diff --git a/evalkit_tf437/lib/python3.10/site-packages/IPython/utils/PyColorize.py b/evalkit_tf437/lib/python3.10/site-packages/IPython/utils/PyColorize.py new file mode 100644 index 0000000000000000000000000000000000000000..86bb9af4c160ff9a9355f2c0982e531d1548928b --- /dev/null +++ b/evalkit_tf437/lib/python3.10/site-packages/IPython/utils/PyColorize.py @@ -0,0 +1,331 @@ +# -*- coding: utf-8 -*- +""" +Class and program to colorize python source code for ANSI terminals. + +Based on an HTML code highlighter by Jurgen Hermann found at: +http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/52298 + +Modifications by Fernando Perez (fperez@colorado.edu). + +Information on the original HTML highlighter follows: + +MoinMoin - Python Source Parser + +Title: Colorize Python source using the built-in tokenizer + +Submitter: Jurgen Hermann +Last Updated:2001/04/06 + +Version no:1.2 + +Description: + +This code is part of MoinMoin (http://moin.sourceforge.net/) and converts +Python source code to HTML markup, rendering comments, keywords, +operators, numeric and string literals in different colors. + +It shows how to use the built-in keyword, token and tokenize modules to +scan Python source code and re-emit it with no changes to its original +formatting (which is the hard part). +""" + +__all__ = ['ANSICodeColors', 'Parser'] + +_scheme_default = 'Linux' + + +# Imports +import keyword +import os +import sys +import token +import tokenize + +generate_tokens = tokenize.generate_tokens + +from IPython.utils.coloransi import TermColors, InputTermColors,ColorScheme, ColorSchemeTable +from .colorable import Colorable +from io import StringIO + +############################################################################# +### Python Source Parser (does Highlighting) +############################################################################# + +_KEYWORD = token.NT_OFFSET + 1 +_TEXT = token.NT_OFFSET + 2 + +#**************************************************************************** +# Builtin color schemes + +Colors = TermColors # just a shorthand + +# Build a few color schemes +NoColor = ColorScheme( + 'NoColor',{ + 'header' : Colors.NoColor, + token.NUMBER : Colors.NoColor, + token.OP : Colors.NoColor, + token.STRING : Colors.NoColor, + tokenize.COMMENT : Colors.NoColor, + token.NAME : Colors.NoColor, + token.ERRORTOKEN : Colors.NoColor, + + _KEYWORD : Colors.NoColor, + _TEXT : Colors.NoColor, + + 'in_prompt' : InputTermColors.NoColor, # Input prompt + 'in_number' : InputTermColors.NoColor, # Input prompt number + 'in_prompt2' : InputTermColors.NoColor, # Continuation prompt + 'in_normal' : InputTermColors.NoColor, # color off (usu. Colors.Normal) + + 'out_prompt' : Colors.NoColor, # Output prompt + 'out_number' : Colors.NoColor, # Output prompt number + + 'normal' : Colors.NoColor # color off (usu. Colors.Normal) + } ) + +LinuxColors = ColorScheme( + 'Linux',{ + 'header' : Colors.LightRed, + token.NUMBER : Colors.LightCyan, + token.OP : Colors.Yellow, + token.STRING : Colors.LightBlue, + tokenize.COMMENT : Colors.LightRed, + token.NAME : Colors.Normal, + token.ERRORTOKEN : Colors.Red, + + _KEYWORD : Colors.LightGreen, + _TEXT : Colors.Yellow, + + 'in_prompt' : InputTermColors.Green, + 'in_number' : InputTermColors.LightGreen, + 'in_prompt2' : InputTermColors.Green, + 'in_normal' : InputTermColors.Normal, # color off (usu. Colors.Normal) + + 'out_prompt' : Colors.Red, + 'out_number' : Colors.LightRed, + + 'normal' : Colors.Normal # color off (usu. Colors.Normal) + } ) + +NeutralColors = ColorScheme( + 'Neutral',{ + 'header' : Colors.Red, + token.NUMBER : Colors.Cyan, + token.OP : Colors.Blue, + token.STRING : Colors.Blue, + tokenize.COMMENT : Colors.Red, + token.NAME : Colors.Normal, + token.ERRORTOKEN : Colors.Red, + + _KEYWORD : Colors.Green, + _TEXT : Colors.Blue, + + 'in_prompt' : InputTermColors.Blue, + 'in_number' : InputTermColors.LightBlue, + 'in_prompt2' : InputTermColors.Blue, + 'in_normal' : InputTermColors.Normal, # color off (usu. Colors.Normal) + + 'out_prompt' : Colors.Red, + 'out_number' : Colors.LightRed, + + 'normal' : Colors.Normal # color off (usu. Colors.Normal) + } ) + +# Hack: the 'neutral' colours are not very visible on a dark background on +# Windows. Since Windows command prompts have a dark background by default, and +# relatively few users are likely to alter that, we will use the 'Linux' colours, +# designed for a dark background, as the default on Windows. Changing it here +# avoids affecting the prompt colours rendered by prompt_toolkit, where the +# neutral defaults do work OK. + +if os.name == 'nt': + NeutralColors = LinuxColors.copy(name='Neutral') + +LightBGColors = ColorScheme( + 'LightBG',{ + 'header' : Colors.Red, + token.NUMBER : Colors.Cyan, + token.OP : Colors.Blue, + token.STRING : Colors.Blue, + tokenize.COMMENT : Colors.Red, + token.NAME : Colors.Normal, + token.ERRORTOKEN : Colors.Red, + + + _KEYWORD : Colors.Green, + _TEXT : Colors.Blue, + + 'in_prompt' : InputTermColors.Blue, + 'in_number' : InputTermColors.LightBlue, + 'in_prompt2' : InputTermColors.Blue, + 'in_normal' : InputTermColors.Normal, # color off (usu. Colors.Normal) + + 'out_prompt' : Colors.Red, + 'out_number' : Colors.LightRed, + + 'normal' : Colors.Normal # color off (usu. Colors.Normal) + } ) + +# Build table of color schemes (needed by the parser) +ANSICodeColors = ColorSchemeTable([NoColor,LinuxColors,LightBGColors, NeutralColors], + _scheme_default) + +Undefined = object() + +class Parser(Colorable): + """ Format colored Python source. + """ + + def __init__(self, color_table=None, out = sys.stdout, parent=None, style=None): + """ Create a parser with a specified color table and output channel. + + Call format() to process code. + """ + + super(Parser, self).__init__(parent=parent) + + self.color_table = color_table if color_table else ANSICodeColors + self.out = out + self.pos = None + self.lines = None + self.raw = None + if not style: + self.style = self.default_style + else: + self.style = style + + + def format(self, raw, out=None, scheme=Undefined): + import warnings + if scheme is not Undefined: + warnings.warn('The `scheme` argument of IPython.utils.PyColorize:Parser.format is deprecated since IPython 6.0.' + 'It will have no effect. Set the parser `style` directly.', + stacklevel=2) + return self.format2(raw, out)[0] + + def format2(self, raw, out = None): + """ Parse and send the colored source. + + If out and scheme are not specified, the defaults (given to + constructor) are used. + + out should be a file-type object. Optionally, out can be given as the + string 'str' and the parser will automatically return the output in a + string.""" + + string_output = 0 + if out == 'str' or self.out == 'str' or \ + isinstance(self.out, StringIO): + # XXX - I don't really like this state handling logic, but at this + # point I don't want to make major changes, so adding the + # isinstance() check is the simplest I can do to ensure correct + # behavior. + out_old = self.out + self.out = StringIO() + string_output = 1 + elif out is not None: + self.out = out + else: + raise ValueError('`out` or `self.out` should be file-like or the value `"str"`') + + # Fast return of the unmodified input for NoColor scheme + if self.style == 'NoColor': + error = False + self.out.write(raw) + if string_output: + return raw, error + return None, error + + # local shorthands + colors = self.color_table[self.style].colors + self.colors = colors # put in object so __call__ sees it + + # Remove trailing whitespace and normalize tabs + self.raw = raw.expandtabs().rstrip() + + # store line offsets in self.lines + self.lines = [0, 0] + pos = 0 + raw_find = self.raw.find + lines_append = self.lines.append + while True: + pos = raw_find('\n', pos) + 1 + if not pos: + break + lines_append(pos) + lines_append(len(self.raw)) + + # parse the source and write it + self.pos = 0 + text = StringIO(self.raw) + + error = False + try: + for atoken in generate_tokens(text.readline): + self(*atoken) + except tokenize.TokenError as ex: + msg = ex.args[0] + line = ex.args[1][0] + self.out.write("%s\n\n*** ERROR: %s%s%s\n" % + (colors[token.ERRORTOKEN], + msg, self.raw[self.lines[line]:], + colors.normal) + ) + error = True + self.out.write(colors.normal+'\n') + if string_output: + output = self.out.getvalue() + self.out = out_old + return (output, error) + return (None, error) + + + def _inner_call_(self, toktype, toktext, start_pos): + """like call but write to a temporary buffer""" + buff = StringIO() + srow, scol = start_pos + colors = self.colors + owrite = buff.write + + # line separator, so this works across platforms + linesep = os.linesep + + # calculate new positions + oldpos = self.pos + newpos = self.lines[srow] + scol + self.pos = newpos + len(toktext) + + # send the original whitespace, if needed + if newpos > oldpos: + owrite(self.raw[oldpos:newpos]) + + # skip indenting tokens + if toktype in [token.INDENT, token.DEDENT]: + self.pos = newpos + buff.seek(0) + return buff.read() + + # map token type to a color group + if token.LPAR <= toktype <= token.OP: + toktype = token.OP + elif toktype == token.NAME and keyword.iskeyword(toktext): + toktype = _KEYWORD + color = colors.get(toktype, colors[_TEXT]) + + # Triple quoted strings must be handled carefully so that backtracking + # in pagers works correctly. We need color terminators on _each_ line. + if linesep in toktext: + toktext = toktext.replace(linesep, '%s%s%s' % + (colors.normal,linesep,color)) + + # send text + owrite('%s%s%s' % (color,toktext,colors.normal)) + buff.seek(0) + return buff.read() + + + def __call__(self, toktype, toktext, start_pos, end_pos, line): + """ Token handler, with syntax highlighting.""" + self.out.write( + self._inner_call_(toktype, toktext, start_pos)) diff --git a/evalkit_tf437/lib/python3.10/site-packages/IPython/utils/jsonutil.py b/evalkit_tf437/lib/python3.10/site-packages/IPython/utils/jsonutil.py new file mode 100644 index 0000000000000000000000000000000000000000..2672e09e16970b490a70f003cb1d596e6d20b941 --- /dev/null +++ b/evalkit_tf437/lib/python3.10/site-packages/IPython/utils/jsonutil.py @@ -0,0 +1,5 @@ +from warnings import warn + +warn("IPython.utils.jsonutil has moved to jupyter_client.jsonutil", stacklevel=2) + +from jupyter_client.jsonutil import * diff --git 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b/evalkit_tf437/lib/python3.10/site-packages/pytz/zoneinfo/UTC differ diff --git a/evalkit_tf446/lib/python3.10/site-packages/sympy/codegen/abstract_nodes.py b/evalkit_tf446/lib/python3.10/site-packages/sympy/codegen/abstract_nodes.py new file mode 100644 index 0000000000000000000000000000000000000000..ae0a8b3e996a7112edf2568c00138e11c3f3327d --- /dev/null +++ b/evalkit_tf446/lib/python3.10/site-packages/sympy/codegen/abstract_nodes.py @@ -0,0 +1,18 @@ +"""This module provides containers for python objects that are valid +printing targets but are not a subclass of SymPy's Printable. +""" + + +from sympy.core.containers import Tuple + + +class List(Tuple): + """Represents a (frozen) (Python) list (for code printing purposes).""" + def __eq__(self, other): + if isinstance(other, list): + return self == List(*other) + else: + return self.args == other + + def __hash__(self): + return super().__hash__() diff --git a/evalkit_tf446/lib/python3.10/site-packages/sympy/codegen/futils.py b/evalkit_tf446/lib/python3.10/site-packages/sympy/codegen/futils.py new file mode 100644 index 0000000000000000000000000000000000000000..4a1f5751fbd4d6b44d99c69a74ad89a8496f8648 --- /dev/null +++ b/evalkit_tf446/lib/python3.10/site-packages/sympy/codegen/futils.py @@ -0,0 +1,40 @@ +from itertools import chain +from sympy.codegen.fnodes import Module +from sympy.core.symbol import Dummy +from sympy.printing.fortran import FCodePrinter + +""" This module collects utilities for rendering Fortran code. """ + + +def render_as_module(definitions, name, declarations=(), printer_settings=None): + """ Creates a ``Module`` instance and renders it as a string. + + This generates Fortran source code for a module with the correct ``use`` statements. + + Parameters + ========== + + definitions : iterable + Passed to :class:`sympy.codegen.fnodes.Module`. + name : str + Passed to :class:`sympy.codegen.fnodes.Module`. + declarations : iterable + Passed to :class:`sympy.codegen.fnodes.Module`. It will be extended with + use statements, 'implicit none' and public list generated from ``definitions``. + printer_settings : dict + Passed to ``FCodePrinter`` (default: ``{'standard': 2003, 'source_format': 'free'}``). + + """ + printer_settings = printer_settings or {'standard': 2003, 'source_format': 'free'} + printer = FCodePrinter(printer_settings) + dummy = Dummy() + if isinstance(definitions, Module): + raise ValueError("This function expects to construct a module on its own.") + mod = Module(name, chain(declarations, [dummy]), definitions) + fstr = printer.doprint(mod) + module_use_str = ' %s\n' % ' \n'.join(['use %s, only: %s' % (k, ', '.join(v)) for + k, v in printer.module_uses.items()]) + module_use_str += ' implicit none\n' + module_use_str += ' private\n' + module_use_str += ' public %s\n' % ', '.join([str(node.name) for node in definitions if getattr(node, 'name', None)]) + return fstr.replace(printer.doprint(dummy), module_use_str) diff --git a/evalkit_tf446/lib/python3.10/site-packages/sympy/codegen/pynodes.py b/evalkit_tf446/lib/python3.10/site-packages/sympy/codegen/pynodes.py new file mode 100644 index 0000000000000000000000000000000000000000..f0a08b4a79d32f63d345947d6be310b44504dbf5 --- /dev/null +++ b/evalkit_tf446/lib/python3.10/site-packages/sympy/codegen/pynodes.py @@ -0,0 +1,11 @@ +from .abstract_nodes import List as AbstractList +from .ast import Token + + +class List(AbstractList): + pass + + +class NumExprEvaluate(Token): + """represents a call to :class:`numexpr`s :func:`evaluate`""" + __slots__ = _fields = ('expr',) diff --git a/evalkit_tf446/lib/python3.10/site-packages/sympy/codegen/pyutils.py b/evalkit_tf446/lib/python3.10/site-packages/sympy/codegen/pyutils.py new file mode 100644 index 0000000000000000000000000000000000000000..e14eabe92ce50105a4055b71a49767aae04610b9 --- /dev/null +++ b/evalkit_tf446/lib/python3.10/site-packages/sympy/codegen/pyutils.py @@ -0,0 +1,24 @@ +from sympy.printing.pycode import PythonCodePrinter + +""" This module collects utilities for rendering Python code. """ + + +def render_as_module(content, standard='python3'): + """Renders Python code as a module (with the required imports). + + Parameters + ========== + + standard : + See the parameter ``standard`` in + :meth:`sympy.printing.pycode.pycode` + """ + + printer = PythonCodePrinter({'standard':standard}) + pystr = printer.doprint(content) + if printer._settings['fully_qualified_modules']: + module_imports_str = '\n'.join('import %s' % k for k in printer.module_imports) + else: + module_imports_str = '\n'.join(['from %s import %s' % (k, ', '.join(v)) for + k, v in printer.module_imports.items()]) + return module_imports_str + '\n\n' + pystr diff --git a/evalkit_tf446/lib/python3.10/site-packages/sympy/codegen/rewriting.py b/evalkit_tf446/lib/python3.10/site-packages/sympy/codegen/rewriting.py new file mode 100644 index 0000000000000000000000000000000000000000..274b7770b46ded6711468ab2a01db3a53d6fde87 --- /dev/null +++ b/evalkit_tf446/lib/python3.10/site-packages/sympy/codegen/rewriting.py @@ -0,0 +1,357 @@ +""" +Classes and functions useful for rewriting expressions for optimized code +generation. Some languages (or standards thereof), e.g. C99, offer specialized +math functions for better performance and/or precision. + +Using the ``optimize`` function in this module, together with a collection of +rules (represented as instances of ``Optimization``), one can rewrite the +expressions for this purpose:: + + >>> from sympy import Symbol, exp, log + >>> from sympy.codegen.rewriting import optimize, optims_c99 + >>> x = Symbol('x') + >>> optimize(3*exp(2*x) - 3, optims_c99) + 3*expm1(2*x) + >>> optimize(exp(2*x) - 1 - exp(-33), optims_c99) + expm1(2*x) - exp(-33) + >>> optimize(log(3*x + 3), optims_c99) + log1p(x) + log(3) + >>> optimize(log(2*x + 3), optims_c99) + log(2*x + 3) + +The ``optims_c99`` imported above is tuple containing the following instances +(which may be imported from ``sympy.codegen.rewriting``): + +- ``expm1_opt`` +- ``log1p_opt`` +- ``exp2_opt`` +- ``log2_opt`` +- ``log2const_opt`` + + +""" +from sympy.core.function import expand_log +from sympy.core.singleton import S +from sympy.core.symbol import Wild +from sympy.functions.elementary.complexes import sign +from sympy.functions.elementary.exponential import (exp, log) +from sympy.functions.elementary.miscellaneous import (Max, Min) +from sympy.functions.elementary.trigonometric import (cos, sin, sinc) +from sympy.assumptions import Q, ask +from sympy.codegen.cfunctions import log1p, log2, exp2, expm1 +from sympy.codegen.matrix_nodes import MatrixSolve +from sympy.core.expr import UnevaluatedExpr +from sympy.core.power import Pow +from sympy.codegen.numpy_nodes import logaddexp, logaddexp2 +from sympy.codegen.scipy_nodes import cosm1, powm1 +from sympy.core.mul import Mul +from sympy.matrices.expressions.matexpr import MatrixSymbol +from sympy.utilities.iterables import sift + + +class Optimization: + """ Abstract base class for rewriting optimization. + + Subclasses should implement ``__call__`` taking an expression + as argument. + + Parameters + ========== + cost_function : callable returning number + priority : number + + """ + def __init__(self, cost_function=None, priority=1): + self.cost_function = cost_function + self.priority=priority + + def cheapest(self, *args): + return min(args, key=self.cost_function) + + +class ReplaceOptim(Optimization): + """ Rewriting optimization calling replace on expressions. + + Explanation + =========== + + The instance can be used as a function on expressions for which + it will apply the ``replace`` method (see + :meth:`sympy.core.basic.Basic.replace`). + + Parameters + ========== + + query : + First argument passed to replace. + value : + Second argument passed to replace. + + Examples + ======== + + >>> from sympy import Symbol + >>> from sympy.codegen.rewriting import ReplaceOptim + >>> from sympy.codegen.cfunctions import exp2 + >>> x = Symbol('x') + >>> exp2_opt = ReplaceOptim(lambda p: p.is_Pow and p.base == 2, + ... lambda p: exp2(p.exp)) + >>> exp2_opt(2**x) + exp2(x) + + """ + + def __init__(self, query, value, **kwargs): + super().__init__(**kwargs) + self.query = query + self.value = value + + def __call__(self, expr): + return expr.replace(self.query, self.value) + + +def optimize(expr, optimizations): + """ Apply optimizations to an expression. + + Parameters + ========== + + expr : expression + optimizations : iterable of ``Optimization`` instances + The optimizations will be sorted with respect to ``priority`` (highest first). + + Examples + ======== + + >>> from sympy import log, Symbol + >>> from sympy.codegen.rewriting import optims_c99, optimize + >>> x = Symbol('x') + >>> optimize(log(x+3)/log(2) + log(x**2 + 1), optims_c99) + log1p(x**2) + log2(x + 3) + + """ + + for optim in sorted(optimizations, key=lambda opt: opt.priority, reverse=True): + new_expr = optim(expr) + if optim.cost_function is None: + expr = new_expr + else: + expr = optim.cheapest(expr, new_expr) + return expr + + +exp2_opt = ReplaceOptim( + lambda p: p.is_Pow and p.base == 2, + lambda p: exp2(p.exp) +) + + +_d = Wild('d', properties=[lambda x: x.is_Dummy]) +_u = Wild('u', properties=[lambda x: not x.is_number and not x.is_Add]) +_v = Wild('v') +_w = Wild('w') +_n = Wild('n', properties=[lambda x: x.is_number]) + +sinc_opt1 = ReplaceOptim( + sin(_w)/_w, sinc(_w) +) +sinc_opt2 = ReplaceOptim( + sin(_n*_w)/_w, _n*sinc(_n*_w) +) +sinc_opts = (sinc_opt1, sinc_opt2) + +log2_opt = ReplaceOptim(_v*log(_w)/log(2), _v*log2(_w), cost_function=lambda expr: expr.count( + lambda e: ( # division & eval of transcendentals are expensive floating point operations... + e.is_Pow and e.exp.is_negative # division + or (isinstance(e, (log, log2)) and not e.args[0].is_number)) # transcendental + ) +) + +log2const_opt = ReplaceOptim(log(2)*log2(_w), log(_w)) + +logsumexp_2terms_opt = ReplaceOptim( + lambda l: (isinstance(l, log) + and l.args[0].is_Add + and len(l.args[0].args) == 2 + and all(isinstance(t, exp) for t in l.args[0].args)), + lambda l: ( + Max(*[e.args[0] for e in l.args[0].args]) + + log1p(exp(Min(*[e.args[0] for e in l.args[0].args]))) + ) +) + + +class FuncMinusOneOptim(ReplaceOptim): + """Specialization of ReplaceOptim for functions evaluating "f(x) - 1". + + Explanation + =========== + + Numerical functions which go toward one as x go toward zero is often best + implemented by a dedicated function in order to avoid catastrophic + cancellation. One such example is ``expm1(x)`` in the C standard library + which evaluates ``exp(x) - 1``. Such functions preserves many more + significant digits when its argument is much smaller than one, compared + to subtracting one afterwards. + + Parameters + ========== + + func : + The function which is subtracted by one. + func_m_1 : + The specialized function evaluating ``func(x) - 1``. + opportunistic : bool + When ``True``, apply the transformation as long as the magnitude of the + remaining number terms decreases. When ``False``, only apply the + transformation if it completely eliminates the number term. + + Examples + ======== + + >>> from sympy import symbols, exp + >>> from sympy.codegen.rewriting import FuncMinusOneOptim + >>> from sympy.codegen.cfunctions import expm1 + >>> x, y = symbols('x y') + >>> expm1_opt = FuncMinusOneOptim(exp, expm1) + >>> expm1_opt(exp(x) + 2*exp(5*y) - 3) + expm1(x) + 2*expm1(5*y) + + + """ + + def __init__(self, func, func_m_1, opportunistic=True): + weight = 10 # <-- this is an arbitrary number (heuristic) + super().__init__(lambda e: e.is_Add, self.replace_in_Add, + cost_function=lambda expr: expr.count_ops() - weight*expr.count(func_m_1)) + self.func = func + self.func_m_1 = func_m_1 + self.opportunistic = opportunistic + + def _group_Add_terms(self, add): + numbers, non_num = sift(add.args, lambda arg: arg.is_number, binary=True) + numsum = sum(numbers) + terms_with_func, other = sift(non_num, lambda arg: arg.has(self.func), binary=True) + return numsum, terms_with_func, other + + def replace_in_Add(self, e): + """ passed as second argument to Basic.replace(...) """ + numsum, terms_with_func, other_non_num_terms = self._group_Add_terms(e) + if numsum == 0: + return e + substituted, untouched = [], [] + for with_func in terms_with_func: + if with_func.is_Mul: + func, coeff = sift(with_func.args, lambda arg: arg.func == self.func, binary=True) + if len(func) == 1 and len(coeff) == 1: + func, coeff = func[0], coeff[0] + else: + coeff = None + elif with_func.func == self.func: + func, coeff = with_func, S.One + else: + coeff = None + + if coeff is not None and coeff.is_number and sign(coeff) == -sign(numsum): + if self.opportunistic: + do_substitute = abs(coeff+numsum) < abs(numsum) + else: + do_substitute = coeff+numsum == 0 + + if do_substitute: # advantageous substitution + numsum += coeff + substituted.append(coeff*self.func_m_1(*func.args)) + continue + untouched.append(with_func) + + return e.func(numsum, *substituted, *untouched, *other_non_num_terms) + + def __call__(self, expr): + alt1 = super().__call__(expr) + alt2 = super().__call__(expr.factor()) + return self.cheapest(alt1, alt2) + + +expm1_opt = FuncMinusOneOptim(exp, expm1) +cosm1_opt = FuncMinusOneOptim(cos, cosm1) +powm1_opt = FuncMinusOneOptim(Pow, powm1) + +log1p_opt = ReplaceOptim( + lambda e: isinstance(e, log), + lambda l: expand_log(l.replace( + log, lambda arg: log(arg.factor()) + )).replace(log(_u+1), log1p(_u)) +) + +def create_expand_pow_optimization(limit, *, base_req=lambda b: b.is_symbol): + """ Creates an instance of :class:`ReplaceOptim` for expanding ``Pow``. + + Explanation + =========== + + The requirements for expansions are that the base needs to be a symbol + and the exponent needs to be an Integer (and be less than or equal to + ``limit``). + + Parameters + ========== + + limit : int + The highest power which is expanded into multiplication. + base_req : function returning bool + Requirement on base for expansion to happen, default is to return + the ``is_symbol`` attribute of the base. + + Examples + ======== + + >>> from sympy import Symbol, sin + >>> from sympy.codegen.rewriting import create_expand_pow_optimization + >>> x = Symbol('x') + >>> expand_opt = create_expand_pow_optimization(3) + >>> expand_opt(x**5 + x**3) + x**5 + x*x*x + >>> expand_opt(x**5 + x**3 + sin(x)**3) + x**5 + sin(x)**3 + x*x*x + >>> opt2 = create_expand_pow_optimization(3, base_req=lambda b: not b.is_Function) + >>> opt2((x+1)**2 + sin(x)**2) + sin(x)**2 + (x + 1)*(x + 1) + + """ + return ReplaceOptim( + lambda e: e.is_Pow and base_req(e.base) and e.exp.is_Integer and abs(e.exp) <= limit, + lambda p: ( + UnevaluatedExpr(Mul(*([p.base]*+p.exp), evaluate=False)) if p.exp > 0 else + 1/UnevaluatedExpr(Mul(*([p.base]*-p.exp), evaluate=False)) + )) + +# Optimization procedures for turning A**(-1) * x into MatrixSolve(A, x) +def _matinv_predicate(expr): + # TODO: We should be able to support more than 2 elements + if expr.is_MatMul and len(expr.args) == 2: + left, right = expr.args + if left.is_Inverse and right.shape[1] == 1: + inv_arg = left.arg + if isinstance(inv_arg, MatrixSymbol): + return bool(ask(Q.fullrank(left.arg))) + + return False + +def _matinv_transform(expr): + left, right = expr.args + inv_arg = left.arg + return MatrixSolve(inv_arg, right) + + +matinv_opt = ReplaceOptim(_matinv_predicate, _matinv_transform) + + +logaddexp_opt = ReplaceOptim(log(exp(_v)+exp(_w)), logaddexp(_v, _w)) +logaddexp2_opt = ReplaceOptim(log(Pow(2, _v)+Pow(2, _w)), logaddexp2(_v, _w)*log(2)) + +# Collections of optimizations: +optims_c99 = (expm1_opt, log1p_opt, exp2_opt, log2_opt, log2const_opt) + +optims_numpy = optims_c99 + (logaddexp_opt, logaddexp2_opt,) + sinc_opts + +optims_scipy = (cosm1_opt, powm1_opt) diff --git a/evalkit_tf446/lib/python3.10/site-packages/sympy/codegen/tests/__init__.py b/evalkit_tf446/lib/python3.10/site-packages/sympy/codegen/tests/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git 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a/evalkit_tf446/lib/python3.10/site-packages/sympy/codegen/tests/__pycache__/test_scipy_nodes.cpython-310.pyc b/evalkit_tf446/lib/python3.10/site-packages/sympy/codegen/tests/__pycache__/test_scipy_nodes.