"""
Julia code printer
The `JuliaCodePrinter` converts SymPy expressions into Julia expressions.
A complete code generator, which uses `julia_code` extensively, can be found
in `sympy.utilities.codegen`. The `codegen` module can be used to generate
complete source code files.
"""
from __future__ import print_function, division
from ..core import Mul, Pow, S, Rational
from ..core.compatibility import string_types, range
from ..core.mul import _keep_coeff
from .codeprinter import CodePrinter, Assignment
from .precedence import precedence, PRECEDENCE
from re import search
# List of known functions. First, those that have the same name in
# SymPy and Julia. This is almost certainly incomplete!
known_fcns_src1 = ["sin", "cos", "tan", "cot", "sec", "csc",
"asin", "acos", "atan", "acot", "asec", "acsc",
"sinh", "cosh", "tanh", "coth", "sech", "csch",
"asinh", "acosh", "atanh", "acoth", "asech", "acsch"
"sinc", "atan2", "sign", "floor", "log", "exp",
"cbrt", "sqrt", "erf", "erfc", "erfi",
"factorial", "gamma", "digamma", "trigamma",
"polygamma", "beta",
"airyai", "airyaiprime", "airybi", "airybiprime",
"besselj", "bessely", "besseli", "besselk",
"erfinv", "erfcinv"]
# These functions have different names ("Sympy": "Julia"), more
# generally a mapping to (argument_conditions, julia_function).
known_fcns_src2 = {
"Abs": "abs",
"ceiling": "ceil",
"conjugate": "conj",
"hankel1": "hankelh1",
"hankel2": "hankelh2",
"im": "imag",
"re": "real"
}
[docs]class JuliaCodePrinter(CodePrinter):
"""
A printer to convert expressions to strings of Julia code.
"""
printmethod = "_julia"
language = "Julia"
_operators = {
'and': '&&',
'or': '||',
'not': '!',
}
_default_settings = {
'order': None,
'full_prec': 'auto',
'precision': 16,
'user_functions': {},
'human': True,
'contract': True,
'inline': True,
}
# Note: contract is for expressing tensors as loops (if True), or just
# assignment (if False). FIXME: this should be looked a more carefully
# for Julia.
def __init__(self, settings={}):
super(JuliaCodePrinter, self).__init__(settings)
self.known_functions = dict(zip(known_fcns_src1, known_fcns_src1))
self.known_functions.update(dict(known_fcns_src2))
userfuncs = settings.get('user_functions', {})
self.known_functions.update(userfuncs)
def _rate_index_position(self, p):
return p*5
def _get_statement(self, codestring):
return "%s" % codestring
def _get_comment(self, text):
return "# {0}".format(text)
def _declare_number_const(self, name, value):
return "const {0} = {1}".format(name, value)
def _format_code(self, lines):
return self.indent_code(lines)
def _traverse_matrix_indices(self, mat):
# Julia uses Fortran order (column-major)
rows, cols = mat.shape
return ((i, j) for j in range(cols) for i in range(rows))
def _get_loop_opening_ending(self, indices):
open_lines = []
close_lines = []
for i in indices:
# Julia arrays start at 1 and end at dimension
var, start, stop = map(self._print,
[i.label, i.lower + 1, i.upper + 1])
open_lines.append("for %s = %s:%s" % (var, start, stop))
close_lines.append("end")
return open_lines, close_lines
def _print_Mul(self, expr):
# print complex numbers nicely in Julia
if (expr.is_number and expr.is_imaginary and
expr.as_coeff_Mul()[0].is_integer):
return "%sim" % self._print(-S.ImaginaryUnit*expr)
# cribbed from str.py
prec = precedence(expr)
c, e = expr.as_coeff_Mul()
if c < 0:
expr = _keep_coeff(-c, e)
sign = "-"
else:
sign = ""
a = [] # items in the numerator
b = [] # items that are in the denominator (if any)
if self.order not in ('old', 'none'):
args = expr.as_ordered_factors()
else:
# use make_args in case expr was something like -x -> x
args = Mul.make_args(expr)
# Gather args for numerator/denominator
for item in args:
if (item.is_commutative and item.is_Pow and item.exp.is_Rational
and item.exp.is_negative):
if item.exp != -1:
b.append(Pow(item.base, -item.exp, evaluate=False))
else:
b.append(Pow(item.base, -item.exp))
elif item.is_Rational and item is not S.Infinity:
if item.p != 1:
a.append(Rational(item.p))
if item.q != 1:
b.append(Rational(item.q))
else:
a.append(item)
a = a or [S.One]
a_str = [self.parenthesize(x, prec) for x in a]
b_str = [self.parenthesize(x, prec) for x in b]
# from here it differs from str.py to deal with "*" and ".*"
def multjoin(a, a_str):
# here we probably are assuming the constants will come first
r = a_str[0]
for i in range(1, len(a)):
mulsym = '*' if a[i-1].is_number else '.*'
r = r + mulsym + a_str[i]
return r
if len(b) == 0:
