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From t.@apache.org
Subject [05/82] [partial] [math] Update for next development iteration: commons-math4
Date Mon, 16 Feb 2015 22:39:35 GMT
http://git-wip-us.apache.org/repos/asf/commons-math/blob/a7b4803f/src/main/java/org/apache/commons/math3/linear/BlockRealMatrix.java
----------------------------------------------------------------------
diff --git a/src/main/java/org/apache/commons/math3/linear/BlockRealMatrix.java b/src/main/java/org/apache/commons/math3/linear/BlockRealMatrix.java
deleted file mode 100644
index 1ea22b6..0000000
--- a/src/main/java/org/apache/commons/math3/linear/BlockRealMatrix.java
+++ /dev/null
@@ -1,1581 +0,0 @@
-/*
- * 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.commons.math3.linear;
-
-import java.io.Serializable;
-import java.util.Arrays;
-
-import org.apache.commons.math3.exception.DimensionMismatchException;
-import org.apache.commons.math3.exception.NoDataException;
-import org.apache.commons.math3.exception.NotStrictlyPositiveException;
-import org.apache.commons.math3.exception.NullArgumentException;
-import org.apache.commons.math3.exception.NumberIsTooSmallException;
-import org.apache.commons.math3.exception.OutOfRangeException;
-import org.apache.commons.math3.exception.util.LocalizedFormats;
-import org.apache.commons.math3.util.FastMath;
-import org.apache.commons.math3.util.MathUtils;
-
-/**
- * Cache-friendly implementation of RealMatrix using a flat arrays to store
- * square blocks of the matrix.
- * <p>
- * This implementation is specially designed to be cache-friendly. Square blocks are
- * stored as small arrays and allow efficient traversal of data both in row major direction
- * and columns major direction, one block at a time. This greatly increases performances
- * for algorithms that use crossed directions loops like multiplication or transposition.
- * </p>
- * <p>
- * The size of square blocks is a static parameter. It may be tuned according to the cache
- * size of the target computer processor. As a rule of thumbs, it should be the largest
- * value that allows three blocks to be simultaneously cached (this is necessary for example
- * for matrix multiplication). The default value is to use 52x52 blocks which is well suited
- * for processors with 64k L1 cache (one block holds 2704 values or 21632 bytes). This value
- * could be lowered to 36x36 for processors with 32k L1 cache.
- * </p>
- * <p>
- * The regular blocks represent {@link #BLOCK_SIZE} x {@link #BLOCK_SIZE} squares. Blocks
- * at right hand side and bottom side which may be smaller to fit matrix dimensions. The square
- * blocks are flattened in row major order in single dimension arrays which are therefore
- * {@link #BLOCK_SIZE}<sup>2</sup> elements long for regular blocks. The blocks are themselves
- * organized in row major order.
- * </p>
- * <p>
- * As an example, for a block size of 52x52, a 100x60 matrix would be stored in 4 blocks.
- * Block 0 would be a double[2704] array holding the upper left 52x52 square, block 1 would be
- * a double[416] array holding the upper right 52x8 rectangle, block 2 would be a double[2496]
- * array holding the lower left 48x52 rectangle and block 3 would be a double[384] array
- * holding the lower right 48x8 rectangle.
- * </p>
- * <p>
- * The layout complexity overhead versus simple mapping of matrices to java
- * arrays is negligible for small matrices (about 1%). The gain from cache efficiency leads
- * to up to 3-fold improvements for matrices of moderate to large size.
- * </p>
- * @since 2.0
- */
-public class BlockRealMatrix extends AbstractRealMatrix implements Serializable {
-    /** Block size. */
-    public static final int BLOCK_SIZE = 52;
-    /** Serializable version identifier */
-    private static final long serialVersionUID = 4991895511313664478L;
-    /** Blocks of matrix entries. */
-    private final double blocks[][];
-    /** Number of rows of the matrix. */
-    private final int rows;
-    /** Number of columns of the matrix. */
-    private final int columns;
-    /** Number of block rows of the matrix. */
-    private final int blockRows;
-    /** Number of block columns of the matrix. */
-    private final int blockColumns;
-
-    /**
-     * Create a new matrix with the supplied row and column dimensions.
-     *
-     * @param rows  the number of rows in the new matrix
-     * @param columns  the number of columns in the new matrix
-     * @throws NotStrictlyPositiveException if row or column dimension is not
-     * positive.
-     */
-    public BlockRealMatrix(final int rows, final int columns)
-        throws NotStrictlyPositiveException {
-        super(rows, columns);
-        this.rows = rows;
-        this.columns = columns;
-
-        // number of blocks
-        blockRows = (rows + BLOCK_SIZE - 1) / BLOCK_SIZE;
-        blockColumns = (columns + BLOCK_SIZE - 1) / BLOCK_SIZE;
-
-        // allocate storage blocks, taking care of smaller ones at right and bottom
-        blocks = createBlocksLayout(rows, columns);
-    }
-
-    /**
-     * Create a new dense matrix copying entries from raw layout data.
-     * <p>The input array <em>must</em> already be in raw layout.</p>
-     * <p>Calling this constructor is equivalent to call:
-     * <pre>matrix = new BlockRealMatrix(rawData.length, rawData[0].length,
-     *                                   toBlocksLayout(rawData), false);</pre>
-     * </p>
-     *
-     * @param rawData data for new matrix, in raw layout
-     * @throws DimensionMismatchException if the shape of {@code blockData} is
-     * inconsistent with block layout.
-     * @throws NotStrictlyPositiveException if row or column dimension is not
-     * positive.
-     * @see #BlockRealMatrix(int, int, double[][], boolean)
-     */
-    public BlockRealMatrix(final double[][] rawData)
-        throws DimensionMismatchException, NotStrictlyPositiveException {
-        this(rawData.length, rawData[0].length, toBlocksLayout(rawData), false);
-    }
-
-    /**
-     * Create a new dense matrix copying entries from block layout data.
-     * <p>The input array <em>must</em> already be in blocks layout.</p>
-     *
-     * @param rows Number of rows in the new matrix.
-     * @param columns Number of columns in the new matrix.
-     * @param blockData data for new matrix
-     * @param copyArray Whether the input array will be copied or referenced.
-     * @throws DimensionMismatchException if the shape of {@code blockData} is
-     * inconsistent with block layout.
-     * @throws NotStrictlyPositiveException if row or column dimension is not
-     * positive.
-     * @see #createBlocksLayout(int, int)
-     * @see #toBlocksLayout(double[][])
-     * @see #BlockRealMatrix(double[][])
-     */
-    public BlockRealMatrix(final int rows, final int columns,
-                           final double[][] blockData, final boolean copyArray)
-        throws DimensionMismatchException, NotStrictlyPositiveException {
-        super(rows, columns);
-        this.rows = rows;
-        this.columns = columns;
-
-        // number of blocks
-        blockRows = (rows + BLOCK_SIZE - 1) / BLOCK_SIZE;
-        blockColumns = (columns + BLOCK_SIZE - 1) / BLOCK_SIZE;
-
-        if (copyArray) {
-            // allocate storage blocks, taking care of smaller ones at right and bottom
-            blocks = new double[blockRows * blockColumns][];
-        } else {
-            // reference existing array
-            blocks = blockData;
-        }
-
-        int index = 0;
-        for (int iBlock = 0; iBlock < blockRows; ++iBlock) {
-            final int iHeight = blockHeight(iBlock);
-            for (int jBlock = 0; jBlock < blockColumns; ++jBlock, ++index) {
-                if (blockData[index].length != iHeight * blockWidth(jBlock)) {
-                    throw new DimensionMismatchException(blockData[index].length,
-                                                         iHeight * blockWidth(jBlock));
-                }
-                if (copyArray) {
-                    blocks[index] = blockData[index].clone();
-                }
-            }
-        }
-    }
-
-    /**
-     * Convert a data array from raw layout to blocks layout.
-     * <p>
-     * Raw layout is the straightforward layout where element at row i and
-     * column j is in array element <code>rawData[i][j]</code>. Blocks layout
-     * is the layout used in {@link BlockRealMatrix} instances, where the matrix
-     * is split in square blocks (except at right and bottom side where blocks may
-     * be rectangular to fit matrix size) and each block is stored in a flattened
-     * one-dimensional array.
-     * </p>
-     * <p>
-     * This method creates an array in blocks layout from an input array in raw layout.
-     * It can be used to provide the array argument of the {@link
-     * #BlockRealMatrix(int, int, double[][], boolean)} constructor.
-     * </p>
-     * @param rawData Data array in raw layout.
-     * @return a new data array containing the same entries but in blocks layout.
-     * @throws DimensionMismatchException if {@code rawData} is not rectangular.
-     * @see #createBlocksLayout(int, int)
-     * @see #BlockRealMatrix(int, int, double[][], boolean)
-     */
-    public static double[][] toBlocksLayout(final double[][] rawData)
-        throws DimensionMismatchException {
-        final int rows = rawData.length;
-        final int columns = rawData[0].length;
-        final int blockRows = (rows    + BLOCK_SIZE - 1) / BLOCK_SIZE;
-        final int blockColumns = (columns + BLOCK_SIZE - 1) / BLOCK_SIZE;
-
-        // safety checks
-        for (int i = 0; i < rawData.length; ++i) {
-            final int length = rawData[i].length;
-            if (length != columns) {
-                throw new DimensionMismatchException(columns, length);
-            }
-        }
-
-        // convert array
-        final double[][] blocks = new double[blockRows * blockColumns][];
-        int blockIndex = 0;
-        for (int iBlock = 0; iBlock < blockRows; ++iBlock) {
-            final int pStart = iBlock * BLOCK_SIZE;
-            final int pEnd = FastMath.min(pStart + BLOCK_SIZE, rows);
-            final int iHeight = pEnd - pStart;
-            for (int jBlock = 0; jBlock < blockColumns; ++jBlock) {
-                final int qStart = jBlock * BLOCK_SIZE;
-                final int qEnd = FastMath.min(qStart + BLOCK_SIZE, columns);
-                final int jWidth = qEnd - qStart;
-
-                // allocate new block
-                final double[] block = new double[iHeight * jWidth];
-                blocks[blockIndex] = block;
-
-                // copy data
-                int index = 0;
-                for (int p = pStart; p < pEnd; ++p) {
-                    System.arraycopy(rawData[p], qStart, block, index, jWidth);
-                    index += jWidth;
-                }
-                ++blockIndex;
-            }
-        }
-
-        return blocks;
-    }
-
-    /**
-     * Create a data array in blocks layout.
