LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
cla_porpvgrw.f
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00001 *> \brief \b CLA_PORPVGRW
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download CLA_PORPVGRW + dependencies 
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00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       REAL FUNCTION CLA_PORPVGRW( UPLO, NCOLS, A, LDA, AF, LDAF, WORK )
00022 * 
00023 *       .. Scalar Arguments ..
00024 *       CHARACTER*1        UPLO
00025 *       INTEGER            NCOLS, LDA, LDAF
00026 *       ..
00027 *       .. Array Arguments ..
00028 *       COMPLEX            A( LDA, * ), AF( LDAF, * )
00029 *       REAL               WORK( * )
00030 *       ..
00031 *  
00032 *
00033 *> \par Purpose:
00034 *  =============
00035 *>
00036 *> \verbatim
00037 *>
00038 *> 
00039 *> CLA_PORPVGRW computes the reciprocal pivot growth factor
00040 *> norm(A)/norm(U). The "max absolute element" norm is used. If this is
00041 *> much less than 1, the stability of the LU factorization of the
00042 *> (equilibrated) matrix A could be poor. This also means that the
00043 *> solution X, estimated condition numbers, and error bounds could be
00044 *> unreliable.
00045 *> \endverbatim
00046 *
00047 *  Arguments:
00048 *  ==========
00049 *
00050 *> \param[in] UPLO
00051 *> \verbatim
00052 *>          UPLO is CHARACTER*1
00053 *>       = 'U':  Upper triangle of A is stored;
00054 *>       = 'L':  Lower triangle of A is stored.
00055 *> \endverbatim
00056 *>
00057 *> \param[in] NCOLS
00058 *> \verbatim
00059 *>          NCOLS is INTEGER
00060 *>     The number of columns of the matrix A. NCOLS >= 0.
00061 *> \endverbatim
00062 *>
00063 *> \param[in] A
00064 *> \verbatim
00065 *>          A is COMPLEX array, dimension (LDA,N)
00066 *>     On entry, the N-by-N matrix A.
00067 *> \endverbatim
00068 *>
00069 *> \param[in] LDA
00070 *> \verbatim
00071 *>          LDA is INTEGER
00072 *>     The leading dimension of the array A.  LDA >= max(1,N).
00073 *> \endverbatim
00074 *>
00075 *> \param[in] AF
00076 *> \verbatim
00077 *>          AF is COMPLEX array, dimension (LDAF,N)
00078 *>     The triangular factor U or L from the Cholesky factorization
00079 *>     A = U**T*U or A = L*L**T, as computed by CPOTRF.
00080 *> \endverbatim
00081 *>
00082 *> \param[in] LDAF
00083 *> \verbatim
00084 *>          LDAF is INTEGER
00085 *>     The leading dimension of the array AF.  LDAF >= max(1,N).
00086 *> \endverbatim
00087 *>
00088 *> \param[in] WORK
00089 *> \verbatim
00090 *>          WORK is COMPLEX array, dimension (2*N)
00091 *> \endverbatim
00092 *
00093 *  Authors:
00094 *  ========
00095 *
00096 *> \author Univ. of Tennessee 
00097 *> \author Univ. of California Berkeley 
00098 *> \author Univ. of Colorado Denver 
00099 *> \author NAG Ltd. 
00100 *
00101 *> \date November 2011
00102 *
00103 *> \ingroup complexPOcomputational
00104 *
00105 *  =====================================================================
00106       REAL FUNCTION CLA_PORPVGRW( UPLO, NCOLS, A, LDA, AF, LDAF, WORK )
00107 *
00108 *  -- LAPACK computational routine (version 3.4.0) --
00109 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00110 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00111 *     November 2011
00112 *
00113 *     .. Scalar Arguments ..
00114       CHARACTER*1        UPLO
00115       INTEGER            NCOLS, LDA, LDAF
00116 *     ..
00117 *     .. Array Arguments ..
