zlalsa.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．

         DO 40 JCOL = 1, NRHS
            DO 30 JROW = NLF, NLF + NL - 1
               J = J + 1
               RWORK( J ) = DIMAG( B( JROW, JCOL ) )
   30       CONTINUE
   40    CONTINUE
         OPS = OPS + DOPBL3( 'DGEMM ', NL, NRHS, NL ) 
         CALL DGEMM( 'T', 'N', NL, NRHS, NL, ONE, U( NLF, 1 ), LDU,
     $               RWORK( 1+NL*NRHS*2 ), NL, ZERO, RWORK( 1+NL*NRHS ),
     $               NL )
         JREAL = 0
         JIMAG = NL*NRHS
         DO 60 JCOL = 1, NRHS
            DO 50 JROW = NLF, NLF + NL - 1
               JREAL = JREAL + 1
               JIMAG = JIMAG + 1
               BX( JROW, JCOL ) = DCMPLX( RWORK( JREAL ),
     $                            RWORK( JIMAG ) )
   50       CONTINUE
   60    CONTINUE
*
*        Since B and BX are complex, the following call to DGEMM
*        is performed in two steps (real and imaginary parts).
*
*        CALL DGEMM( 'T', 'N', NR, NRHS, NR, ONE, U( NRF, 1 ), LDU,
*    $               B( NRF, 1 ), LDB, ZERO, BX( NRF, 1 ), LDBX )
*
         J = NR*NRHS*2
         DO 80 JCOL = 1, NRHS
            DO 70 JROW = NRF, NRF + NR - 1
               J = J + 1
               RWORK( J ) = DBLE( B( JROW, JCOL ) )
   70       CONTINUE
   80    CONTINUE
         OPS = OPS + DOPBL3( 'DGEMM ', NR, NRHS, NR ) 
         CALL DGEMM( 'T', 'N', NR, NRHS, NR, ONE, U( NRF, 1 ), LDU,
     $               RWORK( 1+NR*NRHS*2 ), NR, ZERO, RWORK( 1 ), NR )
         J = NR*NRHS*2
         DO 100 JCOL = 1, NRHS
            DO 90 JROW = NRF, NRF + NR - 1
               J = J + 1
               RWORK( J ) = DIMAG( B( JROW, JCOL ) )
   90       CONTINUE
  100    CONTINUE
         OPS = OPS + DOPBL3( 'DGEMM ', NR, NRHS, NR ) 
         CALL DGEMM( 'T', 'N', NR, NRHS, NR, ONE, U( NRF, 1 ), LDU,
     $               RWORK( 1+NR*NRHS*2 ), NR, ZERO, RWORK( 1+NR*NRHS ),
     $               NR )
         JREAL = 0
         JIMAG = NR*NRHS
         DO 120 JCOL = 1, NRHS
            DO 110 JROW = NRF, NRF + NR - 1
               JREAL = JREAL + 1
               JIMAG = JIMAG + 1
               BX( JROW, JCOL ) = DCMPLX( RWORK( JREAL ),
     $                            RWORK( JIMAG ) )
  110       CONTINUE
  120    CONTINUE
*
  130 CONTINUE
*
*     Next copy the rows of B that correspond to unchanged rows
*     in the bidiagonal matrix to BX.
*
      DO 140 I = 1, ND
         IC = IWORK( INODE+I-1 )
         CALL ZCOPY( NRHS, B( IC, 1 ), LDB, BX( IC, 1 ), LDBX )
  140 CONTINUE
*
*     Finally go through the left singular vector matrices of all
*     the other subproblems bottom-up on the tree.
