org.apache.commons.math3.linear

## Class BlockRealMatrix

- java.lang.Object
- - org.apache.commons.math3.linear.RealLinearOperator
  - - org.apache.commons.math3.linear.AbstractRealMatrix
    - - org.apache.commons.math3.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
  See Also:
    Serialized Form

- - ### Field Summary

    Fields
    Modifier and Type | Field and Description
    --- | ---
    `static int` | `BLOCK_SIZE` Block size.

  - ### Constructor Summary

    Constructors
    Constructor and Description
    `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

    Methods
    Modifier and Type | Method and Description
    --- | ---
    `BlockRealMatrix` | `add(BlockRealMatrix m)` Compute the sum of this matrix and `m`.
    `BlockRealMatrix` | `add(RealMatrix m)` Returns the sum of `this` and `m`.
    `void` | `addToEntry(int row, int column, double increment)` Adds (in place) the specified value to the specified entry of `this` matrix.
    `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)` Get the entries at the given column index as an array.
    `int` | `getColumnDimension()` Returns the number of columns of this matrix.
    `BlockRealMatrix` | `getColumnMatrix(int column)` Get the entries at the given column index as a column matrix.
    `RealVector` | `getColumnVector(int column)` Get the entries at the given column index as a vector.
    `double[][]` | `getData()` Returns matrix entries as a two-dimensional array.
    `double` | `getEntry(int row, int column)` Get 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)` Get the entries at the given row index.
    `int` | `getRowDimension()` Returns the number of rows of this matrix.
    `BlockRealMatrix` | `getRowMatrix(int row)` Get the entries at the given row index 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)` Multiplies (in place) the specified entry of `this` matrix by the specified value.
    `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 of multiplying each entry of `this` by `d`.
    `void` | `setColumn(int column, double[] array)` Sets the specified `column` of `this` matrix to the entries of the specified `array`.
    `void` | `setColumnMatrix(int column, RealMatrix matrix)` Sets the specified `column` of `this` matrix to the entries of the specified column `matrix`.
    `void` | `setColumnVector(int column, RealVector vector)` Sets the specified `column` of `this` matrix to the entries of the specified `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 specified `row` of `this` matrix to the entries of the specified `array`.
    `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 specified `row` of `this` matrix to the entries of the specified row `matrix`.
    `void` | `setRowVector(int row, RealVector vector)` Sets the specified `row` of `this` matrix to the entries of the specified `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)` Subtract `m` from this matrix.
    `BlockRealMatrix` | `subtract(RealMatrix m)` Returns `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.math3.linear.AbstractRealMatrix

      `copySubMatrix, copySubMatrix, equals, getSubMatrix, getTrace, hashCode, isSquare, operate, power, preMultiply, preMultiply, toString, walkInColumnOrder, walkInColumnOrder, walkInColumnOrder, walkInColumnOrder`

    - ### Methods inherited from class org.apache.commons.math3.linear.RealLinearOperator

      `isTransposable, operateTranspose`

    - ### 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 NotStrictlyPositiveException

      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:
        `NotStrictlyPositiveException` - if row or column dimension is not positive.

    - #### BlockRealMatrix

          public BlockRealMatrix(double[][] rawData)
                          throws DimensionMismatchException,
                                 NotStrictlyPositiveException

      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:
        `DimensionMismatchException` - if the shape of `blockData` is inconsistent with block layout.
        `NotStrictlyPositiveException` - if row or column dimension is not positive.
      See Also:
        `BlockRealMatrix(int, int, double[][], boolean)`

    - #### BlockRealMatrix

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

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

      The input array must already be in blocks layout.

      Parameters:
        `rows` - Number of rows in the new matrix.
        `columns` - Number of columns in the new matrix.
        `blockData` - data for new matrix
        `copyArray` - Whether the input array will be copied or referenced.
      Throws:
        `DimensionMismatchException` - if the shape of `blockData` is inconsistent with block layout.
        `NotStrictlyPositiveException` - if row or column dimension is not positive.
      See Also:
        `createBlocksLayout(int, int)`, `toBlocksLayout(double[][])`, `BlockRealMatrix(double[][])`

  - ### Method Detail

    - #### toBlocksLayout

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

      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:
        `DimensionMismatchException` - if `rawData` is not rectangular.
      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` - Number of rows in the new matrix.
        `columns` - 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 NotStrictlyPositiveException

      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:
        `NotStrictlyPositiveException` - 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 MatrixDimensionMismatchException

      Returns 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:
        `MatrixDimensionMismatchException` - if `m` is not the same size as `this`.

