Provided by: liblapack-doc_3.12.1-2_all 
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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Version 3.12.0 Tue Jan 28 2025 00:54:31 la_lin_berr(3)