spsurfun

Evaluate the sparse grid interpolant at a single point.

spsurfun is provided for conveniece to be used as an alternative to spinterp, where the point Y to be evaluated is given as a row or column vector. This functional form is often adopted by multivariate optimization algorithms in Matlab.

Note that this form allows the evaluation of the sparse grid interpolant at a single point only. Therefore, It is recommended to use spinterp instead if multiple evaluations of the interpolant can be performed simultaneously.

Syntax

IP = spsurfun(Y,Z)
[IP,IPGRAD] = spsurfun(Y,Z)

Description

IP = spsurfun(Y,Z) Computes the interpolated value IP at the single point [Y1, ..., YD] for the sparse grid interpolant Z.

[IP,IPGRAD] = spsurfun(...) Computes the interpolated value IP and the gradient vector IPGRAD.

Two additional options are available with spsurfun that are set by adding a field to the structure Z:

• selectOutput [ integer {1} ] Set the output variable number if an interpolant with multiple output variables was constructed with spvals.
• continuousDerivatives [ 'on' | {'off'} ] Enable augmented continuous derivatives for the Clenshaw-Curtis grid.

Examples

The following code shows how to use spsurfun. Note that as opposed to the spinterp syntax, the second argument is the sparse grid interpolant, not the first one.

f = inline('x.^2 + y.^2 - 2.*z');
z = spvals(f,3,[],spset('GridType','Chebyshev'));
[ip,ipgrad] = spinterp(z, 0.5, 0.2, 0.2)
[ip,ipgrad] = spsurfun([0.5, 0.2, 0.2], z)

in =
   -0.1100
ipgrad = 
    [3x1 double]
ip =
   -0.1100
ipgrad =
    1.0000
    0.4000
   -2.0000

See the help page on sparse grid optimization for an example where spsurfun is used with an optimization method from Mathwork's Optimization Toolbox.

See Also

spinterp.