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Java example source code file (BlockFieldMatrix.java)

This example Java source code file (BlockFieldMatrix.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

arrayfieldvector, block_size, blockfieldmatrix, classcastexception, fieldelement, fieldmatrixchangingvisitor, fieldmatrixpreservingvisitor, fieldvector, matrixdimensionmismatchexception, notstrictlypositiveexception, numberistoosmallexception, outofrangeexception, override

The BlockFieldMatrix.java Java example source code

/*
 * 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 org.apache.commons.math3.Field;
import org.apache.commons.math3.FieldElement;
import org.apache.commons.math3.exception.NoDataException;
import org.apache.commons.math3.exception.DimensionMismatchException;
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.MathArrays;
import org.apache.commons.math3.util.MathUtils;

/**
 * Cache-friendly implementation of FieldMatrix 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 36x36 blocks.
 * </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 elements long for regular blocks. The blocks are themselves
 * organized in row major order.
 * </p>
 * <p>
 * As an example, for a block size of 36x36, a 100x60 matrix would be stored in 6 blocks.
 * Block 0 would be a Field[1296] array holding the upper left 36x36 square, block 1 would be
 * a Field[1296] array holding the upper center 36x36 square, block 2 would be a Field[1008]
 * array holding the upper right 36x28 rectangle, block 3 would be a Field[864] array holding
 * the lower left 24x36 rectangle, block 4 would be a Field[864] array holding the lower center
 * 24x36 rectangle and block 5 would be a Field[672] array holding the lower right 24x28
 * 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>
 * @param <T> the type of the field elements
 * @since 2.0
 */
public class BlockFieldMatrix<T extends FieldElement extends AbstractFieldMatrix implements Serializable {
    /** Block size. */
    public static final int BLOCK_SIZE = 36;
    /** Serializable version identifier. */
    private static final long serialVersionUID = -4602336630143123183L;
    /** Blocks of matrix entries. */
    private final T 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 field Field to which the elements belong.
     * @param rows Number of rows in the new matrix.
     * @param columns Number of columns in the new matrix.
     * @throws NotStrictlyPositiveException if row or column dimension is not
     * positive.
     */
    public BlockFieldMatrix(final Field<T> field, final int rows,
                            final int columns)
        throws NotStrictlyPositiveException {
        super(field, 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(field, rows, columns);
    }

    /**
     * Create a new dense matrix copying entries from raw layout data.
     * <p>The input array must already be in raw layout.

* <p>Calling this constructor is equivalent to call: * <pre>matrix = new BlockFieldMatrix(getField(), rawData.length, rawData[0].length, * toBlocksLayout(rawData), false);</pre> * </p> * * @param rawData Data for the new matrix, in raw layout. * @throws DimensionMismatchException if the {@code blockData} shape is * inconsistent with block layout. * @see #BlockFieldMatrix(int, int, FieldElement[][], boolean) */ public BlockFieldMatrix(final T[][] rawData) throws DimensionMismatchException { this(rawData.length, rawData[0].length, toBlocksLayout(rawData), false); } /** * Create a new dense matrix copying entries from block layout data. * <p>The input array must already be in blocks layout.

* @param rows the number of rows in the new matrix * @param columns the number of columns in the new matrix * @param blockData data for new matrix * @param copyArray if true, the input array will be copied, otherwise * it will be referenced * * @throws DimensionMismatchException if the {@code blockData} shape is * inconsistent with block layout. * @throws NotStrictlyPositiveException if row or column dimension is not * positive. * @see #createBlocksLayout(Field, int, int) * @see #toBlocksLayout(FieldElement[][]) * @see #BlockFieldMatrix(FieldElement[][]) */ public BlockFieldMatrix(final int rows, final int columns, final T[][] blockData, final boolean copyArray) throws DimensionMismatchException, NotStrictlyPositiveException { super(extractField(blockData), 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 = MathArrays.buildArray(getField(), blockRows * blockColumns, -1); } 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]. Blocks layout * is the layout used in {@link BlockFieldMatrix} 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 * #BlockFieldMatrix(int, int, FieldElement[][], boolean)} * constructor. * </p> * @param <T> Type of the field elements. * @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 * (not all rows have the same length). * @see #createBlocksLayout(Field, int, int) * @see #BlockFieldMatrix(int, int, FieldElement[][], boolean) */ public static <T extends FieldElement T[][] toBlocksLayout(final T[][] 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 Field<T> field = extractField(rawData); final T[][] blocks = MathArrays.buildArray(field, blockRows * blockColumns, -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); 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 T[] block = MathArrays.buildArray(field, 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 * #BlockFieldMatrix(int, int, FieldElement[][], boolean)} * constructor. * </p> * @param <T> Type of the field elements. * @param field Field to which the elements belong. * @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(FieldElement[][]) * @see #BlockFieldMatrix(int, int, FieldElement[][], boolean) */ public static <T extends FieldElement T[][] createBlocksLayout(final Field field, 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 T[][] blocks = MathArrays.buildArray(field, blockRows * blockColumns, -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); 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] = MathArrays.buildArray(field, iHeight * jWidth); ++blockIndex; } } return blocks; } /** {@inheritDoc} */ @Override public FieldMatrix<T> createMatrix(final int rowDimension, final int columnDimension) throws NotStrictlyPositiveException { return new BlockFieldMatrix<T>(getField(), rowDimension, columnDimension); } /** {@inheritDoc} */ @Override public FieldMatrix<T> copy() { // create an empty matrix BlockFieldMatrix<T> copied = new BlockFieldMatrix(getField(), 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 FieldMatrix<T> add(final FieldMatrix m) throws MatrixDimensionMismatchException { try { return add((BlockFieldMatrix<T>) m); } catch (ClassCastException cce) { // safety check checkAdditionCompatible(m); final BlockFieldMatrix<T> out = new BlockFieldMatrix(getField(), 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 T[] outBlock = out.blocks[blockIndex]; final T[] 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].add(m.getEntry(p, q)); ++k; } } // go to next block ++blockIndex; } } return out; } } /** * Compute the sum of {@code this} and {@code m}. * * @param m matrix to be added * @return {@code this + m} * @throws MatrixDimensionMismatchException if {@code m} is not the same * size as {@code this} */ public BlockFieldMatrix<T> add(final BlockFieldMatrix m) throws MatrixDimensionMismatchException { // safety check checkAdditionCompatible(m); final BlockFieldMatrix<T> out = new BlockFieldMatrix(getField(), rows, columns); // perform addition block-wise, to ensure good cache behavior for (int blockIndex = 0; blockIndex < out.blocks.length; ++blockIndex) { final T[] outBlock = out.blocks[blockIndex]; final T[] tBlock = blocks[blockIndex]; final T[] mBlock = m.blocks[blockIndex]; for (int k = 0; k < outBlock.length; ++k) { outBlock[k] = tBlock[k].add(mBlock[k]); } } return out; } /** {@inheritDoc} */ @Override public FieldMatrix<T> subtract(final FieldMatrix m) throws MatrixDimensionMismatchException { try { return subtract((BlockFieldMatrix<T>) m); } catch (ClassCastException cce) { // safety check checkSubtractionCompatible(m); final BlockFieldMatrix<T> out = new BlockFieldMatrix(getField(), 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 T[] outBlock = out.blocks[blockIndex]; final T[] 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].subtract(m.getEntry(p, q)); ++k; } } // go to next block ++blockIndex; } } return out; } } /** * Compute {@code this - m}. * * @param m matrix to be subtracted * @return {@code this - m} * @throws MatrixDimensionMismatchException if {@code m} is not the same * size as {@code this} */ public