dgelsd.f

来自「famous linear algebra library (LAPACK) p」· F 代码 · 共 529 行 · 第 1/2 页

         RETURN
      ELSE IF( LQUERY ) THEN
         GO TO 10
      END IF
*
*     Quick return if possible.
*
      IF( M.EQ.0 .OR. N.EQ.0 ) THEN
         RANK = 0
         RETURN
      END IF
*
*     Get machine parameters.
*
      EPS = DLAMCH( 'P' )
      SFMIN = DLAMCH( 'S' )
      SMLNUM = SFMIN / EPS
      BIGNUM = ONE / SMLNUM
      CALL DLABAD( SMLNUM, BIGNUM )
*
*     Scale A if max entry outside range [SMLNUM,BIGNUM].
*
      ANRM = DLANGE( 'M', M, N, A, LDA, WORK )
      IASCL = 0
      IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
*
*        Scale matrix norm up to SMLNUM.
*
         CALL DLASCL( 'G', 0, 0, ANRM, SMLNUM, M, N, A, LDA, INFO )
         IASCL = 1
      ELSE IF( ANRM.GT.BIGNUM ) THEN
*
*        Scale matrix norm down to BIGNUM.
*
         CALL DLASCL( 'G', 0, 0, ANRM, BIGNUM, M, N, A, LDA, INFO )
         IASCL = 2
      ELSE IF( ANRM.EQ.ZERO ) THEN
*
*        Matrix all zero. Return zero solution.
*
         CALL DLASET( 'F', MAX( M, N ), NRHS, ZERO, ZERO, B, LDB )
         CALL DLASET( 'F', MINMN, 1, ZERO, ZERO, S, 1 )
         RANK = 0
         GO TO 10
      END IF
*
*     Scale B if max entry outside range [SMLNUM,BIGNUM].
*
      BNRM = DLANGE( 'M', M, NRHS, B, LDB, WORK )
      IBSCL = 0
      IF( BNRM.GT.ZERO .AND. BNRM.LT.SMLNUM ) THEN
*
*        Scale matrix norm up to SMLNUM.
*
         CALL DLASCL( 'G', 0, 0, BNRM, SMLNUM, M, NRHS, B, LDB, INFO )
         IBSCL = 1
      ELSE IF( BNRM.GT.BIGNUM ) THEN
*
*        Scale matrix norm down to BIGNUM.
*
         CALL DLASCL( 'G', 0, 0, BNRM, BIGNUM, M, NRHS, B, LDB, INFO )
         IBSCL = 2
      END IF
*
*     If M < N make sure certain entries of B are zero.
*
      IF( M.LT.N )
     $   CALL DLASET( 'F', N-M, NRHS, ZERO, ZERO, B( M+1, 1 ), LDB )
*
*     Overdetermined case.
*
      IF( M.GE.N ) THEN
*
*        Path 1 - overdetermined or exactly determined.
*
         MM = M
         IF( M.GE.MNTHR ) THEN
*
*           Path 1a - overdetermined, with many more rows than columns.
*
            MM = N
            ITAU = 1
            NWORK = ITAU + N
*
*           Compute A=Q*R.
*           (Workspace: need 2*N, prefer N+N*NB)
*
            CALL DGEQRF( M, N, A, LDA, WORK( ITAU ), WORK( NWORK ),
     $                   LWORK-NWORK+1, INFO )
*
*           Multiply B by transpose(Q).
*           (Workspace: need N+NRHS, prefer N+NRHS*NB)
*
            CALL DORMQR( 'L', 'T', M, NRHS, N, A, LDA, WORK( ITAU ), B,
     $                   LDB, WORK( NWORK ), LWORK-NWORK+1, INFO )
*
*           Zero out below R.
*
            IF( N.GT.1 ) THEN
               CALL DLASET( 'L', N-1, N-1, ZERO, ZERO, A( 2, 1 ), LDA )
            END IF
         END IF
*
         IE = 1
         ITAUQ = IE + N
         ITAUP = ITAUQ + N
         NWORK = ITAUP + N
*
*        Bidiagonalize R in A.
*        (Workspace: need 3*N+MM, prefer 3*N+(MM+N)*NB)
*
         CALL DGEBRD( MM, N, A, LDA, S, WORK( IE ), WORK( ITAUQ ),
     $                WORK( ITAUP ), WORK( NWORK ), LWORK-NWORK+1,
     $                INFO )
*
*        Multiply B by transpose of left bidiagonalizing vectors of R.
*        (Workspace: need 3*N+NRHS, prefer 3*N+NRHS*NB)
*
         CALL DORMBR( 'Q', 'L', 'T', MM, NRHS, N, A, LDA, WORK( ITAUQ ),
     $                B, LDB, WORK( NWORK ), LWORK-NWORK+1, INFO )
*
*        Solve the bidiagonal least squares problem.
*
         CALL DLALSD( 'U', SMLSIZ, N, NRHS, S, WORK( IE ), B, LDB,
     $                RCOND, RANK, WORK( NWORK ), IWORK, INFO )
         IF( INFO.NE.0 ) THEN
            GO TO 10
         END IF
*
*        Multiply B by right bidiagonalizing vectors of R.
*
         CALL DORMBR( 'P', 'L', 'N', N, NRHS, N, A, LDA, WORK( ITAUP ),
     $                B, LDB, WORK( NWORK ), LWORK-NWORK+1, INFO )
*
      ELSE IF( N.GE.MNTHR .AND. LWORK.GE.4*M+M*M+
     $         MAX( M, 2*M-4, NRHS, N-3*M, WLALSD ) ) THEN
*
*        Path 2a - underdetermined, with many more columns than rows
*        and sufficient workspace for an efficient algorithm.
