forked from johannesgerer/jburkardt-cpp
-
Notifications
You must be signed in to change notification settings - Fork 0
/
test_zero.html
898 lines (865 loc) · 26.8 KB
/
test_zero.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
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
<html>
<head>
<title>
TEST_ZERO - Zero Finder Tests
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TEST_ZERO <br> Zero Finder Tests
</h1>
<hr>
<p>
<b>TEST_ZERO</b>
is a C++ library which
defines nonlinear functions that may be used to test zero finders.
</p>
<p>
Zero finders are programs that seek a (scalar) root of
a scalar equation F(X) = 0. Some zero finders require
that an initial "change-of-sign" interval [A,B] be supplied,
with the function having opposite sign at the two endpoints,
thus guaranteeing that there is some value C between A and
B for which F(C) = 0 (assuming that the function F is continuous).
In other cases, a particular zero finder may want information
about the first or second derivative of the function. And some
zero finders can handle situations where the function has a
multiple root, or where the function is a polynomial.
</p>
<p>
<b>TEST_ZERO</b> supplies a set of nonlinear functions, along
with change of sign interval, first and second derivatives,
suggested starting points, so that the behavior of any zero
finder can be analyzed.
</p>
<p>
<b>TEST_ZERO</b> also includes implementations of some simple
zero finders, as a demonstration of how the package might be used.
</p>
<p>
The functions, which are accessible by number, are
<ol>
<li>
f(x) = sin ( x ) - x / 2.
</li>
<li>
f(x) = 2 * x - exp ( - x ).
</li>
<li>
f(x) = x * exp ( - x ).
</li>
<li>
f(x) = exp ( x ) - 1 / ( 10 * x )^2.
</li>
<li>
f(x) = ( x + 3 ) * ( x - 1 )^2.
</li>
<li>
f(x) = exp ( x ) - 2 - 1 / ( 10 * x )^2 + 2 / ( 100 * x )^3.
</li>
<li>
f(x) = x^3.
</li>
<li>
f(x) = cos ( x ) - x.
</li>
<li>
the Newton Baffler.
</li>
<li>
the Repeller.
</li>
<li>
the Pinhead.
</li>
<li>
Flat Stanley.
</li>
<li>
Lazy Boy.
</li>
<li>
the Camel.
</li>
<li>
a pathological function for Newton's method.
</li>
<li>
Kepler's Equation.
</li>
<li>
f(x) = x^3 - 2*x - 5, Wallis's function.
</li>
<li>
f(x) = (x-1)^7, written term by term.
</li>
<li>
f(x) = cos(100*x)-4*erf(30*x-10), the jumping cosine.
</li>
</ol>
</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_ZERO</b> is available in
<a href = "../../c_src/test_zero/test_zero.html">a C version</a> and
<a href = "../../cpp_src/test_zero/test_zero.html">a C++ version</a> and
<a href = "../../f77_src/test_zero/test_zero.html">a FORTRAN77 version</a> and
<a href = "../../f_src/test_zero/test_zero.html">a FORTRAN90 version</a> and
<a href = "../../m_src/test_zero/test_zero.html">a MATLAB version.</a>
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/bisection_rc/bisection_rc.html">
BISECTION_RC</a>,
a C++ library which
seeks a solution to the equation F(X)=0 using bisection
within a user-supplied change of sign interval [A,B].
The procedure is written using reverse communication.
</p>
<p>
<a href = "../../cpp_src/brent/brent.html">
BRENT</a>,
a C++ library which
contains Richard Brent's routines for finding the zero, local minimizer,
or global minimizer of a scalar function of a scalar argument, without
the use of derivative information.
</p>
<p>
<a href = "../../cpp_src/gsl/gsl.html">
GSL</a>,
a C++ library which
includes rootfinding routines.
</p>
<p>
<a href = "../../cpp_src/zero_rc/zero_rc.html">
ZERO_RC</a>,
a C++ library which
seeks solutions of a scalar nonlinear equation f(x) = 0,
or a system of nonlinear equations,
using reverse communication.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Richard Brent,<br>
Algorithms for Minimization without Derivatives,<br>
Dover, 2002,<br>
ISBN: 0-486-41998-3,<br>
LC: QA402.5.B74.
