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

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

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

All Implemented Interfaces:
  AnyMatrix, FieldMatrix<T>

Direct Known Subclasses:
  Array2DRowFieldMatrix, BlockFieldMatrix, SparseFieldMatrix

    public abstract class AbstractFieldMatrix<T extends FieldElement<T>>

extends Object
implements FieldMatrix<T>

Basic implementation of `FieldMatrix` methods regardless of the underlying storage.

All the methods implemented here use `getEntry(int, int)` to access matrix elements. Derived class can provide faster implementations.

Since:
  2.0
Version:
  $Revision: 1073158 $ $Date: 2011-02-21 22:46:52 +0100 (lun. 21 févr. 2011) $

Field Summary
`private Field<T>` | `field` Field to which the elements belong.

Constructor Summary
`protected` | `AbstractFieldMatrix()` Constructor for use with Serializable
`protected` | `AbstractFieldMatrix(Field<T> field)` Creates a matrix with no data
`protected` | `AbstractFieldMatrix(Field<T> field, int rowDimension, int columnDimension)` Create a new FieldMatrix with the supplied row and column dimensions.

Method Summary
`FieldMatrix<T>` | `add(FieldMatrix<T> m)` Compute the sum of this and m.
`abstract void` | `addToEntry(int row, int column, T increment)` Change an entry in the specified row and column.
`protected static
`<T extends FieldElement<T>> T[]`
` | `buildArray(Field<T> field, int length)` Build an array of elements.
`protected static
`<T extends FieldElement<T>> T[][]`
` | `buildArray(Field<T> field, int rows, int columns)` Build an array of elements.
`protected void` | `checkAdditionCompatible(FieldMatrix<T> m)` Check if a matrix is addition compatible with the instance
`protected void` | `checkColumnIndex(int column)` Check if a column index is valid.
`protected void` | `checkMultiplicationCompatible(FieldMatrix<T> m)` Check if a matrix is multiplication compatible with the instance
`protected void` | `checkRowIndex(int row)` Check if a row index is valid.
`protected void` | `checkSubMatrixIndex(int[] selectedRows, int[] selectedColumns)` Check if submatrix ranges indices are valid.
`protected void` | `checkSubMatrixIndex(int startRow, int endRow, int startColumn, int endColumn)` Check if submatrix ranges indices are valid.
`protected void` | `checkSubtractionCompatible(FieldMatrix<T> m)` Check if a matrix is subtraction compatible with the instance
`abstract 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.
`abstract 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.
`boolean` | `equals(Object object)` Returns true iff `object` is a `FieldMatrix` instance with the same dimensions as this and all corresponding matrix entries are equal.
`protected static
`<T extends FieldElement<T>> Field<T>`
` | `extractField(T[] d)` Get the elements type from an array.
`protected static
`<T extends FieldElement<T>> Field<T>`
` | `extractField(T[][] d)` Get the elements type from an array.
`T[]` | `getColumn(int column)` Returns the entries in column number `col` as an array.
`abstract int` | `getColumnDimension()` Returns the number of columns in the matrix.
`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.
`abstract 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.
`abstract int` | `getRowDimension()` Returns the number of rows in the matrix.
`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).
`int` | `hashCode()` Computes a hashcode for the matrix.
`boolean` | `isSquare()` Is this a square matrix?
`FieldMatrix<T>` | `multiply(FieldMatrix<T> m)` Returns the result of postmultiplying this by m.
`abstract 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.
`abstract 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.
`String` | `toString()` Get a string representation for 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 class java.lang.Object
`clone, finalize, getClass, notify, notifyAll, wait, wait, wait`

Field Detail

### field

    private final Field<T extends FieldElement<T>> field

  Field to which the elements belong.

Constructor Detail

### AbstractFieldMatrix

    protected AbstractFieldMatrix()

  Constructor for use with Serializable

### AbstractFieldMatrix

    protected AbstractFieldMatrix(Field<T> field)

  Creates a matrix with no data

  Parameters:
    `field` - field to which the elements belong

### AbstractFieldMatrix

    protected AbstractFieldMatrix(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

Method Detail

### extractField

    protected static <T extends FieldElement<T>> Field<T> extractField(T[][] d)
                                                            throws IllegalArgumentException

  Get the elements type from an array.

