.. _method-bayes_calibration-queso-emulator-pce-expansion_order-collocation_points:

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collocation_points
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Number of collocation points used to estimate expansion coefficients


.. toctree::
   :hidden:
   :maxdepth: 1

   method-bayes_calibration-queso-emulator-pce-expansion_order-collocation_points-least_squares
   method-bayes_calibration-queso-emulator-pce-expansion_order-collocation_points-orthogonal_matching_pursuit
   method-bayes_calibration-queso-emulator-pce-expansion_order-collocation_points-basis_pursuit
   method-bayes_calibration-queso-emulator-pce-expansion_order-collocation_points-basis_pursuit_denoising
   method-bayes_calibration-queso-emulator-pce-expansion_order-collocation_points-least_angle_regression
   method-bayes_calibration-queso-emulator-pce-expansion_order-collocation_points-least_absolute_shrinkage
   method-bayes_calibration-queso-emulator-pce-expansion_order-collocation_points-cross_validation
   method-bayes_calibration-queso-emulator-pce-expansion_order-collocation_points-ratio_order
   method-bayes_calibration-queso-emulator-pce-expansion_order-collocation_points-response_scaling
   method-bayes_calibration-queso-emulator-pce-expansion_order-collocation_points-use_derivatives
   method-bayes_calibration-queso-emulator-pce-expansion_order-collocation_points-tensor_grid
   method-bayes_calibration-queso-emulator-pce-expansion_order-collocation_points-reuse_points
   method-bayes_calibration-queso-emulator-pce-expansion_order-collocation_points-max_solver_iterations


**Specification**

- *Alias:* None

- *Arguments:* INTEGER


**Child Keywords:**

+-------------------------+--------------------+---------------------------------+---------------------------------------------+
| Required/Optional       | Description of     | Dakota Keyword                  | Dakota Keyword Description                  |
|                         | Group              |                                 |                                             |
+=========================+====================+=================================+=============================================+
| Optional (Choose One)   | Regression         | `least_squares`__               | Compute the coefficients of a polynomial    |
|                         | Algorithm          |                                 | expansion using least squares               |
|                         |                    +---------------------------------+---------------------------------------------+
|                         |                    | `orthogonal_matching_pursuit`__ | Compute the coefficients of a polynomial    |
|                         |                    |                                 | expansion using orthogonal matching pursuit |
|                         |                    |                                 | (OMP)                                       |
|                         |                    +---------------------------------+---------------------------------------------+
|                         |                    | `basis_pursuit`__               | Compute the coefficients of a polynomial    |
|                         |                    |                                 | expansion by solving the Basis Pursuit      |
|                         |                    |                                 | :math:`\ell_1` -minimization problem using  |
|                         |                    |                                 | linear programming.                         |
|                         |                    +---------------------------------+---------------------------------------------+
|                         |                    | `basis_pursuit_denoising`__     | Compute the coefficients of a polynomial    |
|                         |                    |                                 | expansion by solving the Basis Pursuit      |
|                         |                    |                                 | Denoising :math:`\ell_1` -minimization      |
|                         |                    |                                 | problem using second order cone             |
|                         |                    |                                 | optimization.                               |
|                         |                    +---------------------------------+---------------------------------------------+
|                         |                    | `least_angle_regression`__      | Compute the coefficients of a polynomial    |
|                         |                    |                                 | expansion by using the greedy least angle   |
|                         |                    |                                 | regression (LAR) method.                    |
|                         |                    +---------------------------------+---------------------------------------------+
|                         |                    | `least_absolute_shrinkage`__    | Compute the coefficients of a polynomial    |
|                         |                    |                                 | expansion by using the LASSO problem.       |
+-------------------------+--------------------+---------------------------------+---------------------------------------------+
| Optional                                     | `cross_validation`__            | Use cross validation to choose the 'best'   |
|                                              |                                 | polynomial order of a polynomial chaos      |
|                                              |                                 | expansion.                                  |
+----------------------------------------------+---------------------------------+---------------------------------------------+
| Optional                                     | `ratio_order`__                 | Specify a non-linear the relationship       |
|                                              |                                 | between the expansion order of a polynomial |
|                                              |                                 | chaos expansion and the number of samples   |
|                                              |                                 | that will be used to compute the PCE        |
|                                              |                                 | coefficients.                               |
+----------------------------------------------+---------------------------------+---------------------------------------------+
| Optional                                     | `response_scaling`__            | Perform bounds-scaling on response values   |
|                                              |                                 | prior to surrogate emulation                |
+----------------------------------------------+---------------------------------+---------------------------------------------+
| Optional                                     | `use_derivatives`__             | Use derivative data to construct surrogate  |
|                                              |                                 | models                                      |
+----------------------------------------------+---------------------------------+---------------------------------------------+
| Optional                                     | `tensor_grid`__                 | Use sub-sampled tensor-product quadrature   |
|                                              |                                 | points to build a polynomial chaos          |
|                                              |                                 | expansion.                                  |
+----------------------------------------------+---------------------------------+---------------------------------------------+
| Optional                                     | `reuse_points`__                | This describes the behavior of reuse of     |
|                                              |                                 | points in constructing polynomial chaos     |
|                                              |                                 | expansion models.                           |
+----------------------------------------------+---------------------------------+---------------------------------------------+
| Optional                                     | `max_solver_iterations`__       | Maximum iterations in determining           |
|                                              |                                 | polynomial coefficients                     |
+----------------------------------------------+---------------------------------+---------------------------------------------+

.. __: method-bayes_calibration-queso-emulator-pce-expansion_order-collocation_points-least_squares.html
__ method-bayes_calibration-queso-emulator-pce-expansion_order-collocation_points-orthogonal_matching_pursuit.html
__ method-bayes_calibration-queso-emulator-pce-expansion_order-collocation_points-basis_pursuit.html
__ method-bayes_calibration-queso-emulator-pce-expansion_order-collocation_points-basis_pursuit_denoising.html
__ method-bayes_calibration-queso-emulator-pce-expansion_order-collocation_points-least_angle_regression.html
__ method-bayes_calibration-queso-emulator-pce-expansion_order-collocation_points-least_absolute_shrinkage.html
__ method-bayes_calibration-queso-emulator-pce-expansion_order-collocation_points-cross_validation.html
__ method-bayes_calibration-queso-emulator-pce-expansion_order-collocation_points-ratio_order.html
__ method-bayes_calibration-queso-emulator-pce-expansion_order-collocation_points-response_scaling.html
__ method-bayes_calibration-queso-emulator-pce-expansion_order-collocation_points-use_derivatives.html
__ method-bayes_calibration-queso-emulator-pce-expansion_order-collocation_points-tensor_grid.html
__ method-bayes_calibration-queso-emulator-pce-expansion_order-collocation_points-reuse_points.html
__ method-bayes_calibration-queso-emulator-pce-expansion_order-collocation_points-max_solver_iterations.html



**Description**


Specify the number of collocation points used to estimate expansion coefficients
using regression approaches.

A corresponding sequence specification is documented at, e.g.,
:ref:`method-multifidelity_polynomial_chaos-expansion_order_sequence-collocation_ratio-collocation_points_sequence<method-multifidelity_polynomial_chaos-expansion_order_sequence-collocation_ratio-collocation_points_sequence>` and
:ref:`method-multilevel_polynomial_chaos-expansion_order_sequence-collocation_ratio-collocation_points_sequence<method-multilevel_polynomial_chaos-expansion_order_sequence-collocation_ratio-collocation_points_sequence>`