diff libcruft/lapack/clalsd.f @ 7789:82be108cc558

First attempt at single precision tyeps * * * corrections to qrupdate single precision routines * * * prefer demotion to single over promotion to double * * * Add single precision support to log2 function * * * Trivial PROJECT file update * * * Cache optimized hermitian/transpose methods * * * Add tests for tranpose/hermitian and ChangeLog entry for new transpose code
author David Bateman <dbateman@free.fr>
date Sun, 27 Apr 2008 22:34:17 +0200
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+      SUBROUTINE CLALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND,
+     $                   RANK, WORK, RWORK, IWORK, INFO )
+*
+*  -- LAPACK routine (version 3.1) --
+*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
+*     November 2006
+*
+*     .. Scalar Arguments ..
+      CHARACTER          UPLO
+      INTEGER            INFO, LDB, N, NRHS, RANK, SMLSIZ
+      REAL               RCOND
+*     ..
+*     .. Array Arguments ..
+      INTEGER            IWORK( * )
+      REAL               D( * ), E( * ), RWORK( * )
+      COMPLEX            B( LDB, * ), WORK( * )
+*     ..
+*
+*  Purpose
+*  =======
+*
+*  CLALSD uses the singular value decomposition of A to solve the least
+*  squares problem of finding X to minimize the Euclidean norm of each
+*  column of A*X-B, where A is N-by-N upper bidiagonal, and X and B
+*  are N-by-NRHS. The solution X overwrites B.
+*
+*  The singular values of A smaller than RCOND times the largest
+*  singular value are treated as zero in solving the least squares
+*  problem; in this case a minimum norm solution is returned.
+*  The actual singular values are returned in D in ascending order.
+*
+*  This code makes very mild assumptions about floating point
+*  arithmetic. It will work on machines with a guard digit in
+*  add/subtract, or on those binary machines without guard digits
+*  which subtract like the Cray XMP, Cray YMP, Cray C 90, or Cray 2.
+*  It could conceivably fail on hexadecimal or decimal machines
+*  without guard digits, but we know of none.
+*
+*  Arguments
+*  =========
+*
+*  UPLO   (input) CHARACTER*1
+*         = 'U': D and E define an upper bidiagonal matrix.
+*         = 'L': D and E define a  lower bidiagonal matrix.
+*
+*  SMLSIZ (input) INTEGER
+*         The maximum size of the subproblems at the bottom of the
+*         computation tree.
+*
+*  N      (input) INTEGER
+*         The dimension of the  bidiagonal matrix.  N >= 0.
+*
+*  NRHS   (input) INTEGER
+*         The number of columns of B. NRHS must be at least 1.
+*
+*  D      (input/output) REAL array, dimension (N)
+*         On entry D contains the main diagonal of the bidiagonal
+*         matrix. On exit, if INFO = 0, D contains its singular values.
+*
+*  E      (input/output) REAL array, dimension (N-1)
+*         Contains the super-diagonal entries of the bidiagonal matrix.
+*         On exit, E has been destroyed.
+*
+*  B      (input/output) COMPLEX array, dimension (LDB,NRHS)
+*         On input, B contains the right hand sides of the least
+*         squares problem. On output, B contains the solution X.
+*
+*  LDB    (input) INTEGER
+*         The leading dimension of B in the calling subprogram.
+*         LDB must be at least max(1,N).
+*
+*  RCOND  (input) REAL
+*         The singular values of A less than or equal to RCOND times
+*         the largest singular value are treated as zero in solving
+*         the least squares problem. If RCOND is negative,
+*         machine precision is used instead.
+*         For example, if diag(S)*X=B were the least squares problem,
+*         where diag(S) is a diagonal matrix of singular values, the
+*         solution would be X(i) = B(i) / S(i) if S(i) is greater than
+*         RCOND*max(S), and X(i) = 0 if S(i) is less than or equal to
+*         RCOND*max(S).
+*
+*  RANK   (output) INTEGER
+*         The number of singular values of A greater than RCOND times
+*         the largest singular value.
