Annotation of rpl/lapack/lapack/zla_lin_berr.f, revision 1.5
1.5 ! bertrand 1: *> \brief \b ZLA_LIN_BERR
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZLA_LIN_BERR + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zla_lin_berr.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zla_lin_berr.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zla_lin_berr.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZLA_LIN_BERR ( N, NZ, NRHS, RES, AYB, BERR )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * INTEGER N, NZ, NRHS
! 25: * ..
! 26: * .. Array Arguments ..
! 27: * DOUBLE PRECISION AYB( N, NRHS ), BERR( NRHS )
! 28: * COMPLEX*16 RES( N, NRHS )
! 29: * ..
! 30: *
! 31: *
! 32: *> \par Purpose:
! 33: * =============
! 34: *>
! 35: *> \verbatim
! 36: *>
! 37: *> ZLA_LIN_BERR computes componentwise relative backward error from
! 38: *> the formula
! 39: *> max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
! 40: *> where abs(Z) is the componentwise absolute value of the matrix
! 41: *> or vector Z.
! 42: *> \endverbatim
! 43: *
! 44: * Arguments:
! 45: * ==========
! 46: *
! 47: *> \param[in] N
! 48: *> \verbatim
! 49: *> N is INTEGER
! 50: *> The number of linear equations, i.e., the order of the
! 51: *> matrix A. N >= 0.
! 52: *> \endverbatim
! 53: *>
! 54: *> \param[in] NZ
! 55: *> \verbatim
! 56: *> NZ is INTEGER
! 57: *> We add (NZ+1)*SLAMCH( 'Safe minimum' ) to R(i) in the numerator to
! 58: *> guard against spuriously zero residuals. Default value is N.
! 59: *> \endverbatim
! 60: *>
! 61: *> \param[in] NRHS
! 62: *> \verbatim
! 63: *> NRHS is INTEGER
! 64: *> The number of right hand sides, i.e., the number of columns
! 65: *> of the matrices AYB, RES, and BERR. NRHS >= 0.
! 66: *> \endverbatim
! 67: *>
! 68: *> \param[in] RES
! 69: *> \verbatim
! 70: *> RES is DOUBLE PRECISION array, dimension (N,NRHS)
! 71: *> The residual matrix, i.e., the matrix R in the relative backward
! 72: *> error formula above.
! 73: *> \endverbatim
! 74: *>
! 75: *> \param[in] AYB
! 76: *> \verbatim
! 77: *> AYB is DOUBLE PRECISION array, dimension (N, NRHS)
! 78: *> The denominator in the relative backward error formula above, i.e.,
! 79: *> the matrix abs(op(A_s))*abs(Y) + abs(B_s). The matrices A, Y, and B
! 80: *> are from iterative refinement (see zla_gerfsx_extended.f).
! 81: *> \endverbatim
! 82: *>
! 83: *> \param[out] BERR
! 84: *> \verbatim
! 85: *> BERR is COMPLEX*16 array, dimension (NRHS)
! 86: *> The componentwise relative backward error from the formula above.
! 87: *> \endverbatim
! 88: *
! 89: * Authors:
! 90: * ========
! 91: *
! 92: *> \author Univ. of Tennessee
! 93: *> \author Univ. of California Berkeley
! 94: *> \author Univ. of Colorado Denver
! 95: *> \author NAG Ltd.
! 96: *
! 97: *> \date November 2011
! 98: *
! 99: *> \ingroup complex16OTHERcomputational
! 100: *
! 101: * =====================================================================
1.1 bertrand 102: SUBROUTINE ZLA_LIN_BERR ( N, NZ, NRHS, RES, AYB, BERR )
103: *
1.5 ! bertrand 104: * -- LAPACK computational routine (version 3.4.0) --
! 105: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 106: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 107: * November 2011
1.1 bertrand 108: *
109: * .. Scalar Arguments ..
110: INTEGER N, NZ, NRHS
111: * ..
112: * .. Array Arguments ..
113: DOUBLE PRECISION AYB( N, NRHS ), BERR( NRHS )
114: COMPLEX*16 RES( N, NRHS )
115: * ..
116: *
117: * =====================================================================
118: *
119: * .. Local Scalars ..
120: DOUBLE PRECISION TMP
121: INTEGER I, J
122: COMPLEX*16 CDUM
123: * ..
124: * .. Intrinsic Functions ..
125: INTRINSIC ABS, REAL, DIMAG, MAX
126: * ..
127: * .. External Functions ..
128: EXTERNAL DLAMCH
129: DOUBLE PRECISION DLAMCH
130: DOUBLE PRECISION SAFE1
131: * ..
132: * .. Statement Functions ..
133: COMPLEX*16 CABS1
134: * ..
135: * .. Statement Function Definitions ..
136: CABS1( CDUM ) = ABS( DBLE( CDUM ) ) + ABS( DIMAG( CDUM ) )
137: * ..
138: * .. Executable Statements ..
139: *
140: * Adding SAFE1 to the numerator guards against spuriously zero
141: * residuals. A similar safeguard is in the CLA_yyAMV routine used
142: * to compute AYB.
143: *
144: SAFE1 = DLAMCH( 'Safe minimum' )
145: SAFE1 = (NZ+1)*SAFE1
146:
147: DO J = 1, NRHS
148: BERR(J) = 0.0D+0
149: DO I = 1, N
150: IF (AYB(I,J) .NE. 0.0D+0) THEN
151: TMP = (SAFE1 + CABS1(RES(I,J)))/AYB(I,J)
152: BERR(J) = MAX( BERR(J), TMP )
153: END IF
154: *
155: * If AYB is exactly 0.0 (and if computed by CLA_yyAMV), then we know
156: * the true residual also must be exactly 0.0.
157: *
158: END DO
159: END DO
160: END
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