113 lines
3.0 KiB
C++
113 lines
3.0 KiB
C++
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// Copyright 2005, Ondra Kamenik
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// Product quadrature.
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/* This file defines a product multidimensional quadrature. If $Q_k$
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denotes the one dimensional quadrature, then the product quadrature
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$Q$ of $k$ level and dimension $d$ takes the form
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$$Qf=\sum_{i_1=1}^{n_k}\ldots\sum_{i_d=1}^{n^k}w_{i_1}\cdot\ldots\cdot w_{i_d}
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f(x_{i_1},\ldots,x_{i_d})$$
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which can be written in terms of the one dimensional quadrature $Q_k$ as
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$$Qf=(Q_k\otimes\ldots\otimes Q_k)f$$
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Here we define the product quadrature iterator |prodpit| and plug it
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into |QuadratureImpl| to obtains |ProductQuadrature|. */
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#ifndef PRODUCT_H
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#define PRODUCT_H
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#include "int_sequence.h"
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#include "vector_function.hh"
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#include "quadrature.hh"
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/* This defines a product point iterator. We have to maintain the
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following: a pointer to product quadrature in order to know the
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dimension and the underlying one dimensional quadrature, then level,
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number of points in the level, integer sequence of indices, signal,
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the coordinates of the point and the weight.
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The point indices, signal, and point coordinates are implmented as
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pointers in order to allow for empty constructor.
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The constructor |prodpit(const ProductQuadrature& q, int j0, int l)|
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constructs an iterator pointing to $(j0,0,\ldots,0)$, which is used by
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|begin| dictated by |QuadratureImpl|. */
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class ProductQuadrature;
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class prodpit
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{
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protected:
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const ProductQuadrature *prodq;
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int level;
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int npoints;
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IntSequence *jseq;
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bool end_flag;
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ParameterSignal *sig;
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Vector *p;
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double w;
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public:
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prodpit();
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prodpit(const ProductQuadrature &q, int j0, int l);
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prodpit(const prodpit &ppit);
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~prodpit();
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bool operator==(const prodpit &ppit) const;
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bool
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operator!=(const prodpit &ppit) const
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{
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return !operator==(ppit);
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}
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const prodpit &operator=(const prodpit &spit);
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prodpit &operator++();
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const ParameterSignal &
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signal() const
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{
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return *sig;
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}
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const Vector &
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point() const
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{
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return *p;
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}
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double
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weight() const
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{
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return w;
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}
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void print() const;
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protected:
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void setPointAndWeight();
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};
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/* The product quadrature is just |QuadratureImpl| with the product
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iterator plugged in. The object is constructed by just giving the
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underlying one dimensional quadrature, and the dimension. The only
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extra method is |designLevelForEvals| which for the given maximum
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number of evaluations (and dimension and underlying quadrature from
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the object) returns a maximum level yeilding number of evaluations
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less than the given number. */
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class ProductQuadrature : public QuadratureImpl<prodpit>
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{
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friend class prodpit;
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const OneDQuadrature &uquad;
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public:
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ProductQuadrature(int d, const OneDQuadrature &uq);
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virtual ~ProductQuadrature()
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{
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}
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int
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numEvals(int l) const
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{
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int res = 1;
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for (int i = 0; i < dimen(); i++)
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res *= uquad.numPoints(l);
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return res;
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}
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void designLevelForEvals(int max_eval, int &lev, int &evals) const;
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protected:
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prodpit begin(int ti, int tn, int level) const;
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};
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#endif
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