  Type Parameters:
    `T` - the type of the field elements
  Parameters:
    `d` - data array
  Returns:
    field to which array elements belong
  Throws:
    `IllegalArgumentException` - if array is empty

### extractField

    protected static <T extends FieldElement<T>> Field<T> extractField(T[] d)
                                                            throws IllegalArgumentException

  Get the elements type from an array.

  Type Parameters:
    `T` - the type of the field elements
  Parameters:
    `d` - data array
  Returns:
    field to which array elements belong
  Throws:
    `IllegalArgumentException` - if array is empty

### buildArray

    protected static <T extends FieldElement<T>> T[][] buildArray(Field<T> field,
                                                                  int rows,
                                                                  int columns)

  Build an array of elements.

  Complete arrays are filled with field.getZero()

  Type Parameters:
    `T` - the type of the field elements
  Parameters:
    `field` - field to which array elements belong
    `rows` - number of rows
    `columns` - number of columns (may be negative to build partial arrays in the same way `new Field[rows][]` works)
  Returns:
    a new array

### buildArray

    protected static <T extends FieldElement<T>> T[] buildArray(Field<T> field,
                                                                int length)

  Build an array of elements.

  Arrays are filled with field.getZero()

  Type Parameters:
    `T` - the type of the field elements
  Parameters:
    `field` - field to which array elements belong
    `length` - of the array
  Returns:
    a new array

### getField

    public Field<T> getField()

  Get the type of field elements of the matrix.

  Specified by:
    `getField` in interface `FieldMatrix<T extends FieldElement<T>>`
  Returns:
    type of field elements of the matrix

### createMatrix

    public abstract 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>>`
  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 abstract FieldMatrix<T> copy()

  Returns a (deep) copy of this.

  Specified by:
    `copy` in interface `FieldMatrix<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>>`
  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>>`
  Parameters:
    `m` - matrix to be subtracted
  Returns:
    this + m
  Throws:
    `IllegalArgumentException` - if m is not the same size as this

### scalarAdd

    public FieldMatrix<T> scalarAdd(T d)

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

  Specified by:
    `scalarAdd` in interface `FieldMatrix<T extends FieldElement<T>>`
  Parameters:
    `d` - value to be added to each entry
  Returns:
    d + this

### scalarMultiply

    public FieldMatrix<T> scalarMultiply(T d)

  Returns the result multiplying each entry of this by d.

  Specified by:
    `scalarMultiply` in interface `FieldMatrix<T extends FieldElement<T>>`
  Parameters:
    `d` - value to multiply all entries by
  Returns:
    d * 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>>`
  Parameters:
    `m` - matrix to postmultiply by
  Returns:
    this * m
  Throws:
    `IllegalArgumentException` - if columnDimension(this) != rowDimension(m)

### preMultiply

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

  Returns the result premultiplying this by `m`.

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

### getData

    public T[][] getData()

  Returns matrix entries as a two-dimensional array.

  Specified by:
    `getData` in interface `FieldMatrix<T extends FieldElement<T>>`
  Returns:
    2-dimensional array of entries

### getSubMatrix

    public 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.

  Specified by:
    `getSubMatrix` in interface `FieldMatrix<T extends FieldElement<T>>`
  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

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

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

  Specified by:
    `getSubMatrix` in interface `FieldMatrix<T extends FieldElement<T>>`
  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

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

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

  Specified by:
    `copySubMatrix` in interface `FieldMatrix<T extends FieldElement<T>>`
  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
    `IllegalArgumentException` - if the destination array is too small

### copySubMatrix

    public void copySubMatrix(int[] selectedRows,
                              int[] selectedColumns,
                              T[][] destination)
                       throws MatrixIndexException,
                              IllegalArgumentException

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

  Specified by:
    `copySubMatrix` in interface `FieldMatrix<T extends FieldElement<T>>`
  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
    `IllegalArgumentException` - if the destination array is too small

### 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>>`
  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)

### getRowMatrix

    public FieldMatrix<T> getRowMatrix(int row)
                                                        throws MatrixIndexException

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

  Specified by:
    `getRowMatrix` in interface `FieldMatrix<T extends FieldElement<T>>`
  Parameters:
    `row` - the row to be fetched
  Returns:
    row matrix
  Throws:
    `MatrixIndexException` - if the specified row index is invalid

### setRowMatrix

    public 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.

