org.apache.commons.math3.linear

## Interface FieldMatrix<T extends FieldElement<T>>

Type Parameters:
  `T` - the type of the field elements

All Superinterfaces:
  AnyMatrix

All Known Implementing Classes:
  AbstractFieldMatrix, Array2DRowFieldMatrix, BlockFieldMatrix, SparseFieldMatrix

    public interface FieldMatrix<T extends FieldElement<T>>
    extends AnyMatrix

Interface defining field-valued matrix with basic algebraic operations.

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

Version:
  $Id: FieldMatrix.java 1416643 2012-12-03 19:37:14Z tn $

### Method Summary

Methods
`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()` Make a (deep) copy of this.
`void` `copySubMatrix(int[] selectedRows, int[] selectedColumns, T[][] destination)` Copy a submatrix.
`void` `copySubMatrix(int startRow, int endRow, int startColumn, int endColumn, T[][] destination)` Copy a submatrix.
`FieldMatrix<T>` `createMatrix(int rowDimension, int columnDimension)` Create a new FieldMatrix<T> of the same type as the instance with the supplied row and column dimensions.
`T[]` `getColumn(int column)` Get the entries in column number `col` as an array.
`FieldMatrix<T>` `getColumnMatrix(int column)` Get the entries in column number `column` as a column matrix.
`FieldVector<T>` `getColumnVector(int column)` Returns the entries in column number `column` as a vector.
`T[][]` `getData()` Returns matrix entries as a two-dimensional array.
`T` `getEntry(int row, int column)` Returns the entry in the specified row and column.
`Field<T>` `getField()` Get the type of field elements of the matrix.
`T[]` `getRow(int row)` Get the entries in row number `row` as an array.
`FieldMatrix<T>` `getRowMatrix(int row)` Get the entries in row number `row` as a row matrix.
`FieldVector<T>` `getRowVector(int row)` Get the entries in row number `row` as a vector.
`FieldMatrix<T>` `getSubMatrix(int[] selectedRows, int[] selectedColumns)` Get a submatrix.
`FieldMatrix<T>` `getSubMatrix(int startRow, int endRow, int startColumn, int endColumn)` Get a submatrix.
`T` `getTrace()` Returns the trace of the matrix (the sum of the elements on the main diagonal).
`FieldMatrix<T>` `multiply(FieldMatrix<T> m)` Postmultiply this matrix by `m`.
`void` `multiplyEntry(int row, int column, T factor)` Change an entry in the specified row and column.
`FieldVector<T>` `operate(FieldVector<T> v)` Returns the result of multiplying this by the vector `v`.
`T[]` `operate(T[] v)` Returns the result of multiplying this by the vector `v`.
`FieldMatrix<T>` `power(int p)` Returns the result multiplying this with itself `p` times.
`FieldMatrix<T>` `preMultiply(FieldMatrix<T> m)` Premultiply this matrix by `m`.
`FieldVector<T>` `preMultiply(FieldVector<T> v)` Returns the (row) vector result of premultiplying this by the vector `v`.
`T[]` `preMultiply(T[] v)` Returns the (row) vector result of premultiplying this by the vector `v`.
`FieldMatrix<T>` `scalarAdd(T d)` Increment each entry of this matrix.
`FieldMatrix<T>` `scalarMultiply(T d)` Multiply each entry by `d`.
`void` `setColumn(int column, T[] array)` Set the entries in column number `column` as a column matrix.
`void` `setColumnMatrix(int column, FieldMatrix<T> matrix)` Set the entries in column number `column` as a column matrix.
`void` `setColumnVector(int column, FieldVector<T> vector)` Set the entries in column number `column` as a vector.
`void` `setEntry(int row, int column, T value)` Set the entry in the specified row and column.
`void` `setRow(int row, T[] array)` Set the entries in row number `row` as a row matrix.
`void` `setRowMatrix(int row, FieldMatrix<T> matrix)` Set the entries in row number `row` as a row matrix.
`void` `setRowVector(int row, FieldVector<T> vector)` Set the entries in row number `row` as a vector.
`void` `setSubMatrix(T[][] subMatrix, int row, int column)` Replace the submatrix starting at `(row, column)` using data in the input `subMatrix` array.
`FieldMatrix<T>` `subtract(FieldMatrix<T> m)` Subtract `m` from this matrix.
`FieldMatrix<T>` `transpose()` Returns the transpose of 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` `walkInOptimizedOrder(FieldMatrixChangingVisitor<T> visitor)` Visit (and possibly change) all matrix entries using the fastest possible order.
`T` `walkInOptimizedOrder(FieldMatrixChangingVisitor<T> visitor, int startRow, int endRow, int startColumn, int endColumn)` Visit (and possibly change) some matrix entries using the fastest possible order.
`T` `walkInOptimizedOrder(FieldMatrixPreservingVisitor<T> visitor)` Visit (but don't change) all matrix entries using the fastest possible order.
`T` `walkInOptimizedOrder(FieldMatrixPreservingVisitor<T> visitor, int startRow, int endRow, int startColumn, int endColumn)` Visit (but don't change) some matrix entries using the fastest possible 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 interface org.apache.commons.math3.linear.AnyMatrix

