On Jul 20, 2009, at 12:37 PM, Golam Mortuza Hossain wrote:
> Hi,
>
> On Sun, Jul 19, 2009 at 3:11 PM, William Stein<wst...@gmail.com>
> wrote:
>>>> Or should we just restore old "diff" by simply sub-classing it
>>>> from SFunction like what is being done for "integration"
>>>> and others?
>>
>> At first glance doing this sounds like a really good idea. How hard
>> would it be for you to make a mock-up prototype of this to more
>> clearly demonstrate it? I'm definitely not opposed.
>
> OK, here is a prototype implementation.
>
> This is based on the principle that we stop applying chain rule
> when we hit a symbolic function and whose derivative isn't defined
> in sage/pynac.
>
> These are the output from my sage console
> ---------
> sage: f(x) = function('f',x)
>
> sage: f(x).diff(x)
> diff(f(x), x, 1)
>
> sage: f(x).diff(x,2)
> diff(f(x), x, 2)
>
> sage: sin(cos(f(x))).diff(x)
> -sin(f(x))*cos(cos(f(x)))*diff(f(x), x, 1)
>
> sage: f(sin(x)).diff(x)
> diff(f(sin(x)), x, 1)
> ---------
>
> I have done three things:
>
> (1) Defined a symbolic derivative wrapper SFunction (attached).
> Frankly, this is not much different than: diff = function('diff')
>
>
> (2) Added a small wrapper cython function in symbolic/pynac.pyx as
>
> cdef public object py_derivative(unsigned id, object var, object
> args) except +:
> """
> """
> cdef SFunction func = get_sfunction_from_serial(id)
> assert(func is not None)
> from sage.symbolic.derivative import newdiff
> return newdiff(func(*args), var)
>
>
> (3) Added a condition in "function.cpp" in pynac such that it calls
> "py_derivative" instead of applying chain rule when it hits
> a symbolic function and whose derivative function is not defined.
>
> // No derivative defined? Then dont apply chain rule
> if (opt.derivative_f == NULL) {
> // convert seq to a PyTuple of Expressions
> PyObject* args = exvector_to_PyTuple(seq);
> PyObject* dvar = ex_to_pyExpression(s);
> PyObject* pyresult = py_derivative(serial, dvar, args);
> Py_DECREF(args);
> Py_DECREF(dvar);
> if (!pyresult) {
> throw(std::runtime_error("function::derivative():
> python function raised exception"));
> }
> // convert output Expression to an ex
> ex result = pyExpression_to_ex(pyresult);
> Py_DECREF(pyresult);
> if (PyErr_Occurred()) {
> throw(std::runtime_error("function::derivative():
> python function (pyExpression_to_ex) raised exception"));
> }
> return result;
>
>
> Notes: This is not the fastest implementation but my current priority
> is to get my work done even if it takes bit longer rather than not
> able to do at all.
Excellent idea!
- Robert
--~--~---------~--~----~------------~-------~--~----~
To post to this group, send email to sage-devel@googlegroups.com
To unsubscribe from this group, send email to
sage-devel-unsubscr...@googlegroups.com
For more options, visit this group at http://groups.google.com/group/sage-devel
URLs: http://www.sagemath.org
-~----------~----~----~----~------~----~------~--~---
