forked from johannesgerer/jburkardt-m
-
Notifications
You must be signed in to change notification settings - Fork 0
/
test_interp_2d.html
572 lines (533 loc) · 16.4 KB
/
test_interp_2d.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
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
<html>
<head>
<title>
TEST_INTERP_2D - Test Interpolation Data Z(X,Y) of a 2D Argument
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TEST_INTERP_2D <br> Test Interpolation Data Z(X,Y) of a 2D Argument
</h1>
<hr>
<p>
<b>TEST_INTERP_2D</b>
is a MATLAB library which
defines test problems for interpolation of data z(x,y)
depending on a 2D argument.
</p>
<p>
The test for <b>TEST_INTERP_2D</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_2D</b> is available in
<a href = "../../c_src/test_interp_2d/test_interp_2d.html">a C version</a> and
<a href = "../../cpp_src/test_interp_2d/test_interp_2d.html">a C++ version</a> and
<a href = "../../f77_src/test_interp_2d/test_interp_2d.html">a FORTRAN77 version</a> and
<a href = "../../f_src/test_interp_2d/test_interp_2d.html">a FORTRAN90 version</a> and
<a href = "../../m_src/test_interp_2d/test_interp_2d.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/lagrange_interp_2d/lagrange_interp_2d.html">
LAGRANGE_INTERP_2D</a>,
a MATLAB library which
defines and evaluates the Lagrange polynomial p(x,y)
which interpolates a set of data depending on a 2D argument
that was evaluated on a product grid,
so that p(x(i),y(j)) = z(i,j).
</p>
<p>
<a href = "../../m_src/matlab_surf/matlab_surf.html">
MATLAB_SURF</a>,
a MATLAB library which
demonstrates the MATLAB surf() function for displaying a 3D surface
of the form Z=F(X,Y).
</p>
<p>
<a href = "../../m_src/padua/padua.html">
PADUA</a>,
a MATLAB library which
returns the points and weights for Padu sets, useful for interpolation
in 2D. MATLAB graphics are used to plot the points.
</p>
<p>
<a href = "../../m_src/pwl_interp_2d/pwl_interp_2d.html">
PWL_INTERP_2D</a>,
a MATLAB library which
evaluates a piecewise linear interpolant to data defined on
a regular 2D grid.
</p>
<p>
<a href = "../../m_src/r8lib/r8lib.html">
R8LIB</a>,
a MATLAB library which
contains many utility routines, using double precision real (R8) arithmetic.
</p>
<p>
<a href = "../../m_src/rbf_interp_2d/rbf_interp_2d.html">
RBF_INTERP_2D</a>,
a MATLAB library which
defines and evaluates radial basis function (RBF) interpolants to 2D data.
</p>
<p>
<a href = "../../m_src/shepard_interp_2d/shepard_interp_2d.html">
SHEPARD_INTERP_2D</a>,
a MATLAB library which
defines and evaluates Shepard interpolants to 2D data,
which are based on inverse distance weighting.
</p>
<p>
<a href = "../../m_src/test_interp/test_interp.html">
TEST_INTERP</a>,
a MATLAB library which
defines a number of test problems for interpolation,
provided as a set of (x,y(x)) data.
</p>
<p>
<a href = "../../m_src/test_interp_1d/test_interp_1d.html">
TEST_INTERP_1D</a>,
a MATLAB library which
defines test problems for interpolation of data y(x),
depending on a 2D argument.
</p>
<p>
<a href = "../../m_src/test_interp_nd/test_interp_nd.html">
TEST_INTERP_ND</a>,
a MATLAB library which
defines test problems for interpolation of data z(x),
depending on an M-dimensional argument.
</p>
<p>
<a href = "../../m_src/toms886/toms886.html">
TOMS886</a>,
a MATLAB library which
defines the Padua points for interpolation in a 2D region,
including the rectangle, triangle, and ellipse,
by Marco Caliari, Stefano de Marchi, Marco Vianello.
This is a MATLAB version of ACM TOMS algorithm 886.
</p>
<p>
<a href = "../../m_src/vandermonde_approx_2d/vandermonde_approx_2d.html">
VANDERMONDE_APPROX_2D</a>,
a MATLAB library which
finds a polynomial approximant p(x,y) to data of a 2D argument by setting up and
solving an overdetermined linear system for the polynomial coefficients
involving the Vandermonde matrix.
</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>
Richard Franke,<br>
A Critical Comparison of Some Methods for Interpolation of Scattered Data,<br>
Naval Postgraduate School Technical Report,<br>
NPS-53-79-003, 1979.
</li>
<li>
Robert Renka, Ron Brown,<br>
Algorithm 792:
Accuracy Tests of ACM Algorithms for Interpolation of Scattered Data in the Plane,<br>
ACM Transactions on Mathematical Software,<br>
Volume 25, Number 1, March 1999, pages 78-94.