    - #### add

          public BlockRealMatrix add(BlockRealMatrix m)
                              throws MatrixDimensionMismatchException

      Compute the sum of this matrix and `m`.
      Parameters:
        `m` - Matrix to be added.
      Returns:
        `this` + m.
      Throws:
        `MatrixDimensionMismatchException` - if `m` is not the same size as this matrix.

    - #### subtract

          public BlockRealMatrix subtract(RealMatrix m)
                                   throws MatrixDimensionMismatchException

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

    - #### subtract

          public BlockRealMatrix subtract(BlockRealMatrix m)
                                   throws MatrixDimensionMismatchException

      Subtract `m` from this matrix.
      Parameters:
        `m` - Matrix to be subtracted.
      Returns:
        `this` - m.
      Throws:
        `MatrixDimensionMismatchException` - if `m` is not the same size as this matrix.

    - #### scalarAdd

          public BlockRealMatrix scalarAdd(double d)

      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`

    - #### scalarMultiply

          public RealMatrix scalarMultiply(double d)

      Returns the result of 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`

    - #### multiply

          public BlockRealMatrix multiply(RealMatrix m)
                                   throws DimensionMismatchException

      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:
        `DimensionMismatchException` - if `columnDimension(this) != rowDimension(m)`

    - #### multiply

          public BlockRealMatrix multiply(BlockRealMatrix m)
                                   throws DimensionMismatchException

      Returns the result of postmultiplying this by `m`.
      Parameters:
        `m` - Matrix to postmultiply by.
      Returns:
        `this` * m.
      Throws:
        `DimensionMismatchException` - if the matrices are not compatible.

    - #### 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 OutOfRangeException,
                                              NumberIsTooSmallException

      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:
        `OutOfRangeException` - if the indices are not valid.
        `NumberIsTooSmallException` - if `endRow < startRow` or `endColumn < startColumn`.

    - #### setSubMatrix

          public void setSubMatrix(double[][] subMatrix,
                          int row,
                          int column)
                            throws OutOfRangeException,
                                   NoDataException,
                                   NullArgumentException,
                                   DimensionMismatchException

      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:
        `OutOfRangeException` - if `subMatrix` does not fit into this matrix from element in `(row, column)`.
        `NoDataException` - if `subMatrix` is empty.
        `NullArgumentException` - if `subMatrix` is `null`.
        `DimensionMismatchException` - if `subMatrix` is not rectangular (not all rows have the same length) or empty.

    - #### getRowMatrix

          public BlockRealMatrix getRowMatrix(int row)
                                       throws OutOfRangeException

      Get the entries at the given row index as a row matrix. Row indices start at 0.
      Specified by:
        `getRowMatrix` in interface `RealMatrix`
      Overrides:
        `getRowMatrix` in class `AbstractRealMatrix`
      Parameters:
        `row` - Row to be fetched.
      Returns:
        row Matrix.
      Throws:
        `OutOfRangeException` - if the specified row index is invalid.

    - #### setRowMatrix

          public void setRowMatrix(int row,
                          RealMatrix matrix)
                            throws OutOfRangeException,
                                   MatrixDimensionMismatchException

      Sets the specified `row` of `this` matrix to the entries of the specified row `matrix`. Row indices start at 0.
      Specified by:
        `setRowMatrix` in interface `RealMatrix`
      Overrides:
        `setRowMatrix` in class `AbstractRealMatrix`
      Parameters:
        `row` - Row to be set.
        `matrix` - Row matrix to be copied (must have one row and the same number of columns as the instance).
      Throws:
        `OutOfRangeException` - if the specified row index is invalid.
        `MatrixDimensionMismatchException` - if the row dimension of the `matrix` is not `1`, or the column dimensions of `this` and `matrix` do not match.

    - #### setRowMatrix

          public void setRowMatrix(int row,
                          BlockRealMatrix matrix)
                            throws OutOfRangeException,
                                   MatrixDimensionMismatchException

      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:
        `OutOfRangeException` - if the specified row index is invalid.
        `MatrixDimensionMismatchException` - if the matrix dimensions do not match one instance row.

    - #### getColumnMatrix

          public BlockRealMatrix getColumnMatrix(int column)
                                          throws OutOfRangeException

      Get the entries at the given column index as a column matrix. Column indices start at 0.
      Specified by:
        `getColumnMatrix` in interface `RealMatrix`
      Overrides:
        `getColumnMatrix` in class `AbstractRealMatrix`
      Parameters:
        `column` - Column to be fetched.
      Returns:
        column Matrix.
      Throws:
        `OutOfRangeException` - if the specified column index is invalid.

