.. highlightlang:: us

.. _interpol:

interpol
========

.. index:: interpol

.. us.tag  interpol ENGLISH Interpolation New420 Changed424

The :ref:`interpol` function executes a linear interpolation or cosine 
interpolation for the given x-coordinates.

.. function::  rvYi = interpol(rvX, rvY, rvXi)
    rvYi = interpol(rvX, rvY, rvXi, rsMissing)
    rvYi = interpol(rvX, rvY, rvXi, rsMissing, ssType)

.. us.return

**Return Value**

*rvYi*

.. us.params

**Parameters**

.. uparam:: rvX

   *rvX* is a real vector with at least 2 elements. The coordinates must be sorted
   monoton increasing or decreasing.

.. uparam:: rvY

   *rvY* is a real vector with at least 2 elements. The number of points must
   be identical with *rvX*.

.. uparam:: rvXi

   *rvXi* is a real vector with at least one point. 

.. uparam:: rsMissing

   1.) Values in *rvYi* >= *rsMissing* will be ignored in the interpolation.
   All elements in *rvYi* will be set to missing for *rvYi* >= *rsMissing*.
   2.) If an extrapolation is necessary, the extrapolated values in *rvYi* are
   set to *rsMissing*. Default value is 0.

.. uparam:: ssType

   *ssType* is a string with the text ``linear`` or ``cosine``.  Default value
   is ``linear``. 

.. us.example

**Example**

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

::

   x = [1,3,5,8]
   y = [0,5,8,2]
   h = plot(x,y)
   yi = interpol(x, y, xi = linspace(1, 8, 5));
   h = plot(xi, yi, h[2])
   XYSetProps(h[3], "marker='1' marker-style='circle' curve-style='dash'");

   x = [1,3,5,8]
   y = [0,5,8,2]
   h = plot(x,y)
   yi = interpol(x, y, xi = linspace(1, 8, 5));
   h = plot(xi, yi, h[2], 1e10, "cosine")
   XYSetProps(h[3], "marker='1' marker-style='circle' curve-style='dash'");

If an error occures interpol returns an error object (see :ref:`error_create`). 

::

   x = [1,3,4, 5,8]
   y = [0,5,8,2]
   yi = interpol(x, y, [1,2,2]);
   if (type(yi) == "error") {
       print yi.message;
   }

.. us.history

**History**

.. list-table::
   :header-rows: 1

   * - Version
     - Description
   * - R2018.12
     - New parameter *ssType*
   * - 4.2.4
     - *rvXi* can be non-monotonic.
   * - 4.2.0
     - New

.. seealso::
   :ref:`overview-mathematic`,
   :ref:`fspline`,
   :ref:`pspline`,
   :ref:`rspline`,
   :ref:`akimaspline`

:sub:`id-2113436`