ctbcon(3)

NAME

CTBCON - estimate the reciprocal of the condition number

of a triangular band matrix A, in either the 1-norm or the infin

ity-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 com

puted 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 as

sumed 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 ma

trix 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 ille

gal value

LAPACK version 3.0 15 June 2000

CTBCON(3)