return sign + multjoin(a, a_str)
elif len(b) == 1:
divsym = '/' if b[0].is_number else './'
return sign + multjoin(a, a_str) + divsym + b_str[0]
else:
divsym = '/' if all([bi.is_number for bi in b]) else './'
return (sign + multjoin(a, a_str) +
divsym + "(%s)" % multjoin(b, b_str))
def _print_Pow(self, expr):
powsymbol = '^' if all([x.is_number for x in expr.args]) else '.^'
PREC = precedence(expr)
if expr.exp == S.Half:
return "sqrt(%s)" % self._print(expr.base)
if expr.is_commutative:
if expr.exp == -S.Half:
sym = '/' if expr.base.is_number else './'
return "1" + sym + "sqrt(%s)" % self._print(expr.base)
if expr.exp == -S.One:
sym = '/' if expr.base.is_number else './'
return "1" + sym + "%s" % self.parenthesize(expr.base, PREC)
return '%s%s%s' % (self.parenthesize(expr.base, PREC), powsymbol,
self.parenthesize(expr.exp, PREC))
def _print_MatPow(self, expr):
PREC = precedence(expr)
return '%s^%s' % (self.parenthesize(expr.base, PREC),
self.parenthesize(expr.exp, PREC))
def _print_Pi(self, expr):
if self._settings["inline"]:
return "pi"
else:
return super(JuliaCodePrinter, self)._print_NumberSymbol(expr)
def _print_ImaginaryUnit(self, expr):
return "im"
def _print_Exp1(self, expr):
if self._settings["inline"]:
return "e"
else:
return super(JuliaCodePrinter, self)._print_NumberSymbol(expr)
def _print_EulerGamma(self, expr):
if self._settings["inline"]:
return "eulergamma"
else:
return super(JuliaCodePrinter, self)._print_NumberSymbol(expr)
def _print_Catalan(self, expr):
if self._settings["inline"]:
return "catalan"
else:
return super(JuliaCodePrinter, self)._print_NumberSymbol(expr)
def _print_GoldenRatio(self, expr):
if self._settings["inline"]:
return "golden"
else:
return super(JuliaCodePrinter, self)._print_NumberSymbol(expr)
def _print_NumberSymbol(self, expr):
if self._settings["inline"]:
return self._print(expr.evalf(self._settings["precision"]))
else:
# assign to a variable, perhaps more readable for longer program
return super(JuliaCodePrinter, self)._print_NumberSymbol(expr)
def _print_Assignment(self, expr):
from ..functions.elementary.piecewise import Piecewise
from ..tensor.indexed import IndexedBase
# Copied from codeprinter, but remove special MatrixSymbol treatment
lhs = expr.lhs
rhs = expr.rhs
# We special case assignments that take multiple lines
if not self._settings["inline"] and isinstance(expr.rhs, Piecewise):
# Here we modify Piecewise so each expression is now
# an Assignment, and then continue on the print.
expressions = []
conditions = []
for (e, c) in rhs.args:
expressions.append(Assignment(lhs, e))
conditions.append(c)
temp = Piecewise(*zip(expressions, conditions))
return self._print(temp)
if self._settings["contract"] and (lhs.has(IndexedBase) or
rhs.has(IndexedBase)):
# Here we check if there is looping to be done, and if so
# print the required loops.
return self._doprint_loops(rhs, lhs)
else:
lhs_code = self._print(lhs)
rhs_code = self._print(rhs)
return self._get_statement("%s = %s" % (lhs_code, rhs_code))
def _print_Infinity(self, expr):
return 'Inf'
def _print_NegativeInfinity(self, expr):
return '-Inf'
def _print_NaN(self, expr):
return 'NaN'
def _print_list(self, expr):
return 'Any[' + ', '.join(self._print(a) for a in expr) + ']'
def _print_tuple(self, expr):
if len(expr) == 1:
return "(%s,)" % self._print(expr[0])
else:
return "(%s)" % self.stringify(expr, ", ")
_print_Tuple = _print_tuple
def _print_BooleanTrue(self, expr):
return "true"
def _print_BooleanFalse(self, expr):
return "false"
def _print_bool(self, expr):
return str(expr).lower()
# Could generate quadrature code for definite Integrals?
#_print_Integral = _print_not_supported
def _print_MatrixBase(self, A):
# Handle zero dimensions:
if A.rows == 0 or A.cols == 0:
return 'zeros(%s, %s)' % (A.rows, A.cols)
elif (A.rows, A.cols) == (1, 1):
return "[%s]" % A[0, 0]
elif A.rows == 1:
return "[%s]" % A.table(self, rowstart='', rowend='', colsep=' ')
elif A.cols == 1:
# note .table would unnecessarily equispace the rows
return "[%s]" % ", ".join([self._print(a) for a in A])
return "[%s]" % A.table(self, rowstart='', rowend='',
rowsep=';\n', colsep=' ')
def _print_SparseMatrix(self, A):
from ..matrices import Matrix
L = A.col_list();
# make row vectors of the indices and entries
I = Matrix([k[0] + 1 for k in L])
J = Matrix([k[1] + 1 for k in L])
AIJ = Matrix([k[2] for k in L])
return "sparse(%s, %s, %s, %s, %s)" % (self._print(I), self._print(J),
self._print(AIJ), A.rows, A.cols)
