LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
sstevr.f
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1 *> \brief <b> SSTEVR computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices</b>
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
9 *> Download SSTEVR + dependencies
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11 *> [TGZ]</a>
12 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sstevr.f">
13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sstevr.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE SSTEVR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABSTOL,
22 * M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK,
23 * LIWORK, INFO )
24 *
25 * .. Scalar Arguments ..
26 * CHARACTER JOBZ, RANGE
27 * INTEGER IL, INFO, IU, LDZ, LIWORK, LWORK, M, N
28 * REAL ABSTOL, VL, VU
29 * ..
30 * .. Array Arguments ..
31 * INTEGER ISUPPZ( * ), IWORK( * )
32 * REAL D( * ), E( * ), W( * ), WORK( * ), Z( LDZ, * )
33 * ..
34 *
35 *
36 *> \par Purpose:
37 * =============
38 *>
39 *> \verbatim
40 *>
41 *> SSTEVR computes selected eigenvalues and, optionally, eigenvectors
42 *> of a real symmetric tridiagonal matrix T. Eigenvalues and
43 *> eigenvectors can be selected by specifying either a range of values
44 *> or a range of indices for the desired eigenvalues.
45 *>
46 *> Whenever possible, SSTEVR calls SSTEMR to compute the
47 *> eigenspectrum using Relatively Robust Representations. SSTEMR
48 *> computes eigenvalues by the dqds algorithm, while orthogonal
49 *> eigenvectors are computed from various "good" L D L^T representations
50 *> (also known as Relatively Robust Representations). Gram-Schmidt
51 *> orthogonalization is avoided as far as possible. More specifically,
52 *> the various steps of the algorithm are as follows. For the i-th
53 *> unreduced block of T,
54 *> (a) Compute T - sigma_i = L_i D_i L_i^T, such that L_i D_i L_i^T
55 *> is a relatively robust representation,
56 *> (b) Compute the eigenvalues, lambda_j, of L_i D_i L_i^T to high
57 *> relative accuracy by the dqds algorithm,
58 *> (c) If there is a cluster of close eigenvalues, "choose" sigma_i
59 *> close to the cluster, and go to step (a),
60 *> (d) Given the approximate eigenvalue lambda_j of L_i D_i L_i^T,
61 *> compute the corresponding eigenvector by forming a
62 *> rank-revealing twisted factorization.
63 *> The desired accuracy of the output can be specified by the input
64 *> parameter ABSTOL.
65 *>
66 *> For more details, see "A new O(n^2) algorithm for the symmetric
67 *> tridiagonal eigenvalue/eigenvector problem", by Inderjit Dhillon,
68 *> Computer Science Division Technical Report No. UCB//CSD-97-971,
69 *> UC Berkeley, May 1997.
70 *>
71 *>
72 *> Note 1 : SSTEVR calls SSTEMR when the full spectrum is requested
73 *> on machines which conform to the ieee-754 floating point standard.
74 *> SSTEVR calls SSTEBZ and SSTEIN on non-ieee machines and
75 *> when partial spectrum requests are made.
76 *>
77 *> Normal execution of SSTEMR may create NaNs and infinities and
78 *> hence may abort due to a floating point exception in environments
79 *> which do not handle NaNs and infinities in the ieee standard default
80 *> manner.
81 *> \endverbatim
82 *
83 * Arguments:
84 * ==========
85 *
86 *> \param[in] JOBZ
87 *> \verbatim
88 *> JOBZ is CHARACTER*1
89 *> = 'N': Compute eigenvalues only;
90 *> = 'V': Compute eigenvalues and eigenvectors.
91 *> \endverbatim
92 *>
93 *> \param[in] RANGE
94 *> \verbatim
95 *> RANGE is CHARACTER*1
96 *> = 'A': all eigenvalues will be found.
97 *> = 'V': all eigenvalues in the half-open interval (VL,VU]
98 *> will be found.
99 *> = 'I': the IL-th through IU-th eigenvalues will be found.
