DLAQPS(3)

🌸 DLAQPS(3) — like, the QR-step girlies' manual page 💅

okay so bestie, this is the page for dlaqps.f(3) out of the Library Functions Manual, and no cap it lives at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dlaqps.f — that's literally the whole NAME situation, it's giving "the path IS the name" energy ✨

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✨ SYNOPSIS ✨

Functions/Subroutines

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

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

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👑 Function/Subroutine Documentation 👑

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

DLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3. fr fr that's the whole gig 🫶

🦋 Purpose

!>
!> DLAQPS 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.
!>

so yeah — it tries to factorize NB columns starting at row OFFSET+1, and updates everything with Blas-3 xGEMM. but catastrophic cancellations are a thing 😭 so it might not manage all NB, and the actual count comes back in KB. block A(1:OFFSET,1:N) gets pivoted accordingly but not factorized. periodt.

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🌈 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. (the "already done, don't touch" era)
• NB — NB is INTEGER. The number of columns to factorize. (the goal)
• KB — KB is INTEGER. The number of columns actually factorized. (the reality 💀)
• A — A is DOUBLE PRECISION 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.

and yes, "but no factorized" is literally what it says, i'm not fixing the original's grammar, that's canon 🫶

• 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. (iykyk, it's the permutation receipts)
• TAU — TAU is DOUBLE PRECISION array, dimension (KB). The scalar factors of the elementary reflectors. ✨
• VN1 — VN1 is DOUBLE PRECISION array, dimension (N). The vector with the partial column norms.
• VN2 — VN2 is DOUBLE PRECISION array, dimension (N). The vector with the exact column norms. (the more precise sibling, main character energy)
• AUXV — AUXV is DOUBLE PRECISION array, dimension (NB). Auxiliary vector. 🧚
• F — F is DOUBLE PRECISION 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). 💜

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🎀 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 175 of file dlaqps.f. 🦋

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⭐ Author ⭐

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the whole thing bestie, you ate 💅 — this page is from LAPACK, Version 3.12.0, file /home/abui...RC/dlaqps.f(3), and it was auto-generated by Doxygen for LAPACK straight from the source code, so blame the robots not me 🙈 🍓