SRC/dgelqf.f(3)

okay bestie, welcome to the <pink>SRC/dgelqf.f(3)</pink> page from the Library Functions Manual — yes, we are doing LAPACK linear algebra today and it's gonna be iconic. 🫶✨

✨ NAME ✨

SRC/dgelqf.f — that's the page name, periodt. 💅

🦋 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 🌸

okay so <hotpink>DGELQF</hotpink> computes an LQ factorization of a real M-by-N matrix A, and the glow-up is literally:

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.

No cap, that's the whole vibe. 🎀

🍓 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 >= 1, if MIN(M,N) = 0, and LWORK >= M, otherwise. 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 143 of file dgelqf.f.

💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code. 🤖✨

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LAPACK Version 3.12.0, page SRC/dgelqf.f(3) — that's the footer tea, bestie. fr fr, slay. 💅💖