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## org.apache.commons.math.linear
Class Array2DRowFieldMatrix<T extends FieldElement<T>>

    java.lang.Object
      org.apache.commons.math.linear.AbstractFieldMatrix<T>
          org.apache.commons.math.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.

Version:
  $Revision: 1073158 $ $Date: 2011-02-21 22:46:52 +0100 (lun. 21 févr. 2011) $
See Also:
  Serialized Form

Field Summary
`protected T[][]` | `data` Entries of the matrix
`private static long` | `serialVersionUID` Serializable version identifier

Constructor Summary
`Array2DRowFieldMatrix(Field<T> field)` Creates a matrix with no data
`Array2DRowFieldMatrix(Field<T> field, int rowDimension, int columnDimension)` Create a new FieldMatrix with the supplied row and column dimensions.
`Array2DRowFieldMatrix(T[] v)` Create a new (column) FieldMatrix using `v` as the data for the unique column of the `v.length x 1` matrix created.
`Array2DRowFieldMatrix(T[][] d)` Create a new FieldMatrix using the input array as the underlying data array.
`Array2DRowFieldMatrix(T[][] d, boolean copyArray)` Create a new FieldMatrix using the input array as the underlying data array.

Method Summary
`Array2DRowFieldMatrix<T>` | `add(Array2DRowFieldMatrix<T> m)` Compute the sum of this and `m`.
`FieldMatrix<T>` | `add(FieldMatrix<T> m)` Compute the sum of this and m.
`void` | `addToEntry(int row, int column, T increment)` Change an entry in the specified row and column.
`FieldMatrix<T>` | `copy()` Returns a (deep) copy of this.
`private void` | `copyIn(T[][] in)` Replaces data with a fresh copy of the input array.
`private T[][]` | `copyOut()` Returns a fresh copy of the underlying data array.
`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()` Returns 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)` Returns the result of postmultiplying this by `m`.
`FieldMatrix<T>` | `multiply(FieldMatrix<T> m)` Returns the result of postmultiplying this 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)` Compute this minus `m`.
`FieldMatrix<T>` | `subtract(FieldMatrix<T> m)` Compute this minus m.
`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.math.linear.AbstractFieldMatrix
`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, operate, preMultiply, preMultiply, scalarAdd, scalarMultiply, setColumn, setColumnMatrix, setColumnVector, setRow, setRowMatrix, setRowVector, toString, transpose, walkInOptimizedOrder, walkInOptimizedOrder, walkInOptimizedOrder, walkInOptimizedOrder`

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

Field Detail

### serialVersionUID

    private static final long serialVersionUID

  Serializable version identifier

  See Also:
    Constant Field Values

### data

    protected T extends FieldElement<T>[][] data

  Entries of the matrix

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 IllegalArgumentException

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

  Parameters:
    `field` - field to which the elements belong
    `rowDimension` - the number of rows in the new matrix
    `columnDimension` - the number of columns in the new matrix
  Throws:
    `IllegalArgumentException` - if row or column dimension is not positive

### Array2DRowFieldMatrix

    public Array2DRowFieldMatrix(T[][] d)
                          throws IllegalArgumentException,
                                 NullPointerException

  Create a new FieldMatrix 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 new matrix
  Throws:
    `IllegalArgumentException` - if `d` is not rectangular (not all rows have the same length) or empty
    `NullPointerException` - if `d` is null
  See Also:
    `Array2DRowFieldMatrix(FieldElement[][], boolean)`

### Array2DRowFieldMatrix

    public Array2DRowFieldMatrix(T[][] d,
                                 boolean copyArray)
                          throws IllegalArgumentException,
                                 NullPointerException

  Create a new FieldMatrix using the input array as the underlying data array.

  If an array is built specially in order to be embedded in a FieldMatrix and not used directly, the `copyArray` may be set to `false`

  Parameters:
    `d` - data for new matrix
    `copyArray` - if true, the input array will be copied, otherwise it will be referenced
  Throws:
    `IllegalArgumentException` - if `d` is not rectangular (not all rows have the same length) or empty
    `NullPointerException` - if `d` is null
  See Also:
    `Array2DRowFieldMatrix(FieldElement[][])`

### Array2DRowFieldMatrix

    public Array2DRowFieldMatrix(T[] v)

  Create a new (column) FieldMatrix using `v` as the data for the unique column of the `v.length x 1` matrix created.

  The input array is copied, not referenced.

  Parameters:
    `v` - column vector holding data for new matrix

Method Detail

### createMatrix

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

  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:
    `IllegalArgumentException` - if row or column dimension is not positive

### copy

    public FieldMatrix<T> copy()

  Returns 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:
    matrix copy

### add

    public FieldMatrix<T> add(FieldMatrix<T> m)
                                               throws IllegalArgumentException

  Compute the sum of this and m.

