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]

Dimension-adaptive sparse grids

• 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]
• Adjusting the adaptivity degree during interpolant construction [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]

Providing additional options

• 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]