</li>
<li>
Peter Colwell,<br>
Solving Kepler's Equation Over Three Centuries,<br>
Willmann-Bell, 1993,<br>
ISBN: 0943396409,<br>
LC: QB355.5.C65.
</li>
<li>
George Donovan, Arnold Miller, Timothy Moreland,<br>
Pathological Functions for Newton's Method,<br>
American Mathematical Monthly, January 1993, pages 53-58.
</li>
<li>
Arnold Krommer, Christoph Ueberhuber,<br>
Numerical Integration on Advanced Computer Systems,<br>
Springer, 1994,<br>
ISBN: 3540584102,<br>
LC: QA299.3.K76.
</li>
<li>
Jean Meeus,<br>
Astronomical Algorithms,<br>
Second Edition,<br>
Willman-Bell, 1998,<br>
ISBN: 0943396611,<br>
LC: QB51.3.E43M42.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "test_zero.cpp">test_zero.cpp</a>, the source code;
</li>
<li>
<a href = "test_zero.hpp">test_zero.hpp</a>, the include file;
</li>
<li>
<a href = "test_zero.sh">test_zero.sh</a>,
commands to compile the source code;
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "test_zero_prb.cpp">test_zero_prb.cpp</a>, the calling
program;
</li>
<li>
<a href = "test_zero_prb.sh">test_zero_prb.sh</a>,
commands to compile, link and run the calling program;
</li>
<li>
<a href = "test_zero_prb_output.txt">test_zero_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<p>
PNG images of the graphs of some of the functions were made using MATLAB:
<ul>
<li>
<a href = "p01_fx.png">p01_fx.png</a>,
an image of P01_FX(X) over [-4,+4].
</li>
<li>
<a href = "p02_fx.png">p02_fx.png</a>,
an image of P02_FX(X) over [-0.5, +3.0].
</li>
<li>
<a href = "p03_fx.png">p03_fx.png</a>,
an image of P03_FX(X) over [-0.1,+4].
</li>
<li>
<a href = "p04_fx.png">p04_fx.png</a>,
an image of P04_FX(X) over [-4,+2].
</li>
<li>
<a href = "p05_fx.png">p05_fx.png</a>,
an image of P05_FX(X) over [-4,+2].
</li>
<li>
<a href = "p06_fx.png">p06_fx.png</a>,
an image of P06_FX(X) over [-4,+2].
</li>
<li>
<a href = "p07_fx.png">p07_fx.png</a>,
an image of P07_FX(X) over [-1,+1].
</li>
<li>
<a href = "p08_fx.png">p08_fx.png</a>,
an image of P08_FX(X) over [-4,+4].
</li>
<li>
<a href = "p09_fx.png">p09_fx.png</a>,
an image of P09_FX(X) over [5,7].
</li>
<li>
<a href = "p10_fx.png">p10_fx.png</a>,
an image of P10_FX(X) over [-2,+2].
</li>
<li>
<a href = "p11_fx.png">p11_fx.png</a>,
an image of P11_FX(X) over [+1,+10].
</li>
<li>
<a href = "p12_fx.png">p12_fx.png</a>,
an image of P12_FX(X) over [-0.5,+0.5].
</li>
<li>
<a href = "p13_fx.png">p13_fx.png</a>,
an image of P13_FX(X) over [0,100].
</li>
<li>
<a href = "p14_fx.png">p14_fx.png</a>,
an image of P14_FX(X) over [-0.5,+2.0].
</li>
<li>
<a href = "p15_fx.png">p15_fx.png</a>,
an image of P15_FX(X) over [-4,+4].
</li>
<li>
<a href = "p16_fx.png">p16_fx.png</a>,
an image of P16_FX(X) over [0,50].
</li>
<li>
<a href = "p17_fx.png">p17_fx.png</a>,
an image of P17_FX(X) over [-2,+4].
</li>
<li>
<a href = "p18_fx.png">p18_fx.png</a>,
an image of P18_FX(X) over [0.988,1.012].
