Sparse Grid Interpolation Toolbox

# Major examples

Use this example index to jump to code examples in the documentation. The examples marked [demo] are available at the Matlab command line or from the Sparse Grid Interpolation demo page within the Matlab help browser.

## Grid visualization

• Plot available sparse grid types for level `N = 3`, `D = 2` [example]
• Plot a 3D sparse grid with points colored according to level [example]
• Plot the set of multi-indices `S_k` of a two-dimensional dimension-adaptive sparse grid interpolant [example]
• `cmpgrids`: Plot available sparse grid types for level `N = 4`, `D = 2` [demo]

## Piecewise linear basis functions

• Interpolate a simple two-dimensional function [example]
• Construct an interpolant of Branin's function [example]
• Perform multiple evaluations at once: vectorized call to `spinterp` [example], [example]
• `spdemo`: Interpolate a simple two-dimensional function [demo]
• `spcompare`: Compare multilinear interpolation schemes for the test functions of Gerz [demo]

## Polynomial basis functions

• Construct a polynomial interpolant of Branin's function (dimension-adaptive and non-adaptive) [example]
• `spcomparepoly`: Error plots for multilinear vs. polynomial basis functions [demo]

• Recovery of a quadratic function with a tridiagonal Hessian (`d = 100`, piecewise linear and polynomial basis functions) [example]
• `spadaptdemo`: Dimension-adaptive interpolation of a simple two-dimensional function [demo]
• `spadaptanim`: Illustrates the dimension-adaptive construction[demo]
• `spadapterror`: Compares the error: adaptive vs. non-adaptive [demo]
• Comparison of different degrees of dimensional adaptivity [example]

## Computing Derivatives

• Computing the derivatives of a bivariate piecewise multilinear interpolant [example]
• Augmented derivatives to achieve continuity [example]
• Derivatives of polynomial interpolants [example]
• `spcomparederiv`: Error plots for the derivative computation schemes [demo]

## Numerical Integration

• Comparison of regular sparse grids for a 5d test problem [example]
• Integrating a high-dimensional dimension-adaptive interpolant [example]

## Optimization

• Using the optimization algorithms: `spcgsearch` [example], `spcompsearch` [example], `spfminsearch` [example], `spmultistart` [example]
• Optimizing a high-dimensional interpolant [example]
• Using third-party optimization methods [example]

• Setting the minimum/maximum number of support nodes [example]
• Re-using previous results [example]
• Using the VariablePositions property [example]

## Functions with multiple outputs

• Call to `spvals`: Function header type examples 6 [example], 7 [example], 8 [example], and 9 [example]
• Construct interpolant and compute interpolated values [example]
• Approximate ODE output simultaneously at multiple time steps [example]
• `spdemovarout`: Interpolate a function with multiple output arguments [demo]

## Performance related examples and demos

• Vectorizing the objective function [example]
• Re-using previous results [example], [example]
• Using `sppurge` to increase the performance when evaluating the sparse grid interpolants [example], [example]
• `timespvals`: Measure the performance of the hierarchical construction of the interpolant [demo]
• `timespvalsdct`: Measure the performance of the hierarchical construction of Chebyshev-polynomial-based interpolants, with and without using a fast DCT [demo]
• `timespinterp`: Measure the performance of computing 1000 interpolated values [demo]
• `timespderiv`: Measure the performance of computing both interpolated values and gradients [demo]