C++

A brief introduction to features of C++ that are not found in C, using C++11 features where possible. We will assume the following #includes in the code snippets. As usual, we will exclude classes and any discussion of object-oriented programming.

#include <iostream>
#include <vector>
#include <unordered_map>
#include <algorithm>
#include <numeric>
#include <iterator>
#include "/usr/local/include/armadillo"

Hello, world

Note the use of the iostream library and the standard namepace qualification std::cout.

int main()
{
    std::cout << "Hello, world!\n";
}

Output

Hello, world!

Namespaces

Just like Python, C++ has namespaces that allow us to build large libraries without worrying about name collisions. In the Hello world program, we used the explicit name std::cout indicating that cout is a member of the standard workspace. We can also use the using keyword to import selected functions or classes from a namespace.

using std::cout;

int main()
{
    cout << "Hello, world!\n";
}

For small programs, we sometimes import the entire namespace for convenience, but this may cause namespace collisions in larger programs.

using namespace std;

int main()
{
    cout << "Hello, world!\n";
}

You can easily create your own namespace.

namespace sta_663 {
    const double pi=2.14159;

    void greet(string name) {
        cout << "\nTraditional first program\n";
        cout << "Hello, " << name << "\n";
    }
}

int main()
{
    cout << "\nUsing namespaces\n";
    string name = "Tom";
    cout << sta_663::pi << "\n";
    sta_663::greet(name);
}

Output

Using namespaces
2.14159

Traditional first program
Hello, Tom

Looping

Note the traditional for loop and the new range for loop. There is also a while loop (not shown).

// for loops
int main()
{
    int x[] = {1, 2, 3, 4, 5};

    cout << "\nTraditional for loop\n";
    for (int i=0; i < sizeof(x)/sizeof(x[0]); i++) {
        cout << i << endl;
    }

    cout << "\nRanged for loop\n\n";
    for (auto &i : x) {
        cout << i << endl;
    }
}

Output

Traditional for loop
0
1
2
3
4

Ranged for loop

1
2
3
4
5

Exercise 1

Use loop to generate the 12 by 12 times table. Compile and run. You don’t have to worry much about formatting, but the output should have 12 rows with numbers separated by spaces.

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Functions and Lambdas

// simple function
int add0(int a, int b) {
    return a + b;
}

// simple function with reference variables
void add1(int a, int b, int& c) {
    c = a + b;
}

// When to use values and when to use refernces in function arguments?

// Use values when the variable is small (e.g. a double)
double f1(double x) { return 2 * x; };

// Use const references when the variable is large to avoid copying
double f2(const vector<dohble>& v) {
    double s = 0.0;
    for (auto x: v) {
        s += x;
    }
    return s;
}

// Use references when you want to change the variable within the function
void f3(vector<double>& v) {
    for (auto& x: v) {
      x++;
    }
}

// lambda function
auto add2 = [] (int a, int b) { return a + b; };

int main() {

    cout << "\nStandard function\n";
    int a = 3, b = 4;
    cout << add0(a, b) <<  endl;

    int c = 0;
    cout << "\nStandard with reference varaibles\n";

    add1(a, b, c);
    cout << c <<  endl;

    cout << "\nLambda function\n";
    cout << add2(a, b) <<  endl;

    auto add3 = [c] (int a, int b) { return c * add2(a, b); };

    c -= 5;
    cout << "\nLambda function with value capture\n";
    cout << add3(a, b) <<  endl;

    auto add4 = [&c] (int a, int b) { return c * add2(a, b); };

    cout << "\nLambda function with reference capture\n";
    cout << add4(a, b) <<  endl;

}

Output

Standard function
7

Standard with reference varaibles
7

Lambda function
7

Lambda function with value capture
49

Lambda function with reference capture
14

Templates

// templates
template <typename T>
T add5(T a, T b) { return a + b; }

int main()
{

    cout << "\nTemplate function with ints\n";
    cout << add5(3, 4) << endl;

    cout << "\nTemplate function with doubles\n";
    cout << add5(3.14, 2.78) << endl;
}

Output

Template function with ints
7

Template function with doubles
5.92

Iterators

int main()
{
    int x[] = {1, 2, 3, 4, 5};

    cout << "\nUsing iterators\n";
    for (auto it=begin(x); it != end(x); it++) {
        cout << *it << endl;
    }
}

