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---
:name: dlaqps
:md5sum: cd53ffb1ef39ff1b9a7f507f393e88d5
:category: :subroutine
:arguments:
- m:
:type: integer
:intent: input
- n:
:type: integer
:intent: input
- offset:
:type: integer
:intent: input
- nb:
:type: integer
:intent: input
- kb:
:type: integer
:intent: output
- a:
:type: doublereal
:intent: input/output
:dims:
- lda
- n
- lda:
:type: integer
:intent: input
- jpvt:
:type: integer
:intent: input/output
:dims:
- n
- tau:
:type: doublereal
:intent: output
:dims:
- kb
- vn1:
:type: doublereal
:intent: input/output
:dims:
- n
- vn2:
:type: doublereal
:intent: input/output
:dims:
- n
- auxv:
:type: doublereal
:intent: input/output
:dims:
- nb
- f:
:type: doublereal
:intent: input/output
:dims:
- ldf
- nb
- ldf:
:type: integer
:intent: input
:substitutions:
kb: nb
:fortran_help: " SUBROUTINE DLAQPS( M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1, VN2, AUXV, F, LDF )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DLAQPS computes a step of QR factorization with column pivoting\n\
* of a real M-by-N matrix A by using Blas-3. It tries to factorize\n\
* NB columns from A starting from the row OFFSET+1, and updates all\n\
* of the matrix with Blas-3 xGEMM.\n\
*\n\
* In some cases, due to catastrophic cancellations, it cannot\n\
* factorize NB columns. Hence, the actual number of factorized\n\
* columns is returned in KB.\n\
*\n\
* Block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* M (input) INTEGER\n\
* The number of rows of the matrix A. M >= 0.\n\
*\n\
* N (input) INTEGER\n\
* The number of columns of the matrix A. N >= 0\n\
*\n\
* OFFSET (input) INTEGER\n\
* The number of rows of A that have been factorized in\n\
* previous steps.\n\
*\n\
* NB (input) INTEGER\n\
* The number of columns to factorize.\n\
*\n\
* KB (output) INTEGER\n\
* The number of columns actually factorized.\n\
*\n\
* A (input/output) DOUBLE PRECISION array, dimension (LDA,N)\n\
* On entry, the M-by-N matrix A.\n\
* On exit, block A(OFFSET+1:M,1:KB) is the triangular\n\
* factor obtained and block A(1:OFFSET,1:N) has been\n\
* accordingly pivoted, but no factorized.\n\
* The rest of the matrix, block A(OFFSET+1:M,KB+1:N) has\n\
* been updated.\n\
*\n\
* LDA (input) INTEGER\n\
* The leading dimension of the array A. LDA >= max(1,M).\n\
*\n\
* JPVT (input/output) INTEGER array, dimension (N)\n\
* JPVT(I) = K <==> Column K of the full matrix A has been\n\
* permuted into position I in AP.\n\
*\n\
* TAU (output) DOUBLE PRECISION array, dimension (KB)\n\
* The scalar factors of the elementary reflectors.\n\
*\n\
* VN1 (input/output) DOUBLE PRECISION array, dimension (N)\n\
* The vector with the partial column norms.\n\
*\n\
* VN2 (input/output) DOUBLE PRECISION array, dimension (N)\n\
* The vector with the exact column norms.\n\
*\n\
* AUXV (input/output) DOUBLE PRECISION array, dimension (NB)\n\
* Auxiliar vector.\n\
*\n\
* F (input/output) DOUBLE PRECISION array, dimension (LDF,NB)\n\
* Matrix F' = L*Y'*A.\n\
*\n\
* LDF (input) INTEGER\n\
* The leading dimension of the array F. LDF >= max(1,N).\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* Based on contributions by\n\
* G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain\n\
* X. Sun, Computer Science Dept., Duke University, USA\n\
*\n\
* Partial column norm updating strategy modified by\n\
* Z. Drmac and Z. Bujanovic, Dept. of Mathematics,\n\
* University of Zagreb, Croatia.\n\
* June 2010\n\
* For more details see LAPACK Working Note 176.\n\
* =====================================================================\n\
*\n"
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