*
         LDWORK = M
         IF( LWORK.GE.MAX( 4*M+M*LDA+MAX( M, 2*M-4, NRHS, N-3*M ),
     $       M*LDA+M+M*NRHS, 4*M+M*LDA+WLALSD ) )LDWORK = LDA
         ITAU = 1
         NWORK = M + 1
*
*        Compute A=L*Q.
*        (Workspace: need 2*M, prefer M+M*NB)
*
         CALL DGELQF( M, N, A, LDA, WORK( ITAU ), WORK( NWORK ),
     $                LWORK-NWORK+1, INFO )
         IL = NWORK
*
*        Copy L to WORK(IL), zeroing out above its diagonal.
*
         CALL DLACPY( 'L', M, M, A, LDA, WORK( IL ), LDWORK )
         CALL DLASET( 'U', M-1, M-1, ZERO, ZERO, WORK( IL+LDWORK ),
     $                LDWORK )
         IE = IL + LDWORK*M
         ITAUQ = IE + M
         ITAUP = ITAUQ + M
         NWORK = ITAUP + M
*
*        Bidiagonalize L in WORK(IL).
*        (Workspace: need M*M+5*M, prefer M*M+4*M+2*M*NB)
*
         CALL DGEBRD( M, M, WORK( IL ), LDWORK, S, WORK( IE ),
     $                WORK( ITAUQ ), WORK( ITAUP ), WORK( NWORK ),
     $                LWORK-NWORK+1, INFO )
*
*        Multiply B by transpose of left bidiagonalizing vectors of L.
*        (Workspace: need M*M+4*M+NRHS, prefer M*M+4*M+NRHS*NB)
*
         CALL DORMBR( 'Q', 'L', 'T', M, NRHS, M, WORK( IL ), LDWORK,
     $                WORK( ITAUQ ), B, LDB, WORK( NWORK ),
     $                LWORK-NWORK+1, INFO )
*
*        Solve the bidiagonal least squares problem.
*
         CALL DLALSD( 'U', SMLSIZ, M, NRHS, S, WORK( IE ), B, LDB,
     $                RCOND, RANK, WORK( NWORK ), IWORK, INFO )
         IF( INFO.NE.0 ) THEN
            GO TO 10
         END IF
*
*        Multiply B by right bidiagonalizing vectors of L.
*
         CALL DORMBR( 'P', 'L', 'N', M, NRHS, M, WORK( IL ), LDWORK,
     $                WORK( ITAUP ), B, LDB, WORK( NWORK ),
     $                LWORK-NWORK+1, INFO )
*
*        Zero out below first M rows of B.
*
         CALL DLASET( 'F', N-M, NRHS, ZERO, ZERO, B( M+1, 1 ), LDB )
         NWORK = ITAU + M
*
*        Multiply transpose(Q) by B.
*        (Workspace: need M+NRHS, prefer M+NRHS*NB)
*
         CALL DORMLQ( 'L', 'T', N, NRHS, M, A, LDA, WORK( ITAU ), B,
     $                LDB, WORK( NWORK ), LWORK-NWORK+1, INFO )
*
      ELSE
*
*        Path 2 - remaining underdetermined cases.
*
         IE = 1
         ITAUQ = IE + M
         ITAUP = ITAUQ + M
         NWORK = ITAUP + M
*
*        Bidiagonalize A.
*        (Workspace: need 3*M+N, prefer 3*M+(M+N)*NB)
*
         CALL DGEBRD( M, N, A, LDA, S, WORK( IE ), WORK( ITAUQ ),
     $                WORK( ITAUP ), WORK( NWORK ), LWORK-NWORK+1,
     $                INFO )
*
*        Multiply B by transpose of left bidiagonalizing vectors.
*        (Workspace: need 3*M+NRHS, prefer 3*M+NRHS*NB)
*
         CALL DORMBR( 'Q', 'L', 'T', M, NRHS, N, A, LDA, WORK( ITAUQ ),
     $                B, LDB, WORK( NWORK ), LWORK-NWORK+1, INFO )
*
*        Solve the bidiagonal least squares problem.
*
         CALL DLALSD( 'L', SMLSIZ, M, NRHS, S, WORK( IE ), B, LDB,
     $                RCOND, RANK, WORK( NWORK ), IWORK, INFO )
         IF( INFO.NE.0 ) THEN
            GO TO 10
         END IF
*
*        Multiply B by right bidiagonalizing vectors of A.
*
         CALL DORMBR( 'P', 'L', 'N', N, NRHS, M, A, LDA, WORK( ITAUP ),
     $                B, LDB, WORK( NWORK ), LWORK-NWORK+1, INFO )
*
      END IF
*
*     Undo scaling.
*
      IF( IASCL.EQ.1 ) THEN
         CALL DLASCL( '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 DLASCL( '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 DLASCL( 'G', 0, 0, SMLNUM, BNRM, N, NRHS, B, LDB, INFO )
      ELSE IF( IBSCL.EQ.2 ) THEN
         CALL DLASCL( 'G', 0, 0, BIGNUM, BNRM, N, NRHS, B, LDB, INFO )
      END IF
*
   10 CONTINUE
      WORK( 1 ) = MAXWRK
      RETURN
*
*     End of DGELSD
*
      END