    - #### setColumnMatrix

          public void setColumnMatrix(int column,
                             RealMatrix matrix)
                               throws OutOfRangeException,
                                      MatrixDimensionMismatchException

      Sets the specified `column` of `this` matrix to the entries of the specified column `matrix`. Column indices start at 0.
      Specified by:
        `setColumnMatrix` in interface `RealMatrix`
      Overrides:
        `setColumnMatrix` in class `AbstractRealMatrix`
      Parameters:
        `column` - Column to be set.
        `matrix` - Column matrix to be copied (must have one column and the same number of rows as the instance).
      Throws:
        `OutOfRangeException` - if the specified column index is invalid.
        `MatrixDimensionMismatchException` - if the column dimension of the `matrix` is not `1`, or the row dimensions of `this` and `matrix` do not match.

    - #### getRowVector

          public RealVector getRowVector(int row)
                                  throws OutOfRangeException

      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` - Row to be fetched.
      Returns:
        a row vector.
      Throws:
        `OutOfRangeException` - if the specified row index is invalid.

    - #### setRowVector

          public void setRowVector(int row,
                          RealVector vector)
                            throws OutOfRangeException,
                                   MatrixDimensionMismatchException

      Sets the specified `row` of `this` matrix to the entries of the specified `vector`. Row indices start at 0.
      Specified by:
        `setRowVector` in interface `RealMatrix`
      Overrides:
        `setRowVector` in class `AbstractRealMatrix`
      Parameters:
        `row` - Row to be set.
        `vector` - row vector to be copied (must have the same number of column as the instance).
      Throws:
        `OutOfRangeException` - if the specified row index is invalid.
        `MatrixDimensionMismatchException` - if the `vector` dimension does not match the column dimension of `this` matrix.

    - #### getColumnVector

          public RealVector getColumnVector(int column)
                                     throws OutOfRangeException

      Get the entries at the given column index as a vector. Column indices start at 0.
      Specified by:
        `getColumnVector` in interface `RealMatrix`
      Overrides:
        `getColumnVector` in class `AbstractRealMatrix`
      Parameters:
        `column` - Column to be fetched.
      Returns:
        a column vector.
      Throws:
        `OutOfRangeException` - if the specified column index is invalid

    - #### setColumnVector

          public void setColumnVector(int column,
                             RealVector vector)
                               throws OutOfRangeException,
                                      MatrixDimensionMismatchException

      Sets the specified `column` of `this` matrix to the entries of the specified `vector`. Column indices start at 0.
      Specified by:
        `setColumnVector` in interface `RealMatrix`
      Overrides:
        `setColumnVector` in class `AbstractRealMatrix`
      Parameters:
        `column` - Column to be set.
        `vector` - column vector to be copied (must have the same number of rows as the instance).
      Throws:
        `OutOfRangeException` - if the specified column index is invalid.
        `MatrixDimensionMismatchException` - if the `vector` dimension does not match the row dimension of `this` matrix.

    - #### getRow

          public double[] getRow(int row)
                          throws OutOfRangeException

      Get the entries at the given row index. Row indices start at 0.
      Specified by:
        `getRow` in interface `RealMatrix`
      Overrides:
        `getRow` in class `AbstractRealMatrix`
      Parameters:
        `row` - Row to be fetched.
      Returns:
        the array of entries in the row.
      Throws:
        `OutOfRangeException` - if the specified row index is not valid.

    - #### setRow

          public void setRow(int row,
                    double[] array)
                      throws OutOfRangeException,
                             MatrixDimensionMismatchException

      Sets the specified `row` of `this` matrix to the entries of the specified `array`. Row indices start at 0.
      Specified by:
        `setRow` in interface `RealMatrix`
      Overrides:
        `setRow` in class `AbstractRealMatrix`
      Parameters:
        `row` - Row to be set.
        `array` - Row matrix to be copied (must have the same number of columns as the instance)
      Throws:
        `OutOfRangeException` - if the specified row index is invalid.
        `MatrixDimensionMismatchException` - if the `array` length does not match the column dimension of `this` matrix.

    - #### getColumn

          public double[] getColumn(int column)
                             throws OutOfRangeException

      Get the entries at the given column index as an array. Column indices start at 0.
      Specified by:
        `getColumn` in interface `RealMatrix`
      Overrides:
        `getColumn` in class `AbstractRealMatrix`
      Parameters:
        `column` - Column to be fetched.
      Returns:
        the array of entries in the column.
      Throws:
        `OutOfRangeException` - if the specified column index is not valid.

