# ztpt05.f - Man Page

TESTING/LIN/ztpt05.f

## Synopsis

### Functions/Subroutines

subroutine ztpt05 (uplo, trans, diag, n, nrhs, ap, b, ldb, x, ldx, xact, ldxact, ferr, berr, reslts)
ZTPT05

## Function/Subroutine Documentation

### subroutine ztpt05 (character uplo, character trans, character diag, integer n, integer nrhs, complex*16, dimension( * ) ap, 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)

ZTPT05

Purpose:

``` ZTPT05 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.

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.```

AP

```          AP is COMPLEX*16 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

```          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 / ( (n+1)*EPS + (*) )```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 173 of file ztpt05.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page ztpt05(3) is an alias of ztpt05.f(3).

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