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switching to high quality piper tts and added label translations

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Matthias Hinrichs
2026-01-29 23:48:19 +01:00
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""" rewrite of lambdify - This stuff is not stable at all.
It is for internal use in the new plotting module.
It may (will! see the Q'n'A in the source) be rewritten.
It's completely self contained. Especially it does not use lambdarepr.
It does not aim to replace the current lambdify. Most importantly it will never
ever support anything else than SymPy expressions (no Matrices, dictionaries
and so on).
"""
import re
from sympy.core.numbers import (I, NumberSymbol, oo, zoo)
from sympy.core.symbol import Symbol
from sympy.utilities.iterables import numbered_symbols
# We parse the expression string into a tree that identifies functions. Then
# we translate the names of the functions and we translate also some strings
# that are not names of functions (all this according to translation
# dictionaries).
# If the translation goes to another module (like numpy) the
# module is imported and 'func' is translated to 'module.func'.
# If a function can not be translated, the inner nodes of that part of the
# tree are not translated. So if we have Integral(sqrt(x)), sqrt is not
# translated to np.sqrt and the Integral does not crash.
# A namespace for all this is generated by crawling the (func, args) tree of
# the expression. The creation of this namespace involves many ugly
# workarounds.
# The namespace consists of all the names needed for the SymPy expression and
# all the name of modules used for translation. Those modules are imported only
# as a name (import numpy as np) in order to keep the namespace small and
# manageable.
# Please, if there is a bug, do not try to fix it here! Rewrite this by using
# the method proposed in the last Q'n'A below. That way the new function will
# work just as well, be just as simple, but it wont need any new workarounds.
# If you insist on fixing it here, look at the workarounds in the function
# sympy_expression_namespace and in lambdify.
# Q: Why are you not using Python abstract syntax tree?
# A: Because it is more complicated and not much more powerful in this case.
# Q: What if I have Symbol('sin') or g=Function('f')?
# A: You will break the algorithm. We should use srepr to defend against this?
# The problem with Symbol('sin') is that it will be printed as 'sin'. The
# parser will distinguish it from the function 'sin' because functions are
# detected thanks to the opening parenthesis, but the lambda expression won't
# understand the difference if we have also the sin function.
# The solution (complicated) is to use srepr and maybe ast.
# The problem with the g=Function('f') is that it will be printed as 'f' but in
# the global namespace we have only 'g'. But as the same printer is used in the
# constructor of the namespace there will be no problem.
# Q: What if some of the printers are not printing as expected?
# A: The algorithm wont work. You must use srepr for those cases. But even
# srepr may not print well. All problems with printers should be considered
# bugs.
# Q: What about _imp_ functions?
# A: Those are taken care for by evalf. A special case treatment will work
# faster but it's not worth the code complexity.
# Q: Will ast fix all possible problems?
# A: No. You will always have to use some printer. Even srepr may not work in
# some cases. But if the printer does not work, that should be considered a
# bug.
# Q: Is there same way to fix all possible problems?
# A: Probably by constructing our strings ourself by traversing the (func,
# args) tree and creating the namespace at the same time. That actually sounds
# good.
from sympy.external import import_module
import warnings
#TODO debugging output
class vectorized_lambdify:
""" Return a sufficiently smart, vectorized and lambdified function.
Returns only reals.
Explanation
===========
This function uses experimental_lambdify to created a lambdified
expression ready to be used with numpy. Many of the functions in SymPy
are not implemented in numpy so in some cases we resort to Python cmath or
even to evalf.
The following translations are tried:
only numpy complex
- on errors raised by SymPy trying to work with ndarray:
only Python cmath and then vectorize complex128
When using Python cmath there is no need for evalf or float/complex
because Python cmath calls those.
This function never tries to mix numpy directly with evalf because numpy
does not understand SymPy Float. If this is needed one can use the
float_wrap_evalf/complex_wrap_evalf options of experimental_lambdify or
better one can be explicit about the dtypes that numpy works with.
Check numpy bug http://projects.scipy.org/numpy/ticket/1013 to know what
types of errors to expect.
"""
def __init__(self, args, expr):
self.args = args
self.expr = expr
self.np = import_module('numpy')
self.lambda_func_1 = experimental_lambdify(
args, expr, use_np=True)
self.vector_func_1 = self.lambda_func_1
self.lambda_func_2 = experimental_lambdify(
args, expr, use_python_cmath=True)
self.vector_func_2 = self.np.vectorize(
self.lambda_func_2, otypes=[complex])
self.vector_func = self.vector_func_1
self.failure = False
def __call__(self, *args):
np = self.np
try:
temp_args = (np.array(a, dtype=complex) for a in args)
results = self.vector_func(*temp_args)
results = np.ma.masked_where(
np.abs(results.imag) > 1e-7 * np.abs(results),
results.real, copy=False)
return results
except ValueError:
if self.failure:
raise
self.failure = True
self.vector_func = self.vector_func_2
warnings.warn(
'The evaluation of the expression is problematic. '
'We are trying a failback method that may still work. '
'Please report this as a bug.')
return self.__call__(*args)
class lambdify:
"""Returns the lambdified function.
Explanation
===========
This function uses experimental_lambdify to create a lambdified
expression. It uses cmath to lambdify the expression. If the function
is not implemented in Python cmath, Python cmath calls evalf on those
functions.
"""
def __init__(self, args, expr):
self.args = args
self.expr = expr
self.lambda_func_1 = experimental_lambdify(
args, expr, use_python_cmath=True, use_evalf=True)
self.lambda_func_2 = experimental_lambdify(
args, expr, use_python_math=True, use_evalf=True)
self.lambda_func_3 = experimental_lambdify(
args, expr, use_evalf=True, complex_wrap_evalf=True)
self.lambda_func = self.lambda_func_1
self.failure = False
def __call__(self, args):
try:
#The result can be sympy.Float. Hence wrap it with complex type.
result = complex(self.lambda_func(args))
if abs(result.imag) > 1e-7 * abs(result):
return None
return result.real
except (ZeroDivisionError, OverflowError):
return None
except TypeError as e:
if self.failure:
raise e
if self.lambda_func == self.lambda_func_1:
self.lambda_func = self.lambda_func_2
return self.__call__(args)
self.failure = True
self.lambda_func = self.lambda_func_3
warnings.warn(
'The evaluation of the expression is problematic. '
'We are trying a failback method that may still work. '
'Please report this as a bug.', stacklevel=2)
return self.__call__(args)
def experimental_lambdify(*args, **kwargs):
l = Lambdifier(*args, **kwargs)
return l
class Lambdifier:
def __init__(self, args, expr, print_lambda=False, use_evalf=False,
float_wrap_evalf=False, complex_wrap_evalf=False,
use_np=False, use_python_math=False, use_python_cmath=False,
use_interval=False):
self.print_lambda = print_lambda
self.use_evalf = use_evalf
self.float_wrap_evalf = float_wrap_evalf
self.complex_wrap_evalf = complex_wrap_evalf
self.use_np = use_np
self.use_python_math = use_python_math
self.use_python_cmath = use_python_cmath
self.use_interval = use_interval
# Constructing the argument string
# - check
if not all(isinstance(a, Symbol) for a in args):
raise ValueError('The arguments must be Symbols.')
