CLAQPS(3)

🌸 claqps.f(3) — Library Functions Manual but make it fashion 🌸

okay so bestie, welcome to the claqps.f(3) page from the Library Functions Manual ✨ this is a LAPACK subroutine and it's lowkey iconic. No cap, we're keeping every parameter, every type, every >=, every author, every reference — the whole vibe check. Periodt. 💅

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✨ NAME ✨

The name is literally this whole path, bestie — it's giving very full, very unbothered 🫶

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

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🦋 SYNOPSIS 🦋

🧚 Functions/Subroutines 🧚

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)

okay so CLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3. (Yes, the synopsis says real; I'm literally not editing it, bestie 😭)

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💖 Function/Subroutine Documentation 💖

here's the signature again because the original ate and left no crumbs:

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)

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

🎯 Purpose: 🎯

so the actual mission, per the source: 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. (No cap, that's the whole mood.)

🔥 Parameters 🔥

one by one, bestie, no skipping:

• 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 (their exact wording, bestie 💀). 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).

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👑 Author 👑

the institutions behind this masterpiece, fr fr:

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

🌈 Contributors: 🌈

the besties who contributed, no cap:

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

and also: 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.

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🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code.

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okay bye bestie, final footer vibe check: LAPACK Version 3.12.0 and claqps.f(3), no date in the footer, that's all we got — mwah 💋🫶