D-M4th

D-M4th es una librería escrita en C++ con métodos para un fácil manejo de operaciones con vectores, matrices, arreglos dinámicos de N dimensiones y números complejos.

Características

• Clase tipo NDArray que permitirán manejar vectores, matrices y arreglos de N dimensiones.

  • Modificar el número de elementos y dimensiones de un arreglo con métodos resize() o reshape().
  • Inserción y eliminación de elementos con push() y pop().
  • Operaciones algebráicas entre arreglos y escalares usando operadores de suma, resta, multiplicación, división, residuo, etc. Ejemplo: arr1+arr2, arr1*10, etc.
  • Operaciones relacionales y lógicas entre arreglos y escalares usando operadores relacionales o lógicos. Ejemplo: arr1==arr2, arr1<=arr2, arr>4 || (arr2 + 1)<5, etc.
  • Sistema de conteo de referencias por array que permitirán administrar memoria sin pensar en punteros por parte del programador.
  • Obtener subArreglos (array slicing) de forma similar a Matlab y Python con el método view() y slice().
    • Un array slicing en numpy (Python) como arr[1:5], su equivalente en DM4th sería arr.view(slice(1,5))
    • Para 2 dimensiones, el equivalente de arr[:, 4:] en DM4th sería arr.view(ALL, slice(4,END)).
    • El equivalente de arr[2:6, 3, :3] en DM4th sería arr.view(slice(2,6), 3, slice(0,3)) y así sucesivamente.
  • Métodos para realizar operaciones de álgebra lineal en paralelo usando OpenMP.

• Métodos numéricos de utilidad para diferentes operaciones de cálculo diferencial e integral, álgebra lineal, entre otros.

Instalación y compilación

• D-M4th es un header-only library. No es necesario compilar dependencias para instalar. Basta con descargar o clonar la librería dentro de tu proyecto e incluir la cabecera #include "DM4th/DM4th.h".

  Si no tienes ningún entorno de desarrollo instalado, puedes instalar un editor de código y compilador de C++ recomendado:

  • Instalar compilador de C++ y Visual Studio Code para Windows.

  NOTA: D-M4th es compatible con versiones de C++11 en adelante.

• Si usas g++, la siguiente instrucción de compilación con D-M4th puede ser suficiente:

  g++ -std=c++11 main.cpp

Ejemplos

• Programa Hola Mundo con D-M4th

  • Código

  #include "DM4th/DM4th.h"
  
  using namespace std;
  using namespace DM4th;
  
  int main()
  {
      NDArray<string> hello  = items<string>("Hello", "World");
      NDArray<number> myList = range<number>(10);
  
      cout << hello << endl;
      cout << myList << endl;
  
      cin.get();
      return 0;
  }

  • Salida

  ["Hello", "World"]
  [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]

Operaciones con números complejos

• Código

  #include "DM4th/DM4th.h"
  
  using namespace std;
  using namespace DM4th;
  
  int main()
  {
      number a = 5+7i;
      number b = 10-2i;
      number c = -25;
  
      cout<< "sum:  " << a+b << endl;
      cout<< "sub:  " << a-b << endl;
      cout<< "mult: " << a*b << endl;
      cout<< "div:  " << a/b << endl;
      cout<< "sqrt: " << sqrt(c) << endl;
      cout<< "sin:  " << sin(rad(c)) << endl;
      
      cin.get();
      return 0;
  }

• Salida

  sum:  15+5i
  sub:  -5+9i
  mult: 64+60i
  div:  0.346154+0.769231i
  sqrt: 5i
  sin:  -0.422618

Operaciones con arreglos

• Código

  #include "DM4th/DM4th.h"
  
  using namespace std;
  using namespace DM4th;
  
  int main()
  {
      NDArray<number> arr1 = range<number>(5);
      NDArray<number> arr2 = range<number>(10,5,-1);
      number value = 10;
      
      cout<< "arr1: " << arr1 << endl;
      cout<< "arr2: " << arr2 << endl;
      cout<< "sum:  " << arr1+arr2 << endl;
      cout<< "sub:  " << arr1-arr2 << endl;
      cout<< "mult: " << arr1*arr2 << endl;
      cout<< "div:  " << arr1/value << endl;
  
      cin.get();
      return 0;
  }

• Salida

  arr1: [0, 1, 2, 3, 4]
  arr2: [10, 9, 8, 7, 6]
  sum:  [10, 10, 10, 10, 10]
  sub:  [-10, -8, -6, -4, -2]
  mult: [70]
  div:  [0, 0.1, 0.2, 0.3, 0.4]

