zgelss.f.html

来自「famous linear algebra library (LAPACK) p」· HTML 代码 · 共 659 行 · 第 1/4 页

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         INFO = -2
      ELSE IF( NRHS.LT.0 ) THEN
         INFO = -3
      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">       CWorkspace refers to complex workspace, and RWorkspace refers
</span><span class="comment">*</span><span class="comment">       to real workspace. NB refers to the optimal block size for the
</span><span class="comment">*</span><span class="comment">       immediately following subroutine, as returned by <a name="ILAENV.162"></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.169"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 6, <span class="string">'<a name="ZGELSS.169"></a><a href="zgelss.f.html#ZGELSS.1">ZGELSS</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.176"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="ZGEQRF.176"></a><a href="zgeqrf.f.html#ZGEQRF.1">ZGEQRF</a>'</span>, <span class="string">' '</span>, M,
     $                       N, -1, -1 ) )
               MAXWRK = MAX( MAXWRK, N + NRHS*<a name="ILAENV.178"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="ZUNMQR.178"></a><a href="zunmqr.f.html#ZUNMQR.1">ZUNMQR</a>'</span>, <span class="string">'LC'</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>               MAXWRK = MAX( MAXWRK, 2*N + ( MM + N )*<a name="ILAENV.185"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1,
     $                       <span class="string">'<a name="ZGEBRD.186"></a><a href="zgebrd.f.html#ZGEBRD.1">ZGEBRD</a>'</span>, <span class="string">' '</span>, MM, N, -1, -1 ) )
               MAXWRK = MAX( MAXWRK, 2*N + NRHS*<a name="ILAENV.187"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="ZUNMBR.187"></a><a href="zunmbr.f.html#ZUNMBR.1">ZUNMBR</a>'</span>,
     $                       <span class="string">'QLC'</span>, MM, NRHS, N, -1 ) )
               MAXWRK = MAX( MAXWRK, 2*N + ( N - 1 )*<a name="ILAENV.189"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1,
     $                       <span class="string">'<a name="ZUNGBR.190"></a><a href="zungbr.f.html#ZUNGBR.1">ZUNGBR</a>'</span>, <span class="string">'P'</span>, N, N, N, -1 ) )
               MAXWRK = MAX( MAXWRK, N*NRHS )
               MINWRK = 2*N + MAX( NRHS, M )
            END IF
            IF( N.GT.M ) THEN
               MINWRK = 2*M + MAX( NRHS, N )
               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.201"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="ZGELQF.201"></a><a href="zgelqf.f.html#ZGELQF.1">ZGELQF</a>'</span>, <span class="string">' '</span>, M, N, -1,
     $                     -1 )
                  MAXWRK = MAX( MAXWRK, 3*M + M*M + 2*M*<a name="ILAENV.203"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1,
     $                          <span class="string">'<a name="ZGEBRD.204"></a><a href="zgebrd.f.html#ZGEBRD.1">ZGEBRD</a>'</span>, <span class="string">' '</span>, M, M, -1, -1 ) )
                  MAXWRK = MAX( MAXWRK, 3*M + M*M + NRHS*<a name="ILAENV.205"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1,
     $                          <span class="string">'<a name="ZUNMBR.206"></a><a href="zunmbr.f.html#ZUNMBR.1">ZUNMBR</a>'</span>, <span class="string">'QLC'</span>, M, NRHS, M, -1 ) )
                  MAXWRK = MAX( MAXWRK, 3*M + M*M + ( M - 1 )*<a name="ILAENV.207"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1,
     $                          <span class="string">'<a name="ZUNGBR.208"></a><a href="zungbr.f.html#ZUNGBR.1">ZUNGBR</a>'</span>, <span class="string">'P'</span>, M, M, M, -1 ) )
                  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.214"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="ZUNMLQ.214"></a><a href="zunmlq.f.html#ZUNMLQ.1">ZUNMLQ</a>'</span>,
     $                          <span class="string">'LC'</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 = 2*M + ( N + M )*<a name="ILAENV.220"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="ZGEBRD.220"></a><a href="zgebrd.f.html#ZGEBRD.1">ZGEBRD</a>'</span>, <span class="string">' '</span>, M,
     $                     N, -1, -1 )
                  MAXWRK = MAX( MAXWRK, 2*M + NRHS*<a name="ILAENV.222"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="ZUNMBR.222"></a><a href="zunmbr.f.html#ZUNMBR.1">ZUNMBR</a>'</span>,
     $                          <span class="string">'QLC'</span>, M, NRHS, M, -1 ) )
                  MAXWRK = MAX( MAXWRK, 2*M + M*<a name="ILAENV.224"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="ZUNGBR.224"></a><a href="zungbr.f.html#ZUNGBR.1">ZUNGBR</a>'</span>,
     $                          <span class="string">'P'</span>, M, N, M, -1 ) )
                  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.238"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="ZGELSS.238"></a><a href="zgelss.f.html#ZGELSS.1">ZGELSS</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="DLAMCH.253"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>( <span class="string">'P'</span> )
      SFMIN = <a name="DLAMCH.254"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>( <span class="string">'S'</span> )
      SMLNUM = SFMIN / EPS
      BIGNUM = ONE / SMLNUM
      CALL <a name="DLABAD.257"></a><a href="dlabad.f.html#DLABAD.1">DLABAD</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="ZLANGE.261"></a><a href="zlange.f.html#ZLANGE.1">ZLANGE</a>( <span class="string">'M'</span>, M, N, A, LDA, RWORK )
      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="ZLASCL.267"></a><a href="zlascl.f.html#ZLASCL.1">ZLASCL</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="ZLASCL.273"></a><a href="zlascl.f.html#ZLASCL.1">ZLASCL</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="ZLASET.279"></a><a href="zlaset.f.html#ZLASET.1">ZLASET</a>( <span class="string">'F'</span>, MAX( M, N ), NRHS, CZERO, CZERO, B, LDB )
         CALL <a name="DLASET.280"></a><a href="dlaset.f.html#DLASET.1">DLASET</a>( <span class="string">'F'</span>, MINMN, 1, ZERO, ZERO, S, MINMN )
         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="ZLANGE.287"></a><a href="zlange.f.html#ZLANGE.1">ZLANGE</a>( <span class="string">'M'</span>, M, NRHS, B, LDB, RWORK )
      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="ZLASCL.293"></a><a href="zlascl.f.html#ZLASCL.1">ZLASCL</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="ZLASCL.299"></a><a href="zlascl.f.html#ZLASCL.1">ZLASCL</a>( <span class="string">'G'</span>, 0, 0, BNRM, BIGNUM, M, NRHS, B, LDB, INFO )
         IBSCL = 2
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Overdetermined case
</span><span class="comment">*</span><span class="comment">
</span>      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>         MM = M
         IF( M.GE.MNTHR ) THEN
<span class="comment">*</span><span class="comment">
1234

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