-     * <p>
-     * This method can be used to create the array argument of the {@link
-     * #BlockRealMatrix(int, int, double[][], boolean)} constructor.
-     * </p>
-     * @param rows Number of rows in the new matrix.
-     * @param columns Number of columns in the new matrix.
-     * @return a new data array in blocks layout.
-     * @see #toBlocksLayout(double[][])
-     * @see #BlockRealMatrix(int, int, double[][], boolean)
-     */
-    public static double[][] createBlocksLayout(final int rows, final int columns) {
-        final int blockRows = (rows    + BLOCK_SIZE - 1) / BLOCK_SIZE;
-        final int blockColumns = (columns + BLOCK_SIZE - 1) / BLOCK_SIZE;
-
-        final double[][] blocks = new double[blockRows * blockColumns][];
-        int blockIndex = 0;
-        for (int iBlock = 0; iBlock < blockRows; ++iBlock) {
-            final int pStart = iBlock * BLOCK_SIZE;
-            final int pEnd = FastMath.min(pStart + BLOCK_SIZE, rows);
-            final int iHeight = pEnd - pStart;
-            for (int jBlock = 0; jBlock < blockColumns; ++jBlock) {
-                final int qStart = jBlock * BLOCK_SIZE;
-                final int qEnd = FastMath.min(qStart + BLOCK_SIZE, columns);
-                final int jWidth = qEnd - qStart;
-                blocks[blockIndex] = new double[iHeight * jWidth];
-                ++blockIndex;
-            }
-        }
-
-        return blocks;
-    }
-
-    /** {@inheritDoc} */
-    @Override
-    public BlockRealMatrix createMatrix(final int rowDimension,
-                                        final int columnDimension)
-        throws NotStrictlyPositiveException {
-        return new BlockRealMatrix(rowDimension, columnDimension);
-    }
-
-    /** {@inheritDoc} */
-    @Override
-    public BlockRealMatrix copy() {
-        // create an empty matrix
-        BlockRealMatrix copied = new BlockRealMatrix(rows, columns);
-
-        // copy the blocks
-        for (int i = 0; i < blocks.length; ++i) {
-            System.arraycopy(blocks[i], 0, copied.blocks[i], 0, blocks[i].length);
-        }
-
-        return copied;
-    }
-
-    /** {@inheritDoc} */
-    @Override
-    public BlockRealMatrix add(final RealMatrix m)
-        throws MatrixDimensionMismatchException {
-        try {
-            return add((BlockRealMatrix) m);
-        } catch (ClassCastException cce) {
-            // safety check
-            MatrixUtils.checkAdditionCompatible(this, m);
-
-            final BlockRealMatrix out = new BlockRealMatrix(rows, columns);
-
-            // perform addition block-wise, to ensure good cache behavior
-            int blockIndex = 0;
-            for (int iBlock = 0; iBlock < out.blockRows; ++iBlock) {
-                for (int jBlock = 0; jBlock < out.blockColumns; ++jBlock) {
-
-                    // perform addition on the current block
-                    final double[] outBlock = out.blocks[blockIndex];
-                    final double[] tBlock   = blocks[blockIndex];
-                    final int pStart = iBlock * BLOCK_SIZE;
-                    final int pEnd = FastMath.min(pStart + BLOCK_SIZE, rows);
-                    final int qStart = jBlock * BLOCK_SIZE;
-                    final int qEnd = FastMath.min(qStart + BLOCK_SIZE, columns);
-                    int k = 0;
-                    for (int p = pStart; p < pEnd; ++p) {
-                        for (int q = qStart; q < qEnd; ++q) {
-                            outBlock[k] = tBlock[k] + m.getEntry(p, q);
-                            ++k;
-                        }
-                    }
-                    // go to next block
-                    ++blockIndex;
-                }
-            }
-
-            return out;
-        }
-    }
-
-    /**
-     * Compute the sum of this matrix and {@code m}.
-     *
-     * @param m Matrix to be added.
-     * @return {@code this} + m.
-     * @throws MatrixDimensionMismatchException if {@code m} is not the same
-     * size as this matrix.
-     */
-    public BlockRealMatrix add(final BlockRealMatrix m)
-        throws MatrixDimensionMismatchException {
-        // safety check
-        MatrixUtils.checkAdditionCompatible(this, m);
-
-        final BlockRealMatrix out = new BlockRealMatrix(rows, columns);
-
-        // perform addition block-wise, to ensure good cache behavior
-        for (int blockIndex = 0; blockIndex < out.blocks.length; ++blockIndex) {
-            final double[] outBlock = out.blocks[blockIndex];
-            final double[] tBlock = blocks[blockIndex];
-            final double[] mBlock = m.blocks[blockIndex];
-            for (int k = 0; k < outBlock.length; ++k) {
-                outBlock[k] = tBlock[k] + mBlock[k];
-            }
-        }
-
-        return out;
-    }
-
-    /** {@inheritDoc} */
-    @Override
-    public BlockRealMatrix subtract(final RealMatrix m)
-        throws MatrixDimensionMismatchException {
-        try {
-            return subtract((BlockRealMatrix) m);
-        } catch (ClassCastException cce) {
-            // safety check
-            MatrixUtils.checkSubtractionCompatible(this, m);
-
-            final BlockRealMatrix out = new BlockRealMatrix(rows, columns);
-
-            // perform subtraction block-wise, to ensure good cache behavior
-            int blockIndex = 0;
-            for (int iBlock = 0; iBlock < out.blockRows; ++iBlock) {
-                for (int jBlock = 0; jBlock < out.blockColumns; ++jBlock) {
-
-                    // perform subtraction on the current block
-                    final double[] outBlock = out.blocks[blockIndex];
-                    final double[] tBlock = blocks[blockIndex];
-                    final int pStart = iBlock * BLOCK_SIZE;
-                    final int pEnd = FastMath.min(pStart + BLOCK_SIZE, rows);
-                    final int qStart = jBlock * BLOCK_SIZE;
-                    final int qEnd = FastMath.min(qStart + BLOCK_SIZE, columns);
-                    int k = 0;
-                    for (int p = pStart; p < pEnd; ++p) {
-                        for (int q = qStart; q < qEnd; ++q) {
-                            outBlock[k] = tBlock[k] - m.getEntry(p, q);
-                            ++k;
-                        }
-                    }
-                    // go to next block
-                    ++blockIndex;
-                }
-            }
-
-            return out;
-        }
-    }
-
-    /**
-     * Subtract {@code m} from this matrix.
-     *
-     * @param m Matrix to be subtracted.
-     * @return {@code this} - m.
-     * @throws MatrixDimensionMismatchException if {@code m} is not the
-     * same size as this matrix.
-     */
-    public BlockRealMatrix subtract(final BlockRealMatrix m)
-        throws MatrixDimensionMismatchException {
-        // safety check
-        MatrixUtils.checkSubtractionCompatible(this, m);
-
-        final BlockRealMatrix out = new BlockRealMatrix(rows, columns);
-
-        // perform subtraction block-wise, to ensure good cache behavior
-        for (int blockIndex = 0; blockIndex < out.blocks.length; ++blockIndex) {
-            final double[] outBlock = out.blocks[blockIndex];
-            final double[] tBlock = blocks[blockIndex];
-            final double[] mBlock = m.blocks[blockIndex];
-            for (int k = 0; k < outBlock.length; ++k) {
-                outBlock[k] = tBlock[k] - mBlock[k];
-            }
-        }
-
-        return out;
-    }
-
-    /** {@inheritDoc} */
-    @Override
-    public BlockRealMatrix scalarAdd(final double d) {
-
-        final BlockRealMatrix out = new BlockRealMatrix(rows, columns);
-
-        // perform subtraction block-wise, to ensure good cache behavior
-        for (int blockIndex = 0; blockIndex < out.blocks.length; ++blockIndex) {
-            final double[] outBlock = out.blocks[blockIndex];
-            final double[] tBlock = blocks[blockIndex];
-            for (int k = 0; k < outBlock.length; ++k) {
-                outBlock[k] = tBlock[k] + d;
-            }
-        }
-
-        return out;
-    }
-
-    /** {@inheritDoc} */
-    @Override
-    public RealMatrix scalarMultiply(final double d) {
-        final BlockRealMatrix out = new BlockRealMatrix(rows, columns);
-
-        // perform subtraction block-wise, to ensure good cache behavior
-        for (int blockIndex = 0; blockIndex < out.blocks.length; ++blockIndex) {
-            final double[] outBlock = out.blocks[blockIndex];
-            final double[] tBlock = blocks[blockIndex];
-            for (int k = 0; k < outBlock.length; ++k) {
-                outBlock[k] = tBlock[k] * d;
-            }
-        }
-
-        return out;
-    }
-
-    /** {@inheritDoc} */
-    @Override
-    public BlockRealMatrix multiply(final RealMatrix m)
-        throws DimensionMismatchException {
-        try {
-            return multiply((BlockRealMatrix) m);
-        } catch (ClassCastException cce) {
-            // safety check
-            MatrixUtils.checkMultiplicationCompatible(this, m);
-
-            final BlockRealMatrix out = new BlockRealMatrix(rows, m.getColumnDimension());
-
-            // perform multiplication block-wise, to ensure good cache behavior
-            int blockIndex = 0;
-            for (int iBlock = 0; iBlock < out.blockRows; ++iBlock) {
-                final int pStart = iBlock * BLOCK_SIZE;
-                final int pEnd = FastMath.min(pStart + BLOCK_SIZE, rows);
-
-                for (int jBlock = 0; jBlock < out.blockColumns; ++jBlock) {
-                    final int qStart = jBlock * BLOCK_SIZE;
-                    final int qEnd = FastMath.min(qStart + BLOCK_SIZE, m.getColumnDimension());
-
-                    // select current block
-                    final double[] outBlock = out.blocks[blockIndex];
-
-                    // perform multiplication on current block
-                    for (int kBlock = 0; kBlock < blockColumns; ++kBlock) {
-                        final int kWidth = blockWidth(kBlock);
-                        final double[] tBlock = blocks[iBlock * blockColumns + kBlock];
-                        final int rStart = kBlock * BLOCK_SIZE;
-                        int k = 0;
-                        for (int p = pStart; p < pEnd; ++p) {
-                            final int lStart = (p - pStart) * kWidth;
-                            final int lEnd = lStart + kWidth;
-                            for (int q = qStart; q < qEnd; ++q) {
-                                double sum = 0;
-                                int r = rStart;
-                                for (int l = lStart; l < lEnd; ++l) {
-                                    sum += tBlock[l] * m.getEntry(r, q);
-                                    ++r;
-                                }
-                                outBlock[k] += sum;
-                                ++k;
-                            }
-                        }
-                    }
-                    // go to next block
-                    ++blockIndex;
-                }
-            }
-
-            return out;
-        }
-    }
-
-    /**
-     * Returns the result of postmultiplying this by {@code m}.
