TESTING/LIN/cgbt01.f(3)

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💖 CGBT01 — TESTING/LIN/cgbt01.f 💖

okay so bestie, this is the Library Functions Manual page for TESTING/LIN/cgbt01.f, and we're talking about CGBT01 — yes, the reconstruction/residual-check girlie. No cap, it's giving numerical linear algebra realness. 💅

✨ NAME ✨

TESTING/LIN/cgbt01.f

🌸 SYNOPSIS 🌸

🎀 Functions/Subroutines 🎀

subroutine cgbt01 (m, n, kl, ku, a, lda, afac, ldafac, ipiv, work,
    resid)

CGBT01

🦋 Function/Subroutine Documentation 🦋

💜 CGBT01 💜

subroutine cgbt01 (integer m, integer n, integer kl, integer ku, complex,
    dimension( lda, * ) a, integer lda, complex, dimension( ldafac, * )
    afac, integer ldafac, integer, dimension( * ) ipiv, complex, dimension(
    * ) work, real resid)

CGBT01

🎀 Purpose 🎀

CGBT01 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. iconic.

The expression L*U - A is computed one column at a time, so A and AFAC are not modified. no touching, no mutating, just checking. 🫶

💅 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 COMPLEX 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 COMPLEX 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 CGBTRF. 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 CGBTRF 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 CGBTRF.
  • WORK — WORK is COMPLEX array, dimension (2*KL+KU+1).
  • RESID — RESID is REAL; 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 cgbt01.f.

🌟 Author 🌟

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