Solutions

sheet1/G/.vscode/settings.json

@@ -0,0 +1,6 @@
+{
+    "files.associations": {
+        "vector": "cpp",
+        "ostream": "cpp"
+    }
+}

sheet1/G/Makefile

@@ -0,0 +1,30 @@
+#
+# use GNU-Compiler tools
+COMPILER=GCC_
+# alternatively from the shell
+# export COMPILER=GCC_
+# or, alternatively from the shell
+# make COMPILER=GCC_
+
+# use Intel compilers
+#COMPILER=ICC_
+
+# use PGI compilers
+# COMPILER=PGI_
+
+
+SOURCES = main.cpp mylib.cpp
+OBJECTS = $(SOURCES:.cpp=.o)
+
+PROGRAM	= main.${COMPILER}
+
+# uncomment the next to lines for debugging and detailed performance analysis
+CXXFLAGS += -g
+LINKFLAGS += -g
+# do not use -pg with PGI compilers
+
+ifndef COMPILER
+  COMPILER=GCC_
+endif
+
+include ../${COMPILER}default.mk

sheet1/G/main.cpp

@@ -0,0 +1,109 @@
+#include "mylib.h"
+#include <iostream>
+#include <cassert>
+#include <vector>
+using namespace std;
+int main()
+{
+
+    //b)
+    DenseMatrix const M(5,3); // Dense matrix, also initialized
+    vector<double> const u{{1,2,3}};
+    vector<double> f1 = M.Mult(u);
+    vector<double> const v{{-1,2,-3,4,-5}};
+    vector<double> f2 = M.MultT(v);
+
+    for(unsigned int i = 0; i < f1.size(); i++)
+    {
+        cout << f1.at(i) << " ";
+    }
+    cout << endl;
+    for(unsigned int i = 0; i < f2.size(); i++)
+    {
+        cout << f2.at(i) << " ";
+    }
+    cout << endl;
+
+
+    //c)
+    int n=5000;
+    DenseMatrix const A(n,n);
+    vector<double> w = {};
+    for(int i = -n/2; i < n/2; i++)
+    {
+        w.push_back(i);
+    } 
+
+
+    int const NLOOPS=100;
+
+    double t1 = clock(); // start timer
+    vector<double> f3 = A.Mult(w);
+    for (int k=1; k<NLOOPS; ++k)
+    {
+        f3 = A.Mult(w);
+    }
+    t1 = (clock()-t1)/CLOCKS_PER_SEC/NLOOPS;
+    cout << "Time for Mult per it: " << t1 << endl;
+
+    double t2 = clock(); // start timer
+    vector<double> f4 = A.MultT(w);
+    for (int k=1; k<NLOOPS; ++k)
+    {
+        f4 = A.MultT(w);
+    }
+    t2 = (clock()-t2)/CLOCKS_PER_SEC/NLOOPS;
+    cout << "Time for MultT per it: " << t2 << endl; 
+    //slower because consecutive calls to data vector of Matrix are more apart (+m) due to column wise access (non contiguous memory)
+
+    double maxDiff = 0.0;
+    for (size_t i = 0; i < f3.size(); ++i) {
+        double diff = abs(f3[i] - f4[i]);
+        if (diff > maxDiff) {
+            maxDiff = diff;
+        }
+    }
+    cout << "difference f3 and f4: " << maxDiff << endl;
+
+
+    //d)
+    cout << "-----------------DYADIC------------------" <<endl;
+    vector<double> x = {};
+    for(int k=0; k < n; k++)
+    {
+        x.push_back(f(k, n));
+    }
+    Dyadic const D(x,x);
+
+    double t3 = clock(); // start timer
+    vector<double> f5 = D.Mult(w);
+    for (int k=1; k<NLOOPS; ++k)
+    {
+        f5 = D.Mult(w);
+    }
+    t3 = (clock()-t3)/CLOCKS_PER_SEC/NLOOPS;
+    cout << "Time for Mult per it: " << t3 << endl;
+
+    double t4 = clock(); // start timer
+    vector<double> f6 = D.MultT(w);
+    for (int k=1; k<NLOOPS; ++k)
+    {
+        f6 = D.MultT(w);
+    }
+    t4 = (clock()-t4)/CLOCKS_PER_SEC/NLOOPS;
+    cout << "Time for MultT per it: " << t4 << endl; 
+    //slower because consecutive calls to data vector of Matrix are more apart (+m) due to column wise access (non contiguous memory)
+
+    double maxDiff2 = 0.0;
+    for (size_t i = 0; i < f5.size(); ++i) {
+        double diff = abs(f5[i] - f6[i]);
+        if (diff > maxDiff2) {
+            maxDiff2 = diff;
+        }
+    }
+    cout << "difference f5 and f6: " << maxDiff2 << endl;
+
+
+    
+    return 0;
+}

