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Diffstat (limited to 'src/main/java/org/apache/commons/math/linear/BlockFieldMatrix.java')
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diff --git a/src/main/java/org/apache/commons/math/linear/BlockFieldMatrix.java b/src/main/java/org/apache/commons/math/linear/BlockFieldMatrix.java new file mode 100644 index 0000000..35ae1c2 --- /dev/null +++ b/src/main/java/org/apache/commons/math/linear/BlockFieldMatrix.java @@ -0,0 +1,1670 @@ +/* + * 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.math.linear; + +import java.io.Serializable; + +import org.apache.commons.math.Field; +import org.apache.commons.math.FieldElement; +import org.apache.commons.math.MathRuntimeException; +import org.apache.commons.math.linear.MatrixVisitorException; +import org.apache.commons.math.exception.util.LocalizedFormats; +import org.apache.commons.math.util.FastMath; + +/** + * 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</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 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 + * @version $Revision: 1073158 $ $Date: 2011-02-21 22:46:52 +0100 (lun. 21 févr. 2011) $ + * @since 2.0 + */ +public class BlockFieldMatrix<T extends FieldElement<T>> extends AbstractFieldMatrix<T> 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 the number of rows in the new matrix + * @param columns the number of columns in the new matrix + * @throws IllegalArgumentException if row or column dimension is not + * positive + */ + public BlockFieldMatrix(final Field<T> field, final int rows, final int columns) + throws IllegalArgumentException { + + 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 <em>must</em> already be in raw layout.</p> + * <p>Calling this constructor is equivalent to call: + * <pre>matrix = new BlockFieldMatrix<T>(getField(), rawData.length, rawData[0].length, + * toBlocksLayout(rawData), false);</pre> + * </p> + * @param rawData data for new matrix, in raw layout + * + * @exception IllegalArgumentException if <code>blockData</code> shape is + * inconsistent with block layout + * @see #BlockFieldMatrix(int, int, FieldElement[][], boolean) + */ + public BlockFieldMatrix(final T[][] rawData) + throws IllegalArgumentException { + 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 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 + * + * @exception IllegalArgumentException if <code>blockData</code> shape is + * inconsistent with block layout + * @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 IllegalArgumentException { + + 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 = 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 MathRuntimeException.createIllegalArgumentException( + LocalizedFormats.WRONG_BLOCK_LENGTH, + 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 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> the 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 + * @exception IllegalArgumentException if <code>rawData</code> 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>> T[][] toBlocksLayout(final T[][] rawData) + throws IllegalArgumentException { + + 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 MathRuntimeException.createIllegalArgumentException( + LocalizedFormats.DIFFERENT_ROWS_LENGTHS, + columns, length); + } + } + + // convert array + final Field<T> field = extractField(rawData); + final T[][] blocks = 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 = 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> the type of the field elements + * @param field field to which the elements belong + * @param rows the number of rows in the new matrix + * @param columns the 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>> T[][] createBlocksLayout(final Field<T> 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 = 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] = buildArray(field, iHeight * jWidth); + ++blockIndex; + } + } + + return blocks; + + } + + /** {@inheritDoc} */ + @Override + public FieldMatrix<T> createMatrix(final int rowDimension, final int columnDimension) + throws IllegalArgumentException { + return new BlockFieldMatrix<T>(getField(), rowDimension, columnDimension); + } + + /** {@inheritDoc} */ + @Override + public FieldMatrix<T> copy() { + + // create an empty matrix + BlockFieldMatrix<T> copied = new BlockFieldMatrix<T>(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<T> m) + throws IllegalArgumentException { + try { + return add((BlockFieldMatrix<T>) m); + } catch (ClassCastException cce) { + + // safety check + checkAdditionCompatible(m); + + final BlockFieldMatrix<T> out = new BlockFieldMatrix<T>(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 this and <code>m</code>. + * + * @param m matrix to be added + * @return this + m + * @throws IllegalArgumentException if m is not the same size as this + */ + public BlockFieldMatrix<T> add(final BlockFieldMatrix<T> m) + throws IllegalArgumentException { + + // safety check + checkAdditionCompatible(m); + + final BlockFieldMatrix<T> out = new BlockFieldMatrix<T>(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<T> m) + throws IllegalArgumentException { + try { + return subtract((BlockFieldMatrix<T>) m); + } catch (ClassCastException cce) { + + // safety check + checkSubtractionCompatible(m); + + final BlockFieldMatrix<T> out = new BlockFieldMatrix<T>(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 this minus <code>m</code>. + * + * @param m matrix to be subtracted + * @return this - m + * @throws IllegalArgumentException if m is not the same size as this + */ + public BlockFieldMatrix<T> subtract(final BlockFieldMatrix<T> m) + throws IllegalArgumentException { + + // safety check + checkSubtractionCompatible(m); + + final BlockFieldMatrix<T> out = new BlockFieldMatrix<T>(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) + throws IllegalArgumentException { + + final BlockFieldMatrix<T> out = new BlockFieldMatrix<T>(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) + throws IllegalArgumentException { + + final BlockFieldMatrix<T> out = new BlockFieldMatrix<T>(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<T> m) + throws IllegalArgumentException { + try { + return multiply((BlockFieldMatrix<T>) m); + } catch (ClassCastException cce) { + + // safety check + checkMultiplicationCompatible(m); + + final BlockFieldMatrix<T> out = new BlockFieldMatrix<T>(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 this by m. + * + * @param m matrix to postmultiply by + * @return this * m + * @throws IllegalArgumentException + * if columnDimension(this) != rowDimension(m) + */ + public BlockFieldMatrix<T> multiply(BlockFieldMatrix<T> m) throws IllegalArgumentException { + + // safety check + checkMultiplicationCompatible(m); + + final BlockFieldMatrix<T> out = new BlockFieldMatrix<T>(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 = 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 MatrixIndexException { + + // 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 MatrixIndexException { + + // safety checks + final int refLength = subMatrix[0].length; + if (refLength < 1) { + throw MathRuntimeException.createIllegalArgumentException(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 MathRuntimeException.createIllegalArgumentException( + LocalizedFormats.DIFFERENT_ROWS_LENGTHS, + 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 MatrixIndexException { + + checkRowIndex(row); + final BlockFieldMatrix<T> out = new BlockFieldMatrix<T>(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 MatrixIndexException, InvalidMatrixException { + try { + setRowMatrix(row, (BlockFieldMatrix<T>) 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 MatrixIndexException if the specified row index is invalid + * @throws InvalidMatrixException if the matrix dimensions do not match one + * instance row + */ + public void setRowMatrix(final int row, final BlockFieldMatrix<T> matrix) + throws MatrixIndexException, InvalidMatrixException { + + checkRowIndex(row); + final int nCols = getColumnDimension(); + if ((matrix.getRowDimension() != 1) || + (matrix.getColumnDimension() != nCols)) { + throw new InvalidMatrixException( + LocalizedFormats.DIMENSIONS_MISMATCH_2x2, + 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 MatrixIndexException { + + checkColumnIndex(column); + final BlockFieldMatrix<T> out = new BlockFieldMatrix<T>(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 MatrixIndexException, InvalidMatrixException { + try { + setColumnMatrix(column, (BlockFieldMatrix<T>) 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 MatrixIndexException if the specified column index is invalid + * @throws InvalidMatrixException if the matrix dimensions do not match one + * instance column + */ + void setColumnMatrix(final int column, final BlockFieldMatrix<T> matrix) + throws MatrixIndexException, InvalidMatrixException { + + checkColumnIndex(column); + final int nRows = getRowDimension(); + if ((matrix.getRowDimension() != nRows) || + (matrix.getColumnDimension() != 1)) { + throw new InvalidMatrixException( + LocalizedFormats.DIMENSIONS_MISMATCH_2x2, + 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 MatrixIndexException { + + checkRowIndex(row); + final T[] outData = 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>(outData, false); + + } + + /** {@inheritDoc} */ + @Override + public void setRowVector(final int row, final