org.apache.commons.math3.linear

## Class Array2DRowFieldMatrix<T extends FieldElement<T>>

- java.lang.Object
- - org.apache.commons.math3.linear.AbstractFieldMatrix<T>
  - - org.apache.commons.math3.linear.Array2DRowFieldMatrix<T>

- Type Parameters:
    `T` - the type of the field elements
  All Implemented Interfaces:
    Serializable, AnyMatrix, FieldMatrix<T>

      public class Array2DRowFieldMatrix<T extends FieldElement<T>>
      extends AbstractFieldMatrix<T>
      implements Serializable

  Implementation of FieldMatrix using a `FieldElement`[][] array to store entries.

  As specified in the `FieldMatrix` interface, matrix element indexing is 0-based -- e.g., `getEntry(0, 0)` returns the element in the first row, first column of the matrix.

See Also:
  Serialized Form

- - ### Constructor Summary

    Constructors
    Constructor and Description
    `Array2DRowFieldMatrix(Field<T> field)` Creates a matrix with no data
    `Array2DRowFieldMatrix(Field<T> field, int rowDimension, int columnDimension)` Create a new `FieldMatrix<T>` with the supplied row and column dimensions.
    `Array2DRowFieldMatrix(Field<T> field, T[] v)` Create a new (column) `FieldMatrix<T>` using `v` as the data for the unique column of the created matrix.
    `Array2DRowFieldMatrix(Field<T> field, T[][] d)` Create a new `FieldMatrix<T>` using the input array as the underlying data array.
    `Array2DRowFieldMatrix(Field<T> field, T[][] d, boolean copyArray)` Create a new `FieldMatrix<T>` using the input array as the underlying data array.
    `Array2DRowFieldMatrix(T[] v)` Create a new (column) `FieldMatrix<T>` using `v` as the data for the unique column of the created matrix.
    `Array2DRowFieldMatrix(T[][] d)` Create a new `FieldMatrix<T>` using the input array as the underlying data array.
    `Array2DRowFieldMatrix(T[][] d, boolean copyArray)` Create a new `FieldMatrix<T>` using the input array as the underlying data array.

  - ### Method Summary

    Methods
    Modifier and Type | Method and Description
    --- | ---
    `Array2DRowFieldMatrix<T>` | `add(Array2DRowFieldMatrix<T> m)` Add `m` to this matrix.
    `void` | `addToEntry(int row, int column, T increment)` Change an entry in the specified row and column.
    `FieldMatrix<T>` | `copy()` Make a (deep) copy of this.
    `FieldMatrix<T>` | `createMatrix(int rowDimension, int columnDimension)` Create a new FieldMatrix of the same type as the instance with the supplied row and column dimensions.
    `int` | `getColumnDimension()` Returns the number of columns in the matrix.
    `T[][]` | `getData()` Returns matrix entries as a two-dimensional array.
    `T[][]` | `getDataRef()` Get a reference to the underlying data array.
    `T` | `getEntry(int row, int column)` Returns the entry in the specified row and column.
    `int` | `getRowDimension()` Returns the number of rows in the matrix.
    `Array2DRowFieldMatrix<T>` | `multiply(Array2DRowFieldMatrix<T> m)` Postmultiplying this matrix by `m`.
    `void` | `multiplyEntry(int row, int column, T factor)` Change an entry in the specified row and column.
    `T[]` | `operate(T[] v)` Returns the result of multiplying this by the vector `v`.
    `T[]` | `preMultiply(T[] v)` Returns the (row) vector result of premultiplying this by the vector `v`.
    `void` | `setEntry(int row, int column, T value)` Set the entry in the specified row and column.
    `void` | `setSubMatrix(T[][] subMatrix, int row, int column)` Replace the submatrix starting at `(row, column)` using data in the input `subMatrix` array.
    `Array2DRowFieldMatrix<T>` | `subtract(Array2DRowFieldMatrix<T> m)` Subtract `m` from this matrix.
    `T` | `walkInColumnOrder(FieldMatrixChangingVisitor<T> visitor)` Visit (and possibly change) all matrix entries in column order.
    `T` | `walkInColumnOrder(FieldMatrixChangingVisitor<T> visitor, int startRow, int endRow, int startColumn, int endColumn)` Visit (and possibly change) some matrix entries in column order.
    `T` | `walkInColumnOrder(FieldMatrixPreservingVisitor<T> visitor)` Visit (but don't change) all matrix entries in column order.
    `T` | `walkInColumnOrder(FieldMatrixPreservingVisitor<T> visitor, int startRow, int endRow, int startColumn, int endColumn)` Visit (but don't change) some matrix entries in column order.
    `T` | `walkInRowOrder(FieldMatrixChangingVisitor<T> visitor)` Visit (and possibly change) all matrix entries in row order.
    `T` | `walkInRowOrder(FieldMatrixChangingVisitor<T> visitor, int startRow, int endRow, int startColumn, int endColumn)` Visit (and possibly change) some matrix entries in row order.
    `T` | `walkInRowOrder(FieldMatrixPreservingVisitor<T> visitor)` Visit (but don't change) all matrix entries in row order.
    `T` | `walkInRowOrder(FieldMatrixPreservingVisitor<T> 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.AbstractFieldMatrix