# - use numbered symbols
syms = numbered_symbols(exclude=expr.free_symbols)
newargs = [next(syms) for _ in args]
expr = expr.xreplace(dict(zip(args, newargs)))
argstr = ', '.join([str(a) for a in newargs])
del syms, newargs, args
# Constructing the translation dictionaries and making the translation
self.dict_str = self.get_dict_str()
self.dict_fun = self.get_dict_fun()
exprstr = str(expr)
newexpr = self.tree2str_translate(self.str2tree(exprstr))
# Constructing the namespaces
namespace = {}
namespace.update(self.sympy_atoms_namespace(expr))
namespace.update(self.sympy_expression_namespace(expr))
# XXX Workaround
# Ugly workaround because Pow(a,Half) prints as sqrt(a)
# and sympy_expression_namespace can not catch it.
from sympy.functions.elementary.miscellaneous import sqrt
namespace.update({'sqrt': sqrt})
namespace.update({'Eq': lambda x, y: x == y})
namespace.update({'Ne': lambda x, y: x != y})
# End workaround.
if use_python_math:
namespace.update({'math': __import__('math')})
if use_python_cmath:
namespace.update({'cmath': __import__('cmath')})
if use_np:
try:
namespace.update({'np': __import__('numpy')})
except ImportError:
raise ImportError(
'experimental_lambdify failed to import numpy.')
if use_interval:
namespace.update({'imath': __import__(
'sympy.plotting.intervalmath', fromlist=['intervalmath'])})
namespace.update({'math': __import__('math')})
# Construct the lambda
if self.print_lambda:
print(newexpr)
eval_str = 'lambda %s : ( %s )' % (argstr, newexpr)
self.eval_str = eval_str
exec("MYNEWLAMBDA = %s" % eval_str, namespace)
self.lambda_func = namespace['MYNEWLAMBDA']
def __call__(self, *args, **kwargs):
return self.lambda_func(*args, **kwargs)
##############################################################################
# Dicts for translating from SymPy to other modules
##############################################################################
###
# builtins
###
# Functions with different names in builtins
builtin_functions_different = {
'Min': 'min',
'Max': 'max',
'Abs': 'abs',
}
# Strings that should be translated
builtin_not_functions = {
'I': '1j',
# 'oo': '1e400',
}
###
# numpy
###
# Functions that are the same in numpy
numpy_functions_same = [
'sin', 'cos', 'tan', 'sinh', 'cosh', 'tanh', 'exp', 'log',
'sqrt', 'floor', 'conjugate', 'sign',
]
# Functions with different names in numpy
numpy_functions_different = {
"acos": "arccos",
"acosh": "arccosh",
"arg": "angle",
"asin": "arcsin",
"asinh": "arcsinh",
"atan": "arctan",
"atan2": "arctan2",
"atanh": "arctanh",
"ceiling": "ceil",
"im": "imag",
"ln": "log",
"Max": "amax",
"Min": "amin",
"re": "real",
"Abs": "abs",
}
# Strings that should be translated
numpy_not_functions = {
'pi': 'np.pi',
'oo': 'np.inf',
'E': 'np.e',
}
###
# Python math
###
# Functions that are the same in math
math_functions_same = [
'sin', 'cos', 'tan', 'asin', 'acos', 'atan', 'atan2',
'sinh', 'cosh', 'tanh', 'asinh', 'acosh', 'atanh',
'exp', 'log', 'erf', 'sqrt', 'floor', 'factorial', 'gamma',
]
# Functions with different names in math
math_functions_different = {
'ceiling': 'ceil',
'ln': 'log',
'loggamma': 'lgamma'
}
# Strings that should be translated
math_not_functions = {
'pi': 'math.pi',
'E': 'math.e',
}
###
# Python cmath
###
# Functions that are the same in cmath
cmath_functions_same = [
'sin', 'cos', 'tan', 'asin', 'acos', 'atan',
'sinh', 'cosh', 'tanh', 'asinh', 'acosh', 'atanh',
'exp', 'log', 'sqrt',
]
# Functions with different names in cmath
cmath_functions_different = {
'ln': 'log',
'arg': 'phase',
}
# Strings that should be translated
cmath_not_functions = {
'pi': 'cmath.pi',
'E': 'cmath.e',
}
###
# intervalmath
###
interval_not_functions = {
'pi': 'math.pi',
'E': 'math.e'
}
interval_functions_same = [
'sin', 'cos', 'exp', 'tan', 'atan', 'log',
'sqrt', 'cosh', 'sinh', 'tanh', 'floor',
'acos', 'asin', 'acosh', 'asinh', 'atanh',
'Abs', 'And', 'Or'
]
interval_functions_different = {
'Min': 'imin',
'Max': 'imax',
'ceiling': 'ceil',
}
###
# mpmath, etc
###
#TODO
###
# Create the final ordered tuples of dictionaries
###
# For strings
def get_dict_str(self):
dict_str = dict(self.builtin_not_functions)
if self.use_np:
dict_str.update(self.numpy_not_functions)
if self.use_python_math:
dict_str.update(self.math_not_functions)
if self.use_python_cmath:
dict_str.update(self.cmath_not_functions)
if self.use_interval:
dict_str.update(self.interval_not_functions)
return dict_str
# For functions
def get_dict_fun(self):
dict_fun = dict(self.builtin_functions_different)
if self.use_np:
for s in self.numpy_functions_same:
dict_fun[s] = 'np.' + s
for k, v in self.numpy_functions_different.items():
dict_fun[k] = 'np.' + v
if self.use_python_math:
for s in self.math_functions_same:
dict_fun[s] = 'math.' + s
for k, v in self.math_functions_different.items():
dict_fun[k] = 'math.' + v
if self.use_python_cmath:
for s in self.cmath_functions_same:
dict_fun[s] = 'cmath.' + s
for k, v in self.cmath_functions_different.items():
dict_fun[k] = 'cmath.' + v
if self.use_interval:
for s in self.interval_functions_same:
dict_fun[s] = 'imath.' + s
for k, v in self.interval_functions_different.items():
dict_fun[k] = 'imath.' + v
return dict_fun
##############################################################################
# The translator functions, tree parsers, etc.
##############################################################################
def str2tree(self, exprstr):
"""Converts an expression string to a tree.
Explanation
===========
Functions are represented by ('func_name(', tree_of_arguments).
Other expressions are (head_string, mid_tree, tail_str).
Expressions that do not contain functions are directly returned.
Examples
========
>>> from sympy.abc import x, y, z
>>> from sympy import Integral, sin
>>> from sympy.plotting.experimental_lambdify import Lambdifier
>>> str2tree = Lambdifier([x], x).str2tree
>>> str2tree(str(Integral(x, (x, 1, y))))
('', ('Integral(', 'x, (x, 1, y)'), ')')
>>> str2tree(str(x+y))
'x + y'
>>> str2tree(str(x+y*sin(z)+1))
('x + y*', ('sin(', 'z'), ') + 1')
>>> str2tree('sin(y*(y + 1.1) + (sin(y)))')
('', ('sin(', ('y*(y + 1.1) + (', ('sin(', 'y'), '))')), ')')
"""
#matches the first 'function_name('
first_par = re.search(r'(\w+\()', exprstr)
if first_par is None:
return exprstr
else:
start = first_par.start()
end = first_par.end()
head = exprstr[:start]
func = exprstr[start:end]
tail = exprstr[end:]
count = 0
for i, c in enumerate(tail):
if c == '(':
count += 1
elif c == ')':
count -= 1
if count == -1:
break
func_tail = self.str2tree(tail[:i])
tail = self.str2tree(tail[i:])
return (head, (func, func_tail), tail)
@classmethod
def tree2str(cls, tree):
"""Converts a tree to string without translations.
Examples
========
>>> from sympy.abc import x, y, z
>>> from sympy import sin
>>> from sympy.plotting.experimental_lambdify import Lambdifier
>>> str2tree = Lambdifier([x], x).str2tree
>>> tree2str = Lambdifier([x], x).tree2str
>>> tree2str(str2tree(str(x+y*sin(z)+1)))
'x + y*sin(z) + 1'
"""
if isinstance(tree, str):
return tree
else:
return ''.join(map(cls.tree2str, tree))
def tree2str_translate(self, tree):
"""Converts a tree to string with translations.
