Inspired by this ask.sagemath.org question
<https://ask.sagemath.org/question/65949/problem-with-solving-equation-and-finding-the-maximum-and-minimum/>.
Let
sage: f = x^2*sin(x) - cos(x)*e^(-x) + log(x^2 + 1) - log(sqrt(1991))
Then, one would may like to accelerate f evaluation via cythonization. but :
sage: cf=cython_lambda('double x', f)
---------------------------------------------------------------------------
CompileError Traceback (most recent call last) File
/usr/local/sage-9/src/sage/misc/cython.py:358, in cython(filename, verbose,
compile_message, use_cache, create_local_c_file, annotate, sage_namespace,
create_local_so_file) 357 with cython_namespace_package_support(): --> 358
ext, = cythonize([ext], 359 aliases=aliases, 360 include_path=includes, 361
compiler_directives=directives, 362 quiet=(verbose <= 0), 363
errors_to_stderr=False, 364 use_listing_file=True) 365 finally: 366 # Read
the "listing file" which is the file containing 367 # warning and error
messages generated by Cython. File
/usr/local/sage-9/local/var/lib/sage/venv-python3.10/lib/python3.10/site-packages/Cython/Build/Dependencies.py:1127,
in cythonize(module_list, exclude, nthreads, aliases, quiet, force,
language, exclude_failures, **options) 1126 for args in to_compile: -> 1127
cythonize_one(*args) 1129 if exclude_failures: File
/usr/local/sage-9/local/var/lib/sage/venv-python3.10/lib/python3.10/site-packages/Cython/Build/Dependencies.py:1250,
in cythonize_one(pyx_file, c_file, fingerprint, quiet, options,
raise_on_failure, embedded_metadata, full_module_name, progress) 1249 if
raise_on_failure: -> 1250 raise CompileError(None, pyx_file) 1251 elif
os.path.exists(c_file): CompileError:
/tmp/tmpx6ekg9s7/spyx/_tmp_tmpgo2z5pbk_tmp_q3q1r4on_pyx/_tmp_tmpgo2z5pbk_tmp_q3q1r4on_pyx_0.pyx
During handling of the above exception, another exception occurred:
RuntimeError Traceback (most recent call last) Cell In [40], line 1 ----> 1
cf=cython_lambda('double x', f) File
/usr/local/sage-9/src/sage/misc/lazy_import.pyx:402, in
sage.misc.lazy_import.LazyImport.__call__() 400 True 401 """ --> 402 return
self.get_object()(*args, **kwds) 403 404 def __repr__(self): File
/usr/local/sage-9/src/sage/misc/cython.py:510, in cython_lambda(vars, expr,
verbose, **kwds) 507 f.write(s) 509 d = {} --> 510
cython_import_all(tmpfile, d, verbose=verbose, **kwds) 511 return d['f']
File /usr/local/sage-9/src/sage/misc/cython.py:563, in
cython_import_all(filename, globals, **kwds) 548 def
cython_import_all(filename, globals, **kwds): 549 """ 550 Imports all
non-private (i.e., not beginning with an underscore) 551 attributes of the
specified Cython module into the given context. (...) 561 code 562 """ -->
563 m = cython_import(filename, **kwds) 564 for k, x in m.__dict__.items():
565 if k[0] != '_': File /usr/local/sage-9/src/sage/misc/cython.py:534, in
cython_import(filename, **kwds) 517 def cython_import(filename, **kwds):
518 """ 519 Compile a file containing Cython code, then import and return
the 520 module. Raises an ``ImportError`` if anything goes wrong. (...) 532
- the module that contains the compiled Cython code. 533 """ --> 534 name,
build_dir = cython(filename, **kwds) 536 oldpath = sys.path 537 try: File
/usr/local/sage-9/src/sage/misc/cython.py:374, in cython(filename, verbose,
compile_message, use_cache, create_local_c_file, annotate, sage_namespace,
create_local_so_file) 372 cython_messages = "Error compiling Cython file"
373 except CompileError: --> 374 raise
RuntimeError(cython_messages.strip()) 376 if verbose >= 0: 377
sys.stderr.write(cython_messages) RuntimeError: Error compiling Cython
file: ------------------------------------------------------------ ...
