DGELQF(3)

💅 DGELQF(3) — Library Functions Manual

okay so this page is the DGELQF(3) glow-up from the Library Functions Manual, and the header path is /home/abui...RC/dgelqf.f(3). Bestie, we're doing LAPACK math and we're doing it cute. 💖

💅 NAME

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

That's the file this page is serving, no cap. 🫶

✨ SYNOPSIS

🌀 Functions/Subroutines

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

🧚 Function/Subroutine Documentation

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

🎯 Purpose

DGELQF computes an LQ factorization of a real M-by-N matrix A:

A = ( L 0 ) * Q

where:

• Q is a N-by-N orthogonal matrix;
• L is a lower-triangular M-by-M matrix;
• 0 is a M-by-(N-M) zero matrix, if M < N.

🌸 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 below the diagonal of the array contain the m-by-min(m,n) lower trapezoidal matrix L (L is lower triangular if m <= n); the elements above the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of 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. LWORK >= max(1,M). 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(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(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n), and tau in TAU(i).

Definition at line 142 of file dgelqf.f.

💖 Author (Doxygen's autogenerated note)

Generated automatically by Doxygen for LAPACK from the source code.

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okay bestie, that's the whole page 💅 — LAPACK Version 3.12.0, source /home/abui...RC/dgelqf.f(3). Bye! 🫶