sheet1/G/mylib.cpp

@@ -0,0 +1,109 @@
+#include "mylib.h"
+#include <cmath>
+#include <iostream>
+using namespace std;
+
+double f(unsigned int k, unsigned int nm) {
+    
+    return 1.0 / (1.0 + exp(-(10.0*k/(nm-1)-5)));
+}
+
+DenseMatrix::DenseMatrix(unsigned int n, unsigned int m): n_(n), m_(m), data_(n*m)
+{
+    unsigned int nm = max(n,m);
+    for(unsigned int rowIt = 0; rowIt < n_; rowIt++)
+    {
+        for(unsigned int colIt=0; colIt <m_; colIt++)
+        {
+            data_.at(rowIt*m+colIt) = (f(rowIt,nm)*f(colIt,nm));
+        }
+    }
+}
+
+vector<double> DenseMatrix::Mult(const vector<double> &u) const{
+    if(u.size() !=  m_)
+    {
+        cout << "Dimension mismatch: expected " << m_ << " but got " << u.size() << "!" << endl;
+        return {};
+    }
+    vector<double> f1 = {};
+    double sum;
+    for(unsigned int rowIt = 0; rowIt < n_; rowIt++)
+    {
+        sum = 0;
+        for(unsigned int colIt=0; colIt <m_; colIt++)
+        {
+            sum += data_.at(rowIt*m_+colIt) * u.at(colIt);
+        }
+        f1.push_back(sum);
+    }
+    return f1;
+}
+
+vector<double> DenseMatrix::MultT(const vector<double> &v) const{
+    if(v.size() !=  n_)
+    {
+       cout << "Dimension mismatch: expected " << n_ << " but got " << v.size() << "!" << endl;
+        return {};
+    }
+    vector<double> f2 = {};
+    double sum;
+    for(unsigned int colIt = 0; colIt < m_; colIt++)
+    {
+        sum = 0;
+        for(unsigned int rowIt=0; rowIt <n_; rowIt++)
+        {
+            sum += data_.at(rowIt*m_+colIt) * v.at(rowIt);
+        }
+        f2.push_back(sum);
+    }
+    return f2;
+}
+
+
+//-----------------------------------------------------------------------------------------------
+Dyadic::Dyadic(vector<double>& u, vector<double>& v):u_(u), v_(v){
+
+}
+
+vector<double> Dyadic::Mult(const vector<double> &w) const{
+    unsigned int m = v_.size();
+    if(w.size() !=  m)
+    {
+        cout << "Dimension mismatch!" << endl;
+        return {};
+    }
+    vector<double> f1 = {};
+    double skalar = 0;
+    for(unsigned int vIt = 0; vIt < m; vIt++)
+    {
+        skalar += v_.at(vIt)*w.at(vIt);
+    }
+    for(unsigned int uIt=0; uIt < u_.size(); uIt++)
+    {
+        f1.push_back(u_.at(uIt)*skalar);
+    }
+
+    return f1;
+}
+
+vector<double> Dyadic::MultT(const vector<double> &w) const{
+    unsigned int n = u_.size();
+    if(w.size() !=  n)
+    {
+        cout << "Dimension mismatch!" << endl;
+        return {};
+    }
+    vector<double> f1 = {};
+    double skalar = 0;
+    for(unsigned int uIt = 0; uIt < n; uIt++)
+    {
+        skalar += u_.at(uIt)*w.at(uIt);
+    }
+    for(unsigned int vIt=0; vIt < v_.size(); vIt++)
+    {
+        f1.push_back(v_.at(vIt)*skalar);
+    }
+
+    return f1;
+}

sheet1/G/mylib.h

@@ -0,0 +1,36 @@
+#ifndef MYLIB_H_INCLUDED
+#define MYLIB_H_INCLUDED
+
+#include <vector>
+using namespace std;
+
+double f(unsigned int k, unsigned int nm);
+
+class DenseMatrix{
+
+    public:
+    DenseMatrix(unsigned int n, unsigned int m);
+    
+    vector<double> Mult(const vector<double> &u) const;
+    vector<double> MultT(const vector<double> &v) const;
+
+
+    private:
+    unsigned int n_,m_;
+    vector<double> data_;
+};
+
+class Dyadic{
+    public:
+    Dyadic(vector<double>& u, vector<double>& v);
+    
+    vector<double> Mult(const vector<double> &u) const;
+    vector<double> MultT(const vector<double> &v) const;
+
+
+    private:
+    vector<double> u_;
+    vector<double> v_;
+};
+
+#endif // MYLIB_H_INCLUDED