SRC/dgelq2.f(3)

💖 SRC/dgelq2.f(3) 💖

okay bestie, this page is from the Library Functions Manual — yes, the manual name is folded in right here like a little name tag. ✨ The star of the show is SRC/dgelq2.f, and she’s serving unblocked LQ factorization realness. 💅

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💖 NAME 💖

SRC/dgelq2.f — that’s the file/page name, periodt. 🎀

✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine dgelq2 (m, n, a, lda, tau, work, info) — DGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm. 🦋

🧚 Function/Subroutine Documentation 🧚

subroutine dgelq2 (integer m, integer n, double precision, dimension( lda, *
) a, integer lda, double precision, dimension( * ) tau, double
precision, dimension( * ) work, integer info)

DGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm. 🌈

Purpose:

okay so the purpose is literally this — here’s the exact math vibe:

!>
!> DGELQ2 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 — the row count, bestie. Exact deets:

!>          M is INTEGER
!>          The number of rows of the matrix A.  M >= 0.
!>

• N — the column count, no cap:

!>          N is INTEGER
!>          The number of columns of the matrix A.  N >= 0.
!>

• A — the big matrix energy. On entry / on exit is giving transformation:

!>          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 — leading dimension check, iconic:

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,M).
!>

• TAU — scalar factors of the elementary reflectors. Further Details below, iykyk:

!>          TAU is DOUBLE PRECISION array, dimension (min(M,N))
!>          The scalar factors of the elementary reflectors (see Further
!>          Details).
!>

• WORK — the workspace bestie, dimension (M):

!>          WORK is DOUBLE PRECISION array, dimension (M)
!>

• INFO — exit status energy:

!>          INFO is INTEGER
!>          = 0: successful exit
!>          < 0: if INFO = -i, the i-th argument had an illegal value
!>

Author

the academic icons behind it: 🎓

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

🌈 Further Details: 🌈

this is where Q gets her elementary-reflector moment, and it’s honestly iconic:

!>
!>  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 128 of file dgelq2.f. 🎀

🌸 Author 🌸

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