LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
cla_syrcond_c.f
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00001 *> \brief \b CLA_SYRCOND_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_SYRCOND_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_SYRCOND_C( UPLO, N, A, LDA, AF, LDAF, IPIV, C,
00022 *                                    CAPPLY, INFO, WORK, RWORK )
00023 * 
00024 *       .. Scalar Arguments ..
00025 *       CHARACTER          UPLO
00026 *       LOGICAL            CAPPLY
00027 *       INTEGER            N, LDA, LDAF, INFO
00028 *       ..
00029 *       .. Array Arguments ..
00030 *       INTEGER            IPIV( * )
00031 *       COMPLEX            A( LDA, * ), AF( LDAF, * ), WORK( * )
00032 *       REAL               C( * ), RWORK( * )
00033 *       ..
00034 *  
00035 *
00036 *> \par Purpose:
00037 *  =============
00038 *>
00039 *> \verbatim
00040 *>
00041 *>    CLA_SYRCOND_C Computes the infinity norm condition number of
00042 *>    op(A) * inv(diag(C)) where C is a REAL vector.
00043 *> \endverbatim
00044 *
00045 *  Arguments:
00046 *  ==========
00047 *
00048 *> \param[in] UPLO
00049 *> \verbatim
00050 *>          UPLO is CHARACTER*1
00051 *>       = 'U':  Upper triangle of A is stored;
00052 *>       = 'L':  Lower triangle of A is stored.
00053 *> \endverbatim
00054 *>
00055 *> \param[in] N
00056 *> \verbatim
00057 *>          N is INTEGER
00058 *>     The number of linear equations, i.e., the order of the
00059 *>     matrix A.  N >= 0.
00060 *> \endverbatim
00061 *>
00062 *> \param[in] A
00063 *> \verbatim
00064 *>          A is COMPLEX array, dimension (LDA,N)
00065 *>     On entry, the N-by-N matrix A
00066 *> \endverbatim
00067 *>
00068 *> \param[in] LDA
00069 *> \verbatim
00070 *>          LDA is INTEGER
00071 *>     The leading dimension of the array A.  LDA >= max(1,N).
00072 *> \endverbatim
00073 *>
00074 *> \param[in] AF
00075 *> \verbatim
00076 *>          AF is COMPLEX array, dimension (LDAF,N)
00077 *>     The block diagonal matrix D and the multipliers used to
00078 *>     obtain the factor U or L as computed by CSYTRF.
00079 *> \endverbatim
00080 *>
00081 *> \param[in] LDAF
00082 *> \verbatim
00083 *>          LDAF is INTEGER
00084 *>     The leading dimension of the array AF.  LDAF >= max(1,N).
00085 *> \endverbatim
00086 *>
00087 *> \param[in] IPIV
00088 *> \verbatim
00089 *>          IPIV is INTEGER array, dimension (N)
00090 *>     Details of the interchanges and the block structure of D
00091 *>     as determined by CSYTRF.
00092 *> \endverbatim
00093 *>
00094 *> \param[in] C
00095 *> \verbatim
00096 *>          C is REAL array, dimension (N)
00097 *>     The vector C in the formula op(A) * inv(diag(C)).
00098 *> \endverbatim
00099 *>
00100 *> \param[in] CAPPLY
00101 *> \verbatim
00102 *>          CAPPLY is LOGICAL
00103 *>     If .TRUE. then access the vector C in the formula above.
00104 *> \endverbatim
00105 *>
00106 *> \param[out] INFO
00107 *> \verbatim
00108 *>          INFO is INTEGER
00109 *>       = 0:  Successful exit.
00110 *>     i > 0:  The ith argument is invalid.
00111 *> \endverbatim
00112 *>
00113 *> \param[in] WORK
00114 *> \verbatim
00115 *>          WORK is COMPLEX array, dimension (2*N).
00116 *>     Workspace.
00117 *> \endverbatim
00118 *>
00119 *> \param[in] RWORK
00120 *> \verbatim
00121 *>          RWORK is REAL array, dimension (N).
00122 *>     Workspace.
00123 *> \endverbatim
00124 *
00125 *  Authors:
00126 *  ========
00127 *
00128 *> \author Univ. of Tennessee 
00129 *> \author Univ. of California Berkeley 
00130 *> \author Univ. of Colorado Denver 
00131 *> \author NAG Ltd. 
00132 *
00133 *> \date November 2011
00134 *
00135 *> \ingroup complexSYcomputational
00136 *
00137 *  =====================================================================
00138       REAL FUNCTION CLA_SYRCOND_C( UPLO, N, A, LDA, AF, LDAF, IPIV, C,
00139      $                             CAPPLY, INFO, WORK, RWORK )
00140 *
00141 *  -- LAPACK computational routine (version 3.4.0) --
00142 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00143 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00144 *     November 2011
00145 *
00146 *     .. Scalar Arguments ..
00147       CHARACTER          UPLO
00148       LOGICAL            CAPPLY
00149       INTEGER            N, LDA, LDAF, INFO
00150 *     ..
00151 *     .. Array Arguments ..
00152       INTEGER            IPIV( * )
00153       COMPLEX            A( LDA, * ), AF( LDAF, * ), WORK( * )
00154       REAL               C( * ), RWORK( * )
00155 *     ..
00156 *
00157 *  =====================================================================
00158 *
00159 *     .. Local Scalars ..
00160       INTEGER            KASE
00161       REAL               AINVNM, ANORM, TMP
00162       INTEGER            I, J
00163       LOGICAL            UP, UPPER
00164       COMPLEX            ZDUM
00165 *     ..
