npstat::QuadraticOrthoPolyND Class Reference
Detailed DescriptionClass for figuring out the coefficients of multivariate quadratic orthogonal polynomials generated with an arbitrary weight functions Constructor & Destructor Documentation◆ QuadraticOrthoPolyND()
"weight" is the weigh function used to build the orthogonal polynomials. "nSteps" is the number of integration intervals in each dimension (numerical integration is used for orthogonalization of the basis polynomials and for subsequent construction of polynomial series). "nStepsDim" is the number of elements in the "nSteps" array and also the dimensionality of the coordinate space. The integration region is defined by the "boundingBox" argument whose dimensionality must be consistent with "nStepsDim". Integration will be performed by simply evaluating the functions at the interval centers. Use a sufficiently large number of integration points if high precision is desired. Member Function Documentation◆ dim()
Inspect object properties ◆ fit()
template<class T , typename Numeric >
The following method fits orthogonal polynomial series to an object which has its own method with signature "Numeric method(const double* x, unsigned dimX) const". The arguments which will be fed into this method will be shifted and scaled from the box coordinates according to x[i] = (boxCoordinate[i] - location[i])/scale[i]. It must be possible to perform a static cast from "Numeric" to double. "nCoeffs" can have multiple values, as in the "series" method. The bounding box and the number of integration intervals are assumed to be the same as in the constructor. ◆ gradient()
The gradient of the series expansion. The size of the result array must be equal to "dim()". Note that the code does not check whether the coordinate is inside the original box. ◆ hessian()
The hessian of the series expansion. The size of the result array must be equal to "dim()*(dim()+1)/2". Hessian matrix is returned in the upper-trangular form. The result is, of course, coordinate-independent. ◆ monomialCoefficient()
Coefficient in the expansion of the orthogonal series polynomial in the monomial basis. The order of the monomials is 1, x0, x1, ..., xN, x0^2, x0*x1, ..., x0*xN, x1^2, x1*x2, ... The number of the polynomials is, of course, the same as the number of monomials and equals "nTerms()". ◆ series()
Series expansion at the given coordinate "x". The number of coefficients provided, nCoeffs, is allowed to take the following values: 1 – just return the constant term dim() + 1 – use linear terms only nTerms() – use the full expansion Note that the code does not check whether the coordinate is inside the original box. If the "individualPolynomials" array is not 0, the values of the individual polynomials will be stored there. They represent the gradient of the series expansion at the given point with respect to the series coefficients. There must be at least nCoeffs elements in the "individualPolynomials" array. ◆ value()
Value of a certain polynomial at the given coordinate "x". The argument "polyN" is the polynomial number which should be less than "nTerms()". Note that the code does not check whether the coordinate is inside the original box. The documentation for this class was generated from the following file: Generated by  1.9.1
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