  The condition number of a linear function of the indefinite least squares
solution is called the partial condition number for the indefinite least
squares problem. In this paper, based on a new and very general condition
number which can be called the unified condition number, the expression of the
partial unified condition number is first presented when the data space is
measured by the general weighted product norm. Then, by setting the specific
norms and weight parameters, we obtain the expressions of the partial normwise,
mixed and componentwise condition numbers. Moreover, the corresponding
structured partial condition numbers are also taken into consideration when the
problem is structured, whose expressions are given. Considering the connections
between the indefinite and total least squares problems, we derive the
(structured) partial condition numbers for the latter, which generalize the
ones in the literature. To estimate these condition numbers effectively and
reliably, the probabilistic spectral norm estimator and the small-sample
statistical condition estimation method are applied and three related
algorithms are devised. Finally, the obtained results are illustrated by
numerical experiments.
