LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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◆ dlalsa()

subroutine dlalsa ( integer icompq,
integer smlsiz,
integer n,
integer nrhs,
double precision, dimension( ldb, * ) b,
integer ldb,
double precision, dimension( ldbx, * ) bx,
integer ldbx,
double precision, dimension( ldu, * ) u,
integer ldu,
double precision, dimension( ldu, * ) vt,
integer, dimension( * ) k,
double precision, dimension( ldu, * ) difl,
double precision, dimension( ldu, * ) difr,
double precision, dimension( ldu, * ) z,
double precision, dimension( ldu, * ) poles,
integer, dimension( * ) givptr,
integer, dimension( ldgcol, * ) givcol,
integer ldgcol,
integer, dimension( ldgcol, * ) perm,
double precision, dimension( ldu, * ) givnum,
double precision, dimension( * ) c,
double precision, dimension( * ) s,
double precision, dimension( * ) work,
integer, dimension( * ) iwork,
integer info )

DLALSA computes the SVD of the coefficient matrix in compact form. Used by sgelsd.

Download DLALSA + dependencies [TGZ] [ZIP] [TXT]

Purpose:
!>
!> DLALSA is an intermediate step in solving the least squares problem
!> by computing the SVD of the coefficient matrix in compact form (The
!> singular vectors are computed as products of simple orthogonal
!> matrices.).
!>
!> If ICOMPQ = 0, DLALSA applies the inverse of the left singular vector
!> matrix of an upper bidiagonal matrix to the right hand side; and if
!> ICOMPQ = 1, DLALSA applies the right singular vector matrix to the
!> right hand side. The singular vector matrices were generated in
!> compact form by DLALSA.
!>
Parameters
[in]ICOMPQ
!>          ICOMPQ is INTEGER
!>         Specifies whether the left or the right singular vector
!>         matrix is involved.
!>         = 0: Left singular vector matrix
!>         = 1: Right singular vector matrix
!>
[in]SMLSIZ
!>          SMLSIZ is INTEGER
!>         The maximum size of the subproblems at the bottom of the
!>         computation tree.
!>
[in]N
!>          N is INTEGER
!>         The row and column dimensions of the upper bidiagonal matrix.
!>
[in]NRHS
!>          NRHS is INTEGER
!>         The number of columns of B and BX. NRHS must be at least 1.
!>
[in,out]B
!>          B is DOUBLE PRECISION array, dimension ( LDB, NRHS )
!>         On input, B contains the right hand sides of the least
!>         squares problem in rows 1 through M.
!>         On output, B contains the solution X in rows 1 through N.
!>
[in]LDB
!>          LDB is INTEGER
!>         The leading dimension of B in the calling subprogram.
!>         LDB must be at least max(1,MAX( M, N ) ).
!>
[out]BX
!>          BX is DOUBLE PRECISION array, dimension ( LDBX, NRHS )
!>         On exit, the result of applying the left or right singular
!>         vector matrix to B.
!>
[in]LDBX
!>          LDBX is INTEGER
!>         The leading dimension of BX.
!>
[in]U
!>          U is DOUBLE PRECISION array, dimension ( LDU, SMLSIZ ).
!>         On entry, U contains the left singular vector matrices of all
!>         subproblems at the bottom level.
!>
[in]LDU
!>          LDU is INTEGER, LDU = > N.
!>         The leading dimension of arrays U, VT, DIFL, DIFR,
!>         POLES, GIVNUM, and Z.
!>
[in]VT
!>          VT is DOUBLE PRECISION array, dimension ( LDU, SMLSIZ+1 ).
!>         On entry, VT**T contains the right singular vector matrices of
!>         all subproblems at the bottom level.
!>
[in]K
!>          K is INTEGER array, dimension ( N ).
!>
[in]DIFL
!>          DIFL is DOUBLE PRECISION array, dimension ( LDU, NLVL ).
!>         where NLVL = INT(log_2 (N/(SMLSIZ+1))) + 1.
!>
[in]DIFR
!>          DIFR is DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ).
