interp2d
========

bicubic spline (2d) evaluation function



Calling Sequence
~~~~~~~~~~~~~~~~


::

    [zp[,dzpdx,dzpdy[,d2zpdxx,d2zpdxy,d2zpdyy]]]=interp2d(xp,yp,x,y,C [,out_mode])




Arguments
~~~~~~~~~

:xp, yp real vectors or matrices of same size
: :x,y,C real vectors defining a bicubic spline or sub-spline function
  (called `s` in the following)
: :out_mode (optional) string defining the evaluation of `s` outside
  [x(1),x(nx)]x[y(1),y(ny)]
: :zp vector or matrix of same format than `xp` and `yp`, elementwise
  evaluation of `s` on these points.
: :dzpdx, dzpdy vectors (or matrices) of same format than `xp` and
  `yp`, elementwise evaluation of the first derivatives of `s` on these
  points.
: :d2zpdxx, d2zpdxy, d2zpdyy vectors (or matrices) of same format than
  `xp` and `yp`, elementwise evaluation of the second derivatives of `s`
  on these points.
:



Description
~~~~~~~~~~~

Given three vectors `(x,y,C)` defining a bicubic spline or sub-spline
function (see `splin2d`_) this function evaluates *s* (and *ds/dx,
ds/dy, d2s/dxx, d2s/dxy, d2s/dyy* if needed) at *(xp(i),yp(i))* :

The `out_mode` parameter defines the evaluation rule for
extrapolation, i.e. for *(xp(i),yp(i)) not in
[x(1),x(nx)]x[y(1),y(ny)]* :

:"by_zero" an extrapolation by zero is done
: :"by_nan" extrapolation by Nan
: :"C0" the extrapolation is defined as follows :

::

    s(x,y) = s(`proj`_(x,y)) `where`_ proj(x,y) is nearest point 
                          of [x(1),x(nx)]x[y(1),y(ny)] from (x,y)


: :"natural" the extrapolation is done by using the nearest bicubic-
  patch from (x,y).
: :"periodic" `s` is extended by periodicity.
:



Examples
~~~~~~~~


::

    // see the examples of splin2d
    
    // this example shows some different extrapolation features
    // interpolation of cos(x)cos(y)
    n = 7;  // a n x n interpolation grid
    x = `linspace`_(0,2*%pi,n); y = x;
    z = `cos`_(x')*`cos`_(y);
    C = `splin2d`_(x, y, z, "periodic");
    
    // now evaluate on a bigger domain than [0,2pi]x [0,2pi]
    m = 80; // discretisation parameter of the evaluation grid
    xx = `linspace`_(-0.5*%pi,2.5*%pi,m); yy = xx;
    [XX,YY] = `ndgrid`_(xx,yy);
    zz1 = interp2d(XX,YY, x, y, C, "C0");
    zz2 = interp2d(XX,YY, x, y, C, "by_zero");
    zz3 = interp2d(XX,YY, x, y, C, "periodic");
    zz4 = interp2d(XX,YY, x, y, C, "natural");
    `clf`_()
    `subplot`_(2,2,1)
    `plot3d`_(xx, yy, zz1, flag=[2 6 4])
    `xtitle`_("extrapolation with the C0 outmode")
    `subplot`_(2,2,2)
    `plot3d`_(xx, yy, zz2, flag=[2 6 4])
    `xtitle`_("extrapolation with the by_zero outmode")
    `subplot`_(2,2,3)
    `plot3d`_(xx, yy, zz3, flag=[2 6 4])
    `xtitle`_("extrapolation with the periodic outmode")
    `subplot`_(2,2,4)
    `plot3d`_(xx, yy, zz4, flag=[2 6 4])
    `xtitle`_("extrapolation with the natural outmode")
    `show_window`_()




See Also
~~~~~~~~


+ `splin2d`_ bicubic spline gridded 2d interpolation




History
~~~~~~~
Version Description 5.4.0 previously, imaginary part of input
arguments were implicitly ignored.
.. _splin2d: splin2d.html