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    1: *> \brief \b DSYTRI2
    2: *
    3: *  =========== DOCUMENTATION ===========
    4: *
    5: * Online html documentation available at 
    6: *            http://www.netlib.org/lapack/explore-html/ 
    7: *
    8: *> \htmlonly
    9: *> Download DSYTRI2 + dependencies 
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsytri2.f"> 
   11: *> [TGZ]</a> 
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsytri2.f"> 
   13: *> [ZIP]</a> 
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsytri2.f"> 
   15: *> [TXT]</a>
   16: *> \endhtmlonly 
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       SUBROUTINE DSYTRI2( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
   22: * 
   23: *       .. Scalar Arguments ..
   24: *       CHARACTER          UPLO
   25: *       INTEGER            INFO, LDA, LWORK, N
   26: *       ..
   27: *       .. Array Arguments ..
   28: *       INTEGER            IPIV( * )
   29: *       DOUBLE PRECISION   A( LDA, * ), WORK( * )
   30: *       ..
   31: *  
   32: *
   33: *> \par Purpose:
   34: *  =============
   35: *>
   36: *> \verbatim
   37: *>
   38: *> DSYTRI2 computes the inverse of a DOUBLE PRECISION hermitian indefinite matrix
   39: *> A using the factorization A = U*D*U**T or A = L*D*L**T computed by
   40: *> DSYTRF. DSYTRI2 sets the LEADING DIMENSION of the workspace
   41: *> before calling DSYTRI2X that actually computes the inverse.
   42: *> \endverbatim
   43: *
   44: *  Arguments:
   45: *  ==========
   46: *
   47: *> \param[in] UPLO
   48: *> \verbatim
   49: *>          UPLO is CHARACTER*1
   50: *>          Specifies whether the details of the factorization are stored
   51: *>          as an upper or lower triangular matrix.
   52: *>          = 'U':  Upper triangular, form is A = U*D*U**T;
   53: *>          = 'L':  Lower triangular, form is A = L*D*L**T.
   54: *> \endverbatim
   55: *>
   56: *> \param[in] N
   57: *> \verbatim
   58: *>          N is INTEGER
   59: *>          The order of the matrix A.  N >= 0.
   60: *> \endverbatim
   61: *>
   62: *> \param[in,out] A
   63: *> \verbatim
   64: *>          A is DOUBLE PRECISION array, dimension (LDA,N)
   65: *>          On entry, the NB diagonal matrix D and the multipliers
   66: *>          used to obtain the factor U or L as computed by DSYTRF.
   67: *>
   68: *>          On exit, if INFO = 0, the (symmetric) inverse of the original
   69: *>          matrix.  If UPLO = 'U', the upper triangular part of the
   70: *>          inverse is formed and the part of A below the diagonal is not
   71: *>          referenced; if UPLO = 'L' the lower triangular part of the
   72: *>          inverse is formed and the part of A above the diagonal is
   73: *>          not referenced.
   74: *> \endverbatim
   75: *>
   76: *> \param[in] LDA
   77: *> \verbatim
   78: *>          LDA is INTEGER
   79: *>          The leading dimension of the array A.  LDA >= max(1,N).
   80: *> \endverbatim
   81: *>
   82: *> \param[in] IPIV
   83: *> \verbatim
   84: *>          IPIV is INTEGER array, dimension (N)
   85: *>          Details of the interchanges and the NB structure of D
   86: *>          as determined by DSYTRF.
   87: *> \endverbatim
   88: *>
   89: *> \param[out] WORK
   90: *> \verbatim
   91: *>          WORK is DOUBLE PRECISION array, dimension (N+NB+1)*(NB+3)
   92: *> \endverbatim
   93: *>
   94: *> \param[in] LWORK
   95: *> \verbatim
   96: *>          LWORK is INTEGER
   97: *>          The dimension of the array WORK.
