## org.apache.commons.math.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:
  $Revision: 811786 $ $Date: 2009-09-06 05:36:08 -0400 (Sun, 06 Sep 2009) $

Method Summary
`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.
`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)` Returns the entries in column number `col` as an array.
`FieldMatrix<T>` `getColumnMatrix(int column)` Returns 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)` Returns the entries in row number `row` as an array.
`FieldMatrix<T>` `getRowMatrix(int row)` Returns the entries in row number `row` as a row matrix.
`FieldVector<T>` `getRowVector(int row)` Returns the entries in row number `row` as a vector.
`FieldMatrix<T>` `getSubMatrix(int[] selectedRows, int[] selectedColumns)` Gets a submatrix.
`FieldMatrix<T>` `getSubMatrix(int startRow, int endRow, int startColumn, int endColumn)` Gets 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)` 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.
`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>` `preMultiply(FieldMatrix<T> m)` Returns the result premultiplying this 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)` Returns the result of adding d to each entry of this.
`FieldMatrix<T>` `scalarMultiply(T d)` Returns the result multiplying each entry of this by d.
`void` `setColumn(int column, T[] array)` Sets the entries in column number `column` as a column matrix.
`void` `setColumnMatrix(int column, FieldMatrix<T> matrix)` Sets the entries in column number `column` as a column matrix.
`void` `setColumnVector(int column, FieldVector<T> vector)` Sets 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)` Sets the entries in row number `row` as a row matrix.
`void` `setRowMatrix(int row, FieldMatrix<T> matrix)` Sets the entries in row number `row` as a row matrix.
`void` `setRowVector(int row, FieldVector<T> vector)` Sets 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)` Compute this minus m.
`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.math.linear.AnyMatrix
`getColumnDimension, getRowDimension, isSquare`

Method Detail

### getField

    Field<T> getField()

  Get the type of field elements of the matrix.

  Returns:
    type of field elements of the matrix

### createMatrix

    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.

  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:
    `java.lang.IllegalArgumentException` - if row or column dimension is not positive
  Since:
    2.0

### copy

    FieldMatrix<T> copy()

  Returns a (deep) copy of this.

  Returns:
    matrix copy

### add

    FieldMatrix<T> add(FieldMatrix<T> m)
                                               throws java.lang.IllegalArgumentException

  Compute the sum of this and m.

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

### subtract

    FieldMatrix<T> subtract(FieldMatrix<T> m)
                                                    throws java.lang.IllegalArgumentException

  Compute this minus m.

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

### scalarAdd

    FieldMatrix<T> scalarAdd(T d)

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

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

### scalarMultiply

    FieldMatrix<T> scalarMultiply(T d)

  Returns the result multiplying each entry of this by d.

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

### multiply

    FieldMatrix<T> multiply(FieldMatrix<T> m)
                                                    throws java.lang.IllegalArgumentException

  Returns the result of postmultiplying this by m.

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

### preMultiply

    FieldMatrix<T> preMultiply(FieldMatrix<T> m)
                                                       throws java.lang.IllegalArgumentException

  Returns the result premultiplying this by `m`.

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

### getData

    T[][] getData()

  Returns matrix entries as a two-dimensional array.

  Returns:
    2-dimensional array of entries

### getSubMatrix

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

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

  Parameters:
    `startRow` - Initial row index
    `endRow` - Final row index (inclusive)
    `startColumn` - Initial column index
    `endColumn` - Final column index (inclusive)
  Returns:
    The subMatrix containing the data of the specified rows and columns
  Throws:
    `MatrixIndexException` - if the indices are not valid

### getSubMatrix

    FieldMatrix<T> getSubMatrix(int[] selectedRows,
                                int[] selectedColumns)
                                                        throws MatrixIndexException

  Gets 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 subMatrix containing the data in the specified rows and columns
  Throws:
    `MatrixIndexException` - if row or column selections are not valid

### copySubMatrix

    void copySubMatrix(int startRow,
                       int endRow,
                       int startColumn,
                       int endColumn,
                       T[][] destination)
                       throws MatrixIndexException,
                              java.lang.IllegalArgumentException

  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:
    `MatrixIndexException` - 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 MatrixIndexException,
                              java.lang.IllegalArgumentException

  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` - The arrays where the submatrix data should be copied (if larger than rows/columns counts, only the upper-left part will be used)
  Throws:
    `MatrixIndexException` - if the indices are not valid
    `java.lang.IllegalArgumentException` - if the destination array is too small

