SLAQPS(3)

okay bestie, welcome to the Library Functions Manual page for SLAQPS(3) — yes, we're doing QR factorization step content today, and it's lowkey iconic 💅✨

💖 NAME 💖

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/slaqps.f

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

• subroutine SLAQPS (m, n, offset, nb, kb, a, lda, jpvt, tau, vn1, vn2, auxv, f, ldf) — SLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3.

🔥 Function/Subroutine Documentation 🔥

subroutine SLAQPS (integer m, integer n, integer offset, integer nb, integer kb, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) jpvt, real, dimension( * ) tau, real, dimension( * ) vn1, real, dimension( * ) vn2, real, dimension( * ) auxv, real, dimension( ldf, * ) f, integer ldf)

SLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3.

🎯 Purpose 🎯

SLAQPS computes a step of QR factorization with column pivoting of a real M-by-N matrix A by using Blas-3. It tries to factorize NB columns from A starting from the row OFFSET+1, and updates all of the matrix with Blas-3 xGEMM.

In some cases, due to catastrophic cancellations, it cannot factorize NB columns. Hence, the actual number of factorized columns is returned in KB.

Block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized.

🧚 Parameters 🧚

• M — M is INTEGER. The number of rows of the matrix A. M >= 0.
• N — N is INTEGER. The number of columns of the matrix A. N >= 0
• OFFSET — OFFSET is INTEGER. The number of rows of A that have been factorized in previous steps.
• NB — NB is INTEGER. The number of columns to factorize.
• KB — KB is INTEGER. The number of columns actually factorized.
• A — A is REAL array, dimension (LDA,N). On entry, the M-by-N matrix A. On exit, block A(OFFSET+1:M,1:KB) is the triangular factor obtained and block A(1:OFFSET,1:N) has been accordingly pivoted, but not factorized. The rest of the matrix, block A(OFFSET+1:M,KB+1:N), has been updated.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).
• JPVT — JPVT is INTEGER array, dimension (N). JPVT(I) = K <==> Column K of the full matrix A has been permuted into position I in AP.
• TAU — TAU is REAL array, dimension (KB). The scalar factors of the elementary reflectors.
• VN1 — VN1 is REAL array, dimension (N). The vector with the partial column norms.
• VN2 — VN2 is REAL array, dimension (N). The vector with the exact column norms.
• AUXV — AUXV is REAL array, dimension (NB). Auxiliary vector.
• F — F is REAL array, dimension (LDF,NB). Matrix F**T = L*Y**T*A.
• LDF — LDF is INTEGER. The leading dimension of the array F. LDF >= max(1,N).

👑 Author 👑

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

🫶 Contributors: 🫶

• G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
• X. Sun, Computer Science Dept., Duke University, USA

Partial column norm updating strategy modified on April 2011 Z. Drmac and Z. Bujanovic, Dept. of Mathematics, University of Zagreb, Croatia.

🌈 References: 🌈

• LAPACK Working Note 176

Definition at line 176 of file slaqps.f.

🌸 Author 🌸

Generated automatically by Doxygen for LAPACK from the source code.

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