LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
dlavsy.f
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1 *> \brief \b DLAVSY
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 * Definition:
9 * ===========
10 *
11 * SUBROUTINE DLAVSY( UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B,
12 * LDB, INFO )
13 *
14 * .. Scalar Arguments ..
15 * CHARACTER DIAG, TRANS, UPLO
16 * INTEGER INFO, LDA, LDB, N, NRHS
17 * ..
18 * .. Array Arguments ..
19 * INTEGER IPIV( * )
20 * DOUBLE PRECISION A( LDA, * ), B( LDB, * )
21 * ..
22 *
23 *
24 *> \par Purpose:
25 * =============
26 *>
27 *> \verbatim
28 *>
29 *> DLAVSY performs one of the matrix-vector operations
30 *> x := A*x or x := A'*x,
31 *> where x is an N element vector and A is one of the factors
32 *> from the block U*D*U' or L*D*L' factorization computed by DSYTRF.
33 *>
34 *> If TRANS = 'N', multiplies by U or U * D (or L or L * D)
35 *> If TRANS = 'T', multiplies by U' or D * U' (or L' or D * L')
36 *> If TRANS = 'C', multiplies by U' or D * U' (or L' or D * L')
37 *> \endverbatim
38 *
39 * Arguments:
40 * ==========
41 *
42 *> \param[in] UPLO
43 *> \verbatim
44 *> UPLO is CHARACTER*1
45 *> Specifies whether the factor stored in A is upper or lower
46 *> triangular.
47 *> = 'U': Upper triangular
48 *> = 'L': Lower triangular
49 *> \endverbatim
50 *>
51 *> \param[in] TRANS
52 *> \verbatim
53 *> TRANS is CHARACTER*1
54 *> Specifies the operation to be performed:
55 *> = 'N': x := A*x
56 *> = 'T': x := A'*x
57 *> = 'C': x := A'*x
58 *> \endverbatim
59 *>
60 *> \param[in] DIAG
61 *> \verbatim
62 *> DIAG is CHARACTER*1
63 *> Specifies whether or not the diagonal blocks are unit
64 *> matrices. If the diagonal blocks are assumed to be unit,
65 *> then A = U or A = L, otherwise A = U*D or A = L*D.
66 *> = 'U': Diagonal blocks are assumed to be unit matrices.
67 *> = 'N': Diagonal blocks are assumed to be non-unit matrices.
68 *> \endverbatim
69 *>
70 *> \param[in] N
71 *> \verbatim
72 *> N is INTEGER
73 *> The number of rows and columns of the matrix A. N >= 0.
74 *> \endverbatim
75 *>
76 *> \param[in] NRHS
77 *> \verbatim
78 *> NRHS is INTEGER
79 *> The number of right hand sides, i.e., the number of vectors
80 *> x to be multiplied by A. NRHS >= 0.
81 *> \endverbatim
82 *>
83 *> \param[in] A
84 *> \verbatim
85 *> A is DOUBLE PRECISION array, dimension (LDA,N)
86 *> The block diagonal matrix D and the multipliers used to
87 *> obtain the factor U or L as computed by DSYTRF.
88 *> Stored as a 2-D triangular matrix.
89 *> \endverbatim
90 *>
91 *> \param[in] LDA
92 *> \verbatim
93 *> LDA is INTEGER
94 *> The leading dimension of the array A. LDA >= max(1,N).
95 *> \endverbatim
96 *>
97 *> \param[in] IPIV
98 *> \verbatim
99 *> IPIV is INTEGER array, dimension (N)
100 *> Details of the interchanges and the block structure of D,
101 *> as determined by DSYTRF.
102 *>
103 *> If UPLO = 'U':
104 *> If IPIV(k) > 0, then rows and columns k and IPIV(k)
105 *> were interchanged and D(k,k) is a 1-by-1 diagonal block.
106 *> (If IPIV( k ) = k, no interchange was done).