*
      J = 2**NLVL
      SQRE = 0
*
      DO 160 LVL = NLVL, 1, -1
         LVL2 = 2*LVL - 1
*
*        find the first node LF and last node LL on
*        the current level LVL
*
         IF( LVL.EQ.1 ) THEN
            LF = 1
            LL = 1
         ELSE
            LF = 2**( LVL-1 )
            LL = 2*LF - 1
         END IF
         DO 150 I = LF, LL
            IM1 = I - 1
            IC = IWORK( INODE+IM1 )
            NL = IWORK( NDIML+IM1 )
            NR = IWORK( NDIMR+IM1 )
            NLF = IC - NL
            NRF = IC + 1
            J = J - 1
            CALL ZLALS0( ICOMPQ, NL, NR, SQRE, NRHS, BX( NLF, 1 ), LDBX,
     $                   B( NLF, 1 ), LDB, PERM( NLF, LVL ),
     $                   GIVPTR( J ), GIVCOL( NLF, LVL2 ), LDGCOL,
     $                   GIVNUM( NLF, LVL2 ), LDU, POLES( NLF, LVL2 ),
     $                   DIFL( NLF, LVL ), DIFR( NLF, LVL2 ),
     $                   Z( NLF, LVL ), K( J ), C( J ), S( J ), RWORK,
     $                   INFO )
  150    CONTINUE
  160 CONTINUE
      GO TO 330
*
*     ICOMPQ = 1: applying back the right singular vector factors.
*
  170 CONTINUE
*
*     First now go through the right singular vector matrices of all
*     the tree nodes top-down.
*
      J = 0
      DO 190 LVL = 1, NLVL
         LVL2 = 2*LVL - 1
*
*        Find the first node LF and last node LL on
*        the current level LVL.
*
         IF( LVL.EQ.1 ) THEN
            LF = 1
            LL = 1
         ELSE
            LF = 2**( LVL-1 )
            LL = 2*LF - 1
         END IF
         DO 180 I = LL, LF, -1
            IM1 = I - 1
            IC = IWORK( INODE+IM1 )
            NL = IWORK( NDIML+IM1 )
            NR = IWORK( NDIMR+IM1 )
            NLF = IC - NL
            NRF = IC + 1
            IF( I.EQ.LL ) THEN
               SQRE = 0
            ELSE
               SQRE = 1
            END IF
            J = J + 1
            CALL ZLALS0( ICOMPQ, NL, NR, SQRE, NRHS, B( NLF, 1 ), LDB,
     $                   BX( NLF, 1 ), LDBX, PERM( NLF, LVL ),
     $                   GIVPTR( J ), GIVCOL( NLF, LVL2 ), LDGCOL,
     $                   GIVNUM( NLF, LVL2 ), LDU, POLES( NLF, LVL2 ),
     $                   DIFL( NLF, LVL ), DIFR( NLF, LVL2 ),
     $                   Z( NLF, LVL ), K( J ), C( J ), S( J ), RWORK,
     $                   INFO )
  180    CONTINUE
  190 CONTINUE
*
*     The nodes on the bottom level of the tree were solved
*     by DLASDQ. The corresponding right singular vector
*     matrices are in explicit form. Apply them back.
*
      NDB1 = ( ND+1 ) / 2
      DO 320 I = NDB1, ND
         I1 = I - 1
         IC = IWORK( INODE+I1 )
         NL = IWORK( NDIML+I1 )
         NR = IWORK( NDIMR+I1 )
         NLP1 = NL + 1
         IF( I.EQ.ND ) THEN
            NRP1 = NR
         ELSE
            NRP1 = NR + 1
         END IF
         NLF = IC - NL
         NRF = IC + 1
*
*        Since B and BX are complex, the following call to DGEMM is
*        performed in two steps (real and imaginary parts).
