# ctrt05.f - Man Page

TESTING/LIN/ctrt05.f

## Synopsis

### Functions/Subroutines

subroutine ctrt05 (uplo, trans, diag, n, nrhs, a, lda, b, ldb, x, ldx, xact, ldxact, ferr, berr, reslts)
CTRT05

## Function/Subroutine Documentation

### subroutine ctrt05 (character uplo, character trans, character diag, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( ldx, * ) x, integer ldx, complex, dimension( ldxact, * ) xact, integer ldxact, real, dimension( * ) ferr, real, dimension( * ) berr, real, dimension( * ) reslts)

CTRT05

Purpose:

``` CTRT05 tests the error bounds from iterative refinement for the
computed solution to a system of equations A*X = B, where A is a
triangular n by n matrix.

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

```          UPLO is CHARACTER*1
Specifies whether the matrix A is upper or lower triangular.
= 'U':  Upper triangular
= 'L':  Lower triangular```

TRANS

```          TRANS is 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

```          DIAG is CHARACTER*1
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.```

NRHS

```          NRHS is INTEGER
The number of columns of the matrices X, B, and XACT.
NRHS >= 0.```

A

```          A is COMPLEX array, dimension (LDA,N)
The triangular matrix A.  If UPLO = 'U', the leading n by n
upper triangular part of the array A contains the upper
triangular matrix, and the strictly lower triangular part of
A is not referenced.  If UPLO = 'L', the leading n by n lower
triangular part of the array A contains the lower triangular
matrix, and the strictly upper triangular part of A is not
referenced.  If DIAG = 'U', the diagonal elements of A are
also not referenced and are assumed to be 1.```

LDA

```          LDA is INTEGER
The leading dimension of the array A.  LDA >= max(1,N).```

B

```          B is COMPLEX 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 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 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 REAL 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 REAL 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 REAL 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

NAG Ltd.

Definition at line 180 of file ctrt05.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page ctrt05(3) is an alias of ctrt05.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK