.. highlightlang:: us

.. index:: nonlin

.. _nonlin:

nonlin
======

.. us.tag  nonlin ENGLISH interpol-2d Interpolation

:ref:`nonlin` computes the parameters of a given (non linear) function so that
the deviation of the function for the given data points is minimized.

.. function::  pEnd = nonlin(fit, y, x, pStart)
    pEnd = nonlin(fit, y, x, pStart, bPrint)

.. us.return

**Return Value**

*pEnd* are the parameters of the function *fit*.

.. us.params

**Parameters**

.. uparam:: fit

   *fit* is a function provided by the user (see example).

.. uparam:: y

   *y* is a column vector with y-coordinates.

.. uparam:: x

   *x* is a column vector with x-coordinates.

.. uparam:: pStart

   *pStart* is an estimated start vector.

.. uparam:: bPrint

   If *bPrint* is FALSE (0), no information is printed into the command window.

.. us.example

**Example**

::

   def fit_exp(x, p)
   {
       return p[1] + p[2] .* exp(p[3] .* x);
   }
   rmXY = [ ..
       1.2600,      0.4000;
       1.6000,      0.2800;
       1.6300,      0.2900;
       1.6500,      0.2300;
       1.6900,      0.2000;
       1.7000,      0.1850;
       1.7600,      0.1600;
       2.0000,      0.0750;
       2.2300,      0.0550;
       2.5000,      0.0400];
   p_start = [0,0,0];
   p_end = nonlin(fit_exp, rmXY[;2], rmXY[;1], p_start);
   x = linspace(1.2, 2.6, 50);
   y = fit_exp(x', p_end);
   h = plot(x, y);
   h = plot (rmXY[;1], rmXY[;2], h[2]);
   XYShowMarker(h[3], TRUE);
   XYShowLine(h[3], FALSE);
   PageReplot(h[1]);

:ref:`nonlin` kann auch für xyz-Datensätze verwendet werden, hier ein Beispiel:

::

   def fit_xyz_poly2(_x, p)
   {
       x = _x[;1]
       y = _x[;2]
       return p[1] + ..
              p[2] .* x + ..
              p[3] .* y + ..
              p[4] .* x .* x + ..
              p[5] .* y .* y + ..
              p[6] .* x .* y;
   }
   def test2(hDataXYZ)
   {
       rmXYZ = XYZGetData(hDataXYZ);
       p_start = zeros(1,6); [0.1, 1, 1, 1, 0.01, 1];
       p_end = nonlin(fit_xyz_poly2, rmXYZ[;3], rmXYZ[;1,2], p_start);
       Z = fit_xyz_poly2(rmXYZ[;1,2], p_end)
       plotmatrix(rmXYZ[;1], rmXYZ[;2], Z)
   }

.. image:: S:/uniplot-obj/images/fit.*

.. seealso::
   :ref:`overview-mathematic`,
   :ref:`fspline`,
   :ref:`pspline`,
   :ref:`plot`

:sub:`id-697354`