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SUBROUTINE CLAREF( 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) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* May 28, 1999
*
* .. Scalar Arguments ..
LOGICAL BLOCK, WANTZ
CHARACTER TYPE
INTEGER ICOL1, IROW1, ISTART, ISTOP, ITMP1, ITMP2, LDA,
$ LDZ, LIHIZ, LILOZ
COMPLEX T1, T2, T3, V2, V3
* ..
* .. Array Arguments ..
COMPLEX A( LDA, * ), VECS( * ), Z( LDZ, * )
* ..
*
* Purpose
* =======
*
* CLAREF 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) COMPLEX 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) COMPLEX 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) COMPLEX 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) COMPLEX
* This holds information on a single size 3 Householder
* reflector and is read when BLOCK is .FALSE., and
* overwritten when BLOCK is .TRUE.
*
* Further Details
* ===============
*
* Implemented by: M. Fahey, May 28, 1999
*
* =====================================================================
*
* .. Local Scalars ..
INTEGER J, K
COMPLEX A1, A11, A2, A22, A3, A4, A5, B1, B2, B3, B4,
$ B5, H11, H22, SUM, SUM1, SUM2, SUM3, T12, T13,
$ T22, T23, T32, T33, TMP1, TMP2, TMP3, V22, V23,
$ V32, V33
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. Intrinsic Functions ..
INTRINSIC CONJG, MOD
* ..
* .. Executable Statements ..
*
IF( LSAME( TYPE, 'R' ) ) THEN
IF( BLOCK ) THEN
DO 30 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 - MOD( ITMP2-ITMP1+1, 2 ), 2
A1 = A( IROW1, J )
A2 = A( IROW1+1, J )
A3 = A( IROW1+2, J )
A4 = A( IROW1+3, J )
A5 = A( IROW1+4, J )
B1 = A( IROW1, J+1 )
B2 = A( IROW1+1, J+1 )
B3 = A( IROW1+2, J+1 )
B4 = A( IROW1+3, J+1 )
B5 = A( IROW1+4, J+1 )
SUM1 = CONJG( T1 )*A1 + CONJG( T2 )*A2 +
$ CONJG( T3 )*A3
A( IROW1, J ) = A1 - SUM1
H11 = A2 - SUM1*V2
H22 = A3 - SUM1*V3
TMP1 = CONJG( T1 )*B1 + CONJG( T2 )*B2 +
$ CONJG( T3 )*B3
A( IROW1, J+1 ) = B1 - TMP1
A11 = B2 - TMP1*V2
A22 = B3 - TMP1*V3
SUM2 = CONJG( T12 )*H11 + CONJG( T22 )*H22 +
$ CONJG( T32 )*A4
A( IROW1+1, J ) = H11 - SUM2
H11 = H22 - SUM2*V22
H22 = A4 - SUM2*V32
TMP2 = CONJG( T12 )*A11 + CONJG( T22 )*A22 +
$ CONJG( T32 )*B4
A( IROW1+1, J+1 ) = A11 - TMP2
A11 = A22 - TMP2*V22
A22 = B4 - TMP2*V32
SUM3 = CONJG( T13 )*H11 + CONJG( T23 )*H22 +
$ CONJG( T33 )*A5
A( IROW1+2, J ) = H11 - SUM3
A( IROW1+3, J ) = H22 - SUM3*V23
A( IROW1+4, J ) = A5 - SUM3*V33
TMP3 = CONJG( T13 )*A11 + CONJG( T23 )*A22 +
$ CONJG( T33 )*B5
A( IROW1+2, J+1 ) = A11 - TMP3
A( IROW1+3, J+1 ) = A22 - TMP3*V23
A( IROW1+4, J+1 ) = B5 - TMP3*V33
10 CONTINUE
DO 20 J = ITMP2 - MOD( ITMP2-ITMP1+1, 2 ) + 1, ITMP2
SUM = CONJG( T1 )*A( IROW1, J ) +
$ CONJG( T2 )*A( IROW1+1, J ) +
$ CONJG( T3 )*A( IROW1+2, J )
A( IROW1, J ) = A( IROW1, J ) - SUM
H11 = A( IROW1+1, J ) - SUM*V2
H22 = A( IROW1+2, J ) - SUM*V3
SUM = CONJG( T12 )*H11 + CONJG( T22 )*H22 +
$ CONJG( T32 )*A( IROW1+3, J )
A( IROW1+1, J ) = H11 - SUM
H11 = H22 - SUM*V22
H22 = A( IROW1+3, J ) - SUM*V32