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..5f08f1bf4b847f67421766787934032cca465362 Binary files /dev/null and b/evalkit_tf446/lib/python3.10/site-packages/sympy/codegen/tests/__pycache__/test_scipy_nodes.cpython-310.pyc differ diff --git a/evalkit_tf446/lib/python3.10/site-packages/sympy/codegen/tests/test_abstract_nodes.py b/evalkit_tf446/lib/python3.10/site-packages/sympy/codegen/tests/test_abstract_nodes.py new file mode 100644 index 0000000000000000000000000000000000000000..89e1f73ff8cb24a4a865aa51304ec66e9901e3cb --- /dev/null +++ b/evalkit_tf446/lib/python3.10/site-packages/sympy/codegen/tests/test_abstract_nodes.py @@ -0,0 +1,14 @@ +from sympy.core.symbol import symbols +from sympy.codegen.abstract_nodes import List + + +def test_List(): + l = List(2, 3, 4) + assert l == List(2, 3, 4) + assert str(l) == "[2, 3, 4]" + x, y, z = symbols('x y z') + l = List(x**2,y**3,z**4) + # contrary to python's built-in list, we can call e.g. "replace" on List. + m = l.replace(lambda arg: arg.is_Pow and arg.exp>2, lambda p: p.base-p.exp) + assert m == [x**2, y-3, z-4] + hash(m) diff --git a/evalkit_tf446/lib/python3.10/site-packages/sympy/codegen/tests/test_algorithms.py b/evalkit_tf446/lib/python3.10/site-packages/sympy/codegen/tests/test_algorithms.py new file mode 100644 index 0000000000000000000000000000000000000000..09446258d461d71e299408555399c7f09fbd8419 --- /dev/null +++ b/evalkit_tf446/lib/python3.10/site-packages/sympy/codegen/tests/test_algorithms.py @@ -0,0 +1,179 @@ +import tempfile +from sympy import log, Min, Max, sqrt +from sympy.core.numbers import Float +from sympy.core.symbol import Symbol, symbols +from sympy.functions.elementary.trigonometric import cos +from sympy.codegen.ast import Assignment, Raise, RuntimeError_, QuotedString +from sympy.codegen.algorithms import newtons_method, newtons_method_function +from sympy.codegen.cfunctions import expm1 +from sympy.codegen.fnodes import bind_C +from sympy.codegen.futils import render_as_module as f_module +from sympy.codegen.pyutils import render_as_module as py_module +from sympy.external import import_module +from sympy.printing.codeprinter import ccode +from sympy.utilities._compilation import compile_link_import_strings, has_c, has_fortran +from sympy.utilities._compilation.util import may_xfail +from sympy.testing.pytest import skip, raises + +cython = import_module('cython') +wurlitzer = import_module('wurlitzer') + +def test_newtons_method(): + x, dx, atol = symbols('x dx atol') + expr = cos(x) - x**3 + algo = newtons_method(expr, x, atol, dx) + assert algo.has(Assignment(dx, -expr/expr.diff(x))) + + +@may_xfail +def test_newtons_method_function__ccode(): + x = Symbol('x', real=True) + expr = cos(x) - x**3 + func = newtons_method_function(expr, x) + + if not cython: + skip("cython not installed.") + if not has_c(): + skip("No C compiler found.") + + compile_kw = {"std": 'c99'} + with tempfile.TemporaryDirectory() as folder: + mod, info = compile_link_import_strings([ + ('newton.c', ('#include \n' + '#include \n') + ccode(func)), + ('_newton.pyx', ("#cython: language_level={}\n".format("3") + + "cdef extern double newton(double)\n" + "def py_newton(x):\n" + " return newton(x)\n")) + ], build_dir=folder, compile_kwargs=compile_kw) + assert abs(mod.py_newton(0.5) - 0.865474033102) < 1e-12 + + +@may_xfail +def test_newtons_method_function__fcode(): + x = Symbol('x', real=True) + expr = cos(x) - x**3 + func = newtons_method_function(expr, x, attrs=[bind_C(name='newton')]) + + if not cython: + skip("cython not installed.") + if not has_fortran(): + skip("No Fortran compiler found.") + + f_mod = f_module([func], 'mod_newton') + with tempfile.TemporaryDirectory() as folder: + mod, info = compile_link_import_strings([ + ('newton.f90', f_mod), + ('_newton.pyx', ("#cython: language_level={}\n".format("3") + + "cdef extern double newton(double*)\n" + "def py_newton(double x):\n" + " return newton(&x)\n")) + ], build_dir=folder) + assert abs(mod.py_newton(0.5) - 0.865474033102) < 1e-12 + + +def test_newtons_method_function__pycode(): + x = Symbol('x', real=True) + expr = cos(x) - x**3 + func = newtons_method_function(expr, x) + py_mod = py_module(func) + namespace = {} + exec(py_mod, namespace, namespace) + res = eval('newton(0.5)', namespace) + assert abs(res - 0.865474033102) < 1e-12 + + +@may_xfail +def test_newtons_method_function__ccode_parameters(): + args = x, A, k, p = symbols('x A k p') + expr = A*cos(k*x) - p*x**3 + raises(ValueError, lambda: newtons_method_function(expr, x)) + use_wurlitzer = wurlitzer + + func = newtons_method_function(expr, x, args, debug=use_wurlitzer) + + if not has_c(): + skip("No C compiler found.") + if not cython: + skip("cython not installed.") + + compile_kw = {"std": 'c99'} + with tempfile.TemporaryDirectory() as folder: + mod, info = compile_link_import_strings([ + ('newton_par.c', ('#include \n' + '#include \n') + ccode(func)), + ('_newton_par.pyx', ("#cython: language_level={}\n".format("3") + + "cdef extern double newton(double, double, double, double)\n" + "def py_newton(x, A=1, k=1, p=1):\n" + " return newton(x, A, k, p)\n")) + ], compile_kwargs=compile_kw, build_dir=folder) + + if use_wurlitzer: + with wurlitzer.pipes() as (out, err): + result = mod.py_newton(0.5) + else: + result = mod.py_newton(0.5) + + assert abs(result - 0.865474033102) < 1e-12 + + if not use_wurlitzer: + skip("C-level output only tested when package 'wurlitzer' is available.") + + out, err = out.read(), err.read() + assert err == '' + assert out == """\ +x= 0.5 +x= 1.1121 d_x= 0.61214 +x= 0.90967 d_x= -0.20247 +x= 0.86726 d_x= -0.042409 +x= 0.86548 d_x= -0.0017867 +x= 0.86547 d_x= -3.1022e-06 +x= 0.86547 d_x= -9.3421e-12 +x= 0.86547 d_x= 3.6902e-17 +""" # try to run tests with LC_ALL=C if this assertion fails + + +def test_newtons_method_function__rtol_cse_nan(): + a, b, c, N_geo, N_tot = symbols('a b c N_geo N_tot', real=True, nonnegative=True) + i = Symbol('i', integer=True, nonnegative=True) + N_ari = N_tot - N_geo - 1 + delta_ari = (c-b)/N_ari + ln_delta_geo = log(b) + log(-expm1((log(a)-log(b))/N_geo)) + eqb_log = ln_delta_geo - log(delta_ari) + + def _clamp(low, expr, high): + return Min(Max(low, expr), high) + + meth_kw = { + 'clamped_newton': {'delta_fn': lambda e, x: _clamp( + (sqrt(a*x)-x)*0.99, + -e/e.diff(x), + (sqrt(c*x)-x)*0.99 + )}, + 'halley': {'delta_fn': lambda e, x: (-2*(e*e.diff(x))/(2*e.diff(x)**2 - e*e.diff(x, 2)))}, + 'halley_alt': {'delta_fn': lambda e, x: (-e/e.diff(x)/(1-e/e.diff(x)*e.diff(x,2)/2/e.diff(x)))}, + } + args = eqb_log, b + for use_cse in [False, True]: + kwargs = { + 'params': (b, a, c, N_geo, N_tot), 'itermax': 60, 'debug': True, 'cse': use_cse, + 