CPPT03(3)

📦 version 3.12.0, in opensuse-leap 16.0

💖 CPPT03(3) — Library Functions Manual energy 💖

okay so this is the CPPT03(3) page, and the header says it's from the Library Functions Manual (title vibe: cppt03.f(3)). bestie, we're about to get into some Hermitian packed-matrix residual math, and honestly? it's giving precise. 💅

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/cppt03.f

✨ SYNOPSIS ✨

🫶 Functions/Subroutines 🫶

subroutine CPPT03 (uplo, n, a, ainv, work, ldwork, rwork, rcond, resid)

CPPT03

🛠️ Function/Subroutine Documentation 🛠️

subroutine CPPT03 (character uplo, integer n, complex, dimension( * ) a,
    complex, dimension( * ) ainv, complex, dimension( ldwork, * ) work,
    integer ldwork, real, dimension( * ) rwork, real rcond, real resid)

CPPT03

🎯 Purpose 🎯

CPPT03 computes the residual for a Hermitian packed matrix times its inverse, and the formula is literally this:

norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ),

where EPS is the machine epsilon. no cap, that's the whole mission. 🌟

🧾 Parameters 🧾

  • UPLO — UPLO is CHARACTER*1; it says whether the upper or lower triangular part of the Hermitian matrix A is stored:
    • = 'U': Upper triangular
    • = 'L': Lower triangular
  • N — N is INTEGER; it's the number of rows and columns of the matrix A. Constraint: N >= 0.
  • A — A is COMPLEX array, dimension (N*(N+1)/2); this is the original Hermitian matrix A, stored as a packed triangular matrix.
  • AINV — AINV is COMPLEX array, dimension (N*(N+1)/2); this is the (Hermitian) inverse of the matrix A, stored as a packed triangular matrix.
  • WORK — WORK is COMPLEX array, dimension (LDWORK,N).
  • LDWORK — LDWORK is INTEGER; it's the leading dimension of the array WORK. Constraint: LDWORK >= max(1,N).
  • RWORK — RWORK is REAL array, dimension (N).
  • RCOND — RCOND is REAL; it's the reciprocal of the condition number of A, computed as ( 1/norm(A) ) / norm(AINV).
  • RESID — RESID is REAL; it's norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS ).

✍️ Author ✍️

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

📌 Definition at line 📌

Definition at line 108 of file cppt03.f.

💌 Author 💌

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mwah 💋 — signed off with glitter and good vibes: LAPACK, Version 3.12.0, and the footer path is /home/abui...IN/cppt03.f(3). 🎀

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