I'd hazard that it's a limit in the internals of numpy for how they handle
broadcasting, but I can't be certain on that.
However, we can handle this, you just need to frame your problem in a
better way. You're trying to do optimization, so generally you'd frame your
optimal condition as a vector. In SymPy you should do the same (using a
MatrixSymbol). You also don't need ufuncify, because you're not doing any
broadcasting. Instead, you can use `autowrap` to create a function. ufuncs
can't broadcast arrays, so ufuncify won't work for functions that require a
vector as an input for a single iteration. The resulting expression will be
just as fast as a ufunc for a single iteration though, so no harm done.
Here's your toy example, done as described:
import sympyfrom sympy.utilities.autowrap import autowrapimport sys
N = int(sys.argv[1])
x = sympy.MatrixSymbol('x', N, 1)
summation = sum(x)
values = list(range(N))
f = autowrap(summation, args=(x,))print f(values)
This works regardless of how large N is. For your real problem, you can
formulate your expression using symbols, and use subs to form them into a
single vector input. Or you can work directly with the vector by using
elements of it as variables. It's up to you how to formulate it.
-Jim
On Thursday, September 25, 2014 6:55:31 PM UTC-5, Jason Moore wrote:
>
> I'm not saying that SymPy isn't well suited for this task. I'm just saying
> that we don't have an implementation for code generation for summations
> that would help with your problem. You could certainly add one.
>
> I use SymPy for optimization problems myself and generate the symbolic
> Jacobians and Hessians of the objective and constraint functions for
> non-linear programming problems and it works great. So SymPy can likely do
> what you want to do, but you may need to write a code printer for sympy.Sum
> or something similar.
>
>
> Jason
> moorepants.info
> +01 530-601-9791
>
> On Thu, Sep 25, 2014 at 7:03 PM, David Shin <shin....@gmail.com
> <javascript:>> wrote:
>
>> Thanks for the info, Jason.
>>
>> In my opinion, what I am trying to do is not particularly exotic.
>> Consider for example the task of implementing logistic regression
>> optimization via sympy and scipy. You have an n-by-k data matrix X of
>> independent variables, a length-n output vector Y of dependent variables,
>> and wish to approximate each Y[i] as a function of X[i], parameterized by a
>> set of k+1 parameters, theta. This boils down to writing an objective loss
>> function to minimize, which is a symbolic function of theta involving n
>> summands that are individually expressions in terms Y[i], X[i], and theta.
>> As the minimum does not have an analytic solution, you need to employ
>> approximation algorithms, hence scipy.optimize.
>>
>> Of course, there are numerous packages available for vanilla logistic
>> regression. However, if you want to customize it (for example by using an
>> alternative loss function or regularization penalty function), then you
>> kind of need to roll out your own implementation.
>>
>> From what you are saying, it sounds like sympy is not well-suited for
>> this type of task.
>>
>> On Thursday, September 25, 2014 5:31:27 PM UTC-5, Jason Moore wrote:
>>>
>>> I'm not sure this is supported. Ideally you'd create a sympy.Sum object
>>> representing your summation and then the code printers would print a loop
>>> that would look something like:
>>>
>>> >>> sum = sympy.Sum(a, (a, 1, 5))
>>> >>> sympy.ccode(sum, b)
>>> double b = 0;
>>> for (i = 0; i < 5; i++;){
>>> b = b + a[i]
>>> }
>>>
>>> I think Jim Crist is working on this functionality but it doesn't exist
>>> now.
>>>
>>>
>>> Jason
>>> moorepants.info
>>> +01 530-601-9791
>>>
>>> On Thu, Sep 25, 2014 at 5:46 PM, David Shin <shin....@gmail.com> wrote:
>>>
>>>> The function is a sum of thousands of summands, where each summand is a
>>>> small function of a few of the input parameters. These small summand
>>>> functions are composed of basic operations like multiplication, addition,
>>>> and exp().
>>>>
>>>> On Thursday, September 25, 2014 4:21:32 PM UTC-5, Jason Moore wrote:
>>>>>
>>>>> I see. What does your function look like? Does it have summations or
>>>>> things you want to iterate over? Or is it simply a scalar function?
