/*
 * Licensed to the Apache Software Foundation (ASF) under one
 * or more contributor license agreements.  See the NOTICE file
 * distributed with this work for additional information
 * regarding copyright ownership.  The ASF licenses this file
 * to you under the Apache License, Version 2.0 (the
 * "License"); you may not use this file except in compliance
 * with the License.  You may obtain a copy of the License at
 * 
 *   http://www.apache.org/licenses/LICENSE-2.0
 * 
 * Unless required by applicable law or agreed to in writing,
 * software distributed under the License is distributed on an
 * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
 * KIND, either express or implied.  See the License for the
 * specific language governing permissions and limitations
 * under the License.
 */

package org.apache.sysds.runtime.matrix.data;

import org.apache.commons.logging.Log;
import org.apache.commons.logging.LogFactory;
import org.apache.commons.math3.exception.MaxCountExceededException;
import org.apache.commons.math3.linear.Array2DRowRealMatrix;
import org.apache.commons.math3.linear.BlockRealMatrix;
import org.apache.commons.math3.linear.CholeskyDecomposition;
import org.apache.commons.math3.linear.DecompositionSolver;
import org.apache.commons.math3.linear.EigenDecomposition;
import org.apache.commons.math3.linear.LUDecomposition;
import org.apache.commons.math3.linear.QRDecomposition;
import org.apache.commons.math3.linear.RealMatrix;
import org.apache.commons.math3.linear.SingularValueDecomposition;
import org.apache.sysds.runtime.DMLRuntimeException;
import org.apache.sysds.runtime.data.DenseBlock;
import org.apache.sysds.runtime.functionobjects.Multiply;
import org.apache.sysds.runtime.functionobjects.Divide;
import org.apache.sysds.runtime.functionobjects.SwapIndex;
import org.apache.sysds.runtime.functionobjects.MinusMultiply;
import org.apache.sysds.runtime.functionobjects.Builtin;
import org.apache.sysds.runtime.instructions.InstructionUtils;
import org.apache.sysds.runtime.matrix.operators.RightScalarOperator;
import org.apache.sysds.runtime.matrix.operators.LeftScalarOperator;
import org.apache.sysds.runtime.matrix.operators.ScalarOperator;
import org.apache.sysds.runtime.matrix.operators.UnaryOperator;
import org.apache.sysds.runtime.matrix.operators.TernaryOperator;
import org.apache.sysds.runtime.matrix.operators.ReorgOperator;
import org.apache.sysds.runtime.matrix.operators.AggregateBinaryOperator;
import org.apache.sysds.runtime.matrix.operators.BinaryOperator;
import org.apache.sysds.runtime.util.DataConverter;

/**
 * Library for matrix operations that need invocation of 
 * Apache Commons Math library. 
 * 
 * This library currently supports following operations:
 * matrix inverse, matrix decompositions (QR, LU, Eigen), solve 
 */
public class LibCommonsMath 
{
	private static final Log LOG = LogFactory.getLog(LibCommonsMath.class.getName());
	private static final double RELATIVE_SYMMETRY_THRESHOLD = 1e-6;
	private static final double EIGEN_LAMBDA = 1e-8;

	private LibCommonsMath() {
		//prevent instantiation via private constructor
	}
	
	public static boolean isSupportedUnaryOperation( String opcode ) {
		return ( opcode.equals("inverse") || opcode.equals("cholesky") );
	}
	
	public static boolean isSupportedMultiReturnOperation( String opcode ) {
		return ( opcode.equals("qr") || opcode.equals("lu") || opcode.equals("eigen") || opcode.equals("svd") );
	}
	
	public static boolean isSupportedMatrixMatrixOperation( String opcode ) {
		return ( opcode.equals("solve") );
	}
		
	public static MatrixBlock unaryOperations(MatrixBlock inj, String opcode) {
		Array2DRowRealMatrix matrixInput = DataConverter.convertToArray2DRowRealMatrix(inj);
		if(opcode.equals("inverse"))
			return computeMatrixInverse(matrixInput);
		else if (opcode.equals("cholesky"))
			return computeCholesky(matrixInput);
		return null;
	}