Output

Using iterators
1
2
3
4
5

Containers

int main()
{
    vector<double> v = {1,2,3};

    cout << "\nUsing the vector container\n";
    for (auto it=begin(v); it != end(v); it++) {
        cout << *it << endl;
    }

    v.push_back(4);
    v.push_back(5);
    cout << "\nGrowing the vector container\n";
    for (auto it=begin(v); it != end(v); it++) {
        cout << *it << endl;
    }

    v.pop_back();
    cout << "\nShrinking the vector container\n";
    for (auto it=begin(v); it != end(v); it++) {
        cout << *it << endl;
    }

    cout << "\nUsing the unordered_map container\n";
    unordered_map<string, int> dict =  { {"ann", 23}, {"bob", 32}, {"charles", 17}};
    dict["doug"] = 30;
    for (auto it=begin(dict); it != end(dict); it++) {
        cout << it->first << ", " << it->second << endl;
    }

    cout << dict["bob"] << endl;
}

Output

Using the vector container
1
2
3

Growing the vector container
1
2
3
4
5

Shrinking the vector container
1
2
3
4

Using the unordered_map container
doug, 30
charles, 17
bob, 32
ann, 23
32

Exercise 2

Write a function that takes a vector of doubles returns the squared vector. Compile and run the function with the initial vector containing 1.0, 2.0, 3.0, 4.0, 5.0.

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EXercise 3

Convert the function from Exercise 2 so that it works for lists or vectors of ints, floats and doubles.

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Algorithms

int main()
{
void show_algorithms() {
    vector<int> v(10, 0);

    cout << "\nWorking with standard library algorithm\n";
    cout << "\nInitial state\n";
    for (auto it=begin(v); it != end(v); it++) {
        cout << *it << " ";
    }
    cout << endl;

    cout << "\nAfter iota\n";
    iota(begin(v), end(v), 5);
    for (auto it=begin(v); it != end(v); it++) {
        cout << *it << " ";
    }
    cout << endl;

    cout << "\nSimple accumulate\n";
    int s = accumulate(begin(v), end(v), 0);
    cout << s << endl;

    cout << "\nAccumulate with custom sum of squares reduction\n";
    int t = accumulate(begin(v), end(v), 0, [] (int acc, int x) { return acc + x*x; });
    cout << t << endl;
}

Output

Working with standard library algorithm

Initial state
0 0 0 0 0 0 0 0 0 0

After iota
5 6 7 8 9 10 11 12 13 14

Simple accumulate
95

Accumulate with custom sum of squares reduction
985

Exercise 4

Write a function to calculate the mean of a vector of numbers using accumulate from the <numeric> library. Compile and test with some vectors.

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Function pointers

int main()
{
    cout << "\nUsing generalized function pointers\n";
    using func = function<double(double, double)>;

    auto f1 = [](double x, double y) { return x + y; };
    auto f2 = [](double x, double y) { return x * y; };
    auto f3 = [](double x, double y) { return x + y*y; };

    double x = 3, y = 4;

    vector<func> funcs = {f1, f2, f3,};

    for (auto& f : funcs) {
        cout << f(x, y) << "\n";
    }
}

Output

Using generalized function pointers
7
12
19

Exercise 5

Implement Newton’s method in 1D for root finding. Pass in the function and gradient as generalized function pointers. Test your function with some simple polynomial and starting points.

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Random numbers

C++ now comes with its own collection of random number generators and quite a broad selection of distributions. See here for a great explanation.

int main()
{
    cout << "\nGenerating random numbers\n";

    // start random number engine wiht fixed seed
    default_random_engine re{12345};

    uniform_int_distribution<int> uniform(1,6); // lower and upper bounds
    poisson_distribution<int> poisson(30); // rate
    student_t_distribution<double> t(10); // degrees of freedom

    auto runif = bind (uniform, re);
    auto rpois = bind(poisson, re);
    auto rt = bind(t, re);

    for (int i=0; i<10; i++) {
        cout << runif() << ", " << rpois() <<  ", " << rt() << "\n";

    }
}

Output

Generating random numbers
3, 30, 0.0796641
5, 38, 0.163947
3, 26, -0.570003
6, 27, 0.872475
6, 33, -0.260322
2, 28, 0.798292
1, 22, 0.00164128
4, 29, 0.633913
5, 41, 1.00468
6, 31, -0.00420647

Exercise 6

Generate 1000 random points from the exponential distribution and save as a comma-separated values (CSV) file. Open the file in Python and plot the distribution using plt.hist.

