DPPT05(3)

💅 NAME 💅

okay bestie, this is the dppt05.f(3) page from the Library Functions Manual, and the NAME section is literally this source path:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/dppt05.f

That’s the whole NAME vibe — no extra noun, just the file path. 💖

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

subroutine DPPT05 (uplo, n, nrhs, ap, b, ldb, x, ldx, xact, ldxact,
    ferr, berr, reslts)
    DPPT05

🦋 Function/Subroutine Documentation 🦋

subroutine DPPT05 (character uplo, integer n, integer nrhs, double
    precision, dimension( * ) ap, double precision, dimension( ldb, * ) b,
    integer ldb, double precision, dimension( ldx, * ) x, integer ldx,
    double precision, dimension( ldxact, * ) xact, integer ldxact, double
    precision, dimension( * ) ferr, double precision, dimension( * ) berr,
    double precision, dimension( * ) reslts)
    DPPT05

🎀 Purpose 🎀

okay so DPPT05 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. No cap, that’s the whole job. 🫶

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 — DOUBLE PRECISION 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 — DOUBLE PRECISION 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 — DOUBLE PRECISION 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 — DOUBLE PRECISION 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 — DOUBLE PRECISION 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 — DOUBLE PRECISION 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 — DOUBLE PRECISION 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 dppt05.f. 📌

Yep, that’s exactly where it’s defined: line 154 of file dppt05.f. 🔥

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

okay that’s the whole page, bestie — footer vibe check: LAPACK Version 3.12.0, source path /home/abui...IN/dppt05.f(3), and no separate date line is shown here, so I’m not inventing one. 💖