NAME

       la_lin_berr - la_lin_berr: backward error

SYNOPSIS

   Functions
       subroutine cla_lin_berr (n, nz, nrhs, res, ayb, berr)
           CLA_LIN_BERR computes a component-wise relative backward error.
       subroutine dla_lin_berr (n, nz, nrhs, res, ayb, berr)
           DLA_LIN_BERR computes a component-wise relative backward error.
       subroutine sla_lin_berr (n, nz, nrhs, res, ayb, berr)
           SLA_LIN_BERR computes a component-wise relative backward error.
       subroutine zla_lin_berr (n, nz, nrhs, res, ayb, berr)
           ZLA_LIN_BERR computes a component-wise relative backward error.

Detailed Description

Function Documentation

   subroutine cla_lin_berr (integer n, integer nz, integer nrhs, complex, dimension( n, nrhs )
       res, real, dimension( n, nrhs ) ayb, real, dimension( nrhs ) berr)
       CLA_LIN_BERR computes a component-wise relative backward error.

       Purpose:

               CLA_LIN_BERR computes componentwise relative backward error from
               the formula
                   max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
               where abs(Z) is the componentwise absolute value of the matrix
               or vector Z.

       Parameters
           N

                     N is INTEGER
                The number of linear equations, i.e., the order of the
                matrix A.  N >= 0.

           NZ

                     NZ is INTEGER
                We add (NZ+1)*SLAMCH( 'Safe minimum' ) to R(i) in the numerator to
                guard against spuriously zero residuals. Default value is N.

           NRHS

                     NRHS is INTEGER
                The number of right hand sides, i.e., the number of columns
                of the matrices AYB, RES, and BERR.  NRHS >= 0.

           RES

                     RES is COMPLEX array, dimension (N,NRHS)
                The residual matrix, i.e., the matrix R in the relative backward
                error formula above.

           AYB

                     AYB is REAL array, dimension (N, NRHS)
                The denominator in the relative backward error formula above, i.e.,
                the matrix abs(op(A_s))*abs(Y) + abs(B_s). The matrices A, Y, and B
                are from iterative refinement (see cla_gerfsx_extended.f).

           BERR

                     BERR is REAL array, dimension (NRHS)
                The componentwise relative backward error from the formula above.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

   subroutine dla_lin_berr (integer n, integer nz, integer nrhs, double precision, dimension( n,
       nrhs ) res, double precision, dimension( n, nrhs ) ayb, double precision, dimension( nrhs
       ) berr)
       DLA_LIN_BERR computes a component-wise relative backward error.

       Purpose:

               DLA_LIN_BERR computes component-wise relative backward error from
               the formula
                   max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
               where abs(Z) is the component-wise absolute value of the matrix
               or vector Z.

       Parameters
           N

                     N is INTEGER
                The number of linear equations, i.e., the order of the
                matrix A.  N >= 0.

           NZ

                     NZ is INTEGER
                We add (NZ+1)*SLAMCH( 'Safe minimum' ) to R(i) in the numerator to
                guard against spuriously zero residuals. Default value is N.

           NRHS

                     NRHS is INTEGER
                The number of right hand sides, i.e., the number of columns
                of the matrices AYB, RES, and BERR.  NRHS >= 0.

           RES

                     RES is DOUBLE PRECISION array, dimension (N,NRHS)
                The residual matrix, i.e., the matrix R in the relative backward
                error formula above.

           AYB

                     AYB is DOUBLE PRECISION array, dimension (N, NRHS)
                The denominator in the relative backward error formula above, i.e.,
                the matrix abs(op(A_s))*abs(Y) + abs(B_s). The matrices A, Y, and B
                are from iterative refinement (see dla_gerfsx_extended.f).

           BERR

                     BERR is DOUBLE PRECISION array, dimension (NRHS)
                The component-wise relative backward error from the formula above.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

   subroutine sla_lin_berr (integer n, integer nz, integer nrhs, real, dimension( n, nrhs ) res,
       real, dimension( n, nrhs ) ayb, real, dimension( nrhs ) berr)
       SLA_LIN_BERR computes a component-wise relative backward error.

       Purpose:

               SLA_LIN_BERR computes componentwise relative backward error from
               the formula
                   max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
               where abs(Z) is the componentwise absolute value of the matrix
               or vector Z.

       Parameters
           N

                     N is INTEGER
                The number of linear equations, i.e., the order of the
                matrix A.  N >= 0.

           NZ

                     NZ is INTEGER
                We add (NZ+1)*SLAMCH( 'Safe minimum' ) to R(i) in the numerator to
                guard against spuriously zero residuals. Default value is N.

           NRHS

                     NRHS is INTEGER
                The number of right hand sides, i.e., the number of columns
                of the matrices AYB, RES, and BERR.  NRHS >= 0.

           RES

                     RES is REAL array, dimension (N,NRHS)
                The residual matrix, i.e., the matrix R in the relative backward
                error formula above.

           AYB

                     AYB is REAL array, dimension (N, NRHS)
                The denominator in the relative backward error formula above, i.e.,
                the matrix abs(op(A_s))*abs(Y) + abs(B_s). The matrices A, Y, and B
                are from iterative refinement (see sla_gerfsx_extended.f).

           BERR

                     BERR is REAL array, dimension (NRHS)
                The componentwise relative backward error from the formula above.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

   subroutine zla_lin_berr (integer n, integer nz, integer nrhs, complex*16, dimension( n, nrhs )
       res, double precision, dimension( n, nrhs ) ayb, double precision, dimension( nrhs ) berr)
       ZLA_LIN_BERR computes a component-wise relative backward error.

       Purpose:

               ZLA_LIN_BERR computes componentwise relative backward error from
               the formula
                   max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
               where abs(Z) is the componentwise absolute value of the matrix
               or vector Z.

       Parameters
           N

                     N is INTEGER
                The number of linear equations, i.e., the order of the
                matrix A.  N >= 0.

           NZ

                     NZ is INTEGER
                We add (NZ+1)*SLAMCH( 'Safe minimum' ) to R(i) in the numerator to
                guard against spuriously zero residuals. Default value is N.

           NRHS

                     NRHS is INTEGER
                The number of right hand sides, i.e., the number of columns
                of the matrices AYB, RES, and BERR.  NRHS >= 0.

           RES

                     RES is COMPLEX*16 array, dimension (N,NRHS)
                The residual matrix, i.e., the matrix R in the relative backward
                error formula above.

           AYB

                     AYB is DOUBLE PRECISION array, dimension (N, NRHS)
                The denominator in the relative backward error formula above, i.e.,
                the matrix abs(op(A_s))*abs(Y) + abs(B_s). The matrices A, Y, and B
                are from iterative refinement (see zla_gerfsx_extended.f).

           BERR

                     BERR is DOUBLE PRECISION array, dimension (NRHS)
                The componentwise relative backward error from the formula above.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

Author

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