# 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

Univ. of Colorado Denver

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