>>>>>
>>>>>
>>>>> Jason
>>>>> moorepants.info
>>>>> +01 530-601-9791
>>>>>
>>>>> On Thu, Sep 25, 2014 at 5:09 PM, David Shin <shin....@gmail.com>
>>>>> wrote:
>>>>>
>>>>>> Also, I'd like to pass in the gradient and hessian of my function
>>>>>> into scipy.optimize.minimize() to help it along. I don't want to do the
>>>>>> calculus by hand, so I'm using sympy to do it for me.
>>>>>>
>>>>>>
>>>>>> On Thursday, September 25, 2014 4:08:02 PM UTC-5, David Shin wrote:
>>>>>>>
>>>>>>> I'm looking to minimize a complicated function of hundreds of
>>>>>>> variables. I want to ufuncify() my function so that I can pass it into
>>>>>>> scipy.optimize.minimize(). The summation func I gave is just a toy
>>>>>>> example,
>>>>>>> the actual function is much more complicated.
>>>>>>>
>>>>>>> Please let me know if I should be doing this some other way.
>>>>>>>
>>>>>>> On Thursday, September 25, 2014 4:00:04 PM UTC-5, Jason Moore wrote:
>>>>>>>>
>>>>>>>> First, why do you need sympy to do this? Would NumPy be sufficient?
>>>>>>>>
>>>>>>>> import numpy as np
>>>>>>>> values = np.random.random(100)
>>>>>>>> np.sum(values)
>>>>>>>>
>>>>>>>>
>>>>>>>> Jason
>>>>>>>> moorepants.info
>>>>>>>> +01 530-601-9791
>>>>>>>>
>>>>>>>> On Thu, Sep 25, 2014 at 4:52 PM, David Shin <shin....@gmail.com>
>>>>>>>> wrote:
>>>>>>>>
>>>>>>>>> Would you mind showing me how to convert my demo.py to have
>>>>>>>>> ufuncify generate code that has a single length-N array argument
>>>>>>>>> instead of
>>>>>>>>> N separate arguments?
>>>>>>>>>
>>>>>>>>> On Thursday, September 25, 2014 3:40:25 PM UTC-5, Jason Moore
>>>>>>>>> wrote:
>>>>>>>>>>
>>>>>>>>>> It works for the backend='f2py' in master but fails for the
>>>>>>>>>> default backend which is 'numpy'. I get a segmentation fault on the
>>>>>>>>>> 'numpy'
>>>>>>>>>> backend for values greater than 20 or so.
>>>>>>>>>>
>>>>>>>>>> This is an odd use of ufuncify, as summing would better be done
>>>>>>>>>> in a loop with an array as input to the function. You can probably
>>>>>>>>>> used the
>>>>>>>>>> IndexBased class to set up a loop based sum. If you use the tempdir
>>>>>>>>>> kwarg
>>>>>>>>>> to ufuncify you can see the code it generates, and you'll basically
>>>>>>>>>> get a
>>>>>>>>>> Fortran function that has as many input args as your integer value
>>>>>>>>>> which is
>>>>>>>>>> not very efficient.
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Jason
>>>>>>>>>> moorepants.info
>>>>>>>>>> +01 530-601-9791
>>>>>>>>>>
>>>>>>>>>> On Thu, Sep 25, 2014 at 4:29 PM, Jason Moore <moore...@gmail.com>
>>>>>>>>>> wrote:
>>>>>>>>>>
>>>>>>>>>>> David,
>>>>>>>>>>>
>>>>>>>>>>> This is because it wasn't wrapping lines correctly in the
>>>>>>>>>>> generated Fortran code. If you use the development version of SymPy
>>>>>>>>>>> it
>>>>>>>>>>> should work.
>>>>>>>>>>>
>>>>>>>>>>> Here is the PR that fixed it: https://github.com/sympy/sympy
>>>>>>>>>>> /pull/7968
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Jason
>>>>>>>>>>> moorepants.info
>>>>>>>>>>> +01 530-601-9791
>>>>>>>>>>>
>>>>>>>>>>> On Thu, Sep 25, 2014 at 3:42 PM, David Shin <shin....@gmail.com>
>>>>>>>>>>> wrote:
>>>>>>>>>>>
>>>>>>>>>>>> Hi, I recently began trying out sympy and am running into some
>>>>>>>>>>>> difficulty.
