SRC/dla_gbrpvgrw.f(3)

✨ NAME ✨

SRC/dla_gbrpvgrw.f — this is the SRC/dla_gbrpvgrw.f(3) page from the Library Functions Manual, bestie. That’s the name, no cap.

🌈 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. slay.

🫶 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 🎯

DLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U). The source 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. so if that number is tiny, do not trust the vibe of your LU factorization, fr fr. The raw source wraps this whole block in Doxygen !> comment markers, fyi.

if it’s much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor, and 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 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)

LDAB

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

AFB

AFB is 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.

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 dla_gbrpvgrw.f.

💖 Author 💖

Generated automatically by Doxygen for LAPACK from the source code.

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xoxo, this page is from LAPACK Version 3.12.0, page SRC/dla_gbrpvgrw.f(3) — bye bestie! 💅✨