SRC/dgelqt.f(3)

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version 3.12.1 · 7 versions
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NAME

From the Library Functions Manual: SRC/dgelqt.f(3) is the manual page for SRC/dgelqt.f, aka DGELQT 💅✨

SYNOPSIS

Functions/Subroutines

subroutine dgelqt (m, n, mb, a, lda, t, ldt, work, info)

DGELQT — that’s the function name, bestie, and yes it’s giving main character energy 😭👑

Function/Subroutine Documentation ✨

subroutine dgelqt (integer m, integer n, integer mb, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldt, * ) t, integer ldt, double precision, dimension( * ) work, integer info)

subroutine dgelqt (integer m, integer n, integer mb, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldt, * ) t, integer ldt, double precision, dimension( * ) work, integer info)

DGELQT — that’s the subroutine’s name, no cap 🫶

Purpose:

Okay so DGELQT computes a blocked LQ factorization of a real M-by-N matrix A using the compact WY representation of Q. That’s the whole purpose, periodt 💖

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.
  • MB — MB is INTEGER. The block size to be used in the blocked QR. MIN(M,N) >= MB >= 1.
  • 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 are the rows of V.
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).
  • T — T is DOUBLE PRECISION array, dimension (LDT,MIN(M,N)). The upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks. See below for further details.
  • LDT — LDT is INTEGER. The leading dimension of the array T. LDT >= MB.
  • WORK — WORK is DOUBLE PRECISION array, dimension (MB*N).
  • INFO — INFO is INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value.

Author

Shoutout to the author squad, fr fr:

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

Further Details:

Bestie, here’s the matrix tea 🍓 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 )

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. Let K=MIN(M,N). The number of blocks is B = ceiling(K/MB), where each block is of order MB except for the last block, which is of order IB = K - (B-1)*MB. For each of the B blocks, a upper triangular block reflector factor is computed: T1, T2, ..., TB. The MB-by-MB (and IB-by-IB for the last block) T's are stored in the MB-by-K matrix T as

T = (T1 T2 ... TB).

Definition at line 138 of file dgelqt.f.

Author

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Footer vibes, bestie: LAPACK, Version 3.12.0 on the SRC/dgelqt.f(3) page. Date? Not in this footer, so no invented date — that’s the honest group-chat receipt 🫶✨

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