TEST_INTERP
Interpolation Test Data
TEST_INTERP
is a C++ library which
defines data that may be used to test interpolation algorithms.
The following sets of data are available:

p01_plot.png,
18 data points, 2 dimensions.
This example is due to HansJoerg Wenz.
It is an example of good data, which is dense enough in areas
where the expected curvature of the interpolant is large.
Good results can be expected with almost any reasonable
interpolation method.

p02_plot.png,
18 data points, 2 dimensions. This example is due to ETY Lee of Boeing.
Data near the corners is more dense than in regions of small curvature.
A local interpolation method will produce a more plausible
interpolant than a nonlocal interpolation method, such as
cubic splines.

p03_plot.png,
11 data points, 2 dimensions. This example is due to Fred Fritsch and Ralph Carlson.
This data can cause problems for interpolation methods.
There are sudden changes in direction, and at the same time,
sparselyplaced data. This can cause an interpolant to overshoot
the data in a way that seems implausible.

p04_plot.png,
8 data points, 2 dimensions. This example is due to Larry Irvine, Samuel Marin and Philip Smith.
This data can cause problems for interpolation methods.
There are sudden changes in direction, and at the same time,
sparselyplaced data. This can cause an interpolant to overshoot
the data in a way that seems implausible.

p05_plot.png,
9 data points, 2 dimensions. This example is due to Larry Irvine, Samuel Marin and Philip Smith.
This data can cause problems for interpolation methods.
There are sudden changes in direction, and at the same time,
sparselyplaced data. This can cause an interpolant to overshoot
the data in a way that seems implausible.

p06_plot.png,
49 data points, 2 dimensions. The data is due to deBoor and Rice.
The data represents a temperature dependent property of titanium.
The data has been used extensively as an example in spline
approximation with variablyspaced knots.
DeBoor considers two sets of knots:
(595,675,755,835,915,995,1075)
and
(595,725,850,910,975,1040,1075).

p07_plot.png,
4 data points, 2 dimensions. The data is a simple symmetric set of 4 points,
for which it is interesting to develop the Shepard interpolants
for varying values of the exponent p.

p08_plot.png,
12 data points, 2 dimensions. This is equally spaced data for y = x^2,
except for one extra point whose x value is close to another, but whose
y value is not so close. A small disagreement in nearby data can
become a disaster.
TEST_INTERP requires access to a compiled copy of the R8LIB library.
Licensing:
The computer code and data files described and made available on this web page
are distributed under
the GNU LGPL license.
Languages:
TEST_INTERP is available in
a C version and
a C++ version and
a FORTRAN90 version and
a MATLAB version and
a Python version.
Related Data and Programs:
DIVDIF,
a C++ library which
includes many routines to construct and evaluate divided difference
interpolants.
HERMITE,
a C++ library which
computes the Hermite interpolant, a polynomial that matches function values
and derivatives.
INTERPOLATION,
a dataset directory which
contains datasets to be interpolated.
LAGRANGE_INTERP_1D,
a C++ library which
defines and evaluates the Lagrange polynomial p(x)
which interpolates a set of data, so that p(x(i)) = y(i).
NEAREST_INTERP_1D,
a C++ library which
interpolates a set of data using a piecewise constant interpolant
defined by the nearest neighbor criterion.
NEWTON_INTERP_1D,
a C++ library which
finds a polynomial interpolant to data using Newton divided differences.
PWL_INTERP_1D,
a C++ library which
interpolates a set of data using a piecewise linear function.
R8LIB,
a C++ library which
contains many utility routines using double precision real (R8) arithmetic.
RBF_INTERP,
a C++ library which
defines and evaluates radial basis function (RBF) interpolants to multidimensional data.
SPLINE,
a C++ library which
includes many routines to construct and evaluate spline
interpolants and approximants.
TEST_APPROX,
a C++ library which
defines test problems for approximation,
provided as a set of (x,y) data.
TEST_INTERP_ND,
a C++ library which
defines test problems for interpolation of data z(x),
depending on an Mdimensional argument.
Reference:

Carl DeBoor, John Rice,
Leastsquares cubic spline approximation II  variable knots.
Technical Report CSD TR 21,
Purdue University, Lafayette, Indiana, 1968.

Carl DeBoor,
A Practical Guide to Splines,
Springer, 2001,
ISBN: 0387953663,
LC: QA1.A647.v27.

Fred Fritsch, Ralph Carlson,
Monotone Piecewise Cubic Interpolation,
SIAM Journal on Numerical Analysis,
Volume 17, Number 2, April 1980, pages 238246.

Larry Irvine, Samuel Marin, Philip Smith,
Constrained Interpolation and Smoothing,
Constructive Approximation,
Volume 2, Number 1, December 1986, pages 129151.

ETY Lee,
Choosing Nodes in Parametric Curve Interpolation,
ComputerAided Design,
Volume 21, Number 6, July/August 1989, pages 363370.

HansJoerg Wenz,
Interpolation of Curve Data by Blended Generalized Circles,
Computer Aided Geometric Design,
Volume 13, Number 8, November 1996, pages 673680.
Source Code:
Examples and Tests:
List of Routines:

P00_DATA returns the data for any problem.

P00_DATA_NUM returns the number of data points for any problem.

P00_DIM_NUM returns the spatial dimension for any problem.

P00_PROB_NUM returns the number of test problems.

P00_STORY prints the "story" for any problem.

P01_DATA returns the data for problem 01.

P01_DATA_NUM returns the number of data points for problem 01.

P01_DIM_NUM returns the spatial dimension for problem 01.

P01_STORY prints the "story" for problem 01.

P02_DATA returns the data for problem 02.

P02_DATA_NUM returns the number of data points for problem 02.

P02_DIM_NUM returns the spatial dimension for problem 02.

P02_STORY prints the "story" for problem 02.

P03_DATA returns the data for problem 03.

P03_DATA_NUM returns the number of data points for problem 03.

P03_DIM_NUM returns the spatial dimension for problem 03.

P03_STORY prints the "story" for problem 03.

P04_DATA returns the data for problem 04.

P04_DATA_NUM returns the number of data points for problem 04.

P04_DIM_NUM returns the spatial dimension for problem 04.

P04_STORY prints the "story" for problem 04.

P05_DATA returns the data for problem 05.

P05_DATA_NUM returns the number of data points for problem 05.

P05_DIM_NUM returns the spatial dimension for problem 05.

P05_STORY prints the "story" for problem 05.

P06_DATA returns the data for problem 06.

P06_DATA_NUM returns the number of data points for problem 06.

P06_DIM_NUM returns the spatial dimension for problem 06.

P06_STORY prints the "story" for problem 06.

P07_DATA returns the data for problem 07.

P07_DATA_NUM returns the number of data points for problem 07.

P07_DIM_NUM returns the spatial dimension for problem 07.

P07_STORY prints the "story" for problem 07.

P08_DATA returns the data for problem 08.

P08_DATA_NUM returns the number of data points for problem 08.

P08_DIM_NUM returns the spatial dimension for problem 08.

P08_STORY prints the "story" for problem 08.
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the C++ source codes.
Last revised on 04 October 2012.