TESTING/LIN/ztpt01.f(3)

🎀 TESTING/LIN/ztpt01.f 🎀

okay so bestie, welcome to the TESTING/LIN/ztpt01.f(3) page from the Library Functions Manual — LAPACK's own ztpt01 corner of the universe. It's giving "tiny testing routine with main-character energy," and we're gonna read every single detail together, no skips, no cap. 💅

---

✨ NAME ✨

TESTING/LIN/ztpt01.f

🦋 SYNOPSIS 🦋

Functions/Subroutines

   subroutine ztpt01 (uplo, diag, n, ap, ainvp, rcond, rwork, resid)
       ZTPT01

🫶 Function/Subroutine Documentation 🫶

💫 the subroutine signature 💫

   subroutine ztpt01 (character uplo, character diag, integer n, complex*16,
       dimension( * ) ap, complex*16, dimension( * ) ainvp, double precision
       rcond, double precision, dimension( * ) rwork, double precision resid)
       ZTPT01

💡 Purpose

Bestie, here's the tea: ZTPT01 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. That's the whole purpose, and it ate. ✨

🔍 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 COMPLEX*16 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*16 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 bestie, AINVP gets wrecked on exit — that's not a vibe, that's just the spec.

• RCOND — RCOND is DOUBLE PRECISION. The reciprocal condition number of A, computed as 1/(norm(A) * norm(AINV)).
• RWORK — RWORK is DOUBLE PRECISION array, dimension (N).
• RESID — RESID is DOUBLE PRECISION. 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 ztpt01.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

---

bye bestie 💖 — the footer credits LAPACK, Version 3.12.0, and TESTING/LIN/ztpt01.f(3); no separate date is printed on this page, so consider this your cute official sign-off. mwah 🫶