  Specified by:
    `setRowMatrix` in interface `FieldMatrix<T extends FieldElement<T>>`
  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

    public FieldMatrix<T> getColumnMatrix(int column)
                                                           throws MatrixIndexException

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

  Specified by:
    `getColumnMatrix` in interface `FieldMatrix<T extends FieldElement<T>>`
  Parameters:
    `column` - the column to be fetched
  Returns:
    column matrix
  Throws:
    `MatrixIndexException` - if the specified column index is invalid

### setColumnMatrix

    public 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.

  Specified by:
    `setColumnMatrix` in interface `FieldMatrix<T extends FieldElement<T>>`
  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

    public FieldVector<T> getRowVector(int row)
                                                        throws MatrixIndexException

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

  Specified by:
    `getRowVector` in interface `FieldMatrix<T extends FieldElement<T>>`
  Parameters:
    `row` - the row to be fetched
  Returns:
    row vector
  Throws:
    `MatrixIndexException` - if the specified row index is invalid

### setRowVector

    public 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.

  Specified by:
    `setRowVector` in interface `FieldMatrix<T extends FieldElement<T>>`
  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

    public FieldVector<T> getColumnVector(int column)
                                                           throws MatrixIndexException

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

  Specified by:
    `getColumnVector` in interface `FieldMatrix<T extends FieldElement<T>>`
  Parameters:
    `column` - the column to be fetched
  Returns:
    column vector
  Throws:
    `MatrixIndexException` - if the specified column index is invalid

### setColumnVector

    public 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.

  Specified by:
    `setColumnVector` in interface `FieldMatrix<T extends FieldElement<T>>`
  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

    public 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.`

  Specified by:
    `getRow` in interface `FieldMatrix<T extends FieldElement<T>>`
  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

    public 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.

  Specified by:
    `setRow` in interface `FieldMatrix<T extends FieldElement<T>>`
  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

    public 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.`

  Specified by:
    `getColumn` in interface `FieldMatrix<T extends FieldElement<T>>`
  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

    public 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.

  Specified by:
    `setColumn` in interface `FieldMatrix<T extends FieldElement<T>>`
  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

    public abstract 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>>`
  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 abstract 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>>`
  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 abstract 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>>`
  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 abstract 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>>`
  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

### transpose

    public FieldMatrix<T> transpose()

  Returns the transpose of this matrix.

  Specified by:
    `transpose` in interface `FieldMatrix<T extends FieldElement<T>>`
  Returns:
    transpose matrix

### isSquare

    public boolean isSquare()

  Is this a square matrix?

  Specified by:
    `isSquare` in interface `AnyMatrix`
  Returns:
    true if the matrix is square (rowDimension = columnDimension)

### getRowDimension

    public abstract int getRowDimension()

  Returns the number of rows in the matrix.

  Specified by:
    `getRowDimension` in interface `AnyMatrix`
  Returns:
    rowDimension

### getColumnDimension

    public abstract int getColumnDimension()

  Returns the number of columns in the matrix.

  Specified by:
    `getColumnDimension` in interface `AnyMatrix`
  Returns:
    columnDimension

### getTrace

    public T getTrace()
                                       throws NonSquareMatrixException

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

  Specified by:
    `getTrace` in interface `FieldMatrix<T extends FieldElement<T>>`
  Returns:
    trace
  Throws:
    `NonSquareMatrixException` - if the matrix is not square

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

### operate

    public FieldVector<T> operate(FieldVector<T> v)
                                                   throws IllegalArgumentException

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

  Specified by:
    `operate` in interface `FieldMatrix<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>>`
  Parameters:
    `v` - the row vector to premultiply by
  Returns:
    v*this
  Throws:
    `IllegalArgumentException` - if rowDimension != v.size()

### preMultiply

    public FieldVector<T> preMultiply(FieldVector<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>>`
  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>>`
  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>>`
  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>>`
  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>>`
  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>>`
  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>>`
  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>>`
  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>>`
  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)`

### walkInOptimizedOrder

    public 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.

  Specified by:
    `walkInOptimizedOrder` in interface `FieldMatrix<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(FieldMatrixChangingVisitor)`, `FieldMatrix.walkInColumnOrder(FieldMatrixPreservingVisitor)`, `FieldMatrix.walkInColumnOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `FieldMatrix.walkInColumnOrder(FieldMatrixPreservingVisitor, int, int, int, int)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixPreservingVisitor)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixPreservingVisitor, int, int, int, int)`

### walkInOptimizedOrder

    public 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.