      `add, buildArray, buildArray, checkAdditionCompatible, checkColumnIndex, checkMultiplicationCompatible, checkRowIndex, checkSubMatrixIndex, checkSubMatrixIndex, checkSubtractionCompatible, copySubMatrix, copySubMatrix, equals, extractField, extractField, getColumn, getColumnMatrix, getColumnVector, getField, getRow, getRowMatrix, getRowVector, getSubMatrix, getSubMatrix, getTrace, hashCode, isSquare, multiply, operate, power, preMultiply, preMultiply, scalarAdd, scalarMultiply, setColumn, setColumnMatrix, setColumnVector, setRow, setRowMatrix, setRowVector, subtract, toString, transpose, walkInOptimizedOrder, walkInOptimizedOrder, walkInOptimizedOrder, walkInOptimizedOrder`

    - ### Methods inherited from class java.lang.Object

      `clone, finalize, getClass, notify, notifyAll, wait, wait, wait`

- - ### Constructor Detail

    - #### Array2DRowFieldMatrix

          public Array2DRowFieldMatrix(Field<T> field)

      Creates a matrix with no data
      Parameters:
        `field` - field to which the elements belong

    - #### Array2DRowFieldMatrix

          public Array2DRowFieldMatrix(Field<T> field,
                               int rowDimension,
                               int columnDimension)
                                throws NotStrictlyPositiveException

      Create a new `FieldMatrix<T>` with the supplied row and column dimensions.
      Parameters:
        `field` - Field to which the elements belong.
        `rowDimension` - Number of rows in the new matrix.
        `columnDimension` - Number of columns in the new matrix.
      Throws:
        `NotStrictlyPositiveException` - if row or column dimension is not positive.

    - #### Array2DRowFieldMatrix

          public Array2DRowFieldMatrix(T[][] d)
                                throws DimensionMismatchException,
                                       NullArgumentException,
                                       NoDataException

      Create a new `FieldMatrix<T>` using the input array as the underlying data array.

      The input array is copied, not referenced. This constructor has the same effect as calling `Array2DRowFieldMatrix(FieldElement[][], boolean)` with the second argument set to `true`.

      Parameters:
        `d` - Data for the new matrix.
      Throws:
        `DimensionMismatchException` - if `d` is not rectangular.
        `NullArgumentException` - if `d` is `null`.
        `NoDataException` - if there are not at least one row and one column.
      See Also:
        `Array2DRowFieldMatrix(FieldElement[][], boolean)`

    - #### Array2DRowFieldMatrix

          public Array2DRowFieldMatrix(Field<T> field,
                               T[][] d)
                                throws DimensionMismatchException,
                                       NullArgumentException,
                                       NoDataException

      Create a new `FieldMatrix<T>` using the input array as the underlying data array.

