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## org.apache.commons.math.linear
Class BlockRealMatrix

    java.lang.Object
      org.apache.commons.math.linear.AbstractRealMatrix
          org.apache.commons.math.linear.BlockRealMatrix

All Implemented Interfaces:
  Serializable, AnyMatrix, RealMatrix

    public class BlockRealMatrix

extends AbstractRealMatrix
implements Serializable

Cache-friendly implementation of RealMatrix using a flat arrays to store square blocks of the matrix.

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.

The size of square blocks is a static parameter. It may be tuned according to the cache size of the target computer processor. As a rule of thumbs, it should be the largest value that allows three blocks to be simultaneously cached (this is necessary for example for matrix multiplication). The default value is to use 52x52 blocks which is well suited for processors with 64k L1 cache (one block holds 2704 values or 21632 bytes). This value could be lowered to 36x36 for processors with 32k L1 cache.

The regular blocks represent `BLOCK_SIZE` x `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 `BLOCK_SIZE`2 elements long for regular blocks. The blocks are themselves organized in row major order.

As an example, for a block size of 52x52, a 100x60 matrix would be stored in 4 blocks. Block 0 would be a double[2704] array holding the upper left 52x52 square, block 1 would be a double[416] array holding the upper right 52x8 rectangle, block 2 would be a double[2496] array holding the lower left 48x52 rectangle and block 3 would be a double[384] array holding the lower right 48x8 rectangle.

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.

Since:
  2.0
Version:
  $Revision: 1073158 $ $Date: 2011-02-21 22:46:52 +0100 (lun. 21 fÃ©vr. 2011) $
See Also:
  Serialized Form

Field Summary
`static int` | `BLOCK_SIZE` Block size.

Constructor Summary
`BlockRealMatrix(double[][] rawData)` Create a new dense matrix copying entries from raw layout data.
`BlockRealMatrix(int rows, int columns)` Create a new matrix with the supplied row and column dimensions.
`BlockRealMatrix(int rows, int columns, double[][] blockData, boolean copyArray)` Create a new dense matrix copying entries from block layout data.

Method Summary
`BlockRealMatrix` | `add(BlockRealMatrix m)` Compute the sum of this and `m`.
`BlockRealMatrix` | `add(RealMatrix m)` Compute the sum of this and m.
`void` | `addToEntry(int row, int column, double increment)` Change an entry in the specified row and column.
`BlockRealMatrix` | `copy()` Returns a (deep) copy of this.
`static double[][]` | `createBlocksLayout(int rows, int columns)` Create a data array in blocks layout.
`BlockRealMatrix` | `createMatrix(int rowDimension, int columnDimension)` Create a new RealMatrix of the same type as the instance with the supplied row and column dimensions.
`double[]` | `getColumn(int column)` Returns the entries in column number `col` as an array.
`int` | `getColumnDimension()` Returns the number of columns in the matrix.
`BlockRealMatrix` | `getColumnMatrix(int column)` Returns the entries in column number `column` as a column matrix.
`RealVector` | `getColumnVector(int column)` Returns the entries in column number `column` as a vector.
`double[][]` | `getData()` Returns matrix entries as a two-dimensional array.
`double` | `getEntry(int row, int column)` Returns the entry in the specified row and column.
`double` | `getFrobeniusNorm()` Returns the Frobenius norm of the matrix.
`double` | `getNorm()` Returns the maximum absolute row sum norm of the matrix.
`double[]` | `getRow(int row)` Returns the entries in row number `row` as an array.
`int` | `getRowDimension()` Returns the number of rows in the matrix.
`BlockRealMatrix` | `getRowMatrix(int row)` Returns the entries in row number `row` as a row matrix.
`RealVector` | `getRowVector(int row)` Returns the entries in row number `row` as a vector.
`BlockRealMatrix` | `getSubMatrix(int startRow, int endRow, int startColumn, int endColumn)` Gets a submatrix.
`BlockRealMatrix` | `multiply(BlockRealMatrix m)` Returns the result of postmultiplying this by m.
`BlockRealMatrix` | `multiply(RealMatrix m)` Returns the result of postmultiplying this by m.
`void` | `multiplyEntry(int row, int column, double factor)` Change an entry in the specified row and column.
`double[]` | `operate(double[] v)` Returns the result of multiplying this by the vector `v`.
`double[]` | `preMultiply(double[] v)` Returns the (row) vector result of premultiplying this by the vector `v`.
`BlockRealMatrix` | `scalarAdd(double d)` Returns the result of adding d to each entry of this.
`RealMatrix` | `scalarMultiply(double d)` Returns the result multiplying each entry of this by d.
`void` | `setColumn(int column, double[] array)` Sets the entries in column number `column` as a column matrix.
`void` | `setColumnMatrix(int column, RealMatrix matrix)` Sets the entries in column number `column` as a column matrix.
`void` | `setColumnVector(int column, RealVector vector)` Sets the entries in column number `column` as a vector.
`void` | `setEntry(int row, int column, double value)` Set the entry in the specified row and column.
`void` | `setRow(int row, double[] array)` Sets the entries in row number `row` as a row matrix.
`void` | `setRowMatrix(int row, BlockRealMatrix matrix)` Sets the entries in row number `row` as a row matrix.
`void` | `setRowMatrix(int row, RealMatrix matrix)` Sets the entries in row number `row` as a row matrix.
`void` | `setRowVector(int row, RealVector vector)` Sets the entries in row number `row` as a vector.
`void` | `setSubMatrix(double[][] subMatrix, int row, int column)` Replace the submatrix starting at `row, column` using data in the input `subMatrix` array.
`BlockRealMatrix` | `subtract(BlockRealMatrix m)` Compute this minus `m`.
`BlockRealMatrix` | `subtract(RealMatrix m)` Compute this minus m.
`static double[][]` | `toBlocksLayout(double[][] rawData)` Convert a data array from raw layout to blocks layout.
`BlockRealMatrix` | `transpose()` Returns the transpose of this matrix.
`double` | `walkInOptimizedOrder(RealMatrixChangingVisitor visitor)` Visit (and possibly change) all matrix entries using the fastest possible order.
`double` | `walkInOptimizedOrder(RealMatrixChangingVisitor visitor, int startRow, int endRow, int startColumn, int endColumn)` Visit (and possibly change) some matrix entries using the fastest possible order.
`double` | `walkInOptimizedOrder(RealMatrixPreservingVisitor visitor)` Visit (but don't change) all matrix entries using the fastest possible order.
`double` | `walkInOptimizedOrder(RealMatrixPreservingVisitor visitor, int startRow, int endRow, int startColumn, int endColumn)` Visit (but don't change) some matrix entries using the fastest possible order.
`double` | `walkInRowOrder(RealMatrixChangingVisitor visitor)` Visit (and possibly change) all matrix entries in row order.
`double` | `walkInRowOrder(RealMatrixChangingVisitor visitor, int startRow, int endRow, int startColumn, int endColumn)` Visit (and possibly change) some matrix entries in row order.
`double` | `walkInRowOrder(RealMatrixPreservingVisitor visitor)` Visit (but don't change) all matrix entries in row order.
`double` | `walkInRowOrder(RealMatrixPreservingVisitor visitor, int startRow, int endRow, int startColumn, int endColumn)` Visit (but don't change) some matrix entries in row order.

Methods inherited from class org.apache.commons.math.linear.AbstractRealMatrix
`copySubMatrix, copySubMatrix, equals, getDeterminant, getSubMatrix, getTrace, hashCode, inverse, isSingular, isSquare, luDecompose, operate, preMultiply, preMultiply, solve, solve, toString, walkInColumnOrder, walkInColumnOrder, walkInColumnOrder, walkInColumnOrder`

Methods inherited from class java.lang.Object
`clone, finalize, getClass, notify, notifyAll, wait, wait, wait`

Field Detail

### BLOCK_SIZE

    public static final int BLOCK_SIZE

  Block size.

  See Also:
    Constant Field Values

Constructor Detail

### BlockRealMatrix

    public BlockRealMatrix(int rows,
                           int columns)
                    throws IllegalArgumentException

  Create a new matrix with the supplied row and column dimensions.

  Parameters:
    `rows` - the number of rows in the new matrix
    `columns` - the number of columns in the new matrix
  Throws:
    `IllegalArgumentException` - if row or column dimension is not positive

### BlockRealMatrix

    public BlockRealMatrix(double[][] rawData)
                    throws IllegalArgumentException

  Create a new dense matrix copying entries from raw layout data.

  The input array must already be in raw layout.

  Calling this constructor is equivalent to call:

      matrix = new BlockRealMatrix(rawData.length, rawData[0].length,
                                         toBlocksLayout(rawData), false);

  Parameters:
    `rawData` - data for new matrix, in raw layout
  Throws:
    `IllegalArgumentException` - if `blockData` shape is inconsistent with block layout
  See Also:
    `BlockRealMatrix(int, int, double[][], boolean)`

### BlockRealMatrix

    public BlockRealMatrix(int rows,
                           int columns,
                           double[][] blockData,
                           boolean copyArray)
                    throws IllegalArgumentException

  Create a new dense matrix copying entries from block layout data.

  The input array must already be in blocks layout.

