659 lines
23 KiB
Python
659 lines
23 KiB
Python
"""
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Julia code printer
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The `JuliaCodePrinter` converts SymPy expressions into Julia expressions.
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A complete code generator, which uses `julia_code` extensively, can be found
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in `sympy.utilities.codegen`. The `codegen` module can be used to generate
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complete source code files.
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"""
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from __future__ import annotations
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from typing import Any
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from sympy.core import Mul, Pow, S, Rational
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from sympy.core.mul import _keep_coeff
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from sympy.core.numbers import equal_valued
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from sympy.printing.codeprinter import CodePrinter
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from sympy.printing.precedence import precedence, PRECEDENCE
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from re import search
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# List of known functions. First, those that have the same name in
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# SymPy and Julia. This is almost certainly incomplete!
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known_fcns_src1 = ["sin", "cos", "tan", "cot", "sec", "csc",
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"asin", "acos", "atan", "acot", "asec", "acsc",
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"sinh", "cosh", "tanh", "coth", "sech", "csch",
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"asinh", "acosh", "atanh", "acoth", "asech", "acsch",
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"sinc", "atan2", "sign", "floor", "log", "exp",
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"cbrt", "sqrt", "erf", "erfc", "erfi",
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"factorial", "gamma", "digamma", "trigamma",
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"polygamma", "beta",
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"airyai", "airyaiprime", "airybi", "airybiprime",
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"besselj", "bessely", "besseli", "besselk",
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"erfinv", "erfcinv"]
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# These functions have different names ("SymPy": "Julia"), more
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# generally a mapping to (argument_conditions, julia_function).
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known_fcns_src2 = {
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"Abs": "abs",
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"ceiling": "ceil",
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"conjugate": "conj",
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"hankel1": "hankelh1",
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"hankel2": "hankelh2",
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"im": "imag",
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"re": "real"
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}
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class JuliaCodePrinter(CodePrinter):
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"""
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A printer to convert expressions to strings of Julia code.
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"""
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printmethod = "_julia"
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language = "Julia"
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_operators = {
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'and': '&&',
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'or': '||',
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'not': '!',
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}
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_default_settings: dict[str, Any] = {
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'order': None,
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'full_prec': 'auto',
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'precision': 17,
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'user_functions': {},
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'human': True,
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'allow_unknown_functions': False,
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'contract': True,
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'inline': True,
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}
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# Note: contract is for expressing tensors as loops (if True), or just
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# assignment (if False). FIXME: this should be looked a more carefully
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# for Julia.
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def __init__(self, settings={}):
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super().__init__(settings)
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self.known_functions = dict(zip(known_fcns_src1, known_fcns_src1))
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self.known_functions.update(dict(known_fcns_src2))
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userfuncs = settings.get('user_functions', {})
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self.known_functions.update(userfuncs)
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def _rate_index_position(self, p):
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return p*5
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def _get_statement(self, codestring):
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return "%s" % codestring
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def _get_comment(self, text):
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return "# {}".format(text)
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def _declare_number_const(self, name, value):
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return "const {} = {}".format(name, value)
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def _format_code(self, lines):
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return self.indent_code(lines)
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def _traverse_matrix_indices(self, mat):
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# Julia uses Fortran order (column-major)
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rows, cols = mat.shape
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return ((i, j) for j in range(cols) for i in range(rows))
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def _get_loop_opening_ending(self, indices):
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open_lines = []
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close_lines = []
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for i in indices:
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# Julia arrays start at 1 and end at dimension
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var, start, stop = map(self._print,
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[i.label, i.lower + 1, i.upper + 1])
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open_lines.append("for %s = %s:%s" % (var, start, stop))
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close_lines.append("end")
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return open_lines, close_lines
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def _print_Mul(self, expr):
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# print complex numbers nicely in Julia
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if (expr.is_number and expr.is_imaginary and
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expr.as_coeff_Mul()[0].is_integer):
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return "%sim" % self._print(-S.ImaginaryUnit*expr)
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# cribbed from str.py
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prec = precedence(expr)
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c, e = expr.as_coeff_Mul()
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if c < 0:
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expr = _keep_coeff(-c, e)
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sign = "-"
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else:
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sign = ""
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a = [] # items in the numerator
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b = [] # items that are in the denominator (if any)
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pow_paren = [] # Will collect all pow with more than one base element and exp = -1
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if self.order not in ('old', 'none'):
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args = expr.as_ordered_factors()
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else:
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# use make_args in case expr was something like -x -> x
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args = Mul.make_args(expr)
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# Gather args for numerator/denominator
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for item in args:
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if (item.is_commutative and item.is_Pow and item.exp.is_Rational
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and item.exp.is_negative):
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if item.exp != -1:
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b.append(Pow(item.base, -item.exp, evaluate=False))
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else:
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if len(item.args[0].args) != 1 and isinstance(item.base, Mul): # To avoid situations like #14160
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pow_paren.append(item)
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b.append(Pow(item.base, -item.exp))
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elif item.is_Rational and item is not S.Infinity and item.p == 1:
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# Save the Rational type in julia Unless the numerator is 1.