      The input array is copied, not referenced. This constructor has the same effect as calling `Array2DRowFieldMatrix(FieldElement[][], boolean)` with the second argument set to `true`.

      Parameters:
        `field` - Field to which the elements belong.
        `d` - Data for the new matrix.
      Throws:
        `DimensionMismatchException` - if `d` is not rectangular.
        `NullArgumentException` - if `d` is `null`.
        `NoDataException` - if there are not at least one row and one column.
      See Also:
        `Array2DRowFieldMatrix(FieldElement[][], boolean)`

    - #### Array2DRowFieldMatrix

          public Array2DRowFieldMatrix(T[][] d,
                               boolean copyArray)
                                throws DimensionMismatchException,
                                       NoDataException,
                                       NullArgumentException

      Create a new `FieldMatrix<T>` using the input array as the underlying data array.

      If an array is built specially in order to be embedded in a `FieldMatrix<T>` and not used directly, the `copyArray` may be set to `false`. This will prevent the copying and improve performance as no new array will be built and no data will be copied.

      Parameters:
        `d` - Data for the new matrix.
        `copyArray` - Whether to copy or reference the input array.
      Throws:
        `DimensionMismatchException` - if `d` is not rectangular.
        `NoDataException` - if there are not at least one row and one column.
        `NullArgumentException` - if `d` is `null`.
      See Also:
        `Array2DRowFieldMatrix(FieldElement[][])`

    - #### Array2DRowFieldMatrix

          public Array2DRowFieldMatrix(Field<T> field,
                               T[][] d,
                               boolean copyArray)
                                throws DimensionMismatchException,
                                       NoDataException,
                                       NullArgumentException

      Create a new `FieldMatrix<T>` using the input array as the underlying data array.

      If an array is built specially in order to be embedded in a `FieldMatrix<T>` and not used directly, the `copyArray` may be set to `false`. This will prevent the copying and improve performance as no new array will be built and no data will be copied.

      Parameters:
        `field` - Field to which the elements belong.
        `d` - Data for the new matrix.
        `copyArray` - Whether to copy or reference the input array.
      Throws:
        `DimensionMismatchException` - if `d` is not rectangular.
        `NoDataException` - if there are not at least one row and one column.
        `NullArgumentException` - if `d` is `null`.
      See Also:
        `Array2DRowFieldMatrix(FieldElement[][])`

    - #### Array2DRowFieldMatrix

          public Array2DRowFieldMatrix(T[] v)
                                throws NoDataException

      Create a new (column) `FieldMatrix<T>` using `v` as the data for the unique column of the created matrix. The input array is copied.
      Parameters:
        `v` - Column vector holding data for new matrix.
      Throws:
        `NoDataException` - if v is empty

    - #### Array2DRowFieldMatrix

          public Array2DRowFieldMatrix(Field<T> field,
                               T[] v)

      Create a new (column) `FieldMatrix<T>` using `v` as the data for the unique column of the created matrix. The input array is copied.
      Parameters:
        `field` - Field to which the elements belong.
        `v` - Column vector holding data for new matrix.

  - ### Method Detail

    - #### createMatrix

          public FieldMatrix<T> createMatrix(int rowDimension,
                                    int columnDimension)
                                                              throws NotStrictlyPositiveException

      Create a new FieldMatrix of the same type as the instance with the supplied row and column dimensions.
      Specified by:
        `createMatrix` in interface `FieldMatrix<T extends FieldElement<T>>`
      Specified by:
        `createMatrix` in class `AbstractFieldMatrix<T extends FieldElement<T>>`
      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 FieldMatrix<T> copy()

      Make a (deep) copy of this.
      Specified by:
        `copy` in interface `FieldMatrix<T extends FieldElement<T>>`
      Specified by:
        `copy` in class `AbstractFieldMatrix<T extends FieldElement<T>>`
      Returns:
        a copy of this matrix.