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Numeric library

Armadillo is an accessible library for doing numeric operations, much like numpy in Python. Please see official documentation for details. It provides vectors, matrices, tensors, linear algebra, statistical functions and a limited set of convenient random number generators.

int main()
{
    using namespace arma;

    vec u = linspace<vec>(0,1,5);
    vec v = ones<vec>(5);
    mat A = randu<mat>(4,5); // uniform random deviates
    mat B = randn<mat>(4,5); // normal random deviates

    cout << "\nVecotrs in Armadillo\n";
    cout << u << endl;
    cout << v << endl;
    cout << u.t() * v << endl;

    cout << "\nRandom matrices in Armadillo\n";
    cout << A << endl;
    cout << B << endl;
    cout << A * B.t() << endl;
    cout << A * v << endl;

    cout << "\nQR in Armadillo\n";
    mat Q, R;
    qr(Q, R, A.t() * A);
    cout << Q << endl;
    cout << R << endl;
}

Output

Vecotrs in Armadillo
        0
   0.2500
   0.5000
   0.7500
   1.0000

   1.0000
   1.0000
   1.0000
   1.0000
   1.0000

   2.5000


Random matrices in Armadillo
   7.8264e-06   5.3277e-01   6.7930e-01   8.3097e-01   6.7115e-01
   1.3154e-01   2.1896e-01   9.3469e-01   3.4572e-02   7.6982e-03
   7.5561e-01   4.7045e-02   3.8350e-01   5.3462e-02   3.8342e-01
   4.5865e-01   6.7886e-01   5.1942e-01   5.2970e-01   6.6842e-02

  -0.7649   1.2041  -0.7020   1.1862   0.8284
   1.7313   0.0937   1.6814  -0.8631   0.9426
   0.1454  -0.6920   0.2742   0.6810   0.2091
   0.7032   0.2610   0.1752   1.3165  -0.5897

   1.7063   1.1075   0.5238   0.9563
  -0.4457   1.7973   0.1490   0.3544
  -0.4095   2.2726   0.2990   0.4551
   0.7857   1.3368   0.1140   1.2487

   2.7142
   1.3275
   1.6230
   2.2535


QR in Armadillo
  -0.6776   0.6377   0.3253   0.0944  -0.1395
  -0.3188  -0.4409   0.3521   0.4177   0.6368
  -0.5524  -0.2366  -0.7774   0.1504  -0.1092
  -0.2443  -0.5816   0.4071  -0.1709  -0.6380
  -0.2727  -0.0688  -0.0099  -0.8745   0.3950

  -1.1785e+00  -1.3394e+00  -2.1015e+00  -1.3527e+00  -1.0229e+00
        0e+00  -8.3421e-01  -9.7607e-01  -9.9515e-01  -5.3245e-01
        0e+00        0e+00  -4.6336e-01   7.6793e-02  -4.0376e-03
        0e+00        0e+00        0e+00  -2.0273e-01  -3.2745e-01
        0e+00        0e+00        0e+00        0e+00   1.1102e-16

Exercise 7

Use the armadillo library to

• Generate 10 x-coordinates linearly spaced between 10 and 15
• Generate 10 random y-values as \(y = 3x^2 - 7x + 2 + \epsilon\) where \(\epsilon \sim N(0,1)\)
• Find the length of \(x\) and \(y\) and the Euclidean distance between \(x\) and \(y\)
• Find the correlation between \(x\) and \(y\)
• Solve the linear system to find a quadratic fit for this data

In [ ]:

Collected source code

In [2]:

%%file main.cpp
#include <iostream>
#include <vector>
#include <unordered_map>
#include <algorithm>
#include <numeric>
#include <iterator>
#include <functional>
#include <random>
#include <armadillo>

using namespace std;

/* Topics
 *
 * - for loop
 *
 *
 * - functions
 * - lambdas
 * - templates
 *
 * - iterators
 * - containers
 * - algorithms
 * - Armadillo
*/

// hello world
void show_hello() {
    cout << "Hello, world!\n";
}

namespace sta_663 {
    const double pi=2.14159;

    void greet(string name) {
        cout << "\nTraditional first program\n";
        cout << "Hello, " << name << "\n";
    }
}

void show_namespace() {
    cout << "\nUsing namespaces\n";
    string name = "Tom";
    cout << sta_663::pi << "\n";
    sta_663::greet(name);
}


// for loops
void show_for() {
    int x[] = {1, 2, 3, 4, 5};

    cout << "\nTraditional for loop\n";
    for (int i=0; i < sizeof(x)/sizeof(x[0]); i++) {
        cout << i << endl;
    }

    cout << "\nRanged for loop\n\n";
    for (auto &i : x) {
        cout << i << endl;
    }
}

// simple funciton
int add0(int a, int b) {
    return a + b;
}

// simple function with reference variables
void add1(int a, int b, int& c) {
    c = a + b;
}

// lambda function
auto add2 = [] (int a, int b) { return a + b; };

void show_func() {

    cout << "\nStandard function\n";
    int a = 3, b = 4;
    cout << add0(a, b) <<  endl;

    int c = 0;
    cout << "\nStandard with reference varaibles\n";

    add1(a, b, c);
    cout << c <<  endl;

    cout << "\nLambda function\n";
    cout << add2(a, b) <<  endl;

    auto add3 = [c] (int a, int b) { return c * add2(a, b); };

    c -= 5;
    cout << "\nLambda function with value capture\n";
    cout << add3(a, b) <<  endl;

    auto add4 = [&c] (int a, int b) { return c * add2(a, b); };

    cout << "\nLambda function with reference capture\n";
    cout << add4(a, b) <<  endl;

}

// templates
template <typename T>
T add5(T a, T b) { return a + b; }

void show_template() {

    cout << "\nTemplate function with ints\n";
    cout << add5(3, 4) << endl;

    cout << "\nTemplate function with doubles\n";
    cout << add5(3.14, 2.78) << endl;
}

void show_iterators() {
    int x[] = {1, 2, 3, 4, 5};

    cout << "\nUsing iterators\n";
    for (auto it=begin(x); it != end(x); it++) {
        cout << *it << endl;
    }
}

void show_containers() {
    vector<double> v = {1,2,3};

    cout << "\nUsing the vector container\n";
    for (auto it=begin(v); it != end(v); it++) {
        cout << *it << endl;
    }

    v.push_back(4);
    v.push_back(5);
    cout << "\nGrowing the vector container\n";
    for (auto it=begin(v); it != end(v); it++) {
        cout << *it << endl;
    }

    v.pop_back();
    cout << "\nShrinking the vector container\n";
    for (auto it=begin(v); it != end(v); it++) {
        cout << *it << endl;
    }

    cout << "\nUsing the unordered_map container\n";
    unordered_map<string, int> dict =  { {"ann", 23}, {"bob", 32}, {"charles", 17}};
    dict["doug"] = 30;
    for (auto it=begin(dict); it != end(dict); it++) {
        cout << it->first << ", " << it->second << endl;
    }

    cout << dict["bob"] << endl;
}

void show_algorithms() {
    vector<int> v(10, 0);

    cout << "\nWorking with standard library algorithm\n";
    cout << "\nInitial state\n";
    for (auto it=begin(v); it != end(v); it++) {
        cout << *it << " ";
    }
    cout << endl;

    cout << "\nAfter iota\n";
    iota(begin(v), end(v), 5);
    for (auto it=begin(v); it != end(v); it++) {
        cout << *it << " ";
    }
    cout << endl;

    cout << "\nSimple accumulate\n";
    int s = accumulate(begin(v), end(v), 0);
    cout << s << endl;

    cout << "\nAccumulate with custom sum of squares reduction\n";
    int t = accumulate(begin(v), end(v), 0, [] (int acc, int x) { return acc + x*x; });
    cout << t << endl;
}

void show_functional() {

    cout << "\nUsing generalized function pointers\n";
    using func = function<double(double, double)>;

    auto f1 = [](double x, double y) { return x + y; };
    auto f2 = [](double x, double y) { return x * y; };
    auto f3 = [](double x, double y) { return x + y*y; };

    double x = 3, y = 4;

    vector<func> funcs = {f1, f2, f3,};

    for (auto& f : funcs) {
        cout << f(x, y) << "\n";
    }

}

void show_random() {
    cout << "\nGenerating random numbers\n";

