# SPTCON (3) - Linux Man Pages

sptcon.f -

## SYNOPSIS

### Functions/Subroutines

subroutine sptcon (N, D, E, ANORM, RCOND, WORK, INFO)
SPTCON

## Function/Subroutine Documentation

### subroutine sptcon (integerN, real, dimension( * )D, real, dimension( * )E, realANORM, realRCOND, real, dimension( * )WORK, integerINFO)

SPTCON

Purpose:

``` SPTCON 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
SPTTRF.

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 REAL array, dimension (N)
The n diagonal elements of the diagonal matrix D from the
factorization of A, as computed by SPTTRF.
```

E

```          E is REAL 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 SPTTRF.
```

ANORM

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

RCOND

```          RCOND is REAL
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 REAL 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:

September 2012

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 119 of file sptcon.f.

## Author

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