DTRCON(3)

💅 NAME

okay bestie, welcome to DTRCON(3) from the Library Functions Manual 💖 — this page is all about the file /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dtrcon.f, and honestly it’s giving “small but mighty LAPACK icon” energy ✨.

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✨ SYNOPSIS

Functions/Subroutines

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

and the main character is, of course, DTRCON 🎀.

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🦋 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 — say it with me — is the one estimating the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm 🔥.

🌸 Purpose

Bestie, here’s the whole vibe: 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, an estimate is obtained for norm(inv(A)), and then the reciprocal of the condition number is computed as:

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

No cap, that formula is the moment 💅.

🫶 Parameters

• NORM — NORM is CHARACTER*1. It tells us whether the 1-norm condition number or the infinity-norm condition number is required: = '1' or 'O': 1-norm; = 'I': Infinity-norm. Pick your fighter ✨.
• UPLO — UPLO is CHARACTER*1. = 'U': means A is upper triangular; = 'L': means A is lower triangular. Respect the triangle 🎀.
• DIAG — DIAG is CHARACTER*1. = 'N': means A is non-unit triangular; = 'U': means A is unit triangular. We love a clear diag situation 💖.
• N — N is INTEGER. It’s the order of the matrix A. N >= 0. Periodt.
• 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. Iconic behavior, lowkey 🦋.
• LDA — LDA is INTEGER. It’s the leading dimension of the array A. LDA >= max(1,N). Do not play with this one 🙈.
• 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))). That’s the whole point, fr fr 💅.
• WORK — WORK is DOUBLE PRECISION array, dimension (3*N). It’s workspace. Give it room to breathe 🫶.
• IWORK — IWORK is INTEGER array, dimension (N). More workspace, but make it integer energy ✨.
• INFO — INFO is INTEGER. = 0: successful exit; < 0: if INFO = -i, the i-th argument had an illegal value. So if INFO is negative, something in the argument lineup was not slaying 😭.

👑 Author

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

📌 Definition at line 135 of file dtrcon.f.

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🌈 Author

Generated automatically by Doxygen for LAPACK from the source code. Yes bestie, the robots wrote this bit 🤖💖.

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🎀 Sign-off: this footer is LAPACK Version 3.12.0, source path /home/abui...RC/dtrcon.f(3) — no separate date line in the original, so that’s the whole footer vibe. Bye bestie, go estimate those condition numbers responsibly! 💖✨