SRC/zlaqps.f(3)

💅 SRC/zlaqps.f

okay bestie, welcome to the glow-up of a LAPACK subroutine 💖 this is SRC/zlaqps.f, living its best life in the Library Functions Manual. no cap, it's a whole vibe. let's get into it ✨

---

🦋 SYNOPSIS 🦋

Functions/Subroutines

• subroutine zlaqps (m, n, offset, nb, kb, a, lda, jpvt, tau, vn1, vn2, auxv, f, ldf) — ZLAQPS 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 zlaqps (integer m, integer n, integer offset, integer nb, integer
    kb, complex*16, dimension( lda, * ) a, integer lda, integer, dimension(
    * ) jpvt, complex*16, dimension( * ) tau, double precision, dimension( *
    ) vn1, double precision, dimension( * ) vn2, complex*16, dimension( * )
    auxv, complex*16, dimension( ldf, * ) f, integer ldf)

ZLAQPS 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 🌸

!> !> ZLAQPS 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. !>

so like, it tries to factorize NB columns — and when catastrophic cancellations show up and ruin the party 😭, it just tells you how many it actually got done in KB. main character honesty, honestly.

---

✨ 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. (the receipts 💅)
• A — A is COMPLEX*16 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*16 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 ✨accurate✨ queen)
• AUXV — AUXV is COMPLEX*16 array, dimension (NB), auxiliary vector.
• F — F is COMPLEX*16 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 175 of file zlaqps.f.

---

💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code.

---

ok that's the whole page, no skips, no crumbs left behind 🍓 every param, every bound, every contributor stayed. iykyk 💅

and that's the tea, bestie — this beauty is from LAPACK, Version 3.12.0, dated the LAPACK release line, and it's giving timeless icon energy 😭🔥 go factorize something slay ✨🦋👑