LAPACK  3.9.0
LAPACK: Linear Algebra PACKage
dlavsy.f
Go to the documentation of this file.
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 *> \date November 2013
151 *
152 *> \ingroup double_lin
153 *
154 * =====================================================================
155  SUBROUTINE dlavsy( UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B,
156  $ LDB, INFO )
157 *
158 * -- LAPACK test routine (version 3.5.0) --
159 * -- LAPACK is a software package provided by Univ. of Tennessee, --
160 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
161 * November 2013
162 *
163 * .. Scalar Arguments ..
164  CHARACTER DIAG, TRANS, UPLO
165  INTEGER INFO, LDA, LDB, N, NRHS
166 * ..
167 * .. Array Arguments ..
168  INTEGER IPIV( * )
169  DOUBLE PRECISION A( LDA, * ), B( LDB, * )
170 * ..
171 *
172 * =====================================================================
173 *
174 * .. Parameters ..
175  DOUBLE PRECISION ONE
176  parameter( one = 1.0d+0 )
177 * ..
178 * .. Local Scalars ..
179  LOGICAL NOUNIT
180  INTEGER J, K, KP
181  DOUBLE PRECISION D11, D12, D21, D22, T1, T2
182 * ..
183 * .. External Functions ..
184  LOGICAL LSAME
185  EXTERNAL lsame
186 * ..
187 * .. External Subroutines ..
188  EXTERNAL dgemv, dger, dscal, dswap, xerbla
189 * ..
190 * .. Intrinsic Functions ..
191  INTRINSIC abs, max
192 * ..
193 * .. Executable Statements ..
194 *
195 * Test the input parameters.
196 *
197  info = 0
198  IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
199  info = -1
200  ELSE IF( .NOT.lsame( trans, 'N' ) .AND. .NOT.
201  $ lsame( trans, 'T' ) .AND. .NOT.lsame( trans, 'C' ) ) THEN
202  info = -2
203  ELSE IF( .NOT.lsame( diag, 'U' ) .AND. .NOT.lsame( diag, 'N' ) )
204  $ THEN
205  info = -3
206  ELSE IF( n.LT.0 ) THEN
207  info = -4
208  ELSE IF( lda.LT.max( 1, n ) ) THEN
209  info = -6
210  ELSE IF( ldb.LT.max( 1, n ) ) THEN
211  info = -9
212  END IF
213  IF( info.NE.0 ) THEN
214  CALL xerbla( 'DLAVSY ', -info )
215  RETURN
216  END IF
217 *
218 * Quick return if possible.
219 *
220  IF( n.EQ.0 )
221  $ RETURN
222 *
223  nounit = lsame( diag, 'N' )
224 *------------------------------------------
225 *
226 * Compute B := A * B (No transpose)
227 *
228 *------------------------------------------
229  IF( lsame( trans, 'N' ) ) THEN
230 *
231 * Compute B := U*B
232 * where U = P(m)*inv(U(m))* ... *P(1)*inv(U(1))
233 *
234  IF( lsame( uplo, 'U' ) ) THEN
235 *
236 * Loop forward applying the transformations.
237 *
238  k = 1
239  10 CONTINUE
240  IF( k.GT.n )
241  $ GO TO 30
242  IF( ipiv( k ).GT.0 ) THEN
243 *
244 * 1 x 1 pivot block
245 *
246 * Multiply by the diagonal element if forming U * D.
247 *
248  IF( nounit )
249  $ CALL dscal( nrhs, a( k, k ), b( k, 1 ), ldb )
250 *
251 * Multiply by P(K) * inv(U(K)) if K > 1.
252 *
253  IF( k.GT.1 ) THEN
254 *
255 * Apply the transformation.
256 *
257  CALL dger( k-1, nrhs, one, a( 1, k ), 1, b( k, 1 ),
258  $ ldb, b( 1, 1 ), ldb )
259 *
260 * Interchange if P(K) .ne. I.
261 *
262  kp = ipiv( k )
263  IF( kp.NE.k )
264  $ CALL dswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
265  END IF
266  k = k + 1
267  ELSE
268 *
269 * 2 x 2 pivot block
270 *
271 * Multiply by the diagonal block if forming U * D.
272 *
273  IF( nounit ) THEN
274  d11 = a( k, k )
275  d22 = a( k+1, k+1 )
276  d12 = a( k, k+1 )
277  d21 = d12
278  DO 20 j = 1, nrhs
279  t1 = b( k, j )
280  t2 = b( k+1, j )
281  b( k, j ) = d11*t1 + d12*t2
282  b( k+1, j ) = d21*t1 + d22*t2
283  20 CONTINUE
284  END IF
285 *
286 * Multiply by P(K) * inv(U(K)) if K > 1.
287 *
288  IF( k.GT.1 ) THEN
289 *
290 * Apply the transformations.
