zlalsd.f

计算矩阵的经典开源库．全世界都在用它．相信你也不能例外．

         OPS = OPS + DOPBL3( 'DGEMM ', N, NRHS, N ) 
         CALL DGEMM( '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 ) = DIMAG( B( JROW, JCOL ) )
  130       CONTINUE
  140    CONTINUE
         OPS = OPS + DOPBL3( 'DGEMM ', N, NRHS, N ) 
         CALL DGEMM( '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 ) = DCMPLX( RWORK( JREAL ),
     $                           RWORK( JIMAG ) )
  150       CONTINUE
  160    CONTINUE
*
*        Unscale.
*
         OPS = OPS + DBLE( N + 6*N*NRHS )
         CALL DLASCL( 'G', 0, 0, ONE, ORGNRM, N, 1, D, N, INFO )
         CALL DLASRT( 'D', N, D, INFO )
         CALL ZLASCL( 'G', 0, 0, ORGNRM, ONE, N, NRHS, B, LDB, INFO )
*
         RETURN
      END IF
*
*     Book-keeping and setting up some constants.
*
      NLVL = INT( LOG( DBLE( N ) / DBLE( 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 ZCOPY( 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 ZCOPY( NRHS, B( ST, 1 ), LDB, WORK( BX+ST1 ), N )
            ELSE IF( NSIZE.LE.SMLSIZ ) THEN
*
*              This is a small subproblem and is solved by DLASDQ.
*
               CALL DLASET( 'A', NSIZE, NSIZE, ZERO, ONE,
     $                      RWORK( VT+ST1 ), N )
               CALL DLASET( 'A', NSIZE, NSIZE, ZERO, ONE,
     $                      RWORK( U+ST1 ), N )
               CALL DLASDQ( '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 DLASDQ 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 ) = DBLE( B( JROW, JCOL ) )
  180             CONTINUE
  190          CONTINUE
               OPS = OPS + DOPBL3( 'DGEMM ', NSIZE, NRHS, NSIZE ) 
               CALL DGEMM( '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 ) = DIMAG( B( JROW, JCOL ) )
  200             CONTINUE
  210          CONTINUE
               OPS = OPS + DOPBL3( 'DGEMM ', NSIZE, NRHS, NSIZE ) 
               CALL DGEMM( '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 ) = DCMPLX( RWORK( JREAL ),
     $                                 RWORK( JIMAG ) )
  220             CONTINUE
  230          CONTINUE
*
               CALL ZLACPY( 'A', NSIZE, NRHS, B( ST, 1 ), LDB,
     $                      WORK( BX+ST1 ), N )
            ELSE
*
*              A large problem. Solve it using divide and conquer.
*
               CALL DLASDA( 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 ZLALSA( 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.
*
      OPS = OPS + DBLE( 1 )
      TOL = RCOND*ABS( D( IDAMAX( 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 ZLASET( 'A', 1, NRHS, CZERO, CZERO, WORK( BX+I-1 ), N )
         ELSE
            RANK = RANK + 1
            OPS = OPS + DBLE( 6*NRHS )
            CALL ZLASCL( '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 ZCOPY( NRHS, WORK( BXST ), N, B( ST, 1 ), LDB )
         ELSE IF( NSIZE.LE.SMLSIZ ) THEN
*
*           Since B and BX are complex, the following call to DGEMM
*           is performed in two steps (real and imaginary parts).
*
*           CALL DGEMM( '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 ) = DBLE( WORK( J+JROW ) )
  260          CONTINUE
  270       CONTINUE
            OPS = OPS + DOPBL3( 'DGEMM ', NSIZE, NRHS, NSIZE ) 
            CALL DGEMM( '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 ) = DIMAG( WORK( J+JROW ) )
  280          CONTINUE
  290       CONTINUE
            OPS = OPS + DOPBL3( 'DGEMM ', NSIZE, NRHS, NSIZE ) 
            CALL DGEMM( '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 ) = DCMPLX( RWORK( JREAL ),
     $                              RWORK( JIMAG ) )
  300          CONTINUE
  310       CONTINUE
         ELSE
            CALL ZLALSA( 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.
*
      OPS = OPS + DBLE( N + 6*N*NRHS )
      CALL DLASCL( 'G', 0, 0, ONE, ORGNRM, N, 1, D, N, INFO )
      CALL DLASRT( 'D', N, D, INFO )
      CALL ZLASCL( 'G', 0, 0, ORGNRM, ONE, N, NRHS, B, LDB, INFO )
*
      RETURN
*
*     End of ZLALSD
*
      END