ZLA_GBRPVGRW(3)

💖 NAME 💖

okay so bestie, you opened the ZLA_GBRPVGRW(3) page from the Library Functions Manual. The NAME section is literally just this file path, no cap:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zla_gbrpvgrw.f

That’s the whole name vibe. 🎀

✨ SYNOPSIS ✨

🧚 Functions/Subroutines

• double precision function ZLA_GBRPVGRW (n, kl, ku, ncols, ab, ldab, afb, ldafb) — ZLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix.

🫶 Function/Subroutine Documentation 🫶

double precision function ZLA_GBRPVGRW (integer n, integer kl, integer ku,
    integer ncols, complex*16, dimension( ldab, * ) ab, integer ldab,
    complex*16, dimension( ldafb, * ) afb, integer ldafb)

ZLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix. 💅

🎯 Purpose

ZLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U). The doc comment says The norm is used. If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor. This also means that the solution X, estimated condition numbers, and error bounds could be unreliable. 😭

🧮 Parameters

N

N is INTEGER. The number of linear equations, i.e., the order 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.

NCOLS

NCOLS is INTEGER. The number of columns of the matrix A. NCOLS >= 0.

AB

AB is COMPLEX*16 array, dimension (LDAB,N). On entry, the matrix A in band storage, in rows 1 to KL+KU+1. The j-th column of A is stored in the j-th column of the array AB as follows:

AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)

LDAB

LDAB is INTEGER. The leading dimension of the array AB. LDAB >= KL+KU+1.

AFB

AFB is COMPLEX*16 array, dimension (LDAFB,N). Details of the LU factorization of the band matrix A, 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.

LDAFB

LDAFB is INTEGER. The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.

👑 Author 👑

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

Definition at line 115 of file zla_gbrpvgrw.f.

👑 Author (generated) 👑

Generated automatically by Doxygen for LAPACK from the source code.

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okay that’s the whole page, bestie. The footer energy is LAPACK, Version 3.12.0, and the /home/abui..._gbrpvgrw.f(3) path. Mwah 💋🎀✨