SRC/zlaqp2.f(3)

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version 3.12.1 · 7 versions
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💖 SRC/zlaqp2.f 💖

okay so this page is from the Library Functions Manual, and it's literally giving main-character LAPACK energy: zlaqp2 computes a QR factorization with column pivoting of a matrix block. no cap, bestie, it's linear algebra with a little sparkle. 💅✨

✨ NAME ✨

SRC/zlaqp2.f

🌸 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.

🦋 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. That's the assignment, and it ate. 🔥

🎀 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. Lowkey important distinction, bestie. 🫶

🧚 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 the matrix A that must be pivoted but no factorized. OFFSET >= 0.

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.

LDA

LDA is INTEGER. The leading dimension of the array A. 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 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.

WORK

WORK is COMPLEX*16 array, dimension (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 147 of file zlaqp2.f.

📜 Author 📜

Generated automatically by Doxygen for LAPACK from the source code.

okay that's the whole page, bestie — this beauty is LAPACK Version 3.12.0, filed under SRC/zlaqp2.f(3) 🫶✨

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