!>         On entry, DIFL(*, I) and DIFR(*, 2 * I -1) record
!>         distances between singular values on the I-th level and
!>         singular values on the (I -1)-th level, and DIFR(*, 2 * I)
!>         record the normalizing factors of the right singular vectors
!>         matrices of subproblems on I-th level.
!>
[in]Z
!>          Z is DOUBLE PRECISION array, dimension ( LDU, NLVL ).
!>         On entry, Z(1, I) contains the components of the deflation-
!>         adjusted updating row vector for subproblems on the I-th
!>         level.
!>
[in]POLES
!>          POLES is DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ).
!>         On entry, POLES(*, 2 * I -1: 2 * I) contains the new and old
!>         singular values involved in the secular equations on the I-th
!>         level.
!>
[in]GIVPTR
!>          GIVPTR is INTEGER array, dimension ( N ).
!>         On entry, GIVPTR( I ) records the number of Givens
!>         rotations performed on the I-th problem on the computation
!>         tree.
!>
[in]GIVCOL
!>          GIVCOL is INTEGER array, dimension ( LDGCOL, 2 * NLVL ).
!>         On entry, for each I, GIVCOL(*, 2 * I - 1: 2 * I) records the
!>         locations of Givens rotations performed on the I-th level on
!>         the computation tree.
!>
[in]LDGCOL
!>          LDGCOL is INTEGER, LDGCOL = > N.
!>         The leading dimension of arrays GIVCOL and PERM.
!>
[in]PERM
!>          PERM is INTEGER array, dimension ( LDGCOL, NLVL ).
!>         On entry, PERM(*, I) records permutations done on the I-th
!>         level of the computation tree.
!>
[in]GIVNUM
!>          GIVNUM is DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ).
!>         On entry, GIVNUM(*, 2 *I -1 : 2 * I) records the C- and S-
!>         values of Givens rotations performed on the I-th level on the
!>         computation tree.
!>
[in]C
!>          C is DOUBLE PRECISION array, dimension ( N ).
!>         On entry, if the I-th subproblem is not square,
!>         C( I ) contains the C-value of a Givens rotation related to
!>         the right null space of the I-th subproblem.
!>
[in]S
!>          S is DOUBLE PRECISION array, dimension ( N ).
!>         On entry, if the I-th subproblem is not square,
!>         S( I ) contains the S-value of a Givens rotation related to
!>         the right null space of the I-th subproblem.
!>
[out]WORK
!>          WORK is DOUBLE PRECISION array, dimension (N)
!>
[out]IWORK
!>          IWORK is INTEGER array, dimension (3*N)
!>
[out]INFO
!>          INFO is INTEGER
!>          = 0:  successful exit.
!>          < 0:  if INFO = -i, the i-th argument had an illegal value.
!>
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Contributors:
Ming Gu and Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA
Osni Marques, LBNL/NERSC, USA

Definition at line 261 of file dlalsa.f.

266*
267* -- LAPACK computational routine --
268* -- LAPACK is a software package provided by Univ. of Tennessee, --
269* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
270*
271* .. Scalar Arguments ..
272 INTEGER ICOMPQ, INFO, LDB, LDBX, LDGCOL, LDU, N, NRHS,
273 $ SMLSIZ
274* ..
275* .. Array Arguments ..
276 INTEGER GIVCOL( LDGCOL, * ), GIVPTR( * ), IWORK( * ),
277 $ K( * ), PERM( LDGCOL, * )
278 DOUBLE PRECISION B( LDB, * ), BX( LDBX, * ), C( * ),
279 $ DIFL( LDU, * ), DIFR( LDU, * ),
280 $ GIVNUM( LDU, * ), POLES( LDU, * ), S( * ),
281 $ U( LDU, * ), VT( LDU, * ), WORK( * ),
282 $ Z( LDU, * )
283* ..
284*
285* =====================================================================
286*
287* .. Parameters ..
288 DOUBLE PRECISION ZERO, ONE
289 parameter( zero = 0.0d0, one = 1.0d0 )
290* ..
291* .. Local Scalars ..
292 INTEGER I, I1, IC, IM1, INODE, J, LF, LL, LVL, LVL2,
293 $ ND, NDB1, NDIML, NDIMR, NL, NLF, NLP1, NLVL,
294 $ NR, NRF, NRP1, SQRE
295* ..
296* .. External Subroutines ..
297 EXTERNAL dcopy, dgemm, dlals0, dlasdt,
298 $ xerbla
299* ..
300* .. Executable Statements ..
301*
302* Test the input parameters.
303*
304 info = 0
305*
306 IF( ( icompq.LT.0 ) .OR. ( icompq.GT.1 ) ) THEN
307 info = -1
308 ELSE IF( smlsiz.LT.3 ) THEN
309 info = -2
310 ELSE IF( n.LT.smlsiz ) THEN
311 info = -3
312 ELSE IF( nrhs.LT.1 ) THEN
313 info = -4
314 ELSE IF( ldb.LT.n ) THEN
315 info = -6
316 ELSE IF( ldbx.LT.n ) THEN
317 info = -8
318 ELSE IF( ldu.LT.n ) THEN
319 info = -10
320 ELSE IF( ldgcol.LT.n ) THEN
321 info = -19
322 END IF
323 IF( info.NE.0 ) THEN
324 CALL xerbla( 'DLALSA', -info )
325 RETURN
326 END IF
327*
328* Book-keeping and setting up the computation tree.
329*
330 inode = 1
331 ndiml = inode + n
332 ndimr = ndiml + n
333*
334 CALL dlasdt( n, nlvl, nd, iwork( inode ), iwork( ndiml ),
335 $ iwork( ndimr ), smlsiz )
336*
337* The following code applies back the left singular vector factors.
338* For applying back the right singular vector factors, go to 50.
339*
340 IF( icompq.EQ.1 ) THEN
341 GO TO 50
342 END IF
343*
344* The nodes on the bottom level of the tree were solved
345* by DLASDQ. The corresponding left and right singular vector
346* matrices are in explicit form. First apply back the left
347* singular vector matrices.
348*
349 ndb1 = ( nd+1 ) / 2
350 DO 10 i = ndb1, nd
351*
352* IC : center row of each node
353* NL : number of rows of left subproblem
354* NR : number of rows of right subproblem
355* NLF: starting row of the left subproblem
356* NRF: starting row of the right subproblem
357*
358 i1 = i - 1
359 ic = iwork( inode+i1 )
360 nl = iwork( ndiml+i1 )
361 nr = iwork( ndimr+i1 )
362 nlf = ic - nl
363 nrf = ic + 1
364 CALL dgemm( 'T', 'N', nl, nrhs, nl, one, u( nlf, 1 ), ldu,
365 $ b( nlf, 1 ), ldb, zero, bx( nlf, 1 ), ldbx )
366 CALL dgemm( 'T', 'N', nr, nrhs, nr, one, u( nrf, 1 ), ldu,
367 $ b( nrf, 1 ), ldb, zero, bx( nrf, 1 ), ldbx )
368 10 CONTINUE
369*
370* Next copy the rows of B that correspond to unchanged rows
371* in the bidiagonal matrix to BX.
372*
373 DO 20 i = 1, nd
374 ic = iwork( inode+i-1 )
375 CALL dcopy( nrhs, b( ic, 1 ), ldb, bx( ic, 1 ), ldbx )
376 20 CONTINUE
377*
378* Finally go through the left singular vector matrices of all
379* the other subproblems bottom-up on the tree.
380*
381 j = 2**nlvl
382 sqre = 0
383*
384 DO 40 lvl = nlvl, 1, -1
385 lvl2 = 2*lvl - 1
386*
387* find the first node LF and last node LL on
388* the current level LVL
389*
390 IF( lvl.EQ.1 ) THEN
391 lf = 1
392 ll = 1
393 ELSE
394 lf = 2**( lvl-1 )
395 ll = 2*lf - 1
396 END IF
397 DO 30 i = lf, ll
398 im1 = i - 1
399 ic = iwork( inode+im1 )
400 nl = iwork( ndiml+im1 )
401 nr = iwork( ndimr+im1 )
402 nlf = ic - nl
403 nrf = ic + 1
404 j = j - 1
405 CALL dlals0( icompq, nl, nr, sqre, nrhs, bx( nlf, 1 ),
406 $ ldbx,
407 $ b( nlf, 1 ), ldb, perm( nlf, lvl ),
408 $ givptr( j ), givcol( nlf, lvl2 ), ldgcol,
409 $ givnum( nlf, lvl2 ), ldu, poles( nlf, lvl2 ),
410 $ difl( nlf, lvl ), difr( nlf, lvl2 ),
411 $ z( nlf, lvl ), k( j ), c( j ), s( j ), work,
412 $ info )
413 30 CONTINUE
414 40 CONTINUE
415 GO TO 90
416*
417* ICOMPQ = 1: applying back the right singular vector factors.
