dgeqrf.f(3)

💅 NAME 💅

LAPACK manual page for dgeqrf.f — yes bestie, we’re in the LAPACK section, and this is the QR-factorization one. 💖

---

✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

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

---

🦋 Function/Subroutine Documentation 🦋

🌟 subroutine dgeqrf 🌟

subroutine dgeqrf (integer M, integer N, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( * ) TAU, double precision, dimension( * ) WORK, integer LWORK, integer INFO)

DGEQRF VARIANT: left-looking Level 3 BLAS version of the algorithm. 💅

💖 Purpose 💖

DGEQRF computes a QR factorization of a real M-by-N matrix A:

A = Q * R.

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

🌸 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, 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 — 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 (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
• LWORK — LWORK is 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, 'DGEQRF', ' ', 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 — 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.

🎀 Date 🎀

December 2016

🔥 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).

Definition at line 151 of file VARIANTS/qr/LL/dgeqrf.f. 🫶

🌈 Author (the auto-gen one) 🌈

Generated automatically by Doxygen for LAPACK from the source code.

---

🌈 That’s the whole dgeqrf.f(3) page, bestie — LAPACK Version 3.8.0, Tue Nov 14 2017. Stay iconic. 💖✨