class QuadraticFit extends AnyRef
The QuadraticFit class uses multiple regression to fit a quadratic surface
to the function 'f'. This is useful when computing 'f' is costly, for example
in simulation optimization. The fit is over a multi-dimensional grid and
can be used for interpolation and limited extrapolation.
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- new QuadraticFit(f: FunctionV2S, n: Int = 3, k: Int = 5)
- f
the vector-to-scalar function to fit.
- n
the dimensionality of the domain of f
- k
the number (odd number) of values for each dimension, e.g., 5, 7, 9
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- def fit(xx: MatriD, yy: VectoD): Unit
Given a data/input matrix and response/output vector, use multiple regression to fit the surface, i.e., determine the coefficients of the regression equation.
Given a data/input matrix and response/output vector, use multiple regression to fit the surface, i.e., determine the coefficients of the regression equation.
- xx
the data/input matrix
- yy
the response/output vector
- def formGrid(xc: VectoD, xs: VectoD): Unit
Given a center point x, form a square grid around it.
Given a center point x, form a square grid around it. This can be used to create a data/input matrix for use in multiple regression.
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- def printGrid(): Unit
Print all the vectors/points in the grid.
- def qForms(x: VectoD): VectoD
Given a vector 'x', compute the values for all of its quadratic, linear and constant forms/terms, returning them as a vector.
Given a vector 'x', compute the values for all of its quadratic, linear and constant forms/terms, returning them as a vector. for 1D: 'VectorD (1., x(0), x(0)~2.)' for 2D: 'VectorD (1., x(0), x(0)~2., x(1), x(1)*x(0), x(1)~^2.)'
- x
the source vector for creating forms/terms
- def qFormsEval(x: VectoD): Double
Given a point x, use the quadratic regression equation to estimate a value for the function at x.
Given a point x, use the quadratic regression equation to estimate a value for the function at x. for 1D: b(0) + b(1)*x(0) + b(2)*x(0)~2. for 2D: b(0) + b(1)*x(0) + b(2)*x(0)~2. + b(3)*x(1) + b(4)*x(1)*x(0) + b(5)*x(1)~^2.
- x
the point whose functional value is to be predicted
- def reduce(): Unit
Reduce from the full model to one with fewer variable.
Reduce from the full model to one with fewer variable. FIX: adjust 'qFormEval' to skip left out variable
- def response(): (MatriD, VectoD)
Given a grid of design points, create a data/input matrix 'xx' and response vector 'yy' returning them as a tuple.
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