Esempio n. 1
0
        public QRArgs QR_Householder2()
        {
            QRArgs result = new QRArgs();

            result.Hs = new Matrix[Columns];
            result.Qs = new Matrix[Columns];
            result.Rs = new Matrix[Columns];

            Matrix Q = I(Rows);
            Matrix R = this;

            for (int k = 0; k < Columns; k++)
            {
                Vector x = R.GetColumn(k);

                for (int i = 0; i < k; i++)
                {
                    x.Data[i] = 0;
                }

                double[] w_array = new double[x.Data.Length];
                w_array[k] = 1;
                Vector e = new Vector(x.Rows, x.Columns, w_array);

                double norm = x.Length;
                double sign = System.Math.Sign(x.Data[k]);
                Vector u    = x + (sign == 0 ? 1 : sign) * norm * e;
                Vector v    = u / R.Data[k * Columns + k];
                //Vector v = u / u.Length;
                Vector vt = v.Transposed();

                Matrix H = I(x.Data.Length) - 2 * ((v * vt) / (vt * v));
                result.Hs[k] = H;

                R            = H * R;
                result.Rs[k] = R;
                Q            = Q * H;
                result.Qs[k] = H;
            }

            result.Q = Q;
            result.R = R;

            return(result);
        }
Esempio n. 2
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        public QRArgs QR_Householder()
        {
            QRArgs result = new QRArgs();

            result.Hs = new Matrix[Columns];
            result.Qs = new Matrix[Columns];
            result.Rs = new Matrix[Columns];

            Matrix Q = Matrix.I(Rows);
            Matrix R = this;

            for (int k = 0; k < Columns; k++)
            {
                Vector x = R.GetColumn(k);

                for (int i = 0; i < k; i++)
                {
                    x.Data[i] = 0;
                }

                double[] w_array = new double[x.Data.Length];
                w_array[k] = x.Length;
                Vector w = new Vector(x.Rows, x.Columns, w_array);

                Vector v = w - x;

                Matrix I  = Matrix.I(v.Data.Length);
                Vector vt = v.Transposed();

                Matrix H = I - (2 * (v * vt)) * (1 / (vt * v));
                result.Hs[k] = H;

                R            = H * R;
                result.Rs[k] = R;
                Q            = Q * H;
                result.Qs[k] = H;
            }

            result.Q = Q;
            result.R = R;

            return(result);
        }
Esempio n. 3
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        public QRArgs QR_Householder3()
        {
            QRArgs result = new QRArgs();

            result.Hs = new Matrix[Columns];
            result.Qs = new Matrix[Columns];
            result.Rs = new Matrix[Columns];

            Matrix Q = I(Rows);
            Matrix R = this;
            Matrix A = this;

            for (int k = 0; k < Columns; k++)
            {
                if (k != 0)
                {
                    A = A.Minor(0, 0);
                }

                Vector x = A.GetColumn(0);

                Matrix B = Householder2(x);

                Matrix H = I(Rows).Replace(k, k, B);
                result.Hs[k] = H;

                R            = H * R;
                result.Rs[k] = R;
                Q            = Q * H;
                result.Qs[k] = H;
            }

            result.Q = Q;
            result.R = R;

            return(result);
        }