NAME

       DLAREF  -  applie  one or several Householder reflectors of size 3  to one or two matrices
       (if column is specified) on either their  rows or columns

SYNOPSIS

       SUBROUTINE DLAREF( TYPE, A, LDA, WANTZ, Z, LDZ, BLOCK, IROW1, ICOL1, ISTART, ISTOP, ITMP1,
                          ITMP2, LILOZ, LIHIZ, VECS, V2, V3, T1, T2, T3 )

           LOGICAL        BLOCK, WANTZ

           CHARACTER      TYPE

           INTEGER        ICOL1, IROW1, ISTART, ISTOP, ITMP1, ITMP2, LDA, LDZ, LIHIZ, LILOZ

           DOUBLE         PRECISION T1, T2, T3, V2, V3

           DOUBLE         PRECISION A( LDA, * ), VECS( * ), Z( LDZ, * )

PURPOSE

       DLAREF applies one or several Householder reflectors of size 3
          to one or two matrices (if column is specified) on either their
          rows or columns.

ARGUMENTS

       TYPE    (global input) CHARACTER*1
               If  'R':  Apply  reflectors to the rows of the matrix (apply from left) Otherwise:
               Apply reflectors to the columns of the matrix Unchanged on exit.

       A       (global input/output) DOUBLE PRECISION array, (LDA,*)
               On entry, the matrix to receive the reflections.  The updated matrix on exit.

       LDA     (local input) INTEGER
               On entry, the leading dimension of A.  Unchanged on exit.

       WANTZ   (global input) LOGICAL
               If .TRUE., then apply any column reflections to Z as well.  If .FALSE., then do no
               additional work on Z.

       Z       (global input/output) DOUBLE PRECISION array, (LDZ,*)
               On  entry,  the second matrix to receive column reflections.  This is changed only
               if WANTZ is set.

       LDZ     (local input) INTEGER
               On entry, the leading dimension of Z.  Unchanged on exit.

       BLOCK   (global input) LOGICAL
               If .TRUE., then apply several reflectors at once and read their data from the VECS
               array.  If .FALSE., apply the single reflector given by V2, V3, T1, T2, and T3.

       IROW1   (local input/output) INTEGER
               On entry, the local row element of A.  Undefined on output.

       ICOL1   (local input/output) INTEGER
               On entry, the local column element of A.  Undefined on output.

       ISTART  (global input) INTEGER
               Specifies the "number" of the first reflector.  This is used as an index into VECS
               if BLOCK is set.  ISTART is ignored if BLOCK is .FALSE..

       ISTOP   (global input) INTEGER
               Specifies the "number" of the last reflector.  This is used as an index into  VECS
               if BLOCK is set.  ISTOP is ignored if BLOCK is .FALSE..

       ITMP1   (local input) INTEGER
               Starting  range  into  A.  For rows, this is the local first column.  For columns,
               this is the local first row.

       ITMP2   (local input) INTEGER
               Ending range into A.  For rows, this is the local last column.  For columns,  this
               is the local last row.

               LILOZ  LIHIZ    (local  input) INTEGER These serve the same purpose as ITMP1,ITMP2
               but for Z when WANTZ is set.

       VECS    (global input) DOUBLE PRECISION array of size 3*N (matrix
               size) This holds the size 3 reflectors one after another and this is only accessed
               when BLOCK is .TRUE.

               V2  V3 T1 T2 T3      (global input/output) DOUBLE PRECISION This holds information
               on a single size 3 Householder reflector and is read when BLOCK  is  .FALSE.,  and
               overwritten when BLOCK is .TRUE.

               Implemented by:  G. Henry, May 1, 1997