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来自「famous linear algebra library (LAPACK) p」· HTML 代码 · 共 713 行 · 第 1/5 页

</span><span class="comment">*</span><span class="comment">          and no other work except argument checking is performed.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  RWORK   (workspace) DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
</span><span class="comment">*</span><span class="comment">          If JOBZ = 'N', LRWORK &gt;= 5*min(M,N).
</span><span class="comment">*</span><span class="comment">          Otherwise, LRWORK &gt;= 5*min(M,N)*min(M,N) + 7*min(M,N)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  IWORK   (workspace) INTEGER array, dimension (8*min(M,N))
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  INFO    (output) INTEGER
</span><span class="comment">*</span><span class="comment">          = 0:  successful exit.
</span><span class="comment">*</span><span class="comment">          &lt; 0:  if INFO = -i, the i-th argument had an illegal value.
</span><span class="comment">*</span><span class="comment">          &gt; 0:  The updating process of <a name="DBDSDC.136"></a><a href="dbdsdc.f.html#DBDSDC.1">DBDSDC</a> did not converge.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Further Details
</span><span class="comment">*</span><span class="comment">  ===============
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Based on contributions by
</span><span class="comment">*</span><span class="comment">     Ming Gu and Huan Ren, Computer Science Division, University of
</span><span class="comment">*</span><span class="comment">     California at Berkeley, USA
</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>      INTEGER            LQUERV
      PARAMETER          ( LQUERV = -1 )
      COMPLEX*16         CZERO, CONE
      PARAMETER          ( CZERO = ( 0.0D+0, 0.0D+0 ),
     $                   CONE = ( 1.0D+0, 0.0D+0 ) )
      DOUBLE PRECISION   ZERO, ONE
      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      LOGICAL            WNTQA, WNTQAS, WNTQN, WNTQO, WNTQS
      INTEGER            BLK, CHUNK, I, IE, IERR, IL, IR, IRU, IRVT,
     $                   ISCL, ITAU, ITAUP, ITAUQ, IU, IVT, LDWKVT,
     $                   LDWRKL, LDWRKR, LDWRKU, MAXWRK, MINMN, MINWRK,
     $                   MNTHR1, MNTHR2, NRWORK, NWORK, WRKBL
      DOUBLE PRECISION   ANRM, BIGNUM, EPS, 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           <a name="DBDSDC.169"></a><a href="dbdsdc.f.html#DBDSDC.1">DBDSDC</a>, <a name="DLASCL.169"></a><a href="dlascl.f.html#DLASCL.1">DLASCL</a>, <a name="XERBLA.169"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>, <a name="ZGEBRD.169"></a><a href="zgebrd.f.html#ZGEBRD.1">ZGEBRD</a>, <a name="ZGELQF.169"></a><a href="zgelqf.f.html#ZGELQF.1">ZGELQF</a>, ZGEMM,
     $                   <a name="ZGEQRF.170"></a><a href="zgeqrf.f.html#ZGEQRF.1">ZGEQRF</a>, <a name="ZLACP2.170"></a><a href="zlacp2.f.html#ZLACP2.1">ZLACP2</a>, <a name="ZLACPY.170"></a><a href="zlacpy.f.html#ZLACPY.1">ZLACPY</a>, <a name="ZLACRM.170"></a><a href="zlacrm.f.html#ZLACRM.1">ZLACRM</a>, <a name="ZLARCM.170"></a><a href="zlarcm.f.html#ZLARCM.1">ZLARCM</a>, <a name="ZLASCL.170"></a><a href="zlascl.f.html#ZLASCL.1">ZLASCL</a>,
     $                   <a name="ZLASET.171"></a><a href="zlaset.f.html#ZLASET.1">ZLASET</a>, <a name="ZUNGBR.171"></a><a href="zungbr.f.html#ZUNGBR.1">ZUNGBR</a>, <a name="ZUNGLQ.171"></a><a href="zunglq.f.html#ZUNGLQ.1">ZUNGLQ</a>, <a name="ZUNGQR.171"></a><a href="zungqr.f.html#ZUNGQR.1">ZUNGQR</a>, <a name="ZUNMBR.171"></a><a href="zunmbr.f.html#ZUNMBR.1">ZUNMBR</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.174"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      INTEGER            <a name="ILAENV.175"></a><a href="hfy-index.html#ILAENV">ILAENV</a>
      DOUBLE PRECISION   <a name="DLAMCH.176"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>, <a name="ZLANGE.176"></a><a href="zlange.f.html#ZLANGE.1">ZLANGE</a>
      EXTERNAL           <a name="LSAME.177"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, <a name="ILAENV.177"></a><a href="hfy-index.html#ILAENV">ILAENV</a>, <a name="DLAMCH.177"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>, <a name="ZLANGE.177"></a><a href="zlange.f.html#ZLANGE.1">ZLANGE</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          INT, MAX, MIN, 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
      MINMN = MIN( M, N )
      MNTHR1 = INT( MINMN*17.0D0 / 9.0D0 )
      MNTHR2 = INT( MINMN*5.0D0 / 3.0D0 )
      WNTQA = <a name="LSAME.190"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBZ, <span class="string">'A'</span> )
      WNTQS = <a name="LSAME.191"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBZ, <span class="string">'S'</span> )
      WNTQAS = WNTQA .OR. WNTQS
      WNTQO = <a name="LSAME.193"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBZ, <span class="string">'O'</span> )
      WNTQN = <a name="LSAME.194"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBZ, <span class="string">'N'</span> )
      MINWRK = 1
      MAXWRK = 1
<span class="comment">*</span><span class="comment">
</span>      IF( .NOT.( WNTQA .OR. WNTQS .OR. WNTQO .OR. WNTQN ) ) THEN
         INFO = -1
      ELSE IF( M.LT.0 ) THEN
         INFO = -2
      ELSE IF( N.LT.0 ) THEN
         INFO = -3
      ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
         INFO = -5
      ELSE IF( LDU.LT.1 .OR. ( WNTQAS .AND. LDU.LT.M ) .OR.