*
*        CALL DGEMM( 'T', 'N', NLP1, NRHS, NLP1, ONE, VT( NLF, 1 ), LDU,
*    $               B( NLF, 1 ), LDB, ZERO, BX( NLF, 1 ), LDBX )
*
         J = NLP1*NRHS*2
         DO 210 JCOL = 1, NRHS
            DO 200 JROW = NLF, NLF + NLP1 - 1
               J = J + 1
               RWORK( J ) = DBLE( B( JROW, JCOL ) )
  200       CONTINUE
  210    CONTINUE
         OPS = OPS + DOPBL3( 'DGEMM ', NLP1, NRHS, NLP1 ) 
         CALL DGEMM( 'T', 'N', NLP1, NRHS, NLP1, ONE, VT( NLF, 1 ), LDU,
     $               RWORK( 1+NLP1*NRHS*2 ), NLP1, ZERO, RWORK( 1 ),
     $               NLP1 )
         J = NLP1*NRHS*2
         DO 230 JCOL = 1, NRHS
            DO 220 JROW = NLF, NLF + NLP1 - 1
               J = J + 1
               RWORK( J ) = DIMAG( B( JROW, JCOL ) )
  220       CONTINUE
  230    CONTINUE
         OPS = OPS + DOPBL3( 'DGEMM ', NLP1, NRHS, NLP1 ) 
         CALL DGEMM( 'T', 'N', NLP1, NRHS, NLP1, ONE, VT( NLF, 1 ), LDU,
     $               RWORK( 1+NLP1*NRHS*2 ), NLP1, ZERO,
     $               RWORK( 1+NLP1*NRHS ), NLP1 )
         JREAL = 0
         JIMAG = NLP1*NRHS
         DO 250 JCOL = 1, NRHS
            DO 240 JROW = NLF, NLF + NLP1 - 1
               JREAL = JREAL + 1
               JIMAG = JIMAG + 1
               BX( JROW, JCOL ) = DCMPLX( RWORK( JREAL ),
     $                            RWORK( JIMAG ) )
  240       CONTINUE
  250    CONTINUE
*
*        Since B and BX are complex, the following call to DGEMM is
*        performed in two steps (real and imaginary parts).
*
*        CALL DGEMM( 'T', 'N', NRP1, NRHS, NRP1, ONE, VT( NRF, 1 ), LDU,
*    $               B( NRF, 1 ), LDB, ZERO, BX( NRF, 1 ), LDBX )
*
         J = NRP1*NRHS*2
         DO 270 JCOL = 1, NRHS
            DO 260 JROW = NRF, NRF + NRP1 - 1
               J = J + 1
               RWORK( J ) = DBLE( B( JROW, JCOL ) )
  260       CONTINUE
  270    CONTINUE
         OPS = OPS + DOPBL3( 'DGEMM ', NRP1, NRHS, NRP1 ) 
         CALL DGEMM( 'T', 'N', NRP1, NRHS, NRP1, ONE, VT( NRF, 1 ), LDU,
     $               RWORK( 1+NRP1*NRHS*2 ), NRP1, ZERO, RWORK( 1 ),
     $               NRP1 )
         J = NRP1*NRHS*2
         DO 290 JCOL = 1, NRHS
            DO 280 JROW = NRF, NRF + NRP1 - 1
               J = J + 1
               RWORK( J ) = DIMAG( B( JROW, JCOL ) )
  280       CONTINUE
  290    CONTINUE
         OPS = OPS + DOPBL3( 'DGEMM ', NRP1, NRHS, NRP1 ) 
         CALL DGEMM( 'T', 'N', NRP1, NRHS, NRP1, ONE, VT( NRF, 1 ), LDU,
     $               RWORK( 1+NRP1*NRHS*2 ), NRP1, ZERO,
     $               RWORK( 1+NRP1*NRHS ), NRP1 )
         JREAL = 0
         JIMAG = NRP1*NRHS
         DO 310 JCOL = 1, NRHS
            DO 300 JROW = NRF, NRF + NRP1 - 1
               JREAL = JREAL + 1
               JIMAG = JIMAG + 1
               BX( JROW, JCOL ) = DCMPLX( RWORK( JREAL ),
     $                            RWORK( JIMAG ) )
  300       CONTINUE
  310    CONTINUE
*
  320 CONTINUE
*
  330 CONTINUE
*
      RETURN
*
*     End of ZLALSA
*
      END