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.

  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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