100 *> For RANGE = 'V' or 'I' and IU - IL < N - 1, SSTEBZ and
101 *> SSTEIN are called
102 *> \endverbatim
103 *>
104 *> \param[in] N
105 *> \verbatim
106 *> N is INTEGER
107 *> The order of the matrix. N >= 0.
108 *> \endverbatim
109 *>
110 *> \param[in,out] D
111 *> \verbatim
112 *> D is REAL array, dimension (N)
113 *> On entry, the n diagonal elements of the tridiagonal matrix
114 *> A.
115 *> On exit, D may be multiplied by a constant factor chosen
116 *> to avoid over/underflow in computing the eigenvalues.
117 *> \endverbatim
118 *>
119 *> \param[in,out] E
120 *> \verbatim
121 *> E is REAL array, dimension (max(1,N-1))
122 *> On entry, the (n-1) subdiagonal elements of the tridiagonal
123 *> matrix A in elements 1 to N-1 of E.
124 *> On exit, E may be multiplied by a constant factor chosen
125 *> to avoid over/underflow in computing the eigenvalues.
126 *> \endverbatim
127 *>
128 *> \param[in] VL
129 *> \verbatim
130 *> VL is REAL
131 *> If RANGE='V', the lower bound of the interval to
132 *> be searched for eigenvalues. VL < VU.
133 *> Not referenced if RANGE = 'A' or 'I'.
134 *> \endverbatim
135 *>
136 *> \param[in] VU
137 *> \verbatim
138 *> VU is REAL
139 *> If RANGE='V', the upper bound of the interval to
140 *> be searched for eigenvalues. VL < VU.
141 *> Not referenced if RANGE = 'A' or 'I'.
142 *> \endverbatim
143 *>
144 *> \param[in] IL
145 *> \verbatim
146 *> IL is INTEGER
147 *> If RANGE='I', the index of the
148 *> smallest eigenvalue to be returned.
149 *> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
150 *> Not referenced if RANGE = 'A' or 'V'.
151 *> \endverbatim
152 *>
153 *> \param[in] IU
154 *> \verbatim
155 *> IU is INTEGER
156 *> If RANGE='I', the index of the
157 *> largest eigenvalue to be returned.
158 *> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
159 *> Not referenced if RANGE = 'A' or 'V'.
160 *> \endverbatim
161 *>
162 *> \param[in] ABSTOL
163 *> \verbatim
164 *> ABSTOL is REAL
165 *> The absolute error tolerance for the eigenvalues.
166 *> An approximate eigenvalue is accepted as converged
167 *> when it is determined to lie in an interval [a,b]
168 *> of width less than or equal to
169 *>
170 *> ABSTOL + EPS * max( |a|,|b| ) ,
171 *>
172 *> where EPS is the machine precision. If ABSTOL is less than
173 *> or equal to zero, then EPS*|T| will be used in its place,
174 *> where |T| is the 1-norm of the tridiagonal matrix obtained
175 *> by reducing A to tridiagonal form.
176 *>
177 *> See "Computing Small Singular Values of Bidiagonal Matrices
178 *> with Guaranteed High Relative Accuracy," by Demmel and
179 *> Kahan, LAPACK Working Note #3.
180 *>
181 *> If high relative accuracy is important, set ABSTOL to
182 *> SLAMCH( 'Safe minimum' ). Doing so will guarantee that
183 *> eigenvalues are computed to high relative accuracy when
184 *> possible in future releases. The current code does not
185 *> make any guarantees about high relative accuracy, but
186 *> future releases will. See J. Barlow and J. Demmel,
187 *> "Computing Accurate Eigensystems of Scaled Diagonally
188 *> Dominant Matrices", LAPACK Working Note #7, for a discussion
189 *> of which matrices define their eigenvalues to high relative
190 *> accuracy.
191 *> \endverbatim
192 *>
193 *> \param[out] M
194 *> \verbatim
195 *> M is INTEGER
196 *> The total number of eigenvalues found. 0 <= M <= N.
