DGEQLF(3)

NAME 💖

okay so this page is dgeqlf.f(3) from the Library Functions Manual, and the header has that /home/abui...RC/dgeqlf.f(3) path energy on both sides. The NAME entry is literally:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dgeqlf.f

Bestie, that’s the whole NAME section. Slay. 🎀

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SYNOPSIS ✨

Functions/Subroutines 🦋

   Functions/Subroutines
       subroutine DGEQLF (m, n, a, lda, tau, work, lwork, info)
           DGEQLF

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Function/Subroutine Documentation 🎀

Here’s the full signature, no cap:

   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)

Purpose 💜

!>
!> DGEQLF computes a QL factorization of a real M-by-N matrix A:
!> A = Q * L.
!>

Parameters 🌸

M

M is INTEGER. It’s the number of rows of the matrix A. M >= 0.

N

N is INTEGER. It’s the number of columns of the matrix A. N >= 0.

A

A is 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, 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. LDA >= max(1,M).

TAU

TAU is DOUBLE PRECISION array, dimension (min(M,N)). It holds 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. It’s the dimension of the array WORK. LWORK >= max(1,N).

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).
!>

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Definition at line 137 of file dgeqlf.f. 📍

That’s literally the exact line, bestie: Definition at line 137 of file dgeqlf.f.

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Author (Doxygen-generated edition) 🤖

Generated automatically by Doxygen for LAPACK from the source code.

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Cute sign-off time: the footer has LAPACK / Version 3.12.0 and the /home/abui...RC/dgeqlf.f(3) stamp at the very end — that’s the source/version footer vibe, and no separate date line is listed beyond that stamp. 💅✨🫶