# sptcon.f man page

sptcon.f —

## Synopsis

### Functions/Subroutines

subroutinesptcon(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

Univ. of Colorado Denver

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

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

sptcon(3) is an alias of sptcon.f(3).