lagrange_interp_2d_test

lagrange_interp_2d_test, a MATLAB code which calls lagrange_interp_2d(), which defines and evaluates the Lagrange polynomial p(x,y) which interpolates a set of data depending on a 2D argument that was evaluated on a product grid, so that p(x(i),y(j)) = z(i,j).

Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license

Related Data and Programs:

lagrange_interp_2d, a MATLAB code which defines and evaluates the Lagrange polynomial p(x,y) which interpolates a set of data depending on a 2D argument that was evaluated on a product grid, so that p(x(i),y(j)) = z(i,j).

Source Code:

• lagrange_interp_2d_test.m, calls all the tests;
• lagrange_interp_2d_test.sh, runs all the tests;
• lagrange_interp_2d_test.txt, the output file.

• lagrange_interp_2d_test01.m, tests the interpolation condition, and the approximation power of the interpolant at the midpoints.
• lagrange_interp_2d_test02.m, plots a linear interpolant to a triangulation of the original data, and the Lagrange interpolant.

lagrange_interp_2d_test02() plots a piecewise linear interpolant to the original data, and the Lagrange interpolant.

• p01_data.png, a plot of the piecewise linear interpolant to the data for problem p01;
• p01_poly01.png, a plot of the polynomial interpolant for problem p01, degree 1;
• p01_poly02.png, a plot of the polynomial interpolant for problem p01, degree 2;
• p01_poly03.png, a plot of the polynomial interpolant for problem p01, degree 3;
• p01_poly04.png, a plot of the polynomial interpolant for problem p01, degree 4;
• p01_poly08.png, a plot of the polynomial interpolant for problem p01, degree 8;
• p02_data.png, a plot of the piecewise linear interpolant to the data for problem p02;
• p02_poly01.png, a plot of the polynomial interpolant for problem p02, degree 1;
• p02_poly02.png, a plot of the polynomial interpolant for problem p02, degree 2;
• p02_poly03.png, a plot of the polynomial interpolant for problem p02, degree 3;
• p02_poly04.png, a plot of the polynomial interpolant for problem p02, degree 4;
• p02_poly08.png, a plot of the polynomial interpolant for problem p02, degree 8;
• p03_data.png, a plot of the piecewise linear interpolant to the data for problem p03;
• p03_poly01.png, a plot of the polynomial interpolant for problem p03, degree 1;
• p03_poly02.png, a plot of the polynomial interpolant for problem p03, degree 2;
• p03_poly03.png, a plot of the polynomial interpolant for problem p03, degree 3;
• p03_poly04.png, a plot of the polynomial interpolant for problem p03, degree 4;
• p03_poly08.png, a plot of the polynomial interpolant for problem p03, degree 8;
• p04_data.png, a plot of the piecewise linear interpolant to the data for problem p04;
• p04_poly01.png, a plot of the polynomial interpolant for problem p04, degree 1;
• p04_poly02.png, a plot of the polynomial interpolant for problem p04, degree 2;
• p04_poly03.png, a plot of the polynomial interpolant for problem p04, degree 3;
• p04_poly04.png, a plot of the polynomial interpolant for problem p04, degree 4;
• p04_poly08.png, a plot of the polynomial interpolant for problem p04, degree 8;
• p05_data.png, a plot of the piecewise linear interpolant to the data for problem p05;
• p05_poly01.png, a plot of the polynomial interpolant for problem p05, degree 1;
• p05_poly02.png, a plot of the polynomial interpolant for problem p05, degree 2;
• p05_poly03.png, a plot of the polynomial interpolant for problem p05, degree 3;
• p05_poly04.png, a plot of the polynomial interpolant for problem p05, degree 4;
• p05_poly08.png, a plot of the polynomial interpolant for problem p05, degree 8;
• p06_data.png, a plot of the piecewise linear interpolant to the data for problem p06;
• p06_poly01.png, a plot of the polynomial interpolant for problem p06, degree 1;
