forked from johannesgerer/jburkardt-f
-
Notifications
You must be signed in to change notification settings - Fork 1
/
test_interp_nd.html
413 lines (371 loc) · 11.4 KB
/
test_interp_nd.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
<html>
<head>
<title>
TEST_INTERP_ND - Test Functions for Multidimensional Interpolation
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TEST_INTERP_ND <br> Test Functions for Multidimensional Interpolation
</h1>
<hr>
<p>
<b>TEST_INTERP_ND</b>
is a FORTRAN90 library which
provides test functions for multidimensional interpolation.
</p>
<p>
All the functions are defined over the unit hypercube [0,1]^M, for arbitrary
spatial dimension M. They include:
<ol>
<li>
Oscillatory;
</li>
<li>
Product Peak;
</li>
<li>
Corner Peak;
</li>
<li>
Gaussian;
</li>
<li>
Continuous;
</li>
<li>
Discontinuous;
</li>
</ol>
</p>
<p>
For each function, methods are provided to evaluate:
<ul>
<li>
the function, f(x);
</li>
<li>
the derivative with respect to any coordinate, dfdx(i);
</li>
<li>
the integral of f(x) over the unit hypercube;
</li>
</ul>
</p>
<p>
Most of the functions include a shift vector w whose entries can be
chosen randomly in the unit hypercube, and a coefficient vector c
whose entries should be positive, and for which the integration problem
becomes harder as the sum of the entries increases.
</p>
<p>
<b>TEST_INTERP_ND</b> requires access to 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_ND</b> is available in
<a href = "../../c_src/test_interp_nd/test_interp_nd.html">a C version</a> and
<a href = "../../cpp_src/test_interp_nd/test_interp_nd.html">a C++ version</a> and
<a href = "../../f77_src/test_interp_nd/test_interp_nd.html">a FORTRAN77 version</a> and
<a href = "../../f_src/test_interp_nd/test_interp_nd.html">a FORTRAN90 version</a> and
<a href = "../../m_src/test_interp_nd/test_interp_nd.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/lagrange_interp_nd/lagrange_interp_nd.html">
LAGRANGE_INTERP_ND</a>,
a FORTRAN90 library which
defines and evaluates the Lagrange polynomial p(x)
which interpolates a set of data depending on a multidimensional argument x
that was evaluated on a product grid, so that p(x(i)) = z(i).
</p>
<p>
<a href = "../../f_src/r8lib/r8lib.html">
R8LIB</a>,
a FORTRAN90 library which
contains many utility routines using double precision real (R8) arithmetic.
</p>
<p>
<a href = "../../f_src/rbf_interp_nd/rbf_interp_nd.html">
RBF_INTERP_ND</a>,
a FORTRAN90 library which
defines and evaluates radial basis function (RBF) interpolants to multidimensional data.
</p>
<p>
<a href = "../../f_src/shepard_interp_nd/shepard_interp_nd.html">
SHEPARD_INTERP_ND</a>,
a FORTRAN90 library which
defines and evaluates Shepard interpolants to multidimensional data,
based on inverse distance weighting.
</p>
<p>
<a href = "../../f_src/sparse_interp_nd/sparse_interp_nd.html">
SPARSE_INTERP_ND</a>
a FORTRAN90 library which
can be used to define a sparse interpolant to a function f(x) of a
multidimensional argument.
</p>
<p>
<a href = "../../m_src/spinterp/spinterp.html">
SPINTERP</a>,
a MATLAB library which
carries out piecewise multilinear hierarchical sparse grid interpolation;
an earlier version of this software is ACM TOMS Algorithm 847,
by Andreas Klimke;
</p>
<p>
<a href = "../../f_src/test_interp_1d/test_interp_1d.html">
TEST_INTERP_1D</a>,
a FORTRAN90 library which
defines test problems for interpolation of data y(x),
depending on a 1D argument.
</p>
<p>
<a href = "../../f_src/test_interp_2d/test_interp_2d.html">
TEST_INTERP_2D</a>,
a FORTRAN90 library which
defines test problems for interpolation of data z(x,y)),
depending on a 2D argument.
</p>
<p>
<a href = "../../f_src/toms526/toms526.html">
TOMS526</a>,
a FORTRAN90 library which
interpolates scattered bivariate data.
This is a FORTRAN90 version of ACM TOMS algorithm 526,
by Hiroshi Akima;
</p>
<p>
<a href = "../../f_src/toms660/toms660.html">
TOMS660</a>,
a FORTRAN90 library which
takes scattered 2D data and produces an interpolating function F(X,Y).
This is a FORTRAN90 version of ACM TOMS algorithm 660,
called qshep2d,
by Robert Renka.
</p>
<p>
<a href = "../../f_src/toms661/toms661.html">
TOMS661</a>,
a FORTRAN90 library which
takes scattered 3D data and produces an interpolating function F(X,Y,Z).
This is a FORTRAN90 version of ACM TOMS algorithm 661,
called qshep3d,
by Robert Renka.