	public static MatrixBlock[] multiReturnOperations(MatrixBlock in, String opcode) {
		return multiReturnOperations(in, opcode, 1, 1);
	}

	public static MatrixBlock[] multiReturnOperations(MatrixBlock in, String opcode, int threads, int num_iterations, double tol) {
		if(opcode.equals("eigen_qr"))
			return computeEigenQR(in, num_iterations, tol, threads);
		else
			return multiReturnOperations(in, opcode, threads, 1);
	}

	public static MatrixBlock[] multiReturnOperations(MatrixBlock in, String opcode, int threads, long seed) {
		if(opcode.equals("qr"))
			return computeQR(in);
		else if (opcode.equals("qr2"))
			return computeQR2(in, threads);
		else if (opcode.equals("lu"))
			return computeLU(in);
		else if (opcode.equals("eigen"))
			return computeEigen(in);
		else if (opcode.equals("eigen_lanczos"))
			return computeEigenLanczos(in, threads, seed);
		else if (opcode.equals("eigen_qr"))
			return computeEigenQR(in, threads);
		else if (opcode.equals("svd"))
			return computeSvd(in);
		return null;
	}
	
	public static MatrixBlock matrixMatrixOperations(MatrixBlock in1, MatrixBlock in2, String opcode) {
		if(opcode.equals("solve")) {
			if (in1.getNumRows() != in1.getNumColumns())
				throw new DMLRuntimeException("The A matrix, in solve(A,b) should have squared dimensions.");
			return computeSolve(in1, in2);
		}
		return null;
	}
	
	/**
	 * Function to solve a given system of equations.
	 * 
	 * @param in1 matrix object 1
	 * @param in2 matrix object 2
	 * @return matrix block
	 */
	private static MatrixBlock computeSolve(MatrixBlock in1, MatrixBlock in2) {
		//convert to commons math BlockRealMatrix instead of Array2DRowRealMatrix
		//to avoid unnecessary conversion as QR internally creates a BlockRealMatrix
		BlockRealMatrix matrixInput = DataConverter.convertToBlockRealMatrix(in1);
		BlockRealMatrix vectorInput = DataConverter.convertToBlockRealMatrix(in2);
		
		/*LUDecompositionImpl ludecompose = new LUDecompositionImpl(matrixInput);
		DecompositionSolver lusolver = ludecompose.getSolver();
		RealMatrix solutionMatrix = lusolver.solve(vectorInput);*/
		
		// Setup a solver based on QR Decomposition
		QRDecomposition qrdecompose = new QRDecomposition(matrixInput);
		DecompositionSolver solver = qrdecompose.getSolver();
		// Invoke solve
		RealMatrix solutionMatrix = solver.solve(vectorInput);
		
		return DataConverter.convertToMatrixBlock(solutionMatrix);
	}
	
	/**
	 * Function to perform QR decomposition on a given matrix.
	 * 
	 * @param in matrix object
	 * @return array of matrix blocks
	 */
	private static MatrixBlock[] computeQR(MatrixBlock in) {
		Array2DRowRealMatrix matrixInput = DataConverter.convertToArray2DRowRealMatrix(in);
		
		// Perform QR decomposition
		QRDecomposition qrdecompose = new QRDecomposition(matrixInput);
		RealMatrix H = qrdecompose.getH();
		RealMatrix R = qrdecompose.getR();
		
		// Read the results into native format
		MatrixBlock mbH = DataConverter.convertToMatrixBlock(H.getData());
		MatrixBlock mbR = DataConverter.convertToMatrixBlock(R.getData());

		return new MatrixBlock[] { mbH, mbR };
	}
	
	/**
	 * Function to perform LU decomposition on a given matrix.
	 * 
	 * @param in matrix object
	 * @return array of matrix blocks
	 */
	private static MatrixBlock[] computeLU(MatrixBlock in) {
		if(in.getNumRows() != in.getNumColumns()) {
			throw new DMLRuntimeException(
				"LU Decomposition can only be done on a square matrix. Input matrix is rectangular (rows="
					+ in.getNumRows() + ", cols=" + in.getNumColumns() + ")");
		}
		
