la_lin_berr(3)

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.

Definition at line 100 of file cla_lin_berr.f.

  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.

Definition at line 100 of file dla_lin_berr.f.

  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.

Definition at line 100 of file sla_lin_berr.f.

  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.

Definition at line 100 of file zla_lin_berr.f.

Author

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