'counter': i, 'atol': 1e-100, 'rtol': 2e-16, 'bounds': (a,c), + 'handle_nan': Raise(RuntimeError_(QuotedString("encountered NaN."))) + } + func = {k: newtons_method_function(*args, func_name=f"{k}_b", **dict(kwargs, **kw)) for k, kw in meth_kw.items()} + py_mod = {k: py_module(v) for k, v in func.items()} + namespace = {} + root_find_b = {} + for k, v in py_mod.items(): + ns = namespace[k] = {} + exec(v, ns, ns) + root_find_b[k] = ns[f'{k}_b'] + ref = Float('13.2261515064168768938151923226496') + reftol = {'clamped_newton': 2e-16, 'halley': 2e-16, 'halley_alt': 3e-16} + guess = 4.0 + for meth, func in root_find_b.items(): + result = func(guess, 1e-2, 1e2, 50, 100) + req = ref*reftol[meth] + if use_cse: + req *= 2 + assert abs(result - ref) < req diff --git a/evalkit_tf446/lib/python3.10/site-packages/sympy/codegen/tests/test_applications.py b/evalkit_tf446/lib/python3.10/site-packages/sympy/codegen/tests/test_applications.py new file mode 100644 index 0000000000000000000000000000000000000000..26d5d0f699b947db13b658d793f808d632f67a1a --- /dev/null +++ b/evalkit_tf446/lib/python3.10/site-packages/sympy/codegen/tests/test_applications.py @@ -0,0 +1,57 @@ +# This file contains tests that exercise multiple AST nodes + +import tempfile + +from sympy.external import import_module +from sympy.printing.codeprinter import ccode +from sympy.utilities._compilation import compile_link_import_strings, has_c +from sympy.utilities._compilation.util import may_xfail +from sympy.testing.pytest import skip +from sympy.codegen.ast import ( + FunctionDefinition, FunctionPrototype, Variable, Pointer, real, Assignment, + integer, CodeBlock, While +) +from sympy.codegen.cnodes import void, PreIncrement +from sympy.codegen.cutils import render_as_source_file + +cython = import_module('cython') +np = import_module('numpy') + +def _mk_func1(): + declars = n, inp, out = Variable('n', integer), Pointer('inp', real), Pointer('out', real) + i = Variable('i', integer) + whl = While(i2, lambda p: p.base-p.exp) + assert m == [x**2, y-3, z-4] diff --git a/evalkit_tf446/lib/python3.10/site-packages/sympy/codegen/tests/test_pyutils.py b/evalkit_tf446/lib/python3.10/site-packages/sympy/codegen/tests/test_pyutils.py new file mode 100644 index 0000000000000000000000000000000000000000..0a2f0ff358f333635c8d44195a5c39d63ac8f16f --- /dev/null +++ b/evalkit_tf446/lib/python3.10/site-packages/sympy/codegen/tests/test_pyutils.py @@ -0,0 +1,7 @@ +from sympy.codegen.ast import Print +from sympy.codegen.pyutils import render_as_module + +def test_standard(): + ast = Print('x y'.split(), r"coordinate: %12.5g %12.5g\n") + assert render_as_module(ast, standard='python3') == \ + '\n\nprint("coordinate: %12.5g %12.5g\\n" % (x, y), end="")' diff --git a/evalkit_tf446/lib/python3.10/site-packages/sympy/codegen/tests/test_rewriting.py b/evalkit_tf446/lib/python3.10/site-packages/sympy/codegen/tests/test_rewriting.py new file mode 100644 index 0000000000000000000000000000000000000000..51e0c9ecc940f60186cc04d4bf15650281d31cd8 --- /dev/null +++ b/evalkit_tf446/lib/python3.10/site-packages/sympy/codegen/tests/test_rewriting.py @@ -0,0 +1,479 @@ +import tempfile +from sympy.core.numbers import pi, Rational +from sympy.core.power import Pow +from sympy.core.singleton import S +from sympy.core.symbol import Symbol +from sympy.functions.elementary.complexes import Abs +from sympy.functions.elementary.exponential import (exp, log) +from sympy.functions.elementary.trigonometric import (cos, sin, sinc) +from sympy.matrices.expressions.matexpr import MatrixSymbol +from sympy.assumptions import assuming, Q +from sympy.external import import_module +from sympy.printing.codeprinter import ccode +from sympy.codegen.matrix_nodes import MatrixSolve +from sympy.codegen.cfunctions import log2, exp2, expm1, log1p +from sympy.codegen.numpy_nodes import logaddexp, logaddexp2 +from sympy.codegen.scipy_nodes import cosm1, powm1 +from sympy.codegen.rewriting import ( + optimize, cosm1_opt, log2_opt, exp2_opt, expm1_opt, log1p_opt, powm1_opt, optims_c99, + create_expand_pow_optimization, matinv_opt, logaddexp_opt, logaddexp2_opt, + optims_numpy, optims_scipy, sinc_opts, FuncMinusOneOptim +) +from sympy.testing.pytest import XFAIL, skip +from sympy.utilities import lambdify +from sympy.utilities._compilation import compile_link_import_strings, has_c +from sympy.utilities._compilation.util import may_xfail + +cython = import_module('cython') +numpy = import_module('numpy') +scipy = import_module('scipy') + + +def test_log2_opt(): + x = Symbol('x') + expr1 = 7*log(3*x + 5)/(log(2)) + opt1 = optimize(expr1, [log2_opt]) + assert opt1 == 7*log2(3*x + 5) + assert opt1.rewrite(log) == expr1 + + expr2 = 3*log(5*x + 7)/(13*log(2)) + opt2 = optimize(expr2, [log2_opt]) + assert opt2 == 3*log2(5*x + 7)/13 + assert opt2.rewrite(log) == expr2 + + expr3 = log(x)/log(2) + opt3 = optimize(expr3, [log2_opt]) + assert opt3 == log2(x) + assert opt3.rewrite(log) == expr3 + + expr4 = log(x)/log(2) + log(x+1) + opt4 = optimize(expr4, [log2_opt]) + assert opt4 == log2(x) + log(2)*log2(x+1) + assert opt4.rewrite(log) == expr4 + + expr5 = log(17) + opt5 = optimize(expr5, [log2_opt]) + assert opt5 == expr5 + + expr6 = log(x + 3)/log(2) + opt6 = optimize(expr6, [log2_opt]) + assert str(opt6) == 'log2(x + 3)' + assert opt6.rewrite(log) == expr6 + + +def test_exp2_opt(): + x = Symbol('x') + expr1 = 1 + 2**x + opt1 = optimize(expr1, [exp2_opt]) + assert opt1 == 1 + exp2(x) + assert opt1.rewrite(Pow) == expr1 + + expr2 = 1 + 3**x + assert expr2 == optimize(expr2, [exp2_opt]) + + +def test_expm1_opt(): + x = Symbol('x') + + expr1 = exp(x) - 1 + opt1 = optimize(expr1, [expm1_opt]) + assert expm1(x) - opt1 == 0 + assert opt1.rewrite(exp) == expr1 + + expr2 = 3*exp(x) - 3 + opt2 = optimize(expr2, [expm1_opt]) + assert 3*expm1(x) == opt2 + assert opt2.rewrite(exp) == expr2 + + expr3 = 3*exp(x) - 5 + opt3 = optimize(expr3, [expm1_opt]) + assert 3*expm1(x) - 2 == opt3 + assert opt3.rewrite(exp) == expr3 + expm1_opt_non_opportunistic = FuncMinusOneOptim(exp, expm1, opportunistic=False) + assert expr3 == optimize(expr3, [expm1_opt_non_opportunistic]) + assert opt1 == optimize(expr1, [expm1_opt_non_opportunistic]) + assert opt2 == optimize(expr2, [expm1_opt_non_opportunistic]) + + expr4 = 3*exp(x) + log(x) - 3 + opt4 = optimize(expr4, [expm1_opt]) + assert 3*expm1(x) + log(x) == opt4 + assert opt4.rewrite(exp) == expr4 + + expr5 = 3*exp(2*x) - 3 + opt5 = optimize(expr5, [expm1_opt]) + assert 3*expm1(2*x) == opt5 + assert opt5.rewrite(exp) == expr5 + + expr6 = (2*exp(x) + 1)/(exp(x) + 1) + 1 + opt6 = optimize(expr6, [expm1_opt]) + assert opt6.count_ops() <= expr6.count_ops() + + def