ZPTT05(3)

okay so this is ZPTT05(3), straight out of the LAPACK Library Functions Manual 💅 and yes bestie, we're getting into the tridiagonal test-routine tea.

💖 NAME

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/zptt05.f

🌸 SYNOPSIS

🧚 Functions/Subroutines

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

🦋 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)

and the routine's name is, yep, ZPTT05 💫

✨ Purpose

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. 🫶

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.

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

so that's the exact math vibe, no cap 🧮✨

🎀 Parameters

• 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 DOUBLE PRECISION array, dimension (N). These are the n diagonal elements of the tridiagonal matrix A. ⭐
• E — E is COMPLEX*16 array, dimension (N-1). These are the (n-1) subdiagonal elements of the tridiagonal matrix A. 🦋
• B — B is COMPLEX*16 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*16 array, dimension (LDX,NRHS). These are the computed solution vectors. 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*16 array, dimension (LDX,NRHS). These are the exact solution vectors. 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (2). This is 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 zptt05.f. 📌

👑 Author

Generated automatically by Doxygen for LAPACK from the source code. 🤖💖

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and that's the whole zptt05(3) moment, bestie 🎀 the footer says LAPACK Version 3.12.0 and /home/abui...IN/zptt05.f(3) — no extra date line on this footer, just version-and-source energy 🫶💜