		Array2DRowRealMatrix matrixInput = DataConverter.convertToArray2DRowRealMatrix(in);
		
		// Perform LUP decomposition
		LUDecomposition ludecompose = new LUDecomposition(matrixInput);
		RealMatrix P = ludecompose.getP();
		RealMatrix L = ludecompose.getL();
		RealMatrix U = ludecompose.getU();
		
		// Read the results into native format
		MatrixBlock mbP = DataConverter.convertToMatrixBlock(P.getData());
		MatrixBlock mbL = DataConverter.convertToMatrixBlock(L.getData());
		MatrixBlock mbU = DataConverter.convertToMatrixBlock(U.getData());

		return new MatrixBlock[] { mbP, mbL, mbU };
	}
	
	/**
	 * Function to perform Eigen decomposition on a given matrix.
	 * Input must be a symmetric matrix.
	 * 
	 * @param in matrix object
	 * @return array of matrix blocks
	 */
	private static MatrixBlock[] computeEigen(MatrixBlock in) {
		if ( in.getNumRows() != in.getNumColumns() ) {
			throw new DMLRuntimeException("Eigen Decomposition can only be done on a square matrix. "
				+ "Input matrix is rectangular (rows=" + in.getNumRows() + ", cols="+ in.getNumColumns() +")");
		}
		
		EigenDecomposition eigendecompose = null;
		try {
			Array2DRowRealMatrix matrixInput = DataConverter.convertToArray2DRowRealMatrix(in);
			eigendecompose = new EigenDecomposition(matrixInput);
		}
		catch(MaxCountExceededException ex) {
			LOG.warn("Eigen: "+ ex.getMessage()+". Falling back to regularized eigen factorization.");
			eigendecompose = computeEigenRegularized(in);
		}
		
		RealMatrix eVectorsMatrix = eigendecompose.getV();
		double[][] eVectors = eVectorsMatrix.getData();
		double[] eValues = eigendecompose.getRealEigenvalues();

		return sortEVs(eValues, eVectors);
	}

	private static EigenDecomposition computeEigenRegularized(MatrixBlock in) {
		if( in == null || in.isEmptyBlock(false) )
			throw new DMLRuntimeException("Invalid empty block");
		
		//slightly modify input for regularization (pos/neg)
		MatrixBlock in2 = new MatrixBlock(in, false);
		DenseBlock a = in2.getDenseBlock();
		for( int i=0; i<in2.rlen; i++ ) {
			double[] avals = a.values(i);
			int apos = a.pos(i);
			for( int j=0; j<in2.clen; j++ ) {
				double v = avals[apos+j];
				avals[apos+j] += Math.signum(v) * EIGEN_LAMBDA;
			}
		}
		
		//run eigen decomposition
		return new EigenDecomposition(
			DataConverter.convertToArray2DRowRealMatrix(in2));
	}

	/**
	 * Performs Singular Value Decomposition. Calls Apache Commons Math SVD.
	 * X = U * Sigma * Vt, where X is the input matrix,
	 * U is the left singular matrix, Sigma is the singular values matrix returned as a
	 * column matrix and Vt is the transpose of the right singular matrix V.
	 * However, the returned array has  { U, Sigma, V}
	 * 
	 * @param in Input matrix
	 * @return An array containing U, Sigma & V
	 */
	private static MatrixBlock[] computeSvd(MatrixBlock in) {
		Array2DRowRealMatrix matrixInput = DataConverter.convertToArray2DRowRealMatrix(in);

