Spline Toolbox    
stmak

Put together a function in stform

Syntax

Description

stmak(centers,coefs) returns the stform of the function given by

with

the thin-plate spline basis function, and with denoting the Euclidean norm of the vector .

centers and coefs must be matrices with the same number of columns.

st = stmak(centers,x,type) stores in st the stform of the function given by

with the as indicated by the string type, which can be one of the following:

Here are the details.

'tp00'
, =centers(:,j), j=1:n-3

with




'tp10'
, =centers(:,j), j=1:n-1

with , and the partial derivative of wrto


'tp01'
, =centers(:,j), j=1:n-1

with , and the partial derivative of wrto


'tp'
(default)
, =centers(:,j), j=1:n

with

st = stmak(centers,coefs,type,interv) also specifies the basic interval for the stform, with interv{j} specifying, in the form [a,b], the range of the jth variable. The default for interv is the smallest such box that contains all the given centers.

Examples

Example 1. The following generates the figure below, of the thin-plate spline basis function, , but suitably restricted to show that this function is negative near the origin. For this, the extra lines are there to indicate the zero level.

Example 2. We now also generate and plot, on the very same domain, the first partial derivative of the thin-plate spline basis function, with respect to its second argument.

Note that, this time, we have explicitly set the basic interval for the stform.

The resulting figure, below, shows a very strong variation near the origin. This reflects the fact that the second derivatives of have a logarithmic singularity there.

See Also

stcol


  stcol tpaps