DORMBR(3)

💅 DORMBR(3) — like, the LAPACK manual page, but make it make sense 🎀

okay so bestie, you opened the Library Functions Manual for LAPACK and landed on DORMBR(3), and honestly? It's giving "bidiagonal realness" and I'm obsessed. Let me break it down for you, no cap. ✨

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🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dormbr.f — that's the file, that's the whole name section, she's literally just a path and she's thriving. 💅

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🦋 SYNOPSIS 🦋

Functions/Subroutines

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

DORMBR — that's her. That's the whole vibe.

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👑 Function/Subroutine Documentation 👑

subroutine DORMBR (character vect, 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)

DORMBR ✨ (yes, again, she said her name twice, main character energy fr fr)

🧚 Purpose 🧚

okay so here's what she actually does, bestie — read it slow:

If VECT = 'Q', DORMBR 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 If VECT = 'P', DORMBR overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': P * C C * P TRANS = 'T': P**T * C C * P**T

Here Q and P**T are the orthogonal matrices determined by DGEBRD when reducing a real matrix A to bidiagonal form: A = Q * B * P**T. Q and P**T are defined as products of elementary reflectors H(i) and G(i) respectively. 🫶

Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the order of the orthogonal matrix Q or P**T that is applied. (nq is lowkey the moment, honestly. 🎀)

If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:

• if nq >= k, Q = H(1) H(2) . . . H(k);
• if nq < k, Q = H(1) H(2) . . . H(nq-1).

If VECT = 'P', A is assumed to have been a K-by-NQ matrix:

• if k < nq, P = G(1) G(2) . . . G(k);
• if k >= nq, P = G(1) G(2) . . . G(nq-1).

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⭐ Parameters ⭐

VECT

VECT is CHARACTER*1

• = 'Q': apply Q or Q**T;
• = 'P': apply P or P**T.

SIDE

SIDE is CHARACTER*1

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

TRANS

TRANS is CHARACTER*1

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

M

M is INTEGER The number of rows of the matrix C. M >= 0. (not her being non-negative, we love a healthy boundary 😌)

N

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

K

K is INTEGER If VECT = 'Q', the number of columns in the original matrix reduced by DGEBRD. If VECT = 'P', the number of rows in the original matrix reduced by DGEBRD. K >= 0.

A

A is DOUBLE PRECISION array, dimension

                     (LDA,min(nq,K)) if VECT = 'Q'
                     (LDA,nq)        if VECT = 'P'

The vectors which define the elementary reflectors H(i) and G(i), whose products determine the matrices Q and P, as returned by DGEBRD. 💜

LDA

LDA is INTEGER The leading dimension of the array A. If VECT = 'Q', LDA >= max(1,nq); if VECT = 'P', LDA >= max(1,min(nq,K)).

TAU

TAU is DOUBLE PRECISION array, dimension (min(nq,K)) TAU(i) must contain the scalar factor of the elementary reflector H(i) or G(i) which determines Q or P, as returned by DGEBRD in the array argument TAUQ or TAUP.

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 or P*C or P**T*C or C*P or C*P**T. (she ate and left no crumbs, and also left no original C 😭)

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 optimum performance LWORK >= N*NB if SIDE = 'L', and LWORK >= M*NB if SIDE = 'R', where NB is the optimal blocksize.

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 is INTEGER

• = 0: successful exit
• < 0: if INFO = -i, the i-th argument had an illegal value

💀 bestie if INFO comes back negative, that's not a vibe check you passed — that's -i telling you argument number i was illegal. go fix her.

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🎀 Author 🎀

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

Definition at line 193 of file dormbr.f. 📍

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code. (the robots wrote this one, not me, I just gave it a personality 💖)

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✨ okay that's the whole page, you understood it, you slayed it, periodt. ✨

LAPACK — Version 3.12.0 🌸 mwah, go multiply something orthogonal, bestie 🦋💅