ZLAQP2(3)

💅 ZLAQP2(3) — like, the QR-with-column-pivoting of a matrix block, bestie

okay so this is a ZLAQP2(3) situation and the manual says the thing lives at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zlaqp2.f — that's the NAME entry, fr, it's literally just the file path, no cap 🫶

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✨ SYNOPSIS ✨

🎀 Functions/Subroutines

subroutine ZLAQP2 (m, n, offset, a, lda, jpvt, tau, vn1, vn2, work)

ZLAQP2 computes a QR factorization with column pivoting of the matrix block. (yes that's the whole pitch, and it ate 💅)

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🌸 Function/Subroutine Documentation 🌸

subroutine ZLAQP2 (integer m, integer n, integer offset, 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( * ) work)

ZLAQP2 computes a QR factorization with column pivoting of the matrix block.

💖 Purpose:

!>
!> ZLAQP2 computes a QR factorization with column pivoting of
!> the block A(OFFSET+1:M,1:N).
!> The block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized.
!>

so like — the bottom part gets the whole QR glow-up, and the top part just gets shuffled around. pivoted, but not factorized. it's giving "you can sit with us but you're not getting a makeover" 😭✨

🦋 Parameters

• M — M is INTEGER. The number of rows of the matrix A. M >= 0. (zero rows is valid, she's just empty, that's fine 💀)
• N — N is INTEGER. The number of columns of the matrix A. N >= 0.
• OFFSET — OFFSET is INTEGER. The number of rows of the matrix A that must be pivoted but no factorized. OFFSET >= 0. (yes, "no factorized" — that's the manpage's words, i'm not touching it 🫶)
• A — A is COMPLEX*16 array, dimension (LDA,N). On entry, the M-by-N matrix A. On exit, the upper triangle of block A(OFFSET+1:M,1:N) is the triangular factor obtained; the elements in block A(OFFSET+1:M,1:N) below the diagonal, together with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors. Block A(1:OFFSET,1:N) has been accordingly pivoted, but no factorized. (she's changed by the end of this call, bestie, don't act surprised 💅)
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M). (that max(1,M) is doing so much heavy lifting, respect 👑)
• JPVT — JPVT is INTEGER array, dimension (N). On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted to the front of A*P (a leading column); if JPVT(i) = 0, the i-th column of A is a free column. On exit, if JPVT(i) = k, then the i-th column of A*P was the k-th column of A. (she's a receipts-keeper, icon behavior 🧾✨)
• TAU — TAU is COMPLEX*16 array, dimension (min(M,N)). 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. (partial vs exact, they're siblings, different vibes, both valid 🌈)
• WORK — WORK is COMPLEX*16 array, dimension (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 147 of file zlaqp2.f. — go look at line 147 if you wanna see the source material, she's right there 💀

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⭐ Author (the doxygen one, yes there's two, don't @ me)

Generated automatically by Doxygen for LAPACK from the source code.

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no cap, that's the whole page. mwah 💋

— generated with love for LAPACK, Version 3.12.0, dated /home/abui...RC/zlaqp2.f(3) 🦋🎀✨