TESTING/LIN/cptt05.f(3)

💅 NAME 💅

Okay so the page header says TESTING/LIN/cptt05.f(3) and the manual is Library Functions Manual — and this whole page is serving TESTING/LIN/cptt05.f realness. The main-character routine here is cptt05, no cap.

---

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

subroutine cptt05 (n, nrhs, d, e, b, ldb, x, ldx, xact, ldxact, ferr,
    berr, reslts)
           CPTT05

---

🎀 Function/Subroutine Documentation 🎀

Full signature, copied with love and exact characters:

   subroutine cptt05 (integer n, integer nrhs, real, dimension( * ) d, complex,
       dimension( * ) e, complex, dimension( ldb, * ) b, integer ldb, complex,
       dimension( ldx, * ) x, integer ldx, complex, dimension( ldxact, * )
       xact, integer ldxact, real, dimension( * ) ferr, real, dimension( * )
       berr, real, dimension( * ) reslts)
       CPTT05

CPTT05 💅

💖 Purpose 💖

CPTT05 tests the error bounds from iterative refinement for the computed solution to a system of equations A*X = B, where A is a Hermitian tridiagonal matrix of order n.

Here's the first ratio it checks:

RESLTS(1) = test of the error bound
          = norm(X - XACT) / ( norm(X) * FERR )

A large value is returned if this ratio is not less than one. 👀

Then there's the residual situation:

RESLTS(2) = residual from the iterative refinement routine
          = the maximum of BERR / ( NZ*EPS + (*) ), where
            (*) = NZ*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
            and NZ = max. number of nonzeros in any row of A, plus 1

🧚 Parameters 🧚

One bullet per parameter, bestie — exact types and dimensions kept intact:

• N — N is INTEGER. It's the number of rows of the matrices X, B, and XACT, and the order of the matrix A. N >= 0.
• NRHS — NRHS is INTEGER. It's the number of columns of the matrices X, B, and XACT. NRHS >= 0.
• D — D is REAL array, dimension (N). These are the n diagonal elements of the tridiagonal matrix A.
• E — E is COMPLEX array, dimension (N-1). These are the (n-1) subdiagonal elements of the tridiagonal matrix A.
• B — B is COMPLEX array, dimension (LDB,NRHS). These are the right hand side vectors for the system of linear equations.
• LDB — LDB is INTEGER. It's the leading dimension of the array B. LDB >= max(1,N).
• X — X is COMPLEX array, dimension (LDX,NRHS). These are the computed solution vectors, and each vector is stored as a column of the matrix X.
• LDX — LDX is INTEGER. It's the leading dimension of the array X. LDX >= max(1,N).
• XACT — XACT is COMPLEX array, dimension (LDX,NRHS). These are the exact solution vectors, and each vector is stored as a column of the matrix XACT.
• LDXACT — LDXACT is INTEGER. It's the leading dimension of the array XACT. LDXACT >= max(1,N).
• FERR — FERR is REAL array, dimension (NRHS). These are the estimated forward error bounds for each solution vector X. If XTRUE is the true solution, FERR bounds the magnitude of the largest entry in (X - XTRUE) divided by the magnitude of the largest entry in X.
• BERR — BERR is REAL array, dimension (NRHS). This is the componentwise relative backward error of each solution vector, i.e. the smallest relative change in any entry of A or B that makes X an exact solution.
• RESLTS — RESLTS is REAL array, dimension (2). It's the maximum over the NRHS solution vectors of the ratios:

RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
RESLTS(2) = BERR / ( NZ*EPS + (*) )

💖 Author 💖

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

Definition at line 148 of file cptt05.f.

---

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

---

Footer sign-off, bestie: LAPACK, Version 3.12.0, and TESTING/LIN/cptt05.f(3) — that's the source/version/page combo. Mwah 💋✨