SRC/sptcon.f(3)

📦
version 3.12.1 · 7 versions
, in arch rolling

🌸 NAME 🌸

SRC/sptcon.f — okay so this is the LAPACK Library Functions Manual page for the SRC/sptcon.f source file, bestie. It’s giving “source-file energy” and it’s here to document SPTCON. 💅

✨ SYNOPSIS ✨

🧚 Functions/Subroutines

  • subroutine sptcon (n, d, e, anorm, rcond, work, info) — SPTCON

🫶 Function/Subroutine Documentation 🫶

So the actual routine is:

subroutine sptcon (integer n, real, dimension( * ) d, real, dimension( * ) e, real anorm, real rcond, real, dimension( * ) work, integer info)

SPTCON — yup, that’s the main character. 👑

🎯 Purpose

Bestie, SPTCON computes the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite tridiagonal matrix using the factorization A = L*D*L**T or A = U**T*D*U computed by SPTTRF.

Norm(inv(A)) is computed by a direct method, and the reciprocal of the condition number is computed as:

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

No cap, that’s the whole condition-number situation. 💖

🔢 Parameters

🌟 N

N is INTEGER.

The order of the matrix A. N >= 0.

🌟 D

D is REAL array, dimension (N).

The n diagonal elements of the diagonal matrix D from the factorization of A, as computed by SPTTRF.

🌟 E

E is REAL array, dimension (N-1).

The (n-1) off-diagonal elements of the unit bidiagonal factor U or L from the factorization of A, as computed by SPTTRF.

🌟 ANORM

ANORM is REAL.

The 1-norm of the original matrix A.

🌟 RCOND

RCOND is REAL.

The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is the 1-norm of inv(A) computed in this routine.

🌟 WORK

WORK is REAL array, dimension (N).

🌟 INFO

INFO is INTEGER.

  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

🫶 Author

Shoutout to the author squad:

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

🔍 Further Details

The method used is described in Nicholas J. Higham, , SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986.

📍 Definition at line 117 of file sptcon.f

That’s literally where it’s defined: line 117 of file sptcon.f.

👑 Author

Generated automatically by Doxygen for LAPACK from the source code.

LAPACK Version 3.12.0 · SRC/sptcon.f(3) — that’s the cute little footer sign-off, bestie. 🎀✨💖

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