`getColumnDimension, getRowDimension, isSquare`

### Method Detail

#### getField

    Field<T> getField()

Get the type of field elements of the matrix.

Returns:
  the type of field elements of the matrix.

#### createMatrix

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

Create a new FieldMatrix<T> of the same type as the instance with the supplied row and column dimensions.

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.
Since:
  2.0

#### copy

    FieldMatrix<T> copy()

Make a (deep) copy of this.

Returns:
  a copy of this matrix.

#### add

    FieldMatrix<T> add(FieldMatrix<T> m)
                                               throws MatrixDimensionMismatchException

Compute the sum of this and m.

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

#### subtract

    FieldMatrix<T> subtract(FieldMatrix<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.

#### scalarAdd

    FieldMatrix<T> scalarAdd(T d)

Increment each entry of this matrix.

Parameters:
  `d` - Value to be added to each entry.
Returns:
  `d` + `this`.

#### scalarMultiply

    FieldMatrix<T> scalarMultiply(T d)

Multiply each entry by `d`.

Parameters:
  `d` - Value to multiply all entries by.
Returns:
  `d` * `this`.

#### multiply

    FieldMatrix<T> multiply(FieldMatrix<T> m)
                                                    throws DimensionMismatchException

Postmultiply 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 matrix `m`.

#### preMultiply

    FieldMatrix<T> preMultiply(FieldMatrix<T> m)
                                                       throws DimensionMismatchException

Premultiply this matrix by `m`.

Parameters:
  `m` - Matrix to premultiply by.
Returns:
  `m` * `this`.
Throws:
  `DimensionMismatchException` - if the number of columns of `m` differs from the number of rows of `this` matrix.

#### power

    FieldMatrix<T> power(int p)
                                                 throws NonSquareMatrixException,
                                                        NotPositiveException

Returns the result multiplying this with itself `p` times. Depending on the type of the field elements, T, instability for high powers might occur.

Parameters:
  `p` - raise this to power p
Returns:
  this^p
Throws:
  `NotPositiveException` - if `p < 0`
  `NonSquareMatrixException` - if `this matrix` is not square

#### getData

    T[][] getData()

Returns matrix entries as a two-dimensional array.

Returns:
  a 2-dimensional array of entries.

#### getSubMatrix

    FieldMatrix<T> getSubMatrix(int startRow,
                              int endRow,
                              int startColumn,
                              int endColumn)
                                                        throws NumberIsTooSmallException,
                                                               OutOfRangeException

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

Parameters:
  `startRow` - Initial row index
  `endRow` - Final row index (inclusive)
  `startColumn` - Initial column index
  `endColumn` - Final column index (inclusive)
Returns:
  the matrix containing the data of the specified rows and columns.
Throws:
  `NumberIsTooSmallException` - is `endRow < startRow` of `endColumn < startColumn`.
  `OutOfRangeException` - if the indices are not valid.

#### getSubMatrix

    FieldMatrix<T> getSubMatrix(int[] selectedRows,
                              int[] selectedColumns)
                                                        throws NoDataException,
                                                               NullArgumentException,
                                                               OutOfRangeException

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

Parameters:
  `selectedRows` - Array of row indices.
  `selectedColumns` - Array of column indices.
Returns:
  the matrix containing the data in the specified rows and columns.
Throws:
  `NoDataException` - if `selectedRows` or `selectedColumns` is empty
  `NullArgumentException` - if `selectedRows` or `selectedColumns` is `null`.
  `OutOfRangeException` - if row or column selections are not valid.