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# For example:
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# julia_code(Rational(3, 7)*x) --> (3 // 7) * x
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# julia_code(x/3) --> x / 3 but not x * (1 // 3)
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b.append(Rational(item.q))
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else:
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a.append(item)
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a = a or [S.One]
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a_str = [self.parenthesize(x, prec) for x in a]
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b_str = [self.parenthesize(x, prec) for x in b]
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# To parenthesize Pow with exp = -1 and having more than one Symbol
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for item in pow_paren:
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if item.base in b:
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b_str[b.index(item.base)] = "(%s)" % b_str[b.index(item.base)]
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# from here it differs from str.py to deal with "*" and ".*"
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def multjoin(a, a_str):
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# here we probably are assuming the constants will come first
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r = a_str[0]
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for i in range(1, len(a)):
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mulsym = '*' if a[i-1].is_number else '.*'
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r = "%s %s %s" % (r, mulsym, a_str[i])
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return r
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if not b:
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return sign + multjoin(a, a_str)
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elif len(b) == 1:
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divsym = '/' if b[0].is_number else './'
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return "%s %s %s" % (sign+multjoin(a, a_str), divsym, b_str[0])
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else:
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divsym = '/' if all(bi.is_number for bi in b) else './'
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return "%s %s (%s)" % (sign + multjoin(a, a_str), divsym, multjoin(b, b_str))
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def _print_Relational(self, expr):
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lhs_code = self._print(expr.lhs)
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rhs_code = self._print(expr.rhs)
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op = expr.rel_op
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return "{} {} {}".format(lhs_code, op, rhs_code)
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def _print_Pow(self, expr):
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powsymbol = '^' if all(x.is_number for x in expr.args) else '.^'
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PREC = precedence(expr)
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if equal_valued(expr.exp, 0.5):
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return "sqrt(%s)" % self._print(expr.base)
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if expr.is_commutative:
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if equal_valued(expr.exp, -0.5):
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sym = '/' if expr.base.is_number else './'
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return "1 %s sqrt(%s)" % (sym, self._print(expr.base))
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if equal_valued(expr.exp, -1):
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sym = '/' if expr.base.is_number else './'
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return "1 %s %s" % (sym, self.parenthesize(expr.base, PREC))
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return '%s %s %s' % (self.parenthesize(expr.base, PREC), powsymbol,
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self.parenthesize(expr.exp, PREC))
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def _print_MatPow(self, expr):
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PREC = precedence(expr)
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return '%s ^ %s' % (self.parenthesize(expr.base, PREC),
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self.parenthesize(expr.exp, PREC))
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def _print_Pi(self, expr):
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if self._settings["inline"]:
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return "pi"
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else:
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return super()._print_NumberSymbol(expr)
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def _print_ImaginaryUnit(self, expr):
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return "im"
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def _print_Exp1(self, expr):
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if self._settings["inline"]:
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return "e"
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else:
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return super()._print_NumberSymbol(expr)
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def _print_EulerGamma(self, expr):
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if self._settings["inline"]:
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return "eulergamma"
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else:
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return super()._print_NumberSymbol(expr)
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def _print_Catalan(self, expr):
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if self._settings["inline"]:
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return "catalan"
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else:
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return super()._print_NumberSymbol(expr)
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def _print_GoldenRatio(self, expr):
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if self._settings["inline"]:
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return "golden"
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else:
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return super()._print_NumberSymbol(expr)
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def _print_Assignment(self, expr):
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from sympy.codegen.ast import Assignment
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from sympy.functions.elementary.piecewise import Piecewise
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from sympy.tensor.indexed import IndexedBase
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# Copied from codeprinter, but remove special MatrixSymbol treatment
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lhs = expr.lhs
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rhs = expr.rhs
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# We special case assignments that take multiple lines
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if not self._settings["inline"] and isinstance(expr.rhs, Piecewise):
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# Here we modify Piecewise so each expression is now
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# an Assignment, and then continue on the print.
