TESTING/LIN/zptt05.f(3)

Hey bestie! 💖 Welcome to the TESTING/LIN/zptt05.f(3) page from the Library Functions Manual — yes, we're deep in LAPACK testing territory, and it's giving big main-character energy. ✨

🌸 NAME 🌸

TESTING/LIN/zptt05.f — the file behind the zptt05 subroutine, periodt. 💅

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✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

subroutine zptt05 (n, nrhs, d, e, b, ldb, x, ldx, xact, ldxact, ferr,
    berr, reslts)
    ZPTT05

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💅 Function/Subroutine Documentation 💅

subroutine zptt05 (integer n, integer nrhs, double precision, dimension( * )
    d, complex*16, dimension( * ) e, complex*16, dimension( ldb, * ) b,
    integer ldb, complex*16, dimension( ldx, * ) x, integer ldx, complex*16,
    dimension( ldxact, * ) xact, integer ldxact, double precision,
    dimension( * ) ferr, double precision, dimension( * ) berr, double
    precision, dimension( * ) reslts)
    ZPTT05

🎀 Purpose 🎀

Okay so ZPTT05 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 formula tea:

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. 😭 That's the warning sign, bestie.

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 🧚

• N — N is INTEGER. The number of rows of the matrices X, B, and XACT, and the order of the matrix A. Constraint: N >= 0. ✨
• NRHS — NRHS is INTEGER. The number of columns of the matrices X, B, and XACT. Constraint: NRHS >= 0. 💖
• D — D is DOUBLE PRECISION array, dimension (N). The n diagonal elements of the tridiagonal matrix A. 🎀
• E — E is COMPLEX*16 array, dimension (N-1). The (n-1) subdiagonal elements of the tridiagonal matrix A. 🦋
• B — B is COMPLEX*16 array, dimension (LDB,NRHS). The right hand side vectors for the system of linear equations. 🌸
• LDB — LDB is INTEGER. The leading dimension of the array B. Constraint: LDB >= max(1,N). 💅
• X — X is COMPLEX*16 array, dimension (LDX,NRHS). The computed solution vectors. Each vector is stored as a column of the matrix X. 🫶
• LDX — LDX is INTEGER. The leading dimension of the array X. Constraint: LDX >= max(1,N). 😭
• XACT — XACT is COMPLEX*16 array, dimension (LDX,NRHS). The exact solution vectors. Each vector is stored as a column of the matrix XACT. 🔥
• LDXACT — LDXACT is INTEGER. The leading dimension of the array XACT. Constraint: LDXACT >= max(1,N). 👑
• FERR — FERR is DOUBLE PRECISION array, dimension (NRHS). 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 DOUBLE PRECISION array, dimension (NRHS). 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 DOUBLE PRECISION array, dimension (2). The maximum over the NRHS solution vectors of the ratios: RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR ) and RESLTS(2) = BERR / ( NZ*EPS + (*) ). 💀

👑 Author 👑

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

📌 Definition at line 📌

Definition at line 148 of file zptt05.f.

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code. 🙈

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Bye bestie — this page was TESTING/LIN/zptt05.f(3) from LAPACK Version 3.12.0. 💖✨