#### copySubMatrix

    void copySubMatrix(int startRow,
                     int endRow,
                     int startColumn,
                     int endColumn,
                     T[][] destination)
                       throws MatrixDimensionMismatchException,
                              NumberIsTooSmallException,
                              OutOfRangeException

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

Parameters:
  `startRow` - Initial row index.
  `endRow` - Final row index (inclusive).
  `startColumn` - Initial column index.
  `endColumn` - Final column index (inclusive).
  `destination` - The arrays where the submatrix data should be copied (if larger than rows/columns counts, only the upper-left part will be used).
Throws:
  `MatrixDimensionMismatchException` - if the dimensions of `destination` do not match those of `this`.
  `NumberIsTooSmallException` - is `endRow < startRow` of `endColumn < startColumn`.
  `OutOfRangeException` - if the indices are not valid.
  `java.lang.IllegalArgumentException` - if the destination array is too small.

#### copySubMatrix

    void copySubMatrix(int[] selectedRows,
                     int[] selectedColumns,
                     T[][] destination)
                       throws MatrixDimensionMismatchException,
                              NoDataException,
                              NullArgumentException,
                              OutOfRangeException

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

Parameters:
  `selectedRows` - Array of row indices.
  `selectedColumns` - Array of column indices.
  `destination` - Arrays where the submatrix data should be copied (if larger than rows/columns counts, only the upper-left part will be used)
Throws:
  `MatrixDimensionMismatchException` - if the dimensions of `destination` do not match those of `this`.
  `NoDataException` - if `selectedRows` or `selectedColumns` is empty
  `NullArgumentException` - if `selectedRows` or `selectedColumns` is `null`.
  `OutOfRangeException` - if the indices are not valid.

#### setSubMatrix

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

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

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 a row or column of `subMatrix` is empty.
  `DimensionMismatchException` - if `subMatrix` is not rectangular (not all rows have the same length).
  `NullArgumentException` - if `subMatrix` is `null`.
Since:
  2.0

#### getRowMatrix

    FieldMatrix<T> getRowMatrix(int row)
                                                        throws OutOfRangeException

Get the entries in row number `row` as a row matrix.

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

#### setRowMatrix

    void setRowMatrix(int row,
                    FieldMatrix<T> matrix)
                      throws MatrixDimensionMismatchException,
                             OutOfRangeException

Set the entries in row number `row` as a row matrix.

Parameters:
  `row` - 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

    FieldMatrix<T> getColumnMatrix(int column)
                                                           throws OutOfRangeException

Get the entries in column number `column` as a column matrix.

Parameters:
  `column` - Column to be fetched.
Returns:
  a column matrix.
Throws:
  `OutOfRangeException` - if the specified column index is invalid.

#### setColumnMatrix

    void setColumnMatrix(int column,
                       FieldMatrix<T> matrix)
                         throws MatrixDimensionMismatchException,
                                OutOfRangeException

Set the entries in column number `column` as a column matrix.

Parameters:
  `column` - Column to be set.
  `matrix` - column matrix (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 matrix dimensions do not match one instance column.

#### getRowVector

    FieldVector<T> getRowVector(int row)
                                                        throws OutOfRangeException

Get the entries in row number `row` as a vector.

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

#### setRowVector

    void setRowVector(int row,
                    FieldVector<T> vector)
                      throws MatrixDimensionMismatchException,
                             OutOfRangeException

Set the entries in row number `row` as a vector.

Parameters:
  `row` - Row to be set.
  `vector` - row vector (must have the same number of columns as the instance).
Throws:
  `OutOfRangeException` - if the specified row index is invalid.
  `MatrixDimensionMismatchException` - if the vector dimension does not match one instance row.

#### getColumnVector

    FieldVector<T> getColumnVector(int column)
                                                           throws OutOfRangeException

Returns the entries in column number `column` as a vector.

Parameters:
  `column` - Column to be fetched.
Returns:
  a column vector.
Throws:
  `OutOfRangeException` - if the specified column index is invalid.

#### setColumnVector

    void setColumnVector(int column,
                       FieldVector<T> vector)
                         throws MatrixDimensionMismatchException,
                                OutOfRangeException

Set the entries in column number `column` as a vector.

Parameters:
  `column` - Column to be set.
  `vector` - Column vector (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 one instance column.

#### getRow

    T[] getRow(int row)
                                       throws OutOfRangeException

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

Parameters:
  `row` - Row to be fetched.
Returns:
  array of entries in the row.
Throws:
  `OutOfRangeException` - if the specified row index is not valid.

