Convolve

返回两个向量的离散线性卷积

vector vector::Convolve(

  const vector&           v,        // 向量

  ENUM_VECTOR_CONVOLVE    mode      // 模式

   );

参数

[输出] 第二个向量。

mode

[输入] “mode” 参数判定线性卷积计算模式 ENUM_VECTOR_CONVOLVE。

返回值

两个向量的离散，线性卷积。

以 MQL5 实现的计算两个向量卷积的简单算法：

vector VectorConvolutionFull(const vector& a,const vector& b)

  {

   if(a.Size()<b.Size())

      return(VectorConvolutionFull(b,a));



   int    m=(int)a.Size();

   int    n=(int)b.Size();

   int    size=m+n-1;

   vector c=vector::Zeros(size);



   for(int i=0; i<n; i++)

      for(int i_=i; i_<i+m; i_++)

         c[i_]+=b[i]*a[i_-i];



   return(c);

  }

//+------------------------------------------------------------------+

//|                                                                  |

//+------------------------------------------------------------------+

vector VectorConvolutionSame(const vector& a,const vector& b)

  {

   if(a.Size()<b.Size())

      return(VectorConvolutionSame(b,a));



   int    m=(int)a.Size();

   int    n=(int)b.Size();

   int    size=MathMax(m,n);

   vector c=vector::Zeros(size);



   for(int i=0; i<n; i++)

     {

      for(int i_=i; i_<i+m; i_++)

        {

         int k=i_-size/2+1;

         if(k>=0 && k<size)

            c[k]+=b[i]*a[i_-i];

        }

     }



   return(c);

  }

//+------------------------------------------------------------------+

//|                                                                  |

//+------------------------------------------------------------------+

vector VectorConvolutionValid(const vector& a,const vector& b)

  {

   if(a.Size()<b.Size())

      return(VectorConvolutionValid(b,a));



   int    m=(int)a.Size();

   int    n=(int)b.Size();

   int    size=MathMax(m,n)-MathMin(m,n)+1;

   vector c=vector::Zeros(size);



   for(int i=0; i<n; i++)

     {

      for(int i_=i; i_<i+m; i_++)

        {

         int k=i_-n+1;

         if(k>=0 && k<size)

            c[k]+=b[i]*a[i_-i];

        }

     }



   return(c);

  }

MQL5 示例:

  vector a= {1, 2, 3, 4, 5};

  vector b= {0, 1, 0.5};



  Print("full\n", a.Convolve(b, VECTOR_CONVOLVE_FULL));

  Print("same\n", a.Convolve(b, VECTOR_CONVOLVE_SAME));

  Print("valid\n", a.Convolve(b, VECTOR_CONVOLVE_VALID));



  /*

   full

   [0,1,2.5,4,5.5,7,2.5]

   same

   [1,2.5,4,5.5,7]

   valid

   [2.5,4,5.5]

  */

Python 示例:

import numpy as np

a=[1,2,3,4,5]

b=[0,1,0.5]



print("full\n",np.convolve(a,b,'full'))

print("same\n",np.convolve(a,b,'same'));

print("valid\n",np.convolve(a,b,'valid'));





full

 [0.  1.  2.5 4.  5.5 7.  2.5]

same

 [1.  2.5 4.  5.5 7. ]

valid

 [2.5 4.  5.5]