    - #### add

          public Array2DRowFieldMatrix<T> add(Array2DRowFieldMatrix<T> m)
                                                               throws MatrixDimensionMismatchException

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

    - #### subtract

          public Array2DRowFieldMatrix<T> subtract(Array2DRowFieldMatrix<T> 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.

    - #### multiply

          public Array2DRowFieldMatrix<T> multiply(Array2DRowFieldMatrix<T> m)
                                                                    throws DimensionMismatchException

      Postmultiplying this matrix by `m`.
      Parameters:
        `m` - Matrix to postmultiply by.
      Returns:
        `this` * m.
      Throws:
        `DimensionMismatchException` - if the number of columns of this matrix is not equal to the number of rows of `m`.

    - #### getData

          public T[][] getData()

      Returns matrix entries as a two-dimensional array.
      Specified by:
        `getData` in interface `FieldMatrix<T extends FieldElement<T>>`
      Overrides:
        `getData` in class `AbstractFieldMatrix<T extends FieldElement<T>>`
      Returns:
        a 2-dimensional array of entries.

    - #### getDataRef

          public T[][] getDataRef()

      Get a reference to the underlying data array. This methods returns internal data, not fresh copy of it.
      Returns:
        the 2-dimensional array of entries.

    - #### setSubMatrix

          public void setSubMatrix(T[][] subMatrix,
                          int row,
                          int column)
                            throws OutOfRangeException,
                                   NullArgumentException,
                                   NoDataException,
                                   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 `FieldMatrix<T extends FieldElement<T>>`
      Overrides:
        `setSubMatrix` in class `AbstractFieldMatrix<T extends FieldElement<T>>`
      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)`.
        `NullArgumentException` - if `subMatrix` is `null`.
        `NoDataException` - if a row or column of `subMatrix` is empty.
        `DimensionMismatchException` - if `subMatrix` is not rectangular (not all rows have the same length).

    - #### getEntry

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

      Returns the entry in the specified row and column.
      Specified by:
        `getEntry` in interface `FieldMatrix<T extends FieldElement<T>>`
      Specified by:
        `getEntry` in class `AbstractFieldMatrix<T extends FieldElement<T>>`
      Parameters:
        `row` - row location of entry to be fetched
        `column` - column location of entry to be fetched
      Returns:
        matrix entry in row,column
      Throws:
        `OutOfRangeException` - if the row or column index is not valid.

    - #### setEntry

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

      Set the entry in the specified row and column.
      Specified by:
        `setEntry` in interface `FieldMatrix<T extends FieldElement<T>>`
      Specified by:
        `setEntry` in class `AbstractFieldMatrix<T extends FieldElement<T>>`
      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:
        `OutOfRangeException` - if the row or column index is not valid.

    - #### addToEntry

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

      Change an entry in the specified row and column.
      Specified by:
        `addToEntry` in interface `FieldMatrix<T extends FieldElement<T>>`
      Specified by:
        `addToEntry` in class `AbstractFieldMatrix<T extends FieldElement<T>>`
      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:
        `OutOfRangeException` - if the row or column index is not valid.

    - #### multiplyEntry

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

      Change an entry in the specified row and column.
      Specified by:
        `multiplyEntry` in interface `FieldMatrix<T extends FieldElement<T>>`
      Specified by:
        `multiplyEntry` in class `AbstractFieldMatrix<T extends FieldElement<T>>`
      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:
        `OutOfRangeException` - if the row or column index is not valid.

