mirror of
https://github.com/aportelli/LatAnalyze.git
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significant optimisation of covariance routines + checks
This commit is contained in:
parent
c796187d1e
commit
57c6004797
@ -20,7 +20,8 @@ noinst_PROGRAMS = \
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exPValue \
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exRand \
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exRootFinder \
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exThreadPool
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exThreadPool \
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exVarBenchmark
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exCompiledDoubleFunction_SOURCES = exCompiledDoubleFunction.cpp
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exCompiledDoubleFunction_CXXFLAGS = $(COM_CXXFLAGS)
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@ -78,4 +79,8 @@ exThreadPool_SOURCES = exThreadPool.cpp
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exThreadPool_CXXFLAGS = $(COM_CXXFLAGS)
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exThreadPool_LDFLAGS = -L../lib/.libs -lLatAnalyze
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exVarBenchmark_SOURCES = exVarBenchmark.cpp
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exVarBenchmark_CXXFLAGS = $(COM_CXXFLAGS)
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exVarBenchmark_LDFLAGS = -L../lib/.libs -lLatAnalyze
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ACLOCAL_AMFLAGS = -I .buildutils/m4
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119
examples/exVarBenchmark.cpp
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119
examples/exVarBenchmark.cpp
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@ -0,0 +1,119 @@
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#include <LatAnalyze/Io/Io.hpp>
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#include <LatAnalyze/Functional/CompiledFunction.hpp>
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#include <LatAnalyze/Core/Plot.hpp>
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#include <LatAnalyze/Statistics/Random.hpp>
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#include <LatAnalyze/Statistics/MatSample.hpp>
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using namespace std;
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using namespace Latan;
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constexpr Index size = 1000;
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constexpr Index nSample = 2000;
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int main(void)
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{
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random_device rd;
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DMat var(size, size);
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DVec mean(size);
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DMatSample sample(nSample, size, 1), sample2(nSample, size, 1);
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cout << "-- generating " << nSample << " Gaussian random vectors..." << endl;
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var = DMat::Random(size, size);
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var *= var.adjoint();
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mean = DVec::Random(size);
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RandomNormal mgauss(mean, var, rd());
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sample[central] = mgauss();
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FOR_STAT_ARRAY(sample, s)
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{
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sample[s] = mgauss();
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}
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sample2[central] = mgauss();
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FOR_STAT_ARRAY(sample, s)
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{
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sample2[s] = mgauss();
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}
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cout << "-- check new routines" << endl;
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DMat v, vo;
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cout << "var" << endl;
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auto start = chrono::high_resolution_clock::now();
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vo = sample.varianceOld();
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auto end = chrono::high_resolution_clock::now();
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chrono::duration<double> diff = end - start;
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cout << "time " << diff.count() << endl;
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start = chrono::high_resolution_clock::now();
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v = sample.variance();
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end = chrono::high_resolution_clock::now();
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diff = end - start;
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cout << "time " << diff.count() << endl;
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cout << "diff " << (v - vo).norm() << endl;
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cout << "cov" << endl;
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start = chrono::high_resolution_clock::now();
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vo = sample.covarianceOld(sample2);
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end = chrono::high_resolution_clock::now();
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diff = end - start;
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cout << "time " << diff.count() << endl;
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start = chrono::high_resolution_clock::now();
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v = sample.covariance(sample2);
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end = chrono::high_resolution_clock::now();
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diff = end - start;
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cout << "time " << diff.count() << endl;
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cout << "diff " << (v - vo).norm() << endl;
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cout << "mean" << endl;
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start = chrono::high_resolution_clock::now();
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vo = sample.meanOld(3, 5);
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end = chrono::high_resolution_clock::now();
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diff = end - start;
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cout << "time " << diff.count() << endl;
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start = chrono::high_resolution_clock::now();
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v = sample.mean(3, 5);
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end = chrono::high_resolution_clock::now();
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diff = end - start;
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cout << "time " << diff.count() << endl;
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cout << "diff " << (v - vo).norm() << endl;
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cout << "varmat" << endl;
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start = chrono::high_resolution_clock::now();
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vo = sample.varianceMatrixOld();
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end = chrono::high_resolution_clock::now();
