forked from johannesgerer/jburkardt-cpp
-
Notifications
You must be signed in to change notification settings - Fork 0
/
test_interp.html
431 lines (393 loc) · 13.2 KB
/
test_interp.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
<html>
<head>
<title>
TEST_INTERP - Interpolation Test Data
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TEST_INTERP <br> Interpolation Test Data
</h1>
<hr>
<p>
<b>TEST_INTERP</b>
is a C++ library which
defines data that may be used to test interpolation algorithms.
</p>
<p>
The following sets of data are available:
<ol>
<li>
<a href = "p01_plot.png">p01_plot.png</a>,
18 data points, 2 dimensions.
This example is due to Hans-Joerg 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.
</li>
<li>
<a href = "p02_plot.png">p02_plot.png</a>,
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.
</li>
<li>
<a href = "p03_plot.png">p03_plot.png</a>,
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,
sparsely-placed data. This can cause an interpolant to overshoot
the data in a way that seems implausible.
</li>
<li>
<a href = "p04_plot.png">p04_plot.png</a>,
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,
sparsely-placed data. This can cause an interpolant to overshoot
the data in a way that seems implausible.
</li>
<li>
<a href = "p05_plot.png">p05_plot.png</a>,
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,
sparsely-placed data. This can cause an interpolant to overshoot
the data in a way that seems implausible.
</li>
<li>
<a href = "p06_plot.png">p06_plot.png</a>,
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 variably-spaced knots.
DeBoor considers two sets of knots:
(595,675,755,835,915,995,1075)
and
(595,725,850,910,975,1040,1075).
</li>
<li>
<a href = "p07_plot.png">p07_plot.png</a>,
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.
</li>
<li>
<a href = "p08_plot.png">p08_plot.png</a>,
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.
</li>
</ol>
</p>
<p>
<b>TEST_INTERP</b> requires access to a compiled copy of the R8LIB library.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>TEST_INTERP</b> is available in
<a href = "../../c_src/test_interp/test_interp.html">a C version</a> and
<a href = "../../cpp_src/test_interp/test_interp.html">a C++ version</a> and
<a href = "../../f77_src/test_interp/test_interp.html">a FORTRAN77 version</a> and
<a href = "../../f_src/test_interp/test_interp.html">a FORTRAN90 version</a> and
<a href = "../../m_src/test_interp/test_interp.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/divdif/divdif.html">
DIVDIF</a>,
a C++ library which
includes many routines to construct and evaluate divided difference
interpolants.
</p>
<p>
<a href = "../../cpp_src/hermite/hermite.html">
HERMITE</a>,
a C++ library which
computes the Hermite interpolant, a polynomial that matches function values
and derivatives.
</p>
<p>
<a href = "../../datasets/interpolation/interpolation.html">
INTERPOLATION</a>,
a dataset directory which
contains datasets to be interpolated.
</p>
<p>
<a href = "../../cpp_src/lagrange_interp_1d/lagrange_interp_1d.html">
LAGRANGE_INTERP_1D</a>,
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).
</p>
<p>
<a href = "../../cpp_src/nearest_interp_1d/nearest_interp_1d.html">
NEAREST_INTERP_1D</a>,
a C++ library which
interpolates a set of data using a piecewise constant interpolant
defined by the nearest neighbor criterion.
</p>
<p>
<a href = "../../cpp_src/pwl_interp_1d/pwl_interp_1d.html">
PWL_INTERP_1D</a>,
a C++ library which
interpolates a set of data using a piecewise linear function.
</p>
<p>
<a href = "../../cpp_src/r8lib/r8lib.html">
R8LIB</a>,
a C++ library which
contains many utility routines using double precision real (R8) arithmetic.
</p>
<p>
<a href = "../../cpp_src/rbf_interp/rbf_interp.html">
RBF_INTERP</a>,
a C++ library which
defines and evaluates radial basis function (RBF) interpolants to multidimensional data.
</p>
<p>
<a href = "../../cpp_src/spline/spline.html">
SPLINE</a>,
a C++ library which
includes many routines to construct and evaluate spline
interpolants and approximants.
</p>
<p>
<a href = "../../cpp_src/test_approx/test_approx.html">
TEST_APPROX</a>,
a C++ library which
defines test problems for approximation,
provided as a set of (x,y) data.
</p>
<p>
<a href = "../../cpp_src/test_interp_nd/test_interp_nd.html">
TEST_INTERP_ND</a>,
a C++ library which
defines test problems for interpolation of data z(x),
depending on an M-dimensional argument.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Carl DeBoor, John Rice,<br>
Least-squares cubic spline approximation II - variable knots. <br>
Technical Report CSD TR 21, <br>
Purdue University, Lafayette, Indiana, 1968.
