dgtcon()

subroutine dgtcon	(	character	NORM,
		integer	N,
		double precision, dimension( * )	DL,
		double precision, dimension( * )	D,
		double precision, dimension( * )	DU,
		double precision, dimension( * )	DU2,
		integer, dimension( * )	IPIV,
		double precision	ANORM,
		double precision	RCOND,
		double precision, dimension( * )	WORK,
		integer, dimension( * )	IWORK,
		integer	INFO
	)

DGTCON

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Purpose:

 DGTCON estimates the reciprocal of the condition number of a real
 tridiagonal matrix A using the LU factorization as computed by
 DGTTRF.

 An estimate is obtained for norm(inv(A)), and the reciprocal of the
 condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

Parameters

[in]	NORM	NORM is 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.
[in]	N	N is INTEGER The order of the matrix A. N >= 0.
[in]	DL	DL is DOUBLE PRECISION array, dimension (N-1) The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by DGTTRF.
[in]	D	D is DOUBLE PRECISION array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A.
[in]	DU	DU is DOUBLE PRECISION array, dimension (N-1) The (n-1) elements of the first superdiagonal of U.
[in]	DU2	DU2 is DOUBLE PRECISION array, dimension (N-2) The (n-2) elements of the second superdiagonal of U.
[in]	IPIV	IPIV is 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.
[in]	ANORM	ANORM is 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.
[out]	RCOND	RCOND is 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.
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (2*N)
[out]	IWORK	IWORK is INTEGER array, dimension (N)
[out]	INFO	INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date

December 2016

Definition at line 148 of file dgtcon.f.

*
*  -- LAPACK computational routine (version 3.7.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     December 2016
*
*     .. Scalar Arguments ..
      CHARACTER          NORM
      INTEGER            INFO, N
      DOUBLE PRECISION   ANORM, RCOND
*     ..
*     .. Array Arguments ..
      INTEGER            IPIV( * ), IWORK( * )
      DOUBLE PRECISION   D( * ), DL( * ), DU( * ), DU2( * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. 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           dgttrs, dlacn2, xerbla
*     ..
*     .. 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( 'DGTCON', -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.zero )
     $      RETURN
   10 CONTINUE
*
      ainvnm = zero
      IF( onenrm ) THEN
         kase1 = 1
      ELSE
         kase1 = 2
      END IF
      kase = 0
   20 CONTINUE
      CALL dlacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
      IF( kase.NE.0 ) THEN
         IF( kase.EQ.kase1 ) THEN
*
*           Multiply by inv(U)*inv(L).
*
            CALL dgttrs( 'No transpose', n, 1, dl, d, du, du2, ipiv,
     $                   work, n, info )
         ELSE
*
*           Multiply by inv(L**T)*inv(U**T).
*
            CALL dgttrs( '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 DGTCON
*

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