		SingularValueDecomposition svd = new SingularValueDecomposition(matrixInput);
		double[] sigma = svd.getSingularValues();
		RealMatrix u = svd.getU();
		RealMatrix v = svd.getV();
		MatrixBlock U = DataConverter.convertToMatrixBlock(u.getData());
		MatrixBlock Sigma = DataConverter.convertToMatrixBlock(sigma, true);
		Sigma = LibMatrixReorg.diag(Sigma, new MatrixBlock(Sigma.rlen, Sigma.rlen, true));
		MatrixBlock V = DataConverter.convertToMatrixBlock(v.getData());

		return new MatrixBlock[] { U, Sigma, V };
	}
	
	/**
	 * Function to compute matrix inverse via matrix decomposition.
	 * 
	 * @param in commons-math3 Array2DRowRealMatrix
	 * @return matrix block
	 */
	private static MatrixBlock computeMatrixInverse(Array2DRowRealMatrix in) {
		if(!in.isSquare())
			throw new DMLRuntimeException("Input to inv() must be square matrix -- given: a " + in.getRowDimension()
				+ "x" + in.getColumnDimension() + " matrix.");

		QRDecomposition qrdecompose = new QRDecomposition(in);
		DecompositionSolver solver = qrdecompose.getSolver();
		RealMatrix inverseMatrix = solver.getInverse();

		return DataConverter.convertToMatrixBlock(inverseMatrix.getData());
	}

	/**
	 * Function to compute Cholesky decomposition of the given input matrix. 
	 * The input must be a real symmetric positive-definite matrix.
	 * 
	 * @param in commons-math3 Array2DRowRealMatrix
	 * @return matrix block
	 */
	private static MatrixBlock computeCholesky(Array2DRowRealMatrix in) {
		if(!in.isSquare())
			throw new DMLRuntimeException("Input to cholesky() must be square matrix -- given: a "
				+ in.getRowDimension() + "x" + in.getColumnDimension() + " matrix.");
		CholeskyDecomposition cholesky = new CholeskyDecomposition(in, RELATIVE_SYMMETRY_THRESHOLD,
			CholeskyDecomposition.DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD);
		RealMatrix rmL = cholesky.getL();
		return DataConverter.convertToMatrixBlock(rmL.getData());
	}

	/**
	 * Creates a random normalized vector with dim elements.
	 *
	 * @param dim dimension of the created vector
	 * @param threads number of threads
	 * @param seed seed for the random MatrixBlock generation
	 * @return random normalized vector
	 */
	private static MatrixBlock randNormalizedVect(int dim, int threads, long seed) {
		MatrixBlock v1 = MatrixBlock.randOperations(dim, 1, 1.0, 0.0, 1.0, "UNIFORM", seed);

		double v1_sum = v1.sum();
		ScalarOperator op_div_scalar = new RightScalarOperator(Divide.getDivideFnObject(), v1_sum, threads);
		v1 = v1.scalarOperations(op_div_scalar, new MatrixBlock());
		UnaryOperator op_sqrt = new UnaryOperator(Builtin.getBuiltinFnObject(Builtin.BuiltinCode.SQRT), threads, true);
		v1 = v1.unaryOperations(op_sqrt, new MatrixBlock());

		if(Math.abs(v1.sumSq() - 1.0) >= 1e-7)
			throw new DMLRuntimeException("v1 not correctly normalized (maybe try changing the seed)");

		return v1;
	}

	/**
	 * Function to perform the Lanczos algorithm and then computes the Eigendecomposition.
	 * Caution: Lanczos is not numerically stable (see https://en.wikipedia.org/wiki/Lanczos_algorithm)
	 * Input must be a symmetric (and square) matrix.
	 *
	 * @param in matrix object
	 * @param threads number of threads
	 * @param seed seed for the random MatrixBlock generation
	 * @return array of matrix blocks
	 */
	private static MatrixBlock[] computeEigenLanczos(MatrixBlock in, int threads, long seed) {
		if(in.getNumRows() != in.getNumColumns()) {
			throw new DMLRuntimeException(
				"Lanczos algorithm and Eigen Decomposition can only be done on a square matrix. "
					+ "Input matrix is rectangular (rows=" + in.getNumRows() + ", cols=" + in.getNumColumns() + ")");
		}

		int m = in.getNumRows();
		MatrixBlock v0 = new MatrixBlock(m, 1, 0.0);
		MatrixBlock v1 = randNormalizedVect(m, threads, seed);