  Parameters:
    `rows` - the number of rows in the new matrix
    `columns` - the number of columns in the new matrix
    `blockData` - data for new matrix
    `copyArray` - if true, the input array will be copied, otherwise it will be referenced
  Throws:
    `IllegalArgumentException` - if `blockData` shape is inconsistent with block layout
  See Also:
    `createBlocksLayout(int, int)`, `toBlocksLayout(double[][])`, `BlockRealMatrix(double[][])`

Method Detail

### toBlocksLayout

    public static double[][] toBlocksLayout(double[][] rawData)
                                     throws IllegalArgumentException

  Convert a data array from raw layout to blocks layout.

  Raw layout is the straightforward layout where element at row i and column j is in array element `rawData[i][j]`. Blocks layout is the layout used in `BlockRealMatrix` instances, where the matrix is split in square blocks (except at right and bottom side where blocks may be rectangular to fit matrix size) and each block is stored in a flattened one-dimensional array.

  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 `BlockRealMatrix(int, int, double[][], boolean)` constructor.

  Parameters:
    `rawData` - data array in raw layout
  Returns:
    a new data array containing the same entries but in blocks layout
  Throws:
    `IllegalArgumentException` - if `rawData` is not rectangular (not all rows have the same length)
  See Also:
    `createBlocksLayout(int, int)`, `BlockRealMatrix(int, int, double[][], boolean)`

### createBlocksLayout

    public static double[][] createBlocksLayout(int rows,
                                                int columns)

  Create a data array in blocks layout.

  This method can be used to create the array argument of the `BlockRealMatrix(int, int, double[][], boolean)` constructor.

  Parameters:
    `rows` - the number of rows in the new matrix
    `columns` - the number of columns in the new matrix
  Returns:
    a new data array in blocks layout
  See Also:
    `toBlocksLayout(double[][])`, `BlockRealMatrix(int, int, double[][], boolean)`

### createMatrix

    public BlockRealMatrix createMatrix(int rowDimension,
                                        int columnDimension)
                                 throws IllegalArgumentException

  Create a new RealMatrix of the same type as the instance with the supplied row and column dimensions.

  Specified by:
    `createMatrix` in interface `RealMatrix`
  Specified by:
    `createMatrix` in class `AbstractRealMatrix`
  Parameters:
    `rowDimension` - the number of rows in the new matrix
    `columnDimension` - the number of columns in the new matrix
  Returns:
    a new matrix of the same type as the instance
  Throws:
    `IllegalArgumentException` - if row or column dimension is not positive

### copy

    public BlockRealMatrix copy()

  Returns a (deep) copy of this.

  Specified by:
    `copy` in interface `RealMatrix`
  Specified by:
    `copy` in class `AbstractRealMatrix`
  Returns:
    matrix copy

### add

    public BlockRealMatrix add(RealMatrix m)
                        throws IllegalArgumentException

  Compute the sum of this and m.

  Specified by:
    `add` in interface `RealMatrix`
  Overrides:
    `add` in class `AbstractRealMatrix`
  Parameters:
    `m` - matrix to be added
  Returns:
    this + m
  Throws:
    `IllegalArgumentException` - if m is not the same size as this

### add

    public BlockRealMatrix add(BlockRealMatrix m)
                        throws IllegalArgumentException

  Compute the sum of this and `m`.

  Parameters:
    `m` - matrix to be added
  Returns:
    this + m
  Throws:
    `IllegalArgumentException` - if m is not the same size as this

### subtract

    public BlockRealMatrix subtract(RealMatrix m)
                             throws IllegalArgumentException

  Compute this minus m.

  Specified by:
    `subtract` in interface `RealMatrix`
  Overrides:
    `subtract` in class `AbstractRealMatrix`
  Parameters:
    `m` - matrix to be subtracted
  Returns:
    this - m
  Throws:
    `IllegalArgumentException` - if m is not the same size as this

### subtract

    public BlockRealMatrix subtract(BlockRealMatrix m)
                             throws IllegalArgumentException

  Compute this minus `m`.

  Parameters:
    `m` - matrix to be subtracted
  Returns:
    this - m
  Throws:
    `IllegalArgumentException` - if m is not the same size as this

### scalarAdd

    public BlockRealMatrix scalarAdd(double d)
                              throws IllegalArgumentException

  Returns the result of adding d to each entry of this.

  Specified by:
    `scalarAdd` in interface `RealMatrix`
  Overrides:
    `scalarAdd` in class `AbstractRealMatrix`
  Parameters:
    `d` - value to be added to each entry
  Returns:
    d + this
  Throws:
    `IllegalArgumentException`

### scalarMultiply

    public RealMatrix scalarMultiply(double d)
                              throws IllegalArgumentException

  Returns the result multiplying each entry of this by d.