  Specified by:
    `add` in interface `FieldMatrix<T extends FieldElement<T>>`
  Overrides:
    `add` in class `AbstractFieldMatrix<T extends FieldElement<T>>`
  Parameters:
    `m` - matrix to be added
  Returns:
    this + m
  Throws:
    `IllegalArgumentException` - if m is not the same size as this

### add

    public Array2DRowFieldMatrix<T> add(Array2DRowFieldMatrix<T> 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 FieldMatrix<T> subtract(FieldMatrix<T> m)
                                                    throws IllegalArgumentException

  Compute this minus m.

  Specified by:
    `subtract` in interface `FieldMatrix<T extends FieldElement<T>>`
  Overrides:
    `subtract` in class `AbstractFieldMatrix<T extends FieldElement<T>>`
  Parameters:
    `m` - matrix to be subtracted
  Returns:
    this + m
  Throws:
    `IllegalArgumentException` - if m is not the same size as this

### subtract

    public Array2DRowFieldMatrix<T> subtract(Array2DRowFieldMatrix<T> 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

### multiply

    public FieldMatrix<T> multiply(FieldMatrix<T> m)
                                                    throws IllegalArgumentException

  Returns the result of postmultiplying this by m.

  Specified by:
    `multiply` in interface `FieldMatrix<T extends FieldElement<T>>`
  Overrides:
    `multiply` in class `AbstractFieldMatrix<T extends FieldElement<T>>`
  Parameters:
    `m` - matrix to postmultiply by
  Returns:
    this * m
  Throws:
    `IllegalArgumentException` - if columnDimension(this) != rowDimension(m)

### multiply

    public Array2DRowFieldMatrix<T> multiply(Array2DRowFieldMatrix<T> 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 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:
    2-dimensional array of entries

### getDataRef

    public T[][] getDataRef()

  Returns a reference to the underlying data array.

  Does not make a fresh copy of the underlying data.

  Returns:
    2-dimensional array of entries

### setSubMatrix

    public void setSubMatrix(T[][] 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 `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:
    `MatrixIndexException` - if subMatrix does not fit into this matrix from element in (row, column)

### getEntry

    public T 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 `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:
    `MatrixIndexException` - if the row or column index is not valid

### setEntry

    public void setEntry(int row,
                         int column,
                         T 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 `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:
    `MatrixIndexException` - if the row or column index is not valid

### addToEntry

    public void addToEntry(int row,
                           int column,
                           T 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 `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:
    `MatrixIndexException` - if the row or column index is not valid

### multiplyEntry

    public void multiplyEntry(int row,
                              int column,
                              T 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 `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:
    `MatrixIndexException` - 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 IllegalArgumentException

  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:
    `IllegalArgumentException` - if columnDimension != v.size()

### preMultiply

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

  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:
    `IllegalArgumentException` - if rowDimension != v.size()

### walkInRowOrder

    public T walkInRowOrder(FieldMatrixChangingVisitor<T> 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 `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
  Throws:
    `MatrixVisitorException` - if the visitor cannot process an entry
  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)
                                             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 `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
  Throws:
    `MatrixVisitorException` - if the visitor cannot process an entry
  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 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 `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:
    `MatrixIndexException` - if the indices are not valid
    `MatrixVisitorException` - if the visitor cannot process an entry
  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 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 `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:
    `MatrixIndexException` - if the indices are not valid
    `MatrixVisitorException` - if the visitor cannot process an entry
  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)
                                                throws MatrixVisitorException

  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
  Throws:
    `MatrixVisitorException` - if the visitor cannot process an entry
  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)
                                                throws MatrixVisitorException

  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
  Throws:
    `MatrixVisitorException` - if the visitor cannot process an entry
  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 MatrixIndexException,
                                                       MatrixVisitorException

  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:
    `MatrixIndexException` - if the indices are not valid
    `MatrixVisitorException` - if the visitor cannot process an entry
  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 MatrixIndexException,
                                                       MatrixVisitorException

  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:
    `MatrixIndexException` - if the indices are not valid
    `MatrixVisitorException` - if the visitor cannot process an entry
  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)`

### copyOut

    private T[][] copyOut()

  Returns a fresh copy of the underlying data array.

  Returns:
    a copy of the underlying data array.

### copyIn

    private void copyIn(T[][] in)

  Replaces data with a fresh copy of the input array.

  Verifies that the input array is rectangular and non-empty.

  Parameters:
    `in` - data to copy in
  Throws:
    `IllegalArgumentException` - if input array is empty or not rectangular
    `NullPointerException` - if input array is null

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