TESTING/LIN/dpbt01.f(3)

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version 3.12.1 · 2 versions
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✨ NAME ✨

okay bestie, you're looking at TESTING/LIN/dpbt01.f(3) from the Library Functions Manual — and it's giving subroutine main character energy 💅. This is the page for DPBT01.

🦋 SYNOPSIS 🦋

Functions/Subroutines

       subroutine dpbt01 (uplo, n, kd, a, lda, afac, ldafac, rwork, resid)
           DPBT01

🎀 Function/Subroutine Documentation 🎀

   subroutine dpbt01 (character uplo, integer n, integer kd, double precision,
       dimension( lda, * ) a, integer lda, double precision, dimension( ldafac,
       * ) afac, integer ldafac, double precision, dimension( * ) rwork, double
       precision resid)
       DPBT01

DPBT01 — yes, that's the name, and it's iconic. ✨

Purpose

Bestie, DPBT01 reconstructs a symmetric positive definite band matrix A from its L*L' or U'*U factorization and computes the residual

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

where EPS is the machine epsilon, L' is the conjugate transpose of L, and U' is the conjugate transpose of U. No cap, that's the whole assignment. 💖

Parameters

  • UPLO — is CHARACTER*1. Specifies whether the upper or lower triangular part of the symmetric matrix A is stored:
    • = 'U': Upper triangular
    • = 'L': Lower triangular
  • N — is INTEGER. The number of rows and columns of the matrix A. N >= 0.
  • KD — is INTEGER. The number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
  • A — is DOUBLE PRECISION array, dimension (LDA,N). The original symmetric band matrix A. If UPLO = 'U', the upper triangular part of A is stored as a band matrix; if UPLO = 'L', the lower triangular part of A is stored. The columns of the appropriate triangle are stored in the columns of A and the diagonals of the triangle are stored in the rows of A. See DPBTRF for further details.
  • LDA — is INTEGER. The leading dimension of the array A. LDA >= max(1,KD+1).
  • AFAC — is DOUBLE PRECISION array, dimension (LDAFAC,N). The factored form of the matrix A. AFAC contains the factor L or U from the L*L' or U'*U factorization in band storage format, as computed by DPBTRF.
  • LDAFAC — is INTEGER. The leading dimension of the array AFAC. LDAFAC >= max(1,KD+1).
  • RWORK — is DOUBLE PRECISION array, dimension (N).
  • RESID — is DOUBLE PRECISION. If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS ) If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS ).

Author

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

Definition at line 117 of file dpbt01.f.

👑 Author 👑

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