TESTING/LIN/dtbt05.f(3)

✨ NAME ✨

Okay so this page is TESTING/LIN/dtbt05.f(3) from the Library Functions Manual, and the star of the show is TESTING/LIN/dtbt05.f — the Fortran test routine dtbt05. It has main character energy and it knows it. 💅

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🛰️ SYNOPSIS 🛰️

🧚 Functions/Subroutines

• subroutine dtbt05 (uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, x, ldx, xact, ldxact, ferr, berr, reslts) — DTBT05

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🧪 Function/Subroutine Documentation 🧪

subroutine dtbt05 (character uplo, character trans, character diag, integer
    n, integer kd, integer nrhs, double precision, dimension( ldab, * ) ab,
    integer ldab, 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)
    DTBT05

🎯 Purpose

Bestie, <rainbow>DTBT05</rainbow> tests the error bounds from iterative refinement for the computed solution to a system of equations A*X = B, where A is a triangular band matrix. That's the whole vibe.

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 / ( NZ*EPS + (*) ), where
            (*) = NZ*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
            and NZ = max. number of nonzeros in any row of A, plus 1

🧾 Parameters

• UPLO — UPLO is CHARACTER*1. It specifies whether the matrix A is upper or lower triangular:
  • 'U': Upper triangular
  • 'L': Lower triangular
• TRANS — TRANS is CHARACTER*1. It 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 — DIAG is CHARACTER*1. It specifies whether or not the matrix A is unit triangular:
  • 'N': Non-unit triangular
  • 'U': Unit triangular
• N — N is INTEGER. The number of rows of the matrices X, B, and XACT, and the order of the matrix A. N >= 0.
• KD — KD is INTEGER. The number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
• NRHS — NRHS is INTEGER. The number of columns of the matrices X, B, and XACT. NRHS >= 0.
• AB — AB is DOUBLE PRECISION array, dimension (LDAB,N). The upper or lower triangular band matrix A, stored in the first kd+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows:

if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).

If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1.

• LDAB — LDAB is INTEGER. The leading dimension of the array AB. LDAB >= KD+1.
• B — B is DOUBLE PRECISION array, dimension (LDB,NRHS). The right hand side vectors for the system of linear equations.
• LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• X — X is DOUBLE PRECISION array, dimension (LDX,NRHS). The computed solution vectors. Each vector is stored as a column of the matrix X.
• LDX — LDX is INTEGER. The leading dimension of the array X. LDX >= max(1,N).
• XACT — XACT is DOUBLE PRECISION array, dimension (LDX,NRHS). The exact solution vectors. Each vector is stored as a column of the matrix XACT.
• LDXACT — LDXACT is INTEGER. The leading dimension of the array XACT. LDXACT >= max(1,N).
• FERR — FERR is 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 — BERR is 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 — RESLTS is 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 / ( NZ*EPS + (*) )

👑 Author

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

Definition at line 187 of file dtbt05.f.

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👑 Author

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okay bye bestie! 💖 This page signs off with LAPACK, Version 3.12.0, and TESTING/LIN/dtbt05.f(3) from the footer — no separate date is shown there, so that's the whole source/version/date situation, periodt. 🌈