   98: *>          WORK is size >= (N+NB+1)*(NB+3)
   99: *>          If LDWORK = -1, then a workspace query is assumed; the routine
  100: *>           calculates:
  101: *>              - the optimal size of the WORK array, returns
  102: *>          this value as the first entry of the WORK array,
  103: *>              - and no error message related to LDWORK is issued by XERBLA.
  104: *> \endverbatim
  105: *>
  106: *> \param[out] INFO
  107: *> \verbatim
  108: *>          INFO is INTEGER
  109: *>          = 0: successful exit
  110: *>          < 0: if INFO = -i, the i-th argument had an illegal value
  111: *>          > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
  112: *>               inverse could not be computed.
  113: *> \endverbatim
  114: *
  115: *  Authors:
  116: *  ========
  117: *
  118: *> \author Univ. of Tennessee 
  119: *> \author Univ. of California Berkeley 
  120: *> \author Univ. of Colorado Denver 
  121: *> \author NAG Ltd. 
  122: *
  123: *> \date November 2011
  124: *
  125: *> \ingroup doubleSYcomputational
  126: *
  127: *  =====================================================================
  128:       SUBROUTINE DSYTRI2( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
  129: *
  130: *  -- LAPACK computational routine (version 3.4.0) --
  131: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  132: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  133: *     November 2011
  134: *
  135: *     .. Scalar Arguments ..
  136:       CHARACTER          UPLO
  137:       INTEGER            INFO, LDA, LWORK, N
  138: *     ..
  139: *     .. Array Arguments ..
  140:       INTEGER            IPIV( * )
  141:       DOUBLE PRECISION   A( LDA, * ), WORK( * )
  142: *     ..
  143: *
  144: *  =====================================================================
  145: *
  146: *     .. Local Scalars ..
  147:       LOGICAL            UPPER, LQUERY
  148:       INTEGER            MINSIZE, NBMAX
  149: *     ..
  150: *     .. External Functions ..
  151:       LOGICAL            LSAME
  152:       INTEGER            ILAENV
  153:       EXTERNAL           LSAME, ILAENV
  154: *     ..
  155: *     .. External Subroutines ..
  156:       EXTERNAL           DSYTRI2X
  157: *     ..
  158: *     .. Executable Statements ..
  159: *
  160: *     Test the input parameters.
  161: *
  162:       INFO = 0
  163:       UPPER = LSAME( UPLO, 'U' )
  164:       LQUERY = ( LWORK.EQ.-1 )
  165: *     Get blocksize
  166:       NBMAX = ILAENV( 1, 'DSYTRF', UPLO, N, -1, -1, -1 )
  167:       IF ( NBMAX .GE. N ) THEN
  168:          MINSIZE = N
  169:       ELSE
  170:          MINSIZE = (N+NBMAX+1)*(NBMAX+3)
  171:       END IF
  172: *
  173:       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
  174:          INFO = -1
  175:       ELSE IF( N.LT.0 ) THEN
  176:          INFO = -2
  177:       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
  178:          INFO = -4
  179:       ELSE IF (LWORK .LT. MINSIZE .AND. .NOT.LQUERY ) THEN
  180:          INFO = -7
  181:       END IF
  182: *
  183: *     Quick return if possible
  184: *
  185: *
  186:       IF( INFO.NE.0 ) THEN
  187:          CALL XERBLA( 'DSYTRI2', -INFO )
  188:          RETURN
  189:       ELSE IF( LQUERY ) THEN
  190:          WORK(1)=MINSIZE
  191:          RETURN
  192:       END IF
  193:       IF( N.EQ.0 )
  194:      $   RETURN
  195:       
  196:       IF( NBMAX .GE. N ) THEN
  197:          CALL DSYTRI( UPLO, N, A, LDA, IPIV, WORK, INFO )
  198:       ELSE
  199:          CALL DSYTRI2X( UPLO, N, A, LDA, IPIV, WORK, NBMAX, INFO )
  200:       END IF
  201:       RETURN
  202: *
  203: *     End of DSYTRI2
  204: *
  205:       END