		MatrixBlock T = new MatrixBlock(m, m, 0.0);
		MatrixBlock TV = new MatrixBlock(m, m, 0.0);
		MatrixBlock w1;

		ReorgOperator op_t = new ReorgOperator(SwapIndex.getSwapIndexFnObject(), threads);
		TernaryOperator op_minus_mul = new TernaryOperator(MinusMultiply.getFnObject(), threads);
		AggregateBinaryOperator op_mul_agg = InstructionUtils.getMatMultOperator(threads);
		ScalarOperator op_div_scalar = new RightScalarOperator(Divide.getDivideFnObject(), 1, threads);

		MatrixBlock beta = new MatrixBlock(1, 1, 0.0);
		for(int i = 0; i < m; i++) {
			v1.putInto(TV, 0, i, false);
			w1 = in.aggregateBinaryOperations(in, v1, op_mul_agg);
			MatrixBlock alpha = w1.aggregateBinaryOperations(v1.reorgOperations(op_t, new MatrixBlock(), 0, 0, m), w1, op_mul_agg);
			if(i < m - 1) {
				w1 = w1.ternaryOperations(op_minus_mul, v1, alpha, new MatrixBlock());
				w1 = w1.ternaryOperations(op_minus_mul, v0, beta, new MatrixBlock());
				beta.setValue(0, 0, Math.sqrt(w1.sumSq()));
				v0.copy(v1);
				op_div_scalar = op_div_scalar.setConstant(beta.getDouble(0, 0));
				w1.scalarOperations(op_div_scalar, v1);

				T.setValue(i + 1, i, beta.getValue(0, 0));
				T.setValue(i, i + 1, beta.getValue(0, 0));
			}
			T.setValue(i, i, alpha.getValue(0, 0));
		}

		MatrixBlock[] e = multiReturnOperations(T, "eigen");
		TV.setNonZeros((long) m*m);
		e[1] = TV.aggregateBinaryOperations(TV, e[1], op_mul_agg);
		return e;
	}

	/**
	 * Function to perform the QR decomposition.
	 * Input must be a square matrix.
	 * TODO: use Householder transformation and implicit shifts to further speed up QR decompositions
	 *
	 * @param in matrix object
	 * @param threads number of threads
	 * @return array of matrix blocks [Q, R]
	 */
	private static MatrixBlock[] computeQR2(MatrixBlock in, int threads) {
		if(in.getNumRows() != in.getNumColumns()) {
			throw new DMLRuntimeException("QR2 Decomposition can only be done on a square matrix. "
				+ "Input matrix is rectangular (rows=" + in.getNumRows() + ", cols=" + in.getNumColumns() + ")");
		}

		int m = in.rlen;

		MatrixBlock A_n = new MatrixBlock();
		A_n.copy(in);

		MatrixBlock Q_n = new MatrixBlock(m, m, true);
		for(int i = 0; i < m; i++) {
			Q_n.setValue(i, i, 1.0);
		}