# FIXME: Str/CodePrinter could define each of these to call the _print
# method from higher up the class hierarchy (see _print_NumberSymbol).
# Then subclasses like us would not need to repeat all this.
_print_Matrix = \
_print_DenseMatrix = \
_print_MutableDenseMatrix = \
_print_ImmutableMatrix = \
_print_ImmutableDenseMatrix = \
_print_MatrixBase
_print_MutableSparseMatrix = \
_print_ImmutableSparseMatrix = \
_print_SparseMatrix
def _print_MatrixElement(self, expr):
return self.parenthesize(expr.parent, PRECEDENCE["Atom"], strict=True) \
+ '[%s,%s]' % (expr.i + 1, expr.j + 1)
def _print_MatrixSlice(self, expr):
def strslice(x, lim):
l = x[0] + 1
h = x[1]
step = x[2]
lstr = self._print(l)
hstr = 'end' if h == lim else self._print(h)
if step == 1:
if l == 1 and h == lim:
return ':'
if l == h:
return lstr
else:
return lstr + ':' + hstr
else:
return ':'.join((lstr, self._print(step), hstr))
return (self._print(expr.parent) + '[' +
strslice(expr.rowslice, expr.parent.shape[0]) + ',' +
strslice(expr.colslice, expr.parent.shape[1]) + ']')
def _print_Indexed(self, expr):
inds = [ self._print(i) for i in expr.indices ]
return "%s[%s]" % (self._print(expr.base.label), ",".join(inds))
def _print_Idx(self, expr):
return self._print(expr.label)
def _print_Identity(self, expr):
return "eye(%s)" % self._print(expr.shape[0])
# Note: as of 2015, Julia doesn't have spherical Bessel functions
def _print_jn(self, expr):
from ..functions import sqrt, besselj
x = expr.argument
expr2 = sqrt(S.Pi/(2*x))*besselj(expr.order + S.Half, x)
return self._print(expr2)
def _print_yn(self, expr):
from ..functions import sqrt, bessely
x = expr.argument
expr2 = sqrt(S.Pi/(2*x))*bessely(expr.order + S.Half, x)
return self._print(expr2)
def _print_Piecewise(self, expr):
if expr.args[-1].cond != True:
# We need the last conditional to be a True, otherwise the resulting
# function may not return a result.
raise ValueError("All Piecewise expressions must contain an "
"(expr, True) statement to be used as a default "
"condition. Without one, the generated "
"expression may not evaluate to anything under "
"some condition.")
lines = []
if self._settings["inline"]:
# Express each (cond, expr) pair in a nested Horner form:
# (condition) .* (expr) + (not cond) .* (<others>)
# Expressions that result in multiple statements won't work here.
ecpairs = ["({0}) ? ({1}) :".format
(self._print(c), self._print(e))
for e, c in expr.args[:-1]]
elast = " (%s)" % self._print(expr.args[-1].expr)
pw = "\n".join(ecpairs) + elast
# Note: current need these outer brackets for 2*pw. Would be
# nicer to teach parenthesize() to do this for us when needed!
return "(" + pw + ")"
else:
for i, (e, c) in enumerate(expr.args):
if i == 0:
lines.append("if (%s)" % self._print(c))
elif i == len(expr.args) - 1 and c == True:
lines.append("else")
else:
lines.append("elseif (%s)" % self._print(c))
code0 = self._print(e)
lines.append(code0)
if i == len(expr.args) - 1:
lines.append("end")
return "\n".join(lines)
[docs] def indent_code(self, code):
"""Accepts a string of code or a list of code lines"""
# code mostly copied from ccode
if isinstance(code, string_types):
code_lines = self.indent_code(code.splitlines(True))
return ''.join(code_lines)
tab = " "
inc_regex = ('^function ', '^if ', '^elseif ', '^else$', '^for ')
dec_regex = ('^end$', '^elseif ', '^else$')
# pre-strip left-space from the code
code = [ line.lstrip(' \t') for line in code ]
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 == '' or line == '\n':
pretty.append(line)
continue
level -= decrease[n]
pretty.append("%s%s" % (tab*level, line))
level += increase[n]
return pretty
[docs]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 .. import julia_code, symbols, sin, pi
>>> x = symbols('x')
>>> julia_code(sin(x).series(x).removeO())
'x.^5/120 - x.^3/6 + x'
>>> from .. import Rational, ceiling, Abs
>>> 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 .. 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 dimenions must align in the latter case.
>>> from .. 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 .. 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 .. 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 .. import Eq, IndexedBase, Idx, ccode
>>> 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)
[docs]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))