MQL5 中的矩阵和向量

2023-06-19 01:29| 来源: 网络整理| 查看: 265

向量（vector）是一个一维的双精度型（double）数组。针对向量定义了以下运算：加法和乘法，以及获取向量长度或模（module）的范数（Norm）。在程序化过程中，向量通常由同质元素的数组来表示，针对这些不能定义非规则向量运算，即数组不能相加或相乘，并且它们没有范数。

在数学中，向量可以表示为行向量，即由一行和 n 列组成的数组，以及字符串向量，即由一列和 n 行组成的矩阵。在 MQL5 中，“vector（向量）”类型没有行和列子类型，因此程序员必须了解特定运算中所用的是哪种向量类型。

使用以下内置方法创建和初始化向量。

方法NumPy 类比说明void vector.Init( ulong size);创建指定长度的向量，其中的值未定义static vector vector::Ones(ulong size); ones创建指定长度的向量，用一填充static vector vector::Zeros(ulong size); zeros创建指定长度的向量，用零填充static vector vector::Full(ulong size,double value); full创建指定长度的向量，并用指定值填充operator =返回向量的副本void vector.Resize(const vector v);往结尾添加新值来调整向量大小

矢量创建示例：

void OnStart() { //--- vector initialization examples vector v; v.Init(7); Print("v = ", v); vector v1=vector::Ones(5); Print("v1 = ", v1); vector v2=vector::Zeros(3); Print("v2 = ", v2); vector v3=vector::Full(6, 2.5); Print("v3 = ", v3); vector v4{1, 2, 3}; Print("v4 = ", v4); v4.Resize(5); Print("after Resize(5) v4 = ", v4); vector v5=v4; Print("v5 = ", v5); v4.Fill(7); Print("v4 = ", v4, " v5 =",v5); } /* Execution result v = [4,5,6,8,10,12,12] v1 = [1,1,1,1,1] v2 = [0,0,0] v3 = [2.5,2.5,2.5,2.5,2.5,2.5] v4 = [1,2,3] after Resize(5) v4 = [1,2,3,7,7] v5 = [1,2,3,7,7] v4 = [7,7,7,7,7] v5 =[1,2,3,7,7] */

Init() 方法不仅可用于为向量分配内存，还可依据函数值来初始化向量元素。在这种情况下，向量大小作为第一个参数传递给 Init，函数名作为第二个参数。如果函数包含参数，则应在函数名后立即指定这些参数，并用逗号分隔。

函数本身必须包含向量的引用，且作为第一个参数传入。在 Init 调用期间不应传递向量。我们以 Arange 函数为例来查看方法的运算。此函数模仿 numpy.arange。

void OnStart() { //--- vector v; v.Init(7,Arange,10,0,0.5); // 3 parameters are passed with Arange call Print("v = ", v); Print("v.size = ",v.Size()); } //+------------------------------------------------------------------+ //| Values are generated within the half-open interval [start, stop)| //+------------------------------------------------------------------+ void Arange(vector& v, double stop, double start = 0, double step = 1) // the function has 4 parameters { if(start >= stop) { PrintFormat("%s wrong parameters! start=%G stop=%G", __FILE__,start, stop); return; } //--- int size = (int)((stop - start) / step); v.Resize(size); double value = start; for(ulong i = 0; i < v.Size(); i++) { v[i] = value; value += step; } } /* Execution result v = [0,0.5,1,1.5,2,2.5,3,3.5,4,4.5,5,5.5,6,6.5,7,7.5,8,8.5,9,9.5] v.size = 20 */

Arange 函数有两个可选参数，“start” 和 “stop”。因此，Init(7,Arange,10) 的另一个可能调用和相关结果如下：

//+------------------------------------------------------------------+ //| Script program start function | //+------------------------------------------------------------------+ void OnStart() { //--- vector v; v.Init(7,Arange,10); Print("v = ", v); Print("v.size = ",v.Size()); } ... /* v = [0,1,2,3,4,5,6,7,8,9] v.size = 10 */

