lagrange_interp_1d_test

lagrange_interp_1d_test, an Octave code which calls lagrange_interp_1d(), which defines and evaluates the Lagrange polynomial p(x) which interpolates a set of data, so that p(x(i)) = y(i).

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_1d, an Octave code which defines and evaluates the Lagrange polynomial p(x) which interpolates a set of data, so that p(x(i)) = y(i).

Source Code:

• lagrange_interp_1d_test.m, calls all the tests;
• lagrange_interp_1d_test.sh, runs all the tests;
• lagrange_interp_1d_test.txt, the output file.

• lagrange_interp_1d_test01.m, samples a function at ND evenly-spaced points, plots the piecewise linear interpolant to this data, and the Lagrange polynomial interpolant.
• lagrange_interp_1d_test02.m, samples a function at ND Chebyshev-spaced points, plots the piecewise linear interpolant to this data, and the Lagrange polynomial interpolant.
• r8vec_cheby_extreme.m, returns a vector of Chebyshev-spaced points.

lagrange_interp_1d_test01() plots the data and Lagrange interpolant for even spacing.

Images for Problem 1:

• p01_dataeven_04.png
• p01_lageven_04.png
• p01_dataeven_08.png
• p01_lageven_08.png
• p01_dataeven_16.png
• p01_lageven_16.png
• p01_dataeven_32.png
• p01_lageven_32.png
• p01_dataeven_64.png
• p01_lageven_64.png

Images for Problem p02:

• p02_dataeven_04.png
• p02_lageven_04.png
• p02_dataeven_08.png
• p02_lageven_08.png
• p02_dataeven_16.png
• p02_lageven_16.png
• p02_dataeven_32.png
• p02_lageven_32.png
• p02_dataeven_64.png
• p02_lageven_64.png

Images for problem p03:

• p03_dataeven_04.png, a plot of the 4 node even data for problem p03;
• p03_lageven_04.png, a plot of the Lagrange/even 4 node polynomial interpolant for problem p03;
• p03_dataeven_08.png, a plot of the 8 node even data for problem p03;
• p03_lageven_08.png, a plot of the Lagrange/even 8 node polynomial interpolant for problem p03;
• p03_dataeven_16.png, a plot of the 16 node even data for problem p03;
• p03_lageven_16.png, a plot of the Lagrange/even 16 node polynomial interpolant for problem p03;
• p03_dataeven_32.png, a plot of the 32 node even data for problem p03;
• p03_lageven_32.png, a plot of the Lagrange/even 32 node polynomial interpolant for problem p03;
• p03_dataeven_64.png, a plot of the 64 node even data for problem p03;
• p03_lageven_64.png, a plot of the Lagrange/even 64 node polynomial interpolant for problem p03;

Images for problem p04:

• p04_dataeven_04.png, a plot of the 4 node even data for problem p04;
• p04_lageven_04.png, a plot of the Lagrange/even 4 node polynomial interpolant for problem p04;
• p04_dataeven_08.png, a plot of the 8 node even data for problem p04;
• p04_lageven_08.png, a plot of the Lagrange/even 8 node polynomial interpolant for problem p04;
• p04_dataeven_16.png, a plot of the 16 node even data for problem p04;
• p04_lageven_16.png, a plot of the Lagrange/even 16 node polynomial interpolant for problem p04;
• p04_dataeven_32.png, a plot of the 32 node even data for problem p04;
• p04_lageven_32.png, a plot of the Lagrange/even 32 node polynomial interpolant for problem p04;
• p04_dataeven_64.png, a plot of the 64 node even data for problem p04;
• p04_lageven_64.png, a plot of the Lagrange/even 64 node polynomial interpolant for problem p04;

Images for problem p05:

• p05_dataeven_04.png, a plot of the 4 node even data for problem p05;
• p05_lageven_04.png, a plot of the Lagrange/even 4 node polynomial interpolant for problem p05;
• p05_dataeven_08.png, a plot of the 8 node even data for problem p05;
• p05_lageven_08.png, a plot of the Lagrange/even 8 node polynomial interpolant for problem p05;
• p05_dataeven_16.png, a plot of the 16 node even data for problem p05;
• p05_lageven_16.png, a plot of the Lagrange/even 16 node polynomial interpolant for problem p05;
• p05_dataeven_32.png, a plot of the 32 node even data for problem p05;
• p05_lageven_32.png, a plot of the Lagrange/even 32 node polynomial interpolant for problem p05;
• p05_dataeven_64.png, a plot of the 64 node even data for problem p05;
• p05_lageven_64.png, a plot of the Lagrange/even 64 node polynomial interpolant for problem p05;

Images for problem p06:

• p06_dataeven_04.png, a plot of the 4 node even data for problem p06;
• p06_lageven_04.png, a plot of the Lagrange/even 4 node polynomial interpolant for problem p06;
• p06_dataeven_08.png, a plot of the 8 node even data for problem p06;
• p06_lageven_08.png, a plot of the Lagrange/even 8 node polynomial interpolant for problem p06;
• p06_dataeven_16.png, a plot of the 16 node even data for problem p06;
• p06_lageven_16.png, a plot of the Lagrange/even 16 node polynomial interpolant for problem p06;
• p06_dataeven_32.png, a plot of the 32 node even data for problem p06;
• p06_lageven_32.png, a plot of the Lagrange/even 32 node polynomial interpolant for problem p06;
• p06_dataeven_64.png, a plot of the 64 node even data for problem p06;
• p06_lageven_64.png, a plot of the Lagrange/even 64 node polynomial interpolant for problem p06;

Images for problem p07:

• p07_dataeven_04.png, a plot of the 4 node even data for problem p07;
• p07_lageven_04.png, a plot of the Lagrange/even 4 node polynomial interpolant for problem p07;
• p07_dataeven_08.png, a plot of the 8 node even data for problem p07;
• p07_lageven_08.png, a plot of the Lagrange/even 8 node polynomial interpolant for problem p07;
• p07_dataeven_16.png, a plot of the 16 node even data for problem p07;
• p07_lageven_16.png, a plot of the Lagrange/even 16 node polynomial interpolant for problem p07;
• p07_dataeven_32.png, a plot of the 32 node even data for problem p07;
• p07_lageven_32.png, a plot of the Lagrange/even 32 node polynomial interpolant for problem p07;
• p07_dataeven_64.png, a plot of the 64 node even data for problem p07;
• p07_lageven_64.png, a plot of the Lagrange/even 64 node polynomial interpolant for problem p07;

Images for problem p08:

• p08_dataeven_04.png, a plot of the 4 node even data for problem p08;
• p08_lageven_04.png, a plot of the Lagrange/even 4 node polynomial interpolant for problem p08;
• p08_dataeven_08.png, a plot of the 8 node even data for problem p08;
• p08_lageven_08.png, a plot of the Lagrange/even 8 node polynomial interpolant for problem p08;
• p08_dataeven_16.png, a plot of the 16 node even data for problem p08;
• p08_lageven_16.png, a plot of the Lagrange/even 16 node polynomial interpolant for problem p08;
• p08_dataeven_32.png, a plot of the 32 node even data for problem p08;
• p08_lageven_32.png, a plot of the Lagrange/even 32 node polynomial interpolant for problem p08;
• p08_dataeven_64.png, a plot of the 64 node even data for problem p08;
• p08_lageven_64.png, a plot of the Lagrange/even 64 node polynomial interpolant for problem p08;

lagrange_interp_1d_test02() plots the data and Lagrange interpolant for Chebyshev spacing.

• p01_datacheby_04.png
• p01_lagcheby_04.png
• p01_datacheby_08.png
• p01_lagcheby_08.png
• p01_datacheby_16.png
• p01_lagcheby_16.png
• p01_datacheby_32.png
• p01_lagcheby_32.png
• p01_datacheby_64.png
• p01_lagcheby_64.png

Images for Problem p02:

• p02_datacheby_04.png
• p02_lagcheby_04.png
• p02_datacheby_08.png
• p02_lagcheby_08.png
• p02_datacheby_16.png
• p02_lagcheby_16.png
• p02_datacheby_32.png
• p02_lagcheby_32.png
• p02_datacheby_64.png
• p02_lagcheby_64.png