LAPACK  3.10.1
LAPACK: Linear Algebra PACKage

◆ 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.

Download SLA_LIN_BERR + dependencies [TGZ] [ZIP] [TXT]

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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

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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