    - #### getRowDimension

          public int getRowDimension()

      Returns the number of rows in the matrix.
      Specified by:
        `getRowDimension` in interface `AnyMatrix`
      Specified by:
        `getRowDimension` in class `AbstractFieldMatrix<T extends FieldElement<T>>`
      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 `AbstractFieldMatrix<T extends FieldElement<T>>`
      Returns:
        columnDimension

    - #### operate

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

      Returns the result of multiplying this by the vector `v`.
      Specified by:
        `operate` in interface `FieldMatrix<T extends FieldElement<T>>`
      Overrides:
        `operate` in class `AbstractFieldMatrix<T extends FieldElement<T>>`
      Parameters:
        `v` - the vector to operate on
      Returns:
        `this * v`
      Throws:
        `DimensionMismatchException` - if the number of columns of `this` matrix is not equal to the size of the vector `v`.

    - #### preMultiply

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

      Returns the (row) vector result of premultiplying this by the vector `v`.
      Specified by:
        `preMultiply` in interface `FieldMatrix<T extends FieldElement<T>>`
      Overrides:
        `preMultiply` in class `AbstractFieldMatrix<T extends FieldElement<T>>`
      Parameters:
        `v` - the row vector to premultiply by
      Returns:
        `v * this`
      Throws:
        `DimensionMismatchException` - if the number of rows of `this` matrix is not equal to the size of the vector `v`

    - #### walkInRowOrder

          public T walkInRowOrder(FieldMatrixChangingVisitor<T> 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 `FieldMatrix<T extends FieldElement<T>>`
      Overrides:
        `walkInRowOrder` in class `AbstractFieldMatrix<T extends FieldElement<T>>`
      Parameters:
        `visitor` - visitor used to process all matrix entries
      Returns:
        the value returned by `FieldMatrixChangingVisitor.end()` at the end of the walk
      See Also:
        `FieldMatrix.walkInRowOrder(FieldMatrixPreservingVisitor)`, `FieldMatrix.walkInRowOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `FieldMatrix.walkInRowOrder(FieldMatrixPreservingVisitor, int, int, int, int)`, `FieldMatrix.walkInColumnOrder(FieldMatrixChangingVisitor)`, `FieldMatrix.walkInColumnOrder(FieldMatrixPreservingVisitor)`, `FieldMatrix.walkInColumnOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `FieldMatrix.walkInColumnOrder(FieldMatrixPreservingVisitor, int, int, int, int)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixChangingVisitor)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixPreservingVisitor)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixPreservingVisitor, int, int, int, int)`

    - #### walkInRowOrder

          public T walkInRowOrder(FieldMatrixPreservingVisitor<T> 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 `FieldMatrix<T extends FieldElement<T>>`
      Overrides:
        `walkInRowOrder` in class `AbstractFieldMatrix<T extends FieldElement<T>>`
      Parameters:
        `visitor` - visitor used to process all matrix entries
      Returns:
        the value returned by `FieldMatrixPreservingVisitor.end()` at the end of the walk
      See Also:
        `FieldMatrix.walkInRowOrder(FieldMatrixChangingVisitor)`, `FieldMatrix.walkInRowOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `FieldMatrix.walkInRowOrder(FieldMatrixPreservingVisitor, int, int, int, int)`, `FieldMatrix.walkInColumnOrder(FieldMatrixChangingVisitor)`, `FieldMatrix.walkInColumnOrder(FieldMatrixPreservingVisitor)`, `FieldMatrix.walkInColumnOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `FieldMatrix.walkInColumnOrder(FieldMatrixPreservingVisitor, int, int, int, int)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixChangingVisitor)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixPreservingVisitor)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixPreservingVisitor, int, int, int, int)`

