zgelss.f

来自「famous linear algebra library (LAPACK) p」· F 代码 · 共 635 行 · 第 1/2 页

*           (CWorkspace: need 2*N, prefer N+N*NB)
*           (RWorkspace: none)
*
            CALL ZGEQRF( M, N, A, LDA, WORK( ITAU ), WORK( IWORK ),
     $                   LWORK-IWORK+1, INFO )
*
*           Multiply B by transpose(Q)
*           (CWorkspace: need N+NRHS, prefer N+NRHS*NB)
*           (RWorkspace: none)
*
            CALL ZUNMQR( 'L', 'C', M, NRHS, N, A, LDA, WORK( ITAU ), B,
     $                   LDB, WORK( IWORK ), LWORK-IWORK+1, INFO )
*
*           Zero out below R
*
            IF( N.GT.1 )
     $         CALL ZLASET( 'L', N-1, N-1, CZERO, CZERO, A( 2, 1 ),
     $                      LDA )
         END IF
*
         IE = 1
         ITAUQ = 1
         ITAUP = ITAUQ + N
         IWORK = ITAUP + N
*
*        Bidiagonalize R in A
*        (CWorkspace: need 2*N+MM, prefer 2*N+(MM+N)*NB)
*        (RWorkspace: need N)
*
         CALL ZGEBRD( MM, N, A, LDA, S, RWORK( IE ), WORK( ITAUQ ),
     $                WORK( ITAUP ), WORK( IWORK ), LWORK-IWORK+1,
     $                INFO )
*
*        Multiply B by transpose of left bidiagonalizing vectors of R
*        (CWorkspace: need 2*N+NRHS, prefer 2*N+NRHS*NB)
*        (RWorkspace: none)
*
         CALL ZUNMBR( 'Q', 'L', 'C', MM, NRHS, N, A, LDA, WORK( ITAUQ ),
     $                B, LDB, WORK( IWORK ), LWORK-IWORK+1, INFO )
*
*        Generate right bidiagonalizing vectors of R in A
*        (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB)
*        (RWorkspace: none)
*
         CALL ZUNGBR( 'P', N, N, N, A, LDA, WORK( ITAUP ),
     $                WORK( IWORK ), LWORK-IWORK+1, INFO )
         IRWORK = IE + N
*
*        Perform bidiagonal QR iteration
*          multiply B by transpose of left singular vectors
*          compute right singular vectors in A
*        (CWorkspace: none)
*        (RWorkspace: need BDSPAC)
*
         CALL ZBDSQR( 'U', N, N, 0, NRHS, S, RWORK( IE ), A, LDA, VDUM,
     $                1, B, LDB, RWORK( IRWORK ), INFO )
         IF( INFO.NE.0 )
     $      GO TO 70
*
*        Multiply B by reciprocals of singular values
*
         THR = MAX( RCOND*S( 1 ), SFMIN )
         IF( RCOND.LT.ZERO )
     $      THR = MAX( EPS*S( 1 ), SFMIN )
         RANK = 0
         DO 10 I = 1, N
            IF( S( I ).GT.THR ) THEN
               CALL ZDRSCL( NRHS, S( I ), B( I, 1 ), LDB )
               RANK = RANK + 1
            ELSE
               CALL ZLASET( 'F', 1, NRHS, CZERO, CZERO, B( I, 1 ), LDB )
            END IF
   10    CONTINUE
*
*        Multiply B by right singular vectors
*        (CWorkspace: need N, prefer N*NRHS)
*        (RWorkspace: none)
*
         IF( LWORK.GE.LDB*NRHS .AND. NRHS.GT.1 ) THEN
            CALL ZGEMM( 'C', 'N', N, NRHS, N, CONE, A, LDA, B, LDB,
     $                  CZERO, WORK, LDB )
            CALL ZLACPY( 'G', N, NRHS, WORK, LDB, B, LDB )
         ELSE IF( NRHS.GT.1 ) THEN
            CHUNK = LWORK / N
            DO 20 I = 1, NRHS, CHUNK
               BL = MIN( NRHS-I+1, CHUNK )
               CALL ZGEMM( 'C', 'N', N, BL, N, CONE, A, LDA, B( 1, I ),
     $                     LDB, CZERO, WORK, N )
               CALL ZLACPY( 'G', N, BL, WORK, N, B( 1, I ), LDB )
   20       CONTINUE
         ELSE
            CALL ZGEMV( 'C', N, N, CONE, A, LDA, B, 1, CZERO, WORK, 1 )
            CALL ZCOPY( N, WORK, 1, B, 1 )
         END IF
*
      ELSE IF( N.GE.MNTHR .AND. LWORK.GE.3*M+M*M+MAX( M, NRHS, N-2*M ) )
     $          THEN
*
*        Underdetermined case, M much less than N
*
*        Path 2a - underdetermined, with many more columns than rows
*        and sufficient workspace for an efficient algorithm
*
         LDWORK = M
         IF( LWORK.GE.3*M+M*LDA+MAX( M, NRHS, N-2*M ) )
     $      LDWORK = LDA
         ITAU = 1
         IWORK = M + 1
*
*        Compute A=L*Q
*        (CWorkspace: need 2*M, prefer M+M*NB)
*        (RWorkspace: none)
*
         CALL ZGELQF( M, N, A, LDA, WORK( ITAU ), WORK( IWORK ),
     $                LWORK-IWORK+1, INFO )
         IL = IWORK
*
*        Copy L to WORK(IL), zeroing out above it
*
         CALL ZLACPY( 'L', M, M, A, LDA, WORK( IL ), LDWORK )
         CALL ZLASET( 'U', M-1, M-1, CZERO, CZERO, WORK( IL+LDWORK ),
     $                LDWORK )
         IE = 1
         ITAUQ = IL + LDWORK*M
         ITAUP = ITAUQ + M
         IWORK = ITAUP + M
*
*        Bidiagonalize L in WORK(IL)
*        (CWorkspace: need M*M+4*M, prefer M*M+3*M+2*M*NB)
*        (RWorkspace: need M)
*
         CALL ZGEBRD( M, M, WORK( IL ), LDWORK, S, RWORK( IE ),
     $                WORK( ITAUQ ), WORK( ITAUP ), WORK( IWORK ),
     $                LWORK-IWORK+1, INFO )
*
*        Multiply B by transpose of left bidiagonalizing vectors of L
*        (CWorkspace: need M*M+3*M+NRHS, prefer M*M+3*M+NRHS*NB)
*        (RWorkspace: none)
*
         CALL ZUNMBR( 'Q', 'L', 'C', M, NRHS, M, WORK( IL ), LDWORK,
     $                WORK( ITAUQ ), B, LDB, WORK( IWORK ),
     $                LWORK-IWORK+1, INFO )
*
*        Generate right bidiagonalizing vectors of R in WORK(IL)
*        (CWorkspace: need M*M+4*M-1, prefer M*M+3*M+(M-1)*NB)
*        (RWorkspace: none)
*
         CALL ZUNGBR( 'P', M, M, M, WORK( IL ), LDWORK, WORK( ITAUP ),
     $                WORK( IWORK ), LWORK-IWORK+1, INFO )
         IRWORK = IE + M
*
*        Perform bidiagonal QR iteration, computing right singular
*        vectors of L in WORK(IL) and multiplying B by transpose of
*        left singular vectors
*        (CWorkspace: need M*M)
*        (RWorkspace: need BDSPAC)
*