  Specified by:
    `scalarMultiply` in interface `RealMatrix`
  Overrides:
    `scalarMultiply` in class `AbstractRealMatrix`
  Parameters:
    `d` - value to multiply all entries by
  Returns:
    d * this
  Throws:
    `IllegalArgumentException`

### multiply

    public BlockRealMatrix multiply(RealMatrix m)
                             throws IllegalArgumentException

  Returns the result of postmultiplying this by m.

  Specified by:
    `multiply` in interface `RealMatrix`
  Overrides:
    `multiply` in class `AbstractRealMatrix`
  Parameters:
    `m` - matrix to postmultiply by
  Returns:
    this * m
  Throws:
    `IllegalArgumentException` - if columnDimension(this) != rowDimension(m)

### multiply

    public BlockRealMatrix multiply(BlockRealMatrix m)
                             throws IllegalArgumentException

  Returns the result of postmultiplying this by m.

  Parameters:
    `m` - matrix to postmultiply by
  Returns:
    this * m
  Throws:
    `IllegalArgumentException` - if columnDimension(this) != rowDimension(m)

### getData

    public double[][] getData()

  Returns matrix entries as a two-dimensional array.

  Specified by:
    `getData` in interface `RealMatrix`
  Overrides:
    `getData` in class `AbstractRealMatrix`
  Returns:
    2-dimensional array of entries

### getNorm

    public double getNorm()

  Returns the maximum absolute row sum norm of the matrix.

  Specified by:
    `getNorm` in interface `RealMatrix`
  Overrides:
    `getNorm` in class `AbstractRealMatrix`
  Returns:
    norm

### getFrobeniusNorm

    public double getFrobeniusNorm()

  Returns the Frobenius norm of the matrix.

  Specified by:
    `getFrobeniusNorm` in interface `RealMatrix`
  Overrides:
    `getFrobeniusNorm` in class `AbstractRealMatrix`
  Returns:
    norm

### getSubMatrix

    public BlockRealMatrix getSubMatrix(int startRow,
                                        int endRow,
                                        int startColumn,
                                        int endColumn)
                                 throws MatrixIndexException

  Gets a submatrix. Rows and columns are indicated counting from 0 to n-1.

  Specified by:
    `getSubMatrix` in interface `RealMatrix`
  Overrides:
    `getSubMatrix` in class `AbstractRealMatrix`
  Parameters:
    `startRow` - Initial row index
    `endRow` - Final row index (inclusive)
    `startColumn` - Initial column index
    `endColumn` - Final column index (inclusive)
  Returns:
    The subMatrix containing the data of the specified rows and columns
  Throws:
    `MatrixIndexException` - if the indices are not valid

### setSubMatrix

    public void setSubMatrix(double[][] subMatrix,
                             int row,
                             int column)
                      throws MatrixIndexException

  Replace the submatrix starting at `row, column` using data in the input `subMatrix` array. Indexes are 0-based.

  Example:
  Starting with

       1  2  3  4
       5  6  7  8
       9  0  1  2

  and `subMatrix = {{3, 4} {5,6}}`, invoking `setSubMatrix(subMatrix,1,1))` will result in

       1  2  3  4
       5  3  4  8
       9  5  6  2

  Specified by:
    `setSubMatrix` in interface `RealMatrix`
  Overrides:
    `setSubMatrix` in class `AbstractRealMatrix`
  Parameters:
    `subMatrix` - array containing the submatrix replacement data
    `row` - row coordinate of the top, left element to be replaced
    `column` - column coordinate of the top, left element to be replaced
  Throws:
    `MatrixIndexException` - if subMatrix does not fit into this matrix from element in (row, column)

### getRowMatrix

    public BlockRealMatrix getRowMatrix(int row)
                                 throws MatrixIndexException

  Returns the entries in row number `row` as a row matrix. Row indices start at 0.

  Specified by:
    `getRowMatrix` in interface `RealMatrix`
  Overrides:
    `getRowMatrix` in class `AbstractRealMatrix`
  Parameters:
    `row` - the row to be fetched
  Returns:
    row matrix
  Throws:
    `MatrixIndexException` - if the specified row index is invalid

### setRowMatrix

    public void setRowMatrix(int row,
                             RealMatrix matrix)
                      throws MatrixIndexException,
                             InvalidMatrixException

  Sets the entries in row number `row` as a row matrix. Row indices start at 0.

