zpbt05.f - Man Page

subroutine zpbt05 (uplo, n, kd, nrhs, ab, ldab, b, ldb, x, ldx, xact, ldxact, ferr, berr, reslts)
ZPBT05

ZPBT05

Purpose:

 ZPBT05 tests the error bounds from iterative refinement for the
 computed solution to a system of equations A*X = B, where A is a
 Hermitian 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

Parameters

UPLO

          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          Hermitian 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 COMPLEX*16 array, dimension (LDAB,N)
          The upper or lower triangle of the Hermitian 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 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.

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 / ( NZ*EPS + (*) )

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 169 of file zpbt05.f.