#### setRow

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

Set the entries in row number `row` as a row matrix.

Parameters:
  `row` - Row to be set.
  `array` - Row matrix (must have the same number of columns as the instance).
Throws:
  `OutOfRangeException` - if the specified row index is invalid.
  `MatrixDimensionMismatchException` - if the array size does not match one instance row.

#### getColumn

    T[] getColumn(int column)
                                          throws OutOfRangeException

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

Parameters:
  `column` - the column to be fetched
Returns:
  array of entries in the column
Throws:
  `OutOfRangeException` - if the specified column index is not valid.

#### setColumn

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

Set the entries in column number `column` as a column matrix.

Parameters:
  `column` - the column to be set
  `array` - column array (must have the same number of rows as the instance)
Throws:
  `OutOfRangeException` - if the specified column index is invalid.
  `MatrixDimensionMismatchException` - if the array size does not match one instance column.

#### getEntry

    T getEntry(int row,
             int column)
                                       throws OutOfRangeException

Returns the entry in the specified row and column.

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

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

Set the entry in the specified row and column.

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.
Since:
  2.0

#### addToEntry

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

Change an entry in the specified row and column.

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.
Since:
  2.0

#### multiplyEntry

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

Change an entry in the specified row and column.

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.
Since:
  2.0

#### transpose

    FieldMatrix<T> transpose()

Returns the transpose of this matrix.

Returns:
  transpose matrix

#### getTrace

    T getTrace()
                                       throws NonSquareMatrixException

Returns the trace of the matrix (the sum of the elements on the main diagonal).

Returns:
  trace
Throws:
  `NonSquareMatrixException` - if the matrix is not square.

#### operate

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

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

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`.

#### operate

    FieldVector<T> operate(FieldVector<T> v)
                                                   throws DimensionMismatchException

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

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

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

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

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`

#### preMultiply

    FieldVector<T> preMultiply(FieldVector<T> v)
                                                       throws DimensionMismatchException

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

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

    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.

Parameters:
  `visitor` - visitor used to process all matrix entries
Returns:
  the value returned by `FieldMatrixChangingVisitor.end()` at the end of the walk
See Also:
  `walkInRowOrder(FieldMatrixPreservingVisitor)`, `walkInRowOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `walkInRowOrder(FieldMatrixPreservingVisitor, int, int, int, int)`, `walkInColumnOrder(FieldMatrixChangingVisitor)`, `walkInColumnOrder(FieldMatrixPreservingVisitor)`, `walkInColumnOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `walkInColumnOrder(FieldMatrixPreservingVisitor, int, int, int, int)`, `walkInOptimizedOrder(FieldMatrixChangingVisitor)`, `walkInOptimizedOrder(FieldMatrixPreservingVisitor)`, `walkInOptimizedOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `walkInOptimizedOrder(FieldMatrixPreservingVisitor, int, int, int, int)`

#### walkInRowOrder

    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.

Parameters:
  `visitor` - visitor used to process all matrix entries
Returns:
  the value returned by `FieldMatrixPreservingVisitor.end()` at the end of the walk
See Also:
  `walkInRowOrder(FieldMatrixChangingVisitor)`, `walkInRowOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `walkInRowOrder(FieldMatrixPreservingVisitor, int, int, int, int)`, `walkInColumnOrder(FieldMatrixChangingVisitor)`, `walkInColumnOrder(FieldMatrixPreservingVisitor)`, `walkInColumnOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `walkInColumnOrder(FieldMatrixPreservingVisitor, int, int, int, int)`, `walkInOptimizedOrder(FieldMatrixChangingVisitor)`, `walkInOptimizedOrder(FieldMatrixPreservingVisitor)`, `walkInOptimizedOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `walkInOptimizedOrder(FieldMatrixPreservingVisitor, int, int, int, int)`

#### walkInRowOrder

    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.

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:
  `walkInRowOrder(FieldMatrixChangingVisitor)`, `walkInRowOrder(FieldMatrixPreservingVisitor)`, `walkInRowOrder(FieldMatrixPreservingVisitor, int, int, int, int)`, `walkInColumnOrder(FieldMatrixChangingVisitor)`, `walkInColumnOrder(FieldMatrixPreservingVisitor)`, `walkInColumnOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `walkInColumnOrder(FieldMatrixPreservingVisitor, int, int, int, int)`, `walkInOptimizedOrder(FieldMatrixChangingVisitor)`, `walkInOptimizedOrder(FieldMatrixPreservingVisitor)`, `walkInOptimizedOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `walkInOptimizedOrder(FieldMatrixPreservingVisitor, int, int, int, int)`

#### walkInRowOrder

    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.

