# sgtcon.f - Man Page

SRC/sgtcon.f

## Synopsis

### Functions/Subroutines

subroutine **sgtcon** (norm, n, dl, d, du, du2, ipiv, anorm, rcond, work, iwork, info)**SGTCON**

## Function/Subroutine Documentation

### subroutine sgtcon (character norm, integer n, real, dimension( * ) dl, real, dimension( * ) d, real, dimension( * ) du, real, dimension( * ) du2, integer, dimension( * ) ipiv, real anorm, real rcond, real, dimension( * ) work, integer, dimension( * ) iwork, integer info)

**SGTCON**

**Purpose:**

SGTCON estimates the reciprocal of the condition number of a real tridiagonal matrix A using the LU factorization as computed by SGTTRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

**Parameters***NORM*NORM is CHARACTER*1 Specifies whether the 1-norm condition number or the infinity-norm condition number is required: = '1' or 'O': 1-norm; = 'I': Infinity-norm.

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

*DL*DL is REAL array, dimension (N-1) The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by SGTTRF.

*D*D is REAL array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A.

*DU*DU is REAL array, dimension (N-1) The (n-1) elements of the first superdiagonal of U.

*DU2*DU2 is REAL array, dimension (N-2) The (n-2) elements of the second superdiagonal of U.

*IPIV*IPIV is INTEGER array, dimension (N) The pivot indices; for 1 <= i <= n, row i of the matrix was interchanged with row IPIV(i). IPIV(i) will always be either i or i+1; IPIV(i) = i indicates a row interchange was not required.

*ANORM*ANORM is REAL If NORM = '1' or 'O', the 1-norm of the original matrix A. If NORM = 'I', the infinity-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 an estimate of the 1-norm of inv(A) computed in this routine.

*WORK*WORK is REAL array, dimension (2*N)

*IWORK*IWORK is INTEGER 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.

Definition at line **144** of file **sgtcon.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

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