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    1:       SUBROUTINE DPOCON( UPLO, N, A, LDA, ANORM, RCOND, WORK, IWORK,
    2:      $                   INFO )
    3: *
    4: *  -- LAPACK routine (version 3.2) --
    5: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
    6: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
    7: *     November 2006
    8: *
    9: *     Modified to call DLACN2 in place of DLACON, 5 Feb 03, SJH.
   10: *
   11: *     .. Scalar Arguments ..
   12:       CHARACTER          UPLO
   13:       INTEGER            INFO, LDA, N
   14:       DOUBLE PRECISION   ANORM, RCOND
   15: *     ..
   16: *     .. Array Arguments ..
   17:       INTEGER            IWORK( * )
   18:       DOUBLE PRECISION   A( LDA, * ), WORK( * )
   19: *     ..
   20: *
   21: *  Purpose
   22: *  =======
   23: *
   24: *  DPOCON estimates the reciprocal of the condition number (in the
   25: *  1-norm) of a real symmetric positive definite matrix using the
   26: *  Cholesky factorization A = U**T*U or A = L*L**T computed by DPOTRF.
   27: *
   28: *  An estimate is obtained for norm(inv(A)), and the reciprocal of the
   29: *  condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
   30: *
   31: *  Arguments
   32: *  =========
   33: *
   34: *  UPLO    (input) CHARACTER*1
   35: *          = 'U':  Upper triangle of A is stored;
   36: *          = 'L':  Lower triangle of A is stored.
   37: *
   38: *  N       (input) INTEGER
   39: *          The order of the matrix A.  N >= 0.
   40: *
   41: *  A       (input) DOUBLE PRECISION array, dimension (LDA,N)
   42: *          The triangular factor U or L from the Cholesky factorization
   43: *          A = U**T*U or A = L*L**T, as computed by DPOTRF.
   44: *
   45: *  LDA     (input) INTEGER
   46: *          The leading dimension of the array A.  LDA >= max(1,N).
   47: *
   48: *  ANORM   (input) DOUBLE PRECISION
   49: *          The 1-norm (or infinity-norm) of the symmetric matrix A.
   50: *
   51: *  RCOND   (output) DOUBLE PRECISION
   52: *          The reciprocal of the condition number of the matrix A,
   53: *          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
   54: *          estimate of the 1-norm of inv(A) computed in this routine.
   55: *
   56: *  WORK    (workspace) DOUBLE PRECISION array, dimension (3*N)
   57: *
   58: *  IWORK   (workspace) INTEGER array, dimension (N)
   59: *
   60: *  INFO    (output) INTEGER
   61: *          = 0:  successful exit
   62: *          < 0:  if INFO = -i, the i-th argument had an illegal value
   63: *
   64: *  =====================================================================
   65: *
   66: *     .. Parameters ..
   67:       DOUBLE PRECISION   ONE, ZERO
   68:       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
   69: *     ..
   70: *     .. Local Scalars ..
   71:       LOGICAL            UPPER
   72:       CHARACTER          NORMIN
   73:       INTEGER            IX, KASE
   74:       DOUBLE PRECISION   AINVNM, SCALE, SCALEL, SCALEU, SMLNUM
   75: *     ..
   76: *     .. Local Arrays ..
   77:       INTEGER            ISAVE( 3 )
   78: *     ..
   79: *     .. External Functions ..
   80:       LOGICAL            LSAME
   81:       INTEGER            IDAMAX
   82:       DOUBLE PRECISION   DLAMCH
   83:       EXTERNAL           LSAME, IDAMAX, DLAMCH
   84: *     ..
   85: *     .. External Subroutines ..
   86:       EXTERNAL           DLACN2, DLATRS, DRSCL, XERBLA
   87: *     ..
   88: *     .. Intrinsic Functions ..
   89:       INTRINSIC          ABS, MAX
   90: *     ..
   91: *     .. Executable Statements ..
   92: *
   93: *     Test the input parameters.
   94: *
   95:       INFO = 0
   96:       UPPER = LSAME( UPLO, 'U' )
   97:       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
   98:          INFO = -1
   99:       ELSE IF( N.LT.0 ) THEN
  100:          INFO = -2
  101:       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
  102:          INFO = -4
  103:       ELSE IF( ANORM.LT.ZERO ) THEN
  104:          INFO = -5
  105:       END IF
  106:       IF( INFO.NE.0 ) THEN
  107:          CALL XERBLA( 'DPOCON', -INFO )
  108:          RETURN
  109:       END IF
  110: *
  111: *     Quick return if possible
  112: *
  113:       RCOND = ZERO
  114:       IF( N.EQ.0 ) THEN
  115:          RCOND = ONE
  116:          RETURN
  117:       ELSE IF( ANORM.EQ.ZERO ) THEN
  118:          RETURN
  119:       END IF
  120: *
  121:       SMLNUM = DLAMCH( 'Safe minimum' )
  122: *
  123: *     Estimate the 1-norm of inv(A).
  124: *
  125:       KASE = 0
  126:       NORMIN = 'N'
  127:    10 CONTINUE
  128:       CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
  129:       IF( KASE.NE.0 ) THEN
  130:          IF( UPPER ) THEN
  131: *
  132: *           Multiply by inv(U').
  133: *
  134:             CALL DLATRS( 'Upper', 'Transpose', 'Non-unit', NORMIN, N, A,
  135:      $                   LDA, WORK, SCALEL, WORK( 2*N+1 ), INFO )
  136:             NORMIN = 'Y'
  137: *
  138: *           Multiply by inv(U).
  139: *
  140:             CALL DLATRS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N,
  141:      $                   A, LDA, WORK, SCALEU, WORK( 2*N+1 ), INFO )
  142:          ELSE
  143: *
  144: *           Multiply by inv(L).
  145: *
  146:             CALL DLATRS( 'Lower', 'No transpose', 'Non-unit', NORMIN, N,
  147:      $                   A, LDA, WORK, SCALEL, WORK( 2*N+1 ), INFO )
  148:             NORMIN = 'Y'
  149: *
  150: *           Multiply by inv(L').
  151: *
  152:             CALL DLATRS( 'Lower', 'Transpose', 'Non-unit', NORMIN, N, A,
  153:      $                   LDA, WORK, SCALEU, WORK( 2*N+1 ), INFO )
  154:          END IF
  155: *
  156: *        Multiply by 1/SCALE if doing so will not cause overflow.
  157: *
  158:          SCALE = SCALEL*SCALEU
  159:          IF( SCALE.NE.ONE ) THEN
  160:             IX = IDAMAX( N, WORK, 1 )
  161:             IF( SCALE.LT.ABS( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO )
  162:      $         GO TO 20
  163:             CALL DRSCL( N, SCALE, WORK, 1 )
  164:          END IF
  165:          GO TO 10
  166:       END IF
  167: *
  168: *     Compute the estimate of the reciprocal condition number.
  169: *
  170:       IF( AINVNM.NE.ZERO )
  171:      $   RCOND = ( ONE / AINVNM ) / ANORM
  172: *
  173:    20 CONTINUE
  174:       RETURN
  175: *
  176: *     End of DPOCON
  177: *
  178:       END