spbt05.f3

!>
!> SPBT05 tests the error bounds from iterative refinement for the
!> computed solution to a system of equations A*X = B, where A is a
!> symmetric band matrix.
!>
!> 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 / ( NZ*EPS + (*) ), where
!>             (*) = NZ*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
!>             and NZ = max. number of nonzeros in any row of A, plus 1
!> 

UPLO

!>          UPLO is CHARACTER*1
!>          Specifies whether the upper or lower triangular part of the
!>          symmetric matrix A is stored.
!>          = 'U':  Upper triangular
!>          = 'L':  Lower 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.
!> 

KD

!>          KD is INTEGER
!>          The number of super-diagonals of the matrix A if UPLO = 'U',
!>          or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.
!> 

NRHS

!>          NRHS is INTEGER
!>          The number of columns of the matrices X, B, and XACT.
!>          NRHS >= 0.
!> 

AB

!>          AB is REAL array, dimension (LDAB,N)
!>          The upper or lower triangle of the symmetric 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.
!> 

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).
!> 

X

!>          X is REAL 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 REAL 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 REAL 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 REAL 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 REAL array, dimension (2)
!>          The maximum over the NRHS solution vectors of the ratios:
!>          RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
!>          RESLTS(2) = BERR / ( NZ*EPS + (*) )
!> 

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.