</li>
<li>
<a href = "p19_fx.png">p19_fx.png</a>,
an image of P19_FX(X) over [0.0,1.0].
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>BISECTION</b> carries out the bisection method to seek a root of F(X) = 0.
</li>
<li>
<b>BRENT</b> implements the Brent bisection-based zero finder.
</li>
<li>
<b>MULLER</b> carries out Muller's method for seeking a real root of a nonlinear function.
</li>
<li>
<b>NEWTON</b> carries out Newton's method to seek a root of F(X) = 0.
</li>
<li>
<b>P00_FX</b> evaluates a function specified by problem number.
</li>
<li>
<b>P00_FX1</b> evaluates the first derivative of a function specified by problem number.
</li>
<li>
<b>P00_FX2</b> evaluates the second derivative of a function specified by problem number.
</li>
<li>
<b>P00_PROB_NUM</b> returns the number of problems available.
</li>
<li>
<b>P00_RANGE</b> returns an interval bounding the root for any problem.
</li>
<li>
<b>P00_ROOT</b> returns a known root for any problem.
</li>
<li>
<b>P00_ROOT_NUM</b> returns the number of known roots for a problem.
</li>
<li>
<b>P00_START</b> returns starting point for any problem.
</li>
<li>
<b>P00_START_NUM</b> returns the number of starting points for a problem.
</li>
<li>
<b>P00_TITLE</b> returns the title for a given problem.
</li>
<li>
<b>P01_FX</b> evaluates sin ( x ) - x / 2.
</li>
<li>
<b>P01_FX1</b> evaluates the derivative of the function for problem 1.
</li>
<li>
<b>P01_FX2</b> evaluates the second derivative of the function for problem 1.
</li>
<li>
<b>P01_RANGE</b> returns an interval bounding the root for problem 1.
</li>
<li>
<b>P01_ROOT</b> returns a root for problem 1.
</li>
<li>
<b>P01_ROOT_NUM</b> returns the number of known roots for problem 1.
</li>
<li>
<b>P01_START</b> returns a starting point for problem 1.
</li>
<li>
<b>P01_START_NUM</b> returns the number of starting point for problem 1.
</li>
<li>
<b>P01_TITLE</b> returns the title of problem 1.
</li>
<li>
<b>P02_FX</b> evaluates 2 * x - exp ( - x ).
</li>
<li>
<b>P02_FX1</b> evaluates the derivative of the function for problem 2.
</li>
<li>
<b>P02_FX2</b> evaluates the second derivative of the function for problem 2.
</li>
<li>
<b>P02_RANGE</b> returns an interval bounding the root for problem 2.
</li>
<li>
<b>P02_ROOT</b> returns a root for problem 2.
</li>
<li>
<b>P02_ROOT_NUM</b> returns the number of known roots for problem 2.
</li>
<li>
<b>P02_START</b> returns a starting point for problem 2.
</li>
<li>
<b>P02_START_NUM</b> returns the number of starting point for problem 2.
</li>
<li>
<b>P02_TITLE</b> returns the title of problem 2.
</li>
<li>
<b>P03_FX</b> evaluates x * exp ( - x ).
</li>
<li>
<b>P03_FX1</b> evaluates the derivative of the function for problem 3.
</li>
<li>
<b>P03_FX2</b> evaluates the second derivative of the function for problem 3.
</li>
<li>
<b>P03_RANGE</b> returns an interval bounding the root for problem 3.
</li>
<li>
<b>P03_ROOT</b> returns a root for problem 3.
</li>
<li>
<b>P03_ROOT_NUM</b> returns the number of known roots for problem 3.
</li>
<li>
<b>P03_START</b> returns a starting point for problem 3.
</li>
<li>
<b>P03_START_NUM</b> returns the number of starting point for problem 3.
</li>
<li>
<b>P03_TITLE</b> returns the title of problem 3.
</li>
<li>
<b>P04_FX</b> evaluates exp ( x ) - 1 / ( 10 * x )^2.
</li>
<li>
<b>P04_FX1</b> evaluates the derivative of the function for problem 4.