>>>>>>>>>>>>
>>>>>>>>>>>> I wrote the following script, called demo.py:
>>>>>>>>>>>>
>>>>>>>>>>>> import sympyfrom sympy.utilities.autowrap import ufuncifyimport sys
>>>>>>>>>>>>
>>>>>>>>>>>> N = int(sys.argv[1])
>>>>>>>>>>>> theta = []
>>>>>>>>>>>> values = []for n in range(N):
>>>>>>>>>>>> theta.append(sympy.symbols('x%s' % n))
>>>>>>>>>>>> values.append(n)
>>>>>>>>>>>>
>>>>>>>>>>>> summation = sum(theta)
>>>>>>>>>>>> f = ufuncify(theta, summation)print f(*values)[0]
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Running it for small N, it works fine:
>>>>>>>>>>>>
>>>>>>>>>>>> $ python demo.py 21
>>>>>>>>>>>> 210.0
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> But it fails for larger N. Can anyone advise? Thanks in advance.
>>>>>>>>>>>>
>>>>>>>>>>>> $ python demo.py 22
>>>>>>>>>>>> Traceback (most recent call last):
>>>>>>>>>>>> File "demo.py", line 13, in
>>>>>>>>>>>> f = ufuncify(theta, summation)
>>>>>>>>>>>> File
>>>>>>>>>>>> "/opt/user/x86_64/Python-2.7.3/lib/python2.7/site-packages/sympy/utilities/autowrap.py",
>>>>>>>>>>>> line 485, in ufuncify
>>>>>>>>>>>> return autowrap(C.Equality(y[i], f(*args)), **kwargs)
>>>>>>>>>>>> File
>>>>>>>>>>>> "/opt/user/x86_64/Python-2.7.3/lib/python2.7/site-packages/sympy/utilities/autowrap.py",
>>>>>>>>>>>> line 403, in autowrap
>>>>>>>>>>>> return code_wrapper.wrap_code(routine, helpers=helps)
>>>>>>>>>>>> File
>>>>>>>>>>>> "/opt/user/x86_64/Python-2.7.3/lib/python2.7/site-packages/sympy/utilities/autowrap.py",
>>>>>>>>>>>> line 139, in wrap_code
>>>>>>>>>>>> self._process_files(routine)
>>>>>>>>>>>> File
>>>>>>>>>>>> "/opt/user/x86_64/Python-2.7.3/lib/python2.7/site-packages/sympy/utilities/autowrap.py",
>>>>>>>>>>>> line 158, in _process_files
>>>>>>>>>>>> " ".join(command), e.output))
>>>>>>>>>>>> sympy.utilities.autowrap.CodeWrapError: Error while executing
>>>>>>>>>>>> command: f2py -m wrapper_module_0 -c wrapped_code_0.f90. Command
>>>>>>>>>>>> output is:
>>>>>>>>>>>> running build
>>>>>>>>>>>> running config_cc
>>>>>>>>>>>> unifing config_cc, config, build_clib, build_ext, build commands
>>>>>>>>>>>> --compiler options
>>>>>>>>>>>> running config_fc
>>>>>>>>>>>> unifing config_fc, config, build_clib, build_ext, build commands
>>>>>>>>>>>> --fcompiler options
>>>>>>>>>>>> running build_src
>>>>>>>>>>>> build_src
>>>>>>>>>>>> building extension "wrapper_module_0" sources
>>>>>>>>>>>> f2py options: []
>>>>>>>>>>>> f2py:> /tmp/tmpKbJQuO/src.linux-x86_64-2.7/wrapper_module_0module.c
>>>>>>>>>>>> creating /tmp/tmpKbJQuO
>>>>>>>>>>>> creating /tmp/tmpKbJQuO/src.linux-x86_64-2.7
>>>>>>>>>>>> Reading fortran codes...