  Specified by:
    `setRowMatrix` in interface `RealMatrix`
  Overrides:
    `setRowMatrix` in class `AbstractRealMatrix`
  Parameters:
    `row` - the row to be set
    `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
    `InvalidMatrixException` - if the matrix dimensions do not match one instance row

### setRowMatrix

    public void setRowMatrix(int row,
                             BlockRealMatrix matrix)
                      throws MatrixIndexException,
                             InvalidMatrixException

  Sets the entries in row number `row` as a row matrix. Row indices start at 0.

  Parameters:
    `row` - the row to be set
    `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
    `InvalidMatrixException` - if the matrix dimensions do not match one instance row

### getColumnMatrix

    public BlockRealMatrix getColumnMatrix(int column)
                                    throws MatrixIndexException

  Returns the entries in column number `column` as a column matrix. Column indices start at 0.

  Specified by:
    `getColumnMatrix` in interface `RealMatrix`
  Overrides:
    `getColumnMatrix` in class `AbstractRealMatrix`
  Parameters:
    `column` - the column to be fetched
  Returns:
    column matrix
  Throws:
    `MatrixIndexException` - if the specified column index is invalid

### setColumnMatrix

    public void setColumnMatrix(int column,
                                RealMatrix matrix)
                         throws MatrixIndexException,
                                InvalidMatrixException

  Sets the entries in column number `column` as a column matrix. Column indices start at 0.

  Specified by:
    `setColumnMatrix` in interface `RealMatrix`
  Overrides:
    `setColumnMatrix` in class `AbstractRealMatrix`
  Parameters:
    `column` - the column to be set
    `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
    `InvalidMatrixException` - if the matrix dimensions do not match one instance column

### getRowVector

    public RealVector getRowVector(int row)
                            throws MatrixIndexException

  Returns the entries in row number `row` as a vector. Row indices start at 0.

  Specified by:
    `getRowVector` in interface `RealMatrix`
  Overrides:
    `getRowVector` in class `AbstractRealMatrix`
  Parameters:
    `row` - the row to be fetched
  Returns:
    row vector
  Throws:
    `MatrixIndexException` - if the specified row index is invalid

### setRowVector

    public void setRowVector(int row,
                             RealVector vector)
                      throws MatrixIndexException,
                             InvalidMatrixException

  Sets the entries in row number `row` as a vector. Row indices start at 0.

  Specified by:
    `setRowVector` in interface `RealMatrix`
  Overrides:
    `setRowVector` in class `AbstractRealMatrix`
  Parameters:
    `row` - the row to be set
    `vector` - row vector (must have the same number of columns as the instance)
  Throws:
    `MatrixIndexException` - if the specified row index is invalid
    `InvalidMatrixException` - if the vector dimension does not match one instance row

### getColumnVector

    public RealVector getColumnVector(int column)
                               throws MatrixIndexException

  Returns the entries in column number `column` as a vector. Column indices start at 0.

  Specified by:
    `getColumnVector` in interface `RealMatrix`
  Overrides:
    `getColumnVector` in class `AbstractRealMatrix`
  Parameters:
    `column` - the column to be fetched
  Returns:
    column vector
  Throws:
    `MatrixIndexException` - if the specified column index is invalid

### setColumnVector

    public void setColumnVector(int column,
                                RealVector vector)
                         throws MatrixIndexException,
                                InvalidMatrixException

  Sets the entries in column number `column` as a vector. Column indices start at 0.

  Specified by:
    `setColumnVector` in interface `RealMatrix`
  Overrides:
    `setColumnVector` in class `AbstractRealMatrix`
  Parameters:
    `column` - the column to be set
    `vector` - column vector (must have the same number of rows as the instance)
  Throws:
    `MatrixIndexException` - if the specified column index is invalid
    `InvalidMatrixException` - if the vector dimension does not match one instance column

### getRow

    public double[] getRow(int row)
                    throws MatrixIndexException

  Returns the entries in row number `row` as an array.

  Row indices start at 0. A `MatrixIndexException` is thrown unless `0 <= row < rowDimension.`

  Specified by:
    `getRow` in interface `RealMatrix`
  Overrides:
    `getRow` in class `AbstractRealMatrix`
  Parameters:
    `row` - the row to be fetched
  Returns:
    array of entries in the row
  Throws:
    `MatrixIndexException` - if the specified row index is not valid

### setRow

    public void setRow(int row,
                       double[] array)
                throws MatrixIndexException,
                       InvalidMatrixException

  Sets the entries in row number `row` as a row matrix. Row indices start at 0.

  Specified by:
    `setRow` in interface `RealMatrix`
  Overrides:
    `setRow` in class `AbstractRealMatrix`
  Parameters:
    `row` - the row to be set
    `array` - row matrix (must have the same number of columns as the instance)
  Throws:
    `MatrixIndexException` - if the specified row index is invalid
    `InvalidMatrixException` - if the array size does not match one instance row

### getColumn

    public double[] getColumn(int column)
                       throws MatrixIndexException

  Returns the entries in column number `col` as an array.

