LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ cla_lin_berr()

 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
 [in] N ``` N is INTEGER The number of linear equations, i.e., the order of the matrix A. N >= 0.``` [in] 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.``` [in] 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.``` [in] RES ``` RES is COMPLEX array, dimension (N,NRHS) The residual matrix, i.e., the matrix R in the relative backward error formula above.``` [in] 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).``` [out] BERR ``` BERR is REAL array, dimension (NRHS) The componentwise relative backward error from the formula above.```
Date
June 2016

Definition at line 103 of file cla_lin_berr.f.

103 *
104 * -- LAPACK computational routine (version 3.7.0) --
105 * -- LAPACK is a software package provided by Univ. of Tennessee, --
106 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
107 * June 2016
108 *
109 * .. Scalar Arguments ..
110  INTEGER n, nz, nrhs
111 * ..
112 * .. Array Arguments ..
113  REAL ayb( n, nrhs ), berr( nrhs )
114  COMPLEX res( n, nrhs )
115 * ..
116 *
117 * =====================================================================
118 *
119 * .. Local Scalars ..
120  REAL tmp
121  INTEGER i, j
122  COMPLEX cdum
123 * ..
124 * .. Intrinsic Functions ..
125  INTRINSIC abs, REAL, aimag, max
126 * ..
127 * .. External Functions ..
128  EXTERNAL slamch
129  REAL slamch
130  REAL safe1
131 * ..
132 * .. Statement Functions ..
133  COMPLEX cabs1
134 * ..
135 * .. Statement Function Definitions ..
136  cabs1( cdum ) = abs( REAL( CDUM ) ) + abs( aimag( cdum ) )
137 * ..
138 * .. Executable Statements ..
139 *
140 * Adding SAFE1 to the numerator guards against spuriously zero
141 * residuals. A similar safeguard is in the CLA_yyAMV routine used
142 * to compute AYB.
143 *
144  safe1 = slamch( 'Safe minimum' )
145  safe1 = (nz+1)*safe1
146
147  DO j = 1, nrhs
148  berr(j) = 0.0
149  DO i = 1, n
150  IF (ayb(i,j) .NE. 0.0) THEN
151  tmp = (safe1 + cabs1(res(i,j)))/ayb(i,j)
152  berr(j) = max( berr(j), tmp )
153  END IF
154 *
155 * If AYB is exactly 0.0 (and if computed by CLA_yyAMV), then we know
156 * the true residual also must be exactly 0.0.
157 *
158  END DO
159  END DO
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
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