TESTING/LIN/cpot03.f(3)

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🌸 NAME 🌸

TESTING/LIN/cpot03.f

🦋 SYNOPSIS 🦋

✨ Functions/Subroutines ✨

   Functions/Subroutines
       subroutine cpot03 (uplo, n, a, lda, ainv, ldainv, work, ldwork, rwork,
           rcond, resid)
           CPOT03

🎀 Function/Subroutine Documentation 🎀

   subroutine cpot03 (character uplo, integer n, complex, dimension( lda, * )
       a, integer lda, complex, dimension( ldainv, * ) ainv, integer ldainv,
       complex, dimension( ldwork, * ) work, integer ldwork, real, dimension( *
       ) rwork, real rcond, real resid)
       CPOT03

💅 Purpose 💅

The code comment says it best, and it says:

!>
!> CPOT03 computes the residual for a Hermitian matrix times its
!> inverse:
!>    norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ),
!> where EPS is the machine epsilon.
!>

So yes, CPOT03 is out here computing the residual for a Hermitian matrix times its inverse. That formula is the whole vibe check, no cap. 🔥

🌈 Parameters 🌈

• UPLO — this is CHARACTER*1, and it tells you which triangular part of the Hermitian matrix A is stored:
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• N — this is INTEGER, and it's the number of rows and columns of the matrix A. Constraint: N >= 0.
• A — this is COMPLEX array, dimension (LDA,N). It's the original Hermitian matrix A, bestie.
• LDA — this is INTEGER, and it's the leading dimension of the array A. Constraint: LDA >= max(1,N).
• AINV — this is COMPLEX array, dimension (LDAINV,N). On entry, it's the inverse of the matrix A, stored as a Hermitian matrix in the same format as A. In this version, AINV is expanded into a full matrix and multiplied by A, so the opposing triangle of AINV will be changed — like, if the upper triangular part of AINV is stored, the lower triangular part gets used as work space. 🫶
• LDAINV — this is INTEGER, and it's the leading dimension of the array AINV. Constraint: LDAINV >= max(1,N).
• WORK — this is COMPLEX array, dimension (LDWORK,N).
• LDWORK — this is INTEGER, and it's the leading dimension of the array WORK. Constraint: LDWORK >= max(1,N).
• RWORK — this is REAL array, dimension (N).
• RCOND — this is REAL, and it's the reciprocal of the condition number of A, computed as ( 1/norm(A) ) / norm(AINV).
• RESID — this is REAL, and 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 124 of file cpot03.f.

🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code.

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okay bye bestie — this page is from LAPACK Version 3.12.0, and the footer's page name is TESTING/LIN/cpot03.f(3). Those are the source/version deets, periodt. 💅✨