cgtcon.f

          SUBROUTINE CGTCON( NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND,
         $                   WORK, INFO )
    *
    *  -- LAPACK routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     Modified to call CLACN2 in place of CLACON, 10 Feb 03, SJH.
    *
    *     .. Scalar Arguments ..
          CHARACTER          NORM
          INTEGER            INFO, N
          REAL               ANORM, RCOND
    *     ..
    *     .. Array Arguments ..
          INTEGER            IPIV( * )
          COMPLEX            D( * ), DL( * ), DU( * ), DU2( * ), WORK( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  CGTCON estimates the reciprocal of the condition number of a complex
    *  tridiagonal matrix A using the LU factorization as computed by
    *  CGTTRF.
    *
    *  An estimate is obtained for norm(inv(A)), and the reciprocal of the
    *  condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
    *
    *  Arguments
    *  =========
    *
    *  NORM    (input) CHARACTER*1
    *          Specifies whether the 1-norm condition number or the
    *          infinity-norm condition number is required:
    *          = '1' or 'O':  1-norm;
    *          = 'I':         Infinity-norm.
    *
    *  N       (input) INTEGER
    *          The order of the matrix A.  N >= 0.
    *
    *  DL      (input) COMPLEX array, dimension (N-1)
    *          The (n-1) multipliers that define the matrix L from the
    *          LU factorization of A as computed by CGTTRF.
    *
    *  D       (input) COMPLEX array, dimension (N)
    *          The n diagonal elements of the upper triangular matrix U from
    *          the LU factorization of A.
    *
    *  DU      (input) COMPLEX array, dimension (N-1)
    *          The (n-1) elements of the first superdiagonal of U.
    *
    *  DU2     (input) COMPLEX array, dimension (N-2)
    *          The (n-2) elements of the second superdiagonal of U.
    *
    *  IPIV    (input) INTEGER array, dimension (N)
    *          The pivot indices; for 1 <= i <= n, row i of the matrix was
    *          interchanged with row IPIV(i).  IPIV(i) will always be either
    *          i or i+1; IPIV(i) = i indicates a row interchange was not
    *          required.
    *
    *  ANORM   (input) REAL
    *          If NORM = '1' or 'O', the 1-norm of the original matrix A.
    *          If NORM = 'I', the infinity-norm of the original matrix A.
    *
    *  RCOND   (output) REAL
    *          The reciprocal of the condition number of the matrix A,
    *          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
    *          estimate of the 1-norm of inv(A) computed in this routine.
    *
    *  WORK    (workspace) COMPLEX array, dimension (2*N)
    *
    *  INFO    (output) INTEGER
    *          = 0:  successful exit
    *          < 0:  if INFO = -i, the i-th argument had an illegal value
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          REAL               ONE, ZERO
          PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
    *     ..
    *     .. Local Scalars ..
          LOGICAL            ONENRM
          INTEGER            I, KASE, KASE1
          REAL               AINVNM
    *     ..
    *     .. Local Arrays ..
          INTEGER            ISAVE( 3 )
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          EXTERNAL           LSAME
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           CGTTRS, CLACN2, XERBLA
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          CMPLX
    *     ..
    *     .. Executable Statements ..
    *
    *     Test the input arguments.
    *
          INFO = 0
          ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' )
          IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN
             INFO = -1
          ELSE IF( N.LT.0 ) THEN
             INFO = -2
          ELSE IF( ANORM.LT.ZERO ) THEN
             INFO = -8
          END IF
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'CGTCON', -INFO )
             RETURN
          END IF
    *
    *     Quick return if possible
    *
          RCOND = ZERO
          IF( N.EQ.0 ) THEN
             RCOND = ONE
             RETURN
          ELSE IF( ANORM.EQ.ZERO ) THEN
             RETURN
          END IF
    *
    *     Check that D(1:N) is non-zero.
    *
          DO 10 I = 1, N
             IF( D( I ).EQ.CMPLX( ZERO ) )
         $      RETURN
       10 CONTINUE
    *
          AINVNM = ZERO
          IF( ONENRM ) THEN
             KASE1 = 1
          ELSE
             KASE1 = 2
          END IF
          KASE = 0
       20 CONTINUE
          CALL CLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
          IF( KASE.NE.0 ) THEN
             IF( KASE.EQ.KASE1 ) THEN
    *
    *           Multiply by inv(U)*inv(L).
    *
                CALL CGTTRS( 'No transpose', N, 1, DL, D, DU, DU2, IPIV,
         $                   WORK, N, INFO )
             ELSE
    *
    *           Multiply by inv(L')*inv(U').
    *
                CALL CGTTRS( 'Conjugate transpose', N, 1, DL, D, DU, DU2,
         $                   IPIV, WORK, N, INFO )
             END IF
             GO TO 20
          END IF
    *
    *     Compute the estimate of the reciprocal condition number.
    *
          IF( AINVNM.NE.ZERO )
         $   RCOND = ( ONE / AINVNM ) / ANORM
    *
          RETURN
    *
    *     End of CGTCON
    *
          END