193 lines
5.1 KiB
Fortran
193 lines
5.1 KiB
Fortran
*> \brief \b SGELQT
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE SGELQT( M, N, MB, A, LDA, T, LDT, WORK, INFO )
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*
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* .. Scalar Arguments ..
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* INTEGER INFO, LDA, LDT, M, N, MB
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* ..
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* .. Array Arguments ..
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* REAL A( LDA, * ), T( LDT, * ), 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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*> DGELQT computes a blocked LQ factorization of a real M-by-N matrix A
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*> using the compact WY representation of 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] MB
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*> \verbatim
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*> MB is INTEGER
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*> The block size to be used in the blocked QR. MIN(M,N) >= MB >= 1.
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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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*> are the rows of V.
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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] T
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*> \verbatim
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*> T is REAL array, dimension (LDT,MIN(M,N))
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*> The upper triangular block reflectors stored in compact form
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*> as a sequence of upper triangular blocks. See below
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*> for further details.
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*> \endverbatim
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*>
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*> \param[in] LDT
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*> \verbatim
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*> LDT is INTEGER
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*> The leading dimension of the array T. LDT >= MB.
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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 (MB*N)
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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 doubleGEcomputational
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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 V stores the elementary reflectors H(i) in the i-th row
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*> above the diagonal. For example, if M=5 and N=3, the matrix V is
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*>
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*> V = ( 1 v1 v1 v1 v1 )
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*> ( 1 v2 v2 v2 )
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*> ( 1 v3 v3 )
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*>
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*>
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*> where the vi's represent the vectors which define H(i), which are returned
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*> in the matrix A. The 1's along the diagonal of V are not stored in A.
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*> Let K=MIN(M,N). The number of blocks is B = ceiling(K/MB), where each
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*> block is of order MB except for the last block, which is of order
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*> IB = K - (B-1)*MB. For each of the B blocks, a upper triangular block
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*> reflector factor is computed: T1, T2, ..., TB. The MB-by-MB (and IB-by-IB
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*> for the last block) T's are stored in the MB-by-K matrix T as
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*>
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*> T = (T1 T2 ... TB).
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*> \endverbatim
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*>
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* =====================================================================
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SUBROUTINE SGELQT( M, N, MB, A, LDA, T, LDT, 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, LDT, M, N, MB
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* ..
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* .. Array Arguments ..
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REAL A( LDA, * ), T( LDT, * ), WORK( * )
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* ..
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*
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* =====================================================================
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*
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* ..
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* .. Local Scalars ..
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INTEGER I, IB, IINFO, K
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* ..
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* .. External Subroutines ..
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EXTERNAL SGEQRT2, SGEQRT3, SGELQT3, SLARFB, XERBLA
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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( MB.LT.1 .OR. ( MB.GT.MIN(M,N) .AND. MIN(M,N).GT.0 ) )THEN
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INFO = -3
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ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
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INFO = -5
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ELSE IF( LDT.LT.MB ) THEN
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INFO = -7
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'SGELQT', -INFO )
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RETURN
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END IF
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*
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* Quick return if possible
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*
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K = MIN( M, N )
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IF( K.EQ.0 ) RETURN
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*
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* Blocked loop of length K
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*
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DO I = 1, K, MB
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IB = MIN( K-I+1, MB )
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*
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* Compute the LQ factorization of the current block A(I:M,I:I+IB-1)
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*
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CALL SGELQT3( IB, N-I+1, A(I,I), LDA, T(1,I), LDT, IINFO )
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IF( I+IB.LE.M ) THEN
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*
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* Update by applying H**T to A(I:M,I+IB:N) from the right
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*
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CALL SLARFB( 'R', 'N', 'F', 'R', M-I-IB+1, N-I+1, IB,
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$ A( I, I ), LDA, T( 1, I ), LDT,
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$ A( I+IB, I ), LDA, WORK , M-I-IB+1 )
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END IF
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END DO
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RETURN
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*
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* End of SGELQT
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*
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END
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