</li>
<li>
<b>P04_FX2</b> evaluates the second derivative of the function for problem 4.
</li>
<li>
<b>P04_RANGE</b> returns an interval bounding the root for problem 4.
</li>
<li>
<b>P04_ROOT</b> returns a root for problem 4.
</li>
<li>
<b>P04_ROOT_NUM</b> returns the number of known roots for problem 4.
</li>
<li>
<b>P04_START</b> returns a starting point for problem 4.
</li>
<li>
<b>P04_START_NUM</b> returns the number of starting point for problem 4.
</li>
<li>
<b>P04_TITLE</b> returns the title of problem 4.
</li>
<li>
<b>P05_FX</b> evaluates ( x + 3 ) * ( x - 1 )^2.
</li>
<li>
<b>P05_FX1</b> evaluates the derivative of the function for problem 5.
</li>
<li>
<b>P05_FX2</b> evaluates the second derivative of the function for problem 5.
</li>
<li>
<b>P05_RANGE</b> returns an interval bounding the root for problem 5.
</li>
<li>
<b>P05_ROOT</b> returns a root for problem 5.
</li>
<li>
<b>P05_ROOT_NUM</b> returns the number of known roots for problem 5.
</li>
<li>
<b>P05_START</b> returns a starting point for problem 5.
</li>
<li>
<b>P05_START_NUM</b> returns the number of starting point for problem 5.
</li>
<li>
<b>P05_TITLE</b> returns the title of problem 5.
</li>
<li>
<b>P06_FX</b> evaluates exp ( x ) - 2 - 1 / ( 10 * x )^2 + 2 / ( 100 * x )^3.
</li>
<li>
<b>P06_FX1</b> evaluates the derivative of the function for problem 6.
</li>
<li>
<b>P06_FX2</b> evaluates the second derivative of the function for problem 6.
</li>
<li>
<b>P06_RANGE</b> returns an interval bounding the root for problem 6.
</li>
<li>
<b>P06_ROOT</b> returns a root for problem 6.
</li>
<li>
<b>P06_ROOT_NUM</b> returns the number of known roots for problem 6.
</li>
<li>
<b>P06_START</b> returns a starting point for problem 6.
</li>
<li>
<b>P06_START_NUM</b> returns the number of starting point for problem 6.
</li>
<li>
<b>P06_TITLE</b> returns the title of problem 6.
</li>
<li>
<b>P07_FX</b> evaluates x^3.
</li>
<li>
<b>P07_FX1</b> evaluates the derivative of the function for problem 7.
</li>
<li>
<b>P07_FX2</b> evaluates the second derivative of the function for problem 7.
</li>
<li>
<b>P07_RANGE</b> returns an interval bounding the root for problem 7.
</li>
<li>
<b>P07_ROOT</b> returns a root for problem 7.
</li>
<li>
<b>P07_ROOT_NUM</b> returns the number of known roots for problem 7.
</li>
<li>
<b>P07_START</b> returns a starting point for problem 7.
</li>
<li>
<b>P07_START_NUM</b> returns the number of starting point for problem 7.
</li>
<li>
<b>P07_TITLE</b> returns the title of problem 7.
</li>
<li>
<b>P08_FX</b> evaluates cos ( x ) - x.
</li>
<li>
<b>P08_FX1</b> evaluates the derivative of the function for problem 8.
</li>
<li>
<b>P08_FX2</b> evaluates the second derivative of the function for problem 8.
</li>
<li>
<b>P08_RANGE</b> returns an interval bounding the root for problem 8.
</li>
<li>
<b>P08_ROOT</b> returns a root for problem 8.
</li>
<li>
<b>P08_ROOT_NUM</b> returns the number of known roots for problem 8.
</li>
<li>
<b>P08_START</b> returns a starting point for problem 8.
</li>
<li>
<b>P08_START_NUM</b> returns the number of starting point for problem 8.
</li>
<li>
<b>P08_TITLE</b> returns the title of problem 8.
</li>
<li>
<b>P09_FX</b> evaluates the Newton Baffler.
</li>
<li>
<b>P09_FX1</b> evaluates the derivative of the function for problem 9.
