LAPACK  3.10.0
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.

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

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

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
Here is the call graph for this function:
Here is the caller graph for this function: