SPBCON(3)

💅 SPBCON(3) — LAPACK Library Functions Manual 💅

okay so bestie, this is the SPBCON(3) page, and it’s lowkey all about estimating a reciprocal condition number. No cap, it’s giving very specific linear-algebra main character energy. ✨

🎀 NAME 🎀

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/spbcon.f — that’s the source file this page is serving up. Periodt. 💖

✨ SYNOPSIS ✨

Functions/Subroutines

Here’s the callable tea:

subroutine SPBCON (uplo, n, kd, ab, ldab, anorm, rcond, work, iwork,
    info)

SPBCON

🌸 Function/Subroutine Documentation 🌸

The full signature, character for character, because we do not play about details:

subroutine SPBCON (character uplo, integer n, integer kd, real, dimension(
    ldab, * ) ab, integer ldab, real anorm, real rcond, real, dimension( * )
    work, integer, dimension( * ) iwork, integer info)

SPBCON

🎯 Purpose 🎯

SPBCON estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPBTRF. 🦋

An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). That’s the whole purpose, and it ate. 💅

🧸 Parameters 🧸

• UPLO — UPLO is CHARACTER*1. = 'U': Upper triangular factor stored in AB; = 'L': Lower triangular factor stored in AB. 🎀
• N — N is INTEGER. The order of the matrix A. N >= 0. ✨
• KD — KD is INTEGER. The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0. 🌸
• AB — AB is REAL array, dimension (LDAB,N). It’s the triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T of the band matrix A, stored in the first KD+1 rows of the array. The j-th column of U or L is stored in the j-th column of the array AB as follows: if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j; if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd). 🫶
• LDAB — LDAB is INTEGER. The leading dimension of the array AB. LDAB >= KD+1. 🔥
• ANORM — ANORM is REAL. The 1-norm (or infinity-norm) of the symmetric band matrix A. 👑
• RCOND — RCOND is REAL. The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine. 💜
• WORK — WORK is REAL array, dimension (3*N). 🌈
• IWORK — IWORK is INTEGER array, dimension (N). ⭐
• INFO — INFO is INTEGER. = 0: successful exit; < 0: if INFO = -i, the i-th argument had an illegal value. 💀

👑 Author 👑

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

📍 Definition at line 130 of file spbcon.f 📍

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code. 🧚

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Catch you later, bestie 💖 — this page is from LAPACK, Version 3.12.0, and the footer path is /home/abui...RC/spbcon.f(3). Slay. 🫶