</li>
<li>
<b>P09_FX2</b> evaluates the second derivative of the function for problem 9.
</li>
<li>
<b>P09_RANGE</b> returns an interval bounding the root for problem 9.
</li>
<li>
<b>P09_ROOT</b> returns a root for problem 9.
</li>
<li>
<b>P09_ROOT_NUM</b> returns the number of known roots for problem 9.
</li>
<li>
<b>P09_START</b> returns a starting point for problem 9.
</li>
<li>
<b>P09_START_NUM</b> returns the number of starting point for problem 9.
</li>
<li>
<b>P09_TITLE</b> returns the title of problem 9.
</li>
<li>
<b>P10_FX</b> evaluates the Repeller.
</li>
<li>
<b>P10_FX1</b> evaluates the derivative of the function for problem 10.
</li>
<li>
<b>P10_FX2</b> evaluates the second derivative of the function for problem 10.
</li>
<li>
<b>P10_RANGE</b> returns an interval bounding the root for problem 10.
</li>
<li>
<b>P10_ROOT</b> returns a root for problem 10.
</li>
<li>
<b>P10_ROOT_NUM</b> returns the number of known roots for problem 10.
</li>
<li>
<b>P10_START</b> returns a starting point for problem 10.
</li>
<li>
<b>P10_START_NUM</b> returns the number of starting point for problem 10.
</li>
<li>
<b>P10_TITLE</b> returns the title of problem 10.
</li>
<li>
<b>P11_FX</b> evaluates the Pinhead.
</li>
<li>
<b>P11_FX1</b> evaluates the derivative of the function for problem 11.
</li>
<li>
<b>P11_FX2</b> evaluates the second derivative of the function for problem 11.
</li>
<li>
<b>P11_RANGE</b> returns an interval bounding the root for problem 11.
</li>
<li>
<b>P11_ROOT</b> returns a root for problem 11.
</li>
<li>
<b>P11_ROOT_NUM</b> returns the number of known roots for problem 11.
</li>
<li>
<b>P11_START</b> returns a starting point for problem 11.
</li>
<li>
<b>P11_START_NUM</b> returns the number of starting point for problem 11.
</li>
<li>
<b>P11_TITLE</b> returns the title of problem 11.
</li>
<li>
<b>P12_FX</b> evaluates Flat Stanley.
</li>
<li>
<b>P12_FX1</b> evaluates the derivative of the function for problem 12.
</li>
<li>
<b>P12_FX2</b> evaluates the second derivative of the function for problem 12.
</li>
<li>
<b>P12_RANGE</b> returns an interval bounding the root for problem 12.
</li>
<li>
<b>P12_ROOT</b> returns a root for problem 12.
</li>
<li>
<b>P12_ROOT_NUM</b> returns the number of known roots for problem 12.
</li>
<li>
<b>P12_START</b> returns a starting point for problem 12.
</li>
<li>
<b>P12_START_NUM</b> returns the number of starting point for problem 12.
</li>
<li>
<b>P12_TITLE</b> returns the title of problem 12.
</li>
<li>
<b>P13_FX</b> evaluates Lazy Boy.
</li>
<li>
<b>P13_FX1</b> evaluates the derivative of the function for problem 13.
</li>
<li>
<b>P13_FX2</b> evaluates the second derivative of the function for problem 13.
</li>
<li>
<b>P13_RANGE</b> returns an interval bounding the root for problem 13.
</li>
<li>
<b>P13_ROOT</b> returns a root for problem 13.
</li>
<li>
<b>P13_ROOT_NUM</b> returns the number of known roots for problem 13.
</li>
<li>
<b>P13_START</b> returns a starting point for problem 13.
</li>
<li>
<b>P13_START_NUM</b> returns the number of starting point for problem 13.
</li>
<li>
<b>P13_TITLE</b> returns the title of problem 13.
</li>
<li>
<b>P14_FX</b> evaluates the Camel.
</li>
<li>
<b>P14_FX1</b> evaluates the derivative of the function for problem 14.
</li>
<li>
<b>P14_FX2</b> evaluates the second derivative of the function for problem 14.
