LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
cla_syrcond_x.f
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00001 *> \brief \b CLA_SYRCOND_X
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
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00009 *> Download CLA_SYRCOND_X + dependencies 
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00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       REAL FUNCTION CLA_SYRCOND_X( UPLO, N, A, LDA, AF, LDAF, IPIV, X,
00022 *                                    INFO, WORK, RWORK )
00023 * 
00024 *       .. Scalar Arguments ..
00025 *       CHARACTER          UPLO
00026 *       INTEGER            N, LDA, LDAF, INFO
00027 *       ..
00028 *       .. Array Arguments ..
00029 *       INTEGER            IPIV( * )
00030 *       COMPLEX            A( LDA, * ), AF( LDAF, * ), WORK( * ), X( * )
00031 *       REAL               RWORK( * )
00032 *       ..
00033 *  
00034 *
00035 *> \par Purpose:
00036 *  =============
00037 *>
00038 *> \verbatim
00039 *>
00040 *>    CLA_SYRCOND_X Computes the infinity norm condition number of
00041 *>    op(A) * diag(X) where X is a COMPLEX 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 block diagonal matrix D and the multipliers used to
00077 *>     obtain the factor U or L as computed by CSYTRF.
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] IPIV
00087 *> \verbatim
00088 *>          IPIV is INTEGER array, dimension (N)
00089 *>     Details of the interchanges and the block structure of D
00090 *>     as determined by CSYTRF.
00091 *> \endverbatim
00092 *>
00093 *> \param[in] X
00094 *> \verbatim
00095 *>          X is COMPLEX array, dimension (N)
00096 *>     The vector X in the formula op(A) * diag(X).
00097 *> \endverbatim
00098 *>
00099 *> \param[out] INFO
00100 *> \verbatim
00101 *>          INFO is INTEGER
00102 *>       = 0:  Successful exit.
00103 *>     i > 0:  The ith argument is invalid.
00104 *> \endverbatim
00105 *>
00106 *> \param[in] WORK
00107 *> \verbatim
00108 *>          WORK is COMPLEX array, dimension (2*N).
00109 *>     Workspace.
00110 *> \endverbatim
00111 *>
00112 *> \param[in] RWORK
00113 *> \verbatim
00114 *>          RWORK is REAL array, dimension (N).
00115 *>     Workspace.
00116 *> \endverbatim
00117 *
00118 *  Authors:
00119 *  ========
00120 *
00121 *> \author Univ. of Tennessee 
00122 *> \author Univ. of California Berkeley 
00123 *> \author Univ. of Colorado Denver 
00124 *> \author NAG Ltd. 
00125 *
00126 *> \date November 2011
00127 *
00128 *> \ingroup complexSYcomputational
00129 *
00130 *  =====================================================================
00131       REAL FUNCTION CLA_SYRCOND_X( UPLO, N, A, LDA, AF, LDAF, IPIV, X,
00132      $                             INFO, WORK, RWORK )
00133 *
00134 *  -- LAPACK computational routine (version 3.4.0) --
00135 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00136 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00137 *     November 2011
00138 *
00139 *     .. Scalar Arguments ..
00140       CHARACTER          UPLO
00141       INTEGER            N, LDA, LDAF, INFO
00142 *     ..
00143 *     .. Array Arguments ..
00144       INTEGER            IPIV( * )
00145       COMPLEX            A( LDA, * ), AF( LDAF, * ), WORK( * ), X( * )
00146       REAL               RWORK( * )
00147 *     ..
00148 *
00149 *  =====================================================================
00150 *
00151 *     .. Local Scalars ..
00152       INTEGER            KASE
00153       REAL               AINVNM, ANORM, TMP
00154       INTEGER            I, J
00155       LOGICAL            UP, UPPER
00156       COMPLEX            ZDUM
00157 *     ..
00158 *     .. Local Arrays ..
00159       INTEGER            ISAVE( 3 )
00160 *     ..
00161 *     .. External Functions ..
00162       LOGICAL            LSAME
00163       EXTERNAL           LSAME
00164 *     ..
00165 *     .. External Subroutines ..
00166       EXTERNAL           CLACN2, CSYTRS, XERBLA
00167 *     ..
00168 *     .. Intrinsic Functions ..
00169       INTRINSIC          ABS, MAX
00170 *     ..
