """Printing helper function for ``Pow``

        Notes
        =====

        This preprocesses the ``sqrt`` as math formatter and prints division

        Examples
        ========

        >>> from sympy import sqrt
        >>> from sympy.printing.pycode import PythonCodePrinter
        >>> from sympy.abc import x

        Python code printer automatically looks up ``math.sqrt``.

        >>> printer = PythonCodePrinter()
        >>> printer._hprint_Pow(sqrt(x), rational=True)
        'x**(1/2)'
        >>> printer._hprint_Pow(sqrt(x), rational=False)
        'math.sqrt(x)'
        >>> printer._hprint_Pow(1/sqrt(x), rational=True)
        'x**(-1/2)'
        >>> printer._hprint_Pow(1/sqrt(x), rational=False)
        '1/math.sqrt(x)'
        >>> printer._hprint_Pow(1/x, rational=False)
        '1/x'
        >>> printer._hprint_Pow(1/x, rational=True)
        'x**(-1)'

        Using sqrt from numpy or mpmath

        >>> printer._hprint_Pow(sqrt(x), sqrt='numpy.sqrt')
        'numpy.sqrt(x)'
        >>> printer._hprint_Pow(sqrt(x), sqrt='mpmath.sqrt')
        'mpmath.sqrt(x)'

        See Also
        ========

        sympy.printing.str.StrPrinter._print_Pow
        """
        PREC = precedence(expr)

        if expr.exp == S.Half and not rational:
            func = self._module_format(sqrt)
            arg = self._print(expr.base)
            return '{func}({arg})'.format(func=func, arg=arg)

        if expr.is_commutative and not rational:
            if -expr.exp is S.Half:
                func = self._module_format(sqrt)
                num = self._print(S.One)
                arg = self._print(expr.base)
                return f"{num}/{func}({arg})"
            if expr.exp is S.NegativeOne:
                num = self._print(S.One)
                arg = self.parenthesize(expr.base, PREC, strict=False)
                return f"{num}/{arg}"


        base_str = self.parenthesize(expr.base, PREC, strict=False)
        exp_str = self.parenthesize(expr.exp, PREC, strict=False)
        return "{}**{}".format(base_str, exp_str)


class ArrayPrinter:

    def _arrayify(self, indexed):
        from sympy.tensor.array.expressions.from_indexed_to_array import convert_indexed_to_array
        try:
            return convert_indexed_to_array(indexed)
        except Exception:
            return indexed

    def _get_einsum_string(self, subranks, contraction_indices):
        letters = self._get_letter_generator_for_einsum()
        contraction_string = ""
        counter = 0
        d = {j: min(i) for i in contraction_indices for j in i}
        indices = []
        for rank_arg in subranks:
            lindices = []
            for i in range(rank_arg):
                if counter in d:
                    lindices.append(d[counter])
                else:
                    lindices.append(counter)
                counter += 1
            indices.append(lindices)
        mapping = {}
        letters_free = []
        letters_dum = []
        for i in indices:
            for j in i:
                if j not in mapping:
                    l = next(letters)
                    mapping[j] = l
                else:
                    l = mapping[j]
                contraction_string += l
                if j in d:
                    if l not in letters_dum:
                        letters_dum.append(l)
                else:
                    letters_free.append(l)
            contraction_string += ","
        contraction_string = contraction_string[:-1]
        return contraction_string, letters_free, letters_dum

    def _get_letter_generator_for_einsum(self):
        for i in range(97, 123):
            yield chr(i)
        for i in range(65, 91):
            yield chr(i)
        raise ValueError("out of letters")

    def _print_ArrayTensorProduct(self, expr):
        letters = self._get_letter_generator_for_einsum()
        contraction_string = ",".join(["".join([next(letters) for j in range(i)]) for i in expr.subranks])
        return '%s("%s", %s)' % (
                self._module_format(self._module + "." + self._einsum),
                contraction_string,
                ", ".join([self._print(arg) for arg in expr.args])
        )

    def _print_ArrayContraction(self, expr):
        from sympy.tensor.array.expressions.array_expressions import ArrayTensorProduct
        base = expr.expr
        contraction_indices = expr.contraction_indices

        if isinstance(base, ArrayTensorProduct):
            elems = ",".join(["%s" % (self._print(arg)) for arg in base.args])
            ranks = base.subranks
        else:
            elems = self._print(base)
            ranks = [len(base.shape)]

        contraction_string, letters_free, letters_dum = self._get_einsum_string(ranks, contraction_indices)

