TESTING/LIN/zppt05.f(3)

🎀 NAME 🎀

okay so welcome to the TESTING/LIN/zppt05.f(3) page from the Library Functions Manual, bestie — the actual file is TESTING/LIN/zppt05.f, and this whole page is about that icon. ✨

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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 🌸

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 🌺

okay so 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) = 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. 💅
  • = '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 + (*) )

⚠️ bestie, those dimension constraints are not a vibe to ignore — they're literally right there in the parameter list: N >= 0, NRHS >= 0, LDB >= max(1,N), LDX >= max(1,N), and LDXACT >= max(1,N). 💀

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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.

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🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code.

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