dgees.f.html

来自「famous linear algebra library (LAPACK) p」· HTML 代码 · 共 459 行 · 第 1/3 页

</span><span class="comment">*</span><span class="comment">                   could also be caused by underflow due to scaling.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Parameters ..
</span>      DOUBLE PRECISION   ZERO, ONE
      PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      LOGICAL            CURSL, LASTSL, LQUERY, LST2SL, SCALEA, WANTST,
     $                   WANTVS
      INTEGER            HSWORK, I, I1, I2, IBAL, ICOND, IERR, IEVAL,
     $                   IHI, ILO, INXT, IP, ITAU, IWRK, MAXWRK, MINWRK
      DOUBLE PRECISION   ANRM, BIGNUM, CSCALE, EPS, S, SEP, SMLNUM
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Arrays ..
</span>      INTEGER            IDUM( 1 )
      DOUBLE PRECISION   DUM( 1 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           DCOPY, <a name="DGEBAK.155"></a><a href="dgebak.f.html#DGEBAK.1">DGEBAK</a>, <a name="DGEBAL.155"></a><a href="dgebal.f.html#DGEBAL.1">DGEBAL</a>, <a name="DGEHRD.155"></a><a href="dgehrd.f.html#DGEHRD.1">DGEHRD</a>, <a name="DHSEQR.155"></a><a href="dhseqr.f.html#DHSEQR.1">DHSEQR</a>, <a name="DLACPY.155"></a><a href="dlacpy.f.html#DLACPY.1">DLACPY</a>,
     $                   <a name="DLABAD.156"></a><a href="dlabad.f.html#DLABAD.1">DLABAD</a>, <a name="DLASCL.156"></a><a href="dlascl.f.html#DLASCL.1">DLASCL</a>, <a name="DORGHR.156"></a><a href="dorghr.f.html#DORGHR.1">DORGHR</a>, DSWAP, <a name="DTRSEN.156"></a><a href="dtrsen.f.html#DTRSEN.1">DTRSEN</a>, <a name="XERBLA.156"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.159"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      INTEGER            <a name="ILAENV.160"></a><a href="hfy-index.html#ILAENV">ILAENV</a>
      DOUBLE PRECISION   <a name="DLAMCH.161"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>, <a name="DLANGE.161"></a><a href="dlange.f.html#DLANGE.1">DLANGE</a>
      EXTERNAL           <a name="LSAME.162"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, <a name="ILAENV.162"></a><a href="hfy-index.html#ILAENV">ILAENV</a>, <a name="DLAMCH.162"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>, <a name="DLANGE.162"></a><a href="dlange.f.html#DLANGE.1">DLANGE</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          MAX, SQRT
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Test the input arguments
</span><span class="comment">*</span><span class="comment">
</span>      INFO = 0
      LQUERY = ( LWORK.EQ.-1 )
      WANTVS = <a name="LSAME.173"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBVS, <span class="string">'V'</span> )
      WANTST = <a name="LSAME.174"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( SORT, <span class="string">'S'</span> )
      IF( ( .NOT.WANTVS ) .AND. ( .NOT.<a name="LSAME.175"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBVS, <span class="string">'N'</span> ) ) ) THEN
         INFO = -1
      ELSE IF( ( .NOT.WANTST ) .AND. ( .NOT.<a name="LSAME.177"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( SORT, <span class="string">'N'</span> ) ) ) THEN
         INFO = -2
      ELSE IF( N.LT.0 ) THEN
         INFO = -4
      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
         INFO = -6
      ELSE IF( LDVS.LT.1 .OR. ( WANTVS .AND. LDVS.LT.N ) ) THEN
         INFO = -11
      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.192"></a><a href="hfy-index.html#ILAENV">ILAENV</a>.
</span><span class="comment">*</span><span class="comment">       HSWORK refers to the workspace preferred by <a name="DHSEQR.193"></a><a href="dhseqr.f.html#DHSEQR.1">DHSEQR</a>, as
</span><span class="comment">*</span><span class="comment">       calculated below. HSWORK is computed assuming ILO=1 and IHI=N,
</span><span class="comment">*</span><span class="comment">       the worst case.)
