Mercurial > hg > octave-lyh
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> |
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date | Sun, 27 Apr 2008 22:34:17 +0200 |
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new file mode 100644 --- /dev/null +++ b/libcruft/lapack/clalsd.f @@ -0,0 +1,596 @@ + 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