        if not contraction_indices:
            return self._print(base)
        if isinstance(base, ArrayTensorProduct):
            elems = ",".join(["%s" % (self._print(arg)) for arg in base.args])
        else:
            elems = self._print(base)
        return "%s(\"%s\", %s)" % (
            self._module_format(self._module + "." + self._einsum),
            "{}->{}".format(contraction_string, "".join(sorted(letters_free))),
            elems,
        )

    def _print_ArrayDiagonal(self, expr):
        from sympy.tensor.array.expressions.array_expressions import ArrayTensorProduct
        diagonal_indices = list(expr.diagonal_indices)
        if isinstance(expr.expr, ArrayTensorProduct):
            subranks = expr.expr.subranks
            elems = expr.expr.args
        else:
            subranks = expr.subranks
            elems = [expr.expr]
        diagonal_string, letters_free, letters_dum = self._get_einsum_string(subranks, diagonal_indices)
        elems = [self._print(i) for i in elems]
        return '%s("%s", %s)' % (
            self._module_format(self._module + "." + self._einsum),
            "{}->{}".format(diagonal_string, "".join(letters_free+letters_dum)),
            ", ".join(elems)
        )

    def _print_PermuteDims(self, expr):
        return "%s(%s, %s)" % (
            self._module_format(self._module + "." + self._transpose),
            self._print(expr.expr),
            self._print(expr.permutation.array_form),
        )

    def _print_ArrayAdd(self, expr):
        return self._expand_fold_binary_op(self._module + "." + self._add, expr.args)

    def _print_OneArray(self, expr):
        return "%s((%s,))" % (
            self._module_format(self._module+ "." + self._ones),
            ','.join(map(self._print,expr.args))
        )

    def _print_ZeroArray(self, expr):
        return "%s((%s,))" % (
            self._module_format(self._module+ "." + self._zeros),
            ','.join(map(self._print,expr.args))
        )

    def _print_Assignment(self, expr):
        #XXX: maybe this needs to happen at a higher level e.g. at _print or
        #doprint?
        lhs = self._print(self._arrayify(expr.lhs))
        rhs = self._print(self._arrayify(expr.rhs))
        return "%s = %s" % ( lhs, rhs )

    def _print_IndexedBase(self, expr):
        return self._print_ArraySymbol(expr)


class PythonCodePrinter(AbstractPythonCodePrinter):

    def _print_sign(self, e):
        return '(0.0 if {e} == 0 else {f}(1, {e}))'.format(
            f=self._module_format('math.copysign'), e=self._print(e.args[0]))

    def _print_Not(self, expr):
        PREC = precedence(expr)
        return self._operators['not'] + self.parenthesize(expr.args[0], PREC)

    def _print_Indexed(self, expr):
        base = expr.args[0]
        index = expr.args[1:]
        return "{}[{}]".format(str(base), ", ".join([self._print(ind) for ind in index]))

    def _print_Pow(self, expr, rational=False):
        return self._hprint_Pow(expr, rational=rational)

    def _print_Rational(self, expr):
        return '{}/{}'.format(expr.p, expr.q)

    def _print_Half(self, expr):
        return self._print_Rational(expr)

    def _print_frac(self, expr):
        return self._print_Mod(Mod(expr.args[0], 1))

    def _print_Symbol(self, expr):

        name = super()._print_Symbol(expr)

        if name in self.reserved_words:
            if self._settings['error_on_reserved']:
                msg = ('This expression includes the symbol "{}" which is a '
                       'reserved keyword in this language.')
                raise ValueError(msg.format(name))
            return name + self._settings['reserved_word_suffix']
        elif '{' in name:   # Remove curly braces from subscripted variables
            return name.replace('{', '').replace('}', '')
        else:
            return name

    _print_lowergamma = CodePrinter._print_not_supported
    _print_uppergamma = CodePrinter._print_not_supported
    _print_fresnelc = CodePrinter._print_not_supported
    _print_fresnels = CodePrinter._print_not_supported


for k in PythonCodePrinter._kf:
    setattr(PythonCodePrinter, '_print_%s' % k, _print_known_func)

for k in _known_constants_math:
    setattr(PythonCodePrinter, '_print_%s' % k, _print_known_const)


def pycode(expr, **settings):
    """ Converts an expr to a string of Python code

    Parameters
    ==========

    expr : Expr
        A SymPy expression.
    fully_qualified_modules : bool
        Whether or not to write out full module names of functions
        (``math.sin`` vs. ``sin``). default: ``True``.
    standard : str or None, optional
        Only 'python3' (default) is supported.
        This parameter may be removed in the future.