</li>
<li>
Donald Shepard,<br>
A two-dimensional interpolation function for irregularly spaced data,<br>
ACM '68: Proceedings of the 1968 23rd ACM National Conference,<br>
ACM, pages 517-524, 1969.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "f00_f0.m">f00_f0.m</a>
returns the value of any function.
</li>
<li>
<a href = "f00_f1.m">f00_f1.m</a>
returns first derivatives of any function.
</li>
<li>
<a href = "f00_f2.m">f00_f2.m</a>
returns second derivatives of any function.
</li>
<li>
<a href = "f00_num.m">f00_num.m</a>
returns the number of test functions available.
</li>
<li>
<a href = "f00_title.m">f00_title.m</a>
returns the title for any function.
</li>
<li>
<a href = "f01_f0.m">f01_f0.m</a>
returns the value of function 1.
</li>
<li>
<a href = "f01_f1.m">f01_f1.m</a>
returns first derivatives of function 1.
</li>
<li>
<a href = "f01_f2.m">f01_f2.m</a>
returns second derivatives of function 1.
</li>
<li>
<a href = "f01_title.m">f01_title.m</a>
returns the title for function 1.
</li>
<li>
<a href = "f02_f0.m">f02_f0.m</a>
returns the value of function 2.
</li>
<li>
<a href = "f02_f1.m">f02_f1.m</a>
returns first derivatives of function 2.
</li>
<li>
<a href = "f02_f2.m">f02_f2.m</a>
returns second derivatives of function 2.
</li>
<li>
<a href = "f02_title.m">f02_title.m</a>
returns the title for function 2.
</li>
<li>
<a href = "f03_f0.m">f03_f0.m</a>
returns the value of function 3.
</li>
<li>
<a href = "f03_f1.m">f03_f1.m</a>
returns first derivatives of function 3.
</li>
<li>
<a href = "f03_f2.m">f03_f2.m</a>
returns second derivatives of function 3.
</li>
<li>
<a href = "f03_title.m">f03_title.m</a>
returns the title for function 3.
</li>
<li>
<a href = "f04_f0.m">f04_f0.m</a>
returns the value of function 4.
</li>
<li>
<a href = "f04_f1.m">f04_f1.m</a>
returns first derivatives of function 4.
</li>
<li>
<a href = "f04_f2.m">f04_f2.m</a>
returns second derivatives of function 4.
</li>
<li>
<a href = "f04_title.m">f04_title.m</a>
returns the title for function 4.
</li>
<li>
<a href = "f05_f0.m">f05_f0.m</a>
returns the value of function 5.
</li>
<li>
<a href = "f05_f1.m">f05_f1.m</a>
returns first derivatives of function 5.
</li>
<li>
<a href = "f05_f2.m">f05_f2.m</a>
returns second derivatives of function 5.
</li>
<li>
<a href = "f05_title.m">f05_title.m</a>
returns the title for function 5.
</li>
<li>
<a href = "f06_f0.m">f06_f0.m</a>
returns the value of function 6.
</li>
<li>
<a href = "f06_f1.m">f06_f1.m</a>
returns first derivatives of function 6.
</li>
<li>
<a href = "f06_f2.m">f06_f2.m</a>
returns second derivatives of function 6.
</li>
<li>
<a href = "f06_title.m">f06_title.m</a>
returns the title for function 6.
</li>
<li>
<a href = "f07_f0.m">f07_f0.m</a>
returns the value of function 7.
</li>
<li>
<a href = "f07_f1.m">f07_f1.m</a>
returns first derivatives of function 7.
</li>
<li>
<a href = "f07_f2.m">f07_f2.m</a>
returns second derivatives of function 7.
</li>
<li>
<a href = "f07_title.m">f07_title.m</a>
returns the title for function 7.
</li>
<li>
<a href = "f08_f0.m">f08_f0.m</a>
returns the value of function 8.
</li>
<li>
<a href = "f08_f1.m">f08_f1.m</a>
returns first derivatives of function 8.
</li>
<li>
<a href = "f08_f2.m">f08_f2.m</a>
returns second derivatives of function 8.
</li>
<li>
<a href = "f08_title.m">f08_title.m</a>
returns the title for function 8.
</li>
<li>
<a href = "f09_f0.m">f09_f0.m</a>
returns the value of function 9.
</li>
<li>
<a href = "f09_f1.m">f09_f1.m</a>
returns first derivatives of function 9.
</li>
<li>
<a href = "f09_f2.m">f09_f2.m</a>
returns second derivatives of function 9.
</li>
<li>
<a href = "f09_title.m">f09_title.m</a>
returns the title for function 9.
</li>
<li>
<a href = "f10_f0.m">f10_f0.m</a>
returns the value of function f10.
</li>
<li>
<a href = "f10_f1.m">f10_f1.m</a>
returns first derivatives of function f10.
</li>
<li>
<a href = "f10_f2.m">f10_f2.m</a>
returns second derivatives of function f10.
</li>
<li>
<a href = "f10_title.m">f10_title.m</a>
returns the title for function f10.
</li>
<li>
<a href = "f11_f0.m">f11_f0.m</a>
returns the value of function f11.
</li>
<li>
<a href = "f11_f1.m">f11_f1.m</a>
returns first derivatives of function f11.
</li>
<li>
<a href = "f11_f2.m">f11_f2.m</a>
returns second derivatives of function f11.
</li>
<li>
<a href = "f11_title.m">f11_title.m</a>
returns the title for function f11.
</li>
<li>
<a href = "f12_f0.m">f12_f0.m</a>
returns the value of function f12.
</li>
<li>
<a href = "f12_f1.m">f12_f1.m</a>
returns first derivatives of function f12.
</li>
<li>
<a href = "f12_f2.m">f12_f2.m</a>
returns second derivatives of function f12.
</li>
<li>
<a href = "f12_title.m">f12_title.m</a>
returns the title for function f12.
</li>
<li>
<a href = "f13_f0.m">f13_f0.m</a>
returns the value of function f13.
</li>
<li>
<a href = "f13_f1.m">f13_f1.m</a>
returns first derivatives of function f13.
</li>
<li>
<a href = "f13_f2.m">f13_f2.m</a>
returns second derivatives of function f13.
</li>
<li>
<a href = "f13_title.m">f13_title.m</a>
returns the title for function f13.
</li>
<li>
<a href = "g00_num.m">g00_num.m</a>
returns the number of grids available.
</li>
<li>
<a href = "g00_size.m">g00_size.m</a>
returns the size for any grid.
</li>
<li>
<a href = "g00_title.m">g00_title.m</a>
returns the title for any grid.
</li>
<li>
<a href = "g00_xy.m">g00_xy.m</a>
returns the grid points for any grid.
</li>
<li>
<a href = "g01_size.m">g01_size.m</a>
returns the size for grid 1.
</li>
<li>
<a href = "g01_title.m">g01_title.m</a>
returns the title for grid 1.
</li>
<li>
<a href = "g01_xy.m">g01_xy.m</a>
returns the grid points for grid 1.
</li>
<li>
<a href = "g02_size.m">g02_size.m</a>
returns the size for grid 2.
</li>
<li>
<a href = "g02_title.m">g02_title.m</a>
returns the title for grid 2.
</li>
<li>
<a href = "g02_xy.m">g02_xy.m</a>
returns the grid points for grid 2.
</li>
<li>
<a href = "g03_size.m">g03_size.m</a>
returns the size for grid 3.
</li>
<li>
<a href = "g03_title.m">g03_title.m</a>
returns the title for grid 3.
</li>
<li>
<a href = "g03_xy.m">g03_xy.m</a>
returns the grid points for grid 3.
</li>
<li>
<a href = "g04_size.m">g04_size.m</a>
returns the size for grid 4.
</li>
<li>
<a href = "g04_title.m">g04_title.m</a>
returns the title for grid 4.
</li>
<li>
<a href = "g04_xy.m">g04_xy.m</a>
returns the grid points for grid 4.
</li>
<li>
<a href = "g05_size.m">g05_size.m</a>
returns the size for grid 5.
</li>
<li>
<a href = "g05_title.m">g05_title.m</a>
returns the title for grid 5.
</li>
<li>
<a href = "g05_xy.m">g05_xy.m</a>
returns the grid points for grid 5.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "test_interp_2d_test.m">test_interp_2d_test.m</a>,
a sample calling program.
</li>
<li>
<a href = "test_interp_2d_test_output.txt">test_interp_2d_test_output.txt</a>,
the output file.
</li>
<li>
<a href = "test_interp_2d_test01.m">test_interp_2d_test01.m</a>,
simply prints the title of each grid and function.
</li>
<li>
<a href = "test_interp_2d_test02.m">test_interp_2d_test02.m</a>,
samples each function using each grid.
</li>
<li>
<a href = "test_interp_2d_test03.m">test_interp_2d_test03.m</a>,
plots the grid points.
</li>
</ul>
</p>
<p>
<b>test_interp_2d_test03</b> makes plots of each grid:
<ul>
<li>
<a href = "grid_01.png">grid_01.png</a>, Franke's 100 node set.
</li>
<li>
<a href = "grid_02.png">grid_02.png</a>, Franke's 33 node set.
</li>
<li>
<a href = "grid_03.png">grid_03.png</a>, Lawson's 25 node set.
</li>
<li>
<a href = "grid_04.png">grid_04.png</a>, Random 100 node set.
</li>
<li>
<a href = "grid_05.png">grid_05.png</a>, Gridded 81 node set.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 28 July 2012.
</i>
<!-- John Burkardt -->
</body>
<!-- Initial HTML skeleton created by HTMLINDEX. -->
</html>