+*
+*  WORK   (workspace) COMPLEX array, dimension (N * NRHS).
+*
+*  RWORK  (workspace) REAL array, dimension at least
+*         (9*N + 2*N*SMLSIZ + 8*N*NLVL + 3*SMLSIZ*NRHS + (SMLSIZ+1)**2),
+*         where
+*         NLVL = MAX( 0, INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1 )
+*
+*  IWORK  (workspace) INTEGER array, dimension (3*N*NLVL + 11*N).
+*
+*  INFO   (output) INTEGER
+*         = 0:  successful exit.
+*         < 0:  if INFO = -i, the i-th argument had an illegal value.
+*         > 0:  The algorithm failed to compute an singular value while
+*               working on the submatrix lying in rows and columns
+*               INFO/(N+1) through MOD(INFO,N+1).
+*
+*  Further Details
+*  ===============
+*
+*  Based on contributions by
+*     Ming Gu and Ren-Cang Li, Computer Science Division, University of
+*       California at Berkeley, USA
+*     Osni Marques, LBNL/NERSC, USA
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      REAL               ZERO, ONE, TWO
+      PARAMETER          ( ZERO = 0.0E0, ONE = 1.0E0, TWO = 2.0E0 )
+      COMPLEX            CZERO
+      PARAMETER          ( CZERO = ( 0.0E0, 0.0E0 ) )
+*     ..
+*     .. Local Scalars ..
+      INTEGER            BX, BXST, C, DIFL, DIFR, GIVCOL, GIVNUM,
+     $                   GIVPTR, I, ICMPQ1, ICMPQ2, IRWB, IRWIB, IRWRB,
+     $                   IRWU, IRWVT, IRWWRK, IWK, J, JCOL, JIMAG,
+     $                   JREAL, JROW, K, NLVL, NM1, NRWORK, NSIZE, NSUB,
+     $                   PERM, POLES, S, SIZEI, SMLSZP, SQRE, ST, ST1,
+     $                   U, VT, Z
+      REAL               CS, EPS, ORGNRM, R, RCND, SN, TOL
+*     ..
+*     .. External Functions ..
+      INTEGER            ISAMAX
+      REAL               SLAMCH, SLANST
+      EXTERNAL           ISAMAX, SLAMCH, SLANST
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           CCOPY, CLACPY, CLALSA, CLASCL, CLASET, CSROT,
+     $                   SGEMM, SLARTG, SLASCL, SLASDA, SLASDQ, SLASET,
+     $                   SLASRT, XERBLA
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          ABS, AIMAG, CMPLX, INT, LOG, REAL, SIGN
+*     ..
+*     .. Executable Statements ..
+*
+*     Test the input parameters.
+*
+      INFO = 0
+*
+      IF( N.LT.0 ) THEN
+         INFO = -3
+      ELSE IF( NRHS.LT.1 ) THEN
+         INFO = -4
+      ELSE IF( ( LDB.LT.1 ) .OR. ( LDB.LT.N ) ) THEN
+         INFO = -8
+      END IF
+      IF( INFO.NE.0 ) THEN
+         CALL XERBLA( 'CLALSD', -INFO )
+         RETURN
+      END IF
+*
+      EPS = SLAMCH( 'Epsilon' )
+*
+*     Set up the tolerance.
+*
+      IF( ( RCOND.LE.ZERO ) .OR. ( RCOND.GE.ONE ) ) THEN
+         RCND = EPS
+      ELSE
+         RCND = RCOND
+      END IF
+*
+      RANK = 0
+*
+*     Quick return if possible.
+*
+      IF( N.EQ.0 ) THEN
+         RETURN
+      ELSE IF( N.EQ.1 ) THEN
+         IF( D( 1 ).EQ.ZERO ) THEN
+            CALL CLASET( 'A', 1, NRHS, CZERO, CZERO, B, LDB )
+         ELSE
+            RANK = 1
+            CALL CLASCL( 'G', 0, 0, D( 1 ), ONE, 1, NRHS, B, LDB, INFO )
+            D( 1 ) = ABS( D( 1 ) )
+         END IF
+         RETURN
+      END IF
+*
+*     Rotate the matrix if it is lower bidiagonal.
