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

v: [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]

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