193 lines
5.0 KiB
Fortran
193 lines
5.0 KiB
Fortran
*> \brief \b SGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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*> \htmlonly
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*> Download SGELQ2 + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sgelq2.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sgelq2.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sgelq2.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE SGELQ2( M, N, A, LDA, TAU, WORK, INFO )
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*
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* .. Scalar Arguments ..
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* INTEGER INFO, LDA, M, N
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* ..
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* .. Array Arguments ..
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* REAL A( LDA, * ), TAU( * ), WORK( * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> SGELQ2 computes an LQ factorization of a real m by n matrix A:
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*> A = L * Q.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] M
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*> \verbatim
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*> M is INTEGER
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*> The number of rows of the matrix A. M >= 0.
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The number of columns of the matrix A. N >= 0.
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*> \endverbatim
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*>
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*> \param[in,out] A
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*> \verbatim
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*> A is REAL array, dimension (LDA,N)
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*> On entry, the m by n matrix A.
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*> On exit, the elements on and below the diagonal of the array
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*> contain the m by min(m,n) lower trapezoidal matrix L (L is
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*> lower triangular if m <= n); the elements above the diagonal,
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*> with the array TAU, represent the orthogonal matrix Q as a
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*> product of elementary reflectors (see Further Details).
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The leading dimension of the array A. LDA >= max(1,M).
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*> \endverbatim
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*>
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*> \param[out] TAU
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*> \verbatim
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*> TAU is REAL array, dimension (min(M,N))
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*> The scalar factors of the elementary reflectors (see Further
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*> Details).
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is REAL array, dimension (M)
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*> \endverbatim
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*>
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*> \param[out] INFO
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*> \verbatim
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*> INFO is INTEGER
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*> = 0: successful exit
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*> < 0: if INFO = -i, the i-th argument had an illegal value
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \date September 2012
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*
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*> \ingroup realGEcomputational
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*
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*> \par Further Details:
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* =====================
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*>
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*> \verbatim
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*>
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*> The matrix Q is represented as a product of elementary reflectors
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*>
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*> Q = H(k) . . . H(2) H(1), where k = min(m,n).
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*>
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*> Each H(i) has the form
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*>
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*> H(i) = I - tau * v * v**T
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*>
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*> where tau is a real scalar, and v is a real vector with
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*> v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n),
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*> and tau in TAU(i).
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*> \endverbatim
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*>
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* =====================================================================
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SUBROUTINE SGELQ2( M, N, A, LDA, TAU, WORK, INFO )
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*
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* -- LAPACK computational routine (version 3.4.2) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* September 2012
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*
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* .. Scalar Arguments ..
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INTEGER INFO, LDA, M, N
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* ..
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* .. Array Arguments ..
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REAL A( LDA, * ), TAU( * ), WORK( * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ONE
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PARAMETER ( ONE = 1.0E+0 )
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* ..
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* .. Local Scalars ..
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INTEGER I, K
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REAL AII
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* ..
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* .. External Subroutines ..
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EXTERNAL SLARF, SLARFG, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, MIN
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* ..
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* .. Executable Statements ..
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*
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* Test the input arguments
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*
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INFO = 0
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IF( M.LT.0 ) THEN
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INFO = -1
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ELSE IF( N.LT.0 ) THEN
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INFO = -2
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ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
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INFO = -4
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'SGELQ2', -INFO )
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RETURN
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END IF
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*
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K = MIN( M, N )
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*
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DO 10 I = 1, K
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*
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* Generate elementary reflector H(i) to annihilate A(i,i+1:n)
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*
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CALL SLARFG( N-I+1, A( I, I ), A( I, MIN( I+1, N ) ), LDA,
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$ TAU( I ) )
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IF( I.LT.M ) THEN
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*
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* Apply H(i) to A(i+1:m,i:n) from the right
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*
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AII = A( I, I )
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A( I, I ) = ONE
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CALL SLARF( 'Right', M-I, N-I+1, A( I, I ), LDA, TAU( I ),
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$ A( I+1, I ), LDA, WORK )
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A( I, I ) = AII
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END IF
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10 CONTINUE
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RETURN
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*
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* End of SGELQ2
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*
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END
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