08-Jan-2022 09:45:55 sparse_interp_nd_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 Test sparse_interp_nd(). The R8LIB library is also required. SPARSE_INTERP_ND_TEST01: Sparse interpolation for a function f(x) of M-dimensional argument. Use a sequence of sparse grids of levels 0 through SPARSE_MAX. Invoke a general Lagrange interpolant function to do this. Compare the exact function and the interpolants at a grid of points. The "order" is the sum of the orders of all the product grids used to make a particular sparse grid. Spatial dimension M = 1 Maximum sparse grid level = 9 Number of interpolation points is NI = 100 L Order ApproxError 0 1 2.522725e-02 1 3 5.062799e-04 2 5 1.631396e-06 3 9 2.037762e-12 4 17 2.048961e-17 5 33 3.487766e-17 6 65 3.392992e-17 7 129 4.254838e-17 8 257 6.818169e-17 9 513 4.246672e-15 Elapsed time is 0.728660 seconds. SPARSE_INTERP_ND_TEST01: Sparse interpolation for a function f(x) of M-dimensional argument. Use a sequence of sparse grids of levels 0 through SPARSE_MAX. Invoke a general Lagrange interpolant function to do this. Compare the exact function and the interpolants at a grid of points. The "order" is the sum of the orders of all the product grids used to make a particular sparse grid. Spatial dimension M = 2 Maximum sparse grid level = 9 Number of interpolation points is NI = 100 L Order ApproxError 0 1 1.953485e-02 1 7 6.473906e-03 2 25 5.995136e-04 3 67 7.488308e-04 4 161 2.369064e-04 5 371 7.620782e-05 6 837 2.287569e-05 7 1863 1.329944e-05 8 4105 1.258689e-06 9 8971 7.530324e-07 Elapsed time is 4.405118 seconds. SPARSE_INTERP_ND_TEST01: Sparse interpolation for a function f(x) of M-dimensional argument. Use a sequence of sparse grids of levels 0 through SPARSE_MAX. Invoke a general Lagrange interpolant function to do this. Compare the exact function and the interpolants at a grid of points. The "order" is the sum of the orders of all the product grids used to make a particular sparse grid. Spatial dimension M = 3 Maximum sparse grid level = 9 Number of interpolation points is NI = 100 L Order ApproxError 0 1 1.668699e-02 1 10 6.463606e-03 2 52 2.448000e-03 3 195 3.217250e-04 4 609 6.641054e-04 5 1710 3.150076e-04 6 4502 1.408414e-04 7 11369 6.275155e-05 8 27887 3.375686e-05 9 66936 8.420761e-06 Elapsed time is 25.243910 seconds. SPARSE_INTERP_ND_TEST01: Sparse interpolation for a function f(x) of M-dimensional argument. Use a sequence of sparse grids of levels 0 through SPARSE_MAX. Invoke a general Lagrange interpolant function to do this. Compare the exact function and the interpolants at a grid of points. The "order" is the sum of the orders of all the product grids used to make a particular sparse grid. Spatial dimension M = 4 Maximum sparse grid level = 7 Number of interpolation points is NI = 100 L Order ApproxError 0 1 1.363654e-02 1 13 5.663999e-03 2 87 1.780058e-03 3 411 7.507483e-04 4 1573 1.649774e-04 5 5257 2.399414e-04 6 16035 2.645979e-04 7 45879 1.931831e-04 Elapsed time is 18.756200 seconds. sparse_interp_nd_test(): Normal end of execution. 08-Jan-2022 09:46:45