    Examples
    ========

    >>> from sympy import pycode, tan, Symbol
    >>> pycode(tan(Symbol('x')) + 1)
    'math.tan(x) + 1'

    """
    return PythonCodePrinter(settings).doprint(expr)


_not_in_mpmath = 'log1p log2'.split()
_in_mpmath = [(k, v) for k, v in _known_functions_math.items() if k not in _not_in_mpmath]
_known_functions_mpmath = dict(_in_mpmath, **{
    'beta': 'beta',
    'frac': 'frac',
    'fresnelc': 'fresnelc',
    'fresnels': 'fresnels',
    'sign': 'sign',
    'loggamma': 'loggamma',
    'hyper': 'hyper',
    'meijerg': 'meijerg',
    'besselj': 'besselj',
    'bessely': 'bessely',
    'besseli': 'besseli',
    'besselk': 'besselk',
})
_known_constants_mpmath = {
    'Exp1': 'e',
    'Pi': 'pi',
    'GoldenRatio': 'phi',
    'EulerGamma': 'euler',
    'Catalan': 'catalan',
    'NaN': 'nan',
    'Infinity': 'inf',
    'NegativeInfinity': 'ninf'
}


def _unpack_integral_limits(integral_expr):
    """ helper function for _print_Integral that
        - accepts an Integral expression
        - returns a tuple of
           - a list variables of integration
           - a list of tuples of the upper and lower limits of integration
    """
    integration_vars = []
    limits = []
    for integration_range in integral_expr.limits:
        if len(integration_range) == 3:
            integration_var, lower_limit, upper_limit = integration_range
        else:
            raise NotImplementedError("Only definite integrals are supported")
        integration_vars.append(integration_var)
        limits.append((lower_limit, upper_limit))
    return integration_vars, limits


class MpmathPrinter(PythonCodePrinter):
    """
    Lambda printer for mpmath which maintains precision for floats
    """
    printmethod = "_mpmathcode"

    language = "Python with mpmath"

    _kf = dict(chain(
        _known_functions.items(),
        [(k, 'mpmath.' + v) for k, v in _known_functions_mpmath.items()]
    ))
    _kc = {k: 'mpmath.'+v for k, v in _known_constants_mpmath.items()}

    def _print_Float(self, e):
        # XXX: This does not handle setting mpmath.mp.dps. It is assumed that
        # the caller of the lambdified function will have set it to sufficient
        # precision to match the Floats in the expression.

        # Remove 'mpz' if gmpy is installed.
        args = str(tuple(map(int, e._mpf_)))
        return '{func}({args})'.format(func=self._module_format('mpmath.mpf'), args=args)


    def _print_Rational(self, e):
        return "{func}({p})/{func}({q})".format(
            func=self._module_format('mpmath.mpf'),
            q=self._print(e.q),
            p=self._print(e.p)
        )

    def _print_Half(self, e):
        return self._print_Rational(e)

    def _print_uppergamma(self, e):
        return "{}({}, {}, {})".format(
            self._module_format('mpmath.gammainc'),
            self._print(e.args[0]),
            self._print(e.args[1]),
            self._module_format('mpmath.inf'))

    def _print_lowergamma(self, e):
        return "{}({}, 0, {})".format(
            self._module_format('mpmath.gammainc'),
            self._print(e.args[0]),
            self._print(e.args[1]))

    def _print_log2(self, e):
        return '{0}({1})/{0}(2)'.format(
            self._module_format('mpmath.log'), self._print(e.args[0]))

    def _print_log1p(self, e):
        return '{}({})'.format(
            self._module_format('mpmath.log1p'), self._print(e.args[0]))

    def _print_Pow(self, expr, rational=False):
        return self._hprint_Pow(expr, rational=rational, sqrt='mpmath.sqrt')

    def _print_Integral(self, e):
        integration_vars, limits = _unpack_integral_limits(e)

        return "{}(lambda {}: {}, {})".format(
                self._module_format("mpmath.quad"),
                ", ".join(map(self._print, integration_vars)),
                self._print(e.args[0]),
                ", ".join("(%s, %s)" % tuple(map(self._print, l)) for l in limits))


for k in MpmathPrinter._kf:
    setattr(MpmathPrinter, '_print_%s' % k, _print_known_func)

for k in _known_constants_mpmath:
    setattr(MpmathPrinter, '_print_%s' % k, _print_known_const)


class SymPyPrinter(AbstractPythonCodePrinter):

    language = "Python with SymPy"

    def _print_Function(self, expr):
        mod = expr.func.__module__ or ''
        return '%s(%s)' % (self._module_format(mod + ('.' if mod else '') + expr.func.__name__),
                           ', '.join((self._print(arg) for arg in expr.args)))

    def _print_Pow(self, expr, rational=False):
        return self._hprint_Pow(expr, rational=rational, sqrt='sympy.sqrt')