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Cohérence Lapack.

    1: *> \brief \b ZSYCON_ROOK
    2: *
    3: *  =========== DOCUMENTATION ===========
    4: *
    5: * Online html documentation available at 
    6: *            http://www.netlib.org/lapack/explore-html/ 
    7: *
    8: *> \htmlonly
    9: *> Download ZSYCON_ROOK + dependencies 
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zsycon_rook.f"> 
   11: *> [TGZ]</a> 
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zsycon_rook.f"> 
   13: *> [ZIP]</a> 
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zsycon_rook.f"> 
   15: *> [TXT]</a>
   16: *> \endhtmlonly 
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       SUBROUTINE ZSYCON_ROOK( UPLO, N, A, LDA, IPIV, ANORM, RCOND,
   22: *                               WORK, 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: *> ZSYCON_ROOK estimates the reciprocal of the condition number (in the
   41: *> 1-norm) of a complex symmetric matrix A using the factorization
   42: *> A = U*D*U**T or A = L*D*L**T computed by ZSYTRF_ROOK.
   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**T;
   57: *>          = 'L':  Lower triangular, form is A = L*D*L**T.
   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 ZSYTRF_ROOK.
   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 ZSYTRF_ROOK.
   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: *> \date November 2015
  121: *
  122: *> \ingroup complex16SYcomputational
  123: *
  124: *> \par Contributors:
  125: *  ==================
  126: *> \verbatim
  127: *>
  128: *>   November 2015, Igor Kozachenko,
  129: *>                  Computer Science Division,
  130: *>                  University of California, Berkeley
  131: *>
  132: *>  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
  133: *>                  School of Mathematics,
  134: *>                  University of Manchester
  135: *>
  136: *> \endverbatim
  137: *
  138: *  =====================================================================
  139:       SUBROUTINE ZSYCON_ROOK( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
  140:      $                        INFO )
  141: *
  142: *  -- LAPACK computational routine (version 3.6.0) --
  143: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  144: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  145: *     November 2015
  146: *
  147: *     .. Scalar Arguments ..
  148:       CHARACTER          UPLO
  149:       INTEGER            INFO, LDA, N
  150:       DOUBLE PRECISION   ANORM, RCOND
  151: *     ..
  152: *     .. Array Arguments ..
  153:       INTEGER            IPIV( * )
  154:       COMPLEX*16         A( LDA, * ), WORK( * )
  155: *     ..
  156: *
  157: *  =====================================================================
  158: *
  159: *     .. Parameters ..
  160:       DOUBLE PRECISION   ONE, ZERO
  161:       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
  162:       COMPLEX*16            CZERO
  163:       PARAMETER          ( CZERO = ( 0.0D+0, 0.0D+0 ) )
  164: *     ..
  165: *     .. Local Scalars ..
  166:       LOGICAL            UPPER
  167:       INTEGER            I, KASE
  168:       DOUBLE PRECISION   AINVNM
  169: *     ..
  170: *     .. Local Arrays ..
  171:       INTEGER            ISAVE( 3 )
  172: *     ..
  173: *     .. External Functions ..
  174:       LOGICAL            LSAME
  175:       EXTERNAL           LSAME
  176: *     ..
  177: *     .. External Subroutines ..
  178:       EXTERNAL           ZLACN2, ZSYTRS_ROOK, XERBLA
  179: *     ..
  180: *     .. Intrinsic Functions ..
  181:       INTRINSIC          MAX
  182: *     ..
  183: *     .. Executable Statements ..
  184: *
  185: *     Test the input parameters.
  186: *
  187:       INFO = 0
  188:       UPPER = LSAME( UPLO, 'U' )
  189:       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
  190:          INFO = -1
  191:       ELSE IF( N.LT.0 ) THEN
  192:          INFO = -2
  193:       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
  194:          INFO = -4
  195:       ELSE IF( ANORM.LT.ZERO ) THEN
  196:          INFO = -6
  197:       END IF
  198:       IF( INFO.NE.0 ) THEN
  199:          CALL XERBLA( 'ZSYCON_ROOK', -INFO )
  200:          RETURN
  201:       END IF
  202: *
  203: *     Quick return if possible
  204: *
  205:       RCOND = ZERO
  206:       IF( N.EQ.0 ) THEN
  207:          RCOND = ONE
  208:          RETURN
  209:       ELSE IF( ANORM.LE.ZERO ) THEN
  210:          RETURN
  211:       END IF
  212: *
  213: *     Check that the diagonal matrix D is nonsingular.
  214: *
  215:       IF( UPPER ) THEN
  216: *
  217: *        Upper triangular storage: examine D from bottom to top
  218: *
  219:          DO 10 I = N, 1, -1
  220:             IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.CZERO )
  221:      $         RETURN
  222:    10    CONTINUE
  223:       ELSE
  224: *
  225: *        Lower triangular storage: examine D from top to bottom.
  226: *
  227:          DO 20 I = 1, N
  228:             IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.CZERO )
  229:      $         RETURN
  230:    20    CONTINUE
  231:       END IF
  232: *
  233: *     Estimate the 1-norm of the inverse.
  234: *
  235:       KASE = 0
  236:    30 CONTINUE
  237:       CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
  238:       IF( KASE.NE.0 ) THEN
  239: *
  240: *        Multiply by inv(L*D*L**T) or inv(U*D*U**T).
  241: *
  242:          CALL ZSYTRS_ROOK( UPLO, N, 1, A, LDA, IPIV, WORK, N, INFO )
  243:          GO TO 30
  244:       END IF
  245: *
  246: *     Compute the estimate of the reciprocal condition number.
  247: *
  248:       IF( AINVNM.NE.ZERO )
  249:      $   RCOND = ( ONE / AINVNM ) / ANORM
  250: *
  251:       RETURN
  252: *
  253: *     End of ZSYCON_ROOK
  254: *
  255:       END