-     *
-     * @param m Matrix to postmultiply by.
-     * @return {@code this} * m.
-     * @throws DimensionMismatchException if the matrices are not compatible.
-     */
-    public BlockRealMatrix multiply(BlockRealMatrix m)
-        throws DimensionMismatchException {
-        // safety check
-        MatrixUtils.checkMultiplicationCompatible(this, m);
-
-        final BlockRealMatrix out = new BlockRealMatrix(rows, m.columns);
-
-        // perform multiplication block-wise, to ensure good cache behavior
-        int blockIndex = 0;
-        for (int iBlock = 0; iBlock < out.blockRows; ++iBlock) {
-
-            final int pStart = iBlock * BLOCK_SIZE;
-            final int pEnd = FastMath.min(pStart + BLOCK_SIZE, rows);
-
-            for (int jBlock = 0; jBlock < out.blockColumns; ++jBlock) {
-                final int jWidth = out.blockWidth(jBlock);
-                final int jWidth2 = jWidth  + jWidth;
-                final int jWidth3 = jWidth2 + jWidth;
-                final int jWidth4 = jWidth3 + jWidth;
-
-                // select current block
-                final double[] outBlock = out.blocks[blockIndex];
-
-                // perform multiplication on current block
-                for (int kBlock = 0; kBlock < blockColumns; ++kBlock) {
-                    final int kWidth = blockWidth(kBlock);
-                    final double[] tBlock = blocks[iBlock * blockColumns + kBlock];
-                    final double[] mBlock = m.blocks[kBlock * m.blockColumns + jBlock];
-                    int k = 0;
-                    for (int p = pStart; p < pEnd; ++p) {
-                        final int lStart = (p - pStart) * kWidth;
-                        final int lEnd = lStart + kWidth;
-                        for (int nStart = 0; nStart < jWidth; ++nStart) {
-                            double sum = 0;
-                            int l = lStart;
-                            int n = nStart;
-                            while (l < lEnd - 3) {
-                                sum += tBlock[l] * mBlock[n] +
-                                       tBlock[l + 1] * mBlock[n + jWidth] +
-                                       tBlock[l + 2] * mBlock[n + jWidth2] +
-                                       tBlock[l + 3] * mBlock[n + jWidth3];
-                                l += 4;
-                                n += jWidth4;
-                            }
-                            while (l < lEnd) {
-                                sum += tBlock[l++] * mBlock[n];
-                                n += jWidth;
-                            }
-                            outBlock[k] += sum;
-                            ++k;
-                        }
-                    }
-                }
-                // go to next block
-                ++blockIndex;
-            }
-        }
-
-        return out;
-    }
-
-    /** {@inheritDoc} */
-    @Override
-    public double[][] getData() {
-        final double[][] data = new double[getRowDimension()][getColumnDimension()];
-        final int lastColumns = columns - (blockColumns - 1) * BLOCK_SIZE;
-
-        for (int iBlock = 0; iBlock < blockRows; ++iBlock) {
-            final int pStart = iBlock * BLOCK_SIZE;
-            final int pEnd = FastMath.min(pStart + BLOCK_SIZE, rows);
-            int regularPos = 0;
-            int lastPos = 0;
-            for (int p = pStart; p < pEnd; ++p) {
-                final double[] dataP = data[p];
-                int blockIndex = iBlock * blockColumns;
-                int dataPos = 0;
-                for (int jBlock = 0; jBlock < blockColumns - 1; ++jBlock) {
-                    System.arraycopy(blocks[blockIndex++], regularPos, dataP, dataPos, BLOCK_SIZE);
-                    dataPos += BLOCK_SIZE;
-                }
-                System.arraycopy(blocks[blockIndex], lastPos, dataP, dataPos, lastColumns);
-                regularPos += BLOCK_SIZE;
-                lastPos    += lastColumns;
-            }
-        }
-
-        return data;
-    }
-
-    /** {@inheritDoc} */
-    @Override
-    public double getNorm() {
-        final double[] colSums = new double[BLOCK_SIZE];
-        double maxColSum = 0;
-        for (int jBlock = 0; jBlock < blockColumns; jBlock++) {
-            final int jWidth = blockWidth(jBlock);
-            Arrays.fill(colSums, 0, jWidth, 0.0);
-            for (int iBlock = 0; iBlock < blockRows; ++iBlock) {
-                final int iHeight = blockHeight(iBlock);
-                final double[] block = blocks[iBlock * blockColumns + jBlock];
-                for (int j = 0; j < jWidth; ++j) {
-                    double sum = 0;
-                    for (int i = 0; i < iHeight; ++i) {
-                        sum += FastMath.abs(block[i * jWidth + j]);
-                    }
-                    colSums[j] += sum;
-                }
-            }
-            for (int j = 0; j < jWidth; ++j) {
-                maxColSum = FastMath.max(maxColSum, colSums[j]);
-            }
-        }
-        return maxColSum;
-    }
-
-    /** {@inheritDoc} */
-    @Override
-    public double getFrobeniusNorm() {
-        double sum2 = 0;
-        for (int blockIndex = 0; blockIndex < blocks.length; ++blockIndex) {
-            for (final double entry : blocks[blockIndex]) {
-                sum2 += entry * entry;
-            }
-        }
-        return FastMath.sqrt(sum2);
-    }
-
-    /** {@inheritDoc} */
-    @Override
-    public BlockRealMatrix getSubMatrix(final int startRow, final int endRow,
-                                        final int startColumn,
-                                        final int endColumn)
-        throws OutOfRangeException, NumberIsTooSmallException {
-        // safety checks
-        MatrixUtils.checkSubMatrixIndex(this, startRow, endRow, startColumn, endColumn);
-
-        // create the output matrix
-        final BlockRealMatrix out =
-            new BlockRealMatrix(endRow - startRow + 1, endColumn - startColumn + 1);
-
-        // compute blocks shifts
-        final int blockStartRow = startRow / BLOCK_SIZE;
-        final int rowsShift = startRow % BLOCK_SIZE;
-        final int blockStartColumn = startColumn / BLOCK_SIZE;
-        final int columnsShift = startColumn % BLOCK_SIZE;
-
-        // perform extraction block-wise, to ensure good cache behavior
-        int pBlock = blockStartRow;
-        for (int iBlock = 0; iBlock < out.blockRows; ++iBlock) {
-            final int iHeight = out.blockHeight(iBlock);
-            int qBlock = blockStartColumn;
-            for (int jBlock = 0; jBlock < out.blockColumns; ++jBlock) {
-                final int jWidth = out.blockWidth(jBlock);
-
-                // handle one block of the output matrix
-                final int outIndex = iBlock * out.blockColumns + jBlock;
-                final double[] outBlock = out.blocks[outIndex];
-                final int index = pBlock * blockColumns + qBlock;
-                final int width = blockWidth(qBlock);
-
-                final int heightExcess = iHeight + rowsShift - BLOCK_SIZE;
-                final int widthExcess = jWidth + columnsShift - BLOCK_SIZE;
-                if (heightExcess > 0) {
-                    // the submatrix block spans on two blocks rows from the original matrix
-                    if (widthExcess > 0) {
-                        // the submatrix block spans on two blocks columns from the original matrix
-                        final int width2 = blockWidth(qBlock + 1);
-                        copyBlockPart(blocks[index], width,
-                                      rowsShift, BLOCK_SIZE,
-                                      columnsShift, BLOCK_SIZE,
-                                      outBlock, jWidth, 0, 0);
-                        copyBlockPart(blocks[index + 1], width2,
-                                      rowsShift, BLOCK_SIZE,
-                                      0, widthExcess,
-                                      outBlock, jWidth, 0, jWidth - widthExcess);
-                        copyBlockPart(blocks[index + blockColumns], width,
-                                      0, heightExcess,
-                                      columnsShift, BLOCK_SIZE,
-                                      outBlock, jWidth, iHeight - heightExcess, 0);
-                        copyBlockPart(blocks[index + blockColumns + 1], width2,
-                                      0, heightExcess,
-                                      0, widthExcess,
-                                      outBlock, jWidth, iHeight - heightExcess, jWidth - widthExcess);
-                    } else {
-                        // the submatrix block spans on one block column from the original matrix
-                        copyBlockPart(blocks[index], width,
-                                      rowsShift, BLOCK_SIZE,
-                                      columnsShift, jWidth + columnsShift,
-                                      outBlock, jWidth, 0, 0);
-                        copyBlockPart(blocks[index + blockColumns], width,
-                                      0, heightExcess,
-                                      columnsShift, jWidth + columnsShift,
-                                      outBlock, jWidth, iHeight - heightExcess, 0);
-                    }
-                } else {
-                    // the submatrix block spans on one block row from the original matrix
-                    if (widthExcess > 0) {
-                        // the submatrix block spans on two blocks columns from the original matrix
-                        final int width2 = blockWidth(qBlock + 1);
-                        copyBlockPart(blocks[index], width,
-                                      rowsShift, iHeight + rowsShift,
-                                      columnsShift, BLOCK_SIZE,
-                                      outBlock, jWidth, 0, 0);
-                        copyBlockPart(blocks[index + 1], width2,
-                                      rowsShift, iHeight + rowsShift,
-                                      0, widthExcess,
