LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
csycon.f
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00001 *> \brief \b CSYCON
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download CSYCON + 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 *       SUBROUTINE CSYCON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
00022 *                          INFO )
00023 * 
00024 *       .. Scalar Arguments ..
00025 *       CHARACTER          UPLO
00026 *       INTEGER            INFO, LDA, N
00027 *       REAL               ANORM, RCOND
00028 *       ..
00029 *       .. Array Arguments ..
00030 *       INTEGER            IPIV( * )
00031 *       COMPLEX            A( LDA, * ), WORK( * )
00032 *       ..
00033 *  
00034 *
00035 *> \par Purpose:
00036 *  =============
00037 *>
00038 *> \verbatim
00039 *>
00040 *> CSYCON estimates the reciprocal of the condition number (in the
00041 *> 1-norm) of a complex symmetric matrix A using the factorization
00042 *> A = U*D*U**T or A = L*D*L**T computed by CSYTRF.
00043 *>
00044 *> An estimate is obtained for norm(inv(A)), and the reciprocal of the
00045 *> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
00046 *> \endverbatim
00047 *
00048 *  Arguments:
00049 *  ==========
00050 *
00051 *> \param[in] UPLO
00052 *> \verbatim
00053 *>          UPLO is CHARACTER*1
00054 *>          Specifies whether the details of the factorization are stored
00055 *>          as an upper or lower triangular matrix.
00056 *>          = 'U':  Upper triangular, form is A = U*D*U**T;
00057 *>          = 'L':  Lower triangular, form is A = L*D*L**T.
00058 *> \endverbatim
00059 *>
00060 *> \param[in] N
00061 *> \verbatim
00062 *>          N is INTEGER
00063 *>          The order of the matrix A.  N >= 0.
00064 *> \endverbatim
00065 *>
00066 *> \param[in] A
00067 *> \verbatim
00068 *>          A is COMPLEX array, dimension (LDA,N)
00069 *>          The block diagonal matrix D and the multipliers used to
00070 *>          obtain the factor U or L as computed by CSYTRF.
00071 *> \endverbatim
00072 *>
00073 *> \param[in] LDA
00074 *> \verbatim
00075 *>          LDA is INTEGER
00076 *>          The leading dimension of the array A.  LDA >= max(1,N).
00077 *> \endverbatim
00078 *>
00079 *> \param[in] IPIV
00080 *> \verbatim
00081 *>          IPIV is INTEGER array, dimension (N)
00082 *>          Details of the interchanges and the block structure of D
00083 *>          as determined by CSYTRF.
00084 *> \endverbatim
00085 *>
00086 *> \param[in] ANORM
00087 *> \verbatim
00088 *>          ANORM is REAL
00089 *>          The 1-norm of the original matrix A.
00090 *> \endverbatim
00091 *>
00092 *> \param[out] RCOND
00093 *> \verbatim
00094 *>          RCOND is REAL
00095 *>          The reciprocal of the condition number of the matrix A,
00096 *>          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
00097 *>          estimate of the 1-norm of inv(A) computed in this routine.
00098 *> \endverbatim
00099 *>
00100 *> \param[out] WORK
00101 *> \verbatim
00102 *>          WORK is COMPLEX array, dimension (2*N)
00103 *> \endverbatim
00104 *>
00105 *> \param[out] INFO
00106 *> \verbatim
00107 *>          INFO is INTEGER
00108 *>          = 0:  successful exit
00109 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
00110 *> \endverbatim
00111 *
00112 *  Authors:
00113 *  ========
00114 *
00115 *> \author Univ. of Tennessee 
00116 *> \author Univ. of California Berkeley 
00117 *> \author Univ. of Colorado Denver 
00118 *> \author NAG Ltd. 
00119 *
00120 *> \date November 2011
00121 *
00122 *> \ingroup complexSYcomputational
00123 *
00124 *  =====================================================================
00125       SUBROUTINE CSYCON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
00126      $                   INFO )
00127 *
00128 *  -- LAPACK computational routine (version 3.4.0) --
00129 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00130 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00131 *     November 2011
00132 *
00133 *     .. Scalar Arguments ..
00134       CHARACTER          UPLO
00135       INTEGER            INFO, LDA, N
00136       REAL               ANORM, RCOND
00137 *     ..
00138 *     .. Array Arguments ..
00139       INTEGER            IPIV( * )
00140       COMPLEX            A( LDA, * ), WORK( * )
00141 *     ..
00142 *
00143 *  =====================================================================
00144 *
00145 *     .. Parameters ..
00146       REAL               ONE, ZERO
00147       PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
00148 *     ..
00149 *     .. Local Scalars ..
00150       LOGICAL            UPPER
00151       INTEGER            I, KASE
00152       REAL               AINVNM
00153 *     ..
00154 *     .. Local Arrays ..
00155       INTEGER            ISAVE( 3 )
00156 *     ..
00157 *     .. External Functions ..
00158       LOGICAL            LSAME
00159       EXTERNAL           LSAME
00160 *     ..
00161 *     .. External Subroutines ..
00162       EXTERNAL           CLACN2, CSYTRS, XERBLA
00163 *     ..
00164 *     .. Intrinsic Functions ..
00165       INTRINSIC          MAX
00166 *     ..
00167 *     .. Executable Statements ..
00168 *
00169 *     Test the input parameters.
00170 *
00171       INFO = 0
00172       UPPER = LSAME( UPLO, 'U' )
00173       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00174          INFO = -1
00175       ELSE IF( N.LT.0 ) THEN
00176          INFO = -2
00177       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
00178          INFO = -4
00179       ELSE IF( ANORM.LT.ZERO ) THEN
00180          INFO = -6
00181       END IF
00182       IF( INFO.NE.0 ) THEN
00183          CALL XERBLA( 'CSYCON', -INFO )
00184          RETURN
00185       END IF
00186 *
00187 *     Quick return if possible
00188 *
00189       RCOND = ZERO
00190       IF( N.EQ.0 ) THEN
00191          RCOND = ONE
00192          RETURN
00193       ELSE IF( ANORM.LE.ZERO ) THEN
00194          RETURN
00195       END IF
00196 *
00197 *     Check that the diagonal matrix D is nonsingular.
00198 *
00199       IF( UPPER ) THEN
00200 *
00201 *        Upper triangular storage: examine D from bottom to top
00202 *
00203          DO 10 I = N, 1, -1
00204             IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
00205      $         RETURN
00206    10    CONTINUE
00207       ELSE
00208 *
00209 *        Lower triangular storage: examine D from top to bottom.
00210 *
00211          DO 20 I = 1, N
00212             IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
00213      $         RETURN
00214    20    CONTINUE
00215       END IF
00216 *
00217 *     Estimate the 1-norm of the inverse.
00218 *
00219       KASE = 0
00220    30 CONTINUE
00221       CALL CLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
00222       IF( KASE.NE.0 ) THEN
00223 *
00224 *        Multiply by inv(L*D*L**T) or inv(U*D*U**T).
00225 *
00226          CALL CSYTRS( UPLO, N, 1, A, LDA, IPIV, WORK, N, INFO )
00227          GO TO 30
00228       END IF
00229 *
00230 *     Compute the estimate of the reciprocal condition number.
00231 *
00232       IF( AINVNM.NE.ZERO )
00233      $   RCOND = ( ONE / AINVNM ) / ANORM
00234 *
00235       RETURN
00236 *
00237 *     End of CSYCON
00238 *
00239       END
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