SRC/zla_gbrpvgrw.f(3)

okay bestie, welcome to the zla_gbrpvgrw.f(3) page from the Library Functions Manual ✨ this one is all about a banded-matrix girlie who computes reciprocal pivot growth, and she is lowkey iconic 💅

🌸 NAME 🌸

SRC/zla_gbrpvgrw.f — that's the file this page is serving. The main character function is zla_gbrpvgrw, and she computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix. fr fr 🫶

🦋 SYNOPSIS 🦋

Functions/Subroutines

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

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

💖 Function/Subroutine Documentation 💖

Here's the full signature with every type and arg, no cap:

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 🎯

Okay so here's the whole vibe: ZLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U). 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. 😭 so yeah, if that factor is giving tiny-number energy, do not trust the results blindly, bestie.

💅 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. ⭐

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And that's the whole page, bestie 🫶 the footer is giving LAPACK Version 3.12.0 and source file SRC/zla_gbrpvgrw.f(3), plus the generated-by line: Generated automatically by Doxygen for LAPACK from the source code. slay, we're done 💅✨