-                                      outBlock, jWidth, 0, jWidth - widthExcess);
-                    } else {
-                        // the submatrix block spans on one block column from the original matrix
-                        copyBlockPart(blocks[index], width,
-                                      rowsShift, iHeight + rowsShift,
-                                      columnsShift, jWidth + columnsShift,
-                                      outBlock, jWidth, 0, 0);
-                    }
-               }
-                ++qBlock;
-            }
-            ++pBlock;
-        }
-
-        return out;
-    }
-
-    /**
-     * Copy a part of a block into another one
-     * <p>This method can be called only when the specified part fits in both
-     * blocks, no verification is done here.</p>
-     * @param srcBlock source block
-     * @param srcWidth source block width ({@link #BLOCK_SIZE} or smaller)
-     * @param srcStartRow start row in the source block
-     * @param srcEndRow end row (exclusive) in the source block
-     * @param srcStartColumn start column in the source block
-     * @param srcEndColumn end column (exclusive) in the source block
-     * @param dstBlock destination block
-     * @param dstWidth destination block width ({@link #BLOCK_SIZE} or smaller)
-     * @param dstStartRow start row in the destination block
-     * @param dstStartColumn start column in the destination block
-     */
-    private void copyBlockPart(final double[] srcBlock, final int srcWidth,
-                               final int srcStartRow, final int srcEndRow,
-                               final int srcStartColumn, final int srcEndColumn,
-                               final double[] dstBlock, final int dstWidth,
-                               final int dstStartRow, final int dstStartColumn) {
-        final int length = srcEndColumn - srcStartColumn;
-        int srcPos = srcStartRow * srcWidth + srcStartColumn;
-        int dstPos = dstStartRow * dstWidth + dstStartColumn;
-        for (int srcRow = srcStartRow; srcRow < srcEndRow; ++srcRow) {
-            System.arraycopy(srcBlock, srcPos, dstBlock, dstPos, length);
-            srcPos += srcWidth;
-            dstPos += dstWidth;
-        }
-    }
-
-    /** {@inheritDoc} */
-    @Override
-    public void setSubMatrix(final double[][] subMatrix, final int row,
-                             final int column)
-        throws OutOfRangeException, NoDataException, NullArgumentException,
-        DimensionMismatchException {
-        // safety checks
-        MathUtils.checkNotNull(subMatrix);
-        final int refLength = subMatrix[0].length;
-        if (refLength == 0) {
-            throw new NoDataException(LocalizedFormats.AT_LEAST_ONE_COLUMN);
-        }
-        final int endRow = row + subMatrix.length - 1;
-        final int endColumn = column + refLength - 1;
-        MatrixUtils.checkSubMatrixIndex(this, row, endRow, column, endColumn);
-        for (final double[] subRow : subMatrix) {
-            if (subRow.length != refLength) {
-                throw new DimensionMismatchException(refLength, subRow.length);
-            }
-        }
-
-        // compute blocks bounds
-        final int blockStartRow = row / BLOCK_SIZE;
-        final int blockEndRow = (endRow + BLOCK_SIZE) / BLOCK_SIZE;
-        final int blockStartColumn = column / BLOCK_SIZE;
-        final int blockEndColumn = (endColumn + BLOCK_SIZE) / BLOCK_SIZE;
-
-        // perform copy block-wise, to ensure good cache behavior
-        for (int iBlock = blockStartRow; iBlock < blockEndRow; ++iBlock) {
-            final int iHeight = blockHeight(iBlock);
-            final int firstRow = iBlock * BLOCK_SIZE;
-            final int iStart = FastMath.max(row,    firstRow);
-            final int iEnd = FastMath.min(endRow + 1, firstRow + iHeight);
-
-            for (int jBlock = blockStartColumn; jBlock < blockEndColumn; ++jBlock) {
-                final int jWidth = blockWidth(jBlock);
-                final int firstColumn = jBlock * BLOCK_SIZE;
-                final int jStart = FastMath.max(column,    firstColumn);
-                final int jEnd = FastMath.min(endColumn + 1, firstColumn + jWidth);
-                final int jLength = jEnd - jStart;
-
-                // handle one block, row by row
-                final double[] block = blocks[iBlock * blockColumns + jBlock];
-                for (int i = iStart; i < iEnd; ++i) {
-                    System.arraycopy(subMatrix[i - row], jStart - column,
-                                     block, (i - firstRow) * jWidth + (jStart - firstColumn),
-                                     jLength);
-                }
-
-            }
-        }
-    }
-
-    /** {@inheritDoc} */
-    @Override
-    public BlockRealMatrix getRowMatrix(final int row)
-        throws OutOfRangeException {
-        MatrixUtils.checkRowIndex(this, row);
-        final BlockRealMatrix out = new BlockRealMatrix(1, columns);
-
-        // perform copy block-wise, to ensure good cache behavior
-        final int iBlock = row / BLOCK_SIZE;
-        final int iRow = row - iBlock * BLOCK_SIZE;
-        int outBlockIndex = 0;
-        int outIndex = 0;
-        double[] outBlock = out.blocks[outBlockIndex];
-        for (int jBlock = 0; jBlock < blockColumns; ++jBlock) {
-            final int jWidth = blockWidth(jBlock);
-            final double[] block = blocks[iBlock * blockColumns + jBlock];
-            final int available = outBlock.length - outIndex;
-            if (jWidth > available) {
-                System.arraycopy(block, iRow * jWidth, outBlock, outIndex, available);
-                outBlock = out.blocks[++outBlockIndex];
-                System.arraycopy(block, iRow * jWidth, outBlock, 0, jWidth - available);
-                outIndex = jWidth - available;
-            } else {
-                System.arraycopy(block, iRow * jWidth, outBlock, outIndex, jWidth);
-                outIndex += jWidth;
-            }
-        }
-
-        return out;
-    }
-
-    /** {@inheritDoc} */
-    @Override
-    public void setRowMatrix(final int row, final RealMatrix matrix)
-        throws OutOfRangeException, MatrixDimensionMismatchException {
-        try {
-            setRowMatrix(row, (BlockRealMatrix) matrix);
-        } catch (ClassCastException cce) {
-            super.setRowMatrix(row, matrix);
-        }
-    }
-
-    /**
-     * Sets the entries in row number <code>row</code>
-     * as a row matrix.  Row indices start at 0.
-     *
-     * @param row the row to be set
-     * @param matrix row matrix (must have one row and the same number of columns
-     * as the instance)
-     * @throws OutOfRangeException if the specified row index is invalid.
-     * @throws MatrixDimensionMismatchException if the matrix dimensions do
-     * not match one instance row.
-     */
-    public void setRowMatrix(final int row, final BlockRealMatrix matrix)
-        throws OutOfRangeException, MatrixDimensionMismatchException {
-        MatrixUtils.checkRowIndex(this, row);
-        final int nCols = getColumnDimension();
-        if ((matrix.getRowDimension() != 1) ||
-            (matrix.getColumnDimension() != nCols)) {
-            throw new MatrixDimensionMismatchException(matrix.getRowDimension(),
-                                                       matrix.getColumnDimension(),
-                                                       1, nCols);
-        }
-
-        // perform copy block-wise, to ensure good cache behavior
-        final int iBlock = row / BLOCK_SIZE;
-        final int iRow = row - iBlock * BLOCK_SIZE;
-        int mBlockIndex = 0;
-        int mIndex = 0;
-        double[] mBlock = matrix.blocks[mBlockIndex];
-        for (int jBlock = 0; jBlock < blockColumns; ++jBlock) {
-            final int jWidth = blockWidth(jBlock);
-            final double[] block = blocks[iBlock * blockColumns + jBlock];
-            final int available  = mBlock.length - mIndex;
-            if (jWidth > available) {
-                System.arraycopy(mBlock, mIndex, block, iRow * jWidth, available);
-                mBlock = matrix.blocks[++mBlockIndex];
-                System.arraycopy(mBlock, 0, block, iRow * jWidth, jWidth - available);
-                mIndex = jWidth - available;
-            } else {
-                System.arraycopy(mBlock, mIndex, block, iRow * jWidth, jWidth);
-                mIndex += jWidth;
-           }
-        }
-    }
-
-    /** {@inheritDoc} */
-    @Override
-    public BlockRealMatrix getColumnMatrix(final int column)
-        throws OutOfRangeException {
-        MatrixUtils.checkColumnIndex(this, column);
-        final BlockRealMatrix out = new BlockRealMatrix(rows, 1);
-
-        // perform copy block-wise, to ensure good cache behavior
-        final int jBlock = column / BLOCK_SIZE;
-        final int jColumn = column - jBlock * BLOCK_SIZE;
-        final int jWidth = blockWidth(jBlock);
-        int outBlockIndex = 0;
-        int outIndex = 0;
-        double[] outBlock = out.blocks[outBlockIndex];
-        for (int iBlock = 0; iBlock < blockRows; ++iBlock) {
-            final int iHeight = blockHeight(iBlock);
-            final double[] block = blocks[iBlock * blockColumns + jBlock];
-            for (int i = 0; i < iHeight; ++i) {
-                if (outIndex >= outBlock.length) {
-                    outBlock = out.blocks[++outBlockIndex];
-                    outIndex = 0;
-                }
-                outBlock[outIndex++] = block[i * jWidth + jColumn];
-            }
-        }
-
-        return out;
-    }
-
-    /** {@inheritDoc} */
-    @Override
-    public void setColumnMatrix(final int column, final RealMatrix matrix)
-        throws OutOfRangeException, MatrixDimensionMismatchException {
-        try {
-            setColumnMatrix(column, (BlockRealMatrix) matrix);
-        } catch (ClassCastException cce) {
-            super.setColumnMatrix(column, matrix);
-        }
-    }
-
-    /**
-     * Sets the entries in column number <code>column</code>
-     * as a column matrix.  Column indices start at 0.
