SRC/slaqp2.f(3)

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version 3.12.1 · 4 versions
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🎀 SRC/slaqp2.f 🎀

okay so this is the SRC/slaqp2.f(3) page from the Library Functions Manual, and bestie, it's literally all about the slaqp2 subroutine. QR factorization with column pivoting is about to have a moment. ✨

💖 NAME 💖

SRC/slaqp2.f — that's the page name, and it's here to document the slaqp2 subroutine. 💅

🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine slaqp2 (m, n, offset, a, lda, jpvt, tau, vn1, vn2, work)
    SLAQP2 computes a QR factorization with column pivoting of the matrix block.

🦋 Function/Subroutine Documentation 🦋

   subroutine slaqp2 (integer m, integer n, integer offset, real, dimension(
       lda, * ) a, integer lda, integer, dimension( * ) jpvt, real, dimension(
       * ) tau, real, dimension( * ) vn1, real, dimension( * ) vn2, real,
       dimension( * ) work)

SLAQP2 computes a QR factorization with column pivoting of the matrix block. 🫶

Purpose 🌟

SLAQP2 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.

Parameters 💖

M

M is INTEGER. It's the number of rows of the matrix A. Constraint: M >= 0. 💜

N

N is INTEGER. It's the number of columns of the matrix A. Constraint: N >= 0. 🌸

OFFSET

OFFSET is INTEGER. The number of rows of the matrix A that must be pivoted but no factorized. Constraint: OFFSET >= 0. 🎀

A

A is REAL array, dimension (LDA,N). On entry, it's 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. 🦋

LDA

LDA is INTEGER. The leading dimension of the array A. Constraint: LDA >= max(1,M). ✨

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. 💅

TAU

TAU is REAL array, dimension (min(M,N)). 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. 🔥

WORK

WORK is REAL array, dimension (N). That's the whole description in the original — no invented tea, bestie. 🍓

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 slaqp2.f.

That's the coordinates, bestie: Definition at line 147 of file slaqp2.f. 📍

Author 🌈 (the Doxygen auto-gen one)

Generated automatically by Doxygen for LAPACK from the source code. No cap. 🤖✨

okay that's the whole page, periodt. Signing off with LAPACK Version 3.12.0 and SRC/slaqp2.f(3) — 💅✨🎀

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