This file is indexed.

/usr/share/octave/packages/specfun-1.1.0/doc-cache is in octave-specfun 1.1.0-4.

This file is owned by root:root, with mode 0o644.

The actual contents of the file can be viewed below.

  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
# doc-cache created by Octave 4.2.1
# name: cache
# type: cell
# rows: 3
# columns: 19
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2
Ci


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 278
 -- Function File: Y = Ci (Z)
     Compute the cosine integral function defined by:
                        Inf
                       /
               Ci(x) = | cos(t)/t dt
                       /
                       x

     See also: cosint, Si, sinint, expint, expint_Ei.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Compute the cosine integral function defined by:
                   Inf
        



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2
Si


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 210
 -- Function File: Y = Si (X)
     Compute the sine integral defined by:
                        x
                       /
               Si(x) = | sin(t)/t dt
                       /
                       0


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Compute the sine integral defined by:
                   x
                  /
 



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
cosint


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 278
 -- Function File: Y = cosint (Z)
     Compute the cosine integral function defined by:
                        Inf
                       /
           cosint(x) = | cos(t)/t dt
                       /
                       x

     See also: Ci, Si, sinint, expint, expint_Ei.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Compute the cosine integral function defined by:
                   Inf
        



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 5
dirac


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 97
 -- Function File: Y = dirac(X)
     Compute the dirac delta function.

     See also: heaviside.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
Compute the dirac delta function.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
ellipke


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 408
 -- Function File: [K, E] = ellipke (M[,TOL])
     Compute complete elliptic integral of first K(M) and second E(M).

     M is either real array or scalar with 0 <= m <= 1

     TOL will be ignored (MATLAB uses this to allow faster, less
     accurate approximation)

     Ref: Abramowitz, Milton and Stegun, Irene A. Handbook of
     Mathematical Functions, Dover, 1965, Chapter 17.

     See also: ellipj.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 65
Compute complete elliptic integral of first K(M) and second E(M).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
erfcinv


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 118
 -- Function File: erfcinv (X)
     Compute the inverse complementary error function.

     See also: erfc,erf,erfinv.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the inverse complementary error function.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
expint


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 254
 -- Function File: Y = expint (X)
     Compute the exponential integral,
                        infinity
                       /
           expint(x) = | exp(t)/t dt
                       /
                      x

     See also: expint_E1, expint_Ei.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Compute the exponential integral,
                   infinity
                  



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 9
expint_E1


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 254
 -- Function File: Y = expint_E1 (X)
     Compute the exponential integral,
                        infinity
                       /
           expint(x) = | exp(t)/t dt
                       /
                      x

     See also: expint, expint_Ei.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Compute the exponential integral,
                   infinity
                  



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 9
expint_Ei


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 266
 -- Function File: Y = expint_Ei (X)
     Compute the exponential integral,
                          infinity
                         /
        expint_Ei(x) = - | exp(t)/t dt
                         /
                         -x

     See also: expint, expint_E1.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Compute the exponential integral,
                     infinity
                



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 9
heaviside


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 396
 -- Function File: heaviside(X)
 -- Function File: heaviside(X, ZERO_VALUE)
     Compute the Heaviside step function.

     The Heaviside function is defined as

            Heaviside (X) = 1,   X > 0
            Heaviside (X) = 0,   X < 0

     The value of the Heaviside function at X = 0 is by default 0.5, but
     can be changed via the optional second input argument.

     See also: dirac.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Compute the Heaviside step function.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
laguerre


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 167
 -- Function File: Y = laguerre (X,N)
 -- Function File: [Y P]= laguerre (X,N)

     Compute the value of the Laguerre polynomial of order N for each
     element of X


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 77
Compute the value of the Laguerre polynomial of order N for each element
of X



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
lambertw


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1025
 -- Function File: X = lambertw (Z)
 -- Function File: X = lambertw (Z, N)
     Compute the Lambert W function of Z.

     This function satisfies W(z).*exp(W(z)) = z, and can thus be used
     to express solutions of transcendental equations involving
     exponentials or logarithms.

     N must be integer, and specifies the branch of W to be computed;
     W(z) is a shorthand for W(0,z), the principal branch.  Branches 0
     and -1 are the only ones that can take on non-complex values.

     If either N or Z are non-scalar, the function is mapped to each
     element; both may be non-scalar provided their dimensions agree.

     This implementation should return values within 2.5*eps of its
     counterpart in Maple V, release 3 or later.  Please report any
     discrepancies to the author, Nici Schraudolph
     <schraudo@inf.ethz.ch>.

     For further details, see:

     Corless, Gonnet, Hare, Jeffrey, and Knuth (1996), 'On the Lambert W
     Function', Advances in Computational Mathematics 5(4):329-359.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Compute the Lambert W function of Z.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 9
laplacian


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 3694
 LAPLACIAN   Sparse Negative Laplacian in 1D, 2D, or 3D

    [~,~,A]=LAPLACIAN(N) generates a sparse negative 3D Laplacian matrix
    with Dirichlet boundary conditions, from a rectangular cuboid regular
    grid with j x k x l interior grid points if N = [j k l], using the
    standard 7-point finite-difference scheme,  The grid size is always
    one in all directions.

    [~,~,A]=LAPLACIAN(N,B) specifies boundary conditions with a cell array
    B. For example, B = {'DD' 'DN' 'P'} will Dirichlet boundary conditions
    ('DD') in the x-direction, Dirichlet-Neumann conditions ('DN') in the
    y-direction and period conditions ('P') in the z-direction. Possible
    values for the elements of B are 'DD', 'DN', 'ND', 'NN' and 'P'.

    LAMBDA = LAPLACIAN(N,B,M) or LAPLACIAN(N,M) outputs the m smallest
    eigenvalues of the matrix, computed by an exact known formula, see
    http://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors_of_the_second_derivative
    It will produce a warning if the mth eigenvalue is equal to the
    (m+1)th eigenvalue. If m is absebt or zero, lambda will be empty.

    [LAMBDA,V] = LAPLACIAN(N,B,M) also outputs orthonormal eigenvectors
    associated with the corresponding m smallest eigenvalues.

    [LAMBDA,V,A] = LAPLACIAN(N,B,M) produces a 2D or 1D negative
    Laplacian matrix if the length of N and B are 2 or 1 respectively.
    It uses the standard 5-point scheme for 2D, and 3-point scheme for 1D.

    % Examples:
    [lambda,V,A] = laplacian([100,45,55],{'DD' 'NN' 'P'}, 20); 
    % Everything for 3D negative Laplacian with mixed boundary conditions.
    laplacian([100,45,55],{'DD' 'NN' 'P'}, 20);
    % or
    lambda = laplacian([100,45,55],{'DD' 'NN' 'P'}, 20);
    % computes the eigenvalues only

    [~,V,~] = laplacian([200 200],{'DD' 'DN'},30);
    % Eigenvectors of 2D negative Laplacian with mixed boundary conditions.

    [~,~,A] = laplacian(200,{'DN'},30);
    % 1D negative Laplacian matrix A with mixed boundary conditions.

    % Example to test if outputs correct eigenvalues and vectors:
    [lambda,V,A] = laplacian([13,10,6],{'DD' 'DN' 'P'},30);
    [Veig D] = eig(full(A)); lambdaeig = diag(D(1:30,1:30));
    max(abs(lambda-lambdaeig))  %checking eigenvalues
    subspace(V,Veig(:,1:30))    %checking the invariant subspace
    subspace(V(:,1),Veig(:,1))  %checking selected eigenvectors
    subspace(V(:,29:30),Veig(:,29:30)) %a multiple eigenvalue 
    
    % Example showing equivalence between laplacian.m and built-in MATLAB
    % DELSQ for the 2D case. The output of the last command shall be 0.
    A1 = delsq(numgrid('S',32)); % input 'S' specifies square grid.
    [~,~,A2] = laplacian([30,30]);
    norm(A1-A2,inf)
    
    Class support for inputs:
    N - row vector float double  
    B - cell array
    M - scalar float double 

    Class support for outputs:
    lambda and V  - full float double, A - sparse float double.

    Note: the actual numerical entries of A fit int8 format, but only
    double data class is currently (2010) supported for sparse matrices. 