00166 *     .. Local Arrays ..
00167       INTEGER            ISAVE( 3 )
00168 *     ..
00169 *     .. External Functions ..
00170       LOGICAL            LSAME
00171       EXTERNAL           LSAME
00172 *     ..
00173 *     .. External Subroutines ..
00174       EXTERNAL           CLACN2, CSYTRS, XERBLA
00175 *     ..
00176 *     .. Intrinsic Functions ..
00177       INTRINSIC          ABS, MAX
00178 *     ..
00179 *     .. Statement Functions ..
00180       REAL CABS1
00181 *     ..
00182 *     .. Statement Function Definitions ..
00183       CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) )
00184 *     ..
00185 *     .. Executable Statements ..
00186 *
00187       CLA_SYRCOND_C = 0.0E+0
00188 *
00189       INFO = 0
00190       UPPER = LSAME( UPLO, 'U' )
00191       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00192          INFO = -1
00193       ELSE IF( N.LT.0 ) THEN
00194          INFO = -2
00195       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
00196          INFO = -4
00197       ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN
00198          INFO = -6
00199       END IF
00200       IF( INFO.NE.0 ) THEN
00201          CALL XERBLA( 'CLA_SYRCOND_C', -INFO )
00202          RETURN
00203       END IF
00204       UP = .FALSE.
00205       IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE.
00206 *
00207 *     Compute norm of op(A)*op2(C).
00208 *
00209       ANORM = 0.0E+0
00210       IF ( UP ) THEN
00211          DO I = 1, N
00212             TMP = 0.0E+0
00213             IF ( CAPPLY ) THEN
00214                DO J = 1, I
00215                   TMP = TMP + CABS1( A( J, I ) ) / C( J )
00216                END DO
00217                DO J = I+1, N
00218                   TMP = TMP + CABS1( A( I, J ) ) / C( J )
00219                END DO
00220             ELSE
00221                DO J = 1, I
00222                   TMP = TMP + CABS1( A( J, I ) )
00223                END DO
00224                DO J = I+1, N
00225                   TMP = TMP + CABS1( A( I, J ) )
00226                END DO
00227             END IF
00228             RWORK( I ) = TMP
00229             ANORM = MAX( ANORM, TMP )
00230          END DO
00231       ELSE
00232          DO I = 1, N
00233             TMP = 0.0E+0
00234             IF ( CAPPLY ) THEN
00235                DO J = 1, I
00236                   TMP = TMP + CABS1( A( I, J ) ) / C( J )
00237                END DO
00238                DO J = I+1, N
00239                   TMP = TMP + CABS1( A( J, I ) ) / C( J )
00240                END DO
00241             ELSE
00242                DO J = 1, I
00243                   TMP = TMP + CABS1( A( I, J ) )
00244                END DO
00245                DO J = I+1, N
00246                   TMP = TMP + CABS1( A( J, I ) )
00247                END DO
00248             END IF
00249             RWORK( I ) = TMP
00250             ANORM = MAX( ANORM, TMP )
00251          END DO
00252       END IF
00253 *
00254 *     Quick return if possible.
00255 *
00256       IF( N.EQ.0 ) THEN
00257          CLA_SYRCOND_C = 1.0E+0
00258          RETURN
00259       ELSE IF( ANORM .EQ. 0.0E+0 ) THEN
00260          RETURN
00261       END IF
00262 *
00263 *     Estimate the norm of inv(op(A)).
00264 *
00265       AINVNM = 0.0E+0
00266 *
00267       KASE = 0
00268    10 CONTINUE
00269       CALL CLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
00270       IF( KASE.NE.0 ) THEN
00271          IF( KASE.EQ.2 ) THEN
00272 *
00273 *           Multiply by R.
00274 *
00275             DO I = 1, N
00276                WORK( I ) = WORK( I ) * RWORK( I )
00277             END DO
00278 *
00279             IF ( UP ) THEN
00280                CALL CSYTRS( 'U', N, 1, AF, LDAF, IPIV,
00281      $            WORK, N, INFO )
00282             ELSE
00283                CALL CSYTRS( 'L', N, 1, AF, LDAF, IPIV,
00284      $            WORK, N, INFO )
00285             ENDIF
00286 *
00287 *           Multiply by inv(C).
00288 *
00289             IF ( CAPPLY ) THEN
00290                DO I = 1, N
00291                   WORK( I ) = WORK( I ) * C( I )
00292                END DO
00293             END IF
00294          ELSE
00295 *
00296 *           Multiply by inv(C**T).
00297 *
00298             IF ( CAPPLY ) THEN
00299                DO I = 1, N
00300                   WORK( I ) = WORK( I ) * C( I )
00301                END DO
00302             END IF
00303 *
00304             IF ( UP ) THEN
00305                CALL CSYTRS( 'U', N, 1, AF, LDAF, IPIV,
00306      $            WORK, N, INFO )
00307             ELSE
00308                CALL CSYTRS( 'L', N, 1, AF, LDAF, IPIV,
00309      $            WORK, N, INFO )
00310             END IF
00311 *
00312 *           Multiply by R.
00313 *
00314             DO I = 1, N
00315                WORK( I ) = WORK( I ) * RWORK( I )
00316             END DO
00317          END IF
00318          GO TO 10
00319       END IF
00320 *
00321 *     Compute the estimate of the reciprocal condition number.
00322 *
00323       IF( AINVNM .NE. 0.0E+0 )
00324      $   CLA_SYRCOND_C = 1.0E+0 / AINVNM
00325 *
00326       RETURN
00327 *
00328       END
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