SRC/zpocon.f(3)

📦
version 3.12.1 · 7 versions
, in arch rolling

okay bestie, this is SRC/zpocon.f from the Library Functions Manual — zpocon is the main character here, and we're gonna get into the condition-number math together 👑💅

💖 NAME 💖

SRC/zpocon.f — Library Functions Manual page for the zpocon subroutine. Manual name folded in near the top, as requested 🎀

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine zpocon (uplo, n, a, lda, anorm, rcond, work, rwork, info)

ZPOCON

🧚 Function/Subroutine Documentation 🧚

subroutine zpocon (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision anorm, double precision rcond, complex*16, dimension( * ) work, double precision, dimension( * ) rwork, integer info)

ZPOCON — the one and only, no notes 💫

🎯 Purpose 🎯

okay so ZPOCON estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPOTRF.

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

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

🎀 Parameters 🎀

  • UPLO — is CHARACTER*1
    • = 'U': Upper triangle of A is stored;
    • = 'L': Lower triangle of A is stored.
  • N — is INTEGER; the order of the matrix A. N >= 0.
  • A — is COMPLEX*16 array, dimension (LDA,N); the triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, as computed by ZPOTRF.
  • LDA — is INTEGER; the leading dimension of the array A. LDA >= max(1,N).
  • ANORM — is DOUBLE PRECISION; the 1-norm (or infinity-norm) of the Hermitian matrix A.
  • RCOND — is DOUBLE PRECISION; the reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine.
  • WORK — is COMPLEX*16 array, dimension (2*N).
  • RWORK — is DOUBLE PRECISION array, dimension (N).
  • 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 119 of file zpocon.f. 📍

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

okay that's the whole page, bestie — LAPACK Version 3.12.0, source SRC/zpocon.f(3), and the footer doesn't print a date so I'm not inventing one 😭🫶💅

📦 where this page comes from