         CALL ZBDSQR( 'U', M, M, 0, NRHS, S, RWORK( IE ), WORK( IL ),
     $                LDWORK, A, LDA, B, LDB, RWORK( IRWORK ), INFO )
         IF( INFO.NE.0 )
     $      GO TO 70
*
*        Multiply B by reciprocals of singular values
*
         THR = MAX( RCOND*S( 1 ), SFMIN )
         IF( RCOND.LT.ZERO )
     $      THR = MAX( EPS*S( 1 ), SFMIN )
         RANK = 0
         DO 30 I = 1, M
            IF( S( I ).GT.THR ) THEN
               CALL ZDRSCL( NRHS, S( I ), B( I, 1 ), LDB )
               RANK = RANK + 1
            ELSE
               CALL ZLASET( 'F', 1, NRHS, CZERO, CZERO, B( I, 1 ), LDB )
            END IF
   30    CONTINUE
         IWORK = IL + M*LDWORK
*
*        Multiply B by right singular vectors of L in WORK(IL)
*        (CWorkspace: need M*M+2*M, prefer M*M+M+M*NRHS)
*        (RWorkspace: none)
*
         IF( LWORK.GE.LDB*NRHS+IWORK-1 .AND. NRHS.GT.1 ) THEN
            CALL ZGEMM( 'C', 'N', M, NRHS, M, CONE, WORK( IL ), LDWORK,
     $                  B, LDB, CZERO, WORK( IWORK ), LDB )
            CALL ZLACPY( 'G', M, NRHS, WORK( IWORK ), LDB, B, LDB )
         ELSE IF( NRHS.GT.1 ) THEN
            CHUNK = ( LWORK-IWORK+1 ) / M
            DO 40 I = 1, NRHS, CHUNK
               BL = MIN( NRHS-I+1, CHUNK )
               CALL ZGEMM( 'C', 'N', M, BL, M, CONE, WORK( IL ), LDWORK,
     $                     B( 1, I ), LDB, CZERO, WORK( IWORK ), M )
               CALL ZLACPY( 'G', M, BL, WORK( IWORK ), M, B( 1, I ),
     $                      LDB )
   40       CONTINUE
         ELSE
            CALL ZGEMV( 'C', M, M, CONE, WORK( IL ), LDWORK, B( 1, 1 ),
     $                  1, CZERO, WORK( IWORK ), 1 )
            CALL ZCOPY( M, WORK( IWORK ), 1, B( 1, 1 ), 1 )
         END IF
*
*        Zero out below first M rows of B
*
         CALL ZLASET( 'F', N-M, NRHS, CZERO, CZERO, B( M+1, 1 ), LDB )
         IWORK = ITAU + M
*
*        Multiply transpose(Q) by B
*        (CWorkspace: need M+NRHS, prefer M+NHRS*NB)
*        (RWorkspace: none)
*
         CALL ZUNMLQ( 'L', 'C', N, NRHS, M, A, LDA, WORK( ITAU ), B,
     $                LDB, WORK( IWORK ), LWORK-IWORK+1, INFO )
*
      ELSE
*
*        Path 2 - remaining underdetermined cases
*
         IE = 1
         ITAUQ = 1
         ITAUP = ITAUQ + M
         IWORK = ITAUP + M
*
*        Bidiagonalize A
*        (CWorkspace: need 3*M, prefer 2*M+(M+N)*NB)
*        (RWorkspace: need N)
*
         CALL ZGEBRD( M, N, A, LDA, S, RWORK( IE ), WORK( ITAUQ ),
     $                WORK( ITAUP ), WORK( IWORK ), LWORK-IWORK+1,
     $                INFO )
*
*        Multiply B by transpose of left bidiagonalizing vectors
*        (CWorkspace: need 2*M+NRHS, prefer 2*M+NRHS*NB)
*        (RWorkspace: none)
*
         CALL ZUNMBR( 'Q', 'L', 'C', M, NRHS, N, A, LDA, WORK( ITAUQ ),
