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lapack/SRC/clalsd.f
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*> \brief \b CLALSD uses the singular value decomposition of A to solve the least squares problem.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download CLALSD + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/clalsd.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clalsd.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clalsd.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE CLALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND,
* RANK, WORK, RWORK, IWORK, INFO )
*
* .. 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( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> = 'U': D and E define an upper bidiagonal matrix.
*> = 'L': D and E define a lower bidiagonal matrix.
*> \endverbatim
*>
*> \param[in] SMLSIZ
*> \verbatim
*> SMLSIZ is INTEGER
*> The maximum size of the subproblems at the bottom of the
*> computation tree.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The dimension of the bidiagonal matrix. N >= 0.
*> \endverbatim
*>
*> \param[in] NRHS
*> \verbatim
*> NRHS is INTEGER
*> The number of columns of B. NRHS must be at least 1.
*> \endverbatim
*>
*> \param[in,out] D
*> \verbatim
*> D is 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.
*> \endverbatim
*>
*> \param[in,out] E
*> \verbatim
*> E is REAL array, dimension (N-1)
*> Contains the super-diagonal entries of the bidiagonal matrix.
*> On exit, E has been destroyed.
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is 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.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of B in the calling subprogram.
*> LDB must be at least max(1,N).
*> \endverbatim
*>
*> \param[in] RCOND
*> \verbatim
*> RCOND is 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).
*> \endverbatim
*>
*> \param[out] RANK
*> \verbatim
*> RANK is INTEGER
*> The number of singular values of A greater than RCOND times
*> the largest singular value.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX array, dimension (N * NRHS).
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*> RWORK is REAL array, dimension at least
*> (9*N + 2*N*SMLSIZ + 8*N*NLVL + 3*SMLSIZ*NRHS +
*> MAX( (SMLSIZ+1)**2, N*(1+NRHS) + 2*NRHS ),
*> where
*> NLVL = MAX( 0, INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1 )
*> \endverbatim
*>
*> \param[out] IWORK
*> \verbatim
*> IWORK is INTEGER array, dimension (3*N*NLVL + 11*N).
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: The algorithm failed to compute a singular value while
*> working on the submatrix lying in rows and columns
*> INFO/(N+1) through MOD(INFO,N+1).
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complexOTHERcomputational
*
*> \par Contributors:
* ==================
*>
*> Ming Gu and Ren-Cang Li, Computer Science Division, University of
*> California at Berkeley, USA \n
*> Osni Marques, LBNL/NERSC, USA \n
*
* =====================================================================
SUBROUTINE CLALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND,
$ RANK, WORK, RWORK, IWORK, INFO )
*
* -- LAPACK computational routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. 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( * )
* ..
*
* =====================================================================
*
* .. 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**H. 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**H 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**H. 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
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