LegendreBasis¶
This is an introduction to the LegendreBasis class. We write a small overarching summary of the class where we define the algorithm/equation/structure reasoning for having this class or where it fits with the rest of the code.
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class LegendreBasis : public mrcpp::ScalingBasis
Legendre scaling functions as defined by Alpert, SIAM J Math Anal 24 (1), 246 (1993).
Public Functions
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inline LegendreBasis(int k)
- Parameters:
k – [in] Polynomial order of basis,
1 < k < 40
- Returns:
New LegendreBasis object
Private Functions
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void initScalingBasis()¶
Initialise Legendre scaling basis.
Fills std::vector<Polynomial> funcs declared in the base class ScalingBasis with the Legendre scaling functions
\[ \phi_j(x) = \sqrt{ 2j + 1 } P_j(2x - 1) , \quad x \in (0, 1) , \quad j = 0, \ldots, k , \]where \( P_j \) are standard Legendre polynomials. Here \( k \) is order declared in the base class.Note
These Legendre scaling functions are defined on the unit interval \( (0, 1) \).
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void calcQuadratureValues()¶
In Progress by Evgueni…
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void calcCVMaps()¶
In Progress by Evgueni…
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inline LegendreBasis(int k)