SGECON(3)

Hey bestie!! 💖 Welcome to SGECON(3) from the Library Functions Manual — yes, the LAPACK one, and no, it is not scary. It’s giving “let’s estimate a condition number” and honestly? iconic. 🫶

💖 NAME 💖

SGECON lives at this exact source path, bestie — do not lose it:

/home/abuild/rpmbuild/BUILD/lapack-
static-3.12.0-build/lapack-3.12.0/SRC/sgecon.f

🌸 SYNOPSIS 🌸

🧚 Functions/Subroutines 🧚

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

🎀 Function/Subroutine Documentation 🎀

Here’s the exact signature, character-for-character, because we do not play with code:

subroutine SGECON (character norm, integer n, real, dimension( lda, * ) a,
     integer lda, real anorm, real rcond, real, dimension( * ) work, integer,
     dimension( * ) iwork, integer info)

SGECON — that’s the name, and it’s not a phase. ✨

💜 Purpose 💜

Okay so real talk: SGECON 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 SGETRF.

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)) ).

Lowkey important, highkey useful. 💅

🦋 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.
• N — N is INTEGER. The order of the matrix A. N >= 0.
• A — A is REAL array, dimension (LDA,N). The factors L and U from the factorization A = P*L*U as computed by SGETRF.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• ANORM — ANORM is REAL. 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 REAL. The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))).
• WORK — WORK is REAL 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.

👑 Author 👑

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

📍 Definition 📍

Definition at line 130 of file sgecon.f.

🪄 Author (the generated one) 🪄

Generated automatically by Doxygen for LAPACK from the source code.

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Okay that’s the whole page, bestie — go forth and estimate those condition numbers responsibly. 🫶 Signed off with LAPACK Version 3.12.0 energy, from the footer path /home/abui...RC/sgecon.f(3). Mwah!! 💋✨