sgelss.f.html

来自「famous linear algebra library (LAPACK) p」· HTML 代码 · 共 642 行 · 第 1/4 页

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      ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
         INFO = -5
      ELSE IF( LDB.LT.MAX( 1, MAXMN ) ) THEN
         INFO = -7
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Compute workspace
</span><span class="comment">*</span><span class="comment">      (Note: Comments in the code beginning &quot;Workspace:&quot; describe the
</span><span class="comment">*</span><span class="comment">       minimal amount of workspace needed at that point in the code,
</span><span class="comment">*</span><span class="comment">       as well as the preferred amount for good performance.
</span><span class="comment">*</span><span class="comment">       NB refers to the optimal block size for the immediately
</span><span class="comment">*</span><span class="comment">       following subroutine, as returned by <a name="ILAENV.154"></a><a href="hfy-index.html#ILAENV">ILAENV</a>.)
</span><span class="comment">*</span><span class="comment">
</span>      IF( INFO.EQ.0 ) THEN
         MINWRK = 1
         MAXWRK = 1
         IF( MINMN.GT.0 ) THEN
            MM = M
            MNTHR = <a name="ILAENV.161"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 6, <span class="string">'<a name="SGELSS.161"></a><a href="sgelss.f.html#SGELSS.1">SGELSS</a>'</span>, <span class="string">' '</span>, M, N, NRHS, -1 )
            IF( M.GE.N .AND. M.GE.MNTHR ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Path 1a - overdetermined, with many more rows than
</span><span class="comment">*</span><span class="comment">                        columns
</span><span class="comment">*</span><span class="comment">
</span>               MM = N
               MAXWRK = MAX( MAXWRK, N + N*<a name="ILAENV.168"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="SGEQRF.168"></a><a href="sgeqrf.f.html#SGEQRF.1">SGEQRF</a>'</span>, <span class="string">' '</span>, M,
     $                       N, -1, -1 ) )
               MAXWRK = MAX( MAXWRK, N + NRHS*<a name="ILAENV.170"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="SORMQR.170"></a><a href="sormqr.f.html#SORMQR.1">SORMQR</a>'</span>, <span class="string">'LT'</span>,
     $                       M, NRHS, N, -1 ) )
            END IF
            IF( M.GE.N ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Path 1 - overdetermined or exactly determined
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Compute workspace needed for <a name="SBDSQR.177"></a><a href="sbdsqr.f.html#SBDSQR.1">SBDSQR</a>
</span><span class="comment">*</span><span class="comment">
</span>               BDSPAC = MAX( 1, 5*N )
               MAXWRK = MAX( MAXWRK, 3*N + ( MM + N )*<a name="ILAENV.180"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1,
     $                       <span class="string">'<a name="SGEBRD.181"></a><a href="sgebrd.f.html#SGEBRD.1">SGEBRD</a>'</span>, <span class="string">' '</span>, MM, N, -1, -1 ) )
               MAXWRK = MAX( MAXWRK, 3*N + NRHS*<a name="ILAENV.182"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="SORMBR.182"></a><a href="sormbr.f.html#SORMBR.1">SORMBR</a>'</span>,
     $                       <span class="string">'QLT'</span>, MM, NRHS, N, -1 ) )
               MAXWRK = MAX( MAXWRK, 3*N + ( N - 1 )*<a name="ILAENV.184"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1,
     $                       <span class="string">'<a name="SORGBR.185"></a><a href="sorgbr.f.html#SORGBR.1">SORGBR</a>'</span>, <span class="string">'P'</span>, N, N, N, -1 ) )
               MAXWRK = MAX( MAXWRK, BDSPAC )
               MAXWRK = MAX( MAXWRK, N*NRHS )
               MINWRK = MAX( 3*N + MM, 3*N + NRHS, BDSPAC )
               MAXWRK = MAX( MINWRK, MAXWRK )
            END IF
            IF( N.GT.M ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Compute workspace needed for <a name="SBDSQR.193"></a><a href="sbdsqr.f.html#SBDSQR.1">SBDSQR</a>
</span><span class="comment">*</span><span class="comment">
</span>               BDSPAC = MAX( 1, 5*M )
               MINWRK = MAX( 3*M+NRHS, 3*M+N, BDSPAC )
               IF( N.GE.MNTHR ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                 Path 2a - underdetermined, with many more columns
</span><span class="comment">*</span><span class="comment">                 than rows
</span><span class="comment">*</span><span class="comment">
</span>                  MAXWRK = M + M*<a name="ILAENV.202"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="SGELQF.202"></a><a href="sgelqf.f.html#SGELQF.1">SGELQF</a>'</span>, <span class="string">' '</span>, M, N, -1,
     $                                  -1 )
                  MAXWRK = MAX( MAXWRK, M*M + 4*M + 2*M*<a name="ILAENV.204"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1,
     $                          <span class="string">'<a name="SGEBRD.205"></a><a href="sgebrd.f.html#SGEBRD.1">SGEBRD</a>'</span>, <span class="string">' '</span>, M, M, -1, -1 ) )
                  MAXWRK = MAX( MAXWRK, M*M + 4*M + NRHS*<a name="ILAENV.206"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1,
     $                          <span class="string">'<a name="SORMBR.207"></a><a href="sormbr.f.html#SORMBR.1">SORMBR</a>'</span>, <span class="string">'QLT'</span>, M, NRHS, M, -1 ) )
                  MAXWRK = MAX( MAXWRK, M*M + 4*M +
     $                          ( M - 1 )*<a name="ILAENV.209"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="SORGBR.209"></a><a href="sorgbr.f.html#SORGBR.1">SORGBR</a>'</span>, <span class="string">'P'</span>, M,
     $                          M, M, -1 ) )
                  MAXWRK = MAX( MAXWRK, M*M + M + BDSPAC )
                  IF( NRHS.GT.1 ) THEN
                     MAXWRK = MAX( MAXWRK, M*M + M + M*NRHS )
                  ELSE
                     MAXWRK = MAX( MAXWRK, M*M + 2*M )
                  END IF
                  MAXWRK = MAX( MAXWRK, M + NRHS*<a name="ILAENV.217"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="SORMLQ.217"></a><a href="sormlq.f.html#SORMLQ.1">SORMLQ</a>'</span>,
     $                          <span class="string">'LT'</span>, N, NRHS, M, -1 ) )
               ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                 Path 2 - underdetermined
</span><span class="comment">*</span><span class="comment">
</span>                  MAXWRK = 3*M + ( N + M )*<a name="ILAENV.223"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="SGEBRD.223"></a><a href="sgebrd.f.html#SGEBRD.1">SGEBRD</a>'</span>, <span class="string">' '</span>, M,
     $                     N, -1, -1 )
                  MAXWRK = MAX( MAXWRK, 3*M + NRHS*<a name="ILAENV.225"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="SORMBR.225"></a><a href="sormbr.f.html#SORMBR.1">SORMBR</a>'</span>,
     $                          <span class="string">'QLT'</span>, M, NRHS, M, -1 ) )
                  MAXWRK = MAX( MAXWRK, 3*M + M*<a name="ILAENV.227"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="SORGBR.227"></a><a href="sorgbr.f.html#SORGBR.1">SORGBR</a>'</span>,
     $                          <span class="string">'P'</span>, M, N, M, -1 ) )
                  MAXWRK = MAX( MAXWRK, BDSPAC )
                  MAXWRK = MAX( MAXWRK, N*NRHS )
               END IF
            END IF
            MAXWRK = MAX( MINWRK, MAXWRK )
         END IF
         WORK( 1 ) = MAXWRK
<span class="comment">*</span><span class="comment">