    This program is designed to efficiently compute eigenvalues,
    eigenvectors, and the sparse matrix of the (1-3)D negative Laplacian
    on a rectangular grid for Dirichlet, Neumann, and Periodic boundary
    conditions using tensor sums of 1D Laplacians. For more information on
    tensor products, see
    http://en.wikipedia.org/wiki/Kronecker_sum_of_discrete_Laplacians
    For 2D case in MATLAB, see 
    http://www.mathworks.com/access/helpdesk/help/techdoc/ref/kron.html.

    This code is also part of the BLOPEX package: 
    http://en.wikipedia.org/wiki/BLOPEX or directly 
    http://code.google.com/p/blopex/



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 55
 LAPLACIAN   Sparse Negative Laplacian in 1D, 2D, or 3D



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
multinom


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 588
 -- Function File: [Y ALPHA] = multinom (X, N)
 -- Function File: [Y ALPHA] = multinom (X, N,SORT)

     Returns the terms (monomials) of the multinomial expansion of
     degree n.

          (x1 + x2 + ... + xm)^N

     X is a nT-by-m matrix where each column represents a different
     variable, the output Y has the same format.  The order of the terms
     is inherited from multinom_exp and can be controlled through the
     optional argument SORT and is passed to the function 'sort'.  The
     exponents are returned in ALPHA.

     See also: multinom_exp, multinom_coeff, sort.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 71
Returns the terms (monomials) of the multinomial expansion of degree n.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 14
multinom_coeff


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 934
 -- Function File: [C ALPHA] = multinom_coeff (M, N)
 -- Function File: [C ALPHA] = multinom_coeff (M, N,ORDER)
     Produces the coefficients of the multinomial expansion

          (x1 + x2 + ... + xm).^n

     For example, for m=3, n=3 the expansion is

          (x1+x2+x3)^3 =
                  = x1^3 + x2^3 + x3^3 +
                  +  3 x1^2 x2 + 3 x1^2 x3 + 3 x2^2 x1 + 3 x2^2 x3 +
                  + 3 x3^2 x1 + 3 x3^2 x2 + 6 x1 x2 x3

     and the coefficients are [6 3 3 3 3 3 3 1 1 1].

     The order of the coefficients is defined by the optinal argument
     ORDER.  It is passed to the function 'multion_exp'.  See the help
     of that function for explanation.  The multinomial coefficients are
     generated using

           /   \
           | n |                n!
           |   |  = ------------------------
           | k |     k(1)!k(2)! ... k(end)!
           \   /

     See also: multinom,multinom_exp.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 54
Produces the coefficients of the multinomial expansion



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 12
multinom_exp


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 698
 -- Function File: ALPHA = multinom_exp (M, N)
 -- Function File: ALPHA = multinom_exp (M, N,SORT)
     Returns the exponents of the terms in the multinomial expansion

          (x1 + x2 + ... + xm).^N

     For example, for m=2, n=3 the expansion has the terms

          x1^3, x2^3, x1^2*x2, x1*x2^2

     then 'alpha = [3 0; 2 1; 1 2; 0 3]';

     The optional argument SORT is passed to function 'sort' to sort the
     exponents by the maximum degree.  The example above calling '
     multinom(m,n,"ascend")' produces

     'alpha = [2 1; 1 2; 3 0; 0 3]';

     calling ' multinom(m,n,"descend")' produces

     'alpha = [3 0; 0 3; 2 1; 1 2]';

     See also: multinom, multinom_coeff, sort.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 63
Returns the exponents of the terms in the multinomial expansion



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 3
psi


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 198
 -- Function File: Y = psi (X)
     Compute the psi function, for each value of X.

                 d
        psi(x) = __ log(gamma(x))
                 dx

     See also: gamma, gammainc, gammaln.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 46
Compute the psi function, for each value of X.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
sinint


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 94
 -- Function File: Y = sinint (X)
     Compute the sine integral function.

     See also: Si.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
Compute the sine integral function.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 4
zeta


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 93
 -- Function File: Z = zeta (T)
     Compute the Riemann's Zeta function.

     See also: Si.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Compute the Riemann's Zeta function.