ev(e): + return e.subs(x, 3).evalf() + assert abs(ev(expr6) - ev(opt6)) < 1e-15 + + y = Symbol('y') + expr7 = (2*exp(x) - 1)/(1 - exp(y)) - 1/(1-exp(y)) + opt7 = optimize(expr7, [expm1_opt]) + assert -2*expm1(x)/expm1(y) == opt7 + assert (opt7.rewrite(exp) - expr7).factor() == 0 + + expr8 = (1+exp(x))**2 - 4 + opt8 = optimize(expr8, [expm1_opt]) + tgt8a = (exp(x) + 3)*expm1(x) + tgt8b = 2*expm1(x) + expm1(2*x) + # Both tgt8a & tgt8b seem to give full precision (~16 digits for double) + # for x=1e-7 (compare with expr8 which only achieves ~8 significant digits). + # If we can show that either tgt8a or tgt8b is preferable, we can + # change this test to ensure the preferable version is returned. + assert (tgt8a - tgt8b).rewrite(exp).factor() == 0 + assert opt8 in (tgt8a, tgt8b) + assert (opt8.rewrite(exp) - expr8).factor() == 0 + + expr9 = sin(expr8) + opt9 = optimize(expr9, [expm1_opt]) + tgt9a = sin(tgt8a) + tgt9b = sin(tgt8b) + assert opt9 in (tgt9a, tgt9b) + assert (opt9.rewrite(exp) - expr9.rewrite(exp)).factor().is_zero + + +def test_expm1_two_exp_terms(): + x, y = map(Symbol, 'x y'.split()) + expr1 = exp(x) + exp(y) - 2 + opt1 = optimize(expr1, [expm1_opt]) + assert opt1 == expm1(x) + expm1(y) + + +def test_cosm1_opt(): + x = Symbol('x') + + expr1 = cos(x) - 1 + opt1 = optimize(expr1, [cosm1_opt]) + assert cosm1(x) - opt1 == 0 + assert opt1.rewrite(cos) == expr1 + + expr2 = 3*cos(x) - 3 + opt2 = optimize(expr2, [cosm1_opt]) + assert 3*cosm1(x) == opt2 + assert opt2.rewrite(cos) == expr2 + + expr3 = 3*cos(x) - 5 + opt3 = optimize(expr3, [cosm1_opt]) + assert 3*cosm1(x) - 2 == opt3 + assert opt3.rewrite(cos) == expr3 + cosm1_opt_non_opportunistic = FuncMinusOneOptim(cos, cosm1, opportunistic=False) + assert expr3 == optimize(expr3, [cosm1_opt_non_opportunistic]) + assert opt1 == optimize(expr1, [cosm1_opt_non_opportunistic]) + assert opt2 == optimize(expr2, [cosm1_opt_non_opportunistic]) + + expr4 = 3*cos(x) + log(x) - 3 + opt4 = optimize(expr4, [cosm1_opt]) + assert 3*cosm1(x) + log(x) == opt4 + assert opt4.rewrite(cos) == expr4 + + expr5 = 3*cos(2*x) - 3 + opt5 = optimize(expr5, [cosm1_opt]) + assert 3*cosm1(2*x) == opt5 + assert opt5.rewrite(cos) == expr5 + + expr6 = 2 - 2*cos(x) + opt6 = optimize(expr6, [cosm1_opt]) + assert -2*cosm1(x) == opt6 + assert opt6.rewrite(cos) == expr6 + + +def test_cosm1_two_cos_terms(): + x, y = map(Symbol, 'x y'.split()) + expr1 = cos(x) + cos(y) - 2 + opt1 = optimize(expr1, [cosm1_opt]) + assert opt1 == cosm1(x) + cosm1(y) + + +def test_expm1_cosm1_mixed(): + x = Symbol('x') + expr1 = exp(x) + cos(x) - 2 + opt1 = optimize(expr1, [expm1_opt, cosm1_opt]) + assert opt1 == cosm1(x) + expm1(x) + + +def _check_num_lambdify(expr, opt, val_subs, approx_ref, lambdify_kw=None, poorness=1e10): + """ poorness=1e10 signifies that `expr` loses precision of at least ten decimal digits. """ + num_ref = expr.subs(val_subs).evalf() + eps = numpy.finfo(numpy.float64).eps + assert abs(num_ref - approx_ref) < approx_ref*eps + f1 = lambdify(list(val_subs.keys()), opt, **(lambdify_kw or {})) + args_float = tuple(map(float, val_subs.values())) + num_err1 = abs(f1(*args_float) - approx_ref) + assert num_err1 < abs(num_ref*eps) + f2 = lambdify(list(val_subs.keys()), expr, **(lambdify_kw or {})) + num_err2 = abs(f2(*args_float) - approx_ref) + assert num_err2 > abs(num_ref*eps*poorness) # this only ensures that the *test* works as intended + + +def test_cosm1_apart(): + x = Symbol('x') + + expr1 = 1/cos(x) - 1 + opt1 = optimize(expr1, [cosm1_opt]) + assert opt1 == -cosm1(x)/cos(x) + if scipy: + _check_num_lambdify(expr1, opt1, {x: S(10)**-30}, 5e-61, lambdify_kw={"modules": 'scipy'}) + + expr2 = 2/cos(x) - 2 + opt2 = optimize(expr2, optims_scipy) + assert opt2 == -2*cosm1(x)/cos(x) + if scipy: + _check_num_lambdify(expr2, opt2, {x: S(10)**-30}, 1e-60, lambdify_kw={"modules": 'scipy'}) + + expr3 = pi/cos(3*x) - pi + opt3 = optimize(expr3, [cosm1_opt]) + assert opt3 == -pi*cosm1(3*x)/cos(3*x) + if scipy: + _check_num_lambdify(expr3, opt3, {x: S(10)**-30/3}, float(5e-61*pi), lambdify_kw={"modules": 'scipy'}) + + +def test_powm1(): + args = x, y = map(Symbol, "xy") + + expr1 = x**y - 1 + opt1 = optimize(expr1, [powm1_opt]) + assert opt1 == powm1(x, y) + for arg in args: + assert expr1.diff(arg) == opt1.diff(arg) + if scipy and tuple(map(int, scipy.version.version.split('.')[:3])) >= (1, 10, 0): + subs1_a = {x: Rational(*(1.0+1e-13).as_integer_ratio()), y: pi} + ref1_f64_a = 3.139081648208105e-13 + _check_num_lambdify(expr1, opt1, subs1_a, ref1_f64_a, lambdify_kw={"modules": 'scipy'}, poorness=10**11) + + subs1_b = {x: pi, y: Rational(*(1e-10).as_integer_ratio())} + ref1_f64_b = 1.1447298859149205e-10 + _check_num_lambdify(expr1, opt1, subs1_b, ref1_f64_b, lambdify_kw={"modules": 'scipy'}, poorness=10**9) + + +def test_log1p_opt(): + x = Symbol('x') + expr1 = log(x + 1) + opt1 = optimize(expr1, [log1p_opt]) + assert log1p(x) - opt1 == 0 + assert opt1.rewrite(log) == expr1 + + expr2 = log(3*x + 3) + opt2 = optimize(expr2, [log1p_opt]) + assert log1p(x) + log(3) == opt2 + assert (opt2.rewrite(log) - expr2).simplify() == 0 + + expr3 = log(2*x + 1) + opt3 = optimize(expr3, [log1p_opt]) + assert log1p(2*x) - opt3 == 0 + assert opt3.rewrite(log) == expr3 + + expr4 = log(x+3) + opt4 = optimize(expr4, [log1p_opt]) + assert str(opt4) == 'log(x + 3)' + + +def test_optims_c99(): + x = Symbol('x') + + expr1 = 2**x + log(x)/log(2) + log(x + 1) + exp(x) - 1 + opt1 = optimize(expr1, optims_c99).simplify() + assert opt1 == exp2(x) + log2(x) + log1p(x) + expm1(x) + assert opt1.rewrite(exp).rewrite(log).rewrite(Pow) == expr1 + + expr2 = log(x)/log(2) + log(x + 1) + opt2 = optimize(expr2, optims_c99) + assert opt2 == log2(x) + log1p(x) + assert opt2.rewrite(log) == expr2 + + expr3 = log(x)/log(2) + log(17*x + 17) + opt3 = optimize(expr3, optims_c99) + delta3 = opt3 - (log2(x) + log(17) + log1p(x)) + assert delta3 == 0 + assert (opt3.rewrite(log) - expr3).simplify() == 0 + + expr4 = 2**x + 3*log(5*x + 7)/(13*log(2)) + 11*exp(x) - 11 + log(17*x + 17) + opt4 = optimize(expr4, optims_c99).simplify() + delta4 = opt4 - (exp2(x) + 3*log2(5*x + 7)/13 + 11*expm1(x) + log(17) + log1p(x)) + assert delta4 == 0 + assert (opt4.rewrite(exp).rewrite(log).rewrite(Pow) - expr4).simplify() == 0 + + expr5 = 3*exp(2*x) - 3 + opt5 = optimize(expr5, optims_c99) + delta5 = opt5 - 3*expm1(2*x) + assert delta5 == 0 + assert opt5.rewrite(exp) == expr5 + + expr6 = exp(2*x) - 3 + opt6 = optimize(expr6, optims_c99) + assert opt6 in (expm1(2*x) - 2, expr6) # expm1(2*x) - 2 is not better or worse + + expr7 = log(3*x + 3) + opt7 = optimize(expr7, optims_c99) + delta7 = opt7 - (log(3) + log1p(x)) + assert delta7 == 0 + assert (opt7.rewrite(log) - expr7).simplify() == 0 + + expr8 = log(2*x + 3) + opt8 = optimize(expr8, optims_c99) + assert opt8 == expr8 + + +def test_create_expand_pow_optimization(): + cc = lambda x: ccode( + optimize(x, [create_expand_pow_optimization(4)])) + x = Symbol('x') + assert cc(x**4) == 'x*x*x*x' + assert cc(x**4 + x**2) == 'x*x + x*x*x*x' + assert cc(x**5 + x**4) == 'pow(x, 5) + x*x*x*x' + assert cc(sin(x)**4) == 'pow(sin(x), 4)' + # gh issue 15335 + assert cc(x**(-4)) == '1.0/(x*x*x*x)' + assert cc(x**(-5)) == 'pow(x, -5)' + assert cc(-x**4) == '-(x*x*x*x)' + assert cc(x**4 - x**2) == '-(x*x) + x*x*x*x' + i = Symbol('i', integer=True) + assert cc(x**i - x**2) == 'pow(x, i) - (x*x)' + y = Symbol('y', real=True) + assert cc(Abs(exp(y**4))) == "exp(y*y*y*y)" + + # gh issue 20753 + cc2 = lambda x: ccode(optimize(x, [create_expand_pow_optimization( + 4, base_req=lambda b: b.is_Function)])) + assert cc2(x**3 + sin(x)**3) == "pow(x, 3) + sin(x)*sin(x)*sin(x)" + + +def test_matsolve(): + n = Symbol('n', integer=True) + A = MatrixSymbol('A', n, n) + x = MatrixSymbol('x', n, 1) + + with assuming(Q.fullrank(A)): + assert optimize(A**(-1) * x, [matinv_opt]) == MatrixSolve(A, x) + assert optimize(A**(-1) * x + x, [matinv_opt]) == MatrixSolve(A, x) + x + + +def test_logaddexp_opt(): + x, y = map(Symbol, 'x y'.split()) + expr1 = log(exp(x) + exp(y)) + opt1 = optimize(expr1, [logaddexp_opt]) + assert logaddexp(x, y) - opt1 == 0 + assert logaddexp(y, x) - opt1 == 0 + assert opt1.rewrite(log) == expr1 + + +def test_logaddexp2_opt(): + x, y = map(Symbol, 'x y'.split()) + expr1 = log(2**x + 2**y)/log(2) + opt1 = optimize(expr1, [logaddexp2_opt]) + assert logaddexp2(x, y) - opt1 == 0 + assert logaddexp2(y, x) - opt1 == 0 + assert opt1.rewrite(log) == expr1 + + +def test_sinc_opts(): + def check(d): + for k, v in d.items(): + assert optimize(k, sinc_opts) == v + + x = Symbol('x') + check({ + sin(x)/x : sinc(x), + sin(2*x)/(2*x) : sinc(2*x), + sin(3*x)/x : 3*sinc(3*x), + x*sin(x) : x*sin(x) + }) + + y = Symbol('y') + check({ + sin(x*y)/(x*y) : sinc(x*y), + y*sin(x/y)/x : sinc(x/y), + sin(sin(x))/sin(x) : sinc(sin(x)), + sin(3*sin(x))/sin(x) : 3*sinc(3*sin(x)), + sin(x)/y : sin(x)/y + }) + + +def test_optims_numpy(): + def check(d): + for k, v in d.items(): + assert optimize(k, optims_numpy) == v + + x = Symbol('x') + check({ + sin(2*x)/(2*x) + exp(2*x) - 1: sinc(2*x) + expm1(2*x), + log(x+3)/log(2) + log(x**2 + 1): log1p(x**2) + log2(x+3) + }) + + +@XFAIL # room for improvement, ideally this test case should pass. +def test_optims_numpy_TODO(): + def check(d): + for k, v in d.items(): + assert optimize(k, optims_numpy) == v + + x, y = map(Symbol, 'x y'.split()) + check({ + log(x*y)*sin(x*y)*log(x*y+1)/(log(2)*x*y): log2(x*y)*sinc(x*y)*log1p(x*y), + exp(x*sin(y)/y) - 1: expm1(x*sinc(y)) + }) + + +@may_xfail +def test_compiled_ccode_with_rewriting(): + if not cython: + skip("cython not installed.") + if not has_c(): + skip("No C compiler found.") + + x = Symbol('x') + about_two = 2**(58/S(117))*3**(97/S(117))*5**(4/S(39))*7**(92/S(117))/S(30)*pi + # about_two: 1.999999999999581826 + unchanged = 2*exp(x) - about_two + xval = S(10)**-11 + ref = unchanged.subs(x, xval).n(19) # 2.0418173913673213e-11 + + rewritten = optimize(2*exp(x) - about_two, [expm1_opt]) + + # Unfortunately, we need to call ``.n()`` on our expressions before we hand them + # to ``ccode``, and we need to request a large number of significant digits. + # In this test, results converged for double precision when the following number + # of significant digits were chosen: + NUMBER_OF_DIGITS = 25 # TODO: this should ideally be automatically handled. + + func_c = ''' +#include + +double func_unchanged(double x) { + return %(unchanged)s; +} +double func_rewritten(double x) { + return %(rewritten)s; +} +''' % {"unchanged": ccode(unchanged.n(NUMBER_OF_DIGITS)), + "rewritten": ccode(rewritten.n(NUMBER_OF_DIGITS))} + + func_pyx = ''' +#cython: language_level=3 +cdef extern double func_unchanged(double) +cdef extern double func_rewritten(double) +def py_unchanged(x): + return func_unchanged(x) +def py_rewritten(x): + return func_rewritten(x) +''' + with tempfile.TemporaryDirectory() as folder: + mod, info = compile_link_import_strings( + [('func.c', func_c), ('_func.pyx', func_pyx)], + build_dir=folder, compile_kwargs={"std": 'c99'} + ) + err_rewritten = abs(mod.py_rewritten(1e-11) - ref) + err_unchanged = abs(mod.py_unchanged(1e-11) - ref) + assert 1e-27 < err_rewritten < 1e-25 # highly accurate. + assert 1e-19 < err_unchanged < 1e-16 # quite poor. + + # Tolerances used above were determined as follows: + # >>> no_opt = unchanged.subs(x, xval.evalf()).evalf() + # >>> with_opt = rewritten.n(25).subs(x, 1e-11).evalf() + # >>> with_opt - ref, no_opt - ref + # (1.1536301877952077e-26, 1.6547074214222335e-18) diff --git a/evalkit_tf446/lib/python3.10/site-packages/sympy/codegen/tests/test_scipy_nodes.py b/evalkit_tf446/lib/python3.10/site-packages/sympy/codegen/tests/test_scipy_nodes.py new file mode 100644 index 0000000000000000000000000000000000000000..c0d1461037eec81ade0c99b18fbbf5a4517ce0b7 --- /dev/null +++ b/evalkit_tf446/lib/python3.10/site-packages/sympy/codegen/tests/test_scipy_nodes.py @@ -0,0 +1,44 @@ +from itertools import product +from sympy.core.power import Pow +from sympy.core.symbol import symbols +from sympy.functions.elementary.exponential import exp, log +from sympy.functions.elementary.trigonometric import cos +from sympy.core.numbers import pi +from sympy.codegen.scipy_nodes import cosm1, powm1 + +x, y, z = symbols('x y z') + + +def test_cosm1(): + cm1_xy = cosm1(x*y) + ref_xy = cos(x*y) - 1 + for wrt, deriv_order in product([x, y, z], range(3)): + assert ( + cm1_xy.diff(wrt, deriv_order) - + ref_xy.diff(wrt, deriv_order) + ).rewrite(cos).simplify() == 0 + + expr_minus2 = cosm1(pi) + assert expr_minus2.rewrite(cos) == -2 + assert cosm1(3.14).simplify() == cosm1(3.14) # cannot simplify with 3.14 + assert cosm1(pi/2).simplify() == -1 + assert (1/cos(x) - 1 + cosm1(x)/cos(x)).simplify() == 0 + + +def test_powm1(): + cases = { + powm1(x, y): x**y - 1, + powm1(x*y, z): (x*y)**z - 1, + powm1(x, y*z): x**(y*z)-1, + powm1(x*y*z, x*y*z): (x*y*z)**(x*y*z)-1 + } + for pm1_e, ref_e in cases.items(): + for wrt, deriv_order in product([x, y, z], range(3)): + der = pm1_e.diff(wrt, deriv_order) + ref = ref_e.diff(wrt, deriv_order) + delta = (der - ref).rewrite(Pow) + assert delta.simplify() == 0 + + eulers_constant_m1 = powm1(x, 1/log(x)) + assert eulers_constant_m1.rewrite(Pow) == exp(1) - 1 + assert eulers_constant_m1.simplify() == exp(1) - 1