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:
  `walkInRowOrder(FieldMatrixChangingVisitor)`, `walkInRowOrder(FieldMatrixPreservingVisitor)`, `walkInRowOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `walkInColumnOrder(FieldMatrixChangingVisitor)`, `walkInColumnOrder(FieldMatrixPreservingVisitor)`, `walkInColumnOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `walkInColumnOrder(FieldMatrixPreservingVisitor, int, int, int, int)`, `walkInOptimizedOrder(FieldMatrixChangingVisitor)`, `walkInOptimizedOrder(FieldMatrixPreservingVisitor)`, `walkInOptimizedOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `walkInOptimizedOrder(FieldMatrixPreservingVisitor, int, int, int, int)`

#### walkInColumnOrder

    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.

Parameters:
  `visitor` - visitor used to process all matrix entries
Returns:
  the value returned by `FieldMatrixChangingVisitor.end()` at the end of the walk
See Also:
  `walkInRowOrder(FieldMatrixChangingVisitor)`, `walkInRowOrder(FieldMatrixPreservingVisitor)`, `walkInRowOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `walkInRowOrder(FieldMatrixPreservingVisitor, int, int, int, int)`, `walkInColumnOrder(FieldMatrixPreservingVisitor)`, `walkInColumnOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `walkInColumnOrder(FieldMatrixPreservingVisitor, int, int, int, int)`, `walkInOptimizedOrder(FieldMatrixChangingVisitor)`, `walkInOptimizedOrder(FieldMatrixPreservingVisitor)`, `walkInOptimizedOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `walkInOptimizedOrder(FieldMatrixPreservingVisitor, int, int, int, int)`

#### walkInColumnOrder

    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.

Parameters:
  `visitor` - visitor used to process all matrix entries
Returns:
  the value returned by `FieldMatrixPreservingVisitor.end()` at the end of the walk
See Also:
  `walkInRowOrder(FieldMatrixChangingVisitor)`, `walkInRowOrder(FieldMatrixPreservingVisitor)`, `walkInRowOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `walkInRowOrder(FieldMatrixPreservingVisitor, int, int, int, int)`, `walkInColumnOrder(FieldMatrixChangingVisitor)`, `walkInColumnOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `walkInColumnOrder(FieldMatrixPreservingVisitor, int, int, int, int)`, `walkInOptimizedOrder(FieldMatrixChangingVisitor)`, `walkInOptimizedOrder(FieldMatrixPreservingVisitor)`, `walkInOptimizedOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `walkInOptimizedOrder(FieldMatrixPreservingVisitor, int, int, int, int)`

#### walkInColumnOrder

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

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.

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:
  `NumberIsTooSmallException` - if `endRow < startRow` or `endColumn < startColumn`.
  `OutOfRangeException` - if the indices are not valid.
See Also:
  `walkInRowOrder(FieldMatrixChangingVisitor)`, `walkInRowOrder(FieldMatrixPreservingVisitor)`, `walkInRowOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `walkInRowOrder(FieldMatrixPreservingVisitor, int, int, int, int)`, `walkInColumnOrder(FieldMatrixChangingVisitor)`, `walkInColumnOrder(FieldMatrixPreservingVisitor)`, `walkInColumnOrder(FieldMatrixPreservingVisitor, int, int, int, int)`, `walkInOptimizedOrder(FieldMatrixChangingVisitor)`, `walkInOptimizedOrder(FieldMatrixPreservingVisitor)`, `walkInOptimizedOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `walkInOptimizedOrder(FieldMatrixPreservingVisitor, int, int, int, int)`

#### walkInColumnOrder

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

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.

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:
  `NumberIsTooSmallException` - if `endRow < startRow` or `endColumn < startColumn`.
  `OutOfRangeException` - if the indices are not valid.
See Also:
  `walkInRowOrder(FieldMatrixChangingVisitor)`, `walkInRowOrder(FieldMatrixPreservingVisitor)`, `walkInRowOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `walkInRowOrder(FieldMatrixPreservingVisitor, int, int, int, int)`, `walkInColumnOrder(FieldMatrixChangingVisitor)`, `walkInColumnOrder(FieldMatrixPreservingVisitor)`, `walkInColumnOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `walkInOptimizedOrder(FieldMatrixChangingVisitor)`, `walkInOptimizedOrder(FieldMatrixPreservingVisitor)`, `walkInOptimizedOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `walkInOptimizedOrder(FieldMatrixPreservingVisitor, int, int, int, int)`

#### walkInOptimizedOrder

    T walkInOptimizedOrder(FieldMatrixChangingVisitor<T> 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.