</span><span class="comment">*</span><span class="comment">
</span>      IF( INFO.EQ.0 ) THEN
         IF( N.EQ.0 ) THEN
            MINWRK = 1
            MAXWRK = 1
         ELSE
            MAXWRK = 2*N + N*<a name="ILAENV.202"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="DGEHRD.202"></a><a href="dgehrd.f.html#DGEHRD.1">DGEHRD</a>'</span>, <span class="string">' '</span>, N, 1, N, 0 )
            MINWRK = 3*N
<span class="comment">*</span><span class="comment">
</span>            CALL <a name="DHSEQR.205"></a><a href="dhseqr.f.html#DHSEQR.1">DHSEQR</a>( <span class="string">'S'</span>, JOBVS, N, 1, N, A, LDA, WR, WI, VS, LDVS,
     $             WORK, -1, IEVAL )
            HSWORK = WORK( 1 )
<span class="comment">*</span><span class="comment">
</span>            IF( .NOT.WANTVS ) THEN
               MAXWRK = MAX( MAXWRK, N + HSWORK )
            ELSE
               MAXWRK = MAX( MAXWRK, 2*N + ( N - 1 )*<a name="ILAENV.212"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1,
     $                       <span class="string">'<a name="DORGHR.213"></a><a href="dorghr.f.html#DORGHR.1">DORGHR</a>'</span>, <span class="string">' '</span>, N, 1, N, -1 ) )
               MAXWRK = MAX( MAXWRK, N + HSWORK )
            END IF
         END IF
         WORK( 1 ) = MAXWRK
<span class="comment">*</span><span class="comment">
</span>         IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
            INFO = -13
         END IF
      END IF
<span class="comment">*</span><span class="comment">
</span>      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.225"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="DGEES.225"></a><a href="dgees.f.html#DGEES.1">DGEES</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( N.EQ.0 ) THEN
         SDIM = 0
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Get machine constants
</span><span class="comment">*</span><span class="comment">
</span>      EPS = <a name="DLAMCH.240"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>( <span class="string">'P'</span> )
      SMLNUM = <a name="DLAMCH.241"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>( <span class="string">'S'</span> )
      BIGNUM = ONE / SMLNUM
      CALL <a name="DLABAD.243"></a><a href="dlabad.f.html#DLABAD.1">DLABAD</a>( SMLNUM, BIGNUM )
      SMLNUM = SQRT( SMLNUM ) / EPS
      BIGNUM = ONE / SMLNUM
<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="DLANGE.249"></a><a href="dlange.f.html#DLANGE.1">DLANGE</a>( <span class="string">'M'</span>, N, N, A, LDA, DUM )
      SCALEA = .FALSE.
      IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
         SCALEA = .TRUE.
         CSCALE = SMLNUM
      ELSE IF( ANRM.GT.BIGNUM ) THEN
         SCALEA = .TRUE.
         CSCALE = BIGNUM
      END IF
      IF( SCALEA )
     $   CALL <a name="DLASCL.259"></a><a href="dlascl.f.html#DLASCL.1">DLASCL</a>( <span class="string">'G'</span>, 0, 0, ANRM, CSCALE, N, N, A, LDA, IERR )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Permute the matrix to make it more nearly triangular
</span><span class="comment">*</span><span class="comment">     (Workspace: need N)
</span><span class="comment">*</span><span class="comment">
</span>      IBAL = 1
      CALL <a name="DGEBAL.265"></a><a href="dgebal.f.html#DGEBAL.1">DGEBAL</a>( <span class="string">'P'</span>, N, A, LDA, ILO, IHI, WORK( IBAL ), IERR )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Reduce to upper Hessenberg form
</span><span class="comment">*</span><span class="comment">     (Workspace: need 3*N, prefer 2*N+N*NB)
</span><span class="comment">*</span><span class="comment">
</span>      ITAU = N + IBAL
      IWRK = N + ITAU
      CALL <a name="DGEHRD.272"></a><a href="dgehrd.f.html#DGEHRD.1">DGEHRD</a>( N, ILO, IHI, A, LDA, WORK( ITAU ), WORK( IWRK ),
     $             LWORK-IWRK+1, IERR )
<span class="comment">*</span><span class="comment">
</span>      IF( WANTVS ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Copy Householder vectors to VS
</span><span class="comment">*</span><span class="comment">
</span>         CALL <a name="DLACPY.279"></a><a href="dlacpy.f.html#DLACPY.1">DLACPY</a>( <span class="string">'L'</span>, N, N, A, LDA, VS, LDVS )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Generate orthogonal matrix in VS
</span><span class="comment">*</span><span class="comment">        (Workspace: need 3*N-1, prefer 2*N+(N-1)*NB)
</span><span class="comment">*</span><span class="comment">
</span>         CALL <a name="DORGHR.284"></a><a href="dorghr.f.html#DORGHR.1">DORGHR</a>( N, ILO, IHI, VS, LDVS, WORK( ITAU ), WORK( IWRK ),
     $                LWORK-IWRK+1, IERR )
      END IF
<span class="comment">*</span><span class="comment">