107 *>
108 *> If IPIV(k) = IPIV(k-1) < 0, then rows and
109 *> columns k-1 and -IPIV(k) were interchanged,
110 *> D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
111 *>
112 *> If UPLO = 'L':
113 *> If IPIV(k) > 0, then rows and columns k and IPIV(k)
114 *> were interchanged and D(k,k) is a 1-by-1 diagonal block.
115 *> (If IPIV( k ) = k, no interchange was done).
116 *>
117 *> If IPIV(k) = IPIV(k+1) < 0, then rows and
118 *> columns k+1 and -IPIV(k) were interchanged,
119 *> D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
120 *> \endverbatim
121 *>
122 *> \param[in,out] B
123 *> \verbatim
124 *> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
125 *> On entry, B contains NRHS vectors of length N.
126 *> On exit, B is overwritten with the product A * B.
127 *> \endverbatim
128 *>
129 *> \param[in] LDB
130 *> \verbatim
131 *> LDB is INTEGER
132 *> The leading dimension of the array B. LDB >= max(1,N).
133 *> \endverbatim
134 *>
135 *> \param[out] INFO
136 *> \verbatim
137 *> INFO is INTEGER
138 *> = 0: successful exit
139 *> < 0: if INFO = -k, the k-th argument had an illegal value
140 *> \endverbatim
141 *
142 * Authors:
143 * ========
144 *
145 *> \author Univ. of Tennessee
146 *> \author Univ. of California Berkeley
147 *> \author Univ. of Colorado Denver
148 *> \author NAG Ltd.
149 *
150 *> \ingroup double_lin
151 *
152 * =====================================================================
153  SUBROUTINE dlavsy( UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B,
154  $ LDB, INFO )
155 *
156 * -- LAPACK test routine --
157 * -- LAPACK is a software package provided by Univ. of Tennessee, --
158 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
159 *
160 * .. Scalar Arguments ..
161  CHARACTER DIAG, TRANS, UPLO
162  INTEGER INFO, LDA, LDB, N, NRHS
163 * ..
164 * .. Array Arguments ..
165  INTEGER IPIV( * )
166  DOUBLE PRECISION A( LDA, * ), B( LDB, * )
167 * ..
168 *
169 * =====================================================================
170 *
171 * .. Parameters ..
172  DOUBLE PRECISION ONE
173  parameter( one = 1.0d+0 )
174 * ..
175 * .. Local Scalars ..
176  LOGICAL NOUNIT
177  INTEGER J, K, KP
178  DOUBLE PRECISION D11, D12, D21, D22, T1, T2
179 * ..
180 * .. External Functions ..
181  LOGICAL LSAME
182  EXTERNAL lsame
183 * ..
184 * .. External Subroutines ..
185  EXTERNAL dgemv, dger, dscal, dswap, xerbla
186 * ..
187 * .. Intrinsic Functions ..
188  INTRINSIC abs, max
189 * ..
190 * .. Executable Statements ..
191 *
192 * Test the input parameters.
193 *
194  info = 0
195  IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
196  info = -1
197  ELSE IF( .NOT.lsame( trans, 'N' ) .AND. .NOT.
198  $ lsame( trans, 'T' ) .AND. .NOT.lsame( trans, 'C' ) ) THEN
199  info = -2
200  ELSE IF( .NOT.lsame( diag, 'U' ) .AND. .NOT.lsame( diag, 'N' ) )
201  $ THEN
202  info = -3
203  ELSE IF( n.LT.0 ) THEN
204  info = -4
205  ELSE IF( lda.LT.max( 1, n ) ) THEN
206  info = -6
207  ELSE IF( ldb.LT.max( 1, n ) ) THEN
208  info = -9
209  END IF
210  IF( info.NE.0 ) THEN
211  CALL xerbla( 'DLAVSY ', -info )
212  RETURN
213  END IF
214 *
215 * Quick return if possible.