418*
419 50 CONTINUE
420*
421* First now go through the right singular vector matrices of all
422* the tree nodes top-down.
423*
424 j = 0
425 DO 70 lvl = 1, nlvl
426 lvl2 = 2*lvl - 1
427*
428* Find the first node LF and last node LL on
429* the current level LVL.
430*
431 IF( lvl.EQ.1 ) THEN
432 lf = 1
433 ll = 1
434 ELSE
435 lf = 2**( lvl-1 )
436 ll = 2*lf - 1
437 END IF
438 DO 60 i = ll, lf, -1
439 im1 = i - 1
440 ic = iwork( inode+im1 )
441 nl = iwork( ndiml+im1 )
442 nr = iwork( ndimr+im1 )
443 nlf = ic - nl
444 nrf = ic + 1
445 IF( i.EQ.ll ) THEN
446 sqre = 0
447 ELSE
448 sqre = 1
449 END IF
450 j = j + 1
451 CALL dlals0( icompq, nl, nr, sqre, nrhs, b( nlf, 1 ),
452 $ ldb,
453 $ bx( nlf, 1 ), ldbx, perm( nlf, lvl ),
454 $ givptr( j ), givcol( nlf, lvl2 ), ldgcol,
455 $ givnum( nlf, lvl2 ), ldu, poles( nlf, lvl2 ),
456 $ difl( nlf, lvl ), difr( nlf, lvl2 ),
457 $ z( nlf, lvl ), k( j ), c( j ), s( j ), work,
458 $ info )
459 60 CONTINUE
460 70 CONTINUE
461*
462* The nodes on the bottom level of the tree were solved
463* by DLASDQ. The corresponding right singular vector
464* matrices are in explicit form. Apply them back.
465*
466 ndb1 = ( nd+1 ) / 2
467 DO 80 i = ndb1, nd
468 i1 = i - 1
469 ic = iwork( inode+i1 )
470 nl = iwork( ndiml+i1 )
471 nr = iwork( ndimr+i1 )
472 nlp1 = nl + 1
473 IF( i.EQ.nd ) THEN
474 nrp1 = nr
475 ELSE
476 nrp1 = nr + 1
477 END IF
478 nlf = ic - nl
479 nrf = ic + 1
480 CALL dgemm( 'T', 'N', nlp1, nrhs, nlp1, one, vt( nlf, 1 ),
481 $ ldu,
482 $ b( nlf, 1 ), ldb, zero, bx( nlf, 1 ), ldbx )
483 CALL dgemm( 'T', 'N', nrp1, nrhs, nrp1, one, vt( nrf, 1 ),
484 $ ldu,
485 $ b( nrf, 1 ), ldb, zero, bx( nrf, 1 ), ldbx )
486 80 CONTINUE
487*
488 90 CONTINUE
489*
490 RETURN
491*
492* End of DLALSA
493*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
dcopy
subroutine dcopy(n, dx, incx, dy, incy)
DCOPY
Definition dcopy.f:82
dgemm
subroutine dgemm(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
DGEMM
Definition dgemm.f:188
dlals0
subroutine dlals0(icompq, nl, nr, sqre, nrhs, b, ldb, bx, ldbx, perm, givptr, givcol, ldgcol, givnum, ldgnum, poles, difl, difr, z, k, c, s, work, info)
DLALS0 applies back multiplying factors in solving the least squares problem using divide and conquer...
Definition dlals0.f:267
dlasdt
subroutine dlasdt(n, lvl, nd, inode, ndiml, ndimr, msub)
DLASDT creates a tree of subproblems for bidiagonal divide and conquer. Used by sbdsdc.
Definition dlasdt.f:103
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