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expressions = []
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conditions = []
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for (e, c) in rhs.args:
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expressions.append(Assignment(lhs, e))
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conditions.append(c)
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temp = Piecewise(*zip(expressions, conditions))
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return self._print(temp)
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if self._settings["contract"] and (lhs.has(IndexedBase) or
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rhs.has(IndexedBase)):
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# Here we check if there is looping to be done, and if so
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# print the required loops.
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return self._doprint_loops(rhs, lhs)
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else:
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lhs_code = self._print(lhs)
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rhs_code = self._print(rhs)
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return self._get_statement("%s = %s" % (lhs_code, rhs_code))
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def _print_Infinity(self, expr):
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return 'Inf'
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def _print_NegativeInfinity(self, expr):
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return '-Inf'
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def _print_NaN(self, expr):
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return 'NaN'
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def _print_list(self, expr):
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return 'Any[' + ', '.join(self._print(a) for a in expr) + ']'
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def _print_tuple(self, expr):
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if len(expr) == 1:
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return "(%s,)" % self._print(expr[0])
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else:
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return "(%s)" % self.stringify(expr, ", ")
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_print_Tuple = _print_tuple
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def _print_BooleanTrue(self, expr):
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return "true"
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def _print_BooleanFalse(self, expr):
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return "false"
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def _print_bool(self, expr):
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return str(expr).lower()
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# Could generate quadrature code for definite Integrals?
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#_print_Integral = _print_not_supported
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def _print_MatrixBase(self, A):
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# Handle zero dimensions:
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if S.Zero in A.shape:
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return 'zeros(%s, %s)' % (A.rows, A.cols)
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elif (A.rows, A.cols) == (1, 1):
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return "[%s]" % A[0, 0]
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elif A.rows == 1:
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return "[%s]" % A.table(self, rowstart='', rowend='', colsep=' ')
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elif A.cols == 1:
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# note .table would unnecessarily equispace the rows
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return "[%s]" % ", ".join([self._print(a) for a in A])
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return "[%s]" % A.table(self, rowstart='', rowend='',
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rowsep=';\n', colsep=' ')
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def _print_SparseRepMatrix(self, A):
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from sympy.matrices import Matrix
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L = A.col_list();
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# make row vectors of the indices and entries
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I = Matrix([k[0] + 1 for k in L])
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J = Matrix([k[1] + 1 for k in L])
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AIJ = Matrix([k[2] for k in L])
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return "sparse(%s, %s, %s, %s, %s)" % (self._print(I), self._print(J),
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self._print(AIJ), A.rows, A.cols)
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def _print_MatrixElement(self, expr):
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return self.parenthesize(expr.parent, PRECEDENCE["Atom"], strict=True) \
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+ '[%s,%s]' % (expr.i + 1, expr.j + 1)
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def _print_MatrixSlice(self, expr):
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def strslice(x, lim):
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l = x[0] + 1
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h = x[1]
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step = x[2]
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lstr = self._print(l)
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hstr = 'end' if h == lim else self._print(h)
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if step == 1:
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if l == 1 and h == lim:
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return ':'
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if l == h:
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return lstr
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else:
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return lstr + ':' + hstr
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else:
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return ':'.join((lstr, self._print(step), hstr))
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return (self._print(expr.parent) + '[' +
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strslice(expr.rowslice, expr.parent.shape[0]) + ',' +
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strslice(expr.colslice, expr.parent.shape[1]) + ']')
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def _print_Indexed(self, expr):
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inds = [ self._print(i) for i in expr.indices ]
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return "%s[%s]" % (self._print(expr.base.label), ",".join(inds))
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def _print_Idx(self, expr):
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return self._print(expr.label)
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def _print_Identity(self, expr):
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return "eye(%s)" % self._print(expr.shape[0])
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def _print_HadamardProduct(self, expr):
