TESTING/LIN/zpot05.f(3)

💖 NAME 💖

Hey bestie, welcome to TESTING/LIN/zpot05.f(3) from the Library Functions Manual — this page is about the Fortran testing routine zpot05, and it’s giving “I check error bounds” main character energy. ✨

🌸 SYNOPSIS 🌸

Functions/Subroutines

       subroutine zpot05 (uplo, n, nrhs, a, lda, b, ldb, x, ldx, xact, ldxact,
           ferr, berr, reslts)
           ZPOT05

🦋 Function/Subroutine Documentation 🦋

Here’s the full signature, bestie — every argument, exactly as it appears:

       subroutine zpot05 (character uplo, integer n, integer nrhs, complex*16,
           dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b,
           integer ldb, complex*16, dimension( ldx, * ) x, integer ldx, complex*16,
           dimension( ldxact, * ) xact, integer ldxact, double precision,
           dimension( * ) ferr, double precision, dimension( * ) berr, double
           precision, dimension( * ) reslts)
       ZPOT05

✨ Purpose ✨

ZPOT05 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.

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 Hermitian matrix A is stored. Values: '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*16 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*16 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*16 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*16 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 163 of file zpot05.f.

📝 Author (generated) 📝

Generated automatically by Doxygen for LAPACK from the source code.

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Okay bestie, cute little sign-off time 🫶: source/version is LAPACK Version 3.12.0, the page is TESTING/LIN/zpot05.f(3), and the footer doesn’t list a date, so I’m not inventing one — no cap, just vibes 💅✨