153 lines
4.1 KiB
FortranFixed
153 lines
4.1 KiB
FortranFixed
SUBROUTINE DLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK )
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*
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* -- LAPACK routine (version 3.1) --
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* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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* November 2006
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*
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* .. Scalar Arguments ..
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CHARACTER SIDE
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INTEGER INCV, L, LDC, M, N
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DOUBLE PRECISION TAU
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION C( LDC, * ), V( * ), WORK( * )
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* ..
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*
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* Purpose
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* =======
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*
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* DLARZ applies a real elementary reflector H to a real M-by-N
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* matrix C, from either the left or the right. H is represented in the
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* form
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*
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* H = I - tau * v * v'
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*
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* where tau is a real scalar and v is a real vector.
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*
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* If tau = 0, then H is taken to be the unit matrix.
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*
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*
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* H is a product of k elementary reflectors as returned by DTZRZF.
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*
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* Arguments
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* =========
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*
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* SIDE (input) CHARACTER*1
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* = 'L': form H * C
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* = 'R': form C * H
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*
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* M (input) INTEGER
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* The number of rows of the matrix C.
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*
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* N (input) INTEGER
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* The number of columns of the matrix C.
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*
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* L (input) INTEGER
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* The number of entries of the vector V containing
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* the meaningful part of the Householder vectors.
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* If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
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*
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* V (input) DOUBLE PRECISION array, dimension (1+(L-1)*abs(INCV))
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* The vector v in the representation of H as returned by
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* DTZRZF. V is not used if TAU = 0.
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*
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* INCV (input) INTEGER
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* The increment between elements of v. INCV <> 0.
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*
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* TAU (input) DOUBLE PRECISION
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* The value tau in the representation of H.
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*
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* C (input/output) DOUBLE PRECISION array, dimension (LDC,N)
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* On entry, the M-by-N matrix C.
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* On exit, C is overwritten by the matrix H * C if SIDE = 'L',
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* or C * H if SIDE = 'R'.
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*
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* LDC (input) INTEGER
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* The leading dimension of the array C. LDC >= max(1,M).
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*
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* WORK (workspace) DOUBLE PRECISION array, dimension
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* (N) if SIDE = 'L'
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* or (M) if SIDE = 'R'
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*
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* Further Details
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* ===============
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*
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* Based on contributions by
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* A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ONE, ZERO
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PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
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* ..
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* .. External Subroutines ..
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EXTERNAL DAXPY, DCOPY, DGEMV, DGER
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. Executable Statements ..
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*
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IF( LSAME( SIDE, 'L' ) ) THEN
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*
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* Form H * C
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*
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IF( TAU.NE.ZERO ) THEN
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*
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* w( 1:n ) = C( 1, 1:n )
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*
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CALL DCOPY( N, C, LDC, WORK, 1 )
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*
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* w( 1:n ) = w( 1:n ) + C( m-l+1:m, 1:n )' * v( 1:l )
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*
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CALL DGEMV( 'Transpose', L, N, ONE, C( M-L+1, 1 ), LDC, V,
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$ INCV, ONE, WORK, 1 )
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*
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* C( 1, 1:n ) = C( 1, 1:n ) - tau * w( 1:n )
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*
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CALL DAXPY( N, -TAU, WORK, 1, C, LDC )
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*
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* C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
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* tau * v( 1:l ) * w( 1:n )'
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*
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CALL DGER( L, N, -TAU, V, INCV, WORK, 1, C( M-L+1, 1 ),
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$ LDC )
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END IF
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*
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ELSE
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*
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* Form C * H
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*
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IF( TAU.NE.ZERO ) THEN
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*
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* w( 1:m ) = C( 1:m, 1 )
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*
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CALL DCOPY( M, C, 1, WORK, 1 )
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*
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* w( 1:m ) = w( 1:m ) + C( 1:m, n-l+1:n, 1:n ) * v( 1:l )
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*
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CALL DGEMV( 'No transpose', M, L, ONE, C( 1, N-L+1 ), LDC,
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$ V, INCV, ONE, WORK, 1 )
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*
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* C( 1:m, 1 ) = C( 1:m, 1 ) - tau * w( 1:m )
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*
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CALL DAXPY( M, -TAU, WORK, 1, C, 1 )
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*
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* C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ...
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* tau * w( 1:m ) * v( 1:l )'
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*
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CALL DGER( M, L, -TAU, WORK, 1, V, INCV, C( 1, N-L+1 ),
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$ LDC )
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*
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END IF
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*
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END IF
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*
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RETURN
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*
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* End of DLARZ
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*
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END
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