--- rpl/lapack/lapack/zlaqp2.f 2011/07/22 07:38:17 1.9 +++ rpl/lapack/lapack/zlaqp2.f 2011/11/21 20:43:16 1.10 @@ -1,10 +1,158 @@ +*> \brief \b ZLAQP2 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ZLAQP2 + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE ZLAQP2( M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2, +* WORK ) +* +* .. Scalar Arguments .. +* INTEGER LDA, M, N, OFFSET +* .. +* .. Array Arguments .. +* INTEGER JPVT( * ) +* DOUBLE PRECISION VN1( * ), VN2( * ) +* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ZLAQP2 computes a QR factorization with column pivoting of +*> the block A(OFFSET+1:M,1:N). +*> The block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized. +*> \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] OFFSET +*> \verbatim +*> OFFSET is INTEGER +*> The number of rows of the matrix A that must be pivoted +*> but no factorized. OFFSET >= 0. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is COMPLEX*16 array, dimension (LDA,N) +*> On entry, the M-by-N matrix A. +*> On exit, the upper triangle of block A(OFFSET+1:M,1:N) is +*> the triangular factor obtained; the elements in block +*> A(OFFSET+1:M,1:N) below the diagonal, together with the +*> array TAU, represent the orthogonal matrix Q as a product of +*> elementary reflectors. Block A(1:OFFSET,1:N) has been +*> accordingly pivoted, but no factorized. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,M). +*> \endverbatim +*> +*> \param[in,out] JPVT +*> \verbatim +*> JPVT is INTEGER array, dimension (N) +*> On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted +*> to the front of A*P (a leading column); if JPVT(i) = 0, +*> the i-th column of A is a free column. +*> On exit, if JPVT(i) = k, then the i-th column of A*P +*> was the k-th column of A. +*> \endverbatim +*> +*> \param[out] TAU +*> \verbatim +*> TAU is COMPLEX*16 array, dimension (min(M,N)) +*> The scalar factors of the elementary reflectors. +*> \endverbatim +*> +*> \param[in,out] VN1 +*> \verbatim +*> VN1 is DOUBLE PRECISION array, dimension (N) +*> The vector with the partial column norms. +*> \endverbatim +*> +*> \param[in,out] VN2 +*> \verbatim +*> VN2 is DOUBLE PRECISION array, dimension (N) +*> The vector with the exact column norms. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is COMPLEX*16 array, dimension (N) +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex16OTHERauxiliary +* +*> \par Contributors: +* ================== +*> +*> G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain +*> X. Sun, Computer Science Dept., Duke University, USA +*> \n +*> Partial column norm updating strategy modified on April 2011 +*> Z. Drmac and Z. Bujanovic, Dept. of Mathematics, +*> University of Zagreb, Croatia. +* +*> \par References: +* ================ +*> +*> LAPACK Working Note 176 +* +*> \htmlonly +*> [PDF] +*> \endhtmlonly +* +* ===================================================================== SUBROUTINE ZLAQP2( M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2, $ WORK ) * -* -- LAPACK auxiliary routine (version 3.3.1) -- +* -- LAPACK auxiliary routine (version 3.4.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -- April 2011 -- +* November 2011 * * .. Scalar Arguments .. INTEGER LDA, M, N, OFFSET @@ -15,68 +163,6 @@ COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) * .. * -* Purpose -* ======= -* -* ZLAQP2 computes a QR factorization with column pivoting of -* the block A(OFFSET+1:M,1:N). -* The block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized. -* -* 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. -* -* OFFSET (input) INTEGER -* The number of rows of the matrix A that must be pivoted -* but no factorized. OFFSET >= 0. -* -* A (input/output) COMPLEX*16 array, dimension (LDA,N) -* On entry, the M-by-N matrix A. -* On exit, the upper triangle of block A(OFFSET+1:M,1:N) is -* the triangular factor obtained; the elements in block -* A(OFFSET+1:M,1:N) below the diagonal, together with the -* array TAU, represent the orthogonal matrix Q as a product of -* elementary reflectors. Block A(1:OFFSET,1:N) has been -* accordingly pivoted, but no factorized. -* -* LDA (input) INTEGER -* The leading dimension of the array A. LDA >= max(1,M). -* -* JPVT (input/output) INTEGER array, dimension (N) -* On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted -* to the front of A*P (a leading column); if JPVT(i) = 0, -* the i-th column of A is a free column. -* On exit, if JPVT(i) = k, then the i-th column of A*P -* was the k-th column of A. -* -* TAU (output) COMPLEX*16 array, dimension (min(M,N)) -* The scalar factors of the elementary reflectors. -* -* VN1 (input/output) DOUBLE PRECISION array, dimension (N) -* The vector with the partial column norms. -* -* VN2 (input/output) DOUBLE PRECISION array, dimension (N) -* The vector with the exact column norms. -* -* WORK (workspace) COMPLEX*16 array, dimension (N) -* -* Further Details -* =============== -* -* Based on contributions by -* G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain -* X. Sun, Computer Science Dept., Duke University, USA -* -* Partial column norm updating strategy modified by -* Z. Drmac and Z. Bujanovic, Dept. of Mathematics, -* University of Zagreb, Croatia. -* -- April 2011 -- -* For more details see LAPACK Working Note 176. * ===================================================================== * * .. Parameters ..