  Specified by:
    `walkInOptimizedOrder` in interface `FieldMatrix<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(FieldMatrixPreservingVisitor)`, `FieldMatrix.walkInColumnOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `FieldMatrix.walkInColumnOrder(FieldMatrixPreservingVisitor, int, int, int, int)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixChangingVisitor)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixChangingVisitor, int, int, int, int)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixPreservingVisitor, int, int, int, int)`

### walkInOptimizedOrder

    public 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.

  Specified by:
    `walkInOptimizedOrder` in interface `FieldMatrix<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 (inclusive)
  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(FieldMatrixChangingVisitor, int, int, int, int)`, `FieldMatrix.walkInColumnOrder(FieldMatrixPreservingVisitor, int, int, int, int)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixChangingVisitor)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixPreservingVisitor)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixPreservingVisitor, int, int, int, int)`

### walkInOptimizedOrder

    public 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.

  Specified by:
    `walkInOptimizedOrder` in interface `FieldMatrix<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 (inclusive)
  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.walkInColumnOrder(FieldMatrixPreservingVisitor, int, int, int, int)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixChangingVisitor)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixPreservingVisitor)`, `FieldMatrix.walkInOptimizedOrder(FieldMatrixChangingVisitor, int, int, int, int)`

### toString

    public String toString()

  Get a string representation for this matrix.

  Overrides:
    `toString` in class `Object`
  Returns:
    a string representation for this matrix

### equals

    public boolean equals(Object object)

  Returns true iff `object` is a `FieldMatrix` instance with the same dimensions as this and all corresponding matrix entries are equal.

  Overrides:
    `equals` in class `Object`
  Parameters:
    `object` - the object to test equality against.
  Returns:
    true if object equals this

### hashCode

    public int hashCode()

  Computes a hashcode for the matrix.

  Overrides:
    `hashCode` in class `Object`
  Returns:
    hashcode for matrix

### checkRowIndex

    protected void checkRowIndex(int row)

  Check if a row index is valid.

  Parameters:
    `row` - row index to check
  Throws:
    `MatrixIndexException` - if index is not valid

### checkColumnIndex

    protected void checkColumnIndex(int column)
                             throws MatrixIndexException

  Check if a column index is valid.

  Parameters:
    `column` - column index to check
  Throws:
    `MatrixIndexException` - if index is not valid

### checkSubMatrixIndex

    protected void checkSubMatrixIndex(int startRow,
                                       int endRow,
                                       int startColumn,
                                       int endColumn)

  Check if submatrix ranges indices are valid. Rows and columns are indicated counting from 0 to n-1.

  Parameters:
    `startRow` - Initial row index
    `endRow` - Final row index
    `startColumn` - Initial column index
    `endColumn` - Final column index
  Throws:
    `MatrixIndexException` - if the indices are not valid

### checkSubMatrixIndex

    protected void checkSubMatrixIndex(int[] selectedRows,
                                       int[] selectedColumns)

  Check if submatrix ranges indices are valid. Rows and columns are indicated counting from 0 to n-1.

  Parameters:
    `selectedRows` - Array of row indices.
    `selectedColumns` - Array of column indices.
  Throws:
    `MatrixIndexException` - if row or column selections are not valid

### checkAdditionCompatible

    protected void checkAdditionCompatible(FieldMatrix<T> m)

  Check if a matrix is addition compatible with the instance

  Parameters:
    `m` - matrix to check
  Throws:
    `IllegalArgumentException` - if matrix is not addition compatible with instance

### checkSubtractionCompatible

    protected void checkSubtractionCompatible(FieldMatrix<T> m)

  Check if a matrix is subtraction compatible with the instance

  Parameters:
    `m` - matrix to check
  Throws:
    `IllegalArgumentException` - if matrix is not subtraction compatible with instance

### checkMultiplicationCompatible

    protected void checkMultiplicationCompatible(FieldMatrix<T> m)

  Check if a matrix is multiplication compatible with the instance

  Parameters:
    `m` - matrix to check
  Throws:
    `IllegalArgumentException` - if matrix is not multiplication compatible with instance

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