### setSubMatrix

    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

  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)
    `java.lang.IllegalArgumentException` - if `subMatrix` is not rectangular (not all rows have the same length) or empty
    `java.lang.NullPointerException` - if `subMatrix` is null
  Since:
    2.0

### getRowMatrix

    FieldMatrix<T> getRowMatrix(int row)
                                                        throws MatrixIndexException

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

  Parameters:
    `row` - the row to be fetched
  Returns:
    row matrix
  Throws:
    `MatrixIndexException` - if the specified row index is invalid

### setRowMatrix

    void setRowMatrix(int row,
                      FieldMatrix<T> matrix)
                      throws MatrixIndexException,
                             InvalidMatrixException

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

  Parameters:
    `row` - the row to be set
    `matrix` - row matrix (must have one row and the same number of columns as the instance)
  Throws:
    `MatrixIndexException` - if the specified row index is invalid
    `InvalidMatrixException` - if the matrix dimensions do not match one instance row

### getColumnMatrix

    FieldMatrix<T> getColumnMatrix(int column)
                                                           throws MatrixIndexException

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

  Parameters:
    `column` - the column to be fetched
  Returns:
    column matrix
  Throws:
    `MatrixIndexException` - if the specified column index is invalid

### setColumnMatrix

    void setColumnMatrix(int column,
                         FieldMatrix<T> matrix)
                         throws MatrixIndexException,
                                InvalidMatrixException

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

  Parameters:
    `column` - the column to be set
    `matrix` - column matrix (must have one column and the same number of rows as the instance)
  Throws:
    `MatrixIndexException` - if the specified column index is invalid
    `InvalidMatrixException` - if the matrix dimensions do not match one instance column

### getRowVector

    FieldVector<T> getRowVector(int row)
                                                        throws MatrixIndexException

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

  Parameters:
    `row` - the row to be fetched
  Returns:
    row vector
  Throws:
    `MatrixIndexException` - if the specified row index is invalid

### setRowVector

    void setRowVector(int row,
                      FieldVector<T> vector)
                      throws MatrixIndexException,
                             InvalidMatrixException

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

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

### getColumnVector

    FieldVector<T> getColumnVector(int column)
                                                           throws MatrixIndexException

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

  Parameters:
    `column` - the column to be fetched
  Returns:
    column vector
  Throws:
    `MatrixIndexException` - if the specified column index is invalid

### setColumnVector

    void setColumnVector(int column,
                         FieldVector<T> vector)
                         throws MatrixIndexException,
                                InvalidMatrixException

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

  Parameters:
    `column` - the column to be set
    `vector` - column vector (must have the same number of rows as the instance)
  Throws:
    `MatrixIndexException` - if the specified column index is invalid
    `InvalidMatrixException` - if the vector dimension does not match one instance column

### getRow

    T[] getRow(int row)
                                       throws MatrixIndexException

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

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

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

### setRow

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

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

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

### getColumn

    T[] getColumn(int column)
                                          throws MatrixIndexException

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

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

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

### setColumn

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

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

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

### getEntry

    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.

  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

    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.

  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
  Since:
    2.0

### addToEntry

    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.

  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
  Since:
    2.0

### multiplyEntry

    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.

  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
  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 java.lang.IllegalArgumentException

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

  Parameters:
    `v` - the vector to operate on
  Returns:
    this*v
  Throws:
    `java.lang.IllegalArgumentException` - if columnDimension != v.size()

### operate

    FieldVector<T> operate(FieldVector<T> v)
                                                   throws java.lang.IllegalArgumentException

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

  Parameters:
    `v` - the vector to operate on
  Returns:
    this*v
  Throws:
    `java.lang.IllegalArgumentException` - if columnDimension != v.size()

### preMultiply

    T[] preMultiply(T[] v)
                                            throws java.lang.IllegalArgumentException

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

  Parameters:
    `v` - the row vector to premultiply by
  Returns:
    v*this
  Throws:
    `java.lang.IllegalArgumentException` - if rowDimension != v.size()

### preMultiply

    FieldVector<T> preMultiply(FieldVector<T> v)
                                                       throws java.lang.IllegalArgumentException

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

  Parameters:
    `v` - the row vector to premultiply by
  Returns:
    v*this
  Throws:
    `java.lang.IllegalArgumentException` - if rowDimension != v.size()

### walkInRowOrder

    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.

  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:
    `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)
                                             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.

  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:
    `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 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.

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

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

  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:
    `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)
                                                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.

  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:
    `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 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.

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

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

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

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

  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:
    `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)
                                                   throws MatrixVisitorException

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

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

  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:
    `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 MatrixIndexException,
                                                          MatrixVisitorException

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

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

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

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

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

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

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