+*
+      IF( UPLO.EQ.'L' ) THEN
+         DO 10 I = 1, N - 1
+            CALL SLARTG( D( I ), E( I ), CS, SN, R )
+            D( I ) = R
+            E( I ) = SN*D( I+1 )
+            D( I+1 ) = CS*D( I+1 )
+            IF( NRHS.EQ.1 ) THEN
+               CALL CSROT( 1, B( I, 1 ), 1, B( I+1, 1 ), 1, CS, SN )
+            ELSE
+               RWORK( I*2-1 ) = CS
+               RWORK( I*2 ) = SN
+            END IF
+   10    CONTINUE
+         IF( NRHS.GT.1 ) THEN
+            DO 30 I = 1, NRHS
+               DO 20 J = 1, N - 1
+                  CS = RWORK( J*2-1 )
+                  SN = RWORK( J*2 )
+                  CALL CSROT( 1, B( J, I ), 1, B( J+1, I ), 1, CS, SN )
+   20          CONTINUE
+   30       CONTINUE
+         END IF
+      END IF
+*
+*     Scale.
+*
+      NM1 = N - 1
+      ORGNRM = SLANST( 'M', N, D, E )
+      IF( ORGNRM.EQ.ZERO ) THEN
+         CALL CLASET( 'A', N, NRHS, CZERO, CZERO, B, LDB )
+         RETURN
+      END IF
+*
+      CALL SLASCL( 'G', 0, 0, ORGNRM, ONE, N, 1, D, N, INFO )
+      CALL SLASCL( 'G', 0, 0, ORGNRM, ONE, NM1, 1, E, NM1, INFO )
+*
+*     If N is smaller than the minimum divide size SMLSIZ, then solve
+*     the problem with another solver.
+*
+      IF( N.LE.SMLSIZ ) THEN
+         IRWU = 1
+         IRWVT = IRWU + N*N
+         IRWWRK = IRWVT + N*N
+         IRWRB = IRWWRK
+         IRWIB = IRWRB + N*NRHS
+         IRWB = IRWIB + N*NRHS
+         CALL SLASET( 'A', N, N, ZERO, ONE, RWORK( IRWU ), N )
+         CALL SLASET( 'A', N, N, ZERO, ONE, RWORK( IRWVT ), N )
+         CALL SLASDQ( 'U', 0, N, N, N, 0, D, E, RWORK( IRWVT ), N,
+     $                RWORK( IRWU ), N, RWORK( IRWWRK ), 1,
+     $                RWORK( IRWWRK ), INFO )
+         IF( INFO.NE.0 ) THEN
+            RETURN
+         END IF
+*
+*        In the real version, B is passed to SLASDQ and multiplied
+*        internally by Q'. Here B is complex and that product is
+*        computed below in two steps (real and imaginary parts).