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return ' .* '.join([self.parenthesize(arg, precedence(expr))
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for arg in expr.args])
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def _print_HadamardPower(self, expr):
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PREC = precedence(expr)
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return '.**'.join([
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self.parenthesize(expr.base, PREC),
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self.parenthesize(expr.exp, PREC)
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])
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def _print_Rational(self, expr):
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if expr.q == 1:
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return str(expr.p)
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return "%s // %s" % (expr.p, expr.q)
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# Note: as of 2022, Julia doesn't have spherical Bessel functions
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def _print_jn(self, expr):
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from sympy.functions import sqrt, besselj
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x = expr.argument
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expr2 = sqrt(S.Pi/(2*x))*besselj(expr.order + S.Half, x)
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return self._print(expr2)
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def _print_yn(self, expr):
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from sympy.functions import sqrt, bessely
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x = expr.argument
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expr2 = sqrt(S.Pi/(2*x))*bessely(expr.order + S.Half, x)
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return self._print(expr2)
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def _print_Piecewise(self, expr):
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if expr.args[-1].cond != True:
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# We need the last conditional to be a True, otherwise the resulting
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# function may not return a result.
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raise ValueError("All Piecewise expressions must contain an "
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"(expr, True) statement to be used as a default "
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"condition. Without one, the generated "
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"expression may not evaluate to anything under "
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"some condition.")
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lines = []
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if self._settings["inline"]:
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# Express each (cond, expr) pair in a nested Horner form:
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# (condition) .* (expr) + (not cond) .* (<others>)
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# Expressions that result in multiple statements won't work here.
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ecpairs = ["({}) ? ({}) :".format
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(self._print(c), self._print(e))
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for e, c in expr.args[:-1]]
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elast = " (%s)" % self._print(expr.args[-1].expr)
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pw = "\n".join(ecpairs) + elast
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# Note: current need these outer brackets for 2*pw. Would be
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# nicer to teach parenthesize() to do this for us when needed!
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return "(" + pw + ")"
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else:
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for i, (e, c) in enumerate(expr.args):
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if i == 0:
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lines.append("if (%s)" % self._print(c))
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elif i == len(expr.args) - 1 and c == True:
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lines.append("else")
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else:
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lines.append("elseif (%s)" % self._print(c))
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code0 = self._print(e)
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lines.append(code0)
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if i == len(expr.args) - 1:
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lines.append("end")
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return "\n".join(lines)
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def _print_MatMul(self, expr):
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c, m = expr.as_coeff_mmul()
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sign = ""
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if c.is_number:
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re, im = c.as_real_imag()
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if im.is_zero and re.is_negative:
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expr = _keep_coeff(-c, m)
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sign = "-"
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elif re.is_zero and im.is_negative:
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expr = _keep_coeff(-c, m)
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sign = "-"
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return sign + ' * '.join(
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(self.parenthesize(arg, precedence(expr)) for arg in expr.args)
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)
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def indent_code(self, code):
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"""Accepts a string of code or a list of code lines"""
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# code mostly copied from ccode
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if isinstance(code, str):
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code_lines = self.indent_code(code.splitlines(True))
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return ''.join(code_lines)
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tab = " "
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inc_regex = ('^function ', '^if ', '^elseif ', '^else$', '^for ')
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dec_regex = ('^end$', '^elseif ', '^else$')
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# pre-strip left-space from the code
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code = [ line.lstrip(' \t') for line in code ]
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increase = [ int(any(search(re, line) for re in inc_regex))
|
|
for line in code ]
|
|
decrease = [ int(any(search(re, line) for re in dec_regex))
|
|
for line in code ]
|
|
|
|
pretty = []
|
|
level = 0
|
|
for n, line in enumerate(code):
|
|
if line in ('', '\n'):
|
|
pretty.append(line)
|
|
continue
|
|
level -= decrease[n]
|
|
pretty.append("%s%s" % (tab*level, line))
|
|
level += increase[n]
|
|
return pretty
|
|
|
|
|
|
def julia_code(expr, assign_to=None, **settings):
|
|
r"""Converts `expr` to a string of Julia code.
