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la_lin_berr(3) Library Functions Manual 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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