SRC/sgerq2.f(3)

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💅 SRC/sgerq2.f(3) 💅

okay so bestie, welcome to the Library Functions Manual page for SRC/sgerq2.f(3). This one is all about SGERQ2, and she is lowkey serving unblocked RQ factorization realness. Not me being obsessed with a Fortran subroutine, but here we are. 💖

✨ NAME ✨

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 🌈

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. 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 REAL 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 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.

🫶 Author 🫶

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kisses, bestie 💋 — this page is LAPACK, Version 3.12.0, and the source is SRC/sgerq2.f(3). That's the footer, and she ate. 🎀✨

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