DORGBR(3)

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💖 NAME 💖

the NAME section is literally this file path, bestie:

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

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

   Functions/Subroutines
       subroutine DORGBR (vect, m, n, k, a, lda, tau, work, lwork, info)
           DORGBR

🦋 Function/Subroutine Documentation 🦋

   subroutine DORGBR (character vect, integer m, integer n, integer k, double
       precision, dimension( lda, * ) a, integer lda, double precision,
       dimension( * ) tau, double precision, dimension( * ) work, integer
       lwork, integer info)
       DORGBR

🎀 Purpose 🎀

DORGBR generates one of the real orthogonal matrices Q or P**T 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) 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 DORGBR returns the first n columns of Q, where m >= n >= k;
  • if m < k, Q = H(1) H(2) . . . H(m-1) and DORGBR 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 DORGBR 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 DORGBR returns P**T as an N-by-N matrix.

🌸 Parameters 🌸

💅 VECT 💅

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

• = '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 DGEBRD. If VECT = 'P', the number of rows in the original K-by-N matrix reduced by DGEBRD. K >= 0.

💅 A 💅

A is DOUBLE PRECISION array, dimension (LDA,N) — on entry, the vectors which define the elementary reflectors, as returned by DGEBRD. 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 DOUBLE PRECISION 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 DGEBRD in its array argument TAUQ or TAUP.

💅 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. 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 dorgbr.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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