216 *
217  IF( n.EQ.0 )
218  $ RETURN
219 *
220  nounit = lsame( diag, 'N' )
221 *------------------------------------------
222 *
223 * Compute B := A * B (No transpose)
224 *
225 *------------------------------------------
226  IF( lsame( trans, 'N' ) ) THEN
227 *
228 * Compute B := U*B
229 * where U = P(m)*inv(U(m))* ... *P(1)*inv(U(1))
230 *
231  IF( lsame( uplo, 'U' ) ) THEN
232 *
233 * Loop forward applying the transformations.
234 *
235  k = 1
236  10 CONTINUE
237  IF( k.GT.n )
238  $ GO TO 30
239  IF( ipiv( k ).GT.0 ) THEN
240 *
241 * 1 x 1 pivot block
242 *
243 * Multiply by the diagonal element if forming U * D.
244 *
245  IF( nounit )
246  $ CALL dscal( nrhs, a( k, k ), b( k, 1 ), ldb )
247 *
248 * Multiply by P(K) * inv(U(K)) if K > 1.
249 *
250  IF( k.GT.1 ) THEN
251 *
252 * Apply the transformation.
253 *
254  CALL dger( k-1, nrhs, one, a( 1, k ), 1, b( k, 1 ),
255  $ ldb, b( 1, 1 ), ldb )
256 *
257 * Interchange if P(K) .ne. I.
258 *
259  kp = ipiv( k )
260  IF( kp.NE.k )
261  $ CALL dswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
262  END IF
263  k = k + 1
264  ELSE
265 *
266 * 2 x 2 pivot block
267 *
268 * Multiply by the diagonal block if forming U * D.
269 *
270  IF( nounit ) THEN
271  d11 = a( k, k )
272  d22 = a( k+1, k+1 )
273  d12 = a( k, k+1 )
274  d21 = d12
275  DO 20 j = 1, nrhs
276  t1 = b( k, j )
277  t2 = b( k+1, j )
278  b( k, j ) = d11*t1 + d12*t2
279  b( k+1, j ) = d21*t1 + d22*t2
280  20 CONTINUE
281  END IF
282 *
283 * Multiply by P(K) * inv(U(K)) if K > 1.
284 *
285  IF( k.GT.1 ) THEN
286 *
287 * Apply the transformations.
288 *
289  CALL dger( k-1, nrhs, one, a( 1, k ), 1, b( k, 1 ),
290  $ ldb, b( 1, 1 ), ldb )
291  CALL dger( k-1, nrhs, one, a( 1, k+1 ), 1,
292  $ b( k+1, 1 ), ldb, b( 1, 1 ), ldb )
293 *
294 * Interchange if P(K) .ne. I.
295 *
296  kp = abs( ipiv( k ) )
297  IF( kp.NE.k )
298  $ CALL dswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
299  END IF
300  k = k + 2
301  END IF
302  GO TO 10
303  30 CONTINUE
304 *
305 * Compute B := L*B
306 * where L = P(1)*inv(L(1))* ... *P(m)*inv(L(m)) .
307 *
308  ELSE
309 *
310 * Loop backward applying the transformations to B.
311 *
312  k = n
313  40 CONTINUE
314  IF( k.LT.1 )
315  $ GO TO 60
316 *
317 * Test the pivot index. If greater than zero, a 1 x 1
318 * pivot was used, otherwise a 2 x 2 pivot was used.
319 *
320  IF( ipiv( k ).GT.0 ) THEN
321 *
322 * 1 x 1 pivot block:
323 *
324 * Multiply by the diagonal element if forming L * D.
325 *
326  IF( nounit )
327  $ CALL dscal( nrhs, a( k, k ), b( k, 1 ), ldb )
328 *
329 * Multiply by P(K) * inv(L(K)) if K < N.
330 *
331  IF( k.NE.n ) THEN
332  kp = ipiv( k )
333 *
334 * Apply the transformation.