• p06_poly02.png, a plot of the polynomial interpolant for problem p06, degree 2;
• p06_poly03.png, a plot of the polynomial interpolant for problem p06, degree 3;
• p06_poly04.png, a plot of the polynomial interpolant for problem p06, degree 4;
• p06_poly08.png, a plot of the polynomial interpolant for problem p06, degree 8;
• p07_data.png, a plot of the piecewise linear interpolant to the data for problem p07;
• p07_poly01.png, a plot of the polynomial interpolant for problem p07, degree 1;
• p07_poly03.png, a plot of the polynomial interpolant for problem p07, degree 3;
• p07_poly02.png, a plot of the polynomial interpolant for problem p07, degree 2;
• p07_poly04.png, a plot of the polynomial interpolant for problem p07, degree 4;
• p07_poly08.png, a plot of the polynomial interpolant for problem p07, degree 8;
• p08_data.png, a plot of the piecewise linear interpolant to the data for problem p08;
• p08_poly01.png, a plot of the polynomial interpolant for problem p08, degree 1;
• p08_poly02.png, a plot of the polynomial interpolant for problem p08, degree 2;
• p08_poly03.png, a plot of the polynomial interpolant for problem p08, degree 3;
• p08_poly04.png, a plot of the polynomial interpolant for problem p08, degree 4;
• p08_poly08.png, a plot of the polynomial interpolant for problem p08, degree 8;
• p09_data.png, a plot of the piecewise linear interpolant to the data for problem p09;
• p09_poly01.png, a plot of the polynomial interpolant for problem p09, degree 1;
• p09_poly02.png, a plot of the polynomial interpolant for problem p09, degree 2;
• p09_poly03.png, a plot of the polynomial interpolant for problem p09, degree 3;
• p09_poly04.png, a plot of the polynomial interpolant for problem p09, degree 4;
• p09_poly08.png, a plot of the polynomial interpolant for problem p09, degree 8;
• p10_data.png, a plot of the piecewise linear interpolant to the data for problem p10;
• p10_poly01.png, a plot of the polynomial interpolant for problem p10, degree 1;
• p10_poly02.png, a plot of the polynomial interpolant for problem p10, degree 2;
• p10_poly03.png, a plot of the polynomial interpolant for problem p10, degree 3;
• p10_poly04.png, a plot of the polynomial interpolant for problem p10, degree 4;
• p10_poly08.png, a plot of the polynomial interpolant for problem p10, degree 8;
• p11_data.png, a plot of the piecewise linear interpolant to the data for problem p11;
• p11_poly01.png, a plot of the polynomial interpolant for problem p11, degree 1;
• p11_poly02.png, a plot of the polynomial interpolant for problem p11, degree 2;
• p11_poly03.png, a plot of the polynomial interpolant for problem p11, degree 3;
• p11_poly04.png, a plot of the polynomial interpolant for problem p11, degree 4;
• p11_poly08.png, a plot of the polynomial interpolant for problem p11, degree 8;
• p12_data.png, a plot of the piecewise linear interpolant to the data for problem p12;
• p12_poly01.png, a plot of the polynomial interpolant for problem p12, degree 1;
• p12_poly02.png, a plot of the polynomial interpolant for problem p12, degree 2;
• p12_poly03.png, a plot of the polynomial interpolant for problem p12, degree 3;
• p12_poly04.png, a plot of the polynomial interpolant for problem p12, degree 4;
• p12_poly08.png, a plot of the polynomial interpolant for problem p12, degree 8;
• p13_data.png, a plot of the piecewise linear interpolant to the data for problem p13;
• p13_poly01.png, a plot of the polynomial interpolant for problem p13, degree 1;
• p13_poly02.png, a plot of the polynomial interpolant for problem p13, degree 2;
• p13_poly03.png, a plot of the polynomial interpolant for problem p13, degree 3;
• p13_poly04.png, a plot of the polynomial interpolant for problem p13, degree 4;
• p13_poly08.png, a plot of the polynomial interpolant for problem p13, degree 8;