SRC/dtbcon.f(3)

💅 SRC/dtbcon.f(3) 💅

welcome to the Library Functions Manual corner of the group chat, bestie 🫶 this page is all about the Fortran subroutine dtbcon, and no cap it is giving serious condition-number-detective energy.

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🌸 NAME 🌸

SRC/dtbcon.f

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✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

       subroutine dtbcon (norm, uplo, diag, n, kd, ab, ldab, rcond, work,
           iwork, info)
           DTBCON

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🦋 Function/Subroutine Documentation 🦋

okay so here is the full signature, copied exactly because we do not mess with code 💅

   subroutine dtbcon (character norm, character uplo, character diag, integer
       n, integer kd, double precision, dimension( ldab, * ) ab, integer ldab,
       double precision rcond, double precision, dimension( * ) work, integer,
       dimension( * ) iwork, integer info)
       DTBCON

🔥 Purpose 🔥

DTBCON estimates the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm. periodt 💜

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)) ).

literally the whole vibe: get norm(A), estimate norm(inv(A)), flip it into RCOND ✨

🍓 Parameters 🍓

• NORM — CHARACTER*1. Specifies whether the 1-norm condition number or the infinity-norm condition number is required:
  • = '1' or 'O': 1-norm;
  • = 'I': Infinity-norm.
• UPLO — CHARACTER*1.
  • = 'U': A is upper triangular;
  • = 'L': A is lower triangular.
• DIAG — CHARACTER*1.
  • = 'N': A is non-unit triangular;
  • = 'U': A is unit triangular.
• N — INTEGER. The order of the matrix A. N >= 0.
• KD — INTEGER. The number of superdiagonals or subdiagonals of the triangular band matrix A. KD >= 0.
• AB — DOUBLE PRECISION array, dimension (LDAB,N). 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.

• LDAB — INTEGER. The leading dimension of the array AB. LDAB >= KD+1.
• RCOND — DOUBLE PRECISION. The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))).
• WORK — DOUBLE PRECISION array, dimension (3*N).
• IWORK — INTEGER array, dimension (N).
• INFO — 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 dtbcon.f.

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🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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okay bye bestie 💜 signing off from LAPACK, Version 3.12.0, page SRC/dtbcon.f(3) — slay and stay safe out there 🎀