>>>>>>>>>>>> Reading file 'wrapped_code_0.f90' (format:free)
>>>>>>>>>>>> Post-processing...
>>>>>>>>>>>> Block: wrapper_module_0
>>>>>>>>>>>> Block: autofunc
>>>>>>>>>>>> Post-processing (stage 2)...
>>>>>>>>>>>> Building modules...
>>>>>>>>>>>> Building module "wrapper_module_0"...
>>>>>>>>>>>> Constructing wrapper function "autofunc"...
>>>>>>>>>>>> y_15 =
>>>>>>>>>>>> autofunc(x_16,x1,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19,x2,x20,x21,x3,x4,x5,x6,x7,x8,x9,[m_17])
>>>>>>>>>>>> Wrote C/API module "wrapper_module_0" to file
>>>>>>>>>>>> "/tmp/tmpKbJQuO/src.linux-x86_64-2.7/wrapper_module_0module.c"
>>>>>>>>>>>> adding '/tmp/tmpKbJQuO/src.linux-x86_64-2.7/fortranobject.c' to
>>>>>>>>>>>> sources.
>>>>>>>>>>>> adding '/tmp/tmpKbJQuO/src.linux-x86_64-2.7' to include_dirs.
>>>>>>>>>>>> copying
>>>>>>>>>>>> /opt/user/x86_64/Python-2.7.3/lib/python2.7/site-packages/numpy/f2py/src/fortranobject.c
>>>>>>>>>>>> -> /tmp/tmpKbJQuO/src.linux-x86_64-2.7
>>>>>>>>>>>> copying
>>>>>>>>>>>> /opt/user/x86_64/Python-2.7.3/lib/python2.7/site-packages/numpy/f2py/src/fortranobject.h
>>>>>>>>>>>> -> /tmp/tmpKbJQuO/src.linux-x86_64-2.7
>>>>>>>>>>>> build_src: building npy-pkg config files
>>>>>>>>>>>> running build_ext
>>>>>>>>>>>> customize UnixCCompiler
>>>>>>>>>>>> customize UnixCCompiler using build_ext
>>>>>>>>>>>> customize Gnu95FCompiler
>>>>>>>>>>>> Found executable /opt/user/x86_64/gcc-4.7.2/bin/gfortran
>>>>>>>>>>>> customize Gnu95FCompiler
>>>>>>>>>>>> customize Gnu95FCompiler using build_ext
>>>>>>>>>>>> building 'wrapper_module_0' extension
>>>>>>>>>>>> compiling C sources
>>>>>>>>>>>> C compiler: gcc -pthread -fno-strict-aliasing -g -O2 -DNDEBUG -g
>>>>>>>>>>>> -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
>>>>>>>>>>>>
>>>>>>>>>>>> creating /tmp/tmpKbJQuO/tmp
>>>>>>>>>>>> creating /tmp/tmpKbJQuO/tmp/tmpKbJQuO
>>>>>>>>>>>> creating /tmp/tmpKbJQuO/tmp/tmpKbJQuO/src.linux-x86_64-2.7
>>>>>>>>>>>> compile options: '-I/tmp/tmpKbJQuO/src.linux-x86_64-2.7
>>>>>>>>>>>> -I/opt/user/x86_64/Python-2.7.3/lib/python2.7/site-packages/numpy/core/include
>>>>>>>>>>>> -I/opt/user/x86_64/Python-2.7.3/include/python2.7 -c'
>>>>>>>>>>>> gcc: /tmp/tmpKbJQuO/src.linux-x86_64-2.7/wrapper_module_0module.c
>>>>>>>>>>>> In file included from
>>>>>>>>>>>> /opt/user/x86_64/Python-2.7.3/lib/python2.7/site-packages/numpy/core/include/numpy/ndarraytypes.h:1728:0,
>>>>>>>>>>>> from
>>>>>>>>>>>> /opt/user/x86_64/Python-2.7.3/lib/python2.7/site-packages/numpy/core/include/numpy/ndarrayobject.h:17,
>>>>>>>>>>>> from
>>>>>>>>>>>> /opt/user/x86_64/Python-2.7.3/lib/python2.7/site-packages/numpy/core/include/numpy/arrayobject.h:15,
>>>>>>>>>>>> from
>>>>>>>>>>>> /tmp/tmpKbJQuO/src.linux-x86_64-2.7/fortranobject.h:13,
