SUBROUTINE MB04OY( M, N, V, TAU, A, LDA, B, LDB, DWORK )
C
C PURPOSE
C
C To apply a real elementary reflector H to a real (m+1)-by-n
C matrix C = [ A ], from the left, where A has one row. H is
C [ B ]
C represented in the form
C ( 1 )
C H = I - tau * u *u', u = ( ),
C ( v )
C where tau is a real scalar and v is a real m-vector.
C
C If tau = 0, then H is taken to be the unit matrix.
C
C In-line code is used if H has order < 11.
C
C ARGUMENTS
C
C Input/Output Parameters
C
C M (input) INTEGER
C The number of rows of the matrix B. M >= 0.
C
C N (input) INTEGER
C The number of columns of the matrices A and B. N >= 0.
C
C V (input) DOUBLE PRECISION array, dimension (M)
C The vector v in the representation of H.
C
C TAU (input) DOUBLE PRECISION
C The scalar factor of the elementary reflector H.
C
C A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
C On entry, the leading 1-by-N part of this array must
C contain the matrix A.
C On exit, the leading 1-by-N part of this array contains
C the updated matrix A (the first row of H * C).
C
C LDA INTEGER
C The leading dimension of array A. LDA >= 1.
C
C B (input/output) DOUBLE PRECISION array, dimension (LDB,N)
C On entry, the leading M-by-N part of this array must
C contain the matrix B.
C On exit, the leading M-by-N part of this array contains
C the updated matrix B (the last m rows of H * C).
C
C LDB INTEGER
C The leading dimension of array B. LDB >= MAX(1,M).
C
C Workspace
C
C DWORK DOUBLE PRECISION array, dimension (N)
C DWORK is not referenced if H has order less than 11.
C
C METHOD
C
C The routine applies the elementary reflector H, taking the special
C structure of C into account.
C
C NUMERICAL ASPECTS
C
C The algorithm is backward stable.
C
C CONTRIBUTORS
C
C V. Sima, Katholieke Univ. Leuven, Belgium, Feb. 1997.
C Based on LAPACK routines DLARFX and DLATZM.
C
C REVISIONS
C
C Dec. 1997.
C
C KEYWORDS
C
C Elementary matrix operations, elementary reflector, orthogonal
C transformation.
C
C ******************************************************************
C
C .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
C .. Scalar Arguments ..
INTEGER LDA, LDB, M, N
DOUBLE PRECISION TAU
C .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), B( LDB, * ), DWORK( * ), V( * )
C .. Local Scalars ..
INTEGER J
DOUBLE PRECISION SUM, T1, T2, T3, T4, T5, T6, T7, T8, T9, V1, V2,
$ V3, V4, V5, V6, V7, V8, V9
C .. External Subroutines ..
EXTERNAL DAXPY, DCOPY, DGEMV, DGER
C
C .. Executable Statements ..
C
IF( TAU.EQ.ZERO )
$ RETURN
C
C Form H * C, where H has order m+1.
C
GO TO ( 10, 30, 50, 70, 90, 110, 130, 150,
$ 170, 190 ) M+1
C
C Code for general M. Compute
C
C w := C'*u, C := C - tau * u * w'.
