TESTING/LIN/stbt05.f(3)

NAME
TESTING/LIN/stbt05.f

SYNOPSIS

  Functions/Subroutines
subroutine stbt05 (uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, x, ldx, xact, ldxact, ferr, berr, reslts)
STBT05

Function/Subroutine Documentation

  subroutine stbt05 (character uplo, character trans, character diag, integer n, integer kd, integer nrhs, real, dimension( ldab, * ) ab, integer ldab, real, dimension( ldb, * ) b, integer ldb, real, dimension( ldx, * ) x, integer ldx, real, dimension( ldxact, * ) xact, integer ldxact, real, dimension( * ) ferr, real, dimension( * ) berr, real, dimension( * ) reslts)

STBT05

Purpose:

     STBT05 tests the error bounds from iterative refinement for the
     computed solution to a system of equations A*X = B, where A is a
     triangular 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 matrix A is upper or lower triangular.
              = 'U':  Upper triangular
              = 'L':  Lower triangular

    TRANS

              TRANS is CHARACTER*1
              Specifies the form of the system of equations.
              = '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 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 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).
              If DIAG = 'U', the diagonal elements of A are not referenced
              and are assumed to be 1.

    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 + (*) )

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 187 of file stbt05.f.

Author

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