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stcol - Scattered translates collocation matrix

Syntax

colmat = stcol(centers,x,type) colmat = stcol(...,'tr')

Description

colmat = stcol(centers,x,type) is the matrix whose (i,j)th entry is

with the bivariate functions and the number n depending on the centers and the string type, as detailed in the description of stmak.

centers and x must be matrices with the same number of rows.

The default for type is the string 'tp', and for this default, n equals size(centers,2), and the functions are given by

with the thin-plate spline basis function

and with denoting the Euclidean norm of the vector .

Note See stmak for a description of other possible values for type.

The matrix colmat is the coefficient matrix in the linear system

that the coefficients of the function must satisfy in order that interpolate the value at the site x(:,i), all i.

colmat = stcol(...,'tr') returns the transpose of the matrix returned by stcol(...).

Examples

Example 1. The following evaluates and plots the function

on a regular mesh, with the above thin-plate basis function, and with c1, c2, c3 three points on the unit circle; see the figure below.

a = [0,2/3*pi,4/3*pi]; centers = [cos(a), 0; sin(a), 0];
[xx,yy] = ndgrid(linspace(-2,2,45)); 
xy = [xx(:) yy(:)].';
coefs = [1 1 1 -3.5];
zz = reshape( coefs*stcol(centers,xy,'tr') , size(xx));
surf(xx,yy,zz), view([240,15]), axis off

Example 2. The following also evaluates, on the same mesh, and plots the length of the gradient of the function in Example 1.

zz = reshape( sqrt(...
        ([coefs,0]*stcol(centers,xy,'tp10','tr')).^2 + ...
        ([coefs,0]*stcol(centers,xy,'tr','tp01')).^2), 
size(xx));
figure, surf(xx,yy,zz), view([220,-15]), axis off

stcol - Scattered translates collocation matrix

Syntax

Description

Examples

See Also

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