     $         ( WNTQO .AND. M.LT.N .AND. LDU.LT.M ) ) THEN
         INFO = -8
      ELSE IF( LDVT.LT.1 .OR. ( WNTQA .AND. LDVT.LT.N ) .OR.
     $         ( WNTQS .AND. LDVT.LT.MINMN ) .OR.
     $         ( WNTQO .AND. M.GE.N .AND. LDVT.LT.N ) ) THEN
         INFO = -10
      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 to
</span><span class="comment">*</span><span class="comment">       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.221"></a><a href="hfy-index.html#ILAENV">ILAENV</a>.)
</span><span class="comment">*</span><span class="comment">
</span>      IF( INFO.EQ.0 .AND. M.GT.0 .AND. N.GT.0 ) THEN
         IF( M.GE.N ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           There is no complex work space needed for bidiagonal SVD
</span><span class="comment">*</span><span class="comment">           The real work space needed for bidiagonal SVD is BDSPAC
</span><span class="comment">*</span><span class="comment">           for computing singular values and singular vectors; BDSPAN
</span><span class="comment">*</span><span class="comment">           for computing singular values only.
</span><span class="comment">*</span><span class="comment">           BDSPAC = 5*N*N + 7*N
</span><span class="comment">*</span><span class="comment">           BDSPAN = MAX(7*N+4, 3*N+2+SMLSIZ*(SMLSIZ+8))
</span><span class="comment">*</span><span class="comment">
</span>            IF( M.GE.MNTHR1 ) THEN
               IF( WNTQN ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                 Path 1 (M much larger than N, JOBZ='N')
</span><span class="comment">*</span><span class="comment">
</span>                  MAXWRK = N + N*<a name="ILAENV.238"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="ZGEQRF.238"></a><a href="zgeqrf.f.html#ZGEQRF.1">ZGEQRF</a>'</span>, <span class="string">' '</span>, M, N, -1,
     $                     -1 )
                  MAXWRK = MAX( MAXWRK, 2*N+2*N*
     $                     <a name="ILAENV.241"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="ZGEBRD.241"></a><a href="zgebrd.f.html#ZGEBRD.1">ZGEBRD</a>'</span>, <span class="string">' '</span>, N, N, -1, -1 ) )
                  MINWRK = 3*N
               ELSE IF( WNTQO ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                 Path 2 (M much larger than N, JOBZ='O')
</span><span class="comment">*</span><span class="comment">
</span>                  WRKBL = N + N*<a name="ILAENV.247"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="ZGEQRF.247"></a><a href="zgeqrf.f.html#ZGEQRF.1">ZGEQRF</a>'</span>, <span class="string">' '</span>, M, N, -1, -1 )
                  WRKBL = MAX( WRKBL, N+N*<a name="ILAENV.248"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="ZUNGQR.248"></a><a href="zungqr.f.html#ZUNGQR.1">ZUNGQR</a>'</span>, <span class="string">' '</span>, M,
     $                    N, N, -1 ) )
                  WRKBL = MAX( WRKBL, 2*N+2*N*
     $                    <a name="ILAENV.251"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="ZGEBRD.251"></a><a href="zgebrd.f.html#ZGEBRD.1">ZGEBRD</a>'</span>, <span class="string">' '</span>, N, N, -1, -1 ) )
                  WRKBL = MAX( WRKBL, 2*N+N*
     $                    <a name="ILAENV.253"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="ZUNMBR.253"></a><a href="zunmbr.f.html#ZUNMBR.1">ZUNMBR</a>'</span>, <span class="string">'QLN'</span>, N, N, N, -1 ) )
                  WRKBL = MAX( WRKBL, 2*N+N*
     $                    <a name="ILAENV.255"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="ZUNMBR.255"></a><a href="zunmbr.f.html#ZUNMBR.1">ZUNMBR</a>'</span>, <span class="string">'PRC'</span>, N, N, N, -1 ) )
                  MAXWRK = M*N + N*N + WRKBL
                  MINWRK = 2*N*N + 3*N
               ELSE IF( WNTQS ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                 Path 3 (M much larger than N, JOBZ='S')
</span><span class="comment">*</span><span class="comment">
</span>                  WRKBL = N + N*<a name="ILAENV.262"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="ZGEQRF.262"></a><a href="zgeqrf.f.html#ZGEQRF.1">ZGEQRF</a>'</span>, <span class="string">' '</span>, M, N, -1, -1 )
                  WRKBL = MAX( WRKBL, N+N*<a name="ILAENV.263"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="ZUNGQR.263"></a><a href="zungqr.f.html#ZUNGQR.1">ZUNGQR</a>'</span>, <span class="string">' '</span>, M,
     $                    N, N, -1 ) )
                  WRKBL = MAX( WRKBL, 2*N+2*N*
     $                    <a name="ILAENV.266"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="ZGEBRD.266"></a><a href="zgebrd.f.html#ZGEBRD.1">ZGEBRD</a>'</span>, <span class="string">' '</span>, N, N, -1, -1 ) )
                  WRKBL = MAX( WRKBL, 2*N+N*