DORMLQ(3)

💜 dormlq.f(3) — LAPACK manual, section 3 🎀

okay bestie, welcome to the dormlq.f page from the LAPACK library functions manual ✨. The full path situation is /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dormlq.f — that's literally the file we're out here documenting, no cap 🙈.

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dormlq.f — yes the NAME section is just the whole file path, she's that kind of girl 💅.

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🌸 SYNOPSIS 🌸

Functions/Subroutines

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 👑 (iconic name, no notes)

🦋 Purpose 🦋

ok so listen 👂 — DORMLQ 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 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'. and that's the whole vibe check ✅

🧚 Parameters 🧚

girl, buckle up, there's a lot of them and they all matter:

• 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 is CHARACTER*1.
  • = 'N': No transpose, apply Q;
  • = 'T': Transpose, apply Q**T. 🔁
• M — M is INTEGER. The number of rows of the matrix C. 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'

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 is INTEGER. The leading dimension of the array A. LDA >= max(1,K).
• 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 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. (she gets replaced, main character energy honestly 😭)
• LDC — LDC is INTEGER. The leading dimension of the array C. LDC >= max(1,M).
• WORK — WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal 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.

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. 🩵 (a little spy-mission mode, iykyk)

• 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.

Definition at line 165 of file dormlq.f. 📍

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code. (the robots wrote the docs, we just gave them flair 🤖💅)

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LAPACK · Version 3.12.0 · /home/abui...RC/dormlq.f(3) — okay that's the whole page bestie, go forth and multiply your matrices, xoxo 🍓🦋💜