TESTING/LIN/dtpt01.f(3)

🌸 NAME 🌸

TESTING/LIN/dtpt01.f

okay bestie, welcome to the Library Functions Manual page for TESTING/LIN/dtpt01.f — yes, the title is literally the whole path and she is serving filesystem main character energy 💅✨

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

• subroutine dtpt01 (uplo, diag, n, ap, ainvp, rcond, work, resid) — DTPT01

🎀 Function/Subroutine Documentation 🎀

Here’s the full signature, bestie, copied exactly because we do not play with code 💖

   subroutine dtpt01 (character uplo, character diag, integer n, double
       precision, dimension( * ) ap, double precision, dimension( * ) ainvp,
       double precision rcond, double precision, dimension( * ) work, double
       precision resid)

And the routine’s name is DTPT01, iconic and to the point 🫶

💖 Purpose 💖

okay so DTPT01 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. literally that’s the whole vibe check 🔥

🧚 Parameters 🧚

• UPLO — UPLO is CHARACTER*1. Specifies whether the matrix A is upper or lower triangular:
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• DIAG — DIAG is CHARACTER*1. 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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. no cap, she’s gone 💀

• RCOND — RCOND is DOUBLE PRECISION. The reciprocal condition number of A, computed as 1/(norm(A) * norm(AINV)). 🦋
• WORK — WORK is DOUBLE PRECISION array, dimension (N). ✨
• RESID — RESID is DOUBLE PRECISION. The residual formula is:

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 📍

Definition at line 107 of file dtpt01.f.

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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that’s the whole page, bestie 💜 signing off from LAPACK Version 3.12.0 on TESTING/LIN/dtpt01.f(3) — periodt 🫶✨