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SUBROUTINE DLAREF( TYPE, A, LDA, WANTZ, Z, LDZ, BLOCK, IROW1,
$ ICOL1, ISTART, ISTOP, ITMP1, ITMP2, LILOZ,
$ LIHIZ, VECS, V2, V3, T1, T2, T3 )
*
* -- ScaLAPACK routine (version 1.7) --
* University of Tennessee, Knoxville, Oak Ridge National Laboratory,
* and University of California, Berkeley.
* December 31, 1998
*
* .. Scalar Arguments ..
LOGICAL BLOCK, WANTZ
CHARACTER TYPE
INTEGER ICOL1, IROW1, ISTART, ISTOP, ITMP1, ITMP2, LDA,
$ LDZ, LIHIZ, LILOZ
DOUBLE PRECISION T1, T2, T3, V2, V3
* ..
* .. Array Arguments ..
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, November 17, 1996
*
* =====================================================================
*
* .. Local Scalars ..
INTEGER J, K
DOUBLE PRECISION H11, H22, SUM, T12, T13, T22, T23, T32, T33,
$ V22, V23, V32, V33
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. Intrinsic Functions ..
INTRINSIC MOD
* ..
* .. Executable Statements ..
*
IF( LSAME( TYPE, 'R' ) ) THEN
IF( BLOCK ) THEN
DO 20 K = ISTART, ISTOP - MOD( ISTOP-ISTART+1, 3 ), 3
V2 = VECS( ( K-1 )*3+1 )
V3 = VECS( ( K-1 )*3+2 )
T1 = VECS( ( K-1 )*3+3 )
V22 = VECS( ( K-1 )*3+4 )
V32 = VECS( ( K-1 )*3+5 )
T12 = VECS( ( K-1 )*3+6 )
V23 = VECS( ( K-1 )*3+7 )
V33 = VECS( ( K-1 )*3+8 )
T13 = VECS( ( K-1 )*3+9 )
T2 = T1*V2
T3 = T1*V3
T22 = T12*V22
T32 = T12*V32
T23 = T13*V23
T33 = T13*V33
DO 10 J = ITMP1, ITMP2
SUM = A( IROW1, J ) + V2*A( IROW1+1, J ) +
$ V3*A( IROW1+2, J )
A( IROW1, J ) = A( IROW1, J ) - SUM*T1
H11 = A( IROW1+1, J ) - SUM*T2
H22 = A( IROW1+2, J ) - SUM*T3
SUM = H11 + V22*H22 + V32*A( IROW1+3, J )
A( IROW1+1, J ) = H11 - SUM*T12
H11 = H22 - SUM*T22
H22 = A( IROW1+3, J ) - SUM*T32
SUM = H11 + V23*H22 + V33*A( IROW1+4, J )
A( IROW1+2, J ) = H11 - SUM*T13
A( IROW1+3, J ) = H22 - SUM*T23
A( IROW1+4, J ) = A( IROW1+4, J ) - SUM*T33
10 CONTINUE
IROW1 = IROW1 + 3
20 CONTINUE
DO 40 K = ISTOP - MOD( ISTOP-ISTART+1, 3 ) + 1, ISTOP
V2 = VECS( ( K-1 )*3+1 )
V3 = VECS( ( K-1 )*3+2 )
T1 = VECS( ( K-1 )*3+3 )
T2 = T1*V2
T3 = T1*V3
DO 30 J = ITMP1, ITMP2
SUM = A( IROW1, J ) + V2*A( IROW1+1, J ) +
$ V3*A( IROW1+2, J )
A( IROW1, J ) = A( IROW1, J ) - SUM*T1
A( IROW1+1, J ) = A( IROW1+1, J ) - SUM*T2
A( IROW1+2, J ) = A( IROW1+2, J ) - SUM*T3
30 CONTINUE
IROW1 = IROW1 + 1
40 CONTINUE
ELSE
DO 50 J = ITMP1, ITMP2
SUM = A( IROW1, J ) + V2*A( IROW1+1, J ) +
$ V3*A( IROW1+2, J )
A( IROW1, J ) = A( IROW1, J ) - SUM*T1
A( IROW1+1, J ) = A( IROW1+1, J ) - SUM*T2
A( IROW1+2, J ) = A( IROW1+2, J ) - SUM*T3
50 CONTINUE
END IF
ELSE
*
* Do column transforms
*
IF( BLOCK ) THEN
DO 80 K = ISTART, ISTOP - MOD( ISTOP-ISTART+1, 3 ), 3
V2 = VECS( ( K-1 )*3+1 )
V3 = VECS( ( K-1 )*3+2 )
T1 = VECS( ( K-1 )*3+3 )
V22 = VECS( ( K-1 )*3+4 )
V32 = VECS( ( K-1 )*3+5 )
T12 = VECS( ( K-1 )*3+6 )
V23 = VECS( ( K-1 )*3+7 )
V33 = VECS( ( K-1 )*3+8 )
T13 = VECS( ( K-1 )*3+9 )
T2 = T1*V2
T3 = T1*V3
T22 = T12*V22
T32 = T12*V32
T23 = T13*V23
T33 = T13*V33
DO 60 J = ITMP1, ITMP2
SUM = A( J, ICOL1 ) + V2*A( J, ICOL1+1 ) +
$ V3*A( J, ICOL1+2 )
A( J, ICOL1 ) = A( J, ICOL1 ) - SUM*T1
H11 = A( J, ICOL1+1 ) - SUM*T2
H22 = A( J, ICOL1+2 ) - SUM*T3
SUM = H11 + V22*H22 + V32*A( J, ICOL1+3 )
A( J, ICOL1+1 ) = H11 - SUM*T12
H11 = H22 - SUM*T22
H22 = A( J, ICOL1+3 ) - SUM*T32
SUM = H11 + V23*H22 + V33*A( J, ICOL1+4 )
A( J, ICOL1+2 ) = H11 - SUM*T13
A( J, ICOL1+3 ) = H22 - SUM*T23
A( J, ICOL1+4 ) = A( J, ICOL1+4 ) - SUM*T33
60 CONTINUE
IF( WANTZ ) THEN
DO 70 J = LILOZ, LIHIZ
SUM = Z( J, ICOL1 ) + V2*Z( J, ICOL1+1 ) +
$ V3*Z( J, ICOL1+2 )
Z( J, ICOL1 ) = Z( J, ICOL1 ) - SUM*T1
H11 = Z( J, ICOL1+1 ) - SUM*T2
H22 = Z( J, ICOL1+2 ) - SUM*T3
SUM = H11 + V22*H22 + V32*Z( J, ICOL1+3 )
Z( J, ICOL1+1 ) = H11 - SUM*T12
H11 = H22 - SUM*T22
H22 = Z( J, ICOL1+3 ) - SUM*T32
SUM = H11 + V23*H22 + V33*Z( J, ICOL1+4 )
Z( J, ICOL1+2 ) = H11 - SUM*T13
Z( J, ICOL1+3 ) = H22 - SUM*T23
Z( J, ICOL1+4 ) = Z( J, ICOL1+4 ) - SUM*T33
70 CONTINUE
END IF
ICOL1 = ICOL1 + 3
80 CONTINUE
DO 110 K = ISTOP - MOD( ISTOP-ISTART+1, 3 ) + 1, ISTOP
V2 = VECS( ( K-1 )*3+1 )
V3 = VECS( ( K-1 )*3+2 )
T1 = VECS( ( K-1 )*3+3 )
T2 = T1*V2
T3 = T1*V3
DO 90 J = ITMP1, ITMP2
SUM = A( J, ICOL1 ) + V2*A( J, ICOL1+1 ) +
$ V3*A( J, ICOL1+2 )
A( J, ICOL1 ) = A( J, ICOL1 ) - SUM*T1
A( J, ICOL1+1 ) = A( J, ICOL1+1 ) - SUM*T2
A( J, ICOL1+2 ) = A( J, ICOL1+2 ) - SUM*T3
90 CONTINUE
IF( WANTZ ) THEN
DO 100 J = LILOZ, LIHIZ
SUM = Z( J, ICOL1 ) + V2*Z( J, ICOL1+1 ) +
$ V3*Z( J, ICOL1+2 )
Z( J, ICOL1 ) = Z( J, ICOL1 ) - SUM*T1
Z( J, ICOL1+1 ) = Z( J, ICOL1+1 ) - SUM*T2
Z( J, ICOL1+2 ) = Z( J, ICOL1+2 ) - SUM*T3
100 CONTINUE
END IF
ICOL1 = ICOL1 + 1
110 CONTINUE
ELSE
DO 120 J = ITMP1, ITMP2
SUM = A( J, ICOL1 ) + V2*A( J, ICOL1+1 ) +
$ V3*A( J, ICOL1+2 )
A( J, ICOL1 ) = A( J, ICOL1 ) - SUM*T1
A( J, ICOL1+1 ) = A( J, ICOL1+1 ) - SUM*T2
A( J, ICOL1+2 ) = A( J, ICOL1+2 ) - SUM*T3
120 CONTINUE
END IF
END IF
RETURN
*
* End of DLAREF
*
END
*
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