    - #### setColumn

          public void setColumn(int column,
                       double[] array)
                         throws OutOfRangeException,
                                MatrixDimensionMismatchException

      Sets the specified `column` of `this` matrix to the entries of the specified `array`. Column indices start at 0.
      Specified by:
        `setColumn` in interface `RealMatrix`
      Overrides:
        `setColumn` in class `AbstractRealMatrix`
      Parameters:
        `column` - Column to be set.
        `array` - Column array to be copied (must have the same number of rows as the instance).
      Throws:
        `OutOfRangeException` - if the specified column index is invalid.
        `MatrixDimensionMismatchException` - if the `array` length does not match the row dimension of `this` matrix.

    - #### getEntry

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

      Get the entry in the specified row and column. Row and column indices start at 0.
      Specified by:
        `getEntry` in interface `RealMatrix`
      Specified by:
        `getEntry` in class `AbstractRealMatrix`
      Parameters:
        `row` - Row index of entry to be fetched.
        `column` - Column index of entry to be fetched.
      Returns:
        the matrix entry at `(row, column)`.
      Throws:
        `OutOfRangeException` - if the row or column index is not valid.

    - #### setEntry

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

      Set the entry in the specified row and column. Row and column indices start at 0.
      Specified by:
        `setEntry` in interface `RealMatrix`
      Specified by:
        `setEntry` in class `AbstractRealMatrix`
      Parameters:
        `row` - Row index of entry to be set.
        `column` - Column index of entry to be set.
        `value` - the new value of the entry.
      Throws:
        `OutOfRangeException` - if the row or column index is not valid

    - #### addToEntry

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

      Adds (in place) the specified value to the specified entry of `this` matrix. Row and column indices start at 0.
      Specified by:
        `addToEntry` in interface `RealMatrix`
      Overrides:
        `addToEntry` in class `AbstractRealMatrix`
      Parameters:
        `row` - Row index of the entry to be modified.
        `column` - Column index of the entry to be modified.
        `increment` - value to add to the matrix entry.
      Throws:
        `OutOfRangeException` - if the row or column index is not valid.

    - #### multiplyEntry

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

      Multiplies (in place) the specified entry of `this` matrix by the specified value. Row and column indices start at 0.
      Specified by:
        `multiplyEntry` in interface `RealMatrix`
      Overrides:
        `multiplyEntry` in class `AbstractRealMatrix`
      Parameters:
        `row` - Row index of the entry to be modified.
        `column` - Column index of the entry to be modified.
        `factor` - Multiplication factor for the matrix entry.
      Throws:
        `OutOfRangeException` - 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 of this matrix.
      Specified by:
        `getRowDimension` in interface `AnyMatrix`
      Specified by:
        `getRowDimension` in class `AbstractRealMatrix`
      Returns:
        the number of rows.

    - #### getColumnDimension

          public int getColumnDimension()

      Returns the number of columns of this matrix.
      Specified by:
        `getColumnDimension` in interface `AnyMatrix`
      Specified by:
        `getColumnDimension` in class `AbstractRealMatrix`
      Returns:
        the number of columns.

    - #### operate

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

      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:
        `DimensionMismatchException` - if the length of `v` does not match the column dimension of `this`.

    - #### preMultiply

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

      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:
        `DimensionMismatchException` - if the length of `v` does not match the row dimension of `this`.

    - #### walkInRowOrder

          public double walkInRowOrder(RealMatrixChangingVisitor visitor)

      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
      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)

      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
      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 OutOfRangeException,
                                       NumberIsTooSmallException

      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:
        `OutOfRangeException` - if the indices are not valid.
        `NumberIsTooSmallException` - if `endRow < startRow` or `endColumn < startColumn`.
      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 OutOfRangeException,
                                       NumberIsTooSmallException

      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:
        `OutOfRangeException` - if the indices are not valid.
        `NumberIsTooSmallException` - if `endRow < startRow` or `endColumn < startColumn`.
      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)

      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
      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)

      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
      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 OutOfRangeException,
                                             NumberIsTooSmallException

      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:
        `OutOfRangeException` - if the indices are not valid.
        `NumberIsTooSmallException` - if `endRow < startRow` or `endColumn < startColumn`.
      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 OutOfRangeException,
                                             NumberIsTooSmallException

      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:
        `OutOfRangeException` - if the indices are not valid.
        `NumberIsTooSmallException` - if `endRow < startRow` or `endColumn < startColumn`.
      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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