 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ dla_lin_berr()

 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.

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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
 [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 DOUBLE PRECISION array, dimension (N,NRHS) The residual matrix, i.e., the matrix R in the relative backward error formula above.``` [in] 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).``` [out] BERR ``` BERR is DOUBLE PRECISION array, dimension (NRHS) The component-wise relative backward error from the formula above.```

Definition at line 100 of file dla_lin_berr.f.

101 *
102 * -- LAPACK computational routine --
103 * -- LAPACK is a software package provided by Univ. of Tennessee, --
104 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
105 *
106 * .. Scalar Arguments ..
107  INTEGER N, NZ, NRHS
108 * ..
109 * .. Array Arguments ..
110  DOUBLE PRECISION AYB( N, NRHS ), BERR( NRHS )
111  DOUBLE PRECISION RES( N, NRHS )
112 * ..
113 *
114 * =====================================================================
115 *
116 * .. Local Scalars ..
117  DOUBLE PRECISION TMP
118  INTEGER I, J
119 * ..
120 * .. Intrinsic Functions ..
121  INTRINSIC abs, max
122 * ..
123 * .. External Functions ..
124  EXTERNAL dlamch
125  DOUBLE PRECISION DLAMCH
126  DOUBLE PRECISION SAFE1
127 * ..
128 * .. Executable Statements ..
129 *
130 * Adding SAFE1 to the numerator guards against spuriously zero
131 * residuals. A similar safeguard is in the SLA_yyAMV routine used
132 * to compute AYB.
133 *
134  safe1 = dlamch( 'Safe minimum' )
135  safe1 = (nz+1)*safe1
136
137  DO j = 1, nrhs
138  berr(j) = 0.0d+0
139  DO i = 1, n
140  IF (ayb(i,j) .NE. 0.0d+0) THEN
141  tmp = (safe1+abs(res(i,j)))/ayb(i,j)
142  berr(j) = max( berr(j), tmp )
143  END IF
144 *
145 * If AYB is exactly 0.0 (and if computed by SLA_yyAMV), then we know
146 * the true residual also must be exactly 0.0.
147 *
148  END DO
149  END DO
150 *
151 * End of DLA_LIN_BERR
152 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
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