</li>
<li>
Carl DeBoor,<br>
A Practical Guide to Splines,<br>
Springer, 2001,<br>
ISBN: 0387953663,<br>
LC: QA1.A647.v27.
<li>
Fred Fritsch, Ralph Carlson,<br>
Monotone Piecewise Cubic Interpolation,<br>
SIAM Journal on Numerical Analysis,<br>
Volume 17, Number 2, April 1980, pages 238-246.
</li>
<li>
Larry Irvine, Samuel Marin, Philip Smith,<br>
Constrained Interpolation and Smoothing,<br>
Constructive Approximation,<br>
Volume 2, Number 1, December 1986, pages 129-151.
</li>
<li>
ETY Lee,<br>
Choosing Nodes in Parametric Curve Interpolation,<br>
Computer-Aided Design,<br>
Volume 21, Number 6, July/August 1989, pages 363-370.
</li>
<li>
Hans-Joerg Wenz,<br>
Interpolation of Curve Data by Blended Generalized Circles,<br>
Computer Aided Geometric Design,<br>
Volume 13, Number 8, November 1996, pages 673-680.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "test_interp.cpp">test_interp.cpp</a>, the source code.
</li>
<li>
<a href = "test_interp.hpp">test_interp.hpp</a>, the include file.
</li>
<li>
<a href = "test_interp.sh">test_interp.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "test_interp_prb.cpp">test_interp_prb.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "test_interp_prb.sh">test_interp_prb.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "test_interp_prb_output.txt">test_interp_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>P00_DATA</b> returns the data for any problem.
</li>
<li>
<b>P00_DATA_NUM</b> returns the number of data points for any problem.
</li>
<li>
<b>P00_DIM_NUM</b> returns the spatial dimension for any problem.
</li>
<li>
<b>P00_PROB_NUM</b> returns the number of test problems.
</li>
<li>
<b>P00_STORY</b> prints the "story" for any problem.
</li>
<li>
<b>P01_DATA</b> returns the data for problem 01.
</li>
<li>
<b>P01_DATA_NUM</b> returns the number of data points for problem 01.
</li>
<li>
<b>P01_DIM_NUM</b> returns the spatial dimension for problem 01.
</li>
<li>
<b>P01_STORY</b> prints the "story" for problem 01.
</li>
<li>
<b>P02_DATA</b> returns the data for problem 02.
</li>
<li>
<b>P02_DATA_NUM</b> returns the number of data points for problem 02.
</li>
<li>
<b>P02_DIM_NUM</b> returns the spatial dimension for problem 02.
</li>
<li>
<b>P02_STORY</b> prints the "story" for problem 02.
</li>
<li>
<b>P03_DATA</b> returns the data for problem 03.
</li>
<li>
<b>P03_DATA_NUM</b> returns the number of data points for problem 03.
</li>
<li>
<b>P03_DIM_NUM</b> returns the spatial dimension for problem 03.
</li>
<li>
<b>P03_STORY</b> prints the "story" for problem 03.
</li>
<li>
<b>P04_DATA</b> returns the data for problem 04.
</li>
<li>
<b>P04_DATA_NUM</b> returns the number of data points for problem 04.
</li>
<li>
<b>P04_DIM_NUM</b> returns the spatial dimension for problem 04.
</li>
<li>
<b>P04_STORY</b> prints the "story" for problem 04.
</li>
<li>
<b>P05_DATA</b> returns the data for problem 05.
</li>
<li>
<b>P05_DATA_NUM</b> returns the number of data points for problem 05.
</li>
<li>
<b>P05_DIM_NUM</b> returns the spatial dimension for problem 05.
</li>
<li>
<b>P05_STORY</b> prints the "story" for problem 05.
</li>
<li>
<b>P06_DATA</b> returns the data for problem 06.
</li>
<li>
<b>P06_DATA_NUM</b> returns the number of data points for problem 06.
</li>
<li>
<b>P06_DIM_NUM</b> returns the spatial dimension for problem 06.
</li>
<li>
<b>P06_STORY</b> prints the "story" for problem 06.
</li>
<li>
<b>P07_DATA</b> returns the data for problem 07.
</li>
<li>
<b>P07_DATA_NUM</b> returns the number of data points for problem 07.
</li>
<li>
<b>P07_DIM_NUM</b> returns the spatial dimension for problem 07.
</li>
<li>
<b>P07_STORY</b> prints the "story" for problem 07.
</li>
<li>
<b>P08_DATA</b> returns the data for problem 08.
</li>
<li>
<b>P08_DATA_NUM</b> returns the number of data points for problem 08.
</li>
<li>
<b>P08_DIM_NUM</b> returns the spatial dimension for problem 08.
</li>
<li>
<b>P08_STORY</b> prints the "story" for problem 08.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 04 October 2012.
</i>
<!-- John Burkardt -->
</body>
<!-- Initial HTML skeleton created by HTMLINDEX. -->
</html>