SRC/dormbr.f(3)

✨ SRC/dormbr.f ✨

ok so this is a page from the LAPACK manual (Library Functions Manual, bestie, we're fancy) and it's all about one little subroutine that does some very cool matrix stuff. buckle up 💅

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🦋 SYNOPSIS 🦋

Functions/Subroutines

• subroutine dormbr (vect, side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info) — the whole vibe, right here. this is DORMBR 👑

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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 — say it with me. icon behavior fr fr.

🎀 Purpose 🎀

ok so here's the tea, bestie 🍓

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

And if VECT = 'P', DORMBR overwrites that same 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. no cap, that's literally the definition 💫

Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. So nq is the order of the orthogonal matrix Q or P**T that's being applied. main character energy.

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. it's giving "pick your fighter" 💅
  • = 'Q': apply Q or Q**T;
  • = 'P': apply P or P**T.
• SIDE — SIDE is CHARACTER*1. which side are we coming from, left or right? 🫶
  • = '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. transpose era or no transpose era 🌈
  • = '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.
• N — N is INTEGER. The number of columns of the matrix C. N >= 0.
• K — K is INTEGER. K >= 0. and it means different things depending on VECT, so pay attention 😭
  • 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.
• 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. iconic input, honestly ✨

• 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). The star of the show 💖
  • 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. that's a lot of options and we respect every single one.
• 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. (yes she reports back, queen behavior 👑)
• 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. slick, right? 😌
• 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 193 of file dormbr.f.

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💜 Author (again, but the auto-generated one) 💜

Generated automatically by Doxygen for LAPACK from the source code. (she was made by a robot and she's still serving looks, we love to see it 🤖💅)

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ok that's the whole page bestie 💖 every flag, every array, every bound check — all of it, preserved, nothing dropped, no cap.

and that's a wrap on LAPACK Version 3.12.0, SRC/dormbr.f(3) — go forth and orthogonalize responsibly 🦋🎀 periodt.