//+------------------------------------------------------------------+
//|                                                    MatrixSVD.mq5 |
//|                                  Copyright 2022, MetaQuotes Ltd. |
//|                                             https://www.mql5.com |
//+------------------------------------------------------------------+

//+------------------------------------------------------------------+
//| Script program start function                                    |
//+------------------------------------------------------------------+
void OnStart()
{
   matrix a = {{0, 1, 2, 3, 4, 5, 6, 7, 8}};
   a = a - 4;
   a.Reshape(3, 3);
   Print("matrix a \n", a);

   // run SVD-decomposition:

   matrix U, V;
   vector singular_values;
   a.SVD(U, V, singular_values);
   Print("U \n", U);
   Print("V \n", V);
   Print("singular_values = ", singular_values);
 
   // check the decomposition by equality U * singular diagonal * V = A.

   matrix matrix_s;
   matrix_s.Diag(singular_values);
   Print("matrix_s \n", matrix_s);
   matrix matrix_vt = V.Transpose();
   Print("matrix_vt \n", matrix_vt);
   matrix matrix_usvt = (U.MatMul(matrix_s)).MatMul(matrix_vt);
   Print("matrix_usvt \n", matrix_usvt);

   // compare original and rsulting matrices for discrepancies
 
   ulong errors = (int)a.Compare(matrix_usvt, 1e-9);
   Print("errors=", errors);
}
//+------------------------------------------------------------------+
/*

matrix a
[[-4,-3,-2]
 [-1,0,1]
 [2,3,4]]
U
[[-0.7071067811865474,0.5773502691896254,0.408248290463863]
 [-6.827109697437648e-17,0.5773502691896253,-0.8164965809277256]
 [0.7071067811865472,0.5773502691896255,0.4082482904638627]]
V
[[0.5773502691896258,-0.7071067811865474,-0.408248290463863]
 [0.5773502691896258,1.779939029415334e-16,0.8164965809277258]
 [0.5773502691896256,0.7071067811865474,-0.408248290463863]]
singular_values = [7.348469228349533,2.449489742783175,3.277709923350408e-17]
  
matrix_s
[[7.348469228349533,0,0]
 [0,2.449489742783175,0]
 [0,0,3.277709923350408e-17]]
matrix_vt
[[0.5773502691896258,0.5773502691896258,0.5773502691896256]
 [-0.7071067811865474,1.779939029415334e-16,0.7071067811865474]
 [-0.408248290463863,0.8164965809277258,-0.408248290463863]]
matrix_usvt
[[-3.999999999999997,-2.999999999999999,-2]
 [-0.9999999999999981,-5.977974170712231e-17,0.9999999999999974]
 [2,2.999999999999999,3.999999999999996]]
errors=0

*/
//+------------------------------------------------------------------+