# strrfs.f - Man Page

SRC/strrfs.f

## Synopsis

### Functions/Subroutines

subroutine strrfs (uplo, trans, diag, n, nrhs, a, lda, b, ldb, x, ldx, ferr, berr, work, iwork, info)
STRRFS

## Function/Subroutine Documentation

### subroutine strrfs (character uplo, character trans, character diag, integer n, integer nrhs, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real, dimension( ldx, * ) x, integer ldx, real, dimension( * ) ferr, real, dimension( * ) berr, real, dimension( * ) work, integer, dimension( * ) iwork, integer info)

STRRFS

Purpose:

``` STRRFS provides error bounds and backward error estimates for the
solution to a system of linear equations with a triangular
coefficient matrix.

The solution matrix X must be computed by STRTRS or some other
means before entering this routine.  STRRFS does not do iterative
refinement because doing so cannot improve the backward error.```
Parameters

UPLO

```          UPLO is CHARACTER*1
= 'U':  A is upper triangular;
= 'L':  A is lower triangular.```

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)```

DIAG

```          DIAG is CHARACTER*1
= 'N':  A is non-unit triangular;
= 'U':  A is unit triangular.```

N

```          N is INTEGER
The order of the matrix A.  N >= 0.```

NRHS

```          NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices B and X.  NRHS >= 0.```

A

```          A is REAL 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 REAL array, dimension (LDB,NRHS)
The right hand side matrix B.```

LDB

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

X

```          X is REAL array, dimension (LDX,NRHS)
The solution matrix X.```

LDX

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

FERR

```          FERR is REAL array, dimension (NRHS)
The estimated forward error bound for each solution vector
X(j) (the j-th column of the solution matrix X).
If XTRUE is the true solution corresponding to X(j), FERR(j)
is an estimated upper bound for the magnitude of the largest
element in (X(j) - XTRUE) divided by the magnitude of the
largest element in X(j).  The estimate is as reliable as
the estimate for RCOND, and is almost always a slight
overestimate of the true error.```

BERR

```          BERR is REAL array, dimension (NRHS)
The componentwise relative backward error of each solution
vector X(j) (i.e., the smallest relative change in
any element of A or B that makes X(j) an exact solution).```

WORK

`          WORK is REAL array, dimension (3*N)`

IWORK

`          IWORK is INTEGER array, dimension (N)`

INFO

```          INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 180 of file strrfs.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

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