C
CALL DCOPY( N, A, LDA, DWORK, 1 )
CALL DGEMV( 'Transpose', M, N, ONE, B, LDB, V, 1, ONE, DWORK, 1 )
CALL DAXPY( N, -TAU, DWORK, 1, A, LDA )
CALL DGER( M, N, -TAU, V, 1, DWORK, 1, B, LDB )
GO TO 210
10 CONTINUE
C
C Special code for 1 x 1 Householder
C
T1 = ONE - TAU
DO 20 J = 1, N
A( 1, J ) = T1*A( 1, J )
20 CONTINUE
GO TO 210
30 CONTINUE
C
C Special code for 2 x 2 Householder
C
V1 = V( 1 )
T1 = TAU*V1
DO 40 J = 1, N
SUM = A( 1, J ) + V1*B( 1, J )
A( 1, J ) = A( 1, J ) - SUM*TAU
B( 1, J ) = B( 1, J ) - SUM*T1
40 CONTINUE
GO TO 210
50 CONTINUE
C
C Special code for 3 x 3 Householder
C
V1 = V( 1 )
T1 = TAU*V1
V2 = V( 2 )
T2 = TAU*V2
DO 60 J = 1, N
SUM = A( 1, J ) + V1*B( 1, J ) + V2*B( 2, J )
A( 1, J ) = A( 1, J ) - SUM*TAU
B( 1, J ) = B( 1, J ) - SUM*T1
B( 2, J ) = B( 2, J ) - SUM*T2
60 CONTINUE
GO TO 210
70 CONTINUE
C
C Special code for 4 x 4 Householder
C
V1 = V( 1 )
T1 = TAU*V1
V2 = V( 2 )
T2 = TAU*V2
V3 = V( 3 )
T3 = TAU*V3
DO 80 J = 1, N
SUM = A( 1, J ) + V1*B( 1, J ) + V2*B( 2, J ) + V3*B( 3, J )
A( 1, J ) = A( 1, J ) - SUM*TAU
B( 1, J ) = B( 1, J ) - SUM*T1
B( 2, J ) = B( 2, J ) - SUM*T2
B( 3, J ) = B( 3, J ) - SUM*T3
80 CONTINUE
GO TO 210
90 CONTINUE
C
C Special code for 5 x 5 Householder
C
V1 = V( 1 )
T1 = TAU*V1
V2 = V( 2 )
T2 = TAU*V2
V3 = V( 3 )
T3 = TAU*V3
V4 = V( 4 )
T4 = TAU*V4
DO 100 J = 1, N
SUM = A( 1, J ) + V1*B( 1, J ) + V2*B( 2, J ) + V3*B( 3, J ) +
$ V4*B( 4, J )
A( 1, J ) = A( 1, J ) - SUM*TAU
B( 1, J ) = B( 1, J ) - SUM*T1
B( 2, J ) = B( 2, J ) - SUM*T2
B( 3, J ) = B( 3, J ) - SUM*T3
B( 4, J ) = B( 4, J ) - SUM*T4
100 CONTINUE
GO TO 210
110 CONTINUE
C
C Special code for 6 x 6 Householder
C
V1 = V( 1 )
T1 = TAU*V1
V2 = V( 2 )
T2 = TAU*V2
V3 = V( 3 )
T3 = TAU*V3
V4 = V( 4 )
T4 = TAU*V4
V5 = V( 5 )
T5 = TAU*V5
DO 120 J = 1, N
SUM = A( 1, J ) + V1*B( 1, J ) + V2*B( 2, J ) + V3*B( 3, J ) +
$ V4*B( 4, J ) + V5*B( 5, J )
A( 1, J ) = A( 1, J ) - SUM*TAU
B( 1, J ) = B( 1, J ) - SUM*T1
B( 2, J ) = B( 2, J ) - SUM*T2
B( 3, J ) = B( 3, J ) - SUM*T3
B( 4, J ) = B( 4, J ) - SUM*T4
B( 5, J ) = B( 5, J ) - SUM*T5
120 CONTINUE
GO TO 210
130 CONTINUE
C
C Special code for 7 x 7 Householder
C
V1 = V( 1 )
T1 = TAU*V1
V2 = V( 2 )
T2 = TAU*V2
V3 = V( 3 )
T3 = TAU*V3
V4 = V( 4 )
T4 = TAU*V4
V5 = V( 5 )
T5 = TAU*V5
V6 = V( 6 )
T6 = TAU*V6
DO 140 J = 1, N
SUM = A( 1, J ) + V1*B( 1, J ) + V2*B( 2, J ) + V3*B( 3, J ) +
$ V4*B( 4, J ) + V5*B( 5, J ) + V6*B( 6, J )