		ReorgOperator op_t = new ReorgOperator(SwapIndex.getSwapIndexFnObject(), threads);
		AggregateBinaryOperator op_mul_agg = InstructionUtils.getMatMultOperator(threads);
		BinaryOperator op_sub = InstructionUtils.parseExtendedBinaryOperator("-");
		ScalarOperator op_div_scalar = new RightScalarOperator(Divide.getDivideFnObject(), 1, threads);
		ScalarOperator op_mult_2 = new LeftScalarOperator(Multiply.getMultiplyFnObject(), 2, threads);

		for(int k = 0; k < m; k++) {
			MatrixBlock z = A_n.slice(k, m - 1, k, k);
			MatrixBlock uk = new MatrixBlock(m - k, 1, 0.0);
			uk.copy(z);
			uk.setValue(0, 0, uk.getValue(0, 0) + Math.signum(z.getValue(0, 0)) * Math.sqrt(z.sumSq()));
			op_div_scalar = op_div_scalar.setConstant(Math.sqrt(uk.sumSq()));
			uk = uk.scalarOperations(op_div_scalar, new MatrixBlock());

			MatrixBlock vk = new MatrixBlock(m, 1, 0.0);
			vk.copy(k, m - 1, 0, 0, uk, true);

			MatrixBlock vkt = vk.reorgOperations(op_t, new MatrixBlock(), 0, 0, m);
			MatrixBlock vkt2 = vkt.scalarOperations(op_mult_2, new MatrixBlock());
			MatrixBlock vkvkt2 = vk.aggregateBinaryOperations(vk, vkt2, op_mul_agg);

			A_n = A_n.binaryOperations(op_sub, A_n.aggregateBinaryOperations(vkvkt2, A_n, op_mul_agg));
			Q_n = Q_n.binaryOperations(op_sub, Q_n.aggregateBinaryOperations(Q_n, vkvkt2, op_mul_agg));
		}
		// QR decomp: Q: Q_n; R: A_n
		return new MatrixBlock[] {Q_n, A_n};
	}

	/**
	 * Function that computes the Eigen Decomposition using the QR algorithm.
	 * Caution: check if the QR algorithm is converged, if not increase iterations
	 * Caution: if the input matrix has complex eigenvalues results will be incorrect
	 *
	 * @param in Input matrix
	 * @param threads number of threads
	 * @return array of matrix blocks
	 */
	private static MatrixBlock[] computeEigenQR(MatrixBlock in, int threads) {
		return computeEigenQR(in, 100, 1e-10, threads);
	}

	private static MatrixBlock[] computeEigenQR(MatrixBlock in, int num_iterations, double tol, int threads) {
		if(in.getNumRows() != in.getNumColumns()) {
			throw new DMLRuntimeException("Eigen Decomposition (QR) can only be done on a square matrix. "
				+ "Input matrix is rectangular (rows=" + in.getNumRows() + ", cols=" + in.getNumColumns() + ")");
		}

		int m = in.rlen;
		AggregateBinaryOperator op_mul_agg = InstructionUtils.getMatMultOperator(threads);

		MatrixBlock Q_prod = new MatrixBlock(m, m, 0.0);
		for(int i = 0; i < m; i++) {
			Q_prod.setValue(i, i, 1.0);
		}

		for(int i = 0; i < num_iterations; i++) {
			MatrixBlock[] QR = computeQR2(in, threads);
			Q_prod = Q_prod.aggregateBinaryOperations(Q_prod, QR[0], op_mul_agg);
			in = QR[1].aggregateBinaryOperations(QR[1], QR[0], op_mul_agg);
		}

		// Is converged if all values are below tol and the there only is values on the diagonal.

		double[] check = in.getDenseBlockValues();
		double[] eval = new double[m];
		for(int i = 0; i < m; i++)
			eval[i] = check[i*m+i];
		
		double[] evec = Q_prod.getDenseBlockValues();
		return sortEVs(eval, evec);
	}

	/**
	 * Function to compute the Householder transformation of a Matrix.
	 *
	 * @param in Input Matrix
	 * @param threads number of threads
	 * @return transformed matrix
	 */
	@SuppressWarnings("unused")
	private static MatrixBlock computeHouseholder(MatrixBlock in, int threads) {
		int m = in.rlen;

		MatrixBlock A_n = new MatrixBlock(m, m, 0.0);
		A_n.copy(in);

		for(int k = 0; k < m - 2; k++) {
			MatrixBlock ajk = A_n.slice(0, m - 1, k, k);
			for(int i = 0; i <= k; i++) {
				ajk.setValue(i, 0, 0.0);
			}
			double alpha = Math.sqrt(ajk.sumSq());
			double ak1k = A_n.getDouble(k + 1, k);
			if(ak1k > 0.0)
				alpha *= -1;
			double r = Math.sqrt(0.5 * (alpha * alpha - ak1k * alpha));
			MatrixBlock v = new MatrixBlock(m, 1, 0.0);
			v.copy(ajk);
			v.setValue(k + 1, 0, ak1k - alpha);
			ScalarOperator op_div_scalar = new RightScalarOperator(Divide.getDivideFnObject(), 2 * r, threads);
			v = v.scalarOperations(op_div_scalar, new MatrixBlock());

			MatrixBlock P = new MatrixBlock(m, m, 0.0);
			for(int i = 0; i < m; i++) {
				P.setValue(i, i, 1.0);
			}

			ReorgOperator op_t = new ReorgOperator(SwapIndex.getSwapIndexFnObject(), threads);
			AggregateBinaryOperator op_mul_agg = InstructionUtils.getMatMultOperator(threads);
			BinaryOperator op_add = InstructionUtils.parseExtendedBinaryOperator("+");
			BinaryOperator op_sub = InstructionUtils.parseExtendedBinaryOperator("-");

			MatrixBlock v_t = v.reorgOperations(op_t, new MatrixBlock(), 0, 0, m);
			v_t = v_t.binaryOperations(op_add, v_t);
			MatrixBlock v_v_t_2 = A_n.aggregateBinaryOperations(v, v_t, op_mul_agg);
			P = P.binaryOperations(op_sub, v_v_t_2);
			A_n = A_n.aggregateBinaryOperations(P, A_n.aggregateBinaryOperations(A_n, P, op_mul_agg), op_mul_agg);
		}
		return A_n;
	}

	/**
	 * Sort the eigen values (and vectors) in increasing order (to be compatible w/ LAPACK.DSYEVR())
	 *
	 * @param eValues  Eigenvalues
	 * @param eVectors Eigenvectors
	 * @return array of matrix blocks
	 */
	private static MatrixBlock[] sortEVs(double[] eValues, double[][] eVectors) {
		int n = eValues.length;
		for(int i = 0; i < n; i++) {
			int k = i;
			double p = eValues[i];
			for(int j = i + 1; j < n; j++) {
				if(eValues[j] < p) {
					k = j;
					p = eValues[j];
				}
			}
			if(k != i) {
				eValues[k] = eValues[i];
				eValues[i] = p;
				for(int j = 0; j < n; j++) {
					p = eVectors[j][i];
					eVectors[j][i] = eVectors[j][k];
					eVectors[j][k] = p;
				}
			}
		}

		MatrixBlock eval = DataConverter.convertToMatrixBlock(eValues, true);
		MatrixBlock evec = DataConverter.convertToMatrixBlock(eVectors);
		return new MatrixBlock[] {eval, evec};
	}

	private static MatrixBlock[] sortEVs(double[] eValues, double[] eVectors) {
		int n = eValues.length;
		for(int i = 0; i < n; i++) {
			int k = i;
			double p = eValues[i];
			for(int j = i + 1; j < n; j++) {
				if(eValues[j] < p) {
					k = j;
					p = eValues[j];
				}
			}
			if(k != i) {
				eValues[k] = eValues[i];
				eValues[i] = p;
				for(int j = 0; j < n; j++) {
					p = eVectors[j*n+i];
					eVectors[j*n+i] = eVectors[j*n+k];
					eVectors[j*n+k] = p;
				}
			}
		}

		MatrixBlock eval = DataConverter.convertToMatrixBlock(eValues, true);
		MatrixBlock evec = new MatrixBlock(n, n, false);
		evec.init(eVectors, n, n);
		return new MatrixBlock[] {eval, evec};
	}
}
