zgesvd.f.html

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</span><span class="comment">*</span><span class="comment">          If LWORK = -1, then a workspace query is assumed; the routine
</span><span class="comment">*</span><span class="comment">          only calculates the optimal size of the WORK array, returns
</span><span class="comment">*</span><span class="comment">          this value as the first entry of the WORK array, and no error
</span><span class="comment">*</span><span class="comment">          message related to LWORK is issued by <a name="XERBLA.119"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  RWORK   (workspace) DOUBLE PRECISION array, dimension (5*min(M,N))
</span><span class="comment">*</span><span class="comment">          On exit, if INFO &gt; 0, RWORK(1:MIN(M,N)-1) contains the
</span><span class="comment">*</span><span class="comment">          unconverged superdiagonal elements of an upper bidiagonal
</span><span class="comment">*</span><span class="comment">          matrix B whose diagonal is in S (not necessarily sorted).
</span><span class="comment">*</span><span class="comment">          B satisfies A = U * B * VT, so it has the same singular
</span><span class="comment">*</span><span class="comment">          values as A, and singular vectors related by U and VT.
</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:  if <a name="ZBDSQR.131"></a><a href="zbdsqr.f.html#ZBDSQR.1">ZBDSQR</a> did not converge, INFO specifies how many
</span><span class="comment">*</span><span class="comment">                superdiagonals of an intermediate bidiagonal form B
</span><span class="comment">*</span><span class="comment">                did not converge to zero. See the description of RWORK
</span><span class="comment">*</span><span class="comment">                above for 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">
</span><span class="comment">*</span><span class="comment">     .. Parameters ..
</span>      COMPLEX*16         CZERO, CONE
      PARAMETER          ( CZERO = ( 0.0D0, 0.0D0 ),
     $                   CONE = ( 1.0D0, 0.0D0 ) )
      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            LQUERY, WNTUA, WNTUAS, WNTUN, WNTUO, WNTUS,
     $                   WNTVA, WNTVAS, WNTVN, WNTVO, WNTVS
      INTEGER            BLK, CHUNK, I, IE, IERR, IR, IRWORK, ISCL,
     $                   ITAU, ITAUP, ITAUQ, IU, IWORK, LDWRKR, LDWRKU,
     $                   MAXWRK, MINMN, MINWRK, MNTHR, NCU, NCVT, NRU,
     $                   NRVT, 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>      DOUBLE PRECISION   DUM( 1 )
      COMPLEX*16         CDUM( 1 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="DLASCL.159"></a><a href="dlascl.f.html#DLASCL.1">DLASCL</a>, <a name="XERBLA.159"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>, <a name="ZBDSQR.159"></a><a href="zbdsqr.f.html#ZBDSQR.1">ZBDSQR</a>, <a name="ZGEBRD.159"></a><a href="zgebrd.f.html#ZGEBRD.1">ZGEBRD</a>, <a name="ZGELQF.159"></a><a href="zgelqf.f.html#ZGELQF.1">ZGELQF</a>, ZGEMM,
     $                   <a name="ZGEQRF.160"></a><a href="zgeqrf.f.html#ZGEQRF.1">ZGEQRF</a>, <a name="ZLACPY.160"></a><a href="zlacpy.f.html#ZLACPY.1">ZLACPY</a>, <a name="ZLASCL.160"></a><a href="zlascl.f.html#ZLASCL.1">ZLASCL</a>, <a name="ZLASET.160"></a><a href="zlaset.f.html#ZLASET.1">ZLASET</a>, <a name="ZUNGBR.160"></a><a href="zungbr.f.html#ZUNGBR.1">ZUNGBR</a>, <a name="ZUNGLQ.160"></a><a href="zunglq.f.html#ZUNGLQ.1">ZUNGLQ</a>,
     $                   <a name="ZUNGQR.161"></a><a href="zungqr.f.html#ZUNGQR.1">ZUNGQR</a>, <a name="ZUNMBR.161"></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.164"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      INTEGER            <a name="ILAENV.165"></a><a href="hfy-index.html#ILAENV">ILAENV</a>
      DOUBLE PRECISION   <a name="DLAMCH.166"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>, <a name="ZLANGE.166"></a><a href="zlange.f.html#ZLANGE.1">ZLANGE</a>
      EXTERNAL           <a name="LSAME.167"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, <a name="ILAENV.167"></a><a href="hfy-index.html#ILAENV">ILAENV</a>, <a name="DLAMCH.167"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>, <a name="ZLANGE.167"></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          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 )