+*
+         J = IRWB - 1
+         DO 50 JCOL = 1, NRHS
+            DO 40 JROW = 1, N
+               J = J + 1
+               RWORK( J ) = REAL( B( JROW, JCOL ) )
+   40       CONTINUE
+   50    CONTINUE
+         CALL SGEMM( 'T', 'N', N, NRHS, N, ONE, RWORK( IRWU ), N,
+     $               RWORK( IRWB ), N, ZERO, RWORK( IRWRB ), N )
+         J = IRWB - 1
+         DO 70 JCOL = 1, NRHS
+            DO 60 JROW = 1, N
+               J = J + 1
+               RWORK( J ) = AIMAG( B( JROW, JCOL ) )
+   60       CONTINUE
+   70    CONTINUE
+         CALL SGEMM( 'T', 'N', N, NRHS, N, ONE, RWORK( IRWU ), N,
+     $               RWORK( IRWB ), N, ZERO, RWORK( IRWIB ), N )
+         JREAL = IRWRB - 1
+         JIMAG = IRWIB - 1
+         DO 90 JCOL = 1, NRHS
+            DO 80 JROW = 1, N
+               JREAL = JREAL + 1
+               JIMAG = JIMAG + 1
+               B( JROW, JCOL ) = CMPLX( RWORK( JREAL ), RWORK( JIMAG ) )
+   80       CONTINUE
+   90    CONTINUE
+*
+         TOL = RCND*ABS( D( ISAMAX( N, D, 1 ) ) )
+         DO 100 I = 1, N
+            IF( D( I ).LE.TOL ) THEN
+               CALL CLASET( 'A', 1, NRHS, CZERO, CZERO, B( I, 1 ), LDB )
+            ELSE
+               CALL CLASCL( 'G', 0, 0, D( I ), ONE, 1, NRHS, B( I, 1 ),
+     $                      LDB, INFO )
+               RANK = RANK + 1
+            END IF
+  100    CONTINUE
+*
+*        Since B is complex, the following call to SGEMM is performed
+*        in two steps (real and imaginary parts). That is for V * B
+*        (in the real version of the code V' is stored in WORK).
+*
+*        CALL SGEMM( 'T', 'N', N, NRHS, N, ONE, WORK, N, B, LDB, ZERO,
+*    $               WORK( NWORK ), N )
+*
+         J = IRWB - 1
+         DO 120 JCOL = 1, NRHS
+            DO 110 JROW = 1, N
+               J = J + 1
+               RWORK( J ) = REAL( B( JROW, JCOL ) )
+  110       CONTINUE
+  120    CONTINUE
+         CALL SGEMM( 'T', 'N', N, NRHS, N, ONE, RWORK( IRWVT ), N,
+     $               RWORK( IRWB ), N, ZERO, RWORK( IRWRB ), N )
+         J = IRWB - 1
+         DO 140 JCOL = 1, NRHS
+            DO 130 JROW = 1, N
+               J = J + 1
+               RWORK( J ) = AIMAG( B( JROW, JCOL ) )
+  130       CONTINUE
+  140    CONTINUE
+         CALL SGEMM( 'T', 'N', N, NRHS, N, ONE, RWORK( IRWVT ), N,
+     $               RWORK( IRWB ), N, ZERO, RWORK( IRWIB ), N )
+         JREAL = IRWRB - 1
+         JIMAG = IRWIB - 1
+         DO 160 JCOL = 1, NRHS
+            DO 150 JROW = 1, N
+               JREAL = JREAL + 1
+               JIMAG = JIMAG + 1
+               B( JROW, JCOL ) = CMPLX( RWORK( JREAL ), RWORK( JIMAG ) )
+  150       CONTINUE
+  160    CONTINUE
+*
+*        Unscale.
+*
+         CALL SLASCL( 'G', 0, 0, ONE, ORGNRM, N, 1, D, N, INFO )
+         CALL SLASRT( 'D', N, D, INFO )
+         CALL CLASCL( 'G', 0, 0, ORGNRM, ONE, N, NRHS, B, LDB, INFO )
+*
+         RETURN
+      END IF
+*
+*     Book-keeping and setting up some constants.
+*
+      NLVL = INT( LOG( REAL( N ) / REAL( SMLSIZ+1 ) ) / LOG( TWO ) ) + 1
+*
+      SMLSZP = SMLSIZ + 1
+*
+      U = 1
+      VT = 1 + SMLSIZ*N
+      DIFL = VT + SMLSZP*N
+      DIFR = DIFL + NLVL*N
+      Z = DIFR + NLVL*N*2
+      C = Z + NLVL*N
+      S = C + N
+      POLES = S + N
+      GIVNUM = POLES + 2*NLVL*N
+      NRWORK = GIVNUM + 2*NLVL*N
+      BX = 1
+*
+      IRWRB = NRWORK
+      IRWIB = IRWRB + SMLSIZ*NRHS
+      IRWB = IRWIB + SMLSIZ*NRHS
+*
+      SIZEI = 1 + N
+      K = SIZEI + N
+      GIVPTR = K + N
+      PERM = GIVPTR + N
+      GIVCOL = PERM + NLVL*N
+      IWK = GIVCOL + NLVL*N*2
+*
+      ST = 1
+      SQRE = 0
+      ICMPQ1 = 1
+      ICMPQ2 = 0
+      NSUB = 0
+*
+      DO 170 I = 1, N
+         IF( ABS( D( I ) ).LT.EPS ) THEN
+            D( I ) = SIGN( EPS, D( I ) )
+         END IF
+  170 CONTINUE
+*
+      DO 240 I = 1, NM1
+         IF( ( ABS( E( I ) ).LT.EPS ) .OR. ( I.EQ.NM1 ) ) THEN
+            NSUB = NSUB + 1
+            IWORK( NSUB ) = ST
+*
+*           Subproblem found. First determine its size and then
+*           apply divide and conquer on it.
