示例#1
0
        /**
         * Computes the QR decomposition of the provided matrix.
         *
         * @param A Matrix which is to be decomposed.  Not modified.
         */
        public void decompose(SimpleMatrix <DMatrixRMaj> A)
        {
            this.QR = A.copy() as SimpleMatrix <DMatrixRMaj>;

            int N = Math.Min(A.numCols(), A.numRows());

            gammas = new double[A.numCols()];

            for (int i = 0; i < N; i++)
            {
                // use extract matrix to get the column that is to be zeroed
                SimpleMatrix <DMatrixRMaj> v = QR.extractMatrix(i, SimpleMatrix <DMatrixRMaj> .END, i, i + 1) as SimpleMatrix <DMatrixRMaj>;
                double max = v.elementMaxAbs();

                if (max > 0 && v.getNumElements() > 1)
                {
                    // normalize to reduce overflow issues
                    v = v.divide(max) as SimpleMatrix <DMatrixRMaj>;

                    // compute the magnitude of the vector
                    double tau = v.normF();

                    if (v.get(0) < 0)
                    {
                        tau *= -1.0;
                    }

                    double u_0   = v.get(0) + tau;
                    double gamma = u_0 / tau;

                    v = v.divide(u_0) as SimpleMatrix <DMatrixRMaj>;
                    v.set(0, 1.0);

                    // extract the submatrix of A which is being operated on
                    SimpleBase <DMatrixRMaj> A_small = QR.extractMatrix(i, SimpleMatrix <DMatrixRMaj> .END, i, SimpleMatrix <DMatrixRMaj> .END);

                    // A = (I - &gamma;*u*u<sup>T</sup>)A
                    A_small = A_small.plus(-gamma, v.mult(v.transpose()).mult(A_small));

                    // save the results
                    QR.insertIntoThis(i, i, A_small);
                    QR.insertIntoThis(i + 1, i, v.extractMatrix(1, SimpleMatrix <DMatrixRMaj> .END, 0, 1));

                    // Alternatively, the two lines above can be replaced with in-place equations
                    // READ THE JAVADOC TO UNDERSTAND HOW THIS WORKS!
//                QR.equation("QR(i:,i:) = A","QR",i,"i",A_small,"A");
//                QR.equation("QR((i+1):,i) = v(1:,0)","QR",i,"i",v,"v");

                    // save gamma for recomputing Q later on
                    gammas[i] = gamma;
                }
            }
        }