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# Optimization

`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 `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`

        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:

        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`.

  See also

  `attr_praxis()`, `stop_praxis()`, `pval_praxis()`

`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 `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 `mcell_ran4()`)

`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.

`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 `fit_praxis()`, then praxis will do a single (or i) principal axis calculation and then exit.

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