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Imports: Float64, sum, transpose, zeros
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Function to calculate the chi-squared value. The chi-sqared equation ~~~~~~~~~~~~~~~~~~~~~~~ _n_ \ (yi - yi()) ** 2 Chi2 = > ---------------- /__ sigma_i ** 2 i=1 where: yi are the values of the measured data set. yi() are the values of the back calculated data set. sigma_i are the values of the error set. The chi-squared value is returned. |
Function to create the chi-squared gradient. The chi-sqared gradient ~~~~~~~~~~~~~~~~~~~~~~~ _n_ dChi2 \ / yi - yi() dyi() \ ------- = -2 > | ---------- . ------- | dthetaj /__ \ sigma_i**2 dthetaj / i=1 where: yi are the values of the measured data set. yi() are the values of the back calculated data set. sigma_i are the values of the error set. The chi-squared gradient vector is returned. |
Function to create the chi-squared Hessian. The chi-squared Hessian ~~~~~~~~~~~~~~~~~~~~~~~ _n_ d2chi2 \ 1 / dyi() dyi() d2yi() \ --------------- = 2 > ---------- | ------- . ------- - (yi - yi()) . --------------- | dthetaj.dthetak /__ sigma_i**2 \ dthetaj dthetak dthetaj.dthetak / i=1 where: yi are the values of the measured relaxation data set. yi() are the values of the back calculated relaxation data set. sigma_i are the values of the error set. |
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