     $                B, LDB, WORK( IWORK ), LWORK-IWORK+1, INFO )
*
*        Generate right bidiagonalizing vectors in A
*        (CWorkspace: need 3*M, prefer 2*M+M*NB)
*        (RWorkspace: none)
*
         CALL ZUNGBR( 'P', M, N, M, A, LDA, WORK( ITAUP ),
     $                WORK( IWORK ), LWORK-IWORK+1, INFO )
         IRWORK = IE + M
*
*        Perform bidiagonal QR iteration,
*           computing right singular vectors of A in A and
*           multiplying B by transpose of left singular vectors
*        (CWorkspace: none)
*        (RWorkspace: need BDSPAC)
*
         CALL ZBDSQR( 'L', M, N, 0, NRHS, S, RWORK( IE ), A, LDA, VDUM,
     $                1, B, LDB, RWORK( IRWORK ), INFO )
         IF( INFO.NE.0 )
     $      GO TO 70
*
*        Multiply B by reciprocals of singular values
*
         THR = MAX( RCOND*S( 1 ), SFMIN )
         IF( RCOND.LT.ZERO )
     $      THR = MAX( EPS*S( 1 ), SFMIN )
         RANK = 0
         DO 50 I = 1, M
            IF( S( I ).GT.THR ) THEN
               CALL ZDRSCL( NRHS, S( I ), B( I, 1 ), LDB )
               RANK = RANK + 1
            ELSE
               CALL ZLASET( 'F', 1, NRHS, CZERO, CZERO, B( I, 1 ), LDB )
            END IF
   50    CONTINUE
*
*        Multiply B by right singular vectors of A
*        (CWorkspace: need N, prefer N*NRHS)
*        (RWorkspace: none)
*
         IF( LWORK.GE.LDB*NRHS .AND. NRHS.GT.1 ) THEN
            CALL ZGEMM( 'C', 'N', N, NRHS, M, CONE, A, LDA, B, LDB,
     $                  CZERO, WORK, LDB )
            CALL ZLACPY( 'G', N, NRHS, WORK, LDB, B, LDB )
         ELSE IF( NRHS.GT.1 ) THEN
            CHUNK = LWORK / N
            DO 60 I = 1, NRHS, CHUNK
               BL = MIN( NRHS-I+1, CHUNK )
               CALL ZGEMM( 'C', 'N', N, BL, M, CONE, A, LDA, B( 1, I ),
     $                     LDB, CZERO, WORK, N )
               CALL ZLACPY( 'F', N, BL, WORK, N, B( 1, I ), LDB )
   60       CONTINUE
         ELSE
            CALL ZGEMV( 'C', M, N, CONE, A, LDA, B, 1, CZERO, WORK, 1 )
            CALL ZCOPY( N, WORK, 1, B, 1 )
         END IF
      END IF
*
*     Undo scaling
*
      IF( IASCL.EQ.1 ) THEN
         CALL ZLASCL( 'G', 0, 0, ANRM, SMLNUM, N, NRHS, B, LDB, INFO )
         CALL DLASCL( 'G', 0, 0, SMLNUM, ANRM, MINMN, 1, S, MINMN,
     $                INFO )
      ELSE IF( IASCL.EQ.2 ) THEN
         CALL ZLASCL( 'G', 0, 0, ANRM, BIGNUM, N, NRHS, B, LDB, INFO )
         CALL DLASCL( 'G', 0, 0, BIGNUM, ANRM, MINMN, 1, S, MINMN,
     $                INFO )
      END IF
      IF( IBSCL.EQ.1 ) THEN
         CALL ZLASCL( 'G', 0, 0, SMLNUM, BNRM, N, NRHS, B, LDB, INFO )
      ELSE IF( IBSCL.EQ.2 ) THEN
         CALL ZLASCL( 'G', 0, 0, BIGNUM, BNRM, N, NRHS, B, LDB, INFO )
      END IF
   70 CONTINUE
      WORK( 1 ) = MAXWRK
      RETURN
*
*     End of ZGELSS
*
      END