raise NameError("global {!r} is not defined".format(name)) sage = _s() def
f(double x): return x^2*sin(x) - cos(x)*e^(-x) + log(x^2 + 1) -
log(sqrt(1991)) ^
------------------------------------------------------------
_tmp_tmpgo2z5pbk_tmp_q3q1r4on_pyx_0.pyx:18:15: undeclared name not builtin:
sin Error compiling Cython file:
------------------------------------------------------------ ... raise
NameError("global {!r} is not defined".format(name)) sage = _s() def
f(double x): return x^2*sin(x) - cos(x)*e^(-x) + log(x^2 + 1) -
log(sqrt(1991)) ^
------------------------------------------------------------
_tmp_tmpgo2z5pbk_tmp_q3q1r4on_pyx_0.pyx:18:24: undeclared name not builtin:
cos Error compiling Cython file:
------------------------------------------------------------ ... raise
NameError("global {!r} is not defined".format(name)) sage = _s() def
f(double x): return x^2*sin(x) - cos(x)*e^(-x) + log(x^2 + 1) -
log(sqrt(1991)) ^
------------------------------------------------------------
_tmp_tmpgo2z5pbk_tmp_q3q1r4on_pyx_0.pyx:18:31: undeclared name not builtin:
e Error compiling Cython file:
------------------------------------------------------------ ... raise
NameError("global {!r} is not defined".format(name)) sage = _s() def
f(double x): return x^2*sin(x) - cos(x)*e^(-x) + log(x^2 + 1) -
log(sqrt(1991)) ^
------------------------------------------------------------
_tmp_tmpgo2z5pbk_tmp_q3q1r4on_pyx_0.pyx:18:40: undeclared name not builtin:
log Error compiling Cython file:
------------------------------------------------------------ ... raise
NameError("global {!r} is not defined".format(name)) sage = _s() def
f(double x): return x^2*sin(x) - cos(x)*e^(-x) + log(x^2 + 1) -
log(sqrt(1991)) ^
------------------------------------------------------------
_tmp_tmpgo2z5pbk_tmp_q3q1r4on_pyx_0.pyx:18:45: Invalid operand types for
'^' (double; long) Error compiling Cython file:
------------------------------------------------------------ ... raise
NameError("global {!r} is not defined".format(name)) sage = _s() def
f(double x): return x^2*sin(x) - cos(x)*e^(-x) + log(x^2 + 1) -
log(sqrt(1991)) ^
------------------------------------------------------------
_tmp_tmpgo2z5pbk_tmp_q3q1r4on_pyx_0.pyx:18:59: undeclared name not builtin:
sqrt
Similarly :
sage: cf=cython_lambda('double x', preparse(str(f)))
---------------------------------------------------------------------------
CompileError Traceback (most recent call last) File
/usr/local/sage-9/src/sage/misc/cython.py:358, in cython(filename, verbose,
compile_message, use_cache, create_local_c_file, annotate, sage_namespace,
create_local_so_file) 357 with cython_namespace_package_support(): --> 358
ext, = cythonize([ext], 359 aliases=aliases, 360 include_path=includes, 361
compiler_directives=directives, 362 quiet=(verbose <= 0), 363
errors_to_stderr=False, 364 use_listing_file=True) 365 finally: 366 # Read
the "listing file" which is the file containing 367 # warning and error
messages generated by Cython. File
/usr/local/sage-9/local/var/lib/sage/venv-python3.10/lib/python3.10/site-packages/Cython/Build/Dependencies.py:1127,
in cythonize(module_list, exclude, nthreads, aliases, quiet, force,
language, exclude_failures, **options) 1126 for args in to_compile: -> 1127
cythonize_one(*args) 1129 if exclude_failures: File
/usr/local/sage-9/local/var/lib/sage/venv-python3.10/lib/python3.10/site-packages/Cython/Build/Dependencies.py:1250,
in cythonize_one(pyx_file, c_file, fingerprint, quiet, options,
raise_on_failure, embedded_metadata, full_module_name, progress) 1249 if
raise_on_failure: -> 1250 raise CompileError(None, pyx_file) 1251 elif
os.path.exists(c_file): CompileError:
/tmp/tmpx6ekg9s7/spyx/_tmp_tmpgo2z5pbk_tmp_9kfdyg6w_pyx/_tmp_tmpgo2z5pbk_tmp_9kfdyg6w_pyx_0.pyx
During handling of the above exception, another exception occurred:
RuntimeError Traceback (most recent call last) Cell In [42], line 1 ----> 1
cf=cython_lambda('double x', preparse(str(f))) File
/usr/local/sage-9/src/sage/misc/lazy_import.pyx:402, in
sage.misc.lazy_import.LazyImport.__call__() 400 True 401 """ --> 402 return
self.get_object()(*args, **kwds) 403 404 def __repr__(self): File
/usr/local/sage-9/src/sage/misc/cython.py:510, in cython_lambda(vars, expr,
verbose, **kwds) 507 f.write(s) 509 d = {} --> 510
cython_import_all(tmpfile, d, verbose=verbose, **kwds) 511 return d['f']
File /usr/local/sage-9/src/sage/misc/cython.py:563, in
cython_import_all(filename, globals, **kwds) 548 def
cython_import_all(filename, globals, **kwds): 549 """ 550 Imports all
non-private (i.e., not beginning with an underscore) 551 attributes of the
specified Cython module into the given context. (...) 561 code 562 """ -->
563 m = cython_import(filename, **kwds) 564 for k, x in m.__dict__.items():
565 if k[0] != '_': File /usr/local/sage-9/src/sage/misc/cython.py:534, in
cython_import(filename, **kwds) 517 def cython_import(filename, **kwds):
518 """ 519 Compile a file containing Cython code, then import and return
the 520 module. Raises an ``ImportError`` if anything goes wrong. (...) 532
- the module that contains the compiled Cython code. 533 """ --> 534 name,
build_dir = cython(filename, **kwds) 536 oldpath = sys.path 537 try: File
/usr/local/sage-9/src/sage/misc/cython.py:374, in cython(filename, verbose,
compile_message, use_cache, create_local_c_file, annotate, sage_namespace,
create_local_so_file) 372 cython_messages = "Error compiling Cython file"
373 except CompileError: --> 374 raise
RuntimeError(cython_messages.strip()) 376 if verbose >= 0: 377
sys.stderr.write(cython_messages) RuntimeError: Error compiling Cython
file: ------------------------------------------------------------ ...
