.. hoc:function:: fit_praxis
Syntax:
``min = fit_praxis(n, "funname", &x[0])``
``min = fit_praxis(n, "funname", Vector)``
``min = fit_praxis(..., ..., ..., "after quad statement")``
``min = fit_praxis(efun_as_python_callable, hoc_vector)``
Description:
This is the principal axis method for minimizing a function. See praxis.c
in the scopmath library.
``1 <= n < 20``
is the number of parameters to vary (number
of arguments to *funname*).
*funname*
the name of the function to minimize, eg. least square difference between model and data.
The funname must take two arguments, the first arg, ``$1``,
is the number of elements in second arg vector, ``$&2``. The ith index of the
vector is given by ``$&2[i]``.
*x*
is a double vector of at least length *n*. Prior to the call set
it to a guess of the parameter values. On return it contains the
values of the args that minimize ``funname()``.
*funname* may be either
an interpreted hoc function or a compiled NMODL function.
If the variable stoprun is set to 1 during a call to fit_praxis, it will
return immediately (when the current call to funname returns) with
a return value and varx values set to the best minimum found so far. Use
:hoc:func:`stop_praxis` to stop after finishing the current principal axis calculation.
The fourth argument, if present, specifies a statement to be executed at
the end of each principal axis evaluation.
If the third argument is a Vector, then that style is used to specify
the initial starting point and return the final value. However the
function is still called with second arg as a pointer into a double array.
The Python callable form uses a Python Callable as the function to
minimize and it must take a single hoc Vector argument specifying the
values of the parameters for use in evaluation the function. On entry to
fit_praxis the Vector specifies the number of parameters and the
parameter starting values. On return the vector contains the values of
parameters which generated the least minimum found so far.
Hoc example: minimize ``(x+y - 5)^2 + 5*((x-y) - 15)^2``
.. code-block::
none
objref vec
vec = new Vector(2) // vec.x[0] is x, vec.x[1] is y
func efun() {local x, y
x = $&2[0] y = $&2[1]
return (x+y - 5)^2 + 5*(x-y - 15)^2
}
attr_praxis(1e-5, .5, 0)
e = fit_praxis(vec.size(), "efun", vec)
printf("e=%g x=%g y=%g\n", e, vec.x[0], vec.x[1])
objref paxis
paxis = new Vector()
for i=0, 1 {
pval = pval_praxis(i, paxis)
printf("%d %10g %10g %10g\n", i, pval, paxis.x[0], paxis.x[1])
}
Python example:
.. code-block::
none
from neuron import h
v = h.Vector(2)
def efun(v):
return (v.x[0]+v.x[1] - 5)**2 + 5*(v.x[0]-v.x[1] - 15)**2
h.attr_praxis(1e-5, .5, 0)
e = h.fit_praxis(efun, v)
print "e=%g x=%g y=%g\n"%(e, v.x[0], v.x[1])
.. warning::
Up to version 4.0.1, the arguments to *funname* were an explicit
list of *n* arguments. ie ``numarg()==n``.
.. seealso::
:hoc:func:`attr_praxis`, :hoc:func:`stop_praxis`, :hoc:func:`pval_praxis`
.. hoc:function:: attr_praxis
Syntax:
``attr_praxis(tolerance, maxstepsize, printmode)``
``previous_index = attr_praxis(mcell_ran4_index)``
Description:
Set the attributes of the praxis method. This must be called before
the first call to :hoc:func:`fit_praxis`.
tolerance
praxis attempt to return f(x) such that if x0 is the true
local minimum then ``norm(x-x0) < tolerance``
maxstepsize
should be set to about the maximum distance from
initial guess to the minimum.
printmode=0
no printing
printmode=1,2,3
more and more verbose
The single argument form causes praxis to pick its random numbers from
the the mcellran4 generator beginning at the specified index. This
allows reproducible fitting. The return value is the previously picked
index. (see :hoc:func:`mcell_ran4`)
.. hoc:function:: pval_praxis
Syntax:
``pval = pval_praxis(i)``
``pval = pval_praxis(i, &paxis[0])``
``pval = pval_praxis(i, Vector)``
Description:
Return the ith principal value. If the second argument is present, ``pval_praxis`` also fills
the vector with the ith principal axis.
.. hoc:function:: stop_praxis
Syntax:
``stop_praxis()``
``stop_praxis(i)``
Description:
Set a flag in the praxis function that will cause it to stop after
it finishes the current (or ith subsequent)
principal axis calculation. If this function
is called before :hoc:func:`fit_praxis`, then praxis will do a single
(or i) principal axis calculation and then exit.