# stbt03.f - Man Page

TESTING/LIN/stbt03.f

## Synopsis

### Functions/Subroutines

subroutine stbt03 (uplo, trans, diag, n, kd, nrhs, ab, ldab, scale, cnorm, tscal, x, ldx, b, ldb, work, resid)
STBT03

## Function/Subroutine Documentation

### subroutine stbt03 (character uplo, character trans, character diag, integer n, integer kd, integer nrhs, real, dimension( ldab, * ) ab, integer ldab, real scale, real, dimension( * ) cnorm, real tscal, real, dimension( ldx, * ) x, integer ldx, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) work, real resid)

STBT03

Purpose:

``` STBT03 computes the residual for the solution to a scaled triangular
system of equations  A*x = s*b  or  A'*x = s*b  when A is a
triangular band matrix. Here 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 = 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 order of the matrix A.  N >= 0.```

KD

```          KD is INTEGER
The number of superdiagonals or subdiagonals of the
triangular band matrix A.  KD >= 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.```

AB

```          AB is REAL array, dimension (LDAB,N)
The upper or lower triangular band matrix A, stored in the
first kd+1 rows of the array. The j-th column of A is stored
in the j-th column of the array AB as follows:
if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).```

LDAB

```          LDAB is INTEGER
The leading dimension of the array AB.  LDAB >= KD+1.```

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

NAG Ltd.

Definition at line 172 of file stbt03.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page stbt03(3) is an alias of stbt03.f(3).

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