SHOGUN
6.1.3

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Classes  
class  SGVector< T > 
shogun vector More...  
class  CLinearOperator< T > 
Abstract template base class that represents a linear operator, e.g. a matrix. More...  
class  CRationalApproximation 
Abstract base class of the rational approximation of a function of a linear operator (A) times vector (v) using Cauchy's integral formula  \[f(\text{A})\text{v}=\oint_{\Gamma}f(z)(z\text{I}\text{A})^{1} \text{v}dz\] Computes eigenvalues of linear operator and uses Jacobi elliptic functions and conformal maps [2] for quadrature rule for discretizing the contour integral and computes complex shifts, weights and constant multiplier of the rational approximation of the above expression as \[f(\text{A})\text{v}\approx \eta\text{A}\Im\left(\sum_{l=1}^{N}\alpha_{l} (\text{A}\sigma_{l}\text{I})^{1}\text{v}\right)\] where \(\alpha_{l},\sigma_{l}\in\mathbb{C}\) are respectively the shifts and weights of the linear systems generated from the rational approximation, and \(\eta\in\mathbb{R}\) is the constant multiplier, equals to \(\frac{8K(\lambda_{m}\lambda_{M})^{\frac{1}{4}}}{k\pi N}\). More...  