DGECON(3)

🦋 DGECON(3) · Library Functions Manual 🦋

okay bestie, header check: /home/abui...RC/dgecon.f(3) + Library Functions Manual + /home/abui...RC/dgecon.f(3). This page is literally the DGECON glow-up, and we're keeping every technical detail because that's the whole point 💅.

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dgecon.f — that's the file this whole manual page is about, no cap.

✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine DGECON (norm, n, a, lda, anorm, rcond, work, iwork, info) — DGECON

💅 Function/Subroutine Documentation 💅

subroutine DGECON (character norm, integer n, double precision, dimension(
       lda, * ) a, integer lda, double precision anorm, double precision rcond,
       double precision, dimension( * ) work, integer, dimension( * ) iwork,
       integer info)

DGECON iconic.

🎯 Purpose

okay so DGECON estimates the reciprocal of the condition number of a general real matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by DGETRF.

An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as

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

the way that condition-number math is serving 💅.

📝 Parameters

• NORM — NORM is 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.
• N — N is INTEGER. The order of the matrix A. N >= 0.
• A — A is DOUBLE PRECISION array, dimension (LDA,N). The factors L and U from the factorization A = P*L*U as computed by DGETRF.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• ANORM — ANORM is DOUBLE PRECISION. If NORM = '1' or 'O', the 1-norm of the original matrix A. If NORM = 'I', the infinity-norm of the original matrix A.
• RCOND — RCOND is DOUBLE PRECISION. 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 (4*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. NaNs are illegal values for ANORM, and they propagate to the output parameter RCOND. Infinity is illegal for ANORM, and it propagates to the output parameter RCOND as 0.
  • = 1: if RCOND = NaN, or RCOND = Inf, or the computed norm of the inverse of A is 0. In the latter, RCOND = 0 is returned.

bestie, the info cases are not a drill: INFO = 1 is literally if RCOND = NaN, or RCOND = Inf, or the computed norm of the inverse of A is 0; in the last case, RCOND = 0 is returned. And illegal ANORM NaN/Inf behavior is exactly as spelled out above — no invented lore 💀.

👑 Author

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

Definition at line 130 of file dgecon.f.

🤖 Author

Generated automatically by Doxygen for LAPACK from the source code.

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sign-off time: this page is rockin' LAPACK Version 3.12.0 and the footer path /home/abui...RC/dgecon.f(3). bye bestie, go estimate those condition numbers responsibly 💖✨🎀