Description

FINTERPN Linear N-D interpolation with data from file.

[ Vq ] = FINTERPN( FILENAME(X1, X2, ..., Xn, V), Xq1, Xq2, ..., Xqn) Interpolate data from FILENAME in query points Xq1, Xq2, ..., Xqn.

Interpolation sample point coordinates (X1, X2, ..., Xn) and corresponding function values (V) must be provided by FILENAME in either of the following formats

.csv - ASCII text file with columns of comma separated values
.txt - ASCII text file with columns of space separated values
.xls/xslx - Microsoft Excel table format

The data in FILENAME must be stored as column vectors X1, X2, ..., Xn, and and V consistent to be used with NDGRID, for example of 3D interpolation

x1, y1, z1, v1
x2, y1, z1, v2
x1, y2, z1, v3
x2, y2, z1, v4
x1, y3, z1, v5
x2, y3, z1, v6
      ...
x1, y1, zN, vM-5
      ...
x2, y3, zN, vM

For the .mat file format, must contain a variable named "data"

.mat - MATLAB file with a variable named "data"

where "data" can be an array as defined above, or a cell array containing the interpolation points and function values.

data = {x, y, z, v};  % x/y/z/v size[nx,ny,nz]

Examples

   1) Command line use (1D interpolation)

   x = linspace(0,1,10)';  % Sample point coordinates
   v = (1:10)';  % Values at sample points

   basename = 'test_data';
   data = {x, v};  % Cell data format used by mat file
   save([basename,'.mat'], '-mat', 'data');

   data = [x, v];  % Array data format used by csv/txt file
   csvwrite([basename,'.csv'], data);
   save([basename,'.txt'], '-ascii', 'data');

   results = finterpn([basename,'.csv'], [0.2, 0.5])
   results = finterpn([basename,'.mat'], [0.2, 0.5])
   results = finterpn([basename,'.txt'], [0.2, 0.5])

   2) Equation coefficient (2D interpolation)

   x = linspace(0,1,10);
   y = linspace(0,1,20);
   [xx,yy] = ndgrid(x,y);
   v = rand(size(xx));

   basename = 'test_data';
   data = [xx(:), yy(:), v(:)];
   csvwrite([basename,'.csv'], data);

   fea.sdim = {'x', 'y'};
   fea.geom.objects = {gobj_rectangle};
   fea.grid = rectgrid();
   fea = addphys(fea,@poisson);
   source_term = ['1+2*finterpn('',basename,'.csv'',x,y)'];
   fea.phys.poi.eqn.coef{3,4} = { source_term };

   fea = parsephys(fea);
   fea = parseprob(fea);

   fea.sol.u = solvestat(fea);

   subplot(1,2,1)
   postplot(fea, 'surfexpr', 'u')
   subplot(1,2,2)
   postplot(fea, 'surfexpr', source_term)

See also: csvread, xlsread, load, ndgrid, interpn