SRC/sgerqf.f(3)

NAME 💅

Bestie, you're looking at SRC/sgerqf.f(3) from the Library Functions Manual, and the name is literally just SRC/sgerqf.f. No cap, that's the whole NAME section. This page is all about the SGERQF subroutine, and it's about to serve RQ factorization realness. 💖

SYNOPSIS ✨

Functions/Subroutines 🎀

       subroutine sgerqf (m, n, a, lda, tau, work, lwork, info)
           SGERQF

📚 Function/Subroutine Documentation 📚

Here's the full signature, bestie:

   subroutine sgerqf (integer m, integer n, real, dimension( lda, * ) a,
       integer lda, real, dimension( * ) tau, real, dimension( * ) work,
       integer lwork, integer info)
       SGERQF

Purpose: 🎯

SGERQF computes an RQ factorization of a real M-by-N matrix A:

A = R * Q.

That's the whole purpose, and it ate. 🔥

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 min(m,n) 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 (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
• LWORK — LWORK is INTEGER; the dimension of the array WORK. LWORK >= 1, if MIN(M,N) = 0, and LWORK >= M, otherwise. For optimum performance LWORK >= M*NB, where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
• 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).

📍 Fun fact: Definition at line 138 of file sgerqf.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

---

Okay bestie, that's the page! Footer vibes: LAPACK, Version 3.12.0, and SRC/sgerqf.f(3). Go forth and factor that RQ. 💅✨🦋