291 *
292  CALL dger( k-1, nrhs, one, a( 1, k ), 1, b( k, 1 ),
293  $ ldb, b( 1, 1 ), ldb )
294  CALL dger( k-1, nrhs, one, a( 1, k+1 ), 1,
295  $ b( k+1, 1 ), ldb, b( 1, 1 ), ldb )
296 *
297 * Interchange if P(K) .ne. I.
298 *
299  kp = abs( ipiv( k ) )
300  IF( kp.NE.k )
301  $ CALL dswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
302  END IF
303  k = k + 2
304  END IF
305  GO TO 10
306  30 CONTINUE
307 *
308 * Compute B := L*B
309 * where L = P(1)*inv(L(1))* ... *P(m)*inv(L(m)) .
310 *
311  ELSE
312 *
313 * Loop backward applying the transformations to B.
314 *
315  k = n
316  40 CONTINUE
317  IF( k.LT.1 )
318  $ GO TO 60
319 *
320 * Test the pivot index. If greater than zero, a 1 x 1
321 * pivot was used, otherwise a 2 x 2 pivot was used.
322 *
323  IF( ipiv( k ).GT.0 ) THEN
324 *
325 * 1 x 1 pivot block:
326 *
327 * Multiply by the diagonal element if forming L * D.
328 *
329  IF( nounit )
330  $ CALL dscal( nrhs, a( k, k ), b( k, 1 ), ldb )
331 *
332 * Multiply by P(K) * inv(L(K)) if K < N.
333 *
334  IF( k.NE.n ) THEN
335  kp = ipiv( k )
336 *
337 * Apply the transformation.
338 *
339  CALL dger( n-k, nrhs, one, a( k+1, k ), 1, b( k, 1 ),
340  $ ldb, b( k+1, 1 ), ldb )
341 *
342 * Interchange if a permutation was applied at the
343 * K-th step of the factorization.
344 *
345  IF( kp.NE.k )
346  $ CALL dswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
347  END IF
348  k = k - 1
349 *
350  ELSE
351 *
352 * 2 x 2 pivot block:
353 *
354 * Multiply by the diagonal block if forming L * D.
355 *
356  IF( nounit ) THEN
357  d11 = a( k-1, k-1 )
358  d22 = a( k, k )
359  d21 = a( k, k-1 )
360  d12 = d21
361  DO 50 j = 1, nrhs
362  t1 = b( k-1, j )
363  t2 = b( k, j )
364  b( k-1, j ) = d11*t1 + d12*t2
365  b( k, j ) = d21*t1 + d22*t2
366  50 CONTINUE
367  END IF
368 *
369 * Multiply by P(K) * inv(L(K)) if K < N.
370 *
371  IF( k.NE.n ) THEN
372 *
373 * Apply the transformation.
374 *
375  CALL dger( n-k, nrhs, one, a( k+1, k ), 1, b( k, 1 ),
376  $ ldb, b( k+1, 1 ), ldb )
377  CALL dger( n-k, nrhs, one, a( k+1, k-1 ), 1,
378  $ b( k-1, 1 ), ldb, b( k+1, 1 ), ldb )
379 *
380 * Interchange if a permutation was applied at the
381 * K-th step of the factorization.
382 *
383  kp = abs( ipiv( k ) )
384  IF( kp.NE.k )
385  $ CALL dswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
386  END IF
387  k = k - 2
388  END IF
389  GO TO 40
390  60 CONTINUE
391  END IF
392 *----------------------------------------
393 *
394 * Compute B := A' * B (transpose)
395 *
396 *----------------------------------------
397  ELSE
398 *
399 * Form B := U'*B
400 * where U = P(m)*inv(U(m))* ... *P(1)*inv(U(1))
401 * and U' = inv(U'(1))*P(1)* ... *inv(U'(m))*P(m)
402 *
403  IF( lsame( uplo, 'U' ) ) THEN
404 *
405 * Loop backward applying the transformations.
406 *
407  k = n
408  70 CONTINUE
409  IF( k.LT.1 )
410  $ GO TO 90
411 *
412 * 1 x 1 pivot block.
413 *
414  IF( ipiv( k ).GT.0 ) THEN
415  IF( k.GT.1 ) THEN
416 *
417 * Interchange if P(K) .ne. I.
418 *
419  kp = ipiv( k )
420  IF( kp.NE.k )
421  $ CALL dswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
422 *
423 * Apply the transformation
424 *
425  CALL dgemv( 'Transpose', k-1, nrhs, one, b, ldb,
426  $ a( 1, k ), 1, one, b( k, 1 ), ldb )
427  END IF
428  IF( nounit )
429  $ CALL dscal( nrhs, a( k, k ), b( k, 1 ), ldb )
430  k = k - 1
431 *
432 * 2 x 2 pivot block.