-     *
-     * @param column the column to be set
-     * @param matrix column matrix (must have one column and the same number of rows
-     * as the instance)
-     * @throws OutOfRangeException if the specified column index is invalid.
-     * @throws MatrixDimensionMismatchException if the matrix dimensions do
-     * not match one instance column.
-     */
-    void setColumnMatrix(final int column, final BlockRealMatrix matrix)
-        throws OutOfRangeException, MatrixDimensionMismatchException {
-        MatrixUtils.checkColumnIndex(this, column);
-        final int nRows = getRowDimension();
-        if ((matrix.getRowDimension() != nRows) ||
-            (matrix.getColumnDimension() != 1)) {
-            throw new MatrixDimensionMismatchException(matrix.getRowDimension(),
-                                                       matrix.getColumnDimension(),
-                                                       nRows, 1);
-        }
-
-        // perform copy block-wise, to ensure good cache behavior
-        final int jBlock = column / BLOCK_SIZE;
-        final int jColumn = column - jBlock * BLOCK_SIZE;
-        final int jWidth = blockWidth(jBlock);
-        int mBlockIndex = 0;
-        int mIndex = 0;
-        double[] mBlock = matrix.blocks[mBlockIndex];
-        for (int iBlock = 0; iBlock < blockRows; ++iBlock) {
-            final int iHeight = blockHeight(iBlock);
-            final double[] block = blocks[iBlock * blockColumns + jBlock];
-            for (int i = 0; i < iHeight; ++i) {
-                if (mIndex >= mBlock.length) {
-                    mBlock = matrix.blocks[++mBlockIndex];
-                    mIndex = 0;
-                }
-                block[i * jWidth + jColumn] = mBlock[mIndex++];
-            }
-        }
-    }
-
-    /** {@inheritDoc} */
-    @Override
-    public RealVector getRowVector(final int row)
-        throws OutOfRangeException {
-        MatrixUtils.checkRowIndex(this, row);
-        final double[] outData = new double[columns];
-
-        // perform copy block-wise, to ensure good cache behavior
-        final int iBlock = row / BLOCK_SIZE;
-        final int iRow = row - iBlock * BLOCK_SIZE;
-        int outIndex = 0;
-        for (int jBlock = 0; jBlock < blockColumns; ++jBlock) {
-            final int jWidth = blockWidth(jBlock);
-            final double[] block = blocks[iBlock * blockColumns + jBlock];
-            System.arraycopy(block, iRow * jWidth, outData, outIndex, jWidth);
-            outIndex += jWidth;
-        }
-
-        return new ArrayRealVector(outData, false);
-    }
-
-    /** {@inheritDoc} */
-    @Override
-    public void setRowVector(final int row, final RealVector vector)
-        throws OutOfRangeException, MatrixDimensionMismatchException {
-        try {
-            setRow(row, ((ArrayRealVector) vector).getDataRef());
-        } catch (ClassCastException cce) {
-            super.setRowVector(row, vector);
-        }
-    }
-
-    /** {@inheritDoc} */
-    @Override
-    public RealVector getColumnVector(final int column)
-        throws OutOfRangeException {
-        MatrixUtils.checkColumnIndex(this, column);
-        final double[] outData = new double[rows];
-
-        // perform copy block-wise, to ensure good cache behavior
-        final int jBlock = column / BLOCK_SIZE;
-        final int jColumn = column - jBlock * BLOCK_SIZE;
-        final int jWidth = blockWidth(jBlock);
-        int outIndex = 0;
-        for (int iBlock = 0; iBlock < blockRows; ++iBlock) {
-            final int iHeight = blockHeight(iBlock);
-            final double[] block = blocks[iBlock * blockColumns + jBlock];
-            for (int i = 0; i < iHeight; ++i) {
-                outData[outIndex++] = block[i * jWidth + jColumn];
-            }
-        }
-
-        return new ArrayRealVector(outData, false);
-    }
-
-    /** {@inheritDoc} */
-    @Override
-    public void setColumnVector(final int column, final RealVector vector)
-        throws OutOfRangeException, MatrixDimensionMismatchException {
-        try {
-            setColumn(column, ((ArrayRealVector) vector).getDataRef());
-        } catch (ClassCastException cce) {
-            super.setColumnVector(column, vector);
-        }
-    }
-
-    /** {@inheritDoc} */
-    @Override
-    public double[] getRow(final int row) throws OutOfRangeException {
-        MatrixUtils.checkRowIndex(this, row);
-        final double[] out = new double[columns];
-
-        // perform copy block-wise, to ensure good cache behavior
-        final int iBlock = row / BLOCK_SIZE;
-        final int iRow = row - iBlock * BLOCK_SIZE;
-        int outIndex = 0;
-        for (int jBlock = 0; jBlock < blockColumns; ++jBlock) {
-            final int jWidth     = blockWidth(jBlock);
-            final double[] block = blocks[iBlock * blockColumns + jBlock];
-            System.arraycopy(block, iRow * jWidth, out, outIndex, jWidth);
-            outIndex += jWidth;
-        }
-
-        return out;
-    }
-
-    /** {@inheritDoc} */
-    @Override
-    public void setRow(final int row, final double[] array)
-        throws OutOfRangeException, MatrixDimensionMismatchException {
-        MatrixUtils.checkRowIndex(this, row);
-        final int nCols = getColumnDimension();
-        if (array.length != nCols) {
-            throw new MatrixDimensionMismatchException(1, array.length, 1, nCols);
-        }
-
-        // perform copy block-wise, to ensure good cache behavior
-        final int iBlock = row / BLOCK_SIZE;
-        final int iRow = row - iBlock * BLOCK_SIZE;
-        int outIndex = 0;
-        for (int jBlock = 0; jBlock < blockColumns; ++jBlock) {
-            final int jWidth     = blockWidth(jBlock);
-            final double[] block = blocks[iBlock * blockColumns + jBlock];
-            System.arraycopy(array, outIndex, block, iRow * jWidth, jWidth);
-            outIndex += jWidth;
-        }
-    }
-
-    /** {@inheritDoc} */
-    @Override
-    public double[] getColumn(final int column) throws OutOfRangeException {
-        MatrixUtils.checkColumnIndex(this, column);
-        final double[] out = new double[rows];
-
-        // perform copy block-wise, to ensure good cache behavior
-        final int jBlock  = column / BLOCK_SIZE;
-        final int jColumn = column - jBlock * BLOCK_SIZE;
-        final int jWidth  = blockWidth(jBlock);
-        int outIndex = 0;
-        for (int iBlock = 0; iBlock < blockRows; ++iBlock) {
-            final int iHeight = blockHeight(iBlock);
-            final double[] block = blocks[iBlock * blockColumns + jBlock];
-            for (int i = 0; i < iHeight; ++i) {
-                out[outIndex++] = block[i * jWidth + jColumn];
-            }
-        }
-
-        return out;
-    }
-
-    /** {@inheritDoc} */
-    @Override
-    public void setColumn(final int column, final double[] array)
-        throws OutOfRangeException, MatrixDimensionMismatchException {
-        MatrixUtils.checkColumnIndex(this, column);
-        final int nRows = getRowDimension();
-        if (array.length != nRows) {
-            throw new MatrixDimensionMismatchException(array.length, 1, nRows, 1);
-        }
-
-        // perform copy block-wise, to ensure good cache behavior
-        final int jBlock  = column / BLOCK_SIZE;
-        final int jColumn = column - jBlock * BLOCK_SIZE;
-        final int jWidth = blockWidth(jBlock);
-        int outIndex = 0;
-        for (int iBlock = 0; iBlock < blockRows; ++iBlock) {
-            final int iHeight = blockHeight(iBlock);
-            final double[] block = blocks[iBlock * blockColumns + jBlock];
-            for (int i = 0; i < iHeight; ++i) {
-                block[i * jWidth + jColumn] = array[outIndex++];
-            }
-        }
-    }
-
-    /** {@inheritDoc} */
-    @Override
-    public double getEntry(final int row, final int column)
-        throws OutOfRangeException {
-        MatrixUtils.checkMatrixIndex(this, row, column);
-        final int iBlock = row / BLOCK_SIZE;
-        final int jBlock = column / BLOCK_SIZE;
-        final int k = (row - iBlock * BLOCK_SIZE) * blockWidth(jBlock) +
-            (column - jBlock * BLOCK_SIZE);
-        return blocks[iBlock * blockColumns + jBlock][k];
-    }
-
-    /** {@inheritDoc} */
-    @Override
-    public void setEntry(final int row, final int column, final double value)
-        throws OutOfRangeException {
-        MatrixUtils.checkMatrixIndex(this, row, column);
-        final int iBlock = row / BLOCK_SIZE;
-        final int jBlock = column / BLOCK_SIZE;
-        final int k = (row - iBlock * BLOCK_SIZE) * blockWidth(jBlock) +
-            (column - jBlock * BLOCK_SIZE);
-        blocks[iBlock * blockColumns + jBlock][k] = value;
-    }
-
-    /** {@inheritDoc} */
-    @Override
-    public void addToEntry(final int row, final int column,
-                           final double increment)
-        throws OutOfRangeException {
-        MatrixUtils.checkMatrixIndex(this, row, column);
-        final int iBlock = row    / BLOCK_SIZE;
-        final int jBlock = column / BLOCK_SIZE;
