SRC/dormlq.f(3)

💅 NAME 💅

okay bestie, this is SRC/dormlq.f straight out of the Library Functions Manual, and it's literally the LAPACK routine page for DORMLQ. slay.

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🦋 SYNOPSIS 🦋

✨ Functions/Subroutines ✨

• subroutine dormlq (side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info) — DORMLQ

subroutine dormlq (side, trans, m, n, k, a, lda, tau, c, ldc, work,
    lwork, info)

DORMLQ

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🎀 Function/Subroutine Documentation 🎀

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

DORMLQ

💖 Purpose 💖

okay so DORMLQ overwrites the general real M-by-N matrix C with this exact energy:

                 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 k elementary reflectors:

Q = H(k) . . . H(2) H(1)

as returned by DGELQF. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'. periodt.

🍓 Parameters 🍓

SIDE

• SIDE — SIDE is CHARACTER*1
  • = 'L': apply Q or Q**T from the Left;
  • = 'R': apply Q or Q**T from the Right.

TRANS

• TRANS — TRANS is CHARACTER*1
  • = 'N': No transpose, apply Q;
  • = 'T': Transpose, apply Q**T.

M

• M — M is INTEGER
  • The number of rows of the matrix C. M >= 0.

N

• N — N is INTEGER
  • The number of columns of the matrix C. N >= 0.

K

• 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 — A is DOUBLE PRECISION array, dimension

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

• The i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by DGELQF in the first k rows of its array argument A.

LDA

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

TAU

• TAU — TAU is DOUBLE PRECISION array, dimension (K)
  • TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DGELQF.

C

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

WORK

• WORK — WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
  • On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

• LWORK — LWORK is INTEGER
  • The dimension of the array WORK.
  • If SIDE = 'L', LWORK >= max(1,N);
  • if SIDE = 'R', LWORK >= max(1,M).
  • For good performance, LWORK should generally be larger.

bestie, this next bit is a whole mood: 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 — INFO is INTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

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👑 Author 👑

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

Definition at line 165 of file dormlq.f.

💅 Author 💅

Generated automatically by Doxygen for LAPACK from the source code.

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final sign-off, bestie: LAPACK, Version 3.12.0, page SRC/dormlq.f(3) — that's the footer tea, and there's no date line in the original so I'm not inventing one 🫶💖✨