SORGBR(3)

🌸 NAME 🎀

okay so bestie, welcome to SORGBR(3) from the Library Functions Manual 💖. The header path is literally /home/abui...RC/sorgbr.f(3), and lowkey the NAME section is just this exact file path:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/sorgbr.f

No cap, that’s the name. 🫶

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✨ SYNOPSIS ✨

🫶 Functions/Subroutines 🫶

• subroutine SORGBR (vect, m, n, k, a, lda, tau, work, lwork, info) — SORGBR

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💅 Function/Subroutine Documentation 💅

   subroutine SORGBR (character vect, integer m, integer n, integer k, real,
       dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real,
       dimension( * ) work, integer lwork, integer info)

SORGBR, periodt. 💅

🔥 Purpose 🔥

SORGBR generates one of the real orthogonal matrices Q or P**T 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) or G(i) respectively.

• If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q is of order M:
  • if m >= k, Q = H(1) H(2) . . . H(k) and SORGBR returns the first n columns of Q, where m >= n >= k;
  • if m < k, Q = H(1) H(2) . . . H(m-1) and SORGBR returns Q as an M-by-M matrix.
• If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T is of order N:
  • if k < n, P**T = G(k) . . . G(2) G(1) and SORGBR returns the first m rows of P**T, where n >= m >= k;
  • if k >= n, P**T = G(n-1) . . . G(2) G(1) and SORGBR returns P**T as an N-by-N matrix.

🎀 Parameters 🎀

VECT

VECT is CHARACTER*1 — tells you whether the matrix Q or the matrix P**T is required, as defined in the transformation applied by SGEBRD:

• = 'Q': generate Q;
• = 'P': generate P**T.

M

M is INTEGER — the number of rows of the matrix Q or P**T to be returned. M >= 0.

N

N is INTEGER — the number of columns of the matrix Q or P**T to be returned. N >= 0. If VECT = 'Q', M >= N >= min(M,K); if VECT = 'P', N >= M >= min(N,K).

K

K is INTEGER — if VECT = 'Q', the number of columns in the original M-by-K matrix reduced by SGEBRD. If VECT = 'P', the number of rows in the original K-by-N matrix reduced by SGEBRD. K >= 0.

A

A is REAL array, dimension (LDA,N) — on entry, the vectors which define the elementary reflectors, as returned by SGEBRD. On exit, the M-by-N matrix Q or P**T.

LDA

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

TAU

TAU is REAL array, dimension

(min(M,K)) if VECT = 'Q'
(min(N,K)) if VECT = 'P'

TAU(i) must contain the scalar factor of the elementary reflector H(i) or G(i), which determines Q or P**T, as returned by SGEBRD in its array argument TAUQ or TAUP.

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. LWORK >= max(1,min(M,N)). For optimum performance LWORK >= min(M,N)*NB, 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

🌈 Author 🌈

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 156 of file sorgbr.f.

🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code.

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okay that’s the whole serve, bestie 💖 — the footer is LAPACK Version 3.12.0, and the path down there is /home/abui...RC/sorgbr.f(3). Slay, bye 💅✨