LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ sla_lin_berr()

 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.```

Definition at line 100 of file sla_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 REAL AYB( N, NRHS ), BERR( NRHS )
111 REAL RES( N, NRHS )
112* ..
113*
114* =====================================================================
115*
116* .. Local Scalars ..
117 REAL TMP
118 INTEGER I, J
119* ..
120* .. Intrinsic Functions ..
121 INTRINSIC abs, max
122* ..
123* .. External Functions ..
124 EXTERNAL slamch
125 REAL SLAMCH
126 REAL 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 = slamch( 'Safe minimum' )
135 safe1 = (nz+1)*safe1
136
137 DO j = 1, nrhs
138 berr(j) = 0.0
139 DO i = 1, n
140 IF (ayb(i,j) .NE. 0.0) 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 SLA_LIN_BERR
152*
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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