TESTING/LIN/dgtt05.f(3)

🎀 TESTING/LIN/dgtt05.f 🎀

okay bestie, welcome to TESTING/LIN/dgtt05.f from the Library Functions Manual — section 3, no cap. This is the page for DGTT05, and it is fully giving LAPACK testing-routine energy. Let’s get into it 💅✨

✨ NAME ✨

TESTING/LIN/dgtt05.f

💅 SYNOPSIS 💅

Functions/Subroutines

• subroutine dgtt05 (trans, n, nrhs, dl, d, du, b, ldb, x, ldx, xact, ldxact, ferr, berr, reslts) — DGTT05

🦋 Function/Subroutine Documentation 🦋

subroutine dgtt05 (...)

   subroutine dgtt05 (character trans, integer n, integer nrhs, double
       precision, dimension( * ) dl, double precision, dimension( * ) d, double
       precision, dimension( * ) du, 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)
       DGTT05

The whole moment is called DGTT05, and it is literally here to test error bounds. 🫶

Purpose

DGTT05 tests the error bounds from iterative refinement for the computed solution to a system of equations A*X = B, where A is a general tridiagonal matrix of order n and op(A) = A or A**T, depending on TRANS.

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

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

A large value is returned if this ratio is not less than one. That’s the whole vibe check.

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

RESLTS(2) = the maximum of BERR / ( NZ*EPS + (*) ), where
          (*) = NZ*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )
          and NZ = max. number of nonzeros in any row of A, plus 1

🍓 Parameters 🍓

TRANS

TRANS is CHARACTER*1 — it specifies the form of the system of equations.

• 'N': A * X = B (No transpose)
• 'T': A**T * X = B (Transpose)
• 'C': A**H * X = B (Conjugate transpose = Transpose)

N

N is INTEGER — the number of rows of the matrices X and XACT. N >= 0.

NRHS

NRHS is INTEGER — the number of columns of the matrices X and XACT. NRHS >= 0.

DL

DL is DOUBLE PRECISION array, dimension (N-1) — the (n-1) sub-diagonal elements of A.

D

D is DOUBLE PRECISION array, dimension (N) — the diagonal elements of A.

DU

DU is DOUBLE PRECISION array, dimension (N-1) — the (n-1) super-diagonal elements of A.

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 163 of file dgtt05.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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