CorrCoef

matrix matrix::CorrCoef(
  const bool    rowvar=true // 観測値の行ベクトルまたは列ベクトル
);
 
scalar vector::CorrCoef(
  const vector&  b          // 2番目のベクトル
);
 

double VectorCorrelation(const vector& vector_x,const vector& vector_y)
 {
  ulong n=vector_x.Size()<vector_y.Size() ? vector_x.Size() : vector_y.Size();
  if(n<=1)
    return(0);
 
  ulong i;
  double xmean=0;
  double ymean=0;
  for(i=0; i<n; i++)
    {
    if(!MathIsValidNumber(vector_x[i]))
        return(0);
    if(!MathIsValidNumber(vector_y[i]))
        return(0);
    xmean+=vector_x[i];
    ymean+=vector_y[i];
    }
  xmean/=(double)n;
  ymean/=(double)n;
 
  double s=0;
  double xv=0;
  double yv=0;
  double t1=0;
  double t2=0;
//--- 計算
  s=0;
  for(i=0; i<n; i++)
    {
    t1=vector_x[i]-xmean;
    t2=vector_y[i]-ymean;
    xv+=t1*t1;
    yv+=t2*t2;
    s+=t1*t2;
    }
//--- 確認する
  if(xv==0 || yv==0)
    return(0);
//--- 結果を返す
  return(s/(MathSqrt(xv)*MathSqrt(yv)));
 }

  vectorf vector_a={1,2,3,4,5};
  vectorf vector_b={0,1,0.5,2,2.5};
  Print("vectors correlation ",vector_a.CorrCoef(vector_b));
//---
  matrixf matrix_a={{1,2,3,4,5},
                   {0,1,0.5,2,2.5}};
  Print("matrix rows correlation\n",matrix_a.CorrCoef());
  matrixf matrix_a2=matrix_a.Transpose();
  Print("transposed matrix cols correlation\n",matrix_a2.CorrCoef(false));
  matrixf matrix_a3={{1.0f, 2.0f, 3.0f, 4.0f, 5.0f},
                     {0.0f, 1.0f, 0.5f, 2.0f, 2.5f},
                     {0.1f, 1.0f, 2.0f, 1.0f, 0.3f}};
  Print("rows correlation\n",matrix_a3.CorrCoef());
  Print("cols correlation\n",matrix_a3.CorrCoef(false));
 
 /*
  vectors correlation 0.9149913787841797
  matrix rows correlation
  [[1,0.91499138]
   [0.91499138,1]]
  transposed matrix cols correlation
  [[1,0.91499138]
   [0.91499138,1]]
  rows correlation
  [[1,0.91499138,0.08474271]
   [0.91499138,1,-0.17123166]
   [0.08474271,-0.17123166,1]]
  cols correlation
  [[1,0.99587059,0.85375023,0.91129309,0.83773589]
   [0.99587059,1,0.80295509,0.94491106,0.88385159]
   [0.85375023,0.80295509,1,0.56362146,0.43088508]
   [0.91129309,0.94491106,0.56362146,1,0.98827404]
   [0.83773589,0.88385159,0.43088508,0.98827404,1]]
  */

import numpy as np
va=[1,2,3,4,5]
vb=[0,1,0.5,2,2.5]
print("vectors correlation")
print(np.corrcoef(va,vb))
 
ma=np.zeros((2,5))
ma[0,:]=va
ma[1,:]=vb
print("matrix rows correlation")
print(np.corrcoef(ma))
print("transposed matrix cols correlation")
print(np.corrcoef(np.transpose(ma),rowvar=False))
print("")
 
ma1=[[1,2,3,4,5],[0,1,0.5,2,2.5],[0.1,1,0.2,1,0.3]]
print("rows correlation\n",np.corrcoef(ma1))
print("cols correlation\n",np.corrcoef(ma1,rowvar=False))
 
transposed matrix cols correlation
[[1.         0.91499142]
[0.91499142 1.        ]]
 
rows correlation
[[1.         0.91499142 0.1424941 ]
[0.91499142 1.         0.39657517]
[0.1424941  0.39657517 1.        ]]
cols correlation
[[1.         0.99587059 0.98226063 0.91129318 0.83773586]
[0.99587059 1.         0.99522839 0.94491118 0.88385151]
[0.98226063 0.99522839 1.         0.97234063 0.92527551]
[0.91129318 0.94491118 0.97234063 1.         0.98827406]
[0.83773586 0.88385151 0.92527551 0.98827406 1.        ]]