dlasda.f.html

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</span><span class="comment">*</span><span class="comment">         of Givens rotations performed on the I-th level on the
</span><span class="comment">*</span><span class="comment">         computation tree.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDGCOL (input) INTEGER, LDGCOL = &gt; N.
</span><span class="comment">*</span><span class="comment">         The leading dimension of arrays GIVCOL and PERM.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  PERM   (output) INTEGER array,
</span><span class="comment">*</span><span class="comment">         dimension ( LDGCOL, NLVL ) if ICOMPQ = 1, and not referenced
</span><span class="comment">*</span><span class="comment">         if ICOMPQ = 0. If ICOMPQ = 1, on exit, PERM(1, I) records
</span><span class="comment">*</span><span class="comment">         permutations done on the I-th level of the computation tree.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  GIVNUM (output) DOUBLE PRECISION array,
</span><span class="comment">*</span><span class="comment">         dimension ( LDU,  2 * NLVL ) if ICOMPQ = 1, and not
</span><span class="comment">*</span><span class="comment">         referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I,
</span><span class="comment">*</span><span class="comment">         GIVNUM(1, 2 *I - 1) and GIVNUM(1, 2 *I) record the C- and S-
</span><span class="comment">*</span><span class="comment">         values of Givens rotations performed on the I-th level on
</span><span class="comment">*</span><span class="comment">         the computation tree.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  C      (output) DOUBLE PRECISION array,
</span><span class="comment">*</span><span class="comment">         dimension ( N ) if ICOMPQ = 1, and dimension 1 if ICOMPQ = 0.
</span><span class="comment">*</span><span class="comment">         If ICOMPQ = 1 and the I-th subproblem is not square, on exit,
</span><span class="comment">*</span><span class="comment">         C( I ) contains the C-value of a Givens rotation related to
</span><span class="comment">*</span><span class="comment">         the right null space of the I-th subproblem.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  S      (output) DOUBLE PRECISION array, dimension ( N ) if
</span><span class="comment">*</span><span class="comment">         ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. If ICOMPQ = 1
</span><span class="comment">*</span><span class="comment">         and the I-th subproblem is not square, on exit, S( I )
</span><span class="comment">*</span><span class="comment">         contains the S-value of a Givens rotation related to
</span><span class="comment">*</span><span class="comment">         the right null space of the I-th subproblem.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  WORK   (workspace) DOUBLE PRECISION array, dimension
</span><span class="comment">*</span><span class="comment">         (6 * N + (SMLSIZ + 1)*(SMLSIZ + 1)).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  IWORK  (workspace) INTEGER array.
</span><span class="comment">*</span><span class="comment">         Dimension must be at least (7 * 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:  if INFO = 1, an singular value 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>      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>      INTEGER            I, I1, IC, IDXQ, IDXQI, IM1, INODE, ITEMP, IWK,
     $                   J, LF, LL, LVL, LVL2, M, NCC, ND, NDB1, NDIML,
     $                   NDIMR, NL, NLF, NLP1, NLVL, NR, NRF, NRP1, NRU,
     $                   NWORK1, NWORK2, SMLSZP, SQREI, VF, VFI, VL, VLI
      DOUBLE PRECISION   ALPHA, BETA
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           DCOPY, <a name="DLASD6.183"></a><a href="dlasd6.f.html#DLASD6.1">DLASD6</a>, <a name="DLASDQ.183"></a><a href="dlasdq.f.html#DLASDQ.1">DLASDQ</a>, <a name="DLASDT.183"></a><a href="dlasdt.f.html#DLASDT.1">DLASDT</a>, <a name="DLASET.183"></a><a href="dlaset.f.html#DLASET.1">DLASET</a>, <a name="XERBLA.183"></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">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Test the input parameters.
</span><span class="comment">*</span><span class="comment">
</span>      INFO = 0
<span class="comment">*</span><span class="comment">
</span>      IF( ( ICOMPQ.LT.0 ) .OR. ( ICOMPQ.GT.1 ) ) THEN
         INFO = -1
      ELSE IF( SMLSIZ.LT.3 ) THEN
         INFO = -2
      ELSE IF( N.LT.0 ) THEN
         INFO = -3
      ELSE IF( ( SQRE.LT.0 ) .OR. ( SQRE.GT.1 ) ) THEN
         INFO = -4
      ELSE IF( LDU.LT.( N+SQRE ) ) THEN
         INFO = -8
      ELSE IF( LDGCOL.LT.N ) THEN
         INFO = -17
      END IF
      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.205"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="DLASDA.205"></a><a href="dlasda.f.html#DLASDA.1">DLASDA</a>'</span>, -INFO )
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span>      M = N + SQRE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     If the input matrix is too small, call <a name="DLASDQ.211"></a><a href="dlasdq.f.html#DLASDQ.1">DLASDQ</a> to find the SVD.
</span><span class="comment">*</span><span class="comment">
</span>      IF( N.LE.SMLSIZ ) THEN
         IF( ICOMPQ.EQ.0 ) THEN
            CALL <a name="DLASDQ.215"></a><a href="dlasdq.f.html#DLASDQ.1">DLASDQ</a>( <span class="string">'U'</span>, SQRE, N, 0, 0, 0, D, E, VT, LDU, U, LDU,
     $                   U, LDU, WORK, INFO )
         ELSE
            CALL <a name="DLASDQ.218"></a><a href="dlasdq.f.html#DLASDQ.1">DLASDQ</a>( <span class="string">'U'</span>, SQRE, N, M, N, 0, D, E, VT, LDU, U, LDU,
     $                   U, LDU, WORK, INFO )
         END IF
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Book-keeping and  set up the computation tree.
</span><span class="comment">*</span><span class="comment">
</span>      INODE = 1
      NDIML = INODE + N
      NDIMR = NDIML + N
      IDXQ = NDIMR + N
      IWK = IDXQ + N
<span class="comment">*</span><span class="comment">
</span>      NCC = 0
      NRU = 0
<span class="comment">*</span><span class="comment">
</span>      SMLSZP = SMLSIZ + 1
      VF = 1
      VL = VF + M
      NWORK1 = VL + M
      NWORK2 = NWORK1 + SMLSZP*SMLSZP
<span class="comment">*</span><span class="comment">
</span>      CALL <a name="DLASDT.241"></a><a href="dlasdt.f.html#DLASDT.1">DLASDT</a>( N, NLVL, ND, IWORK( INODE ), IWORK( NDIML ),
     $             IWORK( NDIMR ), SMLSIZ )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     for the nodes on bottom level of the tree, solve
</span><span class="comment">*</span><span class="comment">     their subproblems by <a name="DLASDQ.245"></a><a href="dlasdq.f.html#DLASDQ.1">DLASDQ</a>.
</span><span class="comment">*</span><span class="comment">
</span>      NDB1 = ( ND+1 ) / 2
      DO 30 I = NDB1, ND
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        IC : center row of each node
</span><span class="comment">*</span><span class="comment">        NL : number of rows of left  subproblem
</span><span class="comment">*</span><span class="comment">        NR : number of rows of right subproblem
</span><span class="comment">*</span><span class="comment">        NLF: starting row of the left   subproblem
</span><span class="comment">*</span><span class="comment">        NRF: starting row of the right  subproblem
</span><span class="comment">*</span><span class="comment">
</span>         I1 = I - 1
         IC = IWORK( INODE+I1 )
         NL = IWORK( NDIML+I1 )
         NLP1 = NL + 1