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##

fit

**fit data**
Find the best fit model parameters for the current data by minimizing the
current statistic.

**Syntax:** |
**fit** |
`<fit method parameters>` |

The arguments to fit depend on the fitting method currently in use.
See the method command for details (and for the usage of the
USE_NUMERICAL_DIFFERENTIATION option in the user's startup Xspec.init file).
Output from the fit command also depends on the fitting method
currently in use.

Using the Levenberg-Marquardt algorithm, the parameters accepted are the
maximum `<number of iterations>` before the user is prompted, the
`<critical delta>`, which is the (absolute, not fractional) change in
the statistic between iterations less than which the fit is deemed to
have converged, and `<critical beta>`.

The `<critical beta>` provides an optional second stopping criterion,
and it refers to the |beta|/N value reported during a Levenberg-Marquardt
fit. This is the norm of the vector derivatives of the statistic with
respect to the parameters divided by the number of parameters. At the
best fit this should be zero, and so provides another measure of how well
the fit is converging. `<critical beta>` is set to a negative value
by default, which renders it inactive.

Including the string `delay` as an argument to fit turns on delayed
gratification. It is turned off by `nodelay`. Delayed gratification
modifies the way the damping parameter is set and has been shown in many
cases to speed up convergence. The default is `nodelay`.

If `<number of iterations>`, `<critical delta>`, `<critical beta>`,
`delay`, or `nodelay` is entered through the fit
command, it also becomes the future default value for the currently loaded
fit method (ie. Levenberg-Marquardt).

**Examples:**

XSPEC12> fit
// Fit with the default number of iterations and critical delta
// chi-squared.
XSPEC12> fit 60
// Fit with 60 as the number of iterations.
XSPEC12> fit 50 1.e-3
// Fit with 1.e-3 as the critical delta.
XSPEC12> fit 50 1.e-3 20.
// Same fit, but will now use |beta|/N = 20.0 as another stopping criterion in addition
// to that of the critical delta.
XSPEC12> fit delay
// Same fit, but will now use delayed gratification.

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