LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
ssycon.f
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00001 *> \brief \b SSYCON
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download SSYCON + dependencies 
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00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE SSYCON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
00022 *                          IWORK, INFO )
00023 * 
00024 *       .. Scalar Arguments ..
00025 *       CHARACTER          UPLO
00026 *       INTEGER            INFO, LDA, N
00027 *       REAL               ANORM, RCOND
00028 *       ..
00029 *       .. Array Arguments ..
00030 *       INTEGER            IPIV( * ), IWORK( * )
00031 *       REAL               A( LDA, * ), WORK( * )
00032 *       ..
00033 *  
00034 *
00035 *> \par Purpose:
00036 *  =============
00037 *>
00038 *> \verbatim
00039 *>
00040 *> SSYCON estimates the reciprocal of the condition number (in the
00041 *> 1-norm) of a real symmetric matrix A using the factorization
00042 *> A = U*D*U**T or A = L*D*L**T computed by SSYTRF.
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 REAL 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 SSYTRF.
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 SSYTRF.
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 REAL array, dimension (2*N)
00103 *> \endverbatim
00104 *>
00105 *> \param[out] IWORK
00106 *> \verbatim
00107 *>          IWORK is INTEGER array, dimension (N)
00108 *> \endverbatim
00109 *>
00110 *> \param[out] INFO
00111 *> \verbatim
00112 *>          INFO is INTEGER
00113 *>          = 0:  successful exit
00114 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
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 realSYcomputational
00128 *
00129 *  =====================================================================
00130       SUBROUTINE SSYCON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
00131      $                   IWORK, INFO )
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       INTEGER            INFO, LDA, N
00141       REAL               ANORM, RCOND
00142 *     ..
00143 *     .. Array Arguments ..
00144       INTEGER            IPIV( * ), IWORK( * )
00145       REAL               A( LDA, * ), WORK( * )
00146 *     ..
00147 *
00148 *  =====================================================================
00149 *
00150 *     .. Parameters ..
00151       REAL               ONE, ZERO
00152       PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
00153 *     ..
00154 *     .. Local Scalars ..
00155       LOGICAL            UPPER
00156       INTEGER            I, KASE
00157       REAL               AINVNM
00158 *     ..
00159 *     .. Local Arrays ..
00160       INTEGER            ISAVE( 3 )
00161 *     ..
00162 *     .. External Functions ..
00163       LOGICAL            LSAME
00164       EXTERNAL           LSAME
00165 *     ..
00166 *     .. External Subroutines ..
00167       EXTERNAL           SLACN2, SSYTRS, XERBLA
00168 *     ..
00169 *     .. Intrinsic Functions ..
00170       INTRINSIC          MAX
00171 *     ..
00172 *     .. Executable Statements ..
00173 *
00174 *     Test the input parameters.
00175 *
00176       INFO = 0
00177       UPPER = LSAME( UPLO, 'U' )
00178       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00179          INFO = -1
00180       ELSE IF( N.LT.0 ) THEN
00181          INFO = -2
00182       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
00183          INFO = -4
00184       ELSE IF( ANORM.LT.ZERO ) THEN
00185          INFO = -6
00186       END IF
00187       IF( INFO.NE.0 ) THEN
00188          CALL XERBLA( 'SSYCON', -INFO )
00189          RETURN
00190       END IF
00191 *
00192 *     Quick return if possible
00193 *
00194       RCOND = ZERO
00195       IF( N.EQ.0 ) THEN
00196          RCOND = ONE
00197          RETURN
00198       ELSE IF( ANORM.LE.ZERO ) THEN
00199          RETURN
00200       END IF
00201 *
00202 *     Check that the diagonal matrix D is nonsingular.
00203 *
00204       IF( UPPER ) THEN
00205 *
00206 *        Upper triangular storage: examine D from bottom to top
00207 *
00208          DO 10 I = N, 1, -1
00209             IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
00210      $         RETURN
00211    10    CONTINUE
00212       ELSE
00213 *
00214 *        Lower triangular storage: examine D from top to bottom.
00215 *
00216          DO 20 I = 1, N
00217             IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
00218      $         RETURN
00219    20    CONTINUE
00220       END IF
00221 *
00222 *     Estimate the 1-norm of the inverse.
00223 *
00224       KASE = 0
00225    30 CONTINUE
00226       CALL SLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
00227       IF( KASE.NE.0 ) THEN
00228 *
00229 *        Multiply by inv(L*D*L**T) or inv(U*D*U**T).
00230 *
00231          CALL SSYTRS( UPLO, N, 1, A, LDA, IPIV, WORK, N, INFO )
00232          GO TO 30
00233       END IF
00234 *
00235 *     Compute the estimate of the reciprocal condition number.
00236 *
00237       IF( AINVNM.NE.ZERO )
00238      $   RCOND = ( ONE / AINVNM ) / ANORM
00239 *
00240       RETURN
00241 *
00242 *     End of SSYCON
00243 *
00244       END
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