A( 1, J ) = A( 1, J ) - SUM*TAU
B( 1, J ) = B( 1, J ) - SUM*T1
B( 2, J ) = B( 2, J ) - SUM*T2
B( 3, J ) = B( 3, J ) - SUM*T3
B( 4, J ) = B( 4, J ) - SUM*T4
B( 5, J ) = B( 5, J ) - SUM*T5
B( 6, J ) = B( 6, J ) - SUM*T6
140 CONTINUE
GO TO 210
150 CONTINUE
C
C Special code for 8 x 8 Householder
C
V1 = V( 1 )
T1 = TAU*V1
V2 = V( 2 )
T2 = TAU*V2
V3 = V( 3 )
T3 = TAU*V3
V4 = V( 4 )
T4 = TAU*V4
V5 = V( 5 )
T5 = TAU*V5
V6 = V( 6 )
T6 = TAU*V6
V7 = V( 7 )
T7 = TAU*V7
DO 160 J = 1, N
SUM = A( 1, J ) + V1*B( 1, J ) + V2*B( 2, J ) + V3*B( 3, J ) +
$ V4*B( 4, J ) + V5*B( 5, J ) + V6*B( 6, J ) +
$ V7*B( 7, J )
A( 1, J ) = A( 1, J ) - SUM*TAU
B( 1, J ) = B( 1, J ) - SUM*T1
B( 2, J ) = B( 2, J ) - SUM*T2
B( 3, J ) = B( 3, J ) - SUM*T3
B( 4, J ) = B( 4, J ) - SUM*T4
B( 5, J ) = B( 5, J ) - SUM*T5
B( 6, J ) = B( 6, J ) - SUM*T6
B( 7, J ) = B( 7, J ) - SUM*T7
160 CONTINUE
GO TO 210
170 CONTINUE
C
C Special code for 9 x 9 Householder
C
V1 = V( 1 )
T1 = TAU*V1
V2 = V( 2 )
T2 = TAU*V2
V3 = V( 3 )
T3 = TAU*V3
V4 = V( 4 )
T4 = TAU*V4
V5 = V( 5 )
T5 = TAU*V5
V6 = V( 6 )
T6 = TAU*V6
V7 = V( 7 )
T7 = TAU*V7
V8 = V( 8 )
T8 = TAU*V8
DO 180 J = 1, N
SUM = A( 1, J ) + V1*B( 1, J ) + V2*B( 2, J ) + V3*B( 3, J ) +
$ V4*B( 4, J ) + V5*B( 5, J ) + V6*B( 6, J ) +
$ V7*B( 7, J ) + V8*B( 8, J )
A( 1, J ) = A( 1, J ) - SUM*TAU
B( 1, J ) = B( 1, J ) - SUM*T1
B( 2, J ) = B( 2, J ) - SUM*T2
B( 3, J ) = B( 3, J ) - SUM*T3
B( 4, J ) = B( 4, J ) - SUM*T4
B( 5, J ) = B( 5, J ) - SUM*T5
B( 6, J ) = B( 6, J ) - SUM*T6
B( 7, J ) = B( 7, J ) - SUM*T7
B( 8, J ) = B( 8, J ) - SUM*T8
180 CONTINUE
GO TO 210
190 CONTINUE
C
C Special code for 10 x 10 Householder
C
V1 = V( 1 )
T1 = TAU*V1
V2 = V( 2 )
T2 = TAU*V2
V3 = V( 3 )
T3 = TAU*V3
V4 = V( 4 )
T4 = TAU*V4
V5 = V( 5 )
T5 = TAU*V5
V6 = V( 6 )
T6 = TAU*V6
V7 = V( 7 )
T7 = TAU*V7
V8 = V( 8 )
T8 = TAU*V8
V9 = V( 9 )
T9 = TAU*V9
DO 200 J = 1, N
SUM = A( 1, J ) + V1*B( 1, J ) + V2*B( 2, J ) + V3*B( 3, J ) +
$ V4*B( 4, J ) + V5*B( 5, J ) + V6*B( 6, J ) +
$ V7*B( 7, J ) + V8*B( 8, J ) + V9*B( 9, J )
A( 1, J ) = A( 1, J ) - SUM*TAU
B( 1, J ) = B( 1, J ) - SUM*T1
B( 2, J ) = B( 2, J ) - SUM*T2
B( 3, J ) = B( 3, J ) - SUM*T3
B( 4, J ) = B( 4, J ) - SUM*T4
B( 5, J ) = B( 5, J ) - SUM*T5
B( 6, J ) = B( 6, J ) - SUM*T6
B( 7, J ) = B( 7, J ) - SUM*T7
B( 8, J ) = B( 8, J ) - SUM*T8
B( 9, J ) = B( 9, J ) - SUM*T9
200 CONTINUE
210 CONTINUE
RETURN
C *** Last line of MB04OY ***
END