Inserción y eliminación de elementos en arreglos de una dimensión

• Código

  #include "DM4th/DM4th.h"
  
  using namespace std;
  using namespace DM4th;
  
  int main()
  {
      NDArray<number> arr1 = items<number>(1,3,5,7,9);
      NDArray<number> arr2 = items<number>(2,4,6,8,0);
      number value = 1000;
  
      cout << "arr1: " << arr1 << endl;
      cout << "arr2: " << arr2 << endl << endl;
  
      cout << "value " << value << " inserted into arr1: ";
      arr1.push(value);
      cout << arr1 << endl << endl;
  
      cout << "Inserting arr2 into arr1: ";
      arr1.pushArray(arr2);
      cout << arr1 << endl << endl;
  
      cout << "Inserting " << -999 << " into arr1 at index 3: ";
      arr1.push(-999, 3);
      cout << arr1 << endl << endl;
  
      cout << "Removing some elements from arr1:" << endl;
      arr1.pop();
      cout << arr1 << endl ;
  
      arr1.pop(0);
      cout << arr1 << endl;
  
      cin.get();
      return 0;
  }

• Salida

  arr1: [1, 3, 5, 7, 9]
  arr2: [2, 4, 6, 8, 0]
  
  value 1000 inserted into arr1: [1, 3, 5, 7, 9, 1000]
  
  Inserting arr2 into arr1: [1, 3, 5, 7, 9, 1000, 2, 4, 6, 8, 0]
  
  Inserting -999 into arr1 at index 3: [1, 3, 5, -999, 7, 9, 1000, 2, 4, 6, 8, 0]
  
  Removing some elements from arr1:
  [1, 3, 5, -999, 7, 9, 1000, 2, 4, 6, 8]
  [3, 5, -999, 7, 9, 1000, 2, 4, 6, 8]

Operaciones con arreglos de 2 dimensiones

• Código

  #include "DM4th/DM4th.h"
  
  using namespace std;
  using namespace DM4th;
  
  int main()
  {
      NDArray<number> arr1 = range<number>(10,25);
      cout << "arr1:\n" << arr1 << endl;
  
      arr1.reshape(3,5);
      cout << "Reshape 3x5:\n" << arr1 << endl;
  
      arr1.resize(3,4);
      cout << "Resize 3x4:\n" << arr1 << endl;
  
      arr1.resize(4,4);
      arr1(3,0) = -7i;
      cout << "Resize 4x4:\n" << arr1 << endl;
  
      NDArray<number> arr2 = arr1+arr1;
      cout << "arr2=arr1+arr1:\n" << arr2 << endl;
  
      cout << "arr2*10:\n" << arr2*10 << endl;
  
      cin.get();
      return 0;
  }

• Salida

  arr1:
  [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24]
  Reshape 3x5:
  [
      [10, 11, 12, 13, 14],
      [15, 16, 17, 18, 19],
      [20, 21, 22, 23, 24]
  ]
  Resize 3x4:
  [
      [10, 11, 12, 13],   
      [15, 16, 17, 18],   
      [20, 21, 22, 23]
  ]
  Resize 5x5:
  [
      [10, 11, 12, 13],
      [15, 16, 17, 18],
      [20, 21, 22, 23],
      [-7i, 0, 0, 0]
  ]
  arr2=arr1+arr1:
  [
      [20, 22, 24, 26],
      [30, 32, 34, 36],
      [40, 42, 44, 46],
      [-14i, 0, 0, 0]
  ]
  arr2*10:
  
  [
      [200, 220, 240, 260],
      [300, 320, 340, 360],
      [400, 420, 440, 460],
      [-140i, 0, 0, 0]
  ]