SUM = CONJG( T13 )*H11 + CONJG( T23 )*H22 +
$ CONJG( T33 )*A( IROW1+4, J )
A( IROW1+2, J ) = H11 - SUM
A( IROW1+3, J ) = H22 - SUM*V23
A( IROW1+4, J ) = A( IROW1+4, J ) - SUM*V33
20 CONTINUE
IROW1 = IROW1 + 3
30 CONTINUE
DO 50 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 40 J = ITMP1, ITMP2
SUM = CONJG( T1 )*A( IROW1, J ) +
$ CONJG( T2 )*A( IROW1+1, J ) +
$ CONJG( T3 )*A( IROW1+2, J )
A( IROW1, J ) = A( IROW1, J ) - SUM
A( IROW1+1, J ) = A( IROW1+1, J ) - SUM*V2
A( IROW1+2, J ) = A( IROW1+2, J ) - SUM*V3
40 CONTINUE
IROW1 = IROW1 + 1
50 CONTINUE
ELSE
DO 60 J = ITMP1, ITMP2
SUM = CONJG( T1 )*A( IROW1, J ) +
$ CONJG( T2 )*A( IROW1+1, J ) +
$ CONJG( T3 )*A( IROW1+2, J )
A( IROW1, J ) = A( IROW1, J ) - SUM
A( IROW1+1, J ) = A( IROW1+1, J ) - SUM*V2
A( IROW1+2, J ) = A( IROW1+2, J ) - SUM*V3
60 CONTINUE
END IF
ELSE
*
* Do column transforms
*
IF( BLOCK ) THEN
DO 90 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 70 J = ITMP1, ITMP2
SUM = T1*A( J, ICOL1 ) + T2*A( J, ICOL1+1 ) +
$ T3*A( J, ICOL1+2 )
A( J, ICOL1 ) = A( J, ICOL1 ) - SUM
H11 = A( J, ICOL1+1 ) - SUM*CONJG( V2 )
H22 = A( J, ICOL1+2 ) - SUM*CONJG( V3 )
SUM = T12*H11 + T22*H22 + T32*A( J, ICOL1+3 )
A( J, ICOL1+1 ) = H11 - SUM
H11 = H22 - SUM*CONJG( V22 )
H22 = A( J, ICOL1+3 ) - SUM*CONJG( V32 )
SUM = T13*H11 + T23*H22 + T33*A( J, ICOL1+4 )
A( J, ICOL1+2 ) = H11 - SUM
A( J, ICOL1+3 ) = H22 - SUM*CONJG( V23 )
A( J, ICOL1+4 ) = A( J, ICOL1+4 ) - SUM*CONJG( V33 )
70 CONTINUE
IF( WANTZ ) THEN
DO 80 J = LILOZ, LIHIZ
SUM = T1*Z( J, ICOL1 ) + T2*Z( J, ICOL1+1 ) +
$ T3*Z( J, ICOL1+2 )
Z( J, ICOL1 ) = Z( J, ICOL1 ) - SUM
H11 = Z( J, ICOL1+1 ) - SUM*CONJG( V2 )
H22 = Z( J, ICOL1+2 ) - SUM*CONJG( V3 )
SUM = T12*H11 + T22*H22 + T32*Z( J, ICOL1+3 )
Z( J, ICOL1+1 ) = H11 - SUM
H11 = H22 - SUM*CONJG( V22 )
H22 = Z( J, ICOL1+3 ) - SUM*CONJG( V32 )
SUM = T13*H11 + T23*H22 + T33*Z( J, ICOL1+4 )
Z( J, ICOL1+2 ) = H11 - SUM
Z( J, ICOL1+3 ) = H22 - SUM*CONJG( V23 )
Z( J, ICOL1+4 ) = Z( J, ICOL1+4 ) -
$ SUM*CONJG( V33 )
80 CONTINUE
END IF
ICOL1 = ICOL1 + 3
90 CONTINUE
DO 120 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 100 J = ITMP1, ITMP2
SUM = T1*A( J, ICOL1 ) + T2*A( J, ICOL1+1 ) +
$ T3*A( J, ICOL1+2 )
A( J, ICOL1 ) = A( J, ICOL1 ) - SUM
A( J, ICOL1+1 ) = A( J, ICOL1+1 ) - SUM*CONJG( V2 )
A( J, ICOL1+2 ) = A( J, ICOL1+2 ) - SUM*CONJG( V3 )
100 CONTINUE
IF( WANTZ ) THEN
DO 110 J = LILOZ, LIHIZ
SUM = T1*Z( J, ICOL1 ) + T2*Z( J, ICOL1+1 ) +
$ T3*Z( J, ICOL1+2 )
Z( J, ICOL1 ) = Z( J, ICOL1 ) - SUM
Z( J, ICOL1+1 ) = Z( J, ICOL1+1 ) -
$ SUM*CONJG( V2 )
Z( J, ICOL1+2 ) = Z( J, ICOL1+2 ) -
$ SUM*CONJG( V3 )
110 CONTINUE
END IF
ICOL1 = ICOL1 + 1
120 CONTINUE
ELSE
DO 130 J = ITMP1, ITMP2
SUM = T1*A( J, ICOL1 ) + T2*A( J, ICOL1+1 ) +
$ T3*A( J, ICOL1+2 )
A( J, ICOL1 ) = A( J, ICOL1 ) - SUM
A( J, ICOL1+1 ) = A( J, ICOL1+1 ) - SUM*CONJG( V2 )
A( J, ICOL1+2 ) = A( J, ICOL1+2 ) - SUM*CONJG( V3 )
130 CONTINUE
END IF
END IF
RETURN
*
* End of CLAREF
*
END
|
