ZGBT01(3)

💖 ZGBT01(3) — Library Functions Manual energy ✨

okay so this is the ZGBT01(3) page from the Library Functions Manual, and she is fully here to reconstruct a band matrix from its L*U factorization and compute a residual. No cap. 💅

🎀 NAME 🎀

The NAME section is literally this file path, bestie:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/zgbt01.f

✨ SYNOPSIS ✨

🧚 Functions/Subroutines

The subroutine is ZGBT01, and here is the exact synopsis:

subroutine ZGBT01 (m, n, kl, ku, a, lda, afac, ldafac, ipiv, work,
    resid)
    ZGBT01

🦋 Function/Subroutine Documentation 🦋

Full signature, preserved exactly, because we do not play with source code here:

subroutine ZGBT01 (integer m, integer n, integer kl, integer ku, complex*16,
    dimension( lda, * ) a, integer lda, complex*16, dimension( ldafac, * )
    afac, integer ldafac, integer, dimension( * ) ipiv, complex*16,
    dimension( * ) work, double precision resid)
    ZGBT01

💖 Purpose 💖

ZGBT01 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. Obsessed with the no-mutation energy. ✨

🍓 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*16 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*16 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 ZGBTRF. 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 ZGBTRF 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 ZGBTRF.
• WORK — WORK is COMPLEX*16 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 zgbt01.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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okay that’s the whole page, bestie 🫶. Footer vibe check: LAPACK, Version 3.12.0, and the source path /home/abui...IN/zgbt01.f(3) — no date listed in the footer, just that path energy. Bye 💜