interp2

Two dimensional interpolation.

Syntax

zi = interp2(x,y,z,xi,yi)

zi = interp2(x,y,z,xi,yi,method)

zi = interp2(x,y,z,xi,yi,method,extrap)

Inputs

x,y,z
The point coordinate values with which to interpolate.
See Comments for the dimension options.
Type: double
Dimension: vector | matrix
z
The grid of function values with which to interpolate.
Type: double
Dimension: matrix
xi,yi
The domain points at which to interpolate.
Type: double
Dimension: vector | matrix
method
The available options are:
'linear'
Returns the bilinear interpolation from the nearest neighbors.
'spline'
Returns the bicubic spline interpolation from the nearest neighbors.
Type: string
extrap
The available options are:
'extrap'
Allows extrapolation beyond the intervals.
'noextrap'
Does not allow extrapolation (default).
Type: string

Outputs

zi
The interpolated z values corresponding to (xi,yi) pairs.
Dimension: matrix

Examples

With 'linear' method:

x = [2, 5, 6, 10, 12, 17];
y = [10, 13, 17, 18, 23, 25, 29];
z = [98  184  214  328   386   528;
129  242  281  431   507   694;
170  319  370  568   668   915;
181  339  393  603   709   971;
232  435  504  774   910  1247;
253  474  549  843   991  1358;
294  551  638  980  1152  1579];
xi = [3, 5, 7, 11, 16];
yi = [11, 16, 21, 29]';
zi = interp2(x,y,z,xi,yi,'linear')
zi = [Matrix] 4 x 5
140.00000  203.33333  267.83333   394.33333   551.93333
206.41667  299.75000  394.25000   580.75000   813.35000
273.26667  396.60000  521.10000   767.60000  1075.20000
379.66667  551.00000  723.50000  1066.00000  1493.60000

With 'spline' method:

x = [2, 5, 6, 10, 12, 17];
y = [10, 13, 17, 18, 23, 25, 29];
z = [98  184  214  328   386   528;
129  242  281  431   507   694;
170  319  370  568   668   915;
181  339  393  603   709   971;
232  435  504  774   910  1247;
253  474  549  843   991  1358;
294  551  638  980  1152  1579];
xi = [3, 5, 7, 11, 16];
yi = [11, 16, 21, 29]';
zi = interp2(x,y,z,xi,yi,'spline')
zi = [Matrix] 4 x 5
138.57956  203.66379  268.77725   394.48736   553.65523
204.24151  299.32574  394.43920   580.14931   814.31718
271.79883  396.88307  521.99653   767.70664  1076.87451
377.91577  551.00000  724.11346  1065.82357  1494.99144

Comments

If x and y are vectors, then their lengths must equal the number of columns and rows of z, respectively. If x and y are matrices, then the rows of x are assumed to be identical, and likewise for the columns of y.

If xi and yi are vectors, then their lengths determine the number of columns and rows of zi, respectively. If xi and yi are matrices, then they must have the same dimensions, which will also be the dimensions of zi.

The 'spline' method uses not-a-knot cubic splines on the grid, together with a bicubic interpolation between the grid lines.