SPPT05(3)

💖 NAME 💖

okay so this is SPPT05(3) — that's the manual-page name, bestie. The source file it documents is exactly:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/sppt05.f

No cap, that path is long but iconic.

🦋 SYNOPSIS 🦋

Functions/Subroutines

The callable vibe is:

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

🔥 Function/Subroutine Documentation 🔥

Here's the full subroutine signature with all the types and dimensions, exactly:

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 🎀

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. It's giving numerical auditor energy, honestly.

Here's the exact breakdown:

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 — CHARACTER*1. Specifies whether the upper or lower triangular part of the symmetric matrix A is stored.
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• N — INTEGER. The number of rows of the matrices X, B, and XACT, and the order of the matrix A. N >= 0.
• NRHS — INTEGER. The number of columns of the matrices X, B, and XACT. NRHS >= 0.
• AP — REAL array, dimension (N*(N+1)/2). 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 — 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. 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. 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. 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 / ( (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.

And the page's auto-generated author note says: Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the whole page, bestie 💅. Cute little footer sign-off: source/version is LAPACK Version 3.12.0, and the footer's trailing date/file slot shows /home/abui...IN/sppt05.f(3). Periodt. 🫶