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authorjofret2009-04-28 07:17:00 +0000
committerjofret2009-04-28 07:17:00 +0000
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Moving lapack to right place
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- SUBROUTINE DLATRZ( M, N, L, A, LDA, TAU, WORK )
-*
-* -- LAPACK routine (version 3.1) --
-* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
-* November 2006
-*
-* .. Scalar Arguments ..
- INTEGER L, LDA, M, N
-* ..
-* .. Array Arguments ..
- DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
-* ..
-*
-* Purpose
-* =======
-*
-* DLATRZ factors the M-by-(M+L) real upper trapezoidal matrix
-* [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R 0 ) * Z, by means
-* of orthogonal transformations. Z is an (M+L)-by-(M+L) orthogonal
-* matrix and, R and A1 are M-by-M upper triangular matrices.
-*
-* Arguments
-* =========
-*
-* M (input) INTEGER
-* The number of rows of the matrix A. M >= 0.
-*
-* N (input) INTEGER
-* The number of columns of the matrix A. N >= 0.
-*
-* L (input) INTEGER
-* The number of columns of the matrix A containing the
-* meaningful part of the Householder vectors. N-M >= L >= 0.
-*
-* A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
-* On entry, the leading M-by-N upper trapezoidal part of the
-* array A must contain the matrix to be factorized.
-* On exit, the leading M-by-M upper triangular part of A
-* contains the upper triangular matrix R, and elements N-L+1 to
-* N of the first M rows of A, with the array TAU, represent the
-* orthogonal matrix Z as a product of M elementary reflectors.
-*
-* LDA (input) INTEGER
-* The leading dimension of the array A. LDA >= max(1,M).
-*
-* TAU (output) DOUBLE PRECISION array, dimension (M)
-* The scalar factors of the elementary reflectors.
-*
-* WORK (workspace) DOUBLE PRECISION array, dimension (M)
-*
-* Further Details
-* ===============
-*
-* Based on contributions by
-* A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
-*
-* The factorization is obtained by Householder's method. The kth
-* transformation matrix, Z( k ), which is used to introduce zeros into
-* the ( m - k + 1 )th row of A, is given in the form
-*
-* Z( k ) = ( I 0 ),
-* ( 0 T( k ) )
-*
-* where
-*
-* T( k ) = I - tau*u( k )*u( k )', u( k ) = ( 1 ),
-* ( 0 )
-* ( z( k ) )
-*
-* tau is a scalar and z( k ) is an l element vector. tau and z( k )
-* are chosen to annihilate the elements of the kth row of A2.
-*
-* The scalar tau is returned in the kth element of TAU and the vector
-* u( k ) in the kth row of A2, such that the elements of z( k ) are
-* in a( k, l + 1 ), ..., a( k, n ). The elements of R are returned in
-* the upper triangular part of A1.
-*
-* Z is given by
-*
-* Z = Z( 1 ) * Z( 2 ) * ... * Z( m ).
-*
-* =====================================================================
-*
-* .. Parameters ..
- DOUBLE PRECISION ZERO
- PARAMETER ( ZERO = 0.0D+0 )
-* ..
-* .. Local Scalars ..
- INTEGER I
-* ..
-* .. External Subroutines ..
- EXTERNAL DLARFG, DLARZ
-* ..
-* .. Executable Statements ..
-*
-* Test the input arguments
-*
-* Quick return if possible
-*
- IF( M.EQ.0 ) THEN
- RETURN
- ELSE IF( M.EQ.N ) THEN
- DO 10 I = 1, N
- TAU( I ) = ZERO
- 10 CONTINUE
- RETURN
- END IF
-*
- DO 20 I = M, 1, -1
-*
-* Generate elementary reflector H(i) to annihilate
-* [ A(i,i) A(i,n-l+1:n) ]
-*
- CALL DLARFG( L+1, A( I, I ), A( I, N-L+1 ), LDA, TAU( I ) )
-*
-* Apply H(i) to A(1:i-1,i:n) from the right
-*
- CALL DLARZ( 'Right', I-1, N-I+1, L, A( I, N-L+1 ), LDA,
- $ TAU( I ), A( 1, I ), LDA, WORK )
-*
- 20 CONTINUE
-*
- RETURN
-*
-* End of DLATRZ
-*
- END