public static void LeastSquares(Matrix x, Matrix A, Matrix b)
{
// use svd
// for overdetermined systems A*x = b
// x = V * diag(1/wj) * U T * b
// NRC p. 66
int m = A.m;
int n = A.n;
Matrix U = new Matrix(m, n), V = new Matrix(n, n), w = new Matrix(n, 1), W = new Matrix(n, n);
A.SVD(U, w, V);
w.Reciprocal();
W.Diag(w);
Matrix M = new Matrix(n, n);
M.Mult(V, W);
Matrix N = new Matrix(n, m);
N.MultAAT(M, U);
x.Mult(N, b);
}
public static void LeastSquares(Matrix x, Matrix A, Matrix b)
{
// use svd
// for overdetermined systems A*x = b
// x = V * diag(1/wj) * U T * b
// NRC p. 66
int m = A.m;
int n = A.n;
Matrix U = new Matrix(m, n), V = new Matrix(n, n), w = new Matrix(n, 1), W = new Matrix(n, n);
A.SVD(U, w, V);
w.Reciprocal();
W.Diag(w);
Matrix M = new Matrix(n, n);
M.Mult(V, W);
Matrix N = new Matrix(n, m);
N.MultAAT(M, U);
x.Mult(N, b);
}