  Column indices start at 0. A `MatrixIndexException` is thrown unless `0 <= column < columnDimension.`

  Specified by:
    `getColumn` in interface `RealMatrix`
  Overrides:
    `getColumn` in class `AbstractRealMatrix`
  Parameters:
    `column` - the column to be fetched
  Returns:
    array of entries in the column
  Throws:
    `MatrixIndexException` - if the specified column index is not valid

### setColumn

    public void setColumn(int column,
                          double[] array)
                   throws MatrixIndexException,
                          InvalidMatrixException

  Sets the entries in column number `column` as a column matrix. Column indices start at 0.

  Specified by:
    `setColumn` in interface `RealMatrix`
  Overrides:
    `setColumn` in class `AbstractRealMatrix`
  Parameters:
    `column` - the column to be set
    `array` - column array (must have the same number of rows as the instance)
  Throws:
    `MatrixIndexException` - if the specified column index is invalid
    `InvalidMatrixException` - if the array size does not match one instance column

### getEntry

    public double getEntry(int row,
                           int column)
                    throws MatrixIndexException

  Returns the entry in the specified row and column.

  Row and column indices start at 0 and must satisfy

  - `0 <= row < rowDimension`
  - `0 <= column < columnDimension`
  otherwise a `MatrixIndexException` is thrown.

  Specified by:
    `getEntry` in interface `RealMatrix`
  Specified by:
    `getEntry` in class `AbstractRealMatrix`
  Parameters:
    `row` - row location of entry to be fetched
    `column` - column location of entry to be fetched
  Returns:
    matrix entry in row,column
  Throws:
    `MatrixIndexException` - if the row or column index is not valid

### setEntry

    public void setEntry(int row,
                         int column,
                         double value)
                  throws MatrixIndexException

  Set the entry in the specified row and column.

  Row and column indices start at 0 and must satisfy

  - `0 <= row < rowDimension`
  - `0 <= column < columnDimension`
  otherwise a `MatrixIndexException` is thrown.

  Specified by:
    `setEntry` in interface `RealMatrix`
  Specified by:
    `setEntry` in class `AbstractRealMatrix`
  Parameters:
    `row` - row location of entry to be set
    `column` - column location of entry to be set
    `value` - matrix entry to be set in row,column
  Throws:
    `MatrixIndexException` - if the row or column index is not valid

### addToEntry

    public void addToEntry(int row,
                           int column,
                           double increment)
                    throws MatrixIndexException

  Change an entry in the specified row and column.

  Row and column indices start at 0 and must satisfy

  - `0 <= row < rowDimension`
  - `0 <= column < columnDimension`
  otherwise a `MatrixIndexException` is thrown.

  Specified by:
    `addToEntry` in interface `RealMatrix`
  Specified by:
    `addToEntry` in class `AbstractRealMatrix`
  Parameters:
    `row` - row location of entry to be set
    `column` - column location of entry to be set
    `increment` - value to add to the current matrix entry in row,column
  Throws:
    `MatrixIndexException` - if the row or column index is not valid

### multiplyEntry

    public void multiplyEntry(int row,
                              int column,
                              double factor)
                       throws MatrixIndexException

  Change an entry in the specified row and column.

  Row and column indices start at 0 and must satisfy

  - `0 <= row < rowDimension`
  - `0 <= column < columnDimension`
  otherwise a `MatrixIndexException` is thrown.

  Specified by:
    `multiplyEntry` in interface `RealMatrix`
  Specified by:
    `multiplyEntry` in class `AbstractRealMatrix`
  Parameters:
    `row` - row location of entry to be set
    `column` - column location of entry to be set
    `factor` - multiplication factor for the current matrix entry in row,column
  Throws:
    `MatrixIndexException` - if the row or column index is not valid

### transpose

    public BlockRealMatrix transpose()

  Returns the transpose of this matrix.

  Specified by:
    `transpose` in interface `RealMatrix`
  Overrides:
    `transpose` in class `AbstractRealMatrix`
  Returns:
    transpose matrix

### getRowDimension

    public int getRowDimension()

  Returns the number of rows in the matrix.

  Specified by:
    `getRowDimension` in interface `AnyMatrix`
  Specified by:
    `getRowDimension` in class `AbstractRealMatrix`
  Returns:
    rowDimension

### getColumnDimension

    public int getColumnDimension()

  Returns the number of columns in the matrix.

