zgtcon.f

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      SUBROUTINE ZGTCON( NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND,
     $                   WORK, INFO )
*
*  -- LAPACK routine (version 3.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2006
*
*     Modified to call ZLACN2 in place of ZLACON, 10 Feb 03, SJH.
*
*     .. Scalar Arguments ..
      CHARACTER          NORM
      INTEGER            INFO, N
      DOUBLE PRECISION   ANORM, RCOND
*     ..
*     .. Array Arguments ..
      INTEGER            IPIV( * )
      COMPLEX*16         D( * ), DL( * ), DU( * ), DU2( * ), WORK( * )
*     ..
*
*  Purpose
*  =======
*
*  ZGTCON estimates the reciprocal of the condition number of a complex
*  tridiagonal matrix A using the LU factorization as computed by
*  ZGTTRF.
*
*  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*16 array, dimension (N-1)
*          The (n-1) multipliers that define the matrix L from the
*          LU factorization of A as computed by ZGTTRF.
*
*  D       (input) COMPLEX*16 array, dimension (N)
*          The n diagonal elements of the upper triangular matrix U from
*          the LU factorization of A.
*
*  DU      (input) COMPLEX*16 array, dimension (N-1)
*          The (n-1) elements of the first superdiagonal of U.
*
*  DU2     (input) COMPLEX*16 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) DOUBLE PRECISION
*          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) DOUBLE PRECISION
*          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*16 array, dimension (2*N)
*
*  INFO    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument had an illegal value
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE, ZERO
      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            ONENRM
      INTEGER            I, KASE, KASE1
      DOUBLE PRECISION   AINVNM
*     ..
*     .. Local Arrays ..
      INTEGER            ISAVE( 3 )
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL           XERBLA, ZGTTRS, ZLACN2
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          DCMPLX
*     ..
*     .. 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( 'ZGTCON', -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.DCMPLX( ZERO ) )
     $      RETURN
   10 CONTINUE
*
      AINVNM = ZERO
      IF( ONENRM ) THEN
         KASE1 = 1
      ELSE
         KASE1 = 2
      END IF
      KASE = 0
   20 CONTINUE
      CALL ZLACN2( 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 ZGTTRS( 'No transpose', N, 1, DL, D, DU, DU2, IPIV,
     $                   WORK, N, INFO )
         ELSE
*
*           Multiply by inv(L')*inv(U').
*
            CALL ZGTTRS( '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 ZGTCON
*
      END