CTBCON(3)

📦 version 3.12.0, in opensuse-leap 16.0

CTBCON(3) — Library Functions Manual ✨

🌸 NAME 🌸

okay so bestie, the NAME on this page is literally this Fortran file path, no cap: /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/ctbcon.f 💅

🦋 SYNOPSIS 🦋

Functions/Subroutines

subroutine CTBCON (norm, uplo, diag, n, kd, ab, ldab, rcond, work,
    rwork, info)
CTBCON

💜 Function/Subroutine Documentation 💜

subroutine CTBCON (character norm, character uplo, character diag, integer
    n, integer kd, complex, dimension( ldab, * ) ab, integer ldab, real
    rcond, complex, dimension( * ) work, real, dimension( * ) rwork, integer
    info)
CTBCON

Purpose:

okay so CTBCON estimates the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm — iconic linear algebra behavior 🔥 The norm of A is computed and an estimate is obtained for norm(inv(A)), then the reciprocal of the condition number is computed as

RCOND = 1 / ( norm(A) * norm(inv(A)) ).

Parameters

NORM

NORM is CHARACTER*1. It specifies whether the 1-norm condition number or the infinity-norm condition number is required:

= '1' or 'O':  1-norm;
= 'I':         Infinity-norm.

UPLO

UPLO is CHARACTER*1.

= 'U':  A is upper triangular;
= 'L':  A is lower triangular.

DIAG

DIAG is CHARACTER*1.

= 'N':  A is non-unit triangular;
= 'U':  A is unit triangular.

N

N is INTEGER. It's the order of the matrix A, and bestie, N >= 0 — no negative orders allowed 💀

KD

KD is INTEGER. It's the number of superdiagonals or subdiagonals of the triangular band matrix A. Also KD >= 0 🫶

AB

AB is COMPLEX array, dimension (LDAB,N). It's the upper or lower triangular band matrix A, stored in the first kd+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows:

if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).

If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1. noted, bestie ✨

LDAB

LDAB is INTEGER. It's the leading dimension of the array AB, and LDAB >= KD+1 — that's the vibe check for this one 💅

RCOND

RCOND is REAL. It's the reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))). 🎀

WORK

WORK is COMPLEX array, dimension (2*N).

RWORK

RWORK is REAL 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 141 of file ctbcon.f.

Author

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okay bestie, that's the whole page 💖 this cutie is from LAPACK Version 3.12.0, and the footer source path is /home/abui...RC/ctbcon.f(3) — periodt ✨

📦 where this page comes from