Scattered translates collocation matrix
colmat = stcol(centers,x,type)
colmat = stcol(...,'tr')
colmat = stcol(centers,x,type) is the
matrix whose (
j)th entry is
with the bivariate functions ψj and the
n depending on the
centers and the
character vector or string scalar
type, as detailed in the
x must be matrices with the same
number of rows.
The default for
type is the character vector
'tp', and for this default,
size(centers,2), and the functions
ψj are given by
with ψ the thin-plate spline basis function
and with |x| denoting the Euclidean norm of the vector x.
stmak for a description of
other possible values for
colmat is the coefficient matrix in the linear
that the coefficients aj of the function
must satisfy in order that f interpolate the value
yi at the site
colmat = stcol(...,'tr') returns the
transpose of the matrix returned by
Example 1. The following evaluates and plots the function
on a regular mesh, with ψ 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