added lapack 3.7.0 with latest patches from git
This commit is contained in:
Werner Saar
192
lapack-netlib/SRC/dgelq2.f
Normal file
192
lapack-netlib/SRC/dgelq2.f
Normal file
@@ -0,0 +1,192 @@
|
||||
*> \brief \b DGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.
|
||||
*
|
||||
* =========== DOCUMENTATION ===========
|
||||
*
|
||||
* Online html documentation available at
|
||||
* http://www.netlib.org/lapack/explore-html/
|
||||
*
|
||||
*> \htmlonly
|
||||
*> Download DGELQ2 + dependencies
|
||||
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgelq2.f">
|
||||
*> [TGZ]</a>
|
||||
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgelq2.f">
|
||||
*> [ZIP]</a>
|
||||
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgelq2.f">
|
||||
*> [TXT]</a>
|
||||
*> \endhtmlonly
|
||||
*
|
||||
* Definition:
|
||||
* ===========
|
||||
*
|
||||
* SUBROUTINE DGELQ2( M, N, A, LDA, TAU, WORK, INFO )
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
* INTEGER INFO, LDA, M, N
|
||||
* ..
|
||||
* .. Array Arguments ..
|
||||
* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
|
||||
* ..
|
||||
*
|
||||
*
|
||||
*> \par Purpose:
|
||||
* =============
|
||||
*>
|
||||
*> \verbatim
|
||||
*>
|
||||
*> DGELQ2 computes an LQ factorization of a real m by n matrix A:
|
||||
*> A = L * Q.
|
||||
*> \endverbatim
|
||||
*
|
||||
* Arguments:
|
||||
* ==========
|
||||
*
|
||||
*> \param[in] M
|
||||
*> \verbatim
|
||||
*> M is INTEGER
|
||||
*> The number of rows of the matrix A. M >= 0.
|
||||
*> \endverbatim
|
||||
*>
|
||||
*> \param[in] N
|
||||
*> \verbatim
|
||||
*> N is INTEGER
|
||||
*> The number of columns of the matrix A. N >= 0.
|
||||
*> \endverbatim
|
||||
*>
|
||||
*> \param[in,out] A
|
||||
*> \verbatim
|
||||
*> A is DOUBLE PRECISION array, dimension (LDA,N)
|
||||
*> On entry, the m by n matrix A.
|
||||
*> On exit, the elements on and below the diagonal of the array
|
||||
*> contain the m by min(m,n) lower trapezoidal matrix L (L is
|
||||
*> lower triangular if m <= n); the elements above the diagonal,
|
||||
*> with the array TAU, represent the orthogonal matrix Q as a
|
||||
*> product of elementary reflectors (see Further Details).
|
||||
*> \endverbatim
|
||||
*>
|
||||
*> \param[in] LDA
|
||||
*> \verbatim
|
||||
*> LDA is INTEGER
|
||||
*> The leading dimension of the array A. LDA >= max(1,M).
|
||||
*> \endverbatim
|
||||
*>
|
||||
*> \param[out] TAU
|
||||
*> \verbatim
|
||||
*> TAU is DOUBLE PRECISION array, dimension (min(M,N))
|
||||
*> The scalar factors of the elementary reflectors (see Further
|
||||
*> Details).
|
||||
*> \endverbatim
|
||||
*>
|
||||
*> \param[out] WORK
|
||||
*> \verbatim
|
||||
*> WORK is DOUBLE PRECISION array, dimension (M)
|
||||
*> \endverbatim
|
||||
*>
|
||||
*> \param[out] INFO
|
||||
*> \verbatim
|
||||
*> INFO is INTEGER
|
||||
*> = 0: successful exit
|
||||
*> < 0: if INFO = -i, the i-th argument had an illegal value
|
||||
*> \endverbatim
|
||||
*
|
||||
* Authors:
|
||||
* ========
|
||||
*
|
||||
*> \author Univ. of Tennessee
|
||||
*> \author Univ. of California Berkeley
|
||||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup doubleGEcomputational
|
||||
*
|
||||
*> \par Further Details:
|
||||
* =====================
|
||||
*>
|
||||
*> \verbatim
|
||||
*>
|
||||
*> The matrix Q is represented as a product of elementary reflectors
|
||||
*>
|
||||
*> Q = H(k) . . . H(2) H(1), where k = min(m,n).
|
||||
*>
|
||||
*> Each H(i) has the form
|
||||
*>
|
||||
*> H(i) = I - tau * v * v**T
|
||||
*>
|
||||
*> where tau is a real scalar, and v is a real vector with
|
||||
*> v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n),
|
||||
*> and tau in TAU(i).
|
||||
*> \endverbatim
|
||||
*>
|
||||
* =====================================================================
|
||||
SUBROUTINE DGELQ2( M, N, A, LDA, TAU, WORK, INFO )
|
||||
*
|
||||
* -- LAPACK computational routine (version 3.7.0) --
|
||||
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INFO, LDA, M, N
|
||||
* ..
|
||||
* .. Array Arguments ..
|
||||
DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
|
||||
* ..
|
||||
*
|
||||
* =====================================================================
|
||||
*
|
||||
* .. Parameters ..
|
||||
DOUBLE PRECISION ONE
|
||||
PARAMETER ( ONE = 1.0D+0 )
|
||||
* ..
|
||||
* .. Local Scalars ..
|
||||
INTEGER I, K
|
||||
DOUBLE PRECISION AII
|
||||
* ..
|
||||
* .. External Subroutines ..
|
||||
EXTERNAL DLARF, DLARFG, XERBLA
|
||||
* ..
|
||||
* .. Intrinsic Functions ..
|
||||
INTRINSIC MAX, MIN
|
||||
* ..
|
||||
* .. Executable Statements ..
|
||||
*
|
||||
* Test the input arguments
|
||||
*
|
||||
INFO = 0
|
||||
IF( M.LT.0 ) THEN
|
||||
INFO = -1
|
||||
ELSE IF( N.LT.0 ) THEN
|
||||
INFO = -2
|
||||
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
|
||||
INFO = -4
|
||||
END IF
|
||||
IF( INFO.NE.0 ) THEN
|
||||
CALL XERBLA( 'DGELQ2', -INFO )
|
||||
RETURN
|
||||
END IF
|
||||
*
|
||||
K = MIN( M, N )
|
||||
*
|
||||
DO 10 I = 1, K
|
||||
*
|
||||
* Generate elementary reflector H(i) to annihilate A(i,i+1:n)
|
||||
*
|
||||
CALL DLARFG( N-I+1, A( I, I ), A( I, MIN( I+1, N ) ), LDA,
|
||||
$ TAU( I ) )
|
||||
IF( I.LT.M ) THEN
|
||||
*
|
||||
* Apply H(i) to A(i+1:m,i:n) from the right
|
||||
*
|
||||
AII = A( I, I )
|
||||
A( I, I ) = ONE
|
||||
CALL DLARF( 'Right', M-I, N-I+1, A( I, I ), LDA, TAU( I ),
|
||||
$ A( I+1, I ), LDA, WORK )
|
||||
A( I, I ) = AII
|
||||
END IF
|
||||
10 CONTINUE
|
||||
RETURN
|
||||
*
|
||||
* End of DGELQ2
|
||||
*
|
||||
END
|
||||
Reference in New Issue
Block a user