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    1: *> \brief \b ZHECON
    2: *
    3: *  =========== DOCUMENTATION ===========
    4: *
    5: * Online html documentation available at
    6: *            http://www.netlib.org/lapack/explore-html/
    7: *
    8: *> \htmlonly
    9: *> Download ZHECON + dependencies
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhecon.f">
   11: *> [TGZ]</a>
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhecon.f">
   13: *> [ZIP]</a>
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhecon.f">
   15: *> [TXT]</a>
   16: *> \endhtmlonly
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       SUBROUTINE ZHECON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
   22: *                          INFO )
   23: *
   24: *       .. Scalar Arguments ..
   25: *       CHARACTER          UPLO
   26: *       INTEGER            INFO, LDA, N
   27: *       DOUBLE PRECISION   ANORM, RCOND
   28: *       ..
   29: *       .. Array Arguments ..
   30: *       INTEGER            IPIV( * )
   31: *       COMPLEX*16         A( LDA, * ), WORK( * )
   32: *       ..
   33: *
   34: *
   35: *> \par Purpose:
   36: *  =============
   37: *>
   38: *> \verbatim
   39: *>
   40: *> ZHECON estimates the reciprocal of the condition number of a complex
   41: *> Hermitian matrix A using the factorization A = U*D*U**H or
   42: *> A = L*D*L**H computed by ZHETRF.
   43: *>
   44: *> An estimate is obtained for norm(inv(A)), and the reciprocal of the
   45: *> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
   46: *> \endverbatim
   47: *
   48: *  Arguments:
   49: *  ==========
   50: *
   51: *> \param[in] UPLO
   52: *> \verbatim
   53: *>          UPLO is CHARACTER*1
   54: *>          Specifies whether the details of the factorization are stored
   55: *>          as an upper or lower triangular matrix.
   56: *>          = 'U':  Upper triangular, form is A = U*D*U**H;
   57: *>          = 'L':  Lower triangular, form is A = L*D*L**H.
   58: *> \endverbatim
   59: *>
   60: *> \param[in] N
   61: *> \verbatim
   62: *>          N is INTEGER
   63: *>          The order of the matrix A.  N >= 0.
   64: *> \endverbatim
   65: *>
   66: *> \param[in] A
   67: *> \verbatim
   68: *>          A is COMPLEX*16 array, dimension (LDA,N)
   69: *>          The block diagonal matrix D and the multipliers used to
   70: *>          obtain the factor U or L as computed by ZHETRF.
   71: *> \endverbatim
   72: *>
   73: *> \param[in] LDA
   74: *> \verbatim
   75: *>          LDA is INTEGER
   76: *>          The leading dimension of the array A.  LDA >= max(1,N).
   77: *> \endverbatim
   78: *>
   79: *> \param[in] IPIV
   80: *> \verbatim
   81: *>          IPIV is INTEGER array, dimension (N)
   82: *>          Details of the interchanges and the block structure of D
   83: *>          as determined by ZHETRF.
   84: *> \endverbatim
   85: *>
   86: *> \param[in] ANORM
   87: *> \verbatim
   88: *>          ANORM is DOUBLE PRECISION
   89: *>          The 1-norm of the original matrix A.
   90: *> \endverbatim
   91: *>
   92: *> \param[out] RCOND
   93: *> \verbatim
   94: *>          RCOND is DOUBLE PRECISION
   95: *>          The reciprocal of the condition number of the matrix A,
   96: *>          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
   97: *>          estimate of the 1-norm of inv(A) computed in this routine.
   98: *> \endverbatim
   99: *>
  100: *> \param[out] WORK
  101: *> \verbatim
  102: *>          WORK is COMPLEX*16 array, dimension (2*N)
  103: *> \endverbatim
  104: *>
  105: *> \param[out] INFO
  106: *> \verbatim
  107: *>          INFO is INTEGER
  108: *>          = 0:  successful exit
  109: *>          < 0:  if INFO = -i, the i-th argument had an illegal value
  110: *> \endverbatim
  111: *
  112: *  Authors:
  113: *  ========
  114: *
  115: *> \author Univ. of Tennessee
  116: *> \author Univ. of California Berkeley
  117: *> \author Univ. of Colorado Denver
  118: *> \author NAG Ltd.
