SPTT05(3)

💖 SPTT05 — sptt05.f(3) 💖

okay bestie, welcome to the sptt05.f(3) manual page — header says Library Functions Manual energy, path is /home/abui...IN/sptt05.f(3), and it's giving LAPACK testing subroutine realness. It's a Fortran page, so grab a strawberry 🍓 and let's go.

🎀 NAME 🎀

This page's NAME is literally this source file path:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/sptt05.f

🧩 SYNOPSIS 🧩

Functions/Subroutines

subroutine SPTT05 (n, nrhs, d, e, b, ldb, x, ldx, xact, ldxact, ferr,
           berr, reslts)
           SPTT05

🦋 Function/Subroutine Documentation 🦋

subroutine SPTT05 (integer n, integer nrhs, real, dimension( * ) d, real,
       dimension( * ) e, real, dimension( ldb, * ) b, integer ldb, real,
       dimension( ldx, * ) x, integer ldx, real, dimension( ldxact, * ) xact,
       integer ldxact, real, dimension( * ) ferr, real, dimension( * ) berr,
       real, dimension( * ) reslts)

Yes, the subroutine is SPTT05 again. Main character energy 👑.

🎯 Purpose 🎯

Bestie, SPTT05 tests the error bounds from iterative refinement for the computed solution to a system of equations A*X = B, where A is a symmetric tridiagonal matrix of order n.

The source comment is literally giving:

!> 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

🌸 Parameters 🌸

• N — INTEGER. The number of rows of the matrices X, B, and XACT, and the order of the matrix A. Constraint: N >= 0.
• NRHS — INTEGER. The number of columns of the matrices X, B, and XACT. Constraint: NRHS >= 0.
• D — REAL array, dimension (N). The n diagonal elements of the tridiagonal matrix A.
• E — REAL array, dimension (N-1). The (n-1) subdiagonal elements of the tridiagonal matrix A.
• B — REAL array, dimension (LDB,NRHS). The right hand side vectors for the system of linear equations.
• LDB — INTEGER. The leading dimension of the array B. Constraint: LDB >= max(1,N).
• X — REAL array, dimension (LDX,NRHS). The computed solution vectors. Each vector is stored as a column of the matrix X.
• LDX — INTEGER. The leading dimension of the array X. Constraint: LDX >= max(1,N).
• XACT — REAL array, dimension (LDX,NRHS). The exact solution vectors. Each vector is stored as a column of the matrix XACT.
• LDXACT — INTEGER. The leading dimension of the array XACT. Constraint: LDXACT >= max(1,N).
• FERR — REAL 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 — REAL 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 — REAL array, dimension (2). 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 sptt05.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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