# strt03.f - Man Page

TESTING/LIN/strt03.f

## Synopsis

### Functions/Subroutines

subroutine strt03 (uplo, trans, diag, n, nrhs, a, lda, scale, cnorm, tscal, x, ldx, b, ldb, work, resid)
STRT03

## Function/Subroutine Documentation

### subroutine strt03 (character uplo, character trans, character diag, integer n, integer nrhs, real, dimension( lda, * ) a, integer lda, real scale, real, dimension( * ) cnorm, real tscal, real, dimension( ldx, * ) x, integer ldx, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) work, real resid)

STRT03

Purpose:

``` STRT03 computes the residual for the solution to a scaled triangular
system of equations A*x = s*b  or  A'*x = s*b.
Here A is a triangular matrix, A' is the transpose of A, s is a
scalar, and x and b are N by NRHS matrices.  The test ratio is the
maximum over the number of right hand sides of
norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
where op(A) denotes A or A' and EPS is the machine epsilon.```
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 operation applied to A.
= 'N':  A *x = s*b  (No transpose)
= 'T':  A'*x = s*b  (Transpose)
= 'C':  A'*x = s*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 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 X and B.  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).```

SCALE

```          SCALE is REAL
The scaling factor s used in solving the triangular system.```

CNORM

```          CNORM is REAL array, dimension (N)
The 1-norms of the columns of A, not counting the diagonal.```

TSCAL

```          TSCAL is REAL
The scaling factor used in computing the 1-norms in CNORM.
CNORM actually contains the column norms of TSCAL*A.```

X

```          X is REAL array, dimension (LDX,NRHS)
The computed solution vectors for the system of linear
equations.```

LDX

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

B

```          B is REAL 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).```

WORK

`          WORK is REAL array, dimension (N)`

RESID

```          RESID is REAL
The maximum over the number of right hand sides of
norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).```
Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 167 of file strt03.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page strt03(3) is an alias of strt03.f(3).

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