 LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 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
 [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 REAL 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 sla_gerfsx_extended.f).``` [out] BERR ``` BERR is REAL array, dimension (NRHS) The componentwise relative backward error from the formula above.```
Date
September 2012

Definition at line 103 of file sla_lin_berr.f.

103 *
104 * -- LAPACK computational routine (version 3.4.2) --
105 * -- LAPACK is a software package provided by Univ. of Tennessee, --
106 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
107 * September 2012
108 *
109 * .. Scalar Arguments ..
110  INTEGER n, nz, nrhs
111 * ..
112 * .. Array Arguments ..
113  REAL ayb( n, nrhs ), berr( nrhs )
114  REAL res( n, nrhs )
115 * ..
116 *
117 * =====================================================================
118 *
119 * .. Local Scalars ..
120  REAL tmp
121  INTEGER i, j
122 * ..
123 * .. Intrinsic Functions ..
124  INTRINSIC abs, max
125 * ..
126 * .. External Functions ..
127  EXTERNAL slamch
128  REAL slamch
129  REAL safe1
130 * ..
131 * .. Executable Statements ..
132 *
133 * Adding SAFE1 to the numerator guards against spuriously zero
134 * residuals. A similar safeguard is in the SLA_yyAMV routine used
135 * to compute AYB.
136 *
137  safe1 = slamch( 'Safe minimum' )
138  safe1 = (nz+1)*safe1
139
140  DO j = 1, nrhs
141  berr(j) = 0.0
142  DO i = 1, n
143  IF (ayb(i,j) .NE. 0.0) THEN
144  tmp = (safe1+abs(res(i,j)))/ayb(i,j)
145  berr(j) = max( berr(j), tmp )
146  END IF
147 *
148 * If AYB is exactly 0.0 (and if computed by SLA_yyAMV), then we know
149 * the true residual also must be exactly 0.0.
150 *
151  END DO
152  END DO
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69

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