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MQL5 リファレンス行列とベクトルのメソッドOpenBLASFactored CalculationsPseudo Inverse 

There is no special function in the OpenBLAS library to calculate the pseudo-inverse of a matrix. However, for this purpose can be used singular value decomposition (SVD):

1. Decompose matrix A into U * Σ * VT

2. Invert Σ (non-zero singular values ​​only)

3. Get the pseudo-inverse matrix using the formula

A+ = V * Σ+ * UT

Example

//+------------------------------------------------------------------+
//|  Тест функции PseudoInverse: проверка A * A+ * A ≈ A             |
//+------------------------------------------------------------------+
int TestPseudoInverse(ulong size_m,ulong size_n)
 {
  matrix matrix_a=matrix::Random(size_m,size_n);
  matrix matrix_pi;
  if(!PseudoInverse(matrix_a,matrix_pi))
    return(1000);
 
//--- pseudo inverse test  A * A+ * A = A
  matrix matrix_a2=matrix_a @ matrix_pi @ matrix_a;
  int   errors=(int)matrix_a.Compare(matrix_a2,1e-11);
 
  printf("Pseudo Inverse via SVD %s  matrix size %d x %d  errors=%d",errors==0?"passed":"failed",size_m,size_n,errors);
 
  return(errors);
 }
//+------------------------------------------------------------------+
//| Вычисляет псевдообратную матрицу с помощью сингулярного разлож.  |
//| A+ = V * Σ⁻¹ * Uᵀ                                                |
//+------------------------------------------------------------------+
bool PseudoInverse(matrix& matrix_a,matrix& matrix_pi)
 {
//--- 1. SVD
  matrix matrix_u,matrix_vt;
  vector vector_s;
  if(!matrix_a.SingularValueDecompositionDC(SVDZ_S,vector_s,matrix_u,matrix_vt))
    return(false);
 
//--- 2. inverse diagonal matrix
  ulong diag=vector_s.Size();
  matrix matrix_si=matrix::Zeros(diag,diag);
  for(ulong i=0; i<diag; i++)
    {
    if(vector_s[i]!=0.0)
        matrix_si[i][i]=1.0/vector_s[i];
    }
 
//--- 3. pseudo inverse  A+ = V * Σ+ * UT
  matrix_pi=matrix_vt.Transpose() @ matrix_si @ matrix_u.Transpose();
 
  return(true);
 }