197 *> If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
198 *> \endverbatim
199 *>
200 *> \param[out] W
201 *> \verbatim
202 *> W is REAL array, dimension (N)
203 *> The first M elements contain the selected eigenvalues in
204 *> ascending order.
205 *> \endverbatim
206 *>
207 *> \param[out] Z
208 *> \verbatim
209 *> Z is REAL array, dimension (LDZ, max(1,M) )
210 *> If JOBZ = 'V', then if INFO = 0, the first M columns of Z
211 *> contain the orthonormal eigenvectors of the matrix A
212 *> corresponding to the selected eigenvalues, with the i-th
213 *> column of Z holding the eigenvector associated with W(i).
214 *> Note: the user must ensure that at least max(1,M) columns are
215 *> supplied in the array Z; if RANGE = 'V', the exact value of M
216 *> is not known in advance and an upper bound must be used.
217 *> \endverbatim
218 *>
219 *> \param[in] LDZ
220 *> \verbatim
221 *> LDZ is INTEGER
222 *> The leading dimension of the array Z. LDZ >= 1, and if
223 *> JOBZ = 'V', LDZ >= max(1,N).
224 *> \endverbatim
225 *>
226 *> \param[out] ISUPPZ
227 *> \verbatim
228 *> ISUPPZ is INTEGER array, dimension ( 2*max(1,M) )
229 *> The support of the eigenvectors in Z, i.e., the indices
230 *> indicating the nonzero elements in Z. The i-th eigenvector
231 *> is nonzero only in elements ISUPPZ( 2*i-1 ) through
232 *> ISUPPZ( 2*i ).
233 *> Implemented only for RANGE = 'A' or 'I' and IU - IL = N - 1
234 *> \endverbatim
235 *>
236 *> \param[out] WORK
237 *> \verbatim
238 *> WORK is REAL array, dimension (MAX(1,LWORK))
239 *> On exit, if INFO = 0, WORK(1) returns the optimal (and
240 *> minimal) LWORK.
241 *> \endverbatim
242 *>
243 *> \param[in] LWORK
244 *> \verbatim
245 *> LWORK is INTEGER
246 *> The dimension of the array WORK. LWORK >= 20*N.
247 *>
248 *> If LWORK = -1, then a workspace query is assumed; the routine
249 *> only calculates the optimal sizes of the WORK and IWORK
250 *> arrays, returns these values as the first entries of the WORK
251 *> and IWORK arrays, and no error message related to LWORK or
252 *> LIWORK is issued by XERBLA.
253 *> \endverbatim
254 *>
255 *> \param[out] IWORK
256 *> \verbatim
257 *> IWORK is INTEGER array, dimension (MAX(1,LIWORK))
258 *> On exit, if INFO = 0, IWORK(1) returns the optimal (and
259 *> minimal) LIWORK.
260 *> \endverbatim
261 *>
262 *> \param[in] LIWORK
263 *> \verbatim
264 *> LIWORK is INTEGER
265 *> The dimension of the array IWORK. LIWORK >= 10*N.
266 *>
267 *> If LIWORK = -1, then a workspace query is assumed; the
268 *> routine only calculates the optimal sizes of the WORK and
269 *> IWORK arrays, returns these values as the first entries of
270 *> the WORK and IWORK arrays, and no error message related to
271 *> LWORK or LIWORK is issued by XERBLA.
272 *> \endverbatim
273 *>
274 *> \param[out] INFO
275 *> \verbatim
276 *> INFO is INTEGER
277 *> = 0: successful exit
278 *> < 0: if INFO = -i, the i-th argument had an illegal value
279 *> > 0: Internal error
280 *> \endverbatim
281 *
282 * Authors:
283 * ========
284 *
285 *> \author Univ. of Tennessee
286 *> \author Univ. of California Berkeley
287 *> \author Univ. of Colorado Denver
288 *> \author NAG Ltd.