  Specified by:
    `getColumnDimension` in interface `AnyMatrix`
  Specified by:
    `getColumnDimension` in class `AbstractRealMatrix`
  Returns:
    columnDimension

### operate

    public double[] operate(double[] v)
                     throws IllegalArgumentException

  Returns the result of multiplying this by the vector `v`.

  Specified by:
    `operate` in interface `RealMatrix`
  Overrides:
    `operate` in class `AbstractRealMatrix`
  Parameters:
    `v` - the vector to operate on
  Returns:
    this*v
  Throws:
    `IllegalArgumentException` - if columnDimension != v.size()

### preMultiply

    public double[] preMultiply(double[] v)
                         throws IllegalArgumentException

  Returns the (row) vector result of premultiplying this by the vector `v`.

  Specified by:
    `preMultiply` in interface `RealMatrix`
  Overrides:
    `preMultiply` in class `AbstractRealMatrix`
  Parameters:
    `v` - the row vector to premultiply by
  Returns:
    v*this
  Throws:
    `IllegalArgumentException` - if rowDimension != v.size()

### walkInRowOrder

    public double walkInRowOrder(RealMatrixChangingVisitor visitor)
                          throws MatrixVisitorException

  Visit (and possibly change) all matrix entries in row order.

  Row order starts at upper left and iterating through all elements of a row from left to right before going to the leftmost element of the next row.

  Specified by:
    `walkInRowOrder` in interface `RealMatrix`
  Overrides:
    `walkInRowOrder` in class `AbstractRealMatrix`
  Parameters:
    `visitor` - visitor used to process all matrix entries
  Returns:
    the value returned by `RealMatrixChangingVisitor.end()` at the end of the walk
  Throws:
    `MatrixVisitorException` - if the visitor cannot process an entry
  See Also:
    `RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInRowOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor, int, int, int, int)`, `RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor, int, int, int, int)`, `RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor, int, int, int, int)`

### walkInRowOrder

    public double walkInRowOrder(RealMatrixPreservingVisitor visitor)
                          throws MatrixVisitorException

  Visit (but don't change) all matrix entries in row order.

  Row order starts at upper left and iterating through all elements of a row from left to right before going to the leftmost element of the next row.

  Specified by:
    `walkInRowOrder` in interface `RealMatrix`
  Overrides:
    `walkInRowOrder` in class `AbstractRealMatrix`
  Parameters:
    `visitor` - visitor used to process all matrix entries
  Returns:
    the value returned by `RealMatrixPreservingVisitor.end()` at the end of the walk
  Throws:
    `MatrixVisitorException` - if the visitor cannot process an entry
  See Also:
    `RealMatrix.walkInRowOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInRowOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor, int, int, int, int)`, `RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor, int, int, int, int)`, `RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor, int, int, int, int)`

### walkInRowOrder

    public double walkInRowOrder(RealMatrixChangingVisitor visitor,
                                 int startRow,
                                 int endRow,
                                 int startColumn,
                                 int endColumn)
                          throws MatrixIndexException,
                                 MatrixVisitorException

  Visit (and possibly change) some matrix entries in row order.

  Row order starts at upper left and iterating through all elements of a row from left to right before going to the leftmost element of the next row.

  Specified by:
    `walkInRowOrder` in interface `RealMatrix`
  Overrides:
    `walkInRowOrder` in class `AbstractRealMatrix`
  Parameters:
    `visitor` - visitor used to process all matrix entries
    `startRow` - Initial row index
    `endRow` - Final row index (inclusive)
    `startColumn` - Initial column index
    `endColumn` - Final column index
  Returns:
    the value returned by `RealMatrixChangingVisitor.end()` at the end of the walk
  Throws:
    `MatrixIndexException` - if the indices are not valid
    `MatrixVisitorException` - if the visitor cannot process an entry
  See Also:
    `RealMatrix.walkInRowOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor, int, int, int, int)`, `RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor, int, int, int, int)`, `RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor, int, int, int, int)`

### walkInRowOrder

    public double walkInRowOrder(RealMatrixPreservingVisitor visitor,
                                 int startRow,
                                 int endRow,
                                 int startColumn,
                                 int endColumn)
                          throws MatrixIndexException,
                                 MatrixVisitorException

  Visit (but don't change) some matrix entries in row order.

  Row order starts at upper left and iterating through all elements of a row from left to right before going to the leftmost element of the next row.