Explanation
===========
Function names are translated by translate_func.
Other strings are translated by translate_str.
"""
if isinstance(tree, str):
return self.translate_str(tree)
elif isinstance(tree, tuple) and len(tree) == 2:
return self.translate_func(tree[0][:-1], tree[1])
else:
return ''.join([self.tree2str_translate(t) for t in tree])
def translate_str(self, estr):
"""Translate substrings of estr using in order the dictionaries in
dict_tuple_str."""
for pattern, repl in self.dict_str.items():
estr = re.sub(pattern, repl, estr)
return estr
def translate_func(self, func_name, argtree):
"""Translate function names and the tree of arguments.
Explanation
===========
If the function name is not in the dictionaries of dict_tuple_fun then the
function is surrounded by a float((...).evalf()).
The use of float is necessary as np.<function>(sympy.Float(..)) raises an
error."""
if func_name in self.dict_fun:
new_name = self.dict_fun[func_name]
argstr = self.tree2str_translate(argtree)
return new_name + '(' + argstr
elif func_name in ['Eq', 'Ne']:
op = {'Eq': '==', 'Ne': '!='}
return "(lambda x, y: x {} y)({}".format(op[func_name], self.tree2str_translate(argtree))
else:
template = '(%s(%s)).evalf(' if self.use_evalf else '%s(%s'
if self.float_wrap_evalf:
template = 'float(%s)' % template
elif self.complex_wrap_evalf:
template = 'complex(%s)' % template
# Wrapping should only happen on the outermost expression, which
# is the only thing we know will be a number.
float_wrap_evalf = self.float_wrap_evalf
complex_wrap_evalf = self.complex_wrap_evalf
self.float_wrap_evalf = False
self.complex_wrap_evalf = False
ret = template % (func_name, self.tree2str_translate(argtree))
self.float_wrap_evalf = float_wrap_evalf
self.complex_wrap_evalf = complex_wrap_evalf
return ret
##############################################################################
# The namespace constructors
##############################################################################
@classmethod
def sympy_expression_namespace(cls, expr):
"""Traverses the (func, args) tree of an expression and creates a SymPy
namespace. All other modules are imported only as a module name. That way
the namespace is not polluted and rests quite small. It probably causes much
more variable lookups and so it takes more time, but there are no tests on
that for the moment."""
if expr is None:
return {}
else:
funcname = str(expr.func)
# XXX Workaround
# Here we add an ugly workaround because str(func(x))
# is not always the same as str(func). Eg
# >>> str(Integral(x))
# "Integral(x)"
# >>> str(Integral)
# "<class 'sympy.integrals.integrals.Integral'>"
# >>> str(sqrt(x))
# "sqrt(x)"
# >>> str(sqrt)
# "<function sqrt at 0x3d92de8>"
# >>> str(sin(x))
# "sin(x)"
# >>> str(sin)
# "sin"
# Either one of those can be used but not all at the same time.
# The code considers the sin example as the right one.
regexlist = [
r'<class \'sympy[\w.]*?.([\w]*)\'>$',
# the example Integral
r'<function ([\w]*) at 0x[\w]*>$', # the example sqrt
]
for r in regexlist:
m = re.match(r, funcname)
if m is not None:
funcname = m.groups()[0]
# End of the workaround
# XXX debug: print funcname
args_dict = {}
for a in expr.args:
if (isinstance(a, (Symbol, NumberSymbol)) or a in [I, zoo, oo]):
continue
else:
args_dict.update(cls.sympy_expression_namespace(a))
args_dict.update({funcname: expr.func})
return args_dict
@staticmethod
def sympy_atoms_namespace(expr):
"""For no real reason this function is separated from
sympy_expression_namespace. It can be moved to it."""
atoms = expr.atoms(Symbol, NumberSymbol, I, zoo, oo)
d = {}
for a in atoms:
# XXX debug: print 'atom:' + str(a)
d[str(a)] = a
return d