# dptcon.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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dptcon.f

## SYNOPSIS

### Functions/Subroutines

subroutine dptcon (N, D, E, ANORM, RCOND, WORK, INFO)
DPTCON

## Function/Subroutine Documentation

### subroutine dptcon (integer N, double precision, dimension( * ) D, double precision, dimension( * ) E, double precision ANORM, double precision RCOND, double precision, dimension( * ) WORK, integer INFO)

DPTCON

Purpose:

``` DPTCON computes the reciprocal of the condition number (in the
1-norm) of a real symmetric positive definite tridiagonal matrix
using the factorization A = L*D*L**T or A = U**T*D*U computed by
DPTTRF.

Norm(inv(A)) is computed by a direct method, and the reciprocal of
the condition number is computed as
RCOND = 1 / (ANORM * norm(inv(A))).
```

Parameters:

N

```          N is INTEGER
The order of the matrix A.  N >= 0.
```

D

```          D is DOUBLE PRECISION array, dimension (N)
The n diagonal elements of the diagonal matrix D from the
factorization of A, as computed by DPTTRF.
```

E

```          E is DOUBLE PRECISION array, dimension (N-1)
The (n-1) off-diagonal elements of the unit bidiagonal factor
U or L from the factorization of A,  as computed by DPTTRF.
```

ANORM

```          ANORM is DOUBLE PRECISION
The 1-norm of the original matrix A.
```

RCOND

```          RCOND is DOUBLE PRECISION
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is the
1-norm of inv(A) computed in this routine.
```

WORK

```          WORK is DOUBLE PRECISION array, dimension (N)
```

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

NAG Ltd.

Date:

December 2016

Further Details:

```  The method used is described in Nicholas J. Higham, "Efficient
Algorithms for Computing the Condition Number of a Tridiagonal
Matrix", SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986.
```

Definition at line 120 of file dptcon.f.

## Author

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