289 *
290 *> \ingroup realOTHEReigen
291 *
292 *> \par Contributors:
293 * ==================
294 *>
295 *> Inderjit Dhillon, IBM Almaden, USA \n
296 *> Osni Marques, LBNL/NERSC, USA \n
297 *> Ken Stanley, Computer Science Division, University of
298 *> California at Berkeley, USA \n
299 *> Jason Riedy, Computer Science Division, University of
300 *> California at Berkeley, USA \n
301 *>
302 * =====================================================================
303  SUBROUTINE sstevr( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABSTOL,
304  $ M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK,
305  $ LIWORK, INFO )
306 *
307 * -- LAPACK driver routine --
308 * -- LAPACK is a software package provided by Univ. of Tennessee, --
309 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
310 *
311 * .. Scalar Arguments ..
312  CHARACTER JOBZ, RANGE
313  INTEGER IL, INFO, IU, LDZ, LIWORK, LWORK, M, N
314  REAL ABSTOL, VL, VU
315 * ..
316 * .. Array Arguments ..
317  INTEGER ISUPPZ( * ), IWORK( * )
318  REAL D( * ), E( * ), W( * ), WORK( * ), Z( LDZ, * )
319 * ..
320 *
321 * =====================================================================
322 *
323 * .. Parameters ..
324  REAL ZERO, ONE, TWO
325  PARAMETER ( ZERO = 0.0e+0, one = 1.0e+0, two = 2.0e+0 )
326 * ..
327 * .. Local Scalars ..
328  LOGICAL ALLEIG, INDEIG, TEST, LQUERY, VALEIG, WANTZ,
329  $ TRYRAC
330  CHARACTER ORDER
331  INTEGER I, IEEEOK, IMAX, INDIBL, INDIFL, INDISP,
332  $ indiwo, iscale, j, jj, liwmin, lwmin, nsplit
333  REAL BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, SMLNUM,
334  $ TMP1, TNRM, VLL, VUU
335 * ..
336 * .. External Functions ..
337  LOGICAL LSAME
338  INTEGER ILAENV
339  REAL SLAMCH, SLANST
340  EXTERNAL lsame, ilaenv, slamch, slanst
341 * ..
342 * .. External Subroutines ..
343  EXTERNAL scopy, sscal, sstebz, sstemr, sstein, ssterf,
344  $ sswap, xerbla
345 * ..
346 * .. Intrinsic Functions ..
347  INTRINSIC max, min, sqrt
348 * ..
349 * .. Executable Statements ..
350 *
351 *
352 * Test the input parameters.
353 *
354  ieeeok = ilaenv( 10, 'SSTEVR', 'N', 1, 2, 3, 4 )
355 *
356  wantz = lsame( jobz, 'V' )
357  alleig = lsame( range, 'A' )
358  valeig = lsame( range, 'V' )
359  indeig = lsame( range, 'I' )
360 *
361  lquery = ( ( lwork.EQ.-1 ) .OR. ( liwork.EQ.-1 ) )
362  lwmin = max( 1, 20*n )
363  liwmin = max(1, 10*n )
364 *
365 *
366  info = 0
367  IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
368  info = -1
369  ELSE IF( .NOT.( alleig .OR. valeig .OR. indeig ) ) THEN
370  info = -2
371  ELSE IF( n.LT.0 ) THEN
372  info = -3
373  ELSE
374  IF( valeig ) THEN
375  IF( n.GT.0 .AND. vu.LE.vl )
376  $ info = -7
377  ELSE IF( indeig ) THEN
378  IF( il.LT.1 .OR. il.GT.max( 1, n ) ) THEN
379  info = -8
380  ELSE IF( iu.LT.min( n, il ) .OR. iu.GT.n ) THEN
381  info = -9
382  END IF
383  END IF
384  END IF
385  IF( info.EQ.0 ) THEN
386  IF( ldz.LT.1 .OR. ( wantz .AND. ldz.LT.n ) ) THEN
387  info = -14
388  END IF
389  END IF
390 *
391  IF( info.EQ.0 ) THEN
392  work( 1 ) = lwmin
393  iwork( 1 ) = liwmin
394 *
395  IF( lwork.LT.lwmin .AND. .NOT.lquery ) THEN
396  info = -17
397  ELSE IF( liwork.LT.liwmin .AND. .NOT.lquery ) THEN
398  info = -19
399  END IF
400  END IF
401 *
402  IF( info.NE.0 ) THEN
403  CALL xerbla( 'SSTEVR', -info )
404  RETURN
405  ELSE IF( lquery ) THEN
406  RETURN
407  END IF
408 *
409 * Quick return if possible
410 *
411  m = 0
412  IF( n.EQ.0 )
413  $ RETURN
414 *
415  IF( n.EQ.1 ) THEN
416  IF( alleig .OR. indeig ) THEN
417  m = 1
418  w( 1 ) = d( 1 )
419  ELSE
420  IF( vl.LT.d( 1 ) .AND. vu.GE.d( 1 ) ) THEN
421  m = 1
422  w( 1 ) = d( 1 )
423  END IF
424  END IF
425  IF( wantz )
426  $ z( 1, 1 ) = one
427  RETURN
428  END IF
429 *
430 * Get machine constants.