-        final int k = (row    - iBlock * BLOCK_SIZE) * blockWidth(jBlock) +
-            (column - jBlock * BLOCK_SIZE);
-        blocks[iBlock * blockColumns + jBlock][k] += increment;
-    }
-
-    /** {@inheritDoc} */
-    @Override
-    public void multiplyEntry(final int row, final int column,
-                              final double factor)
-        throws OutOfRangeException {
-        MatrixUtils.checkMatrixIndex(this, row, column);
-        final int iBlock = row / BLOCK_SIZE;
-        final int jBlock = column / BLOCK_SIZE;
-        final int k = (row - iBlock * BLOCK_SIZE) * blockWidth(jBlock) +
-            (column - jBlock * BLOCK_SIZE);
-        blocks[iBlock * blockColumns + jBlock][k] *= factor;
-    }
-
-    /** {@inheritDoc} */
-    @Override
-    public BlockRealMatrix transpose() {
-        final int nRows = getRowDimension();
-        final int nCols = getColumnDimension();
-        final BlockRealMatrix out = new BlockRealMatrix(nCols, nRows);
-
-        // perform transpose block-wise, to ensure good cache behavior
-        int blockIndex = 0;
-        for (int iBlock = 0; iBlock < blockColumns; ++iBlock) {
-            for (int jBlock = 0; jBlock < blockRows; ++jBlock) {
-                // transpose current block
-                final double[] outBlock = out.blocks[blockIndex];
-                final double[] tBlock = blocks[jBlock * blockColumns + iBlock];
-                final int pStart = iBlock * BLOCK_SIZE;
-                final int pEnd = FastMath.min(pStart + BLOCK_SIZE, columns);
-                final int qStart = jBlock * BLOCK_SIZE;
-                final int qEnd = FastMath.min(qStart + BLOCK_SIZE, rows);
-                int k = 0;
-                for (int p = pStart; p < pEnd; ++p) {
-                    final int lInc = pEnd - pStart;
-                    int l = p - pStart;
-                    for (int q = qStart; q < qEnd; ++q) {
-                        outBlock[k] = tBlock[l];
-                        ++k;
-                        l+= lInc;
-                    }
-                }
-                // go to next block
-                ++blockIndex;
-            }
-        }
-
-        return out;
-    }
-
-    /** {@inheritDoc} */
-    @Override
-    public int getRowDimension() {
-        return rows;
-    }
-
-    /** {@inheritDoc} */
-    @Override
-    public int getColumnDimension() {
-        return columns;
-    }
-
-    /** {@inheritDoc} */
-    @Override
-    public double[] operate(final double[] v)
-        throws DimensionMismatchException {
-        if (v.length != columns) {
-            throw new DimensionMismatchException(v.length, columns);
-        }
-        final double[] out = new double[rows];
-
-        // perform multiplication block-wise, to ensure good cache behavior
-        for (int iBlock = 0; iBlock < blockRows; ++iBlock) {
-            final int pStart = iBlock * BLOCK_SIZE;
-            final int pEnd = FastMath.min(pStart + BLOCK_SIZE, rows);
-            for (int jBlock = 0; jBlock < blockColumns; ++jBlock) {
-                final double[] block  = blocks[iBlock * blockColumns + jBlock];
-                final int qStart = jBlock * BLOCK_SIZE;
-                final int qEnd = FastMath.min(qStart + BLOCK_SIZE, columns);
-                int k = 0;
-                for (int p = pStart; p < pEnd; ++p) {
-                    double sum = 0;
-                    int q = qStart;
-                    while (q < qEnd - 3) {
-                        sum += block[k]     * v[q]     +
-                               block[k + 1] * v[q + 1] +
-                               block[k + 2] * v[q + 2] +
-                               block[k + 3] * v[q + 3];
-                        k += 4;
-                        q += 4;
-                    }
-                    while (q < qEnd) {
-                        sum += block[k++] * v[q++];
-                    }
-                    out[p] += sum;
-                }
-            }
-        }
-
-        return out;
-    }
-
-    /** {@inheritDoc} */
-    @Override
-    public double[] preMultiply(final double[] v)
-        throws DimensionMismatchException {
-        if (v.length != rows) {
-            throw new DimensionMismatchException(v.length, rows);
-        }
-        final double[] out = new double[columns];
-
-        // perform multiplication block-wise, to ensure good cache behavior
-        for (int jBlock = 0; jBlock < blockColumns; ++jBlock) {
-            final int jWidth  = blockWidth(jBlock);
-            final int jWidth2 = jWidth  + jWidth;
-            final int jWidth3 = jWidth2 + jWidth;
-            final int jWidth4 = jWidth3 + jWidth;
-            final int qStart = jBlock * BLOCK_SIZE;
-            final int qEnd = FastMath.min(qStart + BLOCK_SIZE, columns);
-            for (int iBlock = 0; iBlock < blockRows; ++iBlock) {
-                final double[] block  = blocks[iBlock * blockColumns + jBlock];
-                final int pStart = iBlock * BLOCK_SIZE;
-                final int pEnd = FastMath.min(pStart + BLOCK_SIZE, rows);
-                for (int q = qStart; q < qEnd; ++q) {
-                    int k = q - qStart;
-                    double sum = 0;
-                    int p = pStart;
-                    while (p < pEnd - 3) {
-                        sum += block[k]           * v[p]     +
-                               block[k + jWidth]  * v[p + 1] +
-                               block[k + jWidth2] * v[p + 2] +
-                               block[k + jWidth3] * v[p + 3];
-                        k += jWidth4;
-                        p += 4;
-                    }
-                    while (p < pEnd) {
-                        sum += block[k] * v[p++];
-                        k += jWidth;
-                    }
-                    out[q] += sum;
-                }
-            }
-        }
-
-        return out;
-    }
-
-    /** {@inheritDoc} */
-    @Override
-    public double walkInRowOrder(final RealMatrixChangingVisitor visitor) {
-        visitor.start(rows, columns, 0, rows - 1, 0, columns - 1);
-        for (int iBlock = 0; iBlock < blockRows; ++iBlock) {
-            final int pStart = iBlock * BLOCK_SIZE;
-            final int pEnd = FastMath.min(pStart + BLOCK_SIZE, rows);
-            for (int p = pStart; p < pEnd; ++p) {
-                for (int jBlock = 0; jBlock < blockColumns; ++jBlock) {
-                    final int jWidth = blockWidth(jBlock);
-                    final int qStart = jBlock * BLOCK_SIZE;
-                    final int qEnd = FastMath.min(qStart + BLOCK_SIZE, columns);
-                    final double[] block = blocks[iBlock * blockColumns + jBlock];
-                    int k = (p - pStart) * jWidth;
-                    for (int q = qStart; q < qEnd; ++q) {
-                        block[k] = visitor.visit(p, q, block[k]);
-                        ++k;
-                    }
-                }
-             }
-        }
-        return visitor.end();
-    }
-
-    /** {@inheritDoc} */
-    @Override
-    public double walkInRowOrder(final RealMatrixPreservingVisitor visitor) {
-        visitor.start(rows, columns, 0, rows - 1, 0, columns - 1);
-        for (int iBlock = 0; iBlock < blockRows; ++iBlock) {
-            final int pStart = iBlock * BLOCK_SIZE;
-            final int pEnd = FastMath.min(pStart + BLOCK_SIZE, rows);
-            for (int p = pStart; p < pEnd; ++p) {
-                for (int jBlock = 0; jBlock < blockColumns; ++jBlock) {
-                    final int jWidth = blockWidth(jBlock);
-                    final int qStart = jBlock * BLOCK_SIZE;
-                    final int qEnd = FastMath.min(qStart + BLOCK_SIZE, columns);
-                    final double[] block = blocks[iBlock * blockColumns + jBlock];
-                    int k = (p - pStart) * jWidth;
-                    for (int q = qStart; q < qEnd; ++q) {
-                        visitor.visit(p, q, block[k]);
-                        ++k;
-                    }
-                }
-             }
-        }
-        return visitor.end();
-    }
-
-    /** {@inheritDoc} */
-    @Override
-    public double walkInRowOrder(final RealMatrixChangingVisitor visitor,
-                                 final int startRow, final int endRow,
-                                 final int startColumn, final int endColumn)
-        throws OutOfRangeException, NumberIsTooSmallException {
-        MatrixUtils.checkSubMatrixIndex(this, startRow, endRow, startColumn, endColumn);
-        visitor.start(rows, columns, startRow, endRow, startColumn, endColumn);
-        for (int iBlock = startRow / BLOCK_SIZE; iBlock < 1 + endRow / BLOCK_SIZE; ++iBlock) {
-            final int p0 = iBlock * BLOCK_SIZE;
-            final int pStart = FastMath.max(startRow, p0);
-            final int pEnd = FastMath.min((iBlock + 1) * BLOCK_SIZE, 1 + endRow);
-            for (int p = pStart; p < pEnd; ++p) {
-                for (int jBlock = startColumn / BLOCK_SIZE; jBlock < 1 + endColumn / BLOCK_SIZE; ++jBlock) {
-                    final int jWidth = blockWidth(jBlock);
-                    final int q0 = jBlock * BLOCK_SIZE;