    - #### walkInRowOrder

          public T walkInRowOrder(FieldMatrixChangingVisitor<T> 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 `FieldMatrix<T extends FieldElement<T>>`
      Overrides:
        `walkInRowOrder` in class `AbstractFieldMatrix<T extends FieldElement<T>>`
      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 `FieldMatrixChangingVisitor.end()` at the end of the walk
      Throws:
        `OutOfRangeException` - if the indices are not valid.
        `NumberIsTooSmallException` - if `endRow < startRow` or `endColumn < startColumn`.
      See Also:
        `FieldMatrix.walkInRowOrder(FieldMatrixChangingVisitor)`, `FieldMatrix.walkInRowOrder(FieldMatrixPreservingVisitor)`, `FieldMatrix.walkInRowOrder(FieldMatrixPreservingVisitor, int, int, int, int)`, `FieldMatrix.walkInColumnOrder(FieldMatrixChangingVisitor)`, `FieldMatrix.walkInColumnOrder(FieldMatrixPreservingVisitor)`, `FieldMatrix.walkInColumnOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `FieldMatrix.walkInColumnOrder(FieldMatrixPreservingVisitor, int, int, int, int)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixChangingVisitor)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixPreservingVisitor)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixPreservingVisitor, int, int, int, int)`

    - #### walkInRowOrder

          public T walkInRowOrder(FieldMatrixPreservingVisitor<T> 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 `FieldMatrix<T extends FieldElement<T>>`
      Overrides:
        `walkInRowOrder` in class `AbstractFieldMatrix<T extends FieldElement<T>>`
      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 `FieldMatrixPreservingVisitor.end()` at the end of the walk
      Throws:
        `OutOfRangeException` - if the indices are not valid.
        `NumberIsTooSmallException` - if `endRow < startRow` or `endColumn < startColumn`.
      See Also:
        `FieldMatrix.walkInRowOrder(FieldMatrixChangingVisitor)`, `FieldMatrix.walkInRowOrder(FieldMatrixPreservingVisitor)`, `FieldMatrix.walkInRowOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `FieldMatrix.walkInColumnOrder(FieldMatrixChangingVisitor)`, `FieldMatrix.walkInColumnOrder(FieldMatrixPreservingVisitor)`, `FieldMatrix.walkInColumnOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `FieldMatrix.walkInColumnOrder(FieldMatrixPreservingVisitor, int, int, int, int)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixChangingVisitor)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixPreservingVisitor)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixPreservingVisitor, int, int, int, int)`

    - #### walkInColumnOrder

          public T walkInColumnOrder(FieldMatrixChangingVisitor<T> visitor)

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

      Column order starts at upper left and iterating through all elements of a column from top to bottom before going to the topmost element of the next column.

      Specified by:
        `walkInColumnOrder` in interface `FieldMatrix<T extends FieldElement<T>>`
      Overrides:
        `walkInColumnOrder` in class `AbstractFieldMatrix<T extends FieldElement<T>>`
      Parameters:
        `visitor` - visitor used to process all matrix entries
      Returns:
        the value returned by `FieldMatrixChangingVisitor.end()` at the end of the walk
      See Also:
        `FieldMatrix.walkInRowOrder(FieldMatrixChangingVisitor)`, `FieldMatrix.walkInRowOrder(FieldMatrixPreservingVisitor)`, `FieldMatrix.walkInRowOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `FieldMatrix.walkInRowOrder(FieldMatrixPreservingVisitor, int, int, int, int)`, `FieldMatrix.walkInColumnOrder(FieldMatrixPreservingVisitor)`, `FieldMatrix.walkInColumnOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `FieldMatrix.walkInColumnOrder(FieldMatrixPreservingVisitor, int, int, int, int)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixChangingVisitor)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixPreservingVisitor)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixPreservingVisitor, int, int, int, int)`

    - #### walkInColumnOrder

          public T walkInColumnOrder(FieldMatrixPreservingVisitor<T> visitor)

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

      Column order starts at upper left and iterating through all elements of a column from top to bottom before going to the topmost element of the next column.