  119: *
  120: *> \ingroup complex16HEcomputational
  121: *
  122: *  =====================================================================
  123:       SUBROUTINE ZHECON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
  124:      $                   INFO )
  125: *
  126: *  -- LAPACK computational routine --
  127: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  128: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  129: *
  130: *     .. Scalar Arguments ..
  131:       CHARACTER          UPLO
  132:       INTEGER            INFO, LDA, N
  133:       DOUBLE PRECISION   ANORM, RCOND
  134: *     ..
  135: *     .. Array Arguments ..
  136:       INTEGER            IPIV( * )
  137:       COMPLEX*16         A( LDA, * ), WORK( * )
  138: *     ..
  139: *
  140: *  =====================================================================
  141: *
  142: *     .. Parameters ..
  143:       DOUBLE PRECISION   ONE, ZERO
  144:       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
  145: *     ..
  146: *     .. Local Scalars ..
  147:       LOGICAL            UPPER
  148:       INTEGER            I, KASE
  149:       DOUBLE PRECISION   AINVNM
  150: *     ..
  151: *     .. Local Arrays ..
  152:       INTEGER            ISAVE( 3 )
  153: *     ..
  154: *     .. External Functions ..
  155:       LOGICAL            LSAME
  156:       EXTERNAL           LSAME
  157: *     ..
  158: *     .. External Subroutines ..
  159:       EXTERNAL           XERBLA, ZHETRS, ZLACN2
  160: *     ..
  161: *     .. Intrinsic Functions ..
  162:       INTRINSIC          MAX
  163: *     ..
  164: *     .. Executable Statements ..
  165: *
  166: *     Test the input parameters.
  167: *
  168:       INFO = 0
  169:       UPPER = LSAME( UPLO, 'U' )
  170:       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
  171:          INFO = -1
  172:       ELSE IF( N.LT.0 ) THEN
  173:          INFO = -2
  174:       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
  175:          INFO = -4
  176:       ELSE IF( ANORM.LT.ZERO ) THEN
  177:          INFO = -6
  178:       END IF
  179:       IF( INFO.NE.0 ) THEN
  180:          CALL XERBLA( 'ZHECON', -INFO )
  181:          RETURN
  182:       END IF
  183: *
  184: *     Quick return if possible
  185: *
  186:       RCOND = ZERO
  187:       IF( N.EQ.0 ) THEN
  188:          RCOND = ONE
  189:          RETURN
  190:       ELSE IF( ANORM.LE.ZERO ) THEN
  191:          RETURN
  192:       END IF
  193: *
  194: *     Check that the diagonal matrix D is nonsingular.
  195: *
  196:       IF( UPPER ) THEN
  197: *
  198: *        Upper triangular storage: examine D from bottom to top
  199: *
  200:          DO 10 I = N, 1, -1
  201:             IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
  202:      $         RETURN
  203:    10    CONTINUE
  204:       ELSE
  205: *
  206: *        Lower triangular storage: examine D from top to bottom.
  207: *
  208:          DO 20 I = 1, N
  209:             IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
  210:      $         RETURN
  211:    20    CONTINUE
  212:       END IF
  213: *
  214: *     Estimate the 1-norm of the inverse.
  215: *
  216:       KASE = 0
  217:    30 CONTINUE
  218:       CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
  219:       IF( KASE.NE.0 ) THEN
  220: *
  221: *        Multiply by inv(L*D*L**H) or inv(U*D*U**H).
  222: *
  223:          CALL ZHETRS( UPLO, N, 1, A, LDA, IPIV, WORK, N, INFO )
  224:          GO TO 30
  225:       END IF
  226: *
  227: *     Compute the estimate of the reciprocal condition number.
  228: *
  229:       IF( AINVNM.NE.ZERO )
  230:      $   RCOND = ( ONE / AINVNM ) / ANORM
  231: *
  232:       RETURN
  233: *
  234: *     End of ZHECON
  235: *
  236:       END