-                    final int qStart = FastMath.max(startColumn, q0);
-                    final int qEnd = FastMath.min((jBlock + 1) * BLOCK_SIZE, 1 + endColumn);
-                    final double[] block = blocks[iBlock * blockColumns + jBlock];
-                    int k = (p - p0) * jWidth + qStart - q0;
-                    for (int q = qStart; q < qEnd; ++q) {
-                        block[k] = visitor.visit(p, q, block[k]);
-                        ++k;
-                    }
-                }
-             }
-        }
-        return visitor.end();
-    }
-
-    /** {@inheritDoc} */
-    @Override
-    public double walkInRowOrder(final RealMatrixPreservingVisitor visitor,
-                                 final int startRow, final int endRow,
-                                 final int startColumn, final int endColumn)
-        throws OutOfRangeException, NumberIsTooSmallException {
-        MatrixUtils.checkSubMatrixIndex(this, startRow, endRow, startColumn, endColumn);
-        visitor.start(rows, columns, startRow, endRow, startColumn, endColumn);
-        for (int iBlock = startRow / BLOCK_SIZE; iBlock < 1 + endRow / BLOCK_SIZE; ++iBlock) {
-            final int p0 = iBlock * BLOCK_SIZE;
-            final int pStart = FastMath.max(startRow, p0);
-            final int pEnd = FastMath.min((iBlock + 1) * BLOCK_SIZE, 1 + endRow);
-            for (int p = pStart; p < pEnd; ++p) {
-                for (int jBlock = startColumn / BLOCK_SIZE; jBlock < 1 + endColumn / BLOCK_SIZE; ++jBlock) {
-                    final int jWidth = blockWidth(jBlock);
-                    final int q0 = jBlock * BLOCK_SIZE;
-                    final int qStart = FastMath.max(startColumn, q0);
-                    final int qEnd = FastMath.min((jBlock + 1) * BLOCK_SIZE, 1 + endColumn);
-                    final double[] block = blocks[iBlock * blockColumns + jBlock];
-                    int k = (p - p0) * jWidth + qStart - q0;
-                    for (int q = qStart; q < qEnd; ++q) {
-                        visitor.visit(p, q, block[k]);
-                        ++k;
-                    }
-                }
-             }
-        }
-        return visitor.end();
-    }
-
-    /** {@inheritDoc} */
-    @Override
-    public double walkInOptimizedOrder(final RealMatrixChangingVisitor visitor) {
-        visitor.start(rows, columns, 0, rows - 1, 0, columns - 1);
-        int blockIndex = 0;
-        for (int iBlock = 0; iBlock < blockRows; ++iBlock) {
-            final int pStart = iBlock * BLOCK_SIZE;
-            final int pEnd = FastMath.min(pStart + BLOCK_SIZE, rows);
-            for (int jBlock = 0; jBlock < blockColumns; ++jBlock) {
-                final int qStart = jBlock * BLOCK_SIZE;
-                final int qEnd = FastMath.min(qStart + BLOCK_SIZE, columns);
-                final double[] block = blocks[blockIndex];
-                int k = 0;
-                for (int p = pStart; p < pEnd; ++p) {
-                    for (int q = qStart; q < qEnd; ++q) {
-                        block[k] = visitor.visit(p, q, block[k]);
-                        ++k;
-                    }
-                }
-                ++blockIndex;
-            }
-        }
-        return visitor.end();
-    }
-
-    /** {@inheritDoc} */
-    @Override
-    public double walkInOptimizedOrder(final RealMatrixPreservingVisitor visitor) {
-        visitor.start(rows, columns, 0, rows - 1, 0, columns - 1);
-        int blockIndex = 0;
-        for (int iBlock = 0; iBlock < blockRows; ++iBlock) {
-            final int pStart = iBlock * BLOCK_SIZE;
-            final int pEnd = FastMath.min(pStart + BLOCK_SIZE, rows);
-            for (int jBlock = 0; jBlock < blockColumns; ++jBlock) {
-                final int qStart = jBlock * BLOCK_SIZE;
-                final int qEnd = FastMath.min(qStart + BLOCK_SIZE, columns);
-                final double[] block = blocks[blockIndex];
-                int k = 0;
-                for (int p = pStart; p < pEnd; ++p) {
-                    for (int q = qStart; q < qEnd; ++q) {
-                        visitor.visit(p, q, block[k]);
-                        ++k;
-                    }
-                }
-                ++blockIndex;
-            }
-        }
-        return visitor.end();
-    }
-
-    /** {@inheritDoc} */
-    @Override
-    public double walkInOptimizedOrder(final RealMatrixChangingVisitor visitor,
-                                       final int startRow, final int endRow,
-                                       final int startColumn,
-                                       final int endColumn)
-        throws OutOfRangeException, NumberIsTooSmallException {
-        MatrixUtils.checkSubMatrixIndex(this, startRow, endRow, startColumn, endColumn);
-        visitor.start(rows, columns, startRow, endRow, startColumn, endColumn);
-        for (int iBlock = startRow / BLOCK_SIZE; iBlock < 1 + endRow / BLOCK_SIZE; ++iBlock) {
-            final int p0 = iBlock * BLOCK_SIZE;
-            final int pStart = FastMath.max(startRow, p0);
-            final int pEnd = FastMath.min((iBlock + 1) * BLOCK_SIZE, 1 + endRow);
-            for (int jBlock = startColumn / BLOCK_SIZE; jBlock < 1 + endColumn / BLOCK_SIZE; ++jBlock) {
-                final int jWidth = blockWidth(jBlock);
-                final int q0 = jBlock * BLOCK_SIZE;
-                final int qStart = FastMath.max(startColumn, q0);
-                final int qEnd = FastMath.min((jBlock + 1) * BLOCK_SIZE, 1 + endColumn);
-                final double[] block = blocks[iBlock * blockColumns + jBlock];
-                for (int p = pStart; p < pEnd; ++p) {
-                    int k = (p - p0) * jWidth + qStart - q0;
-                    for (int q = qStart; q < qEnd; ++q) {
-                        block[k] = visitor.visit(p, q, block[k]);
-                        ++k;
-                    }
-                }
-            }
-        }
-        return visitor.end();
-    }
-
-    /** {@inheritDoc} */
-    @Override
-    public double walkInOptimizedOrder(final RealMatrixPreservingVisitor visitor,
-                                       final int startRow, final int endRow,
-                                       final int startColumn,
-                                       final int endColumn)
-        throws OutOfRangeException, NumberIsTooSmallException {
-        MatrixUtils.checkSubMatrixIndex(this, startRow, endRow, startColumn, endColumn);
-        visitor.start(rows, columns, startRow, endRow, startColumn, endColumn);
-        for (int iBlock = startRow / BLOCK_SIZE; iBlock < 1 + endRow / BLOCK_SIZE; ++iBlock) {
-            final int p0 = iBlock * BLOCK_SIZE;
-            final int pStart = FastMath.max(startRow, p0);
-            final int pEnd = FastMath.min((iBlock + 1) * BLOCK_SIZE, 1 + endRow);
-            for (int jBlock = startColumn / BLOCK_SIZE; jBlock < 1 + endColumn / BLOCK_SIZE; ++jBlock) {
-                final int jWidth = blockWidth(jBlock);
-                final int q0 = jBlock * BLOCK_SIZE;
-                final int qStart = FastMath.max(startColumn, q0);
-                final int qEnd = FastMath.min((jBlock + 1) * BLOCK_SIZE, 1 + endColumn);
-                final double[] block = blocks[iBlock * blockColumns + jBlock];
-                for (int p = pStart; p < pEnd; ++p) {
-                    int k = (p - p0) * jWidth + qStart - q0;
-                    for (int q = qStart; q < qEnd; ++q) {
-                        visitor.visit(p, q, block[k]);
-                        ++k;
-                    }
-                }
-            }
-        }
-        return visitor.end();
-    }
-
-    /**
-     * Get the height of a block.
-     * @param blockRow row index (in block sense) of the block
-     * @return height (number of rows) of the block
-     */
-    private int blockHeight(final int blockRow) {
-        return (blockRow == blockRows - 1) ? rows - blockRow * BLOCK_SIZE : BLOCK_SIZE;
-    }
-
-    /**
-     * Get the width of a block.
-     * @param blockColumn column index (in block sense) of the block
-     * @return width (number of columns) of the block
-     */
-    private int blockWidth(final int blockColumn) {
-        return (blockColumn == blockColumns - 1) ? columns - blockColumn * BLOCK_SIZE : BLOCK_SIZE;
-    }
-}

http://git-wip-us.apache.org/repos/asf/commons-math/blob/a7b4803f/src/main/java/org/apache/commons/math3/linear/CholeskyDecomposition.java
----------------------------------------------------------------------
diff --git a/src/main/java/org/apache/commons/math3/linear/CholeskyDecomposition.java b/src/main/java/org/apache/commons/math3/linear/CholeskyDecomposition.java
deleted file mode 100644
index 63b9a83..0000000
--- a/src/main/java/org/apache/commons/math3/linear/CholeskyDecomposition.java
+++ /dev/null
@@ -1,310 +0,0 @@
-/*
- * 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.commons.math3.linear;
-
-import org.apache.commons.math3.exception.DimensionMismatchException;
-import org.apache.commons.math3.util.FastMath;
-
-
-/**
- * Calculates the Cholesky decomposition of a matrix.