+*
+            IF( I.LT.NM1 ) THEN
+*
+*              A subproblem with E(I) small for I < NM1.
+*
+               NSIZE = I - ST + 1
+               IWORK( SIZEI+NSUB-1 ) = NSIZE
+            ELSE IF( ABS( E( I ) ).GE.EPS ) THEN
+*
+*              A subproblem with E(NM1) not too small but I = NM1.
+*
+               NSIZE = N - ST + 1
+               IWORK( SIZEI+NSUB-1 ) = NSIZE
+            ELSE
+*
+*              A subproblem with E(NM1) small. This implies an
+*              1-by-1 subproblem at D(N), which is not solved
+*              explicitly.
+*
+               NSIZE = I - ST + 1
+               IWORK( SIZEI+NSUB-1 ) = NSIZE
+               NSUB = NSUB + 1
+               IWORK( NSUB ) = N
+               IWORK( SIZEI+NSUB-1 ) = 1
+               CALL CCOPY( NRHS, B( N, 1 ), LDB, WORK( BX+NM1 ), N )
+            END IF
+            ST1 = ST - 1
+            IF( NSIZE.EQ.1 ) THEN
+*
+*              This is a 1-by-1 subproblem and is not solved
+*              explicitly.
+*
+               CALL CCOPY( NRHS, B( ST, 1 ), LDB, WORK( BX+ST1 ), N )
+            ELSE IF( NSIZE.LE.SMLSIZ ) THEN
+*
+*              This is a small subproblem and is solved by SLASDQ.
+*
+               CALL SLASET( 'A', NSIZE, NSIZE, ZERO, ONE,
+     $                      RWORK( VT+ST1 ), N )
+               CALL SLASET( 'A', NSIZE, NSIZE, ZERO, ONE,
+     $                      RWORK( U+ST1 ), N )
+               CALL SLASDQ( 'U', 0, NSIZE, NSIZE, NSIZE, 0, D( ST ),
+     $                      E( ST ), RWORK( VT+ST1 ), N, RWORK( U+ST1 ),
+     $                      N, RWORK( NRWORK ), 1, RWORK( NRWORK ),
+     $                      INFO )
+               IF( INFO.NE.0 ) THEN
+                  RETURN
+               END IF
+*
+*              In the real version, B is passed to SLASDQ and multiplied
+*              internally by Q'. Here B is complex and that product is
+*              computed below in two steps (real and imaginary parts).
