TESTING/LIN/dtpt05.f(3)

💖 TESTING/LIN/dtpt05.f 💖

Okay bestie, quick vibe check: this page is TESTING/LIN/dtpt05.f(3) from the Library Functions Manual — manual name folded in near the top like a lil' bow 🎀. It's all about the DTPT05 subroutine, and no cap, it's giving “triangular matrix error-bound detective” energy.

🌸 NAME 🌸

TESTING/LIN/dtpt05.f

✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine dtpt05 (uplo, trans, diag, n, nrhs, ap, b, ldb, x, ldx, xact, ldxact, ferr, berr, reslts) — DTPT05

subroutine dtpt05 (uplo, trans, diag, n, nrhs, ap, b, ldb, x, ldx, xact,
    ldxact, ferr, berr, reslts)
    DTPT05

💅 Function/Subroutine Documentation 💅

subroutine dtpt05 (character uplo, character trans, character diag, integer
    n, integer nrhs, double precision, dimension( * ) ap, double precision,
    dimension( ldb, * ) b, integer ldb, double precision, dimension( ldx, *
    ) x, integer ldx, double precision, dimension( ldxact, * ) xact, integer
    ldxact, double precision, dimension( * ) ferr, double precision,
    dimension( * ) berr, double precision, dimension( * ) reslts)
    DTPT05

🎀 Purpose 🎀

DTPT05 tests the error bounds from iterative refinement for the computed solution to a system of equations A*X = B, where A is a triangular matrix in packed storage format. Iconic.

The result array RESLTS hits you with two tests:

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. So if that ratio comes back not less than one, expect a large value — that's the test being loud, not me.

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. Tells us whether the matrix A is upper or lower triangular.
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• TRANS — CHARACTER*1. Specifies the form of the system of equations.
  • = 'N': A * X = B (No transpose)
  • = 'T': A'* X = B (Transpose)
  • = 'C': A'* X = B (Conjugate transpose = Transpose)
• DIAG — CHARACTER*1. Says whether A is unit triangular or not.
  • = 'N': Non-unit triangular
  • = 'U': Unit 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 — DOUBLE PRECISION array, dimension (N*(N+1)/2). The upper or lower triangular 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.
  • If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1.
• B — DOUBLE PRECISION 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 — DOUBLE PRECISION 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 — DOUBLE PRECISION 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 172 of file dtpt05.f.

🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code.

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Okay, that's the whole page, bestie. The footer/source-version energy is: LAPACK Version 3.12.0 for TESTING/LIN/dtpt05.f(3). Date check: no date is printed in that footer, so I'm not inventing one — periodt. 💅✨