TESTING/LIN/cpot05.f(3)

💖 CPOT05 — TESTING/LIN/cpot05.f 💖

okay so this is the TESTING/LIN/cpot05.f(3) page from the Library Functions Manual, bestie. It's all about the cpot05 subroutine. no cap, she's an icon.

🌸 NAME 🌸

TESTING/LIN/cpot05.f

🦋 SYNOPSIS 🦋

🧚 Functions/Subroutines 🧚

subroutine cpot05 (uplo, n, nrhs, a, lda, b, ldb, x, ldx, xact, ldxact,
    ferr, berr, reslts)
    CPOT05

✨ Function/Subroutine Documentation ✨

💅 The signature, verbatim 💅

subroutine cpot05 (character uplo, integer n, integer nrhs, complex,
    dimension( lda, * ) a, integer lda, 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)
    CPOT05

💖 Purpose 💖

okay so CPOT05 tests the error bounds from iterative refinement for the computed solution to a system of equations A*X = B, where A is a Hermitian n by n matrix. literally her whole job.

The two result slots, exactly:

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 🎀

here's every parameter, no skipping, periodt:

• UPLO — CHARACTER*1. Specifies whether the upper or lower triangular part of the Hermitian 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.
• A — COMPLEX array, dimension (LDA,N). The Hermitian 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 — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• B — COMPLEX 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 — COMPLEX 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 — COMPLEX 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 163 of file cpot05.f.

👑 Author 👑

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