SRC/dgeqlf.f(3)

NAME ✨

SRC/dgeqlf.f(3) — that’s the page bestie, and it’s from the Library Functions Manual, so yes, we’re fully in Unix manual-page territory. 💅

SYNOPSIS 🌸

Functions/Subroutines

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

DGEQLF

Function/Subroutine Documentation 🫶

subroutine dgeqlf (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer lwork, integer info)

DGEQLF

Purpose 💖

Okay so, DGEQLF computes a QL factorization of a real M-by-N matrix A:

A = Q * L

That’s the whole main-character job, no cap. ✨

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 a DOUBLE PRECISION array, dimension (LDA,N). On entry, it’s the M-by-N matrix A. On exit:
  • if m >= n, the lower triangle of the subarray A(m-n+1:m,1:n) contains the N-by-N lower triangular matrix L;
  • if m <= n, the elements on and below the (n-m)-th superdiagonal contain the M-by-N lower trapezoidal matrix L;
  • the remaining elements, together with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors (see Further Details). 👑
• LDA — LDA is INTEGER. It’s the leading dimension of the array A. Constraint: LDA >= max(1,M).
• TAU — TAU is a DOUBLE PRECISION array, dimension (min(M,N)). It holds the scalar factors of the elementary reflectors (see Further Details).
• WORK — WORK is a DOUBLE PRECISION array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
• LWORK — LWORK is INTEGER. It’s the dimension of the array WORK. LWORK >= 1, if MIN(M,N) = 0, and LWORK >= N, otherwise. For optimum performance, LWORK >= N*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(k) . . . H(2) H(1), 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(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
A(1:m-k+i-1,n-k+i), and tau in TAU(i).

Definition at line 138 of file dgeqlf.f.

Author 🎀 (auto-generated)

Generated automatically by Doxygen for LAPACK from the source code.

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And that’s the sign-off, bestie: LAPACK Version 3.12.0, page SRC/dgeqlf.f(3) — footer secured, facts intact, vibe immaculate. 💅✨