TESTING/LIN/ztpt02.f(3)

🌸 NAME 🌸

TESTING/LIN/ztpt02.f — okay bestie, this is the manual page for the ztpt02 source file. The manual name folded up top is TESTING/LIN/ztpt02.f(3) from the Library Functions Manual, and we are keeping that exact name in the group chat notes 💅.

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

       subroutine ztpt02 (uplo, trans, diag, n, nrhs, ap, x, ldx, b, ldb, work,
           rwork, resid)
           ZTPT02

🧚 Function/Subroutine Documentation 🧚

   subroutine ztpt02 (character uplo, character trans, character diag, integer
       n, integer nrhs, complex*16, dimension( * ) ap, complex*16, dimension(
       ldx, * ) x, integer ldx, complex*16, dimension( ldb, * ) b, integer ldb,
       complex*16, dimension( * ) work, double precision, dimension( * ) rwork,
       double precision resid)
       ZTPT02

ZTPT02 — that's the icon, no notes 💖.

💖 Purpose 💖

Okay so ZTPT02 computes the residual for the computed solution to a triangular system of linear equations op(A)*X = B, when the triangular matrix A is stored in packed format. The test ratio is the maximum over

norm(b - op(A)*x) / ( ||op(A)||_1 * norm(x) * EPS ),

where op(A) = A, A**T, or A**H, b is the column of B, x is the solution vector, and EPS is the machine epsilon. That's the whole plot, no cap 💅.

🍓 Parameters 🍓

• UPLO is CHARACTER*1 — tells you whether matrix A is upper or lower triangular.
  • 'U': Upper triangular
  • 'L': Lower triangular
• TRANS is CHARACTER*1 — tells you which operation gets applied to A.
  • 'N': A * X = B (No transpose)
  • 'T': A**T * X = B (Transpose)
  • 'C': A**H * X = B (Conjugate transpose)
• DIAG is CHARACTER*1 — says whether or not matrix A is unit triangular.
  • 'N': Non-unit triangular
  • 'U': Unit triangular
• N is INTEGER — the order of matrix A. Constraint: N >= 0.
• NRHS is INTEGER — the number of right hand sides, i.e., the number of columns of matrices X and B. Constraint: NRHS >= 0.
• AP is COMPLEX*16 array, dimension (N*(N+1)/2) — the upper or lower triangular matrix A, packed columnwise in a linear array. The j-th column of A is stored in AP like this:

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.

• X is COMPLEX*16 array, dimension (LDX,NRHS) — the computed solution vectors for the system of linear equations.
• LDX is INTEGER — the leading dimension of array X. Constraint: LDX >= max(1,N).
• B is COMPLEX*16 array, dimension (LDB,NRHS) — the right hand side vectors for the system of linear equations.
• LDB is INTEGER — the leading dimension of array B. Constraint: LDB >= max(1,N).
• WORK is COMPLEX*16 array, dimension (N) — that's it, no extra lore.
• RWORK is DOUBLE PRECISION array, dimension (N) — same energy, different precision.
• RESID is DOUBLE PRECISION — the maximum over the number of right hand sides of

norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ).

👑 Author 👑

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

Definition at line 145 of file ztpt02.f.

🦋 Author 🦋

Generated automatically by Doxygen for LAPACK from the source code.

---

Okay bestie, that's the whole page. The footer energy is LAPACK Version 3.12.0 and TESTING/LIN/ztpt02.f(3) — source/version and page name, all present and accounted for, mwah 💋💖