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Annotation of rpl/lapack/lapack/zla_lin_berr.f, revision 1.4

1.1       bertrand    1:       SUBROUTINE ZLA_LIN_BERR ( N, NZ, NRHS, RES, AYB, BERR )
                      2: *
                      3: *     -- LAPACK routine (version 3.2.2)                                 --
                      4: *     -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
                      5: *     -- Jason Riedy of Univ. of California Berkeley.                 --
                      6: *     -- June 2010                                                    --
                      7: *
                      8: *     -- LAPACK is a software package provided by Univ. of Tennessee, --
                      9: *     -- Univ. of California Berkeley and NAG Ltd.                    --
                     10: *
                     11:       IMPLICIT NONE
                     12: *     ..
                     13: *     .. Scalar Arguments ..
                     14:       INTEGER            N, NZ, NRHS
                     15: *     ..
                     16: *     .. Array Arguments ..
                     17:       DOUBLE PRECISION   AYB( N, NRHS ), BERR( NRHS )
                     18:       COMPLEX*16         RES( N, NRHS )
                     19: *     ..
                     20: *
                     21: *  Purpose
                     22: *  =======
                     23: *
                     24: *     ZLA_LIN_BERR computes componentwise relative backward error from
                     25: *     the formula
                     26: *         max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
                     27: *     where abs(Z) is the componentwise absolute value of the matrix
                     28: *     or vector Z.
                     29: *
                     30: *     N       (input) INTEGER
                     31: *     The number of linear equations, i.e., the order of the
                     32: *     matrix A.  N >= 0.
                     33: *
                     34: *     NZ      (input) INTEGER
                     35: *     We add (NZ+1)*SLAMCH( 'Safe minimum' ) to R(i) in the numerator to
                     36: *     guard against spuriously zero residuals. Default value is N.
                     37: *
                     38: *     NRHS    (input) INTEGER
                     39: *     The number of right hand sides, i.e., the number of columns
                     40: *     of the matrices AYB, RES, and BERR.  NRHS >= 0.
                     41: *
                     42: *     RES    (input) DOUBLE PRECISION array, dimension (N,NRHS)
                     43: *     The residual matrix, i.e., the matrix R in the relative backward
                     44: *     error formula above.
                     45: *
                     46: *     AYB    (input) DOUBLE PRECISION array, dimension (N, NRHS)
                     47: *     The denominator in the relative backward error formula above, i.e.,
                     48: *     the matrix abs(op(A_s))*abs(Y) + abs(B_s). The matrices A, Y, and B
                     49: *     are from iterative refinement (see zla_gerfsx_extended.f).
                     50: *     
                     51: *     BERR   (output) COMPLEX*16 array, dimension (NRHS)
                     52: *     The componentwise relative backward error from the formula above.
                     53: *
                     54: *  =====================================================================
                     55: *
                     56: *     .. Local Scalars ..
                     57:       DOUBLE PRECISION   TMP
                     58:       INTEGER            I, J
                     59:       COMPLEX*16         CDUM
                     60: *     ..
                     61: *     .. Intrinsic Functions ..
                     62:       INTRINSIC          ABS, REAL, DIMAG, MAX
                     63: *     ..
                     64: *     .. External Functions ..
                     65:       EXTERNAL           DLAMCH
                     66:       DOUBLE PRECISION   DLAMCH
                     67:       DOUBLE PRECISION   SAFE1
                     68: *     ..
                     69: *     .. Statement Functions ..
                     70:       COMPLEX*16         CABS1
                     71: *     ..
                     72: *     .. Statement Function Definitions ..
                     73:       CABS1( CDUM ) = ABS( DBLE( CDUM ) ) + ABS( DIMAG( CDUM ) )
                     74: *     ..
                     75: *     .. Executable Statements ..
                     76: *
                     77: *     Adding SAFE1 to the numerator guards against spuriously zero
                     78: *     residuals.  A similar safeguard is in the CLA_yyAMV routine used
                     79: *     to compute AYB.
                     80: *
                     81:       SAFE1 = DLAMCH( 'Safe minimum' )
                     82:       SAFE1 = (NZ+1)*SAFE1
                     83: 
                     84:       DO J = 1, NRHS
                     85:          BERR(J) = 0.0D+0
                     86:          DO I = 1, N
                     87:             IF (AYB(I,J) .NE. 0.0D+0) THEN
                     88:                TMP = (SAFE1 + CABS1(RES(I,J)))/AYB(I,J)
                     89:                BERR(J) = MAX( BERR(J), TMP )
                     90:             END IF
                     91: *
                     92: *     If AYB is exactly 0.0 (and if computed by CLA_yyAMV), then we know
                     93: *     the true residual also must be exactly 0.0.
                     94: *
                     95:          END DO
                     96:       END DO
                     97:       END