SRC/zgerq2.f(3)

✨ NAME ✨

SRC/zgerq2.f — from the Library Functions Manual, bestie. This is the source page for zgerq2, the unblocked RQ factorization icon. 💅

✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine zgerq2 (m, n, a, lda, tau, work, info) — ZGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.

✨ Function/Subroutine Documentation ✨

Here's the whole signature, no cap:

subroutine zgerq2 (integer m, integer n, complex*16, dimension( lda, * ) a,
    integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * )
    work, integer info)

ZGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.

Purpose:

okay so the main character moment: ZGERQ2 computes an RQ factorization of a complex m by n matrix A, and it's literally:

A = R * Q.

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. 🦋
• A — A is COMPLEX*16 array, dimension (LDA,N). On entry, the m by n matrix A. On exit, if m <= n, the upper triangle of the subarray A(1:m,n-m+1:n) contains the m by m upper triangular matrix R; if m >= n, the elements on and above the (m-n)-th subdiagonal contain the m by n upper trapezoidal matrix R; the remaining elements, with the array TAU, represent the unitary matrix Q as a product of elementary reflectors (see Further Details). 🔥
• LDA — LDA is INTEGER; the leading dimension of the array A. LDA >= max(1,M). 💅
• TAU — TAU is COMPLEX*16 array, dimension (min(M,N)); the scalar factors of the elementary reflectors (see Further Details). 🎀
• WORK — WORK is COMPLEX*16 array, dimension (M). 🧚
• INFO — INFO is INTEGER; = 0: successful exit; < 0: if INFO = -i, the i-th argument had an illegal value. 😭

Author

Shoutout to the legends who brought you this routine:

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Further Details:

The matrix Q is represented as a product of elementary reflectors:

Q = H(1)**H H(2)**H . . . H(k)**H, where k = min(m,n).

Each H(i) has the form:

H(i) = I - tau * v * v**H

where tau is a complex scalar, and v is a complex vector with v(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i).

📍 Definition at line 122 of file zgerq2.f.

✨ Author ✨

This page was generated automatically by Doxygen for LAPACK from the source code. (iykyk 💀)

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And finally, the vibe check footer: LAPACK, Version 3.12.0, from SRC/zgerq2.f(3). Periodt. 💖✨🎀