BlockFieldMatrix<T> subtract(final BlockFieldMatrix m) throws MatrixDimensionMismatchException { // safety check checkSubtractionCompatible(m); final BlockFieldMatrix<T> out = new BlockFieldMatrix(getField(), rows, columns); // perform subtraction block-wise, to ensure good cache behavior for (int blockIndex = 0; blockIndex < out.blocks.length; ++blockIndex) { final T[] outBlock = out.blocks[blockIndex]; final T[] tBlock = blocks[blockIndex]; final T[] mBlock = m.blocks[blockIndex]; for (int k = 0; k < outBlock.length; ++k) { outBlock[k] = tBlock[k].subtract(mBlock[k]); } } return out; } /** {@inheritDoc} */ @Override public FieldMatrix<T> scalarAdd(final T d) { final BlockFieldMatrix<T> out = new BlockFieldMatrix(getField(), rows, columns); // perform subtraction block-wise, to ensure good cache behavior for (int blockIndex = 0; blockIndex < out.blocks.length; ++blockIndex) { final T[] outBlock = out.blocks[blockIndex]; final T[] tBlock = blocks[blockIndex]; for (int k = 0; k < outBlock.length; ++k) { outBlock[k] = tBlock[k].add(d); } } return out; } /** {@inheritDoc} */ @Override public FieldMatrix<T> scalarMultiply(final T d) { final BlockFieldMatrix<T> out = new BlockFieldMatrix(getField(), rows, columns); // perform subtraction block-wise, to ensure good cache behavior for (int blockIndex = 0; blockIndex < out.blocks.length; ++blockIndex) { final T[] outBlock = out.blocks[blockIndex]; final T[] tBlock = blocks[blockIndex]; for (int k = 0; k < outBlock.length; ++k) { outBlock[k] = tBlock[k].multiply(d); } } return out; } /** {@inheritDoc} */ @Override public FieldMatrix<T> multiply(final FieldMatrix m) throws DimensionMismatchException { try { return multiply((BlockFieldMatrix<T>) m); } catch (ClassCastException cce) { // safety check checkMultiplicationCompatible(m); final BlockFieldMatrix<T> out = new BlockFieldMatrix(getField(), rows, m.getColumnDimension()); final T zero = getField().getZero(); // 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 T[] outBlock = out.blocks[blockIndex]; // perform multiplication on current block for (int kBlock = 0; kBlock < blockColumns; ++kBlock) { final int kWidth = blockWidth(kBlock); final T[] 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) { T sum = zero; int r = rStart; for (int l = lStart; l < lEnd; ++l) { sum = sum.add(tBlock[l].multiply(m.getEntry(r, q))); ++r; } outBlock[k] = outBlock[k].add(sum); ++k; } } } // go to next block ++blockIndex; } } return out; } } /** * Returns the result of postmultiplying {@code this} by {@code m}. * * @param m matrix to postmultiply by * @return {@code this * m} * @throws DimensionMismatchException if the matrices are not compatible. */ public BlockFieldMatrix<T> multiply(BlockFieldMatrix m) throws DimensionMismatchException { // safety check checkMultiplicationCompatible(m); final BlockFieldMatrix<T> out = new BlockFieldMatrix(getField(), rows, m.columns); final T zero = getField().getZero(); // 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 T[] outBlock = out.blocks[blockIndex]; // perform multiplication on current block for (int kBlock = 0; kBlock < blockColumns; ++kBlock) { final int kWidth = blockWidth(kBlock); final T[] tBlock = blocks[iBlock * blockColumns + kBlock]; final T[] 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) { T sum = zero; int l = lStart; int n = nStart; while (l < lEnd - 3) { sum = sum. add(tBlock[l].multiply(mBlock[n])). add(tBlock[l + 1].multiply(mBlock[n + jWidth])). add(tBlock[l + 2].multiply(mBlock[n + jWidth2])). add(tBlock[l + 3].multiply(mBlock[n + jWidth3])); l += 4; n += jWidth4; } while (l < lEnd) { sum = sum.add(tBlock[l++].multiply(mBlock[n])); n += jWidth; } outBlock[k] = outBlock[k].add(sum); ++k; } } } // go to next block ++blockIndex; } } return out; } /** {@inheritDoc} */ @Override public T[][] getData() { final T[][] data = MathArrays.buildArray(getField(), 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 T[] 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 FieldMatrix<T> getSubMatrix(final int startRow, final int endRow, final int startColumn, final int endColumn) throws OutOfRangeException, NumberIsTooSmallException { // safety checks checkSubMatrixIndex(startRow, endRow, startColumn, endColumn); // create the output matrix final BlockFieldMatrix<T> out = new BlockFieldMatrix<T>(getField(), 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 T[] 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 T[] srcBlock, final int srcWidth, final int srcStartRow, final int srcEndRow, final int srcStartColumn, final int srcEndColumn, final T[] 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 T[][] subMatrix, final int row, final int column) throws DimensionMismatchException, OutOfRangeException, NoDataException, NullArgumentException { // 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; checkSubMatrixIndex(row, endRow, column, endColumn); for (final T[] 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 T[] 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 FieldMatrix<T> getRowMatrix(final int row) throws OutOfRangeException { checkRowIndex(row); final BlockFieldMatrix<T> out = new BlockFieldMatrix(getField(), 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; T[] outBlock = out.blocks[outBlockIndex]; for (int jBlock = 0; jBlock < blockColumns; ++jBlock) { final int jWidth = blockWidth(jBlock); final T[] 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 FieldMatrix<T> matrix) throws MatrixDimensionMismatchException, OutOfRangeException { try { setRowMatrix(row, (BlockFieldMatrix<T>) matrix); } catch (ClassCastException cce) { super.setRowMatrix(row, matrix); } } /** * Sets the entries in row number <code>row * 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 MatrixDimensionMismatchException if the matrix dimensions do * not match one instance row. * @throws OutOfRangeException if the specified row index is invalid. */ public void setRowMatrix(final int row, final BlockFieldMatrix<T> matrix) throws MatrixDimensionMismatchException, OutOfRangeException { checkRowIndex(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; T[] mBlock = matrix.blocks[mBlockIndex]; for (int jBlock = 0; jBlock < blockColumns; ++jBlock) { final int jWidth = blockWidth(jBlock); final T[] 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 FieldMatrix<T> getColumnMatrix(final int column) throws OutOfRangeException { checkColumnIndex(column); final BlockFieldMatrix<T> out = new BlockFieldMatrix(getField(), 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; T[] outBlock = out.blocks[outBlockIndex]; for (int iBlock = 0; iBlock < blockRows; ++iBlock) { final int iHeight = blockHeight(iBlock); final T[] 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 FieldMatrix<T> matrix) throws MatrixDimensionMismatchException, OutOfRangeException { try { setColumnMatrix(column, (BlockFieldMatrix<T>) matrix); } catch (ClassCastException cce) { super.setColumnMatrix(column, matrix); } } /** * Sets the entries in column number {@code column} * as a column matrix. Column indices start at 0. * * @param column Column to be set. * @param matrix Column matrix (must have one column and the same number of rows * as the instance). * @throws MatrixDimensionMismatchException if the matrix dimensions do * not match one instance column. * @throws OutOfRangeException if the specified column index is invalid. */ void setColumnMatrix(final int column, final BlockFieldMatrix<T> matrix) throws MatrixDimensionMismatchException, OutOfRangeException { checkColumnIndex(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; T[] mBlock = matrix.blocks[mBlockIndex]; for (int iBlock = 0; iBlock < blockRows; ++iBlock) { final int iHeight = blockHeight(iBlock); final T[] 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 FieldVector<T> getRowVector(final int row) throws OutOfRangeException { checkRowIndex(row); final T[] outData = MathArrays.buildArray(getField(), 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 T[] block = blocks[iBlock * blockColumns + jBlock]; System.arraycopy(block, iRow * jWidth, outData, outIndex, jWidth); outIndex += jWidth; } return new ArrayFieldVector<T>(getField(), outData, false); } /** {@inheritDoc} */ @Override public void setRowVector(final int row, final FieldVector<T> vector) throws MatrixDimensionMismatchException, OutOfRangeException { try { setRow(row, ((ArrayFieldVector<T>) vector).getDataRef()); } catch (ClassCastException cce) { super.setRowVector(row, vector); } } /** {@inheritDoc} */ @Override public FieldVector<T> getColumnVector(final int column) throws OutOfRangeException { checkColumnIndex(column); final T[] outData = MathArrays.buildArray(getField(), 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 T[] block = blocks[iBlock * blockColumns + jBlock]; for (int i = 0; i < iHeight; ++i) { outData[outIndex++] = block[i * jWidth + jColumn]; } } return new ArrayFieldVector<T>(getField(), outData, false); } /** {@inheritDoc} */ @Override public void setColumnVector(final int column, final FieldVector<T> vector) throws OutOfRangeException, MatrixDimensionMismatchException { try { setColumn(column, ((ArrayFieldVector<T>) vector).getDataRef()); } catch (ClassCastException cce) { super.setColumnVector(column, vector); } } /** {@inheritDoc} */ @Override public T[] getRow(final int row) throws OutOfRangeException { checkRowIndex(row); final T[] out = MathArrays.buildArray(getField(), 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 T[] 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 T[] array) throws OutOfRangeException, MatrixDimensionMismatchException { checkRowIndex(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 T[] block = blocks[iBlock * blockColumns + jBlock]; System.arraycopy(array, outIndex, block, iRow * jWidth, jWidth); outIndex += jWidth; } } /** {@inheritDoc} */ @Override public T[] getColumn(final int column) throws OutOfRangeException { checkColumnIndex(column); final T[] out = MathArrays.buildArray(getField(), 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 T[] 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 T[] array) throws MatrixDimensionMismatchException, OutOfRangeException { checkColumnIndex(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 T[] block = blocks[iBlock * blockColumns + jBlock]; for (int i = 0; i < iHeight; ++i) { block[i * jWidth + jColumn] = array[outIndex++]; } } } /** {@inheritDoc} */ @Override public T getEntry(final int row, final int column) throws OutOfRangeException { checkRowIndex(row); checkColumnIndex(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 T value) throws OutOfRangeException { checkRowIndex(row); checkColumnIndex(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 T increment) throws OutOfRangeException { checkRowIndex(row); checkColumnIndex(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); final T[] blockIJ = blocks[iBlock * blockColumns + jBlock]; blockIJ[k] = blockIJ[k].add(increment); } /** {@inheritDoc} */ @Override public void multiplyEntry(final int row, final int column, final T factor) throws OutOfRangeException { checkRowIndex(row); checkColumnIndex(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); final T[] blockIJ = blocks[iBlock * blockColumns + jBlock]; blockIJ[k] = blockIJ[k].multiply(factor); } /** {@inheritDoc} */ @Override public FieldMatrix<T> transpose() { final int nRows = getRowDimension(); final int nCols = getColumnDimension(); final BlockFieldMatrix<T> out = new BlockFieldMatrix(getField(), 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 T[] outBlock = out.blocks[blockIndex]; final T[] 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 T[] operate(final T[] v) throws DimensionMismatchException { if (v.length != columns) { throw new DimensionMismatchException(v.length, columns); } final T[] out = MathArrays.buildArray(getField(), rows); final T zero = getField().getZero(); // 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 T[] 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) { T sum = zero; int q = qStart; while (q < qEnd - 3) { sum = sum. add(block[k].multiply(v[q])). add(block[k + 1].multiply(v[q + 1])). add(block[k + 2].multiply(v[q + 2])). add(block[k + 3].multiply(v[q + 3])); k += 4; q += 4; } while (q < qEnd) { sum = sum.add(block[k++].multiply(v[q++])); } out[p] = out[p].add(sum); } } } return out; } /** {@inheritDoc} */ @Override public T[] preMultiply(final T[] v) throws DimensionMismatchException { if (v.length != rows) { throw new DimensionMismatchException(v.length, rows); } final T[] out = MathArrays.buildArray(getField(), columns); final T zero = getField().getZero(); // 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 T[] 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; T sum = zero; int p = pStart; while (p < pEnd - 3) { sum = sum. add(block[k].multiply(v[p])). add(block[k + jWidth].multiply(v[p + 1])). add(block[k + jWidth2].multiply(v[p + 2])). add(block[k + jWidth3].multiply(v[p + 3])); k += jWidth4; p += 4; } while (p < pEnd) { sum = sum.add(block[k].multiply(v[p++])); k += jWidth; } out[q] = out[q].add(sum); } } } return out; } /** {@inheritDoc} */ @Override public T walkInRowOrder(final FieldMatrixChangingVisitor<T> 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 T[] 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 T walkInRowOrder(final FieldMatrixPreservingVisitor<T> 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 T[] 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 T walkInRowOrder(final FieldMatrixChangingVisitor<T> visitor, final int startRow, final int endRow, final int startColumn, final int endColumn) throws OutOfRangeException, NumberIsTooSmallException { checkSubMatrixIndex(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 T[] 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 T walkInRowOrder(final FieldMatrixPreservingVisitor<T> visitor, final int startRow, final int endRow, final int startColumn, final int endColumn) throws OutOfRangeException, NumberIsTooSmallException { checkSubMatrixIndex(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 T[] 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 T walkInOptimizedOrder(final FieldMatrixChangingVisitor<T> 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 T[] 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 T walkInOptimizedOrder(final FieldMatrixPreservingVisitor<T> 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 T[] 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 T walkInOptimizedOrder(final FieldMatrixChangingVisitor<T> visitor, final int startRow, final int endRow, final int startColumn, final int endColumn) throws OutOfRangeException, NumberIsTooSmallException { checkSubMatrixIndex(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 T[] 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 T walkInOptimizedOrder(final FieldMatrixPreservingVisitor<T> visitor, final int startRow, final int endRow, final int startColumn, final int endColumn) throws OutOfRangeException, NumberIsTooSmallException { checkSubMatrixIndex(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 T[] 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; } }

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