SRC/sormbr.f(3)

🌸 NAME

SRC/sormbr.f — okay so bestie, this is the page from the Library Functions Manual, and it's literally all about the SORMBR subroutine. we're gonna get into every single detail together, no skips 💖

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✨ SYNOPSIS

Functions/Subroutines

here's the function vibe check:

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

SORMBR

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💅 FUNCTION/SUBROUTINE DOCUMENTATION

the full signature is giving very "linear algebra main character energy" 🎀

subroutine sormbr (character vect, character side, character trans, integer
       m, integer n, integer k, real, dimension( lda, * ) a, integer lda, real,
       dimension( * ) tau, real, dimension( ldc, * ) c, integer ldc, real,
       dimension( * ) work, integer lwork, integer info)

SORMBR

🎀 Purpose

okay so here's the tea ☕: if VECT = 'Q', SORMBR 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', SORMBR 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 SGEBRD 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.

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).

🌈 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.

🍓 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 SGEBRD.

If VECT = 'P', the number of rows in the original matrix reduced by SGEBRD.

K >= 0.

🔥 A

A is REAL 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 SGEBRD.

👑 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 REAL 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 SGEBRD in the array argument TAUQ or TAUP.

🌈 C

C is REAL 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.

🫶 LDC

LDC is INTEGER

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

⭐ WORK

WORK is REAL 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.

okay bestie, special case: 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

👑 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 194 of file sormbr.f.

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🌟 Author

Generated automatically by Doxygen for LAPACK from the source code.

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xoxo bestie 💖 — LAPACK Version 3.12.0, source SRC/sormbr.f(3). that's the whole page, periodt 🫶✨