# zgtt05.f - Man Page

TESTING/LIN/zgtt05.f

## Synopsis

### Functions/Subroutines

subroutine zgtt05 (trans, n, nrhs, dl, d, du, b, ldb, x, ldx, xact, ldxact, ferr, berr, reslts)
ZGTT05

## Function/Subroutine Documentation

### subroutine zgtt05 (character trans, integer n, integer nrhs, complex*16, dimension( * ) dl, complex*16, dimension( * ) d, complex*16, dimension( * ) du, 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)

ZGTT05

Purpose:

``` ZGTT05 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) = 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(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
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 COMPLEX*16 array, dimension (N-1)
The (n-1) sub-diagonal elements of A.```

D

```          D is COMPLEX*16 array, dimension (N)
The diagonal elements of A.```

DU

```          DU is COMPLEX*16 array, dimension (N-1)
The (n-1) super-diagonal elements of A.```

B

```          B is COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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

NAG Ltd.

Definition at line 163 of file zgtt05.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zgtt05(3) is an alias of zgtt05.f(3).

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK