sgeqrf.f(3)

okay bestie, you're looking at the LAPACK manual page for sgeqrf.f(3) — section 3, real subroutine energy, QR factorization vibes. let's go 💅

💖 NAME 💖

sgeqrf.f

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

subroutine sgeqrf (M, N, A, LDA, TAU, WORK, LWORK, INFO)
    SGEQRF VARIANT: left-looking Level 3 BLAS version of the algorithm.

🌸 Function/Subroutine Documentation 🌸

subroutine sgeqrf (integer M, integer N, real, dimension( lda, * ) A,
    integer LDA, real, dimension( * ) TAU, real, dimension( * ) WORK,
    integer LWORK, integer INFO)
    SGEQRF VARIANT: left-looking Level 3 BLAS version of the algorithm.

🎀 Purpose 🎀

okay so SGEQRF computes a QR factorization of a real M-by-N matrix A, and the whole equation is literally:

A = Q * R

this is the left-looking Level 3 BLAS version of the algorithm. periodt.

🦋 Parameters 🦋

• M — an INTEGER, bestie. it's the number of rows of the matrix A, and the rule is M >= 0.
• N — also an INTEGER. it's the number of columns of the matrix A, with N >= 0.
• A — a REAL array, dimension (LDA,N). on entry, it's the M-by-N matrix A. on exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if m >= n); the elements below the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) elementary reflectors (see Further Details).
• LDA — an INTEGER, lowkey the leading dimension of the array A. the rule is LDA >= max(1,M).
• TAU — a REAL array, dimension (min(M,N)). highkey these are the scalar factors of the elementary reflectors (see Further Details).
• WORK — a REAL array, dimension (MAX(1,LWORK)). on exit, if INFO = 0, WORK(1) returns the optimal LWORK.
• LWORK — an INTEGER. the dimension of the array WORK. the dimension can be divided into three parts:
  1. the part for the triangular factor T. if the very last T is not bigger than any of the rest, then this part is NB x ceiling(K/NB), otherwise, NB x (K-NT), where K = min(M,N) and NT is the dimension of the very last T.
  2. the part for the very last T when T is bigger than any of the rest T. the size of this part is NT x NT, where NT = K - ceiling ((K-NX)/NB) x NB, where K = min(M,N), NX is calculated by NX = MAX( 0, ILAENV( 3, 'SGEQRF', ' ', M, N, -1, -1 ) ).
  3. the part for dlarfb is of size max((N-M)*K, (N-M)*NB, K*NB, NB*NB).

so LWORK = part1 + part2 + part3.

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 — an INTEGER. no cap:
  • = 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.

🗓️ Date 🗓️

December 2016, fr fr.

🔥 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'

where tau is a real scalar, and v is a real vector with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), and tau in TAU(i). iykyk, the math is the moment.

📌 Definition at line 151 of file VARIANTS/qr/LL/sgeqrf.f.

🎀 Author 🎀

Generated automatically by Doxygen for LAPACK from the source code.

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💖 and that's the whole manual, bestie — sgeqrf.f(3) from LAPACK, Version 3.8.0, dated Tue Nov 14 2017. now go factor that QR like the main character you are. slay ✨💅