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: MatrixD, yy: VectorD): Unit
Given a design matrix and response vector, use multiple regression to fit the surface, i.e., determine the coefficients of the regression equation.
Given a design matrix and response vector, use multiple regression to fit the surface, i.e., determine the coefficients of the regression equation.
- xx
the data/design matrix
- yy
the response vector
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def
formGrid(xc: VectorD, xs: VectorD): 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 design matrix for use in multiple regression.
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def
printGrid(): Unit
Print all the vectors/points in the grid.
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def
qForms(x: VectorD): VectorD
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
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def
qFormsEval(x: VectorD): 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
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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
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def
response(): (MatrixD, VectorD)
Given a grid of design points, create a design matrix 'xx' and response vector 'yy' returning them as a tuple.
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