.. _method-multilevel_function_train-collocation_ratio:

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collocation_ratio
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Set the number of points used to build a PCE via regression to be proportional to the number of terms in the expansion.


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**Specification**

- *Alias:* None

- *Arguments:* REAL

- *Default:* 0.


**Description**


Set the number of points used to build a PCE via regression to be proportional to the number of terms in the expansion. To avoid requiring the user to calculate N from n and p, the collocation_ratio allows for specification of a constant factor applied to N (e.g., collocation_ratio = 2. produces samples = 2N). In addition, the default linear relationship with N can be overridden using a real-valued exponent specified using ratio_order. In this case, the number of samples becomes :math:`cN^o`  where :math:`c`  is the collocation_ratio and :math:`o`  is the ratio_order. The use_derivatives flag informs the regression approach to include derivative matching equations (limited to gradients at present) in the least squares solutions, enabling the use of fewer collocation points for a given expansion order and dimension (number of points required becomes :math:`\frac{cN^o}{n+1}` ).