PWL_APPROX_1D
Approximation in 1D using Piecewise Linear Functions

PWL_APROX_1D is a MATLAB library which defines and evaluates a piecewise linear function, using NC "control points", which approximates a set of ND data points (x(i),y(i)).

PWL_APPROX_1D needs access to the R8LIB library. The test code also needs access to the TEST_INTERP_1D library.

Licensing:

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

Languages:

PWL_APPROX_1D is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

LAGRANGE_APPROX_1D, a MATLAB library which defines and evaluates the Lagrange polynomial p(x) of degree m which approximates a set of nd data points (x(i),y(i)).

PWL_INTERP_1D, a MATLAB library which interpolates a set of data using a piecewise linear function.

R8LIB, a MATLAB library which contains many utility routines using double precision real (R8) arithmetic.

SPLINE, a MATLAB library which constructs and evaluates spline interpolants and approximants.

TEST_APPROX, a MATLAB library which defines test problems for approximation, provided as a set of (x,y) data.

TEST_INTERP, a MATLAB library which defines a number of test problems for interpolation, provided as a set of (x,y) data.

TEST_INTERP_1D, a MATLAB library which defines test problems for interpolation of data y(x), depending on a 2D argument.

VANDERMONDE_APPROX_1D, a MATLAB library which finds a polynomial approximant to data of a 1D argument by setting up and solving an overdetermined linear system for the polynomial coefficients, involving the Vandermonde matrix.

Reference:

1. Kendall Atkinson,
   An Introduction to Numerical Analysis,
   Prentice Hall, 1989,
   ISBN: 0471624896,
   LC: QA297.A94.1989.
2. Philip Davis,
   Interpolation and Approximation,
   Dover, 1975,
   ISBN: 0-486-62495-1,
   LC: QA221.D33
3. David Kahaner, Cleve Moler, Steven Nash,
   Numerical Methods and Software,
   Prentice Hall, 1989,
   ISBN: 0-13-627258-4,
   LC: TA345.K34.

Source Code:

• pwl_approx_1d.m, determines the control points and values to be used by a piecewise linear approximant to given data.
• pwl_approx_1d_matrix.m, evaluates a matrix used to determine the control points.
• pwl_interp_1d.m, evaluates a piecewise linear interpolant.

Examples and Tests:

The test code requires the test_interp_1d library.

• pwl_approx_1d_test.m, calls all the tests;
• pwl_approx_1d_test_output.txt, the output file.
• pwl_approx_1d_test01.m, plots a piecewise linear interpolant to the original data, and the piecewise linear approximant.

pwl_approx_1d_test01() uses nc evenly spaced control points to approximate a set of nd data values.

