zget07.f - Man Page

TESTING/LIN/zget07.f

Synopsis

Functions/Subroutines

subroutine zget07 (trans, n, nrhs, a, lda, b, ldb, x, ldx, xact, ldxact, ferr, chkferr, berr, reslts)
ZGET07

Function/Subroutine Documentation

subroutine zget07 (character trans, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, 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, logical chkferr, double precision, dimension( * ) berr, double precision, dimension( * ) reslts)

ZGET07

Purpose:

``` ZGET07 tests the error bounds from iterative refinement for the
computed solution to a system of equations op(A)*X = B, where A is a
general n by n matrix 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 / ( (n+1)*EPS + (*) ), where
(*) = (n+1)*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )```
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.```

A

```          A is COMPLEX*16 array, dimension (LDA,N)
The original n by n matrix A.```

LDA

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

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.```

CHKFERR

```          CHKFERR is LOGICAL
Set to .TRUE. to check FERR, .FALSE. not to check FERR.
When the test system is ill-conditioned, the 'true'
solution in XACT may be incorrect.```

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

Univ. of Colorado Denver

NAG Ltd.

Definition at line 164 of file zget07.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

The man page zget07(3) is an alias of zget07.f(3).

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