TESTING/LIN/ctpt01.f(3)

💖 NAME 💖

Okay bestie, this is the manual page for TESTING/LIN/ctpt01.f from the Library Functions Manual — it’s giving LAPACK testing-routine energy, and we’re gonna go through every single detail together. No skips, no cap. 💅

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

• subroutine ctpt01 (uplo, diag, n, ap, ainvp, rcond, rwork, resid) — CTPT01

🎀 Function/Subroutine Documentation 🎀

subroutine ctpt01 (character uplo, character diag, integer n, complex, dimension( * ) ap, complex, dimension( * ) ainvp, real rcond, real, dimension( * ) rwork, real resid)

CTPT01

🎯 Purpose 🎯

!>
!> CTPT01 computes the residual for a triangular matrix A times its
!> inverse when A is stored in packed format:
!>    RESID = norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS ),
!> where EPS is the machine epsilon.
!>

🌸 Parameters 🌸

• UPLO — UPLO is CHARACTER*1. It specifies whether the matrix A is upper or lower triangular. = 'U': Upper triangular; = 'L': Lower triangular.
• DIAG — DIAG is CHARACTER*1. It specifies whether or not the matrix A is unit triangular. = 'N': Non-unit triangular; = 'U': Unit triangular.
• N — N is INTEGER. The order of the matrix A. N >= 0.
• AP — AP is COMPLEX array, dimension (N*(N+1)/2). The original upper or lower triangular matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows:

if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
if UPLO = 'L',
   AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.

• AINVP — AINVP is COMPLEX array, dimension (N*(N+1)/2). On entry, the (triangular) inverse of the matrix A, packed columnwise in a linear array as in AP. On exit, the contents of AINVP are destroyed — yes, destroyed, so don’t expect your input back. 💀
• RCOND — RCOND is REAL. The reciprocal condition number of A, computed as 1/(norm(A) * norm(AINV)).
• RWORK — RWORK is REAL array, dimension (N).
• RESID — RESID is REAL. norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS ).

👑 Author 👑

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

Definition at line 108 of file ctpt01.f.

🌈 Author 🌈

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💖 That’s the whole page, bestie! Source page: TESTING/LIN/ctpt01.f(3). Version: LAPACK Version 3.12.0. Date: the footer doesn’t list one, so there’s no date to report — just vibes. 🫶✨