191 lines
5.0 KiB
Fortran
191 lines
5.0 KiB
Fortran
*> \brief \b SGERQ2 computes the RQ 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 SGERQ2 + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sgerq2.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/sgerq2.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/sgerq2.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 SGERQ2( 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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*> SGERQ2 computes an RQ factorization of a real m by n matrix A:
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*> A = R * 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, if m <= n, the upper triangle of the subarray
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*> A(1:m,n-m+1:n) contains the m by m upper triangular matrix R;
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*> if m >= n, the elements on and above the (m-n)-th subdiagonal
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*> contain the m by n upper trapezoidal matrix R; the remaining
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*> elements, with the array TAU, represent the orthogonal matrix
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*> Q as a product of elementary reflectors (see Further
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*> 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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*> \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(1) H(2) . . . H(k), 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(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
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*> A(m-k+i,1:n-k+i-1), and tau in TAU(i).
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*> \endverbatim
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*>
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* =====================================================================
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SUBROUTINE SGERQ2( M, N, A, LDA, TAU, WORK, INFO )
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*
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* -- LAPACK computational routine --
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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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*
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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( 'SGERQ2', -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 = K, 1, -1
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*
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* Generate elementary reflector H(i) to annihilate
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* A(m-k+i,1:n-k+i-1)
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*
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CALL SLARFG( N-K+I, A( M-K+I, N-K+I ), A( M-K+I, 1 ), LDA,
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$ TAU( I ) )
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*
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* Apply H(i) to A(1:m-k+i-1,1:n-k+i) from the right
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*
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AII = A( M-K+I, N-K+I )
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A( M-K+I, N-K+I ) = ONE
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CALL SLARF( 'Right', M-K+I-1, N-K+I, A( M-K+I, 1 ), LDA,
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$ TAU( I ), A, LDA, WORK )
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A( M-K+I, N-K+I ) = AII
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10 CONTINUE
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RETURN
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*
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* End of SGERQ2
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*
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END
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