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

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, * )

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.

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