LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
cla_porcond_c.f
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00001 *> \brief \b CLA_PORCOND_C
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download CLA_PORCOND_C + dependencies 
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00011 *> [TGZ]</a> 
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00013 *> [ZIP]</a> 
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00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       REAL FUNCTION CLA_PORCOND_C( UPLO, N, A, LDA, AF, LDAF, C, CAPPLY,
00022 *                                    INFO, WORK, RWORK )
00023 * 
00024 *       .. Scalar Arguments ..
00025 *       CHARACTER          UPLO
00026 *       LOGICAL            CAPPLY
00027 *       INTEGER            N, LDA, LDAF, INFO
00028 *       ..
00029 *       .. Array Arguments ..
00030 *       COMPLEX            A( LDA, * ), AF( LDAF, * ), WORK( * )
00031 *       REAL               C( * ), RWORK( * )
00032 *       ..
00033 *  
00034 *
00035 *> \par Purpose:
00036 *  =============
00037 *>
00038 *> \verbatim
00039 *>
00040 *>    CLA_PORCOND_C Computes the infinity norm condition number of
00041 *>    op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector
00042 *> \endverbatim
00043 *
00044 *  Arguments:
00045 *  ==========
00046 *
00047 *> \param[in] UPLO
00048 *> \verbatim
00049 *>          UPLO is CHARACTER*1
00050 *>       = 'U':  Upper triangle of A is stored;
00051 *>       = 'L':  Lower triangle of A is stored.
00052 *> \endverbatim
00053 *>
00054 *> \param[in] N
00055 *> \verbatim
00056 *>          N is INTEGER
00057 *>     The number of linear equations, i.e., the order of the
00058 *>     matrix A.  N >= 0.
00059 *> \endverbatim
00060 *>
00061 *> \param[in] A
00062 *> \verbatim
00063 *>          A is COMPLEX array, dimension (LDA,N)
00064 *>     On entry, the N-by-N matrix A
00065 *> \endverbatim
00066 *>
00067 *> \param[in] LDA
00068 *> \verbatim
00069 *>          LDA is INTEGER
00070 *>     The leading dimension of the array A.  LDA >= max(1,N).
00071 *> \endverbatim
00072 *>
00073 *> \param[in] AF
00074 *> \verbatim
00075 *>          AF is COMPLEX array, dimension (LDAF,N)
00076 *>     The triangular factor U or L from the Cholesky factorization
00077 *>     A = U**H*U or A = L*L**H, as computed by CPOTRF.
00078 *> \endverbatim
00079 *>
00080 *> \param[in] LDAF
00081 *> \verbatim
00082 *>          LDAF is INTEGER
00083 *>     The leading dimension of the array AF.  LDAF >= max(1,N).
00084 *> \endverbatim
00085 *>
00086 *> \param[in] C
00087 *> \verbatim
00088 *>          C is REAL array, dimension (N)
00089 *>     The vector C in the formula op(A) * inv(diag(C)).
00090 *> \endverbatim
00091 *>
00092 *> \param[in] CAPPLY
00093 *> \verbatim
00094 *>          CAPPLY is LOGICAL
00095 *>     If .TRUE. then access the vector C in the formula above.
00096 *> \endverbatim
00097 *>
00098 *> \param[out] INFO
00099 *> \verbatim
00100 *>          INFO is INTEGER
00101 *>       = 0:  Successful exit.
00102 *>     i > 0:  The ith argument is invalid.
00103 *> \endverbatim
00104 *>
00105 *> \param[in] WORK
00106 *> \verbatim
00107 *>          WORK is COMPLEX array, dimension (2*N).
00108 *>     Workspace.
00109 *> \endverbatim
00110 *>
00111 *> \param[in] RWORK
00112 *> \verbatim
00113 *>          RWORK is REAL array, dimension (N).
00114 *>     Workspace.
00115 *> \endverbatim
00116 *
00117 *  Authors:
00118 *  ========
00119 *
00120 *> \author Univ. of Tennessee 
00121 *> \author Univ. of California Berkeley 
00122 *> \author Univ. of Colorado Denver 
00123 *> \author NAG Ltd. 
00124 *
00125 *> \date November 2011
00126 *
00127 *> \ingroup complexPOcomputational
00128 *
00129 *  =====================================================================
00130       REAL FUNCTION CLA_PORCOND_C( UPLO, N, A, LDA, AF, LDAF, C, CAPPLY,
00131      $                             INFO, WORK, RWORK )
00132 *
00133 *  -- LAPACK computational routine (version 3.4.0) --
00134 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00135 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00136 *     November 2011
00137 *
00138 *     .. Scalar Arguments ..
00139       CHARACTER          UPLO
00140       LOGICAL            CAPPLY
00141       INTEGER            N, LDA, LDAF, INFO
00142 *     ..
00143 *     .. Array Arguments ..
00144       COMPLEX            A( LDA, * ), AF( LDAF, * ), WORK( * )
00145       REAL               C( * ), RWORK( * )
00146 *     ..
00147 *
00148 *  =====================================================================
00149 *
00150 *     .. Local Scalars ..
00151       INTEGER            KASE
00152       REAL               AINVNM, ANORM, TMP
00153       INTEGER            I, J
00154       LOGICAL            UP, UPPER
00155       COMPLEX            ZDUM
00156 *     ..
00157 *     .. Local Arrays ..
00158       INTEGER            ISAVE( 3 )
00159 *     ..
00160 *     .. External Functions ..
00161       LOGICAL            LSAME
00162       EXTERNAL           LSAME
00163 *     ..
00164 *     .. External Subroutines ..
00165       EXTERNAL           CLACN2, CPOTRS, XERBLA
00166 *     ..
00167 *     .. Intrinsic Functions ..
00168       INTRINSIC          ABS, MAX, REAL, AIMAG
00169 *     ..
00170 *     .. Statement Functions ..
00171       REAL CABS1
00172 *     ..
00173 *     .. Statement Function Definitions ..
00174       CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) )
00175 *     ..
00176 *     .. Executable Statements ..
00177 *
00178       CLA_PORCOND_C = 0.0E+0
00179 *
00180       INFO = 0
00181       UPPER = LSAME( UPLO, 'U' )
00182       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00183          INFO = -1
00184       ELSE IF( N.LT.0 ) THEN
00185          INFO = -2
00186       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
00187          INFO = -4
00188       ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN
00189          INFO = -6
00190       END IF
00191       IF( INFO.NE.0 ) THEN
00192          CALL XERBLA( 'CLA_PORCOND_C', -INFO )
00193          RETURN
00194       END IF
00195       UP = .FALSE.
00196       IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE.
00197 *
00198 *     Compute norm of op(A)*op2(C).
00199 *
00200       ANORM = 0.0E+0
00201       IF ( UP ) THEN
00202          DO I = 1, N
00203             TMP = 0.0E+0
00204             IF ( CAPPLY ) THEN
00205                DO J = 1, I
00206                   TMP = TMP + CABS1( A( J, I ) ) / C( J )
00207                END DO
00208                DO J = I+1, N
00209                   TMP = TMP + CABS1( A( I, J ) ) / C( J )
00210                END DO
00211             ELSE
00212                DO J = 1, I
00213                   TMP = TMP + CABS1( A( J, I ) )
00214                END DO
00215                DO J = I+1, N
00216                   TMP = TMP + CABS1( A( I, J ) )
00217                END DO
00218             END IF
00219             RWORK( I ) = TMP
00220             ANORM = MAX( ANORM, TMP )
00221          END DO
00222       ELSE
00223          DO I = 1, N
00224             TMP = 0.0E+0
00225             IF ( CAPPLY ) THEN
00226                DO J = 1, I
00227                   TMP = TMP + CABS1( A( I, J ) ) / C( J )
00228                END DO
00229                DO J = I+1, N
00230                   TMP = TMP + CABS1( A( J, I ) ) / C( J )
00231                END DO
00232             ELSE
00233                DO J = 1, I
00234                   TMP = TMP + CABS1( A( I, J ) )
00235                END DO
00236                DO J = I+1, N
00237                   TMP = TMP + CABS1( A( J, I ) )
00238                END DO
00239             END IF
00240             RWORK( I ) = TMP
00241             ANORM = MAX( ANORM, TMP )
00242          END DO
00243       END IF
00244 *
00245 *     Quick return if possible.
00246 *
00247       IF( N.EQ.0 ) THEN
00248          CLA_PORCOND_C = 1.0E+0
00249          RETURN
00250       ELSE IF( ANORM .EQ. 0.0E+0 ) THEN
00251          RETURN
00252       END IF
00253 *
00254 *     Estimate the norm of inv(op(A)).
00255 *
00256       AINVNM = 0.0E+0
00257 *
00258       KASE = 0
00259    10 CONTINUE
00260       CALL CLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
00261       IF( KASE.NE.0 ) THEN
00262          IF( KASE.EQ.2 ) THEN
00263 *
00264 *           Multiply by R.
00265 *
00266             DO I = 1, N
00267                WORK( I ) = WORK( I ) * RWORK( I )
00268             END DO
00269 *
00270             IF ( UP ) THEN
00271                CALL CPOTRS( 'U', N, 1, AF, LDAF,
00272      $            WORK, N, INFO )
00273             ELSE
00274                CALL CPOTRS( 'L', N, 1, AF, LDAF,
00275      $            WORK, N, INFO )
00276             ENDIF
00277 *
00278 *           Multiply by inv(C).
00279 *
00280             IF ( CAPPLY ) THEN
00281                DO I = 1, N
00282                   WORK( I ) = WORK( I ) * C( I )
00283                END DO
00284             END IF
00285          ELSE
00286 *
00287 *           Multiply by inv(C**H).
00288 *
00289             IF ( CAPPLY ) THEN
00290                DO I = 1, N
00291                   WORK( I ) = WORK( I ) * C( I )
00292                END DO
00293             END IF
00294 *
00295             IF ( UP ) THEN
00296                CALL CPOTRS( 'U', N, 1, AF, LDAF,
00297      $            WORK, N, INFO )
00298             ELSE
00299                CALL CPOTRS( 'L', N, 1, AF, LDAF,
00300      $            WORK, N, INFO )
00301             END IF
00302 *
00303 *           Multiply by R.
00304 *
00305             DO I = 1, N
00306                WORK( I ) = WORK( I ) * RWORK( I )
00307             END DO
00308          END IF
00309          GO TO 10
00310       END IF
00311 *
00312 *     Compute the estimate of the reciprocal condition number.
00313 *
00314       IF( AINVNM .NE. 0.0E+0 )
00315      $   CLA_PORCOND_C = 1.0E+0 / AINVNM
00316 *
00317       RETURN
00318 *
00319       END
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