431 *
432  safmin = slamch( 'Safe minimum' )
433  eps = slamch( 'Precision' )
434  smlnum = safmin / eps
435  bignum = one / smlnum
436  rmin = sqrt( smlnum )
437  rmax = min( sqrt( bignum ), one / sqrt( sqrt( safmin ) ) )
438 *
439 *
440 * Scale matrix to allowable range, if necessary.
441 *
442  iscale = 0
443  IF( valeig ) THEN
444  vll = vl
445  vuu = vu
446  END IF
447 *
448  tnrm = slanst( 'M', n, d, e )
449  IF( tnrm.GT.zero .AND. tnrm.LT.rmin ) THEN
450  iscale = 1
451  sigma = rmin / tnrm
452  ELSE IF( tnrm.GT.rmax ) THEN
453  iscale = 1
454  sigma = rmax / tnrm
455  END IF
456  IF( iscale.EQ.1 ) THEN
457  CALL sscal( n, sigma, d, 1 )
458  CALL sscal( n-1, sigma, e( 1 ), 1 )
459  IF( valeig ) THEN
460  vll = vl*sigma
461  vuu = vu*sigma
462  END IF
463  END IF
464 
465 * Initialize indices into workspaces. Note: These indices are used only
466 * if SSTERF or SSTEMR fail.
467 
468 * IWORK(INDIBL:INDIBL+M-1) corresponds to IBLOCK in SSTEBZ and
469 * stores the block indices of each of the M<=N eigenvalues.
470  indibl = 1
471 * IWORK(INDISP:INDISP+NSPLIT-1) corresponds to ISPLIT in SSTEBZ and
472 * stores the starting and finishing indices of each block.
473  indisp = indibl + n
474 * IWORK(INDIFL:INDIFL+N-1) stores the indices of eigenvectors
475 * that corresponding to eigenvectors that fail to converge in
476 * SSTEIN. This information is discarded; if any fail, the driver
477 * returns INFO > 0.
478  indifl = indisp + n
479 * INDIWO is the offset of the remaining integer workspace.
480  indiwo = indisp + n
481 *
482 * If all eigenvalues are desired, then
483 * call SSTERF or SSTEMR. If this fails for some eigenvalue, then
484 * try SSTEBZ.
485 *
486 *
487  test = .false.
488  IF( indeig ) THEN
489  IF( il.EQ.1 .AND. iu.EQ.n ) THEN
490  test = .true.
491  END IF
492  END IF
493  IF( ( alleig .OR. test ) .AND. ieeeok.EQ.1 ) THEN
494  CALL scopy( n-1, e( 1 ), 1, work( 1 ), 1 )
495  IF( .NOT.wantz ) THEN
496  CALL scopy( n, d, 1, w, 1 )
497  CALL ssterf( n, w, work, info )
498  ELSE
499  CALL scopy( n, d, 1, work( n+1 ), 1 )
500  IF (abstol .LE. two*n*eps) THEN
501  tryrac = .true.
