interp1
=======

one_dimension interpolation function



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


::

    [yp]=interp1(x, y,xp [, method,[extrapolation]])




Arguments
~~~~~~~~~

:xp reals scalar, vector or matrix (or hypermatrix)
: :x reals vector
: :method (optional) string defining the interpolation method
: :extrapolation (optional) string, or real value defining the yp(j)
  components for xp(j) values outside [x1,xn] interval.
: :yp vector, or matrix (or hypermatrix)
:



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

Given `(x,y,xp)`, this function performs the yp components
corresponding to xp by the interpolation(linear by default) defined by
x and y.

If `yp` is a vector then the length of xp is equal to the length of
`yp,` if `yp` is a matrix then `xp` have the same length than the
length of each columns of yp, if `yp` is a hypermatrix then the length
of `xp` have the same length than the first dimension of `yp.`

If size(y)=[C,M1,M2,M3,...,Mj] and size(xp)=[N1,N2,N3,...,Nk] then
size(yp)=[N1,N2,..,Nk,M1,M2,...Mj] and length of x must be equal to
size(y,1)

The `method` parameter sets the evaluation rule for interpolation

:"linear" the interpolation is defined by linear method (see
  `interpln`_)
: :"spline" the interpolation is defined by cubic spline interpolation
  ( see `splin`_ , `interp`_)
: :"nearest" for each value xp(j), yp(j) takes the value or y(i)
  corresponding to x(i) the nearest neighbor of xp(j)
:

The `extrapolation` parameter sets the evaluation rule for
extrapolation, i.e for `xp(i)`not in [x1,xn] interval

:"extrap" the extrapolation is performed by the defined method.
  yp=interp1(x,y,xp,method,"extrap")
: :real value you can choose a real value for extrapolation, in this
  way yp(i) takes this value for xp(i) not in [x1,xn] interval, for
  example 0 (but also nan or inf). yi=interp1(x,y,xp,method, 0)
: :by default the extrapolation is performed by the defined method
  (for spline method), and by nan for linear and nearest methods.
  yp=interp1(x,y,xp,method)
:



Examples
~~~~~~~~


::

    x=`linspace`_(0,3,20);
    y=x^2;
    xx=`linspace`_(0,3,100);
    yy1=interp1(x,y,xx,'linear');
    yy2=interp1(x,y,xx,'spline');
    yy3=interp1(x,y,xx,'nearest');
    `plot`_(xx,[yy1;yy2;yy3],x,y,'*')
    `xtitle`_('interpolation of square function')
    `legend`_(['linear','spline','nearest'],a=2)




See Also
~~~~~~~~


+ `interp`_ cubic spline evaluation function
+ `interpln`_ linear interpolation
+ `splin`_ cubic spline interpolation




History
~~~~~~~
Version Description 5.4.0 previously, imaginary part of input
arguments were implicitly ignored.
.. _splin: splin.html
.. _interpln: interpln.html
.. _interp: interp.html