matrix a= {{0, 1, 2, 3, 4, 5, 6, 7, 8}};
a=a-4;
Print("matrix a \n", a);
a.Reshape(3, 3);
matrix b=a;
Print("matrix b \n", b);
//--- SVD分解を実行する
matrix U, V;
vector singular_values;
b.SVD(U, V, singular_values);
Print("U \n", U);
Print("V \n", V);
Print("singular_values = ", singular_values);
// チェックブロック
//--- U * 単対角 * 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);
ulong errors=(int)b.Compare(matrix_usvt, 1e-9);
double res=(errors==0);
Print("errors=", errors);
//---- 他のチェック
matrix U_Ut=U.MatMul(U.Transpose());
Print("U_Ut \n", U_Ut);
Print("Ut_U \n", (U.Transpose()).MatMul(U));
matrix vt_V=matrix_vt.MatMul(V);
Print("vt_V \n", vt_V);
Print("V_vt \n", V.MatMul(matrix_vt));
/*
matrix a
[[-4,-3,-2,-1,0,1,2,3,4]]
matrix b
[[-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
U_Ut
[[0.9999999999999993,-1.665334536937735e-16,-1.665334536937735e-16]
[-1.665334536937735e-16,0.9999999999999987,-5.551115123125783e-17]
[-1.665334536937735e-16,-5.551115123125783e-17,0.999999999999999]]
Ut_U
[[0.9999999999999993,-5.551115123125783e-17,-1.110223024625157e-16]
[-5.551115123125783e-17,0.9999999999999987,2.498001805406602e-16]
[-1.110223024625157e-16,2.498001805406602e-16,0.999999999999999]]
vt_V
[[1,-5.551115123125783e-17,0]
[-5.551115123125783e-17,0.9999999999999996,1.110223024625157e-16]
[0,1.110223024625157e-16,0.9999999999999996]]
V_vt
[[0.9999999999999999,1.110223024625157e-16,1.942890293094024e-16]
[1.110223024625157e-16,0.9999999999999998,1.665334536937735e-16]
[1.942890293094024e-16,1.665334536937735e-16,0.9999999999999996]
*/
}
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