SRC/claqps.f(3)

✨ NAME ✨

okay so bestie, this page is SRC/claqps.f(3) — and the NAME line is literally just SRC/claqps.f — from the LAPACK Library Functions Manual. It's giving "subroutine with a very specific job and a lot of array dimensions" energy, and honestly? iconic. 💅

🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine claqps (m, n, offset, nb, kb, a, lda, jpvt, tau, vn1, vn2,
    auxv, f, ldf)

So what does it do? CLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3. That's the synopsis tea. 🫖

🦋 Function/Subroutine Documentation 🦋

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

Same energy as the synopsis, bestie: CLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3. 🎀

Purpose: 🎯

okay so here's the actual plot: CLAQPS computes a step of QR factorization with column pivoting of a complex 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 COMPLEX 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 no 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 COMPLEX 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 COMPLEX array, dimension (NB). Auxiliary vector.
• F — F is COMPLEX array, dimension (LDF,NB). Matrix F**H = L * Y**H * 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 claqps.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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💖 that's the page, bestie — signing off from LAPACK Version 3.12.0, file SRC/claqps.f(3). Go forth and pivot your columns, but, like, carefully. 🎀