+*
+               J = IRWB - 1
+               DO 190 JCOL = 1, NRHS
+                  DO 180 JROW = ST, ST + NSIZE - 1
+                     J = J + 1
+                     RWORK( J ) = REAL( B( JROW, JCOL ) )
+  180             CONTINUE
+  190          CONTINUE
+               CALL SGEMM( 'T', 'N', NSIZE, NRHS, NSIZE, ONE,
+     $                     RWORK( U+ST1 ), N, RWORK( IRWB ), NSIZE,
+     $                     ZERO, RWORK( IRWRB ), NSIZE )
+               J = IRWB - 1
+               DO 210 JCOL = 1, NRHS
+                  DO 200 JROW = ST, ST + NSIZE - 1
+                     J = J + 1
+                     RWORK( J ) = AIMAG( B( JROW, JCOL ) )
+  200             CONTINUE
+  210          CONTINUE
+               CALL SGEMM( 'T', 'N', NSIZE, NRHS, NSIZE, ONE,
+     $                     RWORK( U+ST1 ), N, RWORK( IRWB ), NSIZE,
+     $                     ZERO, RWORK( IRWIB ), NSIZE )
+               JREAL = IRWRB - 1
+               JIMAG = IRWIB - 1
+               DO 230 JCOL = 1, NRHS
+                  DO 220 JROW = ST, ST + NSIZE - 1
+                     JREAL = JREAL + 1
+                     JIMAG = JIMAG + 1
+                     B( JROW, JCOL ) = CMPLX( RWORK( JREAL ),
+     $                                 RWORK( JIMAG ) )
+  220             CONTINUE
+  230          CONTINUE
+*
+               CALL CLACPY( 'A', NSIZE, NRHS, B( ST, 1 ), LDB,
+     $                      WORK( BX+ST1 ), N )
+            ELSE
+*
+*              A large problem. Solve it using divide and conquer.
+*
+               CALL SLASDA( ICMPQ1, SMLSIZ, NSIZE, SQRE, D( ST ),
+     $                      E( ST ), RWORK( U+ST1 ), N, RWORK( VT+ST1 ),
+     $                      IWORK( K+ST1 ), RWORK( DIFL+ST1 ),
+     $                      RWORK( DIFR+ST1 ), RWORK( Z+ST1 ),
+     $                      RWORK( POLES+ST1 ), IWORK( GIVPTR+ST1 ),
+     $                      IWORK( GIVCOL+ST1 ), N, IWORK( PERM+ST1 ),
+     $                      RWORK( GIVNUM+ST1 ), RWORK( C+ST1 ),
+     $                      RWORK( S+ST1 ), RWORK( NRWORK ),
+     $                      IWORK( IWK ), INFO )
+               IF( INFO.NE.0 ) THEN
+                  RETURN
+               END IF
+               BXST = BX + ST1
+               CALL CLALSA( ICMPQ2, SMLSIZ, NSIZE, NRHS, B( ST, 1 ),
+     $                      LDB, WORK( BXST ), N, RWORK( U+ST1 ), N,
+     $                      RWORK( VT+ST1 ), IWORK( K+ST1 ),
+     $                      RWORK( DIFL+ST1 ), RWORK( DIFR+ST1 ),
+     $                      RWORK( Z+ST1 ), RWORK( POLES+ST1 ),
+     $                      IWORK( GIVPTR+ST1 ), IWORK( GIVCOL+ST1 ), N,
+     $                      IWORK( PERM+ST1 ), RWORK( GIVNUM+ST1 ),
+     $                      RWORK( C+ST1 ), RWORK( S+ST1 ),
+     $                      RWORK( NRWORK ), IWORK( IWK ), INFO )
+               IF( INFO.NE.0 ) THEN
+                  RETURN
+               END IF
+            END IF
+            ST = I + 1
+         END IF
+  240 CONTINUE
+*
+*     Apply the singular values and treat the tiny ones as zero.
+*
+      TOL = RCND*ABS( D( ISAMAX( N, D, 1 ) ) )
+*
+      DO 250 I = 1, N
+*
+*        Some of the elements in D can be negative because 1-by-1
+*        subproblems were not solved explicitly.
+*
+         IF( ABS( D( I ) ).LE.TOL ) THEN
+            CALL CLASET( 'A', 1, NRHS, CZERO, CZERO, WORK( BX+I-1 ), N )
+         ELSE
+            RANK = RANK + 1
+            CALL CLASCL( 'G', 0, 0, D( I ), ONE, 1, NRHS,
+     $                   WORK( BX+I-1 ), N, INFO )
+         END IF
+         D( I ) = ABS( D( I ) )
+  250 CONTINUE
+*
+*     Now apply back the right singular vectors.
+*
+      ICMPQ2 = 1
+      DO 320 I = 1, NSUB
+         ST = IWORK( I )
+         ST1 = ST - 1
+         NSIZE = IWORK( SIZEI+I-1 )
+         BXST = BX + ST1
+         IF( NSIZE.EQ.1 ) THEN
+            CALL CCOPY( NRHS, WORK( BXST ), N, B( ST, 1 ), LDB )
+         ELSE IF( NSIZE.LE.SMLSIZ ) THEN
+*
+*           Since B and BX are complex, the following call to SGEMM
+*           is performed in two steps (real and imaginary parts).
+*
+*           CALL SGEMM( 'T', 'N', NSIZE, NRHS, NSIZE, ONE,
+*    $                  RWORK( VT+ST1 ), N, RWORK( BXST ), N, ZERO,
+*    $                  B( ST, 1 ), LDB )
+*
+            J = BXST - N - 1
+            JREAL = IRWB - 1
+            DO 270 JCOL = 1, NRHS
+               J = J + N
+               DO 260 JROW = 1, NSIZE
+                  JREAL = JREAL + 1
+                  RWORK( JREAL ) = REAL( WORK( J+JROW ) )
+  260          CONTINUE
+  270       CONTINUE
+            CALL SGEMM( 'T', 'N', NSIZE, NRHS, NSIZE, ONE,
+     $                  RWORK( VT+ST1 ), N, RWORK( IRWB ), NSIZE, ZERO,
+     $                  RWORK( IRWRB ), NSIZE )
+            J = BXST - N - 1
+            JIMAG = IRWB - 1
+            DO 290 JCOL = 1, NRHS
+               J = J + N
+               DO 280 JROW = 1, NSIZE
+                  JIMAG = JIMAG + 1
+                  RWORK( JIMAG ) = AIMAG( WORK( J+JROW ) )
+  280          CONTINUE
+  290       CONTINUE
+            CALL SGEMM( 'T', 'N', NSIZE, NRHS, NSIZE, ONE,
+     $                  RWORK( VT+ST1 ), N, RWORK( IRWB ), NSIZE, ZERO,
+     $                  RWORK( IRWIB ), NSIZE )
+            JREAL = IRWRB - 1
+            JIMAG = IRWIB - 1
+            DO 310 JCOL = 1, NRHS
+               DO 300 JROW = ST, ST + NSIZE - 1
+                  JREAL = JREAL + 1
+                  JIMAG = JIMAG + 1
+                  B( JROW, JCOL ) = CMPLX( RWORK( JREAL ),
+     $                              RWORK( JIMAG ) )
+  300          CONTINUE
+  310       CONTINUE
+         ELSE
+            CALL CLALSA( ICMPQ2, SMLSIZ, NSIZE, NRHS, WORK( BXST ), N,
+     $                   B( ST, 1 ), LDB, RWORK( U+ST1 ), N,
+     $                   RWORK( VT+ST1 ), IWORK( K+ST1 ),
+     $                   RWORK( DIFL+ST1 ), RWORK( DIFR+ST1 ),
+     $                   RWORK( Z+ST1 ), RWORK( POLES+ST1 ),
+     $                   IWORK( GIVPTR+ST1 ), IWORK( GIVCOL+ST1 ), N,
+     $                   IWORK( PERM+ST1 ), RWORK( GIVNUM+ST1 ),
+     $                   RWORK( C+ST1 ), RWORK( S+ST1 ),
+     $                   RWORK( NRWORK ), IWORK( IWK ), INFO )
+            IF( INFO.NE.0 ) THEN
+               RETURN
+            END IF
+         END IF
+  320 CONTINUE
+*
+*     Unscale and sort the singular values.
+*
+      CALL SLASCL( 'G', 0, 0, ONE, ORGNRM, N, 1, D, N, INFO )
+      CALL SLASRT( 'D', N, D, INFO )
+      CALL CLASCL( 'G', 0, 0, ORGNRM, ONE, N, NRHS, B, LDB, INFO )
+*
+      RETURN
+*
+*     End of CLALSD
+*
+      END