502  ELSE
503  tryrac = .false.
504  END IF
505  CALL sstemr( jobz, 'A', n, work( n+1 ), work, vl, vu, il,
506  $ iu, m, w, z, ldz, n, isuppz, tryrac,
507  $ work( 2*n+1 ), lwork-2*n, iwork, liwork, info )
508 *
509  END IF
510  IF( info.EQ.0 ) THEN
511  m = n
512  GO TO 10
513  END IF
514  info = 0
515  END IF
516 *
517 * Otherwise, call SSTEBZ and, if eigenvectors are desired, SSTEIN.
518 *
519  IF( wantz ) THEN
520  order = 'B'
521  ELSE
522  order = 'E'
523  END IF
524 
525  CALL sstebz( range, order, n, vll, vuu, il, iu, abstol, d, e, m,
526  $ nsplit, w, iwork( indibl ), iwork( indisp ), work,
527  $ iwork( indiwo ), info )
528 *
529  IF( wantz ) THEN
530  CALL sstein( n, d, e, m, w, iwork( indibl ), iwork( indisp ),
531  $ z, ldz, work, iwork( indiwo ), iwork( indifl ),
532  $ info )
533  END IF
534 *
535 * If matrix was scaled, then rescale eigenvalues appropriately.
536 *
537  10 CONTINUE
538  IF( iscale.EQ.1 ) THEN
539  IF( info.EQ.0 ) THEN
540  imax = m
541  ELSE
542  imax = info - 1
543  END IF
544  CALL sscal( imax, one / sigma, w, 1 )
545  END IF
546 *
547 * If eigenvalues are not in order, then sort them, along with
548 * eigenvectors.
549 *
550  IF( wantz ) THEN
551  DO 30 j = 1, m - 1
552  i = 0
553  tmp1 = w( j )
554  DO 20 jj = j + 1, m
555  IF( w( jj ).LT.tmp1 ) THEN
556  i = jj
557  tmp1 = w( jj )
558  END IF
559  20 CONTINUE
560 *
561  IF( i.NE.0 ) THEN
562  w( i ) = w( j )
563  w( j ) = tmp1
564  CALL sswap( n, z( 1, i ), 1, z( 1, j ), 1 )
565  END IF
566  30 CONTINUE
567  END IF
568 *
569 * Causes problems with tests 19 & 20:
570 * IF (wantz .and. INDEIG ) Z( 1,1) = Z(1,1) / 1.002 + .002
571 *
572 *
573  work( 1 ) = lwmin
574  iwork( 1 ) = liwmin
575  RETURN
576 *
577 * End of SSTEVR
578 *
579  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine ssterf(N, D, E, INFO)
SSTERF
Definition: ssterf.f:86
subroutine sstebz(RANGE, ORDER, N, VL, VU, IL, IU, ABSTOL, D, E, M, NSPLIT, W, IBLOCK, ISPLIT, WORK, IWORK, INFO)
SSTEBZ
Definition: sstebz.f:273
subroutine sstemr(JOBZ, RANGE, N, D, E, VL, VU, IL, IU, M, W, Z, LDZ, NZC, ISUPPZ, TRYRAC, WORK, LWORK, IWORK, LIWORK, INFO)
SSTEMR
Definition: sstemr.f:321
subroutine sstein(N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK, IWORK, IFAIL, INFO)
SSTEIN
Definition: sstein.f:174
subroutine sstevr(JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK, LIWORK, INFO)
SSTEVR computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrice...
Definition: sstevr.f:306
subroutine sswap(N, SX, INCX, SY, INCY)
SSWAP
Definition: sswap.f:82
subroutine scopy(N, SX, INCX, SY, INCY)
SCOPY
Definition: scopy.f:82
subroutine sscal(N, SA, SX, INCX)
SSCAL
Definition: sscal.f:79