Trabajando con elementos de Array

• Código

    #include "DM4th/DM4th.h"
  
    using namespace std;
    using namespace DM4th;
  
    int main(){
        NDArray<number> arr1 = range<number>(10,18,2);
        NDArray<number> arr2 = zeros<number>(2,2);
  
        arr1.reshape(2,2);
  
        cout << "arr1:\n" << arr1 << endl;
        cout << "arr2:\n" << arr2 << endl << endl;
  
        cout << "Copying arr1 items into arr2" << endl;
        for(int x=0; x<arr1.shape(0); x++)
        {
            for(int y=0; y<arr1.shape(1); y++)
            {
                arr2(x,y) = arr1(x,y);
            }
        }
        cout << arr2 << endl << endl;
  
        cout << "Access to each arr2 item using a single foreach in C++" << endl;
        for(auto &x: arr2)
        {
            cout << x << endl; // Printing each item of arr2
            x = 15; // assigning 15 into each item of arr2
        }
        cout << arr2 << endl << endl;
  
        cout << "Another way to access each item of arr2 using a single for" << endl; 
        number value = 10;
        for(int x=0; x<arr2.data_size(); x++)
        {
            arr2.data_item(x) = value*x;
        }
        cout << arr2 << endl << endl;
  
        cout << "Copying arr1 items into arr2 using getCopy function" << endl;
        arr2 = arr1.getCopy();
        cout << arr2 << endl << endl;
  
        cin.get();
        return 0;
    }

• Salida

    arr1:
    [
        [10, 12],
        [14, 16]
    ]
    arr2:
    [
        [0, 0],
        [0, 0]
    ]
  
    Copying arr1 items into arr2
    [
        [10, 12],
        [14, 16]
    ]
  
    Access to each arr2 item using a single foreach in C++
    10
    12
    14
    16
    [
        [15, 15],
        [15, 15]
    ]
  
    Another way to access each item of arr2 using a single for
    [
        [0, 10],
        [20, 30]
    ]
  
    Copying arr1 items into arr2 using getCopy function
    [
        [10, 12],
        [14, 16]
    ]

Arreglos dinámicos de más de 2 dimensiones

• Código

    #include "DM4th/DM4th.h"
  
    using namespace std;
    using namespace DM4th;
  
    int main()
    {
        NDArray<number> arr1 = range<number>(0,24,2);
        cout << "arr1\n" << arr1 << endl << endl;
  
        arr1.reshape(2,2,3);
        cout << "Reshape 2x2x3:\n" << arr1 << endl << endl;
  
        arr1 /= 10;
        cout << "arr1/10:\n" << arr1 << endl << endl;
  
        cout << "Assigning 9999 into arr2(1,0,2)" << endl;
        arr1(1,0,2) = 9999;
        cout << arr1 << endl << endl;
  
        arr1.reshape(2,6);
        cout << "Reshape 2x6:\n" << arr1 << endl << endl;
  
        cin.get();
        return 0;
    }

• Salida

  arr1
  [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22]
  
  Reshape 2x2x3:
  [
      [
          [0, 2, 4],
          [6, 8, 10]
      ],
      [
          [12, 14, 16],
          [18, 20, 22] 
      ]
  ]
  
  arr1/10:
  [
      [
          [0, 0.2, 0.4],
          [0.6, 0.8, 1]
      ],
      [
          [1.2, 1.4, 1.6],
          [1.8, 2, 2.2]
      ]
  ]
  
  Assigning 9999 into arr2(1,0,2)
  [
      [
          [0, 0.2, 0.4],
          [0.6, 0.8, 1]
      ],
      [
          [1.2, 1.4, 9999],
          [1.8, 2, 2.2]
      ]
  ]
  
  Reshape 2x6:
  [
      [0, 0.2, 0.4, 0.6, 0.8, 1],
      [1.2, 1.4, 9999, 1.8, 2, 2.2]
  ]

Array Slicing

• Código

  #include "DM4th/DM4th.h"
  
  using namespace std;
  using namespace DM4th;
  
  int main()
  {
      NDArray<number> matrix = items<number>(
          12, 90, 34,
          78, 56, 65,
          87, 43, 21
      ).reshape(3, 3);
  
      cout << "Matrix:\n" << matrix << endl;
  
      cout << "\nGet column 1 of matrix" << endl;
      NDArray<number> vector = matrix.view(ALL, 1); // Like vector = matrix[:, 1] in Python
      cout << vector << endl;
  
      cout << "\nSet 1000 to row 2 of matrix" << endl;
      matrix.view(2) = 1000; // Like matrix[2,:] = 1000 in Python
      cout << matrix << endl;
  
      cout << "\nSet 3+2i to column 0 of matrix" << endl;
      matrix.view(ALL, 0) = 3+2i; // Like matrix[:,0] = complex(3,2) in Python
      cout << matrix << endl;
  
