sgecon(l) [redhat man page]

SGECON(l)								 )								 SGECON(l)

NAME

       SGECON  -  estimate the reciprocal of the condition number of a general real matrix A, in either the 1-norm or the infinity-norm, using the
       LU factorization computed by SGETRF

SYNOPSIS

       SUBROUTINE SGECON( NORM, N, A, LDA, ANORM, RCOND, WORK, IWORK, INFO )

	   CHARACTER	  NORM

	   INTEGER	  INFO, LDA, N

	   REAL 	  ANORM, RCOND

	   INTEGER	  IWORK( * )

	   REAL 	  A( LDA, * ), WORK( * )

PURPOSE

       SGECON estimates the reciprocal of the condition number of a general real matrix A, in either the 1-norm or the infinity-norm, using the LU
       factorization computed by SGETRF.  An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as
	  RCOND = 1 / ( norm(A) * norm(inv(A)) ).

ARGUMENTS

       NORM    (input) 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       (input) INTEGER
	       The order of the matrix A.  N >= 0.

       A       (input) REAL array, dimension (LDA,N)
	       The factors L and U from the factorization A = P*L*U as computed by SGETRF.

       LDA     (input) INTEGER
	       The leading dimension of the array A.  LDA >= max(1,N).

       ANORM   (input) 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   (output) REAL
	       The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))).

       WORK    (workspace) REAL array, dimension (4*N)

       IWORK   (workspace) INTEGER array, dimension (N)

       INFO    (output) INTEGER
	       = 0:  successful exit
	       < 0:  if INFO = -i, the i-th argument had an illegal value

LAPACK version 3.0						   15 June 2000 							 SGECON(l)

SGTCON(l)								 )								 SGTCON(l)

NAME

       SGTCON - estimate the reciprocal of the condition number of a real tridiagonal matrix A using the LU factorization as computed by SGTTRF

SYNOPSIS

       SUBROUTINE SGTCON( NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND, WORK, IWORK, INFO )

	   CHARACTER	  NORM

	   INTEGER	  INFO, N

	   REAL 	  ANORM, RCOND

	   INTEGER	  IPIV( * ), IWORK( * )

	   REAL 	  D( * ), DL( * ), DU( * ), DU2( * ), WORK( * )

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))).

ARGUMENTS

       NORM    (input) 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       (input) INTEGER
	       The order of the matrix A.  N >= 0.

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

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

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

       IPIV    (input) 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   (input) 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   (output) 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    (workspace) REAL array, dimension (2*N)

       IWORK   (workspace) INTEGER array, dimension (N)

       INFO    (output) INTEGER
	       = 0:  successful exit
	       < 0:  if INFO = -i, the i-th argument had an illegal value

LAPACK version 3.0						   15 June 2000 							 SGTCON(l)