  Specified by:
    `walkInRowOrder` in interface `RealMatrix`
  Overrides:
    `walkInRowOrder` in class `AbstractRealMatrix`
  Parameters:
    `visitor` - visitor used to process all matrix entries
    `startRow` - Initial row index
    `endRow` - Final row index (inclusive)
    `startColumn` - Initial column index
    `endColumn` - Final column index
  Returns:
    the value returned by `RealMatrixPreservingVisitor.end()` at the end of the walk
  Throws:
    `MatrixIndexException` - if the indices are not valid
    `MatrixVisitorException` - if the visitor cannot process an entry
  See Also:
    `RealMatrix.walkInRowOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInRowOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor, int, int, int, int)`, `RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor, int, int, int, int)`

### walkInOptimizedOrder

    public double walkInOptimizedOrder(RealMatrixChangingVisitor visitor)
                                throws MatrixVisitorException

  Visit (and possibly change) all matrix entries using the fastest possible order.

  The fastest walking order depends on the exact matrix class. It may be different from traditional row or column orders.

  Specified by:
    `walkInOptimizedOrder` in interface `RealMatrix`
  Overrides:
    `walkInOptimizedOrder` in class `AbstractRealMatrix`
  Parameters:
    `visitor` - visitor used to process all matrix entries
  Returns:
    the value returned by `RealMatrixChangingVisitor.end()` at the end of the walk
  Throws:
    `MatrixVisitorException` - if the visitor cannot process an entry
  See Also:
    `RealMatrix.walkInRowOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInRowOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor, int, int, int, int)`, `RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor, int, int, int, int)`, `RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor, int, int, int, int)`

### walkInOptimizedOrder

    public double walkInOptimizedOrder(RealMatrixPreservingVisitor visitor)
                                throws MatrixVisitorException

  Visit (but don't change) all matrix entries using the fastest possible order.

  The fastest walking order depends on the exact matrix class. It may be different from traditional row or column orders.

  Specified by:
    `walkInOptimizedOrder` in interface `RealMatrix`
  Overrides:
    `walkInOptimizedOrder` in class `AbstractRealMatrix`
  Parameters:
    `visitor` - visitor used to process all matrix entries
  Returns:
    the value returned by `RealMatrixPreservingVisitor.end()` at the end of the walk
  Throws:
    `MatrixVisitorException` - if the visitor cannot process an entry
  See Also:
    `RealMatrix.walkInRowOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInRowOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor, int, int, int, int)`, `RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor, int, int, int, int)`, `RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor, int, int, int, int)`

### walkInOptimizedOrder

    public double walkInOptimizedOrder(RealMatrixChangingVisitor visitor,
                                       int startRow,
                                       int endRow,
                                       int startColumn,
                                       int endColumn)
                                throws MatrixIndexException,
                                       MatrixVisitorException

  Visit (and possibly change) some matrix entries using the fastest possible order.

  The fastest walking order depends on the exact matrix class. It may be different from traditional row or column orders.

  Specified by:
    `walkInOptimizedOrder` in interface `RealMatrix`
  Overrides:
    `walkInOptimizedOrder` in class `AbstractRealMatrix`
  Parameters:
    `visitor` - visitor used to process all matrix entries
    `startRow` - Initial row index
    `endRow` - Final row index (inclusive)
    `startColumn` - Initial column index
    `endColumn` - Final column index (inclusive)
  Returns:
    the value returned by `RealMatrixChangingVisitor.end()` at the end of the walk
  Throws:
    `MatrixIndexException` - if the indices are not valid
    `MatrixVisitorException` - if the visitor cannot process an entry
  See Also:
    `RealMatrix.walkInRowOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInRowOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor, int, int, int, int)`, `RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor, int, int, int, int)`, `RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor, int, int, int, int)`

### walkInOptimizedOrder

    public double walkInOptimizedOrder(RealMatrixPreservingVisitor visitor,
                                       int startRow,
                                       int endRow,
                                       int startColumn,
                                       int endColumn)
                                throws MatrixIndexException,
                                       MatrixVisitorException

  Visit (but don't change) some matrix entries using the fastest possible order.

  The fastest walking order depends on the exact matrix class. It may be different from traditional row or column orders.

  Specified by:
    `walkInOptimizedOrder` in interface `RealMatrix`
  Overrides:
    `walkInOptimizedOrder` in class `AbstractRealMatrix`
  Parameters:
    `visitor` - visitor used to process all matrix entries
    `startRow` - Initial row index
    `endRow` - Final row index (inclusive)
    `startColumn` - Initial column index
    `endColumn` - Final column index (inclusive)
  Returns:
    the value returned by `RealMatrixPreservingVisitor.end()` at the end of the walk
  Throws:
    `MatrixIndexException` - if the indices are not valid
    `MatrixVisitorException` - if the visitor cannot process an entry
  See Also:
    `RealMatrix.walkInRowOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInRowOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor, int, int, int, int)`, `RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor, int, int, int, int)`, `RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor, int, int, int, int)`

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