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diff = end - start;
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cout << "time " << diff.count() << endl;
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start = chrono::high_resolution_clock::now();
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v = sample.varianceMatrix();
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end = chrono::high_resolution_clock::now();
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diff = end - start;
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cout << "time " << diff.count() << endl;
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cout << "diff " << (v - vo).norm() << endl;
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cout << "covarmat" << endl;
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start = chrono::high_resolution_clock::now();
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vo = sample.covarianceMatrixOld(sample2);
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end = chrono::high_resolution_clock::now();
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diff = end - start;
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cout << "time " << diff.count() << endl;
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start = chrono::high_resolution_clock::now();
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v = sample.covarianceMatrix(sample2);
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end = chrono::high_resolution_clock::now();
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diff = end - start;
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cout << "time " << diff.count() << endl;
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cout << "diff " << (v - vo).norm() << endl;
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cout << "corrmat" << endl;
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start = chrono::high_resolution_clock::now();
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vo = sample.correlationMatrixOld();
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end = chrono::high_resolution_clock::now();
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diff = end - start;
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cout << "time " << diff.count() << endl;
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start = chrono::high_resolution_clock::now();
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v = sample.correlationMatrix();
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end = chrono::high_resolution_clock::now();
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diff = end - start;
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cout << "time " << diff.count() << endl;
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cout << "diff " << (v - vo).norm() << endl;
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return EXIT_SUCCESS;
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}
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@ -103,6 +103,10 @@ public:
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const Index nCol);
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// resize all matrices
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void resizeMat(const Index nRow, const Index nCol);
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// covariance matrix
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Mat<T> covarianceMatrix(const MatSample<T> &sample) const;
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Mat<T> varianceMatrix(void) const;
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Mat<T> correlationMatrix(void) const;
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};
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// non-member operators
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@ -379,6 +383,78 @@ void MatSample<T>::resizeMat(const Index nRow, const Index nCol)
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}
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}
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// covariance matrix ///////////////////////////////////////////////////////////
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template <typename T>
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Mat<T> MatSample<T>::covarianceMatrix(const MatSample<T> &sample) const
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{
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if (((*this)[central].cols() != 1) or (sample[central].cols() != 1))
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{
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LATAN_ERROR(Size, "samples have more than one column");
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}
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Index n1 = (*this)[central].rows(), n2 = sample[central].rows();
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Index nSample = this->size();
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Mat<T> tmp1(n1, nSample), tmp2(n2, nSample), res(n1, n2);
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Mat<T> s1(n1, 1), s2(n2, 1), one(nSample, 1);
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one.fill(1.);
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s1.fill(0.);
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s2.fill(0.);
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for (unsigned int s = 0; s < nSample; ++s)
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{
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s1 += (*this)[s];
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tmp1.col(s) = (*this)[s];
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}
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tmp1 -= s1*one.transpose()/static_cast<double>(nSample);
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for (unsigned int s = 0; s < nSample; ++s)
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{
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s2 += sample[s];
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tmp2.col(s) = sample[s];
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}
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tmp2 -= s2*one.transpose()/static_cast<double>(nSample);
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res = tmp1*tmp2.transpose()/static_cast<double>(nSample - 1);
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return res;
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}
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template <typename T>
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Mat<T> MatSample<T>::varianceMatrix(void) const
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{
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if ((*this)[central].cols() != 1)
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{
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LATAN_ERROR(Size, "samples have more than one column");
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}
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Index n1 = (*this)[central].rows();
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Index nSample = this->size();
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Mat<T> tmp1(n1, nSample), res(n1, n1);
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Mat<T> s1(n1, 1), one(nSample, 1);
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one.fill(1.);
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s1.fill(0.);
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for (unsigned int s = 0; s < nSample; ++s)
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{
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s1 += (*this)[s];
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tmp1.col(s) = (*this)[s];
