ctrcon(l) [redhat man page]

CTRCON(l)								 )								 CTRCON(l)

NAME

       CTRCON - estimate the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm

SYNOPSIS

       SUBROUTINE CTRCON( NORM, UPLO, DIAG, N, A, LDA, RCOND, WORK, RWORK, INFO )

	   CHARACTER	  DIAG, NORM, UPLO

	   INTEGER	  INFO, LDA, N

	   REAL 	  RCOND

	   REAL 	  RWORK( * )

	   COMPLEX	  A( LDA, * ), WORK( * )

PURPOSE

       CTRCON estimates the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm.  The norm of A
       is computed and an estimate is obtained for norm(inv(A)), then 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.

       UPLO    (input) CHARACTER*1
	       = 'U':  A is upper triangular;
	       = 'L':  A is lower triangular.

       DIAG    (input) CHARACTER*1
	       = 'N':  A is non-unit triangular;
	       = 'U':  A is unit triangular.

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

       A       (input) COMPLEX array, dimension (LDA,N)
	       The triangular matrix A.  If UPLO = 'U', the leading N-by-N upper triangular part of the array  A  contains  the  upper	triangular
	       matrix,	and the strictly lower triangular part of A is not referenced.	If UPLO = 'L', the leading N-by-N lower triangular part of
	       the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced.  If  DIAG  =  'U',
	       the diagonal elements of A are also not referenced and are assumed to be 1.

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

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

       WORK    (workspace) COMPLEX array, dimension (2*N)

       RWORK   (workspace) REAL 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 							 CTRCON(l)

CTBCON(l)								 )								 CTBCON(l)

NAME

       CTBCON - estimate the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm

SYNOPSIS

       SUBROUTINE CTBCON( NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK, RWORK, INFO )

	   CHARACTER	  DIAG, NORM, UPLO

	   INTEGER	  INFO, KD, LDAB, N

	   REAL 	  RCOND

	   REAL 	  RWORK( * )

	   COMPLEX	  AB( LDAB, * ), WORK( * )

PURPOSE

       CTBCON estimates the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm.  The norm
       of A is computed and an estimate is obtained for norm(inv(A)), then 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.

       UPLO    (input) CHARACTER*1
	       = 'U':  A is upper triangular;
	       = 'L':  A is lower triangular.

       DIAG    (input) CHARACTER*1
	       = 'N':  A is non-unit triangular;
	       = 'U':  A is unit triangular.

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

       KD      (input) INTEGER
	       The number of superdiagonals or subdiagonals of the triangular band matrix A.  KD >= 0.

       AB      (input) COMPLEX array, dimension (LDAB,N)
	       The upper or lower triangular band matrix A, stored in the first kd+1 rows of the array. The j-th column of A is stored in the j-th
	       column  of  the	array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j)	 =
	       A(i,j) for j<=i<=min(n,j+kd).  If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1.

       LDAB    (input) INTEGER
	       The leading dimension of the array AB.  LDAB >= KD+1.

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

       WORK    (workspace) COMPLEX array, dimension (2*N)

       RWORK   (workspace) REAL 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 							 CTBCON(l)