00171 *     .. Statement Functions ..
00172       REAL               CABS1
00173 *     ..
00174 *     .. Statement Function Definitions ..
00175       CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) )
00176 *     ..
00177 *     .. Executable Statements ..
00178 *
00179       CLA_SYRCOND_X = 0.0E+0
00180 *
00181       INFO = 0
00182       UPPER = LSAME( UPLO, 'U' )
00183       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00184          INFO = -1
00185       ELSE IF ( N.LT.0 ) THEN
00186          INFO = -2
00187       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
00188          INFO = -4
00189       ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN
00190          INFO = -6
00191       END IF
00192       IF( INFO.NE.0 ) THEN
00193          CALL XERBLA( 'CLA_SYRCOND_X', -INFO )
00194          RETURN
00195       END IF
00196       UP = .FALSE.
00197       IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE.
00198 *
00199 *     Compute norm of op(A)*op2(C).
00200 *
00201       ANORM = 0.0
00202       IF ( UP ) THEN
00203          DO I = 1, N
00204             TMP = 0.0E+0
00205             DO J = 1, I
00206                TMP = TMP + CABS1( A( J, I ) * X( J ) )
00207             END DO
00208             DO J = I+1, N
00209                TMP = TMP + CABS1( A( I, J ) * X( J ) )
00210             END DO
00211             RWORK( I ) = TMP
00212             ANORM = MAX( ANORM, TMP )
00213          END DO
00214       ELSE
00215          DO I = 1, N
00216             TMP = 0.0E+0
00217             DO J = 1, I
00218                TMP = TMP + CABS1( A( I, J ) * X( J ) )
00219             END DO
00220             DO J = I+1, N
00221                TMP = TMP + CABS1( A( J, I ) * X( J ) )
00222             END DO
00223             RWORK( I ) = TMP
00224             ANORM = MAX( ANORM, TMP )
00225          END DO
00226       END IF
00227 *
00228 *     Quick return if possible.
00229 *
00230       IF( N.EQ.0 ) THEN
00231          CLA_SYRCOND_X = 1.0E+0
00232          RETURN
00233       ELSE IF( ANORM .EQ. 0.0E+0 ) THEN
00234          RETURN
00235       END IF
00236 *
00237 *     Estimate the norm of inv(op(A)).
00238 *
00239       AINVNM = 0.0E+0
00240 *
00241       KASE = 0
00242    10 CONTINUE
00243       CALL CLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
00244       IF( KASE.NE.0 ) THEN
00245          IF( KASE.EQ.2 ) THEN
00246 *
00247 *           Multiply by R.
00248 *
00249             DO I = 1, N
00250                WORK( I ) = WORK( I ) * RWORK( I )
00251             END DO
00252 *
00253             IF ( UP ) THEN
00254                CALL CSYTRS( 'U', N, 1, AF, LDAF, IPIV,
00255      $            WORK, N, INFO )
00256             ELSE
00257                CALL CSYTRS( 'L', N, 1, AF, LDAF, IPIV,
00258      $            WORK, N, INFO )
00259             ENDIF
00260 *
00261 *           Multiply by inv(X).
00262 *
00263             DO I = 1, N
00264                WORK( I ) = WORK( I ) / X( I )
00265             END DO
00266          ELSE
00267 *
00268 *           Multiply by inv(X**T).
00269 *
00270             DO I = 1, N
00271                WORK( I ) = WORK( I ) / X( I )
00272             END DO
00273 *
00274             IF ( UP ) THEN
00275                CALL CSYTRS( 'U', N, 1, AF, LDAF, IPIV,
00276      $            WORK, N, INFO )
00277             ELSE
00278                CALL CSYTRS( 'L', N, 1, AF, LDAF, IPIV,
00279      $            WORK, N, INFO )
00280             END IF
00281 *
00282 *           Multiply by R.
00283 *
00284             DO I = 1, N
00285                WORK( I ) = WORK( I ) * RWORK( I )
00286             END DO
00287          END IF
00288          GO TO 10
00289       END IF
00290 *
00291 *     Compute the estimate of the reciprocal condition number.
00292 *
00293       IF( AINVNM .NE. 0.0E+0 )
00294      $   CLA_SYRCOND_X = 1.0E+0 / AINVNM
00295 *
00296       RETURN
00297 *
00298       END
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