00118       COMPLEX            A( LDA, * ), AF( LDAF, * )
00119       REAL               WORK( * )
00120 *     ..
00121 *
00122 *  =====================================================================
00123 *
00124 *     .. Local Scalars ..
00125       INTEGER            I, J
00126       REAL               AMAX, UMAX, RPVGRW
00127       LOGICAL            UPPER
00128       COMPLEX            ZDUM
00129 *     ..
00130 *     .. External Functions ..
00131       EXTERNAL           LSAME, CLASET
00132       LOGICAL            LSAME
00133 *     ..
00134 *     .. Intrinsic Functions ..
00135       INTRINSIC          ABS, MAX, MIN, REAL, AIMAG
00136 *     ..
00137 *     .. Statement Functions ..
00138       REAL               CABS1
00139 *     ..
00140 *     .. Statement Function Definitions ..
00141       CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) )
00142 *     ..
00143 *     .. Executable Statements ..
00144       UPPER = LSAME( 'Upper', UPLO )
00145 *
00146 *     SPOTRF will have factored only the NCOLSxNCOLS leading minor, so
00147 *     we restrict the growth search to that minor and use only the first
00148 *     2*NCOLS workspace entries.
00149 *
00150       RPVGRW = 1.0
00151       DO I = 1, 2*NCOLS
00152          WORK( I ) = 0.0
00153       END DO
00154 *
00155 *     Find the max magnitude entry of each column.
00156 *
00157       IF ( UPPER ) THEN
00158          DO J = 1, NCOLS
00159             DO I = 1, J
00160                WORK( NCOLS+J ) =
00161      $              MAX( CABS1( A( I, J ) ), WORK( NCOLS+J ) )
00162             END DO
00163          END DO
00164       ELSE
00165          DO J = 1, NCOLS
00166             DO I = J, NCOLS
00167                WORK( NCOLS+J ) =
00168      $              MAX( CABS1( A( I, J ) ), WORK( NCOLS+J ) )
00169             END DO
00170          END DO
00171       END IF
00172 *
00173 *     Now find the max magnitude entry of each column of the factor in
00174 *     AF.  No pivoting, so no permutations.
00175 *
00176       IF ( LSAME( 'Upper', UPLO ) ) THEN
00177          DO J = 1, NCOLS
00178             DO I = 1, J
00179                WORK( J ) = MAX( CABS1( AF( I, J ) ), WORK( J ) )
00180             END DO
00181          END DO
00182       ELSE
00183          DO J = 1, NCOLS
00184             DO I = J, NCOLS
00185                WORK( J ) = MAX( CABS1( AF( I, J ) ), WORK( J ) )
00186             END DO
00187          END DO
00188       END IF
00189 *
00190 *     Compute the *inverse* of the max element growth factor.  Dividing
00191 *     by zero would imply the largest entry of the factor's column is
00192 *     zero.  Than can happen when either the column of A is zero or
00193 *     massive pivots made the factor underflow to zero.  Neither counts
00194 *     as growth in itself, so simply ignore terms with zero
00195 *     denominators.
00196 *
00197       IF ( LSAME( 'Upper', UPLO ) ) THEN
00198          DO I = 1, NCOLS
00199             UMAX = WORK( I )
00200             AMAX = WORK( NCOLS+I )
00201             IF ( UMAX /= 0.0 ) THEN
00202                RPVGRW = MIN( AMAX / UMAX, RPVGRW )
00203             END IF
00204          END DO
00205       ELSE
00206          DO I = 1, NCOLS
00207             UMAX = WORK( I )
00208             AMAX = WORK( NCOLS+I )
00209             IF ( UMAX /= 0.0 ) THEN
00210                RPVGRW = MIN( AMAX / UMAX, RPVGRW )
00211             END IF
00212          END DO
00213       END IF
00214 
00215       CLA_PORPVGRW = RPVGRW
00216       END
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