|
|
|
|
Parameters
|
|
==========
|
|
|
|
expr : Expr
|
|
A SymPy expression to be converted.
|
|
assign_to : optional
|
|
When given, the argument is used as the name of the variable to which
|
|
the expression is assigned. Can be a string, ``Symbol``,
|
|
``MatrixSymbol``, or ``Indexed`` type. This can be helpful for
|
|
expressions that generate multi-line statements.
|
|
precision : integer, optional
|
|
The precision for numbers such as pi [default=16].
|
|
user_functions : dict, optional
|
|
A dictionary where keys are ``FunctionClass`` instances and values are
|
|
their string representations. Alternatively, the dictionary value can
|
|
be a list of tuples i.e. [(argument_test, cfunction_string)]. See
|
|
below for examples.
|
|
human : bool, optional
|
|
If True, the result is a single string that may contain some constant
|
|
declarations for the number symbols. If False, the same information is
|
|
returned in a tuple of (symbols_to_declare, not_supported_functions,
|
|
code_text). [default=True].
|
|
contract: bool, optional
|
|
If True, ``Indexed`` instances are assumed to obey tensor contraction
|
|
rules and the corresponding nested loops over indices are generated.
|
|
Setting contract=False will not generate loops, instead the user is
|
|
responsible to provide values for the indices in the code.
|
|
[default=True].
|
|
inline: bool, optional
|
|
If True, we try to create single-statement code instead of multiple
|
|
statements. [default=True].
|
|
|
|
Examples
|
|
========
|
|
|
|
>>> from sympy import julia_code, symbols, sin, pi
|
|
>>> x = symbols('x')
|
|
>>> julia_code(sin(x).series(x).removeO())
|
|
'x .^ 5 / 120 - x .^ 3 / 6 + x'
|
|
|
|
>>> from sympy import Rational, ceiling
|
|
>>> x, y, tau = symbols("x, y, tau")
|
|
>>> julia_code((2*tau)**Rational(7, 2))
|
|
'8 * sqrt(2) * tau .^ (7 // 2)'
|
|
|
|
Note that element-wise (Hadamard) operations are used by default between
|
|
symbols. This is because its possible in Julia to write "vectorized"
|
|
code. It is harmless if the values are scalars.
|
|
|
|
>>> julia_code(sin(pi*x*y), assign_to="s")
|
|
's = sin(pi * x .* y)'
|
|
|
|
If you need a matrix product "*" or matrix power "^", you can specify the
|
|
symbol as a ``MatrixSymbol``.
|
|
|
|
>>> from sympy import Symbol, MatrixSymbol
|
|
>>> n = Symbol('n', integer=True, positive=True)
|
|
>>> A = MatrixSymbol('A', n, n)
|
|
>>> julia_code(3*pi*A**3)
|
|
'(3 * pi) * A ^ 3'
|
|
|
|
This class uses several rules to decide which symbol to use a product.
|
|
Pure numbers use "*", Symbols use ".*" and MatrixSymbols use "*".
|
|
A HadamardProduct can be used to specify componentwise multiplication ".*"
|
|
of two MatrixSymbols. There is currently there is no easy way to specify
|
|
scalar symbols, so sometimes the code might have some minor cosmetic
|
|
issues. For example, suppose x and y are scalars and A is a Matrix, then
|
|
while a human programmer might write "(x^2*y)*A^3", we generate:
|
|
|
|
>>> julia_code(x**2*y*A**3)
|
|
'(x .^ 2 .* y) * A ^ 3'
|
|
|
|
Matrices are supported using Julia inline notation. When using
|
|
``assign_to`` with matrices, the name can be specified either as a string
|
|
or as a ``MatrixSymbol``. The dimensions must align in the latter case.
|
|
|
|
>>> from sympy import Matrix, MatrixSymbol
|
|
>>> mat = Matrix([[x**2, sin(x), ceiling(x)]])
|
|
>>> julia_code(mat, assign_to='A')
|
|
'A = [x .^ 2 sin(x) ceil(x)]'
|
|
|
|
``Piecewise`` expressions are implemented with logical masking by default.
|
|
Alternatively, you can pass "inline=False" to use if-else conditionals.
|
|
Note that if the ``Piecewise`` lacks a default term, represented by
|
|
``(expr, True)`` then an error will be thrown. This is to prevent
|
|
generating an expression that may not evaluate to anything.
|
|
|
|
>>> from sympy import Piecewise
|
|
>>> pw = Piecewise((x + 1, x > 0), (x, True))
|
|
>>> julia_code(pw, assign_to=tau)
|
|
'tau = ((x > 0) ? (x + 1) : (x))'
|
|
|
|
Note that any expression that can be generated normally can also exist
|
|
inside a Matrix:
|
|
|
|
>>> mat = Matrix([[x**2, pw, sin(x)]])
|
|
>>> julia_code(mat, assign_to='A')
|
|
'A = [x .^ 2 ((x > 0) ? (x + 1) : (x)) sin(x)]'
|
|
|
|
Custom printing can be defined for certain types by passing a dictionary of
|
|
"type" : "function" to the ``user_functions`` kwarg. Alternatively, the
|
|
dictionary value can be a list of tuples i.e., [(argument_test,
|
|
cfunction_string)]. This can be used to call a custom Julia function.
|
|
|
|
>>> from sympy import Function
|
|
>>> f = Function('f')
|
|
>>> g = Function('g')
|
|
>>> custom_functions = {
|
|
... "f": "existing_julia_fcn",
|
|
... "g": [(lambda x: x.is_Matrix, "my_mat_fcn"),
|
|
... (lambda x: not x.is_Matrix, "my_fcn")]
|
|
... }
|
|
>>> mat = Matrix([[1, x]])
|
|
>>> julia_code(f(x) + g(x) + g(mat), user_functions=custom_functions)
|
|
'existing_julia_fcn(x) + my_fcn(x) + my_mat_fcn([1 x])'
|
|
|
|
Support for loops is provided through ``Indexed`` types. With
|
|
``contract=True`` these expressions will be turned into loops, whereas
|
|
``contract=False`` will just print the assignment expression that should be
|
|
looped over:
|
|
|
|
>>> from sympy import Eq, IndexedBase, Idx
|
|
>>> len_y = 5
|
|
>>> y = IndexedBase('y', shape=(len_y,))
|
|
>>> t = IndexedBase('t', shape=(len_y,))
|
|
>>> Dy = IndexedBase('Dy', shape=(len_y-1,))
|
|
>>> i = Idx('i', len_y-1)
|
|
>>> e = Eq(Dy[i], (y[i+1]-y[i])/(t[i+1]-t[i]))
|
|
>>> julia_code(e.rhs, assign_to=e.lhs, contract=False)
|
|
'Dy[i] = (y[i + 1] - y[i]) ./ (t[i + 1] - t[i])'
|
|
"""
|
|
return JuliaCodePrinter(settings).doprint(expr, assign_to)
|
|
|
|
|
|
def print_julia_code(expr, **settings):
|
|
"""Prints the Julia representation of the given expression.
|
|
|
|
See `julia_code` for the meaning of the optional arguments.
|
|
"""
|
|
print(julia_code(expr, **settings))
|