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    1:       SUBROUTINE ZGTCON( NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND,
    2:      $                   WORK, INFO )
    3: *
    4: *  -- LAPACK routine (version 3.3.1) --
    5: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
    6: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
    7: *  -- April 2011                                                      --
    8: *
    9: *     Modified to call ZLACN2 in place of ZLACON, 10 Feb 03, SJH.
   10: *
   11: *     .. Scalar Arguments ..
   12:       CHARACTER          NORM
   13:       INTEGER            INFO, N
   14:       DOUBLE PRECISION   ANORM, RCOND
   15: *     ..
   16: *     .. Array Arguments ..
   17:       INTEGER            IPIV( * )
   18:       COMPLEX*16         D( * ), DL( * ), DU( * ), DU2( * ), WORK( * )
   19: *     ..
   20: *
   21: *  Purpose
   22: *  =======
   23: *
   24: *  ZGTCON estimates the reciprocal of the condition number of a complex
   25: *  tridiagonal matrix A using the LU factorization as computed by
   26: *  ZGTTRF.
   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: *  NORM    (input) CHARACTER*1
   35: *          Specifies whether the 1-norm condition number or the
   36: *          infinity-norm condition number is required:
   37: *          = '1' or 'O':  1-norm;
   38: *          = 'I':         Infinity-norm.
   39: *
   40: *  N       (input) INTEGER
   41: *          The order of the matrix A.  N >= 0.
   42: *
   43: *  DL      (input) COMPLEX*16 array, dimension (N-1)
   44: *          The (n-1) multipliers that define the matrix L from the
   45: *          LU factorization of A as computed by ZGTTRF.
   46: *
   47: *  D       (input) COMPLEX*16 array, dimension (N)
   48: *          The n diagonal elements of the upper triangular matrix U from
   49: *          the LU factorization of A.
   50: *
   51: *  DU      (input) COMPLEX*16 array, dimension (N-1)
   52: *          The (n-1) elements of the first superdiagonal of U.
   53: *
   54: *  DU2     (input) COMPLEX*16 array, dimension (N-2)
   55: *          The (n-2) elements of the second superdiagonal of U.
   56: *
   57: *  IPIV    (input) INTEGER array, dimension (N)
   58: *          The pivot indices; for 1 <= i <= n, row i of the matrix was
   59: *          interchanged with row IPIV(i).  IPIV(i) will always be either
   60: *          i or i+1; IPIV(i) = i indicates a row interchange was not
   61: *          required.
   62: *
   63: *  ANORM   (input) DOUBLE PRECISION
   64: *          If NORM = '1' or 'O', the 1-norm of the original matrix A.
   65: *          If NORM = 'I', the infinity-norm of the original matrix A.
   66: *
   67: *  RCOND   (output) DOUBLE PRECISION
   68: *          The reciprocal of the condition number of the matrix A,
   69: *          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
   70: *          estimate of the 1-norm of inv(A) computed in this routine.
   71: *
   72: *  WORK    (workspace) COMPLEX*16 array, dimension (2*N)
   73: *
   74: *  INFO    (output) INTEGER
   75: *          = 0:  successful exit
   76: *          < 0:  if INFO = -i, the i-th argument had an illegal value
   77: *
   78: *  =====================================================================
   79: *
   80: *     .. Parameters ..
   81:       DOUBLE PRECISION   ONE, ZERO
   82:       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
   83: *     ..
   84: *     .. Local Scalars ..
   85:       LOGICAL            ONENRM
   86:       INTEGER            I, KASE, KASE1
   87:       DOUBLE PRECISION   AINVNM
   88: *     ..
   89: *     .. Local Arrays ..
   90:       INTEGER            ISAVE( 3 )
   91: *     ..
   92: *     .. External Functions ..
   93:       LOGICAL            LSAME
   94:       EXTERNAL           LSAME
   95: *     ..
   96: *     .. External Subroutines ..
   97:       EXTERNAL           XERBLA, ZGTTRS, ZLACN2
   98: *     ..
   99: *     .. Intrinsic Functions ..
  100:       INTRINSIC          DCMPLX
  101: *     ..
  102: *     .. Executable Statements ..
  103: *
  104: *     Test the input arguments.
  105: *
  106:       INFO = 0
  107:       ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' )
  108:       IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN
  109:          INFO = -1
  110:       ELSE IF( N.LT.0 ) THEN
  111:          INFO = -2
  112:       ELSE IF( ANORM.LT.ZERO ) THEN
  113:          INFO = -8
  114:       END IF
  115:       IF( INFO.NE.0 ) THEN
  116:          CALL XERBLA( 'ZGTCON', -INFO )
  117:          RETURN
  118:       END IF
  119: *
  120: *     Quick return if possible
  121: *
  122:       RCOND = ZERO
  123:       IF( N.EQ.0 ) THEN
  124:          RCOND = ONE
  125:          RETURN
  126:       ELSE IF( ANORM.EQ.ZERO ) THEN
  127:          RETURN
  128:       END IF
  129: *
  130: *     Check that D(1:N) is non-zero.
  131: *
  132:       DO 10 I = 1, N
  133:          IF( D( I ).EQ.DCMPLX( ZERO ) )
  134:      $      RETURN
  135:    10 CONTINUE
  136: *
  137:       AINVNM = ZERO
  138:       IF( ONENRM ) THEN
  139:          KASE1 = 1
  140:       ELSE
  141:          KASE1 = 2
  142:       END IF
  143:       KASE = 0
  144:    20 CONTINUE
  145:       CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
  146:       IF( KASE.NE.0 ) THEN
  147:          IF( KASE.EQ.KASE1 ) THEN
  148: *
  149: *           Multiply by inv(U)*inv(L).
  150: *
  151:             CALL ZGTTRS( 'No transpose', N, 1, DL, D, DU, DU2, IPIV,
  152:      $                   WORK, N, INFO )
  153:          ELSE
  154: *
  155: *           Multiply by inv(L**H)*inv(U**H).
  156: *
  157:             CALL ZGTTRS( 'Conjugate transpose', N, 1, DL, D, DU, DU2,
  158:      $                   IPIV, WORK, N, INFO )
  159:          END IF
  160:          GO TO 20
  161:       END IF
  162: *
  163: *     Compute the estimate of the reciprocal condition number.
  164: *
  165:       IF( AINVNM.NE.ZERO )
  166:      $   RCOND = ( ONE / AINVNM ) / ANORM
  167: *
  168:       RETURN
  169: *
  170: *     End of ZGTCON
  171: *
  172:       END