向量运算

通常可以在向量上执行使用标量的加、减、乘、除运算。

//+------------------------------------------------------------------+ //| vector2_article.mq5 | //| Copyright 2021, MetaQuotes Ltd. | //| https://www.mql5.com | //+------------------------------------------------------------------+ #property copyright "Copyright 2021, MetaQuotes Ltd." #property link "https://www.mql5.com" #property version "1.00" //+------------------------------------------------------------------+ //| Script program start function | //+------------------------------------------------------------------+ void OnStart() { //--- vector v= {1, 2, 3, 4, 5}; Print("Examples without saving vector changes"); Print("v = ", v); Print("v+5 = ", v+5); Print("v-Pi= ", v-M_PI); Print("v*2.0= ", v*2); Print("v/3.0= ", v/3.0); Print("Save all vector changes"); Print("v = ", v); Print("v+5 = ", v=v+5); Print("v-Pi= ", v=v-M_PI); Print("v*2.0= ", v= v*2); Print("v/3.0= ", v= v/3.0); } /* Execution result Examples without saving vector changes v = [1,2,3,4,5] v+5 = [6,7,8,9,10] v-Pi= [-2.141592653589793,-1.141592653589793,-0.1415926535897931,0.8584073464102069,1.858407346410207] v*2.0= [2,4,6,8,10] v/3.0= [0.3333333333333333,0.6666666666666666,1,1.333333333333333,1.666666666666667] Save all vector changes v = [1,2,3,4,5] v+5 = [6,7,8,9,10] v-Pi= [2.858407346410207,3.858407346410207,4.858407346410207,5.858407346410207,6.858407346410207] v*2.0= [5.716814692820414,7.716814692820414,9.716814692820414,11.71681469282041,13.71681469282041] v/3.0= [1.905604897606805,2.572271564273471,3.238938230940138,3.905604897606805,4.572271564273471] */ //+------------------------------------------------------------------+

向量支持两个大小相同向量的元素加法、减法、乘法和除法运算。

void OnStart() { //--- vector a = {1, 2, 3}; vector b = {2, 4, 6}; Print("a + b = ", a + b); Print("a - b = ", a - b); Print("a * b = ", a * b); Print("b / a = ", b / a); } /* Execution result a + b = [3,6,9] a - b = [-1,-2,-3] a * b = [2,8,18] b / a = [2,2,2] */

为这些数据类型定义了四种运算。

void OnStart() { //--- vector a={1, 2, 3}; vector b={4, 5, 6}; Print("a = ", a); Print("b = ", b); Print("1) a.Dot(b) = ", a.Dot(b)); Print("2) a.MatMul(b) = ", a.MatMul(b)); Print("3) a.Kron(b) = ", a.Kron(b)); Print("4) a.Outer(b) = \n", a.Outer(b)); } /* Execution result a = [1,2,3] b = [4,5,6] 1) a.Dot(b) = 32.0 2) a.MatMul(b) = 32.0 3) a.Kron(b) = [[4,5,6,8,10,12,12,15,18]] 4) a.Outer(b) = [[4,5,6] [8,10,12] [12,15,18]] */

如您从示例中所见，Outer 方法返回一个矩阵，其中行数和列数对应于相乘向量的大小。 Dot 和 MatMul 的操作方式相同。

向量范数

向量和矩阵范数表示向量长度（量级）和绝对值。计算向量范数的三种可能方法已罗列在 ENUM_VECTOR_NORM 枚举之中。

void OnStart() { //--- struct str_vector_norm { ENUM_VECTOR_NORM norm; int value; }; str_vector_norm vector_norm[]= { {VECTOR_NORM_INF, 0}, {VECTOR_NORM_MINUS_INF, 0}, {VECTOR_NORM_P, 0}, {VECTOR_NORM_P, 1}, {VECTOR_NORM_P, 2}, {VECTOR_NORM_P, 3}, {VECTOR_NORM_P, 4}, {VECTOR_NORM_P, 5}, {VECTOR_NORM_P, 6}, {VECTOR_NORM_P, 7}, {VECTOR_NORM_P, -1}, {VECTOR_NORM_P, -2}, {VECTOR_NORM_P, -3}, {VECTOR_NORM_P, -4}, {VECTOR_NORM_P, -5}, {VECTOR_NORM_P, -6}, {VECTOR_NORM_P, -7} }; vector v{1, 2, 3, 4, 5, 6, 7}; double norm; Print("v = ", v); //--- for(int i=0; i

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