SRC/dgemlq.f(3)

💖 NAME

SRC/dgemlq.f — page SRC/dgemlq.f(3), straight out of the Library Functions Manual, and bestie this is the whole DGEMLQ moment 💅✨

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✨ SYNOPSIS ✨

🫶 Functions/Subroutines

subroutine dgemlq (side, trans, m, n, k, a, lda, t, tsize, c, ldc, work, lwork, info)

DGEMLQ — the icon herself 👑💖

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🌸 Function/Subroutine Documentation 🌸

🦋 The subroutine (DGEMLQ)

subroutine dgemlq (character side, character trans, integer m, integer n,
    integer k, double precision, dimension( lda, * ) a, integer lda, double
    precision, dimension( * ) t, integer tsize, double precision, dimension(
    ldc, * ) c, integer ldc, double precision, dimension( * ) work, integer
    lwork, integer info)

DGEMLQ — yes, that's the name, and yes, she's doing a lot 💅

🌈 Purpose

okay so DGEMLQ overwrites the general real M-by-N matrix C with:

                   SIDE = 'L'     SIDE = 'R'
TRANS = 'N':      Q * C          C * Q
TRANS = 'T':      Q**T * C       C * Q**T

where Q is a real orthogonal matrix defined as the product of blocked elementary reflectors computed by short wide LQ factorization (DGELQ) 🦋✨

🎀 Parameters

🌸 SIDE

SIDE is CHARACTER*1 and it picks the side, bestie:

• = 'L': apply Q or Q**T from the Left;
• = 'R': apply Q or Q**T from the Right.

💜 TRANS

TRANS is CHARACTER*1 and it decides whether we transpose or not:

• = 'N': No transpose, apply Q;
• = 'T': Transpose, apply Q**T.

🦋 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 C. N >= 0.

👑 K

K is INTEGER — the number of elementary reflectors whose product defines the matrix Q.

If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >= 0.

🍓 A

A is DOUBLE PRECISION array, dimension

• (LDA,M) if SIDE = 'L',
• (LDA,N) if SIDE = 'R'.

Part of the data structure to represent Q as returned by DGELQ.

🎀 LDA

LDA is INTEGER — the leading dimension of the array A. LDA >= max(1,K).

🧚 T

T is DOUBLE PRECISION array, dimension (MAX(5,TSIZE)).

Part of the data structure to represent Q as returned by DGELQ.

💖 TSIZE

TSIZE is INTEGER — the dimension of the array T. TSIZE >= 5.

⭐ C

C is DOUBLE PRECISION array, dimension (LDC,N).

On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.

🦋 LDC

LDC is INTEGER — the leading dimension of the array C. LDC >= max(1,M).

💅 WORK

(workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)).

On exit, if INFO = 0, WORK(1) returns the minimal LWORK.

🌸 LWORK

LWORK is INTEGER — the dimension of the array WORK. LWORK >= 1.

If LWORK = -1, then a workspace query is assumed. The routine only calculates the size of the WORK array, returns this value as WORK(1), and no error message related to WORK 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

⚠️ real talk, bestie: these details are particular for this LAPACK implementation. Users should not take them for granted. These details may change in the future, and are not likely true for another LAPACK implementation. These details are relevant if one wants to try to understand the code. They are not part of the interface.

In this version:

• T(2): row block size (MB)
• T(3): column block size (NB)
• T(6:TSIZE): data structure needed for Q, computed by DLASWLQ or DGELQT

Depending on the matrix dimensions M and N, and row and column block sizes MB and NB returned by ILAENV, DGELQ will use either DLASWLQ (if the matrix is wide-and-short) or DGELQT to compute the LQ factorization 🦋

This version of DGEMLQ will use either DLAMSWLQ or DGEMLQT to multiply matrix Q by another matrix.

Further Details in DLAMSWLQ or DGEMLQT ✨

Definition at line 172 of file dgemlq.f.

🤖 Author (the generated-by one)

Generated automatically by Doxygen for LAPACK from the source code.

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That's the whole page, bestie 💖 — sourced from LAPACK Version 3.12.0, for SRC/dgemlq.f(3). Now go slay those orthogonal matrices ✨👑💅