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# Differences

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background_polynomial [2011/08/25 07:31] alancoelho |
background_polynomial [2020/07/16 11:29] (current) |
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====== Background Polynomial ====== | ====== Background Polynomial ====== | ||

- | Chebyshev polynomials of the first kind as described at http://mathworld.wolfram.com/ChebyshevPolynomialoftheFirstKind.html is used by default in Topas. The recurrences relations of Eq. (26) can be used with the x axis normalized to be between -1 and 1. | + | Chebyshev polynomials of the first kind as described at http://mathworld.wolfram.com/ChebyshevPolynomialoftheFirstKind.html is used by default in Topas. The recurrences relations of Eq. (26) can be used with the x axis normalized between -1 and 1. |

- | A Chebychev Polynomial, say order 5, written as a fit_obj can be coded as: | + | A Chebychev Polynomial, say order 5, written as: |

+ | | ||

+ | <code topas>bkg @ 359.793901` 140.27403` 67.3210027` 21.057843` 11.3443248` -4.46398819`</code> | ||

+ | | ||

+ | can be coded as a fit_obj as follows: | ||

<code topas>prm c0 359.79390` | <code topas>prm c0 359.79390` | ||

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Note that X1 and X2 are reserved parameter names that correspond to the start and end of the x-axis. | Note that X1 and X2 are reserved parameter names that correspond to the start and end of the x-axis. | ||

- | The attached AAC.INP and data file demonstrates that the fit_obj coefficients after refinement corresponds exactly to those of the bkg Chebychev Polynomial. | + | --- //[[alan.coelho@bigpond.com|Alan Coelho]] 2011/08/25 19:12// |