</li>
<li>
<b>P14_RANGE</b> returns an interval bounding the root for problem 14.
</li>
<li>
<b>P14_ROOT</b> returns a root for problem 14.
</li>
<li>
<b>P14_ROOT_NUM</b> returns the number of known roots for problem 14.
</li>
<li>
<b>P14_START</b> returns a starting point for problem 14.
</li>
<li>
<b>P14_START_NUM</b> returns the number of starting point for problem 14.
</li>
<li>
<b>P14_TITLE</b> returns the title of problem 14.
</li>
<li>
<b>P15_FX</b> evaluates a pathological function for Newton's method.
</li>
<li>
<b>P15_FX1</b> evaluates the derivative of the function for problem 15.
</li>
<li>
<b>P15_FX2</b> evaluates the second derivative of the function for problem 15.
</li>
<li>
<b>P15_RANGE</b> returns an interval bounding the root for problem 15.
</li>
<li>
<b>P15_ROOT</b> returns a root for problem 15.
</li>
<li>
<b>P15_ROOT_NUM</b> returns the number of known roots for problem 15.
</li>
<li>
<b>P15_START</b> returns a starting point for problem 15.
</li>
<li>
<b>P15_START_NUM</b> returns the number of starting point for problem 15.
</li>
<li>
<b>P15_TITLE</b> returns the title of problem 15.
</li>
<li>
<b>P16_FX</b> evaluates Kepler's Equation.
</li>
<li>
<b>P16_FX1</b> evaluates the derivative of the function for problem 16.
</li>
<li>
<b>P16_FX2</b> evaluates the second derivative of the function for problem 16.
</li>
<li>
<b>P16_RANGE</b> returns an interval bounding the root for problem 16.
</li>
<li>
<b>P16_ROOT</b> returns a root for problem 16.
</li>
<li>
<b>P16_ROOT_NUM</b> returns the number of known roots for problem 16.
</li>
<li>
<b>P16_START</b> returns a starting point for problem 16.
</li>
<li>
<b>P16_START_NUM</b> returns the number of starting point for problem 16.
</li>
<li>
<b>P16_TITLE</b> returns the title of problem 16.
</li>
<li>
<b>P17_FX</b> evaluates Wallis's function, f(x) = x^3 - 2*x - 5.
</li>
<li>
<b>P17_FX1</b> evaluates the derivative of the function for problem 17.
</li>
<li>
<b>P17_FX2</b> evaluates the second derivative of the function for problem 17.
</li>
<li>
<b>P17_RANGE</b> returns an interval bounding the root for problem 17.
</li>
<li>
<b>P17_ROOT</b> returns a root for problem 17.
</li>
<li>
<b>P17_ROOT_NUM</b> returns the number of known roots for problem 17.
</li>
<li>
<b>P17_START</b> returns a starting point for problem 17.
</li>
<li>
<b>P17_START_NUM</b> returns the number of starting point for problem 17.
</li>
<li>
<b>P17_TITLE</b> returns the title of problem 17.
</li>
<li>
<b>R8_ABS</b> returns the absolute value of an R8.
</li>
<li>
<b>R8_ADD</b> adds two R8's.
</li>
<li>
<b>R8_CSQRT</b> returns the complex square root of an R8.
</li>
<li>
<b>R8_CUBE_ROOT</b> returns the cube root of an R8.
</li>
<li>
<b>R8_EPSILON</b> returns the R8 roundoff unit.
</li>
<li>
<b>R8_HUGE</b> returns a "huge" R8.
</li>
<li>
<b>R8_MAX</b> returns the maximum of two R8's.
</li>
<li>
<b>R8_SIGN</b> returns the sign of an R8.
</li>
<li>
<b>R8POLY2_RROOT</b> returns the real parts of the roots of a quadratic polynomial.
</li>
<li>
<b>REGULA_FALSI</b> carries out the Regula Falsi method to seek a root of F(X) = 0.
</li>
<li>
<b>SECANT</b> carries out the secant method to seek a root of F(X) = 0.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</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 16 January 2013.
</i>
<!-- John Burkardt -->
</body>
</html>