SRC/dgelqt3.f(3)

✨ SRC/dgelqt3.f ✨

okay so bestie, this is a page from the LAPACK manual — it's SRC/dgelqt3.f, and honestly? it's giving recursive linear algebra icon. let's get into it 💅

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🌸 SYNOPSIS 🌸

Functions/Subroutines

• recursive subroutine dgelqt3 (m, n, a, lda, t, ldt, info) — DGELQT3 recursively computes a LQ factorization of a general real or complex matrix using the compact WY representation of Q.

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🦋 Function/Subroutine Documentation 🦋

recursive subroutine dgelqt3 (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldt, * ) t, integer ldt, integer info)

DGELQT3 recursively computes a LQ factorization of a general real or complex matrix using the compact WY representation of Q. periodt. 🔥

Purpose:

!>
!> DGELQT3 recursively computes a LQ factorization of a real M-by-N
!> matrix A, using the compact WY representation of Q.
!>
!> Based on the algorithm of Elmroth and Gustavson,
!> IBM J. Res. Develop. Vol 44 No. 4 July 2000.
!>

Parameters

• M

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

• 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 real M-by-N matrix A.  On exit, the elements on and
!>          below the diagonal contain the N-by-N lower triangular matrix L; the
!>          elements above the diagonal are the rows of V.  See below for
!>          further details.
!>

• LDA

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

• T

!>          T is DOUBLE PRECISION array, dimension (LDT,N)
!>          The N-by-N upper triangular factor of the block reflector.
!>          The elements on and above the diagonal contain the block
!>          reflector T; the elements below the diagonal are not used.
!>          See below for further details.
!>

• LDT

!>          LDT is INTEGER
!>          The leading dimension of the array T.  LDT >= max(1,N).
!>

• 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 V stores the elementary reflectors H(i) in the i-th row
!>  above the diagonal. For example, if M=5 and N=3, the matrix V is
!>
!>               V = (  1  v1 v1 v1 v1 )
!>                   (     1  v2 v2 v2 )
!>                   (     1  v3 v3 v3 )
!>
!>
!>  where the vi's represent the vectors which define H(i), which are returned
!>  in the matrix A.  The 1's along the diagonal of V are not stored in A.  The
!>  block reflector H is then given by
!>
!>               H = I - V * T * V**T
!>
!>  where V**T is the transpose of V.
!>
!>  For details of the algorithm, see Elmroth and Gustavson (cited above).
!>

so yeah, that V = I - V * T * V**T situation is literally the whole block reflector vibe — the 1's on the diagonal of V are not stored in A, which is lowkey efficient of her tbh 🎀

Definition at line 130 of file dgelqt3.f. 🫶

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👑 Author 👑

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