FieldVector<T> vector) + throws MatrixIndexException, InvalidMatrixException { + try { + setRow(row, ((ArrayFieldVector<T>) vector).getDataRef()); + } catch (ClassCastException cce) { + super.setRowVector(row, vector); + } + } + + /** {@inheritDoc} */ + @Override + public FieldVector<T> getColumnVector(final int column) + throws MatrixIndexException { + + checkColumnIndex(column); + final T[] outData = 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>(outData, false); + + } + + /** {@inheritDoc} */ + @Override + public void setColumnVector(final int column, final FieldVector<T> vector) + throws MatrixIndexException, InvalidMatrixException { + try { + setColumn(column, ((ArrayFieldVector<T>) vector).getDataRef()); + } catch (ClassCastException cce) { + super.setColumnVector(column, vector); + } + } + + /** {@inheritDoc} */ + @Override + public T[] getRow(final int row) + throws MatrixIndexException { + + checkRowIndex(row); + final T[] out = 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 MatrixIndexException, InvalidMatrixException { + + checkRowIndex(row); + final int nCols = getColumnDimension(); + if (array.length != nCols) { + throw new InvalidMatrixException( + LocalizedFormats.DIMENSIONS_MISMATCH_2x2, + 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 MatrixIndexException { + + checkColumnIndex(column); + final T[] out = 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 MatrixIndexException, InvalidMatrixException { + + checkColumnIndex(column); + final int nRows = getRowDimension(); + if (array.length != nRows) { + throw new InvalidMatrixException( + LocalizedFormats.DIMENSIONS_MISMATCH_2x2, + 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 MatrixIndexException { + try { + 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]; + } catch (ArrayIndexOutOfBoundsException e) { + throw new MatrixIndexException( + LocalizedFormats.NO_SUCH_MATRIX_ENTRY, + row, column, getRowDimension(), getColumnDimension()); + } + } + + /** {@inheritDoc} */ + @Override + public void setEntry(final int row, final int column, final T value) + throws MatrixIndexException { + try { + 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; + } catch (ArrayIndexOutOfBoundsException e) { + throw new MatrixIndexException( + LocalizedFormats.NO_SUCH_MATRIX_ENTRY, + row, column, getRowDimension(), getColumnDimension()); + } + } + + /** {@inheritDoc} */ + @Override + public void addToEntry(final int row, final int column, final T increment) + throws MatrixIndexException { + try { + 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); + } catch (ArrayIndexOutOfBoundsException e) { + throw new MatrixIndexException( + LocalizedFormats.NO_SUCH_MATRIX_ENTRY, + row, column, getRowDimension(), getColumnDimension()); + } + } + + /** {@inheritDoc} */ + @Override + public void multiplyEntry(final int row, final int column, final T factor) + throws MatrixIndexException { + try { + 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); + } catch (ArrayIndexOutOfBoundsException e) { + throw new MatrixIndexException( + LocalizedFormats.NO_SUCH_MATRIX_ENTRY, + row, column, getRowDimension(), getColumnDimension()); + } + } + + /** {@inheritDoc} */ + @Override + public FieldMatrix<T> transpose() { + + final int nRows = getRowDimension(); + final int nCols = getColumnDimension(); + final BlockFieldMatrix<T> out = new BlockFieldMatrix<T>(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 IllegalArgumentException { + + if (v.length != columns) { + throw MathRuntimeException.createIllegalArgumentException( + LocalizedFormats.VECTOR_LENGTH_MISMATCH, + v.length, columns); + } + final T[] out = 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 IllegalArgumentException { + + if (v.length != rows) { + throw MathRuntimeException.createIllegalArgumentException( + LocalizedFormats.VECTOR_LENGTH_MISMATCH, + v.length, rows); + } + final T[] out = 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) + throws MatrixVisitorException { + 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) + throws MatrixVisitorException { + 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 MatrixIndexException, MatrixVisitorException { + 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 MatrixIndexException, MatrixVisitorException { + 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) + throws MatrixVisitorException { + 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) + throws MatrixVisitorException { + 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 MatrixIndexException, MatrixVisitorException { + 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 MatrixIndexException, MatrixVisitorException { + 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; + } + +} |