TESTING/LIN/dgbt01.f(3)

📦
version 3.12.1 · 3 versions
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💖 NAME 💖

TESTING/LIN/dgbt01.f — bestie, this is the manual page for the dgbt01 subroutine, and it’s from the Library Functions Manual with the title TESTING/LIN/dgbt01.f(3). The whole vibe is “testing/LIN routine, but make it documented.” 💅

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

  • subroutine dgbt01 (m, n, kl, ku, a, lda, afac, ldafac, ipiv, work, resid) — DGBT01

🦋 Function/Subroutine Documentation 🦋

🌸 subroutine dgbt01 🌸

   subroutine dgbt01 (integer m, integer n, integer kl, integer ku, double
       precision, dimension( lda, * ) a, integer lda, double precision,
       dimension( ldafac, * ) afac, integer ldafac, integer, dimension( * )
       ipiv, double precision, dimension( * ) work, double precision resid)
       DGBT01

🔥 Purpose: 🔥

Okay so DGBT01 reconstructs a band matrix A from its L*U factorization and computes the residual:

norm(L*U - A) / ( N * norm(A) * EPS ),

where EPS is the machine epsilon. The expression L*U - A is computed one column at a time, so A and AFAC are not modified. Slay, no side effects. ✨

🌈 Parameters 🌈

  • M — M is INTEGER. The number of rows of the matrix A. M >= 0.
  • N — N is INTEGER. The number of columns of the matrix A. N >= 0.
  • KL — KL is INTEGER. The number of subdiagonals within the band of A. KL >= 0.
  • KU — KU is INTEGER. The number of superdiagonals within the band of A. KU >= 0.
  • A — A is DOUBLE PRECISION array, dimension (LDA,N). The original matrix A in band storage, stored in rows 1 to KL+KU+1.
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,KL+KU+1).
  • AFAC — AFAC is DOUBLE PRECISION array, dimension (LDAFAC,N). The factored form of the matrix A. AFAC contains the banded factors L and U from the L*U factorization, as computed by DGBTRF. U is stored as an upper triangular band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and the multipliers used during the factorization are stored in rows KL+KU+2 to 2*KL+KU+1. See DGBTRF for further details.
  • LDAFAC — LDAFAC is INTEGER. The leading dimension of the array AFAC. LDAFAC >= max(1,2*KL*KU+1).
  • IPIV — IPIV is INTEGER array, dimension (min(M,N)). The pivot indices from DGBTRF.
  • WORK — WORK is DOUBLE PRECISION array, dimension (2*KL+KU+1).
  • RESID — RESID is DOUBLE PRECISION. norm(L*U - A) / ( N * norm(A) * EPS ).

👑 Author 👑

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

Definition at line 124 of file dgbt01.f.

📜 Author 📜

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Okay bestie, that’s the whole page. This one is from LAPACK Version 3.12.0, and its page tag is TESTING/LIN/dgbt01.f(3) — stay sparkly and may your residuals be tiny 💅✨🫶

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