335 *
336  CALL dger( n-k, nrhs, one, a( k+1, k ), 1, b( k, 1 ),
337  $ ldb, b( k+1, 1 ), ldb )
338 *
339 * Interchange if a permutation was applied at the
340 * K-th step of the factorization.
341 *
342  IF( kp.NE.k )
343  $ CALL dswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
344  END IF
345  k = k - 1
346 *
347  ELSE
348 *
349 * 2 x 2 pivot block:
350 *
351 * Multiply by the diagonal block if forming L * D.
352 *
353  IF( nounit ) THEN
354  d11 = a( k-1, k-1 )
355  d22 = a( k, k )
356  d21 = a( k, k-1 )
357  d12 = d21
358  DO 50 j = 1, nrhs
359  t1 = b( k-1, j )
360  t2 = b( k, j )
361  b( k-1, j ) = d11*t1 + d12*t2
362  b( k, j ) = d21*t1 + d22*t2
363  50 CONTINUE
364  END IF
365 *
366 * Multiply by P(K) * inv(L(K)) if K < N.
367 *
368  IF( k.NE.n ) THEN
369 *
370 * Apply the transformation.
371 *
372  CALL dger( n-k, nrhs, one, a( k+1, k ), 1, b( k, 1 ),
373  $ ldb, b( k+1, 1 ), ldb )
374  CALL dger( n-k, nrhs, one, a( k+1, k-1 ), 1,
375  $ b( k-1, 1 ), ldb, b( k+1, 1 ), ldb )
376 *
377 * Interchange if a permutation was applied at the
378 * K-th step of the factorization.
379 *
380  kp = abs( ipiv( k ) )
381  IF( kp.NE.k )
382  $ CALL dswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
383  END IF
384  k = k - 2
385  END IF
386  GO TO 40
387  60 CONTINUE
388  END IF
389 *----------------------------------------
390 *
391 * Compute B := A' * B (transpose)
392 *
393 *----------------------------------------
394  ELSE
395 *
396 * Form B := U'*B
397 * where U = P(m)*inv(U(m))* ... *P(1)*inv(U(1))
398 * and U' = inv(U'(1))*P(1)* ... *inv(U'(m))*P(m)
399 *
400  IF( lsame( uplo, 'U' ) ) THEN
401 *
402 * Loop backward applying the transformations.
403 *
404  k = n
405  70 CONTINUE
406  IF( k.LT.1 )
407  $ GO TO 90
408 *
409 * 1 x 1 pivot block.
410 *
411  IF( ipiv( k ).GT.0 ) THEN
412  IF( k.GT.1 ) THEN
413 *
414 * Interchange if P(K) .ne. I.
415 *
416  kp = ipiv( k )
417  IF( kp.NE.k )
418  $ CALL dswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
419 *
420 * Apply the transformation
421 *
422  CALL dgemv( 'Transpose', k-1, nrhs, one, b, ldb,
423  $ a( 1, k ), 1, one, b( k, 1 ), ldb )
424  END IF
425  IF( nounit )
426  $ CALL dscal( nrhs, a( k, k ), b( k, 1 ), ldb )
427  k = k - 1
428 *
429 * 2 x 2 pivot block.
430 *
431  ELSE
432  IF( k.GT.2 ) THEN
433 *
434 * Interchange if P(K) .ne. I.
435 *
436  kp = abs( ipiv( k ) )
437  IF( kp.NE.k-1 )
438  $ CALL dswap( nrhs, b( k-1, 1 ), ldb, b( kp, 1 ),
439  $ ldb )
440 *
441 * Apply the transformations
442 *
443  CALL dgemv( 'Transpose', k-2, nrhs, one, b, ldb,
444  $ a( 1, k ), 1, one, b( k, 1 ), ldb )
445  CALL dgemv( 'Transpose', k-2, nrhs, one, b, ldb,
446  $ a( 1, k-1 ), 1, one, b( k-1, 1 ), ldb )
447  END IF
448 *
449 * Multiply by the diagonal block if non-unit.
