TESTING/LIN/sppt05.f(3)

💖 TESTING/LIN/sppt05.f 💖

Bestie, welcome to the Library Functions Manual page for TESTING/LIN/sppt05.f. This is the sppt05 subroutine, and she is here to test error bounds, periodt. 💅

✨ NAME ✨

TESTING/LIN/sppt05.f — that's the name, that's the file, no extra notes needed 🎀

🦋 SYNOPSIS 🦋

✨ Functions/Subroutines ✨

subroutine sppt05 (uplo, n, nrhs, ap, b, ldb, x, ldx, xact, ldxact,
    ferr, berr, reslts)
    SPPT05

🎀 Function/Subroutine Documentation 🎀

subroutine sppt05 (character uplo, integer n, integer nrhs, real, dimension(
* ) ap, 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)
SPPT05

💜 Purpose 💜

Okay so SPPT05 tests the error bounds from iterative refinement for the computed solution to a system of equations A*X = B, where A is a symmetric matrix in packed storage format. Slay, but make it numerical. ✨

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 / ( (n+1)*EPS + (*) ), where
            (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )

🌸 Parameters 🌸

• UPLO — UPLO is CHARACTER*1. It specifies whether the upper or lower triangular part of the symmetric matrix A is stored.
  • = 'U': upper triangular
  • = 'L': lower triangular
• 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.
• AP — AP is REAL array, dimension (N*(N+1)/2). It holds the upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows:
  • if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
  • if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
• B — B is REAL 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 REAL 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 REAL 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 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 these ratios:

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

👑 Author 👑

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

Definition at line 154 of file sppt05.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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Okay bestie, that's the whole page! Footer sign-off: source/version is LAPACK / Version 3.12.0, the page is TESTING/LIN/sppt05.f(3), and the footer doesn't print a separate date — so I'm not inventing one, fr fr 🫶✨