</p>
<p>
<a href = "../../f_src/toms790/toms790.html">
TOMS790</a>,
a FORTRAN90 library which
computes an interpolating function to a set of scattered data in the plane,
by Robert Renka;
this library is commonly called cshep2d;
this is a FORTRAN90 version of ACM TOMS algorithm 790.
</p>
<p>
<a href = "../../m_src/vandermonde_interp_2d/vandermonde_interp_2d.html">
VANDERMONDE_INTERP_2D</a>,
a MATLAB library which
finds a polynomial interpolant to data z(x,y) of a 2D argument
by setting up and solving a linear system for the polynomial coefficients,
involving the Vandermonde matrix.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Alan Genz,<br>
Testing Multidimensional Integration Routines,<br>
in Tools, Methods, and Languages for Scientific and
Engineering Computation,<br>
edited by B Ford, JC Rault, F Thomasset,<br>
North-Holland, 1984, pages 81-94,<br>
ISBN: 0444875700,<br>
LC: Q183.9.I53.
</li>
<li>
Alan Genz,<br>
A Package for Testing Multiple Integration Subroutines,<br>
in Numerical Integration:
Recent Developments, Software and Applications,<br>
edited by Patrick Keast, Graeme Fairweather,<br>
Reidel, 1987, pages 337-340,<br>
ISBN: 9027725144,<br>
LC: QA299.3.N38.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "test_interp_nd.f90">test_interp_nd.f90</a>, the source code.
</li>
<li>
<a href = "test_interp_nd.sh">test_interp_nd.sh</a>,
BASH commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "test_interp_nd_prb.f90">test_interp_nd_prb.f90</a>,
a sample calling program.
</li>
<li>
<a href = "test_interp_nd_prb.sh">test_interp_nd_prb.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "test_interp_nd_prb_output.txt">test_interp_nd_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>CSEVL</b> evaluates an N term Chebyshev series.
</li>
<li>
<b>INITS</b> estimates the order of an orthogonal series for a given accuracy.
</li>
<li>
<b>P00_CW</b> computes a random C parameter vector for any problem.
</li>
<li>
<b>P00_D</b> returns a derivative component of any function.
</li>
<li>
<b>P00_F</b> returns the value of any function.
</li>
<li>
<b>P00_PROB_NUM</b> returns the number of test functions available.
</li>
<li>
<b>P00_Q</b> returns the integral of any function.
</li>
<li>
<b>P00_TITLE</b> returns the title for any function.
</li>
<li>
<b>P00_W</b> computes a random W parameter vector for any problem.
</li>
<li>
<b>P01_D</b> evaluates any derivative component for problem p01.
</li>
<li>
<b>P01_F</b> evaluates the function for problem p01.
</li>
<li>
<b>P01_Q</b> evaluates the integral for problem p01.
</li>
<li>
<b>P01_TITLE</b> returns the name of problem p01.
</li>
<li>
<b>P02_D</b> evaluates an derivative component for problem p02.
</li>
<li>
<b>P02_F</b> evaluates the function for problem p02.
</li>
<li>
<b>P02_Q</b> evaluates the integral for problem p02.
</li>
<li>
<b>P02_TITLE</b> returns the title of problem p02.
</li>
<li>
<b>P03_D</b> evaluates any derivative component for problem p03.
</li>
<li>
<b>P03_F</b> evaluates the function for problem p03.
</li>
<li>
<b>P03_Q</b> evaluates the integral for problem p03.
</li>
<li>
<b>P03_TITLE</b> returns the title of problem p03.
</li>
<li>
<b>P04_D</b> evaluates any derivative component for problem p04.
</li>
<li>
<b>P04_F</b> evaluates the function for problem p04.
</li>
<li>
<b>P04_Q</b> evaluates the integral for problem p04.
</li>
<li>
<b>P04_TITLE</b> returns the title of problem p04.
</li>
<li>
<b>P05_D</b> evaluates any derivative component for problem p05.
</li>
<li>
<b>P05_F</b> evaluates the function for problem p05.
</li>
<li>
<b>P05_Q</b> evaluates the integral for problem p05.
</li>
<li>
<b>P05_TITLE</b> returns the title of problem p05.
</li>
<li>
<b>P06_D</b> evaluates any derivative component for problem p06.
</li>
<li>
<b>P06_F</b> evaluates the function for problem p06.
</li>
<li>
<b>P06_Q</b> evaluates the integral for problem p06.
</li>
<li>
<b>P06_TITLE</b> returns the title of problem p06.
</li>
<li>
<b>R8_ERROR</b> computes the error function.
</li>
<li>
<b>R8_ERRORC</b> computes the complementary error function.
</li>
<li>
<b>TUPLE_NEXT</b> computes the next element of a tuple space.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 26 August 2012.
</i>
<!-- John Burkardt -->
</body>
<!-- Initial HTML skeleton created by HTMLINDEX. -->
</html>