CLA_GBRPVGRW(3)

💅 CLA_GBRPVGRW(3) 💅

okay so bestie, welcome to the Library Functions Manual corner of the group chat. This page is literally about CLA_GBRPVGRW, and she is giving very specific banded-matrix math main character energy. no cap.

🌸 NAME 🌸

The official NAME is, and I cannot stress this enough, literally this whole path:

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

✨ SYNOPSIS ✨

🫶 Functions/Subroutines 🫶

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

🎀 Function/Subroutine Documentation 🎀

real function CLA_GBRPVGRW (integer n, integer kl, integer ku, integer ncols, complex, dimension( ldab, * ) ab, integer ldab, complex, dimension( ldafb, * ) afb, integer ldafb)

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

🎯 Purpose 🎯

⚠️ okay so here's the tea, bestie: CLA_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. not the vibe.

🌈 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 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 array, dimension (LDAFB,N). Details of the LU factorization of the band matrix A, as computed by CGBTRF. 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 cla_gbrpvgrw.f.

🛠️ Author 🛠️

Generated automatically by Doxygen for LAPACK from the source code.

---

xoxo, LAPACK 💖 — Version 3.12.0 — source/path footer: /home/abui..._gbrpvgrw.f(3). Date? Not listed in this footer, so no invented date, periodt. 🫶