>>>>>>>>>>>> from
>>>>>>>>>>>> /tmp/tmpKbJQuO/src.linux-x86_64-2.7/wrapper_module_0module.c:18:
>>>>>>>>>>>> /opt/user/x86_64/Python-2.7.3/lib/python2.7/site-packages/numpy/core/include/numpy/npy_deprecated_api.h:11:2:
>>>>>>>>>>>> warning: #warning "Using deprecated NumPy API, disable it by
>>>>>>>>>>>> #defining NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION" [-Wcpp]
>>>>>>>>>>>> /tmp/tmpKbJQuO/src.linux-x86_64-2.7/wrapper_module_0module.c:111:12:
>>>>>>>>>>>> warning: âpy_sizeâefined but not used [-Wunused-function]
>>>>>>>>>>>> gcc: /tmp/tmpKbJQuO/src.linux-x86_64-2.7/fortranobject.c
>>>>>>>>>>>> In file included from
>>>>>>>>>>>> /opt/user/x86_64/Python-2.7.3/lib/python2.7/site-packages/numpy/core/include/numpy/ndarraytypes.h:1728:0,
>>>>>>>>>>>> from
>>>>>>>>>>>> /opt/user/x86_64/Python-2.7.3/lib/python2.7/site-packages/numpy/core/include/numpy/ndarrayobject.h:17,
>>>>>>>>>>>> from
>>>>>>>>>>>> /opt/user/x86_64/Python-2.7.3/lib/python2.7/site-packages/numpy/core/include/numpy/arrayobject.h:15,
>>>>>>>>>>>> from
>>>>>>>>>>>> /tmp/tmpKbJQuO/src.linux-x86_64-2.7/fortranobject.h:13,
>>>>>>>>>>>> from
>>>>>>>>>>>> /tmp/tmpKbJQuO/src.linux-x86_64-2.7/fortranobject.c:2:
>>>>>>>>>>>> /opt/user/x86_64/Python-2.7.3/lib/python2.7/site-packages/numpy/core/include/numpy/npy_deprecated_api.h:11:2:
>>>>>>>>>>>> warning: #warning "Using deprecated NumPy API, disable it by
>>>>>>>>>>>> #defining NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION" [-Wcpp]
>>>>>>>>>>>> compiling Fortran sources
>>>>>>>>>>>> Fortran f77 compiler: /opt/user/x86_64/gcc-4.7.2/bin/gfortran
>>>>>>>>>>>> -Wall -ffixed-form -fno-second-underscore -fPIC -O3 -funroll-loops
>>>>>>>>>>>> Fortran f90 compiler: /opt/user/x86_64/gcc-4.7.2/bin/gfortran
>>>>>>>>>>>> -Wall -fno-second-underscore -fPIC -O3 -funroll-loops
>>>>>>>>>>>> Fortran fix compiler: /opt/user/x86_64/gcc-4.7.2/bin/gfortran
>>>>>>>>>>>> -Wall -ffixed-form -fno-second-underscore -Wall
>>>>>>>>>>>> -fno-second-underscore -fPIC -O3 -funroll-loops
>>>>>>>>>>>> compile options: '-I/tmp/tmpKbJQuO/src.linux-x86_64-2.7
>>>>>>>>>>>> -I/opt/user/x86_64/Python-2.7.3/lib/python2.7/site-packages/numpy/core/include
>>>>>>>>>>>> -I/opt/user/x86_64/Python-2.7.3/include/python2.7 -c'
>>>>>>>>>>>> gfortran:f90: wrapped_code_0.f90
>>>>>>>>>>>> wrapped_code_0.f90:1.133:
>>>>>>>>>>>>
>>>>>>>>>>>> 4, x15, x16, x17, x18, x19, x2, x20, x21, x3, x4, x5, x6, x7, x8,
>>>>>>>>>>>> x9, y_15
>>>>>>>>>>>>
>>>>>>>>>>>> 1
>>>>>>>>>>>> Warning: Line truncated at (1)
>>>>>>>>>>>> wrapped_code_0.f90:1.132:
>>>>>>>>>>>>
>>>>>>>>>>>> 14, x15, x16, x17, x18, x19, x2, x20, x21, x3, x4, x5, x6, x7, x8,
>>>>>>>>>>>> x9, y_15
>>>>>>>>>>>>
>>>>>>>>>>>> 1
>>>>>>>>>>>> Error: Unexpected junk in formal argument list at (1)
