SGERQ2(3)

💅 SGERQ2(3) 💅

okay bestie, this one’s from the Library Functions Manual and it’s giving “I do RQ factorization and I do it unblocked.” No cap, SGERQ2 is the main character of this page. 🦋✨

✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-
static-3.12.0-build/lapack-3.12.0/SRC/sgerq2.f

🌸 SYNOPSIS 🌸

🦋 Functions/Subroutines 🦋

• subroutine SGERQ2 (m, n, a, lda, tau, work, info) — SGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm. 💖

🫶 Function/Subroutine Documentation 🫶

Full signature, because we respect the whole cast:

subroutine SGERQ2 (integer m, integer n, real, dimension( lda, * ) a,
    integer lda, real, dimension( * ) tau, real, dimension( * ) work,
    integer info)

SGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm. ✨

🎀 Purpose: 🎀

SGERQ2 computes an RQ factorization of a real m by n matrix A:

A = R * Q.

🍓 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. 💜
• A — A is REAL array, dimension (LDA,N).
  • On entry, it’s 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. Constraint: LDA >= max(1,M). 💅
• TAU — TAU is REAL array, dimension (min(M,N)). The scalar factors of the elementary reflectors (see Further Details). 🫶
• WORK — WORK is REAL 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 sgerq2.f. 📍

That’s the exact spot, bestie: Definition at line 122 of file sgerq2.f. ⭐

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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okay that’s the whole page, bestie 🫶. The footer vibe is LAPACK Version 3.12.0, and the source tag is /home/abui...RC/sgerq2.f(3). There was no separate date in that footer, so I’m not inventing one — periodt. 💅✨