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}
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tmp1 -= s1*one.transpose()/static_cast<double>(nSample);
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res = tmp1*tmp1.transpose()/static_cast<double>(nSample - 1);
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return res;
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}
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template <typename T>
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Mat<T> MatSample<T>::correlationMatrix(void) const
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{
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Mat<T> res = varianceMatrix();
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Mat<T> invDiag(res.rows(), 1);
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invDiag = res.diagonal();
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invDiag = invDiag.cwiseInverse().cwiseSqrt();
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res = (invDiag*invDiag.transpose()).cwiseProduct(res);
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return res;
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}
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END_LATAN_NAMESPACE
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@ -51,14 +51,17 @@ public:
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const T & operator[](const Index s) const;
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// statistics
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void bin(Index binSize);
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T sum(const Index pos = 0, const Index n = -1) const;
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T meanOld(const Index pos = 0, const Index n = -1) const;
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T mean(const Index pos = 0, const Index n = -1) const;
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T covariance(const StatArray<T, os> &array, const Index pos = 0,
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const Index n = -1) const;
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T covarianceMatrix(const StatArray<T, os> &array, const Index pos = 0,
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T covarianceOld(const StatArray<T, os> &array) const;
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T covariance(const StatArray<T, os> &array) const;
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T covarianceMatrixOld(const StatArray<T, os> &array, const Index pos = 0,
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const Index n = -1) const;
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T variance(const Index pos = 0, const Index n = -1) const;
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T varianceMatrix(const Index pos = 0, const Index n = -1) const;
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T correlationMatrix(const Index pos = 0, const Index n = -1) const;
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T varianceOld(void) const;
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T variance(void) const;
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T varianceMatrixOld(const Index pos = 0, const Index n = -1) const;
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T correlationMatrixOld(const Index pos = 0, const Index n = -1) const;
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// IO type
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virtual IoType getType(void) const;
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public:
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@ -66,7 +69,7 @@ public:
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};
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// reduction operations
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namespace ReducOp
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namespace StatOp
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{
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// general templates
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template <typename T>
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@ -149,42 +152,82 @@ void StatArray<T, os>::bin(Index binSize)
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}
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template <typename T, Index os>
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T StatArray<T, os>::mean(const Index pos, const Index n) const
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T StatArray<T, os>::meanOld(const Index pos, const Index n) const
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{
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T result = T();
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const Index m = (n >= 0) ? n : size();
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if (m)
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{
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result = this->segment(pos+os, m).redux(&ReducOp::sum<T>);
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result = this->segment(pos+os, m).redux(&StatOp::sum<T>);
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}
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return result/static_cast<double>(m);
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}
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template <typename T, Index os>
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T StatArray<T, os>::covariance(const StatArray<T, os> &array, const Index pos,
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const Index n) const
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T StatArray<T, os>::sum(const Index pos, const Index n) const
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{
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T result;
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const Index m = (n >= 0) ? n : size();
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result = (*this)[pos];
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for (Index i = pos + 1; i < pos + m; ++i)
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{
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result += (*this)[i];
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}
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return result;
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}
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template <typename T, Index os>
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T StatArray<T, os>::mean(const Index pos, const Index n) const
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{
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const Index m = (n >= 0) ? n : size();
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return sum(pos, n)/static_cast<double>(m);
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}
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template <typename T, Index os>
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T StatArray<T, os>::covarianceOld(const StatArray<T, os> &array) const
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{
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T s1, s2, prs, res = T();
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const Index m = (n >= 0) ? n : size();
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const Index m = size();
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if (m)
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{
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auto arraySeg = array.segment(pos+os, m);
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auto thisSeg = this->segment(pos+os, m);
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auto arraySeg = array.segment(os, m);
