TESTING/LIN/sptt05.f(3)

💖 NAME 💖

okay bestie, this is the Library Functions Manual page for TESTING/LIN/sptt05.f(3). The NAME section is literally TESTING/LIN/sptt05.f — short, sweet, iconic, no notes. 💅

✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

that's the synopsis, typed exactly:

       subroutine sptt05 (n, nrhs, d, e, b, ldb, x, ldx, xact, ldxact, ferr,
           berr, reslts)
           SPTT05

💅 Function/Subroutine Documentation 💅

this is the full signature, bestie — every type and dimension is right there:

   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)
       SPTT05

🎀 Purpose 🎀

okay so 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.

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 — N is INTEGER; the number of rows of the matrices X, B, and XACT, and the order of the matrix A. N >= 0.
• NRHS — NRHS is INTEGER; the number of columns of the matrices X, B, and XACT. NRHS >= 0.
• D — D is REAL array, dimension (N); the n diagonal elements of the tridiagonal matrix A.
• E — E is REAL array, dimension (N-1); the (n-1) subdiagonal elements of the tridiagonal matrix A.
• B — B is REAL 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. LDB >= max(1,N).
• X — X is REAL 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. LDX >= max(1,N).
• XACT — XACT is REAL 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. LDXACT >= max(1,N).
• FERR — FERR is 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 — BERR is 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 — RESLTS is 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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mwah 💋 — footer time: LAPACK Version 3.12.0 and the page TESTING/LIN/sptt05.f(3). The original footer line didn't give a separate date, so I'm not inventing one, bestie 💖✨.