      WNTUA = <a name="LSAME.178"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBU, <span class="string">'A'</span> )
      WNTUS = <a name="LSAME.179"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBU, <span class="string">'S'</span> )
      WNTUAS = WNTUA .OR. WNTUS
      WNTUO = <a name="LSAME.181"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBU, <span class="string">'O'</span> )
      WNTUN = <a name="LSAME.182"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBU, <span class="string">'N'</span> )
      WNTVA = <a name="LSAME.183"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBVT, <span class="string">'A'</span> )
      WNTVS = <a name="LSAME.184"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBVT, <span class="string">'S'</span> )
      WNTVAS = WNTVA .OR. WNTVS
      WNTVO = <a name="LSAME.186"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBVT, <span class="string">'O'</span> )
      WNTVN = <a name="LSAME.187"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBVT, <span class="string">'N'</span> )
      LQUERY = ( LWORK.EQ.-1 )
<span class="comment">*</span><span class="comment">
</span>      IF( .NOT.( WNTUA .OR. WNTUS .OR. WNTUO .OR. WNTUN ) ) THEN
         INFO = -1
      ELSE IF( .NOT.( WNTVA .OR. WNTVS .OR. WNTVO .OR. WNTVN ) .OR.
     $         ( WNTVO .AND. WNTUO ) ) THEN
         INFO = -2
      ELSE IF( M.LT.0 ) THEN
         INFO = -3
      ELSE IF( N.LT.0 ) THEN
         INFO = -4
      ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
         INFO = -6
      ELSE IF( LDU.LT.1 .OR. ( WNTUAS .AND. LDU.LT.M ) ) THEN
         INFO = -9
      ELSE IF( LDVT.LT.1 .OR. ( WNTVA .AND. LDVT.LT.N ) .OR.
     $         ( WNTVS .AND. LDVT.LT.MINMN ) ) 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">       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.214"></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( M.GE.N .AND. MINMN.GT.0 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Space needed for <a name="ZBDSQR.221"></a><a href="zbdsqr.f.html#ZBDSQR.1">ZBDSQR</a> is BDSPAC = 5*N
</span><span class="comment">*</span><span class="comment">
</span>            MNTHR = <a name="ILAENV.223"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 6, <span class="string">'<a name="ZGESVD.223"></a><a href="zgesvd.f.html#ZGESVD.1">ZGESVD</a>'</span>, JOBU // JOBVT, M, N, 0, 0 )
            IF( M.GE.MNTHR ) THEN
               IF( WNTUN ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                 Path 1 (M much larger than N, JOBU='N')
</span><span class="comment">*</span><span class="comment">
</span>                  MAXWRK = N + N*<a name="ILAENV.229"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="ZGEQRF.229"></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.232"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="ZGEBRD.232"></a><a href="zgebrd.f.html#ZGEBRD.1">ZGEBRD</a>'</span>, <span class="string">' '</span>, N, N, -1, -1 ) )
                  IF( WNTVO .OR. WNTVAS )
     $               MAXWRK = MAX( MAXWRK, 2*N+( N-1 )*
     $                        <a name="ILAENV.235"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="ZUNGBR.235"></a><a href="zungbr.f.html#ZUNGBR.1">ZUNGBR</a>'</span>, <span class="string">'P'</span>, N, N, N, -1 ) )
                  MINWRK = 3*N
               ELSE IF( WNTUO .AND. WNTVN ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                 Path 2 (M much larger than N, JOBU='O', JOBVT='N')
</span><span class="comment">*</span><span class="comment">
</span>                  WRKBL = N + N*<a name="ILAENV.241"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="ZGEQRF.241"></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.242"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="ZUNGQR.242"></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.245"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="ZGEBRD.245"></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.247"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="ZUNGBR.247"></a><a href="zungbr.f.html#ZUNGBR.1">ZUNGBR</a>'</span>, <span class="string">'Q'</span>, N, N, N, -1 ) )
                  MAXWRK = MAX( N*N+WRKBL, N*N+M*N )
                  MINWRK = 2*N + M