    // start random number engine wiht fixed seed
    default_random_engine re{12345};

    uniform_int_distribution<int> uniform(1,6); // lower and upper bounds
    poisson_distribution<int> poisson(30); // rate
    student_t_distribution<double> t(10); // degrees of freedom

    auto runif = bind (uniform, re);
    auto rpois = bind(poisson, re);
    auto rt = bind(t, re);

    for (int i=0; i<10; i++) {
        cout << runif() << ", " << rpois() <<  ", " << rt() << "\n";
    }
}

void show_amrmadillo() {
    using namespace arma;

    vec u = linspace<vec>(0,1,5);
    vec v = ones<vec>(5);
    mat A = randu<mat>(4,5);
    mat B = randn<mat>(4,5);

    cout << "\nVecotrs in Armadillo\n";
    cout << u << endl;
    cout << v << endl;
    cout << u.t() * v << endl;

    cout << "\nRandom matrices in Armadillo\n";
    cout << A << endl;
    cout << B << endl;
    cout << A * B.t() << endl;
    cout << A * v << endl;

    cout << "\nQR in Armadillo\n";
    mat Q, R;
    qr(Q, R, A.t() * A);
    cout << Q << endl;
    cout << R << endl;
}

int main() {
    show_hello();
    show_namespace();
    show_for();
    show_func();
    show_template();
    show_iterators();
    show_containers();
    show_algorithms();
    show_functional();
    show_random();
    show_amrmadillo();
}

Overwriting main.cpp

In [5]:

%%bash

g++ -O3 -std=c++11 -larmadillo main.cpp -o main

In [6]:

%%bash

./main

Hello, world!

Using namespaces
2.14159

Traditional first program
Hello, Tom

Traditional for loop
0
1
2
3
4

Ranged for loop

1
2
3
4
5

Standard function
7

Standard with reference varaibles
7

Lambda function
7

Lambda function with value capture
49

Lambda function with reference capture
14

Template function with ints
7

Template function with doubles
5.92

Using iterators
1
2
3
4
5

Using the vector container
1
2
3

Growing the vector container
1
2
3
4
5

Shrinking the vector container
1
2
3
4

Using the unordered_map container
doug, 30
charles, 17
bob, 32
ann, 23
32

Working with standard library algorithm

Initial state
0 0 0 0 0 0 0 0 0 0

After iota
5 6 7 8 9 10 11 12 13 14

Simple accumulate
95

Accumulate with custom sum of squares reduction
985

Using generalized function pointers
7
12
19

Generating random numbers
3, 30, 0.0796641
5, 38, 0.163947
3, 26, -0.570003
6, 27, 0.872475
6, 33, -0.260322
2, 28, 0.798292
1, 22, 0.00164128
4, 29, 0.633913
5, 41, 1.00468
6, 31, -0.00420647

Vecotrs in Armadillo
        0
   0.2500
   0.5000
   0.7500
   1.0000

   1.0000
   1.0000
   1.0000
   1.0000
   1.0000

   2.5000


Random matrices in Armadillo
   7.8264e-06   5.3277e-01   6.7930e-01   8.3097e-01   6.7115e-01
   1.3154e-01   2.1896e-01   9.3469e-01   3.4572e-02   7.6982e-03
   7.5561e-01   4.7045e-02   3.8350e-01   5.3462e-02   3.8342e-01
   4.5865e-01   6.7886e-01   5.1942e-01   5.2970e-01   6.6842e-02

  -0.7649   1.2041  -0.7020   1.1862   0.8284
   1.7313   0.0937   1.6814  -0.8631   0.9426
   0.1454  -0.6920   0.2742   0.6810   0.2091
   0.7032   0.2610   0.1752   1.3165  -0.5897

   1.7063   1.1075   0.5238   0.9563
  -0.4457   1.7973   0.1490   0.3544
  -0.4095   2.2726   0.2990   0.4551
   0.7857   1.3368   0.1140   1.2487

   2.7142
   1.3275
   1.6230
   2.2535


QR in Armadillo
  -0.6776   0.6377   0.3253   0.0944  -0.1395
  -0.3188  -0.4409   0.3521   0.4177   0.6368
  -0.5524  -0.2366  -0.7774   0.1504  -0.1092
  -0.2443  -0.5816   0.4071  -0.1709  -0.6380
  -0.2727  -0.0688  -0.0099  -0.8745   0.3950

  -1.1785e+00  -1.3394e+00  -2.1015e+00  -1.3527e+00  -1.0229e+00
        0e+00  -8.3421e-01  -9.7607e-01  -9.9515e-01  -5.3245e-01
        0e+00        0e+00  -4.6336e-01   7.6793e-02  -4.0376e-03
        0e+00        0e+00        0e+00  -2.0273e-01  -3.2745e-01
        0e+00        0e+00        0e+00        0e+00   1.1102e-16

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