SRC/dtrcon.f(3)

📦
version 3.12.1 · 4 versions
, in arch rolling

💖 NAME 💖

okay so this is the manual page for SRC/dtrcon.f(3), straight out of the Library Functions Manual — and it's all about DTRCON, the icon that estimates reciprocal condition numbers for triangular matrices. no cap, she's serving linear algebra realness. 💅

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

  • subroutine dtrcon (norm, uplo, diag, n, a, lda, rcond, work, iwork, info) — DTRCON

🌸 Function/Subroutine Documentation 🌸

subroutine dtrcon (character norm, character uplo, character diag, integer
       n, double precision, dimension( lda, * ) a, integer lda, double
       precision rcond, double precision, dimension( * ) work, integer,
       dimension( * ) iwork, integer info)

DTRCON

🎀 Purpose 🎀

okay so DTRCON estimates the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm. 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)) ).

That's the whole glow-up. ✨

🧚 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. N >= 0.

A

A is DOUBLE PRECISION array, dimension (LDA,N). It's the triangular matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1.

LDA

LDA is INTEGER. It's the leading dimension of the array A. LDA >= max(1,N).

RCOND

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

WORK

WORK is DOUBLE PRECISION 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 135 of file dtrcon.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

💅 and that's the whole page, bestie! Footer vibes: LAPACK, Version 3.12.0, SRC/dtrcon.f(3) — that's the source/version flex, and no separate date line is listed. 🫶

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