DPBCON(3)

💅 DPBCON(3) — like, the LAPACK library functions manual, bestie 🎀

okay so real talk: this page lives in the Library Functions Manual, and the "name" of the thing is literally this whole path, no cap:

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

yes it's giving "my mom named the file with the entire receipt" 😭 but that's where DPBCON comes from, so we respect it. 🫶

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✨ SYNOPSIS ✨

Functions/Subroutines 🌸

• subroutine DPBCON (uplo, n, kd, ab, ldab, anorm, rcond, work, iwork, info) — the one and only DPBCON, queen of condition-number estimates 👑

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💖 Function/Subroutine Documentation 💖

subroutine DPBCON (character uplo, integer n, integer kd, double precision,
    dimension( ldab, * ) ab, integer ldab, double precision anorm, double
    precision rcond, double precision, dimension( * ) work, integer,
    dimension( * ) iwork, integer info)

🦋 Purpose: 🦋

!> !> DPBCON 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 DPBTRF. !> !> An estimate is obtained for norm(inv(A)), and the reciprocal of the !> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). !>

so basically: you already ran DPBTRF and got your Cholesky factorization A = U**T*U or A = L*L**T of a real symmetric positive definite band matrix. iconic. now DPBCON comes in and tells you how sketchy that matrix is — it estimates norm(inv(A)) and hands you back RCOND = 1 / (ANORM * norm(inv(A))). small RCOND = your matrix is not doing so hot 💀, big-ish RCOND = slay 💅.

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✨ Parameters ✨

• UPLO — UPLO is CHARACTER*1. which triangle of the factorization is chillin' in AB:
  • = '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. like, how big is she.
• 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. the band width, iykyk.
• AB — AB is DOUBLE PRECISION array, dimension (LDAB,N). 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: — and here's the exact mapping, don't @ me:
  • 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. respect the leading dimension, always 🙏.
• ANORM — ANORM is DOUBLE PRECISION. The 1-norm (or infinity-norm) of the symmetric band matrix A. you bring this, the routine does not compute it for you, main character energy only.
• RCOND — RCOND is DOUBLE PRECISION. 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. this is the whole point of the function, the moment, the finale 💖.
• WORK — WORK is DOUBLE PRECISION array, dimension (3*N). that's a 3 times N situation, note it.
• IWORK — IWORK is INTEGER array, dimension (N). integer scratch, dimension N, tyvm.
• INFO — INFO is INTEGER:
  • = 0: successful exit 🎉
  • < 0: if INFO = -i, the i-th argument had an illegal value 🙈 (you fed it something cursed, it's telling you which position)

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👑 Author 👑

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

Definition at line 130 of file dpbcon.f. 📍

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🩷 Author 🩷

Generated automatically by Doxygen for LAPACK from the source code. (yes, a robot wrote this, but I'm the one making it cute 💅)

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okay bestie that's the whole page — and for the cute sign-off: this is LAPACK, Version 3.12.0, and the footer is literally just /home/abui...RC/dpbcon.f(3) again, so consider it signed, sealed, and slayed 🧚‍♀️💜✨