ZPPT05(3)

💅 NAME

okay so this is ZPPT05(3), the Library Functions Manual entry for ZPPT05, and the NAME section is literally just this path — no cap:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/zppt05.f

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✨ SYNOPSIS ✨

Functions/Subroutines

   subroutine ZPPT05 (uplo, n, nrhs, ap, b, ldb, x, ldx, xact, ldxact,
       ferr, berr, reslts)

ZPPT05

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🦋 Function/Subroutine Documentation

ZPPT05

   subroutine ZPPT05 (character uplo, integer n, integer nrhs, complex*16,
       dimension( * ) ap, 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)

ZPPT05

🎀 Purpose

bestie, ZPPT05 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. 💖

RESLTS(1) is the test of the error bound:

RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )

heads up: a large value is returned if this ratio is not less than one. 😭

RESLTS(2) is the residual from the iterative refinement routine:

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. '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. 🫶
• AP — COMPLEX*16 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 — 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 + (*) )

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👑 Author

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 155 of file zppt05.f.

👑 Author

Generated automatically by Doxygen for LAPACK from the source code.

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okay bye bestie! 💖 footer check: LAPACK Version 3.12.0, path /home/abui...IN/zppt05.f(3), and the date isn’t listed — but the vibe is timeless. 😭✨