TESTING/LIN/dppt05.f(3)

💖 TESTING/LIN/dppt05.f 💖

okay so bestie, welcome to the TESTING/LIN/dppt05.f page from the Library Functions Manual. This is the LAPACK testing corner, and we're about to vibe-check one very specific subroutine. No cap.

🌸 NAME 🌸

TESTING/LIN/dppt05.f — that's the name, that's the whole name, and yes it's giving "file path as a name" energy. 💅

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

subroutine dppt05 (uplo, n, nrhs, ap, b, ldb, x, ldx, xact, ldxact,
    ferr, berr, reslts)

DPPT05 — the icon itself.

🦋 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 💖

DPPT05 is literally testing 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. Obsessed with the specificity.

The result formulas are exactly this, and we do not mess with them:

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 — says whether the upper or lower triangular part of the symmetric matrix A is stored.
• 'U': upper triangular.
• 'L': lower triangular.

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.

AP

• AP is 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

• B is DOUBLE PRECISION array, dimension (LDB,NRHS) — the right hand side vectors for the system of linear equations. Very "solve me" of it.

LDB

• LDB is INTEGER — the leading dimension of the array B. LDB >= max(1,N).

X

• X is DOUBLE PRECISION 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 DOUBLE PRECISION 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 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

• BERR is 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

• RESLTS is 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.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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mwah 💋 that's the whole page, bestie: LAPACK Version 3.12.0, page tag TESTING/LIN/dppt05.f(3). The original footer doesn't hand me a separate date line, so I'm not inventing one — keeping it 100. 🫶