</span>         IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY )
     $      INFO = -12
      END IF
<span class="comment">*</span><span class="comment">
</span>      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.242"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="SGELSS.242"></a><a href="sgelss.f.html#SGELSS.1">SGELSS</a>'</span>, -INFO )
         RETURN
      ELSE IF( LQUERY ) THEN
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Quick return if possible
</span><span class="comment">*</span><span class="comment">
</span>      IF( M.EQ.0 .OR. N.EQ.0 ) THEN
         RANK = 0
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Get machine parameters
</span><span class="comment">*</span><span class="comment">
</span>      EPS = <a name="SLAMCH.257"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>( <span class="string">'P'</span> )
      SFMIN = <a name="SLAMCH.258"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>( <span class="string">'S'</span> )
      SMLNUM = SFMIN / EPS
      BIGNUM = ONE / SMLNUM
      CALL <a name="SLABAD.261"></a><a href="slabad.f.html#SLABAD.1">SLABAD</a>( SMLNUM, BIGNUM )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Scale A if max element outside range [SMLNUM,BIGNUM]
</span><span class="comment">*</span><span class="comment">
</span>      ANRM = <a name="SLANGE.265"></a><a href="slange.f.html#SLANGE.1">SLANGE</a>( <span class="string">'M'</span>, M, N, A, LDA, WORK )
      IASCL = 0
      IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Scale matrix norm up to SMLNUM
</span><span class="comment">*</span><span class="comment">
</span>         CALL <a name="SLASCL.271"></a><a href="slascl.f.html#SLASCL.1">SLASCL</a>( <span class="string">'G'</span>, 0, 0, ANRM, SMLNUM, M, N, A, LDA, INFO )
         IASCL = 1
      ELSE IF( ANRM.GT.BIGNUM ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Scale matrix norm down to BIGNUM
</span><span class="comment">*</span><span class="comment">
</span>         CALL <a name="SLASCL.277"></a><a href="slascl.f.html#SLASCL.1">SLASCL</a>( <span class="string">'G'</span>, 0, 0, ANRM, BIGNUM, M, N, A, LDA, INFO )
         IASCL = 2
      ELSE IF( ANRM.EQ.ZERO ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Matrix all zero. Return zero solution.
</span><span class="comment">*</span><span class="comment">
</span>         CALL <a name="SLASET.283"></a><a href="slaset.f.html#SLASET.1">SLASET</a>( <span class="string">'F'</span>, MAX( M, N ), NRHS, ZERO, ZERO, B, LDB )
         CALL <a name="SLASET.284"></a><a href="slaset.f.html#SLASET.1">SLASET</a>( <span class="string">'F'</span>, MINMN, 1, ZERO, ZERO, S, 1 )
         RANK = 0
         GO TO 70
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Scale B if max element outside range [SMLNUM,BIGNUM]
</span><span class="comment">*</span><span class="comment">
</span>      BNRM = <a name="SLANGE.291"></a><a href="slange.f.html#SLANGE.1">SLANGE</a>( <span class="string">'M'</span>, M, NRHS, B, LDB, WORK )
      IBSCL = 0
      IF( BNRM.GT.ZERO .AND. BNRM.LT.SMLNUM ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Scale matrix norm up to SMLNUM
</span><span class="comment">*</span><span class="comment">
</span>         CALL <a name="SLASCL.297"></a><a href="slascl.f.html#SLASCL.1">SLASCL</a>( <span class="string">'G'</span>, 0, 0, BNRM, SMLNUM, M, NRHS, B, LDB, INFO )
         IBSCL = 1
      ELSE IF( BNRM.GT.BIGNUM ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Scale matrix norm down to BIGNUM
</span><span class="comment">*</span><span class="comment">
</span>         CALL <a name="SLASCL.303"></a><a href="slascl.f.html#SLASCL.1">SLASCL</a>( <span class="string">'G'</span>, 0, 0, BNRM, BIGNUM, M, NRHS, B, LDB, INFO )
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