450 *
451  IF( nounit ) THEN
452  d11 = a( k-1, k-1 )
453  d22 = a( k, k )
454  d12 = a( k-1, k )
455  d21 = d12
456  DO 80 j = 1, nrhs
457  t1 = b( k-1, j )
458  t2 = b( k, j )
459  b( k-1, j ) = d11*t1 + d12*t2
460  b( k, j ) = d21*t1 + d22*t2
461  80 CONTINUE
462  END IF
463  k = k - 2
464  END IF
465  GO TO 70
466  90 CONTINUE
467 *
468 * Form B := L'*B
469 * where L = P(1)*inv(L(1))* ... *P(m)*inv(L(m))
470 * and L' = inv(L'(m))*P(m)* ... *inv(L'(1))*P(1)
471 *
472  ELSE
473 *
474 * Loop forward applying the L-transformations.
475 *
476  k = 1
477  100 CONTINUE
478  IF( k.GT.n )
479  $ GO TO 120
480 *
481 * 1 x 1 pivot block
482 *
483  IF( ipiv( k ).GT.0 ) THEN
484  IF( k.LT.n ) THEN
485 *
486 * Interchange if P(K) .ne. I.
487 *
488  kp = ipiv( k )
489  IF( kp.NE.k )
490  $ CALL dswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
491 *
492 * Apply the transformation
493 *
494  CALL dgemv( 'Transpose', n-k, nrhs, one, b( k+1, 1 ),
495  $ ldb, a( k+1, k ), 1, one, b( k, 1 ), ldb )
496  END IF
497  IF( nounit )
498  $ CALL dscal( nrhs, a( k, k ), b( k, 1 ), ldb )
499  k = k + 1
500 *
501 * 2 x 2 pivot block.
502 *
503  ELSE
504  IF( k.LT.n-1 ) THEN
505 *
506 * Interchange if P(K) .ne. I.
507 *
508  kp = abs( ipiv( k ) )
509  IF( kp.NE.k+1 )
510  $ CALL dswap( nrhs, b( k+1, 1 ), ldb, b( kp, 1 ),
511  $ ldb )
512 *
513 * Apply the transformation
514 *
515  CALL dgemv( 'Transpose', n-k-1, nrhs, one,
516  $ b( k+2, 1 ), ldb, a( k+2, k+1 ), 1, one,
517  $ b( k+1, 1 ), ldb )
518  CALL dgemv( 'Transpose', n-k-1, nrhs, one,
519  $ b( k+2, 1 ), ldb, a( k+2, k ), 1, one,
520  $ b( k, 1 ), ldb )
521  END IF
522 *
523 * Multiply by the diagonal block if non-unit.
524 *
525  IF( nounit ) THEN
526  d11 = a( k, k )
527  d22 = a( k+1, k+1 )
528  d21 = a( k+1, k )
529  d12 = d21
530  DO 110 j = 1, nrhs
531  t1 = b( k, j )
532  t2 = b( k+1, j )
533  b( k, j ) = d11*t1 + d12*t2
534  b( k+1, j ) = d21*t1 + d22*t2
535  110 CONTINUE
536  END IF
537  k = k + 2
538  END IF
539  GO TO 100
540  120 CONTINUE
541  END IF
542 *
543  END IF
544  RETURN
545 *
546 * End of DLAVSY
547 *
548  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine dscal(N, DA, DX, INCX)
DSCAL
Definition: dscal.f:79
subroutine dswap(N, DX, INCX, DY, INCY)
DSWAP
Definition: dswap.f:82
subroutine dger(M, N, ALPHA, X, INCX, Y, INCY, A, LDA)
DGER
Definition: dger.f:130
subroutine dgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
DGEMV
Definition: dgemv.f:156
subroutine dlavsy(UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
DLAVSY
Definition: dlavsy.f:155