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auto thisSeg = this->segment(os, m);
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s1 = thisSeg.redux(&ReducOp::sum<T>);
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s2 = arraySeg.redux(&ReducOp::sum<T>);
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prs = thisSeg.binaryExpr(arraySeg, &ReducOp::prod<T>)
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.redux(&ReducOp::sum<T>);
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res = prs - ReducOp::prod(s1, s2)/static_cast<double>(m);
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s1 = thisSeg.redux(&StatOp::sum<T>);
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s2 = arraySeg.redux(&StatOp::sum<T>);
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prs = thisSeg.binaryExpr(arraySeg, &StatOp::prod<T>)
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.redux(&StatOp::sum<T>);
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res = prs - StatOp::prod(s1, s2)/static_cast<double>(m);
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}
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return res/static_cast<double>(m - 1);
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}
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template <typename T, Index os>
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T StatArray<T, os>::covarianceMatrix(const StatArray<T, os> &array,
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T StatArray<T, os>::covariance(const StatArray<T, os> &array) const
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{
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T s1, s2, res;
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s1 = array.sum();
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s2 = this->sum();
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res = StatOp::prod<T>(array[0], (*this)[0]);
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for (Index i = 1; i < size(); ++i)
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{
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res += StatOp::prod<T>(array[i], (*this)[i]);
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}
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res -= StatOp::prod<T>(s1, s2)/static_cast<double>(size());
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res /= static_cast<double>(size() - 1);
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return res;
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}
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template <typename T, Index os>
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T StatArray<T, os>::covarianceMatrixOld(const StatArray<T, os> &array,
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const Index pos, const Index n) const
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{
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T s1, s2, prs, res = T();
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@ -195,32 +238,38 @@ T StatArray<T, os>::covarianceMatrix(const StatArray<T, os> &array,
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auto arraySeg = array.segment(pos+os, m);
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auto thisSeg = this->segment(pos+os, m);
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s1 = thisSeg.redux(&ReducOp::sum<T>);
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s2 = arraySeg.redux(&ReducOp::sum<T>);
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prs = thisSeg.binaryExpr(arraySeg, &ReducOp::tensProd<T>)
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.redux(&ReducOp::sum<T>);
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res = prs - ReducOp::tensProd(s1, s2)/static_cast<double>(m);
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s1 = thisSeg.redux(&StatOp::sum<T>);
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s2 = arraySeg.redux(&StatOp::sum<T>);
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prs = thisSeg.binaryExpr(arraySeg, &StatOp::tensProd<T>)
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.redux(&StatOp::sum<T>);
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res = prs - StatOp::tensProd(s1, s2)/static_cast<double>(m);
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}
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return res/static_cast<double>(m - 1);
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}
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template <typename T, Index os>
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T StatArray<T, os>::variance(const Index pos, const Index n) const
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T StatArray<T, os>::variance(void) const
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{
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return covariance(*this, pos, n);
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return covariance(*this);
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}
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template <typename T, Index os>
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T StatArray<T, os>::varianceMatrix(const Index pos, const Index n) const
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T StatArray<T, os>::varianceOld(void) const
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{
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return covarianceMatrix(*this, pos, n);
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return covarianceOld(*this);
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}
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template <typename T, Index os>
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T StatArray<T, os>::correlationMatrix(const Index pos, const Index n) const
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T StatArray<T, os>::varianceMatrixOld(const Index pos, const Index n) const
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{
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T res = varianceMatrix(pos, n);
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return covarianceMatrixOld(*this, pos, n);
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}
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template <typename T, Index os>
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T StatArray<T, os>::correlationMatrixOld(const Index pos, const Index n) const
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{
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T res = varianceMatrixOld(pos, n);
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T invDiag(res.rows(), 1);
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invDiag = res.diagonal();
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@ -231,8 +280,14 @@ T StatArray<T, os>::correlationMatrix(const Index pos, const Index n) const
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}
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// reduction operations ////////////////////////////////////////////////////////
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namespace ReducOp
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namespace StatOp
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{
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template <typename T>
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inline void zero(T &a)
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{
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a = 0.;
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}
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template <typename T>
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inline T sum(const T &a, const T &b)
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{
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