DLA_GBRPVGRW(3)

💖 NAME 💖

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dla_gbrpvgrw.f — yes bestie, that whole path is the NAME, no cap. Also hi, this page is from the Library Functions Manual, so the manual name is folded in right here near the top 💅✨

✨ SYNOPSIS ✨

Functions/Subroutines 🫶

double precision function DLA_GBRPVGRW (n, kl, ku, ncols, ab, ldab, afb,
    ldafb)

DLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix. Periodt. 💖

🎀 Function/Subroutine Documentation 🎀

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

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

🌈 Purpose 🌈

Okay so the main-character purpose is this: DLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U). The sentence literally says The norm is used. — two spaces and all, bestie. 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. 💀

lowkey important: if that reciprocal pivot growth factor is much less than 1, the stability could be poor, and the solution X, estimated condition numbers, and error bounds could be unreliable.

💅 Parameters 💅

• N — INTEGER. The number of linear equations, i.e., the order of the matrix A. N >= 0. 🫶
• KL — INTEGER. The number of subdiagonals within the band of A. KL >= 0.
• KU — INTEGER. The number of superdiagonals within the band of A. KU >= 0.
• NCOLS — INTEGER. The number of columns of the matrix A. NCOLS >= 0.
• AB — DOUBLE PRECISION 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). Slay, that's the exact storage tea 🌸
• LDAB — INTEGER. The leading dimension of the array AB. LDAB >= KL+KU+1.
• AFB — DOUBLE PRECISION array, dimension (LDAFB,N). Details of the LU factorization of the band matrix A, 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. Iconic 👑
• LDAFB — 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 dla_gbrpvgrw.f.

🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code.

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okay bye bestie, this was LAPACK Version 3.12.0, footer path /home/abui..._gbrpvgrw.f(3) — mwah 💋✨