LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ 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.```

Definition at line 100 of file cla_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 COMPLEX RES( N, NRHS )
112* ..
113*
114* =====================================================================
115*
116* .. Local Scalars ..
117 REAL TMP
118 INTEGER I, J
119 COMPLEX CDUM
120* ..
121* .. Intrinsic Functions ..
122 INTRINSIC abs, real, aimag, max
123* ..
124* .. External Functions ..
125 EXTERNAL slamch
126 REAL SLAMCH
127 REAL SAFE1
128* ..
129* .. Statement Functions ..
130 COMPLEX CABS1
131* ..
132* .. Statement Function Definitions ..
133 cabs1( cdum ) = abs( real( cdum ) ) + abs( aimag( cdum ) )
134* ..
135* .. Executable Statements ..
136*
137* Adding SAFE1 to the numerator guards against spuriously zero
138* residuals. A similar safeguard is in the CLA_yyAMV routine used
139* to compute AYB.
140*
141 safe1 = slamch( 'Safe minimum' )
142 safe1 = (nz+1)*safe1
143
144 DO j = 1, nrhs
145 berr(j) = 0.0
146 DO i = 1, n
147 IF (ayb(i,j) .NE. 0.0) THEN
148 tmp = (safe1 + cabs1(res(i,j)))/ayb(i,j)
149 berr(j) = max( berr(j), tmp )
150 END IF
151*
152* If AYB is exactly 0.0 (and if computed by CLA_yyAMV), then we know
153* the true residual also must be exactly 0.0.
154*
155 END DO
156 END DO
157*
158* End of CLA_LIN_BERR
159*
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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