433 *
434  ELSE
435  IF( k.GT.2 ) THEN
436 *
437 * Interchange if P(K) .ne. I.
438 *
439  kp = abs( ipiv( k ) )
440  IF( kp.NE.k-1 )
441  $ CALL dswap( nrhs, b( k-1, 1 ), ldb, b( kp, 1 ),
442  $ ldb )
443 *
444 * Apply the transformations
445 *
446  CALL dgemv( 'Transpose', k-2, nrhs, one, b, ldb,
447  $ a( 1, k ), 1, one, b( k, 1 ), ldb )
448  CALL dgemv( 'Transpose', k-2, nrhs, one, b, ldb,
449  $ a( 1, k-1 ), 1, one, b( k-1, 1 ), ldb )
450  END IF
451 *
452 * Multiply by the diagonal block if non-unit.
453 *
454  IF( nounit ) THEN
455  d11 = a( k-1, k-1 )
456  d22 = a( k, k )
457  d12 = a( k-1, k )
458  d21 = d12
459  DO 80 j = 1, nrhs
460  t1 = b( k-1, j )
461  t2 = b( k, j )
462  b( k-1, j ) = d11*t1 + d12*t2
463  b( k, j ) = d21*t1 + d22*t2
464  80 CONTINUE
465  END IF
466  k = k - 2
467  END IF
468  GO TO 70
469  90 CONTINUE
470 *
471 * Form B := L'*B
472 * where L = P(1)*inv(L(1))* ... *P(m)*inv(L(m))
473 * and L' = inv(L'(m))*P(m)* ... *inv(L'(1))*P(1)
474 *
475  ELSE
476 *
477 * Loop forward applying the L-transformations.
478 *
479  k = 1
480  100 CONTINUE
481  IF( k.GT.n )
482  $ GO TO 120
483 *
484 * 1 x 1 pivot block
485 *
486  IF( ipiv( k ).GT.0 ) THEN
487  IF( k.LT.n ) THEN
488 *
489 * Interchange if P(K) .ne. I.
490 *
491  kp = ipiv( k )
492  IF( kp.NE.k )
493  $ CALL dswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
494 *
495 * Apply the transformation
496 *
497  CALL dgemv( 'Transpose', n-k, nrhs, one, b( k+1, 1 ),
498  $ ldb, a( k+1, k ), 1, one, b( k, 1 ), ldb )
499  END IF
500  IF( nounit )
501  $ CALL dscal( nrhs, a( k, k ), b( k, 1 ), ldb )
502  k = k + 1
503 *
504 * 2 x 2 pivot block.
505 *
506  ELSE
507  IF( k.LT.n-1 ) THEN
508 *
509 * Interchange if P(K) .ne. I.
510 *
511  kp = abs( ipiv( k ) )
512  IF( kp.NE.k+1 )
513  $ CALL dswap( nrhs, b( k+1, 1 ), ldb, b( kp, 1 ),
514  $ ldb )
515 *
516 * Apply the transformation
517 *
518  CALL dgemv( 'Transpose', n-k-1, nrhs, one,
519  $ b( k+2, 1 ), ldb, a( k+2, k+1 ), 1, one,
520  $ b( k+1, 1 ), ldb )
521  CALL dgemv( 'Transpose', n-k-1, nrhs, one,
522  $ b( k+2, 1 ), ldb, a( k+2, k ), 1, one,
523  $ b( k, 1 ), ldb )
524  END IF
525 *
526 * Multiply by the diagonal block if non-unit.
527 *
528  IF( nounit ) THEN
529  d11 = a( k, k )
530  d22 = a( k+1, k+1 )
531  d21 = a( k+1, k )
532  d12 = d21
533  DO 110 j = 1, nrhs
534  t1 = b( k, j )
535  t2 = b( k+1, j )
536  b( k, j ) = d11*t1 + d12*t2
537  b( k+1, j ) = d21*t1 + d22*t2
538  110 CONTINUE
539  END IF
540  k = k + 2
541  END IF
542  GO TO 100
543  120 CONTINUE
544  END IF
545 *
546  END IF
547  RETURN
548 *
549 * End of DLAVSY
550 *
551  END
dger
subroutine dger(M, N, ALPHA, X, INCX, Y, INCY, A, LDA)
DGER
Definition: dger.f:132
dlavsy
subroutine dlavsy(UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
DLAVSY
Definition: dlavsy.f:157
xerbla
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
dgemv
subroutine dgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
DGEMV
Definition: dgemv.f:158
dswap
subroutine dswap(N, DX, INCX, DY, INCY)
DSWAP
Definition: dswap.f:84
dscal
subroutine dscal(N, DA, DX, INCX)
DSCAL
Definition: dscal.f:81