• p01_pwl_02_16.png, a plot of the piecewise linear approximant with 2 control points approximating 16 data values for problem p01;
• p01_pwl_04_16.png, a plot of the piecewise linear approximant with 4 control points approximating 16 data values for problem p01;
• p01_pwl_08_16.png, a plot of the piecewise linear approximant with 8 control points approximating 16 data values for problem p01;
• p01_pwl_16_16.png, a plot of the piecewise linear approximant with 16 control points approximating 16 data values for problem p01;
• p01_pwl_02_64.png, a plot of the piecewise linear approximant with 2 control points approximating 64 data values for problem p01;
• p01_pwl_04_64.png, a plot of the piecewise linear approximant with 4 control points approximating 64 data values for problem p01;
• p01_pwl_08_64.png, a plot of the piecewise linear approximant with 8 control points approximating 64 data values for problem p01;
• p01_pwl_16_64.png, a plot of the piecewise linear approximant with 16 control points approximating 64 data values for problem p01;
• p02_pwl_02_16.png, a plot of the piecewise linear approximant with 2 control points approximating 16 data values for problem p02;
• p02_pwl_04_16.png, a plot of the piecewise linear approximant with 4 control points approximating 16 data values for problem p02;
• p02_pwl_08_16.png, a plot of the piecewise linear approximant with 8 control points approximating 16 data values for problem p02;
• p02_pwl_16_16.png, a plot of the piecewise linear approximant with 16 control points approximating 16 data values for problem p02;
• p02_pwl_02_64.png, a plot of the piecewise linear approximant with 2 control points approximating 64 data values for problem p02;
• p02_pwl_04_64.png, a plot of the piecewise linear approximant with 4 control points approximating 64 data values for problem p02;
• p02_pwl_08_64.png, a plot of the piecewise linear approximant with 8 control points approximating 64 data values for problem p02;
• p02_pwl_16_64.png, a plot of the piecewise linear approximant with 16 control points approximating 64 data values for problem p02;
• p03_pwl_02_16.png, a plot of the piecewise linear approximant with 2 control points approximating 16 data values for problem p03;
• p03_pwl_04_16.png, a plot of the piecewise linear approximant with 4 control points approximating 16 data values for problem p03;
• p03_pwl_08_16.png, a plot of the piecewise linear approximant with 8 control points approximating 16 data values for problem p03;
• p03_pwl_16_16.png, a plot of the piecewise linear approximant with 16 control points approximating 16 data values for problem p03;
• p03_pwl_02_64.png, a plot of the piecewise linear approximant with 2 control points approximating 64 data values for problem p03;
• p03_pwl_04_64.png, a plot of the piecewise linear approximant with 4 control points approximating 64 data values for problem p03;
• p03_pwl_08_64.png, a plot of the piecewise linear approximant with 8 control points approximating 64 data values for problem p03;
• p03_pwl_16_64.png, a plot of the piecewise linear approximant with 16 control points approximating 64 data values for problem p03;
• p04_pwl_02_16.png, a plot of the piecewise linear approximant with 2 control points approximating 16 data values for problem p04;
• p04_pwl_04_16.png, a plot of the piecewise linear approximant with 4 control points approximating 16 data values for problem p04;
• p04_pwl_08_16.png, a plot of the piecewise linear approximant with 8 control points approximating 16 data values for problem p04;
• p04_pwl_16_16.png, a plot of the piecewise linear approximant with 16 control points approximating 16 data values for problem p04;
• p04_pwl_02_64.png, a plot of the piecewise linear approximant with 2 control points approximating 64 data values for problem p04;
• p04_pwl_04_64.png, a plot of the piecewise linear approximant with 4 control points approximating 64 data values for problem p04;
• p04_pwl_08_64.png, a plot of the piecewise linear approximant with 8 control points approximating 64 data values for problem p04;
• p04_pwl_16_64.png, a plot of the piecewise linear approximant with 16 control points approximating 64 data values for problem p04;
• p05_pwl_02_16.png, a plot of the piecewise linear approximant with 2 control points approximating 16 data values for problem p05;
• p05_pwl_04_16.png, a plot of the piecewise linear approximant with 4 control points approximating 16 data values for problem p05;
• p05_pwl_08_16.png, a plot of the piecewise linear approximant with 8 control points approximating 16 data values for problem p05;
• p05_pwl_16_16.png, a plot of the piecewise linear approximant with 16 control points approximating 16 data values for problem p05;
• p05_pwl_02_64.png, a plot of the piecewise linear approximant with 2 control points approximating 64 data values for problem p05;
• p05_pwl_04_64.png, a plot of the piecewise linear approximant with 4 control points approximating 64 data values for problem p05;
• p05_pwl_08_64.png, a plot of the piecewise linear approximant with 8 control points approximating 64 data values for problem p05;
• p05_pwl_16_64.png, a plot of the piecewise linear approximant with 16 control points approximating 64 data values for problem p05;
• p06_pwl_02_16.png, a plot of the piecewise linear approximant with 2 control points approximating 16 data values for problem p06;
• p06_pwl_04_16.png, a plot of the piecewise linear approximant with 4 control points approximating 16 data values for problem p06;
• p06_pwl_08_16.png, a plot of the piecewise linear approximant with 8 control points approximating 16 data values for problem p06;
• p06_pwl_16_16.png, a plot of the piecewise linear approximant with 16 control points approximating 16 data values for problem p06;
• p06_pwl_02_64.png, a plot of the piecewise linear approximant with 2 control points approximating 64 data values for problem p06;
• p06_pwl_04_64.png, a plot of the piecewise linear approximant with 4 control points approximating 64 data values for problem p06;
• p06_pwl_08_64.png, a plot of the piecewise linear approximant with 8 control points approximating 64 data values for problem p06;
• p06_pwl_16_64.png, a plot of the piecewise linear approximant with 16 control points approximating 64 data values for problem p06;
• p07_pwl_02_16.png, a plot of the piecewise linear approximant with 2 control points approximating 16 data values for problem p07;
• p07_pwl_04_16.png, a plot of the piecewise linear approximant with 4 control points approximating 16 data values for problem p07;
• p07_pwl_08_16.png, a plot of the piecewise linear approximant with 8 control points approximating 16 data values for problem p07;
• p07_pwl_16_16.png, a plot of the piecewise linear approximant with 16 control points approximating 16 data values for problem p07;
• p07_pwl_02_64.png, a plot of the piecewise linear approximant with 2 control points approximating 64 data values for problem p07;
• p07_pwl_04_64.png, a plot of the piecewise linear approximant with 4 control points approximating 64 data values for problem p07;
• p07_pwl_08_64.png, a plot of the piecewise linear approximant with 8 control points approximating 64 data values for problem p07;
• p07_pwl_16_64.png, a plot of the piecewise linear approximant with 16 control points approximating 64 data values for problem p07;
• p08_pwl_02_16.png, a plot of the piecewise linear approximant with 2 control points approximating 16 data values for problem p08;
• p08_pwl_04_16.png, a plot of the piecewise linear approximant with 4 control points approximating 16 data values for problem p08;
• p08_pwl_08_16.png, a plot of the piecewise linear approximant with 8 control points approximating 16 data values for problem p08;
• p08_pwl_16_16.png, a plot of the piecewise linear approximant with 16 control points approximating 16 data values for problem p08;
• p08_pwl_02_64.png, a plot of the piecewise linear approximant with 2 control points approximating 64 data values for problem p08;
• p08_pwl_04_64.png, a plot of the piecewise linear approximant with 4 control points approximating 64 data values for problem p08;
• p08_pwl_08_64.png, a plot of the piecewise linear approximant with 8 control points approximating 64 data values for problem p08;
• p08_pwl_16_64.png, a plot of the piecewise linear approximant with 16 control points approximating 64 data values for problem p08;

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