- * <p>The Cholesky decomposition of a real symmetric positive-definite
- * matrix A consists of a lower triangular matrix L with same size such
- * that: A = LL<sup>T</sup>. In a sense, this is the square root of A.</p>
- * <p>This class is based on the class with similar name from the
- * <a href="http://math.nist.gov/javanumerics/jama/">JAMA</a> library, with the
- * following changes:</p>
- * <ul>
- *   <li>a {@link #getLT() getLT} method has been added,</li>
- *   <li>the {@code isspd} method has been removed, since the constructor of
- *   this class throws a {@link NonPositiveDefiniteMatrixException} when a
- *   matrix cannot be decomposed,</li>
- *   <li>a {@link #getDeterminant() getDeterminant} method has been added,</li>
- *   <li>the {@code solve} method has been replaced by a {@link #getSolver()
- *   getSolver} method and the equivalent method provided by the returned
- *   {@link DecompositionSolver}.</li>
- * </ul>
- *
- * @see <a href="http://mathworld.wolfram.com/CholeskyDecomposition.html">MathWorld</a>
- * @see <a href="http://en.wikipedia.org/wiki/Cholesky_decomposition">Wikipedia</a>
- * @since 2.0 (changed to concrete class in 3.0)
- */
-public class CholeskyDecomposition {
-    /**
-     * Default threshold above which off-diagonal elements are considered too different
-     * and matrix not symmetric.
-     */
-    public static final double DEFAULT_RELATIVE_SYMMETRY_THRESHOLD = 1.0e-15;
-    /**
-     * Default threshold below which diagonal elements are considered null
-     * and matrix not positive definite.
-     */
-    public static final double DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD = 1.0e-10;
-    /** Row-oriented storage for L<sup>T</sup> matrix data. */
-    private double[][] lTData;
-    /** Cached value of L. */
-    private RealMatrix cachedL;
-    /** Cached value of LT. */
-    private RealMatrix cachedLT;
-
-    /**
-     * Calculates the Cholesky decomposition of the given matrix.
-     * <p>
-     * Calling this constructor is equivalent to call {@link
-     * #CholeskyDecomposition(RealMatrix, double, double)} with the
-     * thresholds set to the default values {@link
-     * #DEFAULT_RELATIVE_SYMMETRY_THRESHOLD} and {@link
-     * #DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD}
-     * </p>
-     * @param matrix the matrix to decompose
-     * @throws NonSquareMatrixException if the matrix is not square.
-     * @throws NonSymmetricMatrixException if the matrix is not symmetric.
-     * @throws NonPositiveDefiniteMatrixException if the matrix is not
-     * strictly positive definite.
-     * @see #CholeskyDecomposition(RealMatrix, double, double)
-     * @see #DEFAULT_RELATIVE_SYMMETRY_THRESHOLD
-     * @see #DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD
-     */
-    public CholeskyDecomposition(final RealMatrix matrix) {
-        this(matrix, DEFAULT_RELATIVE_SYMMETRY_THRESHOLD,
-             DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD);
-    }
-
-    /**
-     * Calculates the Cholesky decomposition of the given matrix.
-     * @param matrix the matrix to decompose
-     * @param relativeSymmetryThreshold threshold above which off-diagonal
-     * elements are considered too different and matrix not symmetric
-     * @param absolutePositivityThreshold threshold below which diagonal
-     * elements are considered null and matrix not positive definite
-     * @throws NonSquareMatrixException if the matrix is not square.
-     * @throws NonSymmetricMatrixException if the matrix is not symmetric.
-     * @throws NonPositiveDefiniteMatrixException if the matrix is not
-     * strictly positive definite.
-     * @see #CholeskyDecomposition(RealMatrix)
-     * @see #DEFAULT_RELATIVE_SYMMETRY_THRESHOLD
-     * @see #DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD
-     */
-    public CholeskyDecomposition(final RealMatrix matrix,
-                                     final double relativeSymmetryThreshold,
-                                     final double absolutePositivityThreshold) {
-        if (!matrix.isSquare()) {
-            throw new NonSquareMatrixException(matrix.getRowDimension(),
-                                               matrix.getColumnDimension());
-        }
-
-        final int order = matrix.getRowDimension();
-        lTData   = matrix.getData();
-        cachedL  = null;
-        cachedLT = null;
-
-        // check the matrix before transformation
-        for (int i = 0; i < order; ++i) {
-            final double[] lI = lTData[i];
-
-            // check off-diagonal elements (and reset them to 0)
-            for (int j = i + 1; j < order; ++j) {
-                final double[] lJ = lTData[j];
-                final double lIJ = lI[j];
-                final double lJI = lJ[i];
-                final double maxDelta =
-                    relativeSymmetryThreshold * FastMath.max(FastMath.abs(lIJ), FastMath.abs(lJI));
-                if (FastMath.abs(lIJ - lJI) > maxDelta) {
-                    throw new NonSymmetricMatrixException(i, j, relativeSymmetryThreshold);
-                }
-                lJ[i] = 0;
-           }
-        }
-
-        // transform the matrix
-        for (int i = 0; i < order; ++i) {
-
-            final double[] ltI = lTData[i];
-
-            // check diagonal element
-            if (ltI[i] <= absolutePositivityThreshold) {
-                throw new NonPositiveDefiniteMatrixException(ltI[i], i, absolutePositivityThreshold);
-            }
-
-            ltI[i] = FastMath.sqrt(ltI[i]);
-            final double inverse = 1.0 / ltI[i];
-
-            for (int q = order - 1; q > i; --q) {
-                ltI[q] *= inverse;
-                final double[] ltQ = lTData[q];
-                for (int p = q; p < order; ++p) {
-                    ltQ[p] -= ltI[q] * ltI[p];
-                }
-            }
-        }
-    }
-
-    /**
-     * Returns the matrix L of the decomposition.
-     * <p>L is an lower-triangular matrix</p>
-     * @return the L matrix
-     */
-    public RealMatrix getL() {
-        if (cachedL == null) {
-            cachedL = getLT().transpose();
-        }
-        return cachedL;
-    }
-
-    /**
-     * Returns the transpose of the matrix L of the decomposition.
-     * <p>L<sup>T</sup> is an upper-triangular matrix</p>
-     * @return the transpose of the matrix L of the decomposition
-     */
-    public RealMatrix getLT() {
-
-        if (cachedLT == null) {
-            cachedLT = MatrixUtils.createRealMatrix(lTData);
-        }
-
-        // return the cached matrix
-        return cachedLT;
-    }
-
-    /**
-     * Return the determinant of the matrix
-     * @return determinant of the matrix
-     */
-    public double getDeterminant() {
-        double determinant = 1.0;
-        for (int i = 0; i < lTData.length; ++i) {
-            double lTii = lTData[i][i];
-            determinant *= lTii * lTii;
-        }
-        return determinant;
-    }
-
-    /**
-     * Get a solver for finding the A &times; X = B solution in least square sense.
-     * @return a solver
-     */
-    public DecompositionSolver getSolver() {
-        return new Solver(lTData);
-    }
-
-    /** Specialized solver. */
-    private static class Solver implements DecompositionSolver {
-        /** Row-oriented storage for L<sup>T</sup> matrix data. */
-        private final double[][] lTData;
-
-        /**
-         * Build a solver from decomposed matrix.
-         * @param lTData row-oriented storage for L<sup>T</sup> matrix data
-         */
-        private Solver(final double[][] lTData) {
-            this.lTData = lTData;
-        }
-
-        /** {@inheritDoc} */
-        public boolean isNonSingular() {
-            // if we get this far, the matrix was positive definite, hence non-singular
-            return true;
-        }
-
-        /** {@inheritDoc} */
-        public RealVector solve(final RealVector b) {
-            final int m = lTData.length;
-            if (b.getDimension() != m) {
-                throw new DimensionMismatchException(b.getDimension(), m);
-            }
-
-            final double[] x = b.toArray();
-
-            // Solve LY = b
-            for (int j = 0; j < m; j++) {
-                final double[] lJ = lTData[j];
-                x[j] /= lJ[j];
-                final double xJ = x[j];
-                for (int i = j + 1; i < m; i++) {
-                    x[i] -= xJ * lJ[i];
-                }
-            }
-
-            // Solve LTX = Y
-            for (int j = m - 1; j >= 0; j--) {
-                x[j] /= lTData[j][j];
-                final double xJ = x[j];
-                for (int i = 0; i < j; i++) {
-                    x[i] -= xJ * lTData[i][j];
-                }
-            }
-
-            return new ArrayRealVector(x, false);
-        }
-
-        /** {@inheritDoc} */
-        public RealMatrix solve(RealMatrix b) {
-            final int m = lTData.length;
-            if (b.getRowDimension() != m) {
-                throw new DimensionMismatchException(b.getRowDimension(), m);
-            }
-
-            final int nColB = b.getColumnDimension();
-            final double[][] x = b.getData();
-
-            // Solve LY = b
-            for (int j = 0; j < m; j++) {
-                final double[] lJ = lTData[j];
-                final double lJJ = lJ[j];
-                final double[] xJ = x[j];
-                for (int k = 0; k < nColB; ++k) {
-                    xJ[k] /= lJJ;
-                }
-                for (int i = j + 1; i < m; i++) {
-                    final double[] xI = x[i];
-                    final double lJI = lJ[i];
-                    for (int k = 0; k < nColB; ++k) {
-                        xI[k] -= xJ[k] * lJI;
-                    }
-                }
-            }
-
-            // Solve LTX = Y
-            for (int j = m - 1; j >= 0; j--) {
-                final double lJJ = lTData[j][j];
-                final double[] xJ = x[j];
-                for (int k = 0; k < nColB; ++k) {
-                    xJ[k] /= lJJ;
-                }
-                for (int i = 0; i < j; i++) {
-                    final double[] xI = x[i];
-                    final double lIJ = lTData[i][j];
-                    for (int k = 0; k < nColB; ++k) {
-                        xI[k] -= xJ[k] * lIJ;
-                    }
-                }
-            }
-
-            return new Array2DRowRealMatrix(x);
-        }
-
-        /**
-         * Get the inverse of the decomposed matrix.
-         *
-         * @return the inverse matrix.
-         */
-        public RealMatrix getInverse() {
-            return solve(MatrixUtils.createRealIdentityMatrix(lTData.length));
-        }
-    }
-}


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