SRC/sorgbr.f(3)

SRC/sorgbr.f(3) ✨

Library Functions Manual, bestie — that's the manual name, folded in right here. 💅

🌸 NAME 🌸

SRC/sorgbr.f — yes, the page is literally this file, and the main-character subroutine inside is sorgbr. It's giving LAPACK realness. 🫶

🦋 SYNOPSIS 🦋

🧚 Functions/Subroutines 🧚

subroutine sorgbr (vect, m, n, k, a, lda, tau, work, lwork, info)

That's the one: SORGBR. No cap. ✨

💅 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 — yep, same routine, full glow-up signature.

🎀 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. Specifies 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', or (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 (again, because the page has two) 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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Footer check, bestie: LAPACK Version 3.12.0, source SRC/sorgbr.f(3). Date isn't listed on this page — just pure version-and-source energy. 🫶💖