TESTING/LIN/dpot05.f(3)

💖 NAME 💖

TESTING/LIN/dpot05.f — okay so that's the whole NAME, bestie. And this page is TESTING/LIN/dpot05.f(3) from the Library Functions Manual. We are so in the right place, no cap. 💅

✨ SYNOPSIS ✨

   Functions/Subroutines
       subroutine dpot05 (uplo, n, nrhs, a, lda, b, ldb, x, ldx, xact, ldxact,
           ferr, berr, reslts)
           DPOT05

🦋 Function/Subroutine Documentation 🦋

Here's the full signature, copied exactly because we do not play with signatures—fr fr:

   subroutine dpot05 (character uplo, integer n, integer nrhs, double
       precision, dimension( lda, * ) a, integer lda, 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)
       DPOT05

DPOT05 is the subroutine, and it's giving "I test error bounds and I'm iconic about it." 🫶

🎀 Purpose 🎀

DPOT05 tests the error bounds from iterative refinement for the computed solution to a system of equations A*X = B, where A is a symmetric n by n matrix. ✨

• RESLTS(1) = test of the error bound = norm(X - XACT) / ( norm(X) * FERR )
• 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 )

A large value is returned if this ratio is not less than one. 👀

🌸 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.

A

A is DOUBLE PRECISION array, dimension (LDA,N). It's the symmetric matrix A.

• If UPLO = 'U', the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced.
• If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.

LDA

LDA is INTEGER. It's the leading dimension of the array A. LDA >= max(1,N).

B

B is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDXACT,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 DOUBLE PRECISION array, dimension (NRHS). It's 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). It's 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). It's 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 162 of file dpot05.f.

🧚 Author (Doxygen edition) 🧚

Generated automatically by Doxygen for LAPACK from the source code.

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💖 Cute sign-off: LAPACK Version 3.12.0 · TESTING/LIN/dpot05.f(3) — that's the source/version and page name from the footer, bestie. No extra date was listed, ngl. 💖