>>>>>>>>>>>> wrapped_code_0.f90:33.3:
>>>>>>>>>>>>
>>>>>>>>>>>> end subroutine
>>>>>>>>>>>> 1
>>>>>>>>>>>> Error: Expecting END PROGRAM statement at (1)
>>>>>>>>>>>> Error: Unexpected end of file in 'wrapped_code_0.f90'
>>>>>>>>>>>> wrapped_code_0.f90:1.133:
>>>>>>>>>>>>
>>>>>>>>>>>> 4, x15, x16, x17, x18, x19, x2, x20, x21, x3, x4, x5, x6, x7, x8,
>>>>>>>>>>>> x9, y_15
>>>>>>>>>>>>
>>>>>>>>>>>> 1
>>>>>>>>>>>> Warning: Line truncated at (1)
>>>>>>>>>>>> wrapped_code_0.f90:1.132:
>>>>>>>>>>>>
>>>>>>>>>>>> 14, x15, x16, x17, x18, x19, x2, x20, x21, x3, x4, x5, x6, x7, x8,
>>>>>>>>>>>> x9, y_15
>>>>>>>>>>>>
>>>>>>>>>>>> 1
>>>>>>>>>>>> Error: Unexpected junk in formal argument list at (1)
>>>>>>>>>>>> wrapped_code_0.f90:33.3:
>>>>>>>>>>>>
>>>>>>>>>>>> end subroutine
>>>>>>>>>>>> 1
>>>>>>>>>>>> Error: Expecting END PROGRAM statement at (1)
>>>>>>>>>>>> Error: Unexpected end of file in 'wrapped_code_0.f90'
>>>>>>>>>>>> error: Command "/opt/user/x86_64/gcc-4.7.2/bin/gfortran -Wall
>>>>>>>>>>>> -fno-second-underscore -fPIC -O3 -funroll-loops
>>>>>>>>>>>> -I/tmp/tmpKbJQuO/src.linux-x86_64-2.7
>>>>>>>>>>>> -I/opt/user/x86_64/Python-2.7.3/lib/python2.7/site-packages/numpy/core/include
>>>>>>>>>>>> -I/opt/user/x86_64/Python-2.7.3/include/python2.7 -c -c
>>>>>>>>>>>> wrapped_code_0.f90 -o /tmp/tmpKbJQuO/wrapped_code_0.o" failed with
>>>>>>>>>>>> exit status 1
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> --
>>>>>>>>>>>> You received this message because you are subscribed to the
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>>>>>>>>>>>> To unsubscribe from this group and stop receiving emails from
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>>>>>>>>>>>> To view this discussion on the web visit
>>>>>>>>>>>> https://groups.google.com/d/msgid/sympy/68af9759-5988-4e85-8
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>>>>>>>>>>>> For more options, visit https://groups.google.com/d/optout.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>> --
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>>>>>>>>> .
>>>>>>>>>
>>>>>>>>> For more options, visit https://groups.google.com/d/optout.
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>>>>>> msgid/sympy/6728544e-2ef8-45b5-8e42-01b0f57dbe1a%40googlegroups.com
>>>>>> <https://groups.google.com/d/msgid/sympy/6728544e-2ef8-45b5-8e42-01b0f57dbe1a%40googlegroups.com?utm_medium=email&utm_source=footer>
>>>>>> .
>>>>>>
>>>>>> For more options, visit https://groups.google.com/d/optout.
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>>>>>
>>>>> --
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>>>> .
>>>>
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>>>>
>>>
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