      Specified by:
        `walkInColumnOrder` in interface `FieldMatrix<T extends FieldElement<T>>`
      Overrides:
        `walkInColumnOrder` in class `AbstractFieldMatrix<T extends FieldElement<T>>`
      Parameters:
        `visitor` - visitor used to process all matrix entries
      Returns:
        the value returned by `FieldMatrixPreservingVisitor.end()` at the end of the walk
      See Also:
        `FieldMatrix.walkInRowOrder(FieldMatrixChangingVisitor)`, `FieldMatrix.walkInRowOrder(FieldMatrixPreservingVisitor)`, `FieldMatrix.walkInRowOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `FieldMatrix.walkInRowOrder(FieldMatrixPreservingVisitor, int, int, int, int)`, `FieldMatrix.walkInColumnOrder(FieldMatrixChangingVisitor)`, `FieldMatrix.walkInColumnOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `FieldMatrix.walkInColumnOrder(FieldMatrixPreservingVisitor, int, int, int, int)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixChangingVisitor)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixPreservingVisitor)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixPreservingVisitor, int, int, int, int)`

    - #### walkInColumnOrder

          public T walkInColumnOrder(FieldMatrixChangingVisitor<T> visitor,
                            int startRow,
                            int endRow,
                            int startColumn,
                            int endColumn)
                                                      throws OutOfRangeException,
                                                             NumberIsTooSmallException

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

      Column order starts at upper left and iterating through all elements of a column from top to bottom before going to the topmost element of the next column.

      Specified by:
        `walkInColumnOrder` in interface `FieldMatrix<T extends FieldElement<T>>`
      Overrides:
        `walkInColumnOrder` in class `AbstractFieldMatrix<T extends FieldElement<T>>`
      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 `FieldMatrixChangingVisitor.end()` at the end of the walk
      Throws:
        `OutOfRangeException` - if the indices are not valid.
        `NumberIsTooSmallException` - if `endRow < startRow` or `endColumn < startColumn`.
      See Also:
        `FieldMatrix.walkInRowOrder(FieldMatrixChangingVisitor)`, `FieldMatrix.walkInRowOrder(FieldMatrixPreservingVisitor)`, `FieldMatrix.walkInRowOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `FieldMatrix.walkInRowOrder(FieldMatrixPreservingVisitor, int, int, int, int)`, `FieldMatrix.walkInColumnOrder(FieldMatrixChangingVisitor)`, `FieldMatrix.walkInColumnOrder(FieldMatrixPreservingVisitor)`, `FieldMatrix.walkInColumnOrder(FieldMatrixPreservingVisitor, int, int, int, int)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixChangingVisitor)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixPreservingVisitor)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixPreservingVisitor, int, int, int, int)`

    - #### walkInColumnOrder

          public T walkInColumnOrder(FieldMatrixPreservingVisitor<T> visitor,
                            int startRow,
                            int endRow,
                            int startColumn,
                            int endColumn)
                                                      throws OutOfRangeException,
                                                             NumberIsTooSmallException

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

      Column order starts at upper left and iterating through all elements of a column from top to bottom before going to the topmost element of the next column.

      Specified by:
        `walkInColumnOrder` in interface `FieldMatrix<T extends FieldElement<T>>`
      Overrides:
        `walkInColumnOrder` in class `AbstractFieldMatrix<T extends FieldElement<T>>`
      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 `FieldMatrixPreservingVisitor.end()` at the end of the walk
      Throws:
        `OutOfRangeException` - if the indices are not valid.
        `NumberIsTooSmallException` - if `endRow < startRow` or `endColumn < startColumn`.
      See Also:
        `FieldMatrix.walkInRowOrder(FieldMatrixChangingVisitor)`, `FieldMatrix.walkInRowOrder(FieldMatrixPreservingVisitor)`, `FieldMatrix.walkInRowOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `FieldMatrix.walkInRowOrder(FieldMatrixPreservingVisitor, int, int, int, int)`, `FieldMatrix.walkInColumnOrder(FieldMatrixChangingVisitor)`, `FieldMatrix.walkInColumnOrder(FieldMatrixPreservingVisitor)`, `FieldMatrix.walkInColumnOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixChangingVisitor)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixPreservingVisitor)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixPreservingVisitor, int, int, int, int)`

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