# sptcon.f - Man Page

SRC/sptcon.f

## Synopsis

### Functions/Subroutines

subroutine sptcon (n, d, e, anorm, rcond, work, info)
SPTCON

## Function/Subroutine Documentation

### subroutine sptcon (integer n, real, dimension( * ) d, real, dimension( * ) e, real anorm, real rcond, real, dimension( * ) work, integer info)

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.

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 117 of file sptcon.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page sptcon(3) is an alias of sptcon.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK