TESTING/LIN/cppt05.f(3)

🎀 TESTING/LIN/cppt05.f 🎀

okay bestie, welcome to the Library Functions Manual page for TESTING/LIN/cppt05.f — yes, the filename is the title, iconic. This is the LAPACK testing page for CPPT05, and we are keeping every single detail. No cap. 💅

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🌸 NAME 🌸

TESTING/LIN/cppt05.f

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✨ SYNOPSIS ✨

🧩 Functions/Subroutines

       subroutine cppt05 (uplo, n, nrhs, ap, b, ldb, x, ldx, xact, ldxact,
           ferr, berr, reslts)
           CPPT05

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🧚 Function/Subroutine Documentation 🧚

   subroutine cppt05 (character uplo, integer n, integer nrhs, complex,
       dimension( * ) ap, complex, dimension( ldb, * ) b, integer ldb, complex,
       dimension( ldx, * ) x, integer ldx, complex, dimension( ldxact, * )
       xact, integer ldxact, real, dimension( * ) ferr, real, dimension( * )
       berr, real, dimension( * ) reslts)
       CPPT05

🎯 Purpose

okay so CPPT05 tests the error bounds from iterative refinement for the computed solution to a system of equations A*X = B, where A is a Hermitian matrix in packed storage format. Slay. Here's the receipt:

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. Specifies whether the upper or lower triangular part of the Hermitian 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 COMPLEX array, dimension (N*(N+1)/2). The upper or lower triangle of the Hermitian 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 COMPLEX array, dimension (LDB,NRHS). The right hand side vectors for the system of linear equations.
• LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• X — X is COMPLEX 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 COMPLEX 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 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 — BERR is 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 — RESLTS is 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 155 of file cppt05.f.

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🌈 Author 🌈

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