  
      NDArray<number> arr1 = range<number>(10);
      NDArray<number> arr2 = items<number>(1i, 3i, 5i, 7i, 9i, 11i, 13i, 15i, 17i, 19i);
      cout << "\narr1:" << arr1 << endl;
      cout << "arr2:" << arr2 << endl;
  
      cout << "\nSetting 3rd, 4th and 5th elements of arr1 from some elements of arr2" << endl;
      arr1.view(slice(2,5)) = arr2.view(slice(2,5)); // Like arr1[2:5] = arr2[2:5] in Python 
      cout << arr1 << endl;
  
      cin.get();
      return 0;
  }

• Salida

  Matrix:
  [
      [12, 90, 34],
      [78, 56, 65],
      [87, 43, 21]
  ]
  
  Get column 1 of matrix
  [90, 56, 43]
  
  Set 1000 to row 2 of matrix
  [
      [12, 90, 34],
      [78, 56, 65],
      [1000, 1000, 1000]
  ]
  
  Set 3+2i to column 0 of matrix
  [
      [3+2i, 90, 34],
      [3+2i, 56, 65],
      [3+2i, 1000, 1000]
  ]
  
  arr1:[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
  arr2:[i, 3i, 5i, 7i, 9i, 11i, 13i, 15i, 17i, 19i]
  
  Setting 3rd, 4th and 5th elements of arr1 from some elements of arr2
  [0, 1, 5i, 7i, 9i, 5, 6, 7, 8, 9]
  

Métodos numéricos

• Código

  #include "DM4th/DM4th.h"
  
  using namespace std;
  using namespace DM4th;
  
  number myFunction(number x)
  {
      return x*x + 25;
  }
  
  int main()
  {
      number a = 5;
      number b = 3.5;
      number c = -0.2i;
      
      NDArray<number> polynomial = items<number>(6, 1, -1, -3);
  
      
      cout << "Factorial: " << factorial(a) << " " << factorial(b) << " " << factorial(c) << endl;
  
      // Root of f(x)=x*x+25
      cout << "Root of myFunction: " << newtonRaphson(myFunction) << endl;
  
      // Area of f(x)=x*x+25 [from 0 to 10]
      cout << "Integral: " << integral(myFunction, 0, 10) << endl;
  
      // All roots of f(x)=6x^(3)+x^(2)-x-3
      cout << "Roots: " << bairstowsMethod(polynomial) << endl;
  
      cin.get();
      return 0;
  }

• Salida

  Factorial: 120 11.6317 0.961947
  Root of myFunction: 5i
  Integral: 583.333
  Roots: [-0.486931+0.618327i, -0.486931-0.618327i, 0.807195]

Lectura y escritura de archivos

• Código

  #include "DM4th/DM4th.h"
  
  using namespace std;
  using namespace DM4th;
  
  int main()
  {
      NDArray<number> arr1 = identity<number>(10,10);
  
      arr1.saveFile("example.txt"); // example.txt is created automatically if it doesn't exist
  
      NDArray<number> arr2;
      arr2.loadFile("example.txt");
  
      cout << arr2 << endl;
  
      cin.get();
      return 0;
  }

• Salida

  [
      [1, 0, 0, 0, 0, 0, 0, 0, 0, 0],
      [0, 1, 0, 0, 0, 0, 0, 0, 0, 0],
      [0, 0, 1, 0, 0, 0, 0, 0, 0, 0],
      [0, 0, 0, 1, 0, 0, 0, 0, 0, 0],
      [0, 0, 0, 0, 1, 0, 0, 0, 0, 0],
      [0, 0, 0, 0, 0, 1, 0, 0, 0, 0],
      [0, 0, 0, 0, 0, 0, 1, 0, 0, 0],
      [0, 0, 0, 0, 0, 0, 0, 1, 0, 0],
      [0, 0, 0, 0, 0, 0, 0, 0, 1, 0],
      [0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
  ]