raise NameError("global {!r} is not defined".format(name)) sage = _s() def
f(double x): return x**Integer(2)*sin(x) - cos(x)*e**(-x) +
log(x**Integer(2) + Integer(1)) - log(sqrt(Integer(1991))) ^
------------------------------------------------------------
_tmp_tmpgo2z5pbk_tmp_9kfdyg6w_pyx_0.pyx:18:14: undeclared name not builtin:
Integer Error compiling Cython file:
------------------------------------------------------------ ... raise
NameError("global {!r} is not defined".format(name)) sage = _s() def
f(double x): return x**Integer(2)*sin(x) - cos(x)*e**(-x) +
log(x**Integer(2) + Integer(1)) - log(sqrt(Integer(1991))) ^
------------------------------------------------------------
_tmp_tmpgo2z5pbk_tmp_9kfdyg6w_pyx_0.pyx:18:25: undeclared name not builtin:
sin Error compiling Cython file:
------------------------------------------------------------ ... raise
NameError("global {!r} is not defined".format(name)) sage = _s() def
f(double x): return x**Integer(2)*sin(x) - cos(x)*e**(-x) +
log(x**Integer(2) + Integer(1)) - log(sqrt(Integer(1991))) ^
------------------------------------------------------------
_tmp_tmpgo2z5pbk_tmp_9kfdyg6w_pyx_0.pyx:18:34: undeclared name not builtin:
cos Error compiling Cython file:
------------------------------------------------------------ ... raise
NameError("global {!r} is not defined".format(name)) sage = _s() def
f(double x): return x**Integer(2)*sin(x) - cos(x)*e**(-x) +
log(x**Integer(2) + Integer(1)) - log(sqrt(Integer(1991))) ^
------------------------------------------------------------
_tmp_tmpgo2z5pbk_tmp_9kfdyg6w_pyx_0.pyx:18:41: undeclared name not builtin:
e Error compiling Cython file:
------------------------------------------------------------ ... raise
NameError("global {!r} is not defined".format(name)) sage = _s() def
f(double x): return x**Integer(2)*sin(x) - cos(x)*e**(-x) +
log(x**Integer(2) + Integer(1)) - log(sqrt(Integer(1991))) ^
------------------------------------------------------------
_tmp_tmpgo2z5pbk_tmp_9kfdyg6w_pyx_0.pyx:18:51: undeclared name not builtin:
log Error compiling Cython file:
------------------------------------------------------------ ... raise
NameError("global {!r} is not defined".format(name)) sage = _s() def
f(double x): return x**Integer(2)*sin(x) - cos(x)*e**(-x) +
log(x**Integer(2) + Integer(1)) - log(sqrt(Integer(1991))) ^
------------------------------------------------------------
_tmp_tmpgo2z5pbk_tmp_9kfdyg6w_pyx_0.pyx:18:89: undeclared name not builtin:
sqrt s
What works :
%%cython from sage.functions.trig import sin, cos from sage.misc.functional
import log, sqrt from sage.functions.log import exp cpdef double cf(double
x): return x**2*sin(x) - cos(x)*exp(-x) + log(x**2 + 1) - log(sqrt(1991))
Is cython_lambda a work in progress ?
Trac doesn’t seem to have any *active* cython_lambda ticket.
Advice ?
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