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la_lin_berr(3) LAPACK 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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