Purpose
To estimate the reciprocal of the condition number of a complex upper Hessenberg matrix H, in either the 1-norm or the infinity-norm, using the LU factorization computed by MB02SZ.Specification
SUBROUTINE MB02TZ( NORM, N, HNORM, H, LDH, IPIV, RCOND, DWORK,
$ ZWORK, INFO )
C .. Scalar Arguments ..
CHARACTER NORM
INTEGER INFO, LDH, N
DOUBLE PRECISION HNORM, RCOND
C .. Array Arguments ..
INTEGER IPIV(*)
DOUBLE PRECISION DWORK( * )
COMPLEX*16 H( LDH, * ), ZWORK( * )
Arguments
Mode Parameters
NORM 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.
Input/Output Parameters
N (input) INTEGER
The order of the matrix H. N >= 0.
HNORM (input) DOUBLE PRECISION
If NORM = '1' or 'O', the 1-norm of the original matrix H.
If NORM = 'I', the infinity-norm of the original matrix H.
H (input) COMPLEX*16 array, dimension (LDH,N)
The factors L and U from the factorization H = P*L*U
as computed by MB02SZ.
LDH INTEGER
The leading dimension of the array H. LDH >= max(1,N).
IPIV (input) INTEGER array, dimension (N)
The pivot indices; for 1 <= i <= N, row i of the matrix
was interchanged with row IPIV(i).
RCOND (output) DOUBLE PRECISION
The reciprocal of the condition number of the matrix H,
computed as RCOND = 1/(norm(H) * norm(inv(H))).
Workspace
DWORK DOUBLE PRECISION array, dimension (N) ZWORK COMPLEX*16 array, dimension (2*N)Error Indicator
INFO INTEGER
= 0: successful exit;
< 0: if INFO = -i, the i-th argument had an illegal
value.
Method
An estimate is obtained for norm(inv(H)), and the reciprocal of
the condition number is computed as
RCOND = 1 / ( norm(H) * norm(inv(H)) ).
References
-Numerical Aspects
2 The algorithm requires 0( N ) complex operations.Further Comments
NoneExample
Program Text
NoneProgram Data
NoneProgram Results
None