Previous: One-dimensional Interpolation, Up: Interpolation
There are three multi-dimensional interpolation function in Octave, with similar capabilities. Methods using Delaunay tessellation are described in Interpolation on Scattered Data.
Two-dimensional interpolation. x, y and z describe a surface function. If x and y are vectors their length must correspondent to the size of z. x and Yy must be monotonic. If they are matrices they must have the
meshgrid
format.
interp2 (
x,
y,
Z,
xi,
yi, ...)
- Returns a matrix corresponding to the points described by the matrices XI, YI.
If the last argument is a string, the interpolation method can be specified. The method can be 'linear', 'nearest' or 'cubic'. If it is omitted 'linear' interpolation is assumed.
interp2 (
z,
xi,
yi)
- Assumes x
= 1:rows (
z)
and y= 1:columns (
z)
interp2 (
z,
n)
- Interleaves the Matrix z n-times. If n is ommited a value of n
= 1
is assumed.The variable method defines the method to use for the interpolation. It can take one of the values
- 'nearest'
- Return the nearest neighbor.
- 'linear'
- Linear interpolation from nearest neighbors.
- 'pchip'
- Piece-wise cubic hermite interpolating polynomial (not implemented yet).
- 'cubic'
- Cubic interpolation from four nearest neighbors.
- 'spline'
- Cubic spline interpolation–smooth first and second derivatives throughout the curve.
If a scalar value extrapval is defined as the final value, then values outside the mesh as set to this value. Note that in this case method must be defined as well. If extrapval is not defined then NA is assumed.
See also: interp1.
Perform 3-dimensional interpolation. Each element of then 3-dimensional array v represents a value at a location given by the parameters x, y, and z. The parameters x, x, and z are either 3-dimensional arrays of the same size as the array v in the 'meshgrid' format or vectors. The parameters xi, etc respect a similar format to x, etc, and they represent the points at which the array vi is interpolated.
If x, y, z are ommitted, they are assumed to be
x = 1 : size (
v, 2)
,y = 1 : size (
v, 1)
andz = 1 : size (
v, 3)
. If m is specified, then the interpolation adds a point half way between each of the interplation points. This process is performed m times. If only v is specified, then m is assumed to be1
.Method is one of:
- 'nearest'
- Return the nearest neighbour.
- 'linear'
- Linear interpolation from nearest neighbours.
- 'cubic'
- Cubic interpolation from four nearest neighbours (not implemented yet).
- 'spline'
- Cubic spline interpolation–smooth first and second derivatives throughout the curve.
The default method is 'linear'.
If extrap is the string 'extrap', then extrapolate values beyond the endpoints. If extrap is a number, replace values beyond the endpoints with that number. If extrap is missing, assume NA.
See also: interp1, interp2, spline, meshgrid.
Perform n-dimensional interpolation, where n is at least two. Each element of then n-dimensional array v represents a value at a location given by the parameters x1, x2, ..., xn. The parameters x1, x2, ..., xn are either n-dimensional arrays of the same size as the array v in the 'ndgrid' format or vectors. The parameters y1, etc respect a similar format to x1, etc, and they represent the points at which the array vi is interpolated.
If x1, ..., xn are ommitted, they are assumed to be
x1 = 1 : size (
v, 1)
, etc. If m is specified, then the interpolation adds a point half way between each of the interplation points. This process is performed m times. If only v is specified, then m is assumed to be1
.Method is one of:
- 'nearest'
- Return the nearest neighbour.
- 'linear'
- Linear interpolation from nearest neighbours.
- 'cubic'
- Cubic interpolation from four nearest neighbours (not implemented yet).
- 'spline'
- Cubic spline interpolation–smooth first and second derivatives throughout the curve.
The default method is 'linear'.
If extrap is the string 'extrap', then extrapolate values beyond the endpoints. If extrap is a number, replace values beyond the endpoints with that number. If extrap is missing, assume NA.
See also: interp1, interp2, spline, ndgrid.
A significant difference between interpn
and the other two
multidimensional interpolation function is the fashion in which the
dimensions are treated. For interp2
and interp3
, the 'y'
axis is considered to be the columns of the matrix, whereas the 'x'
axis corresponds to the rows the the array. As Octave indexes arrays in
column major order, the first dimension of any array is the columns, and
so interpn
effectively reverses the 'x' and 'y' dimensions.
Consider the example
x = y = z = -1:1; f = @(x,y,z) x.^2 - y - z.^2; [xx, yy, zz] = meshgrid (x, y, z); v = f (xx,yy,zz); xi = yi = zi = -1:0.1:1; [xxi, yyi, zzi] = meshgrid (xi, yi, zi); vi = interp3(x, y, z, v, xxi, yyi, zzi, 'spline'); [xxi, yyi, zzi] = ndgrid (xi, yi, zi); vi2 = interpn(x, y, z, v, xxi, yyi, zzi, 'spline'); mesh (zi, yi, squeeze (vi2(1,:,:)));
where vi
and vi2
are identical. The reversal of the
dimensions is treated in the meshgrid
and ndgrid
functions
respectively.
In additional the support function bicubic
that underlies the
cubic interpolation of interp2
function can be called directly.
Return a matrix zi corresponding to the bicubic interpolations at xi and yi of the data supplied as x, y and z. Points outside the grid are set to extrapval
See http://wiki.woodpecker.org.cn/moin/Octave/Bicubic for further information.
See also: interp2.