Parameters:
  `visitor` - visitor used to process all matrix entries
Returns:
  the value returned by `FieldMatrixChangingVisitor.end()` at the end of the walk
See Also:
  `walkInRowOrder(FieldMatrixChangingVisitor)`, `walkInRowOrder(FieldMatrixPreservingVisitor)`, `walkInRowOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `walkInRowOrder(FieldMatrixPreservingVisitor, int, int, int, int)`, `walkInColumnOrder(FieldMatrixChangingVisitor)`, `walkInColumnOrder(FieldMatrixPreservingVisitor)`, `walkInColumnOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `walkInColumnOrder(FieldMatrixPreservingVisitor, int, int, int, int)`, `walkInOptimizedOrder(FieldMatrixPreservingVisitor)`, `walkInOptimizedOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `walkInOptimizedOrder(FieldMatrixPreservingVisitor, int, int, int, int)`

#### walkInOptimizedOrder

    T walkInOptimizedOrder(FieldMatrixPreservingVisitor<T> 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.

Parameters:
  `visitor` - visitor used to process all matrix entries
Returns:
  the value returned by `FieldMatrixPreservingVisitor.end()` at the end of the walk
See Also:
  `walkInRowOrder(FieldMatrixChangingVisitor)`, `walkInRowOrder(FieldMatrixPreservingVisitor)`, `walkInRowOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `walkInRowOrder(FieldMatrixPreservingVisitor, int, int, int, int)`, `walkInColumnOrder(FieldMatrixChangingVisitor)`, `walkInColumnOrder(FieldMatrixPreservingVisitor)`, `walkInColumnOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `walkInColumnOrder(FieldMatrixPreservingVisitor, int, int, int, int)`, `walkInOptimizedOrder(FieldMatrixChangingVisitor)`, `walkInOptimizedOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `walkInOptimizedOrder(FieldMatrixPreservingVisitor, int, int, int, int)`

#### walkInOptimizedOrder

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

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.

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 `FieldMatrixChangingVisitor.end()` at the end of the walk
Throws:
  `NumberIsTooSmallException` - if `endRow < startRow` or `endColumn < startColumn`.
  `OutOfRangeException` - if the indices are not valid.
See Also:
  `walkInRowOrder(FieldMatrixChangingVisitor)`, `walkInRowOrder(FieldMatrixPreservingVisitor)`, `walkInRowOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `walkInRowOrder(FieldMatrixPreservingVisitor, int, int, int, int)`, `walkInColumnOrder(FieldMatrixChangingVisitor)`, `walkInColumnOrder(FieldMatrixPreservingVisitor)`, `walkInColumnOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `walkInColumnOrder(FieldMatrixPreservingVisitor, int, int, int, int)`, `walkInOptimizedOrder(FieldMatrixChangingVisitor)`, `walkInOptimizedOrder(FieldMatrixPreservingVisitor)`, `walkInOptimizedOrder(FieldMatrixPreservingVisitor, int, int, int, int)`

#### walkInOptimizedOrder

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

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.

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 `FieldMatrixPreservingVisitor.end()` at the end of the walk
Throws:
  `NumberIsTooSmallException` - if `endRow < startRow` or `endColumn < startColumn`.
  `OutOfRangeException` - if the indices are not valid.
See Also:
  `walkInRowOrder(FieldMatrixChangingVisitor)`, `walkInRowOrder(FieldMatrixPreservingVisitor)`, `walkInRowOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `walkInRowOrder(FieldMatrixPreservingVisitor, int, int, int, int)`, `walkInColumnOrder(FieldMatrixChangingVisitor)`, `walkInColumnOrder(FieldMatrixPreservingVisitor)`, `walkInColumnOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `walkInColumnOrder(FieldMatrixPreservingVisitor, int, int, int, int)`, `walkInOptimizedOrder(FieldMatrixChangingVisitor)`, `walkInOptimizedOrder(FieldMatrixPreservingVisitor)`, `walkInOptimizedOrder(FieldMatrixChangingVisitor, int, int, int, int)`