DGERQ2(3)

💖 NAME 💖

Okay bestie, welcome to the Library Functions Manual page for DGERQ2(3) — the source file is exactly /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dgerq2.f. That's the whole NAME section, no cap. 🫶

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✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

• subroutine DGERQ2 (m, n, a, lda, tau, work, info) — DGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm. 💅

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🧚 Function/Subroutine Documentation 🧚

subroutine DGERQ2 (integer m, integer n, double precision, dimension( lda, *
) a, integer lda, double precision, dimension( * ) tau, double
precision, dimension( * ) work, integer info)

DGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm. It's giving linear algebra main character energy, and the source literally says it twice, so you know it's serious. 🔥

🌟 Purpose: 🌟

DGERQ2 computes an RQ factorization of a real m by n matrix A:

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 DOUBLE PRECISION 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 orthogonal 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 DOUBLE PRECISION array, dimension (min(M,N)). The scalar factors of the elementary reflectors (see Further Details).
• WORK — WORK is DOUBLE PRECISION array, dimension (M).
• INFO — INFO is INTEGER.
  • = 0: successful exit.
  • < 0: if INFO = -i, the i-th argument had an illegal value. 😭

🌸 Author 🌸

• 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(2) . . . H(k), where k = min(m,n).

Each H(i) has the form

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

where tau is a real scalar, and v is a real vector with v(n-k+i+1:n) = 0 and v(n-k+i) = 1; 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 dgerq2.f.

🎀 Author 🎀

Generated automatically by Doxygen for LAPACK from the source code.

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Cute sign-off: LAPACK Version 3.12.0, footer path /home/abui...RC/dgerq2.f(3). Date: not shown in this footer, so no invented date — periodt. 💖✨