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SUBROUTINE DLATZM( SIDE, M, N, V, INCV, TAU, C1, C2, LDC, WORK )
*
* -- LAPACK routine (version 2.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* February 29, 1992
*
* .. Scalar Arguments ..
CHARACTER SIDE
INTEGER INCV, LDC, M, N
DOUBLE PRECISION TAU
* ..
* .. Array Arguments ..
DOUBLE PRECISION C1( LDC, * ), C2( LDC, * ), V( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* DLATZM applies a Householder matrix generated by DTZRQF to a matrix.
*
* Let P = I - tau*u*u', u = ( 1 ),
* ( v )
* where v is an (m-1) vector if SIDE = 'L', or a (n-1) vector if
* SIDE = 'R'.
*
* If SIDE equals 'L', let
* C = [ C1 ] 1
* [ C2 ] m-1
* n
* Then C is overwritten by P*C.
*
* If SIDE equals 'R', let
* C = [ C1, C2 ] m
* 1 n-1
* Then C is overwritten by C*P.
*
* Arguments
* =========
*
* SIDE (input) CHARACTER*1
* = 'L': form P * C
* = 'R': form C * P
*
* M (input) INTEGER
* The number of rows of the matrix C.
*
* N (input) INTEGER
* The number of columns of the matrix C.
*
* V (input) DOUBLE PRECISION array, dimension
* (1 + (M-1)*abs(INCV)) if SIDE = 'L'
* (1 + (N-1)*abs(INCV)) if SIDE = 'R'
* The vector v in the representation of P. V is not used
* if TAU = 0.
*
* INCV (input) INTEGER
* The increment between elements of v. INCV <> 0
*
* TAU (input) DOUBLE PRECISION
* The value tau in the representation of P.
*
* C1 (input/output) DOUBLE PRECISION array, dimension
* (LDC,N) if SIDE = 'L'
* (M,1) if SIDE = 'R'
* On entry, the n-vector C1 if SIDE = 'L', or the m-vector C1
* if SIDE = 'R'.
*
* On exit, the first row of P*C if SIDE = 'L', or the first
* column of C*P if SIDE = 'R'.
*
* C2 (input/output) DOUBLE PRECISION array, dimension
* (LDC, N) if SIDE = 'L'
* (LDC, N-1) if SIDE = 'R'
* On entry, the (m - 1) x n matrix C2 if SIDE = 'L', or the
* m x (n - 1) matrix C2 if SIDE = 'R'.
*
* On exit, rows 2:m of P*C if SIDE = 'L', or columns 2:m of C*P
* if SIDE = 'R'.
*
* LDC (input) INTEGER
* The leading dimension of the arrays C1 and C2. LDC >= (1,M).
*
* WORK (workspace) DOUBLE PRECISION array, dimension
* (N) if SIDE = 'L'
* (M) if SIDE = 'R'
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
* ..
* .. External Subroutines ..
EXTERNAL DAXPY, DCOPY, DGEMV, DGER
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. Intrinsic Functions ..
INTRINSIC MIN
* ..
* .. Executable Statements ..
*
IF( ( MIN( M, N ).EQ.0 ) .OR. ( TAU.EQ.ZERO ) )
$ RETURN
*
IF( LSAME( SIDE, 'L' ) ) THEN
*
* w := C1 + v' * C2
*
CALL DCOPY( N, C1, LDC, WORK, 1 )
CALL DGEMV( 'Transpose', M-1, N, ONE, C2, LDC, V, INCV, ONE,
$ WORK, 1 )
*
* [ C1 ] := [ C1 ] - tau* [ 1 ] * w'
* [ C2 ] [ C2 ] [ v ]
*
CALL DAXPY( N, -TAU, WORK, 1, C1, LDC )
CALL DGER( M-1, N, -TAU, V, INCV, WORK, 1, C2, LDC )
*
ELSE IF( LSAME( SIDE, 'R' ) ) THEN
*
* w := C1 + C2 * v
*
CALL DCOPY( M, C1, 1, WORK, 1 )
CALL DGEMV( 'No transpose', M, N-1, ONE, C2, LDC, V, INCV, ONE,
$ WORK, 1 )
*
* [ C1, C2 ] := [ C1, C2 ] - tau* w * [ 1 , v']
*
CALL DAXPY( M, -TAU, WORK, 1, C1, 1 )
CALL DGER( M, N-1, -TAU, WORK, 1, V, INCV, C2, LDC )
END IF
*
RETURN
*
* End of DLATZM
*
END
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