AbstractFieldMatrix (Commons Math 3.0 API)

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

Type Parameters:
T - 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:

$Id: AbstractFieldMatrix.java 1244107 2012-02-14 16:17:55Z erans $

Constructor Summary

Constructors
Modifier	Constructor and Description
`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

Methods
Modifier and Type	Method and Description
`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()` Make a (deep) copy of this.
`void`	`copySubMatrix(int[] selectedRows, int[] selectedColumns, T[][] destination)` Copy a submatrix.
`void`	`copySubMatrix(int startRow, int endRow, int startColumn, int endColumn, T[][] destination)` Copy a submatrix.
`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)` Get 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)` Get the entries in column number `column` as a column matrix.
`FieldVector<T>`	`getColumnVector(int column)` Returns the entries in column number `column` as a vector.
`T[][]`	`getData()` Returns matrix entries as a two-dimensional array.
`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)` Get 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)` Get the entries in row number `row` as a row matrix.
`FieldVector<T>`	`getRowVector(int row)` Get the entries in row number `row` as a vector.
`FieldMatrix<T>`	`getSubMatrix(int[] selectedRows, int[] selectedColumns)` Get a submatrix.
`FieldMatrix<T>`	`getSubMatrix(int startRow, int endRow, int startColumn, int endColumn)` Get a submatrix.
`T`	`getTrace()` Returns the trace of the matrix (the sum of the elements on the main diagonal).
`int`	`hashCode()` Computes a hashcode for the matrix.
`boolean`	`isSquare()` Is this a square matrix?
`FieldMatrix<T>`	`multiply(FieldMatrix<T> m)` Postmultiply this matrix 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>`	`power(int p)` Returns the result multiplying this with itself `p` times.
`FieldMatrix<T>`	`preMultiply(FieldMatrix<T> m)` Premultiply this matrix by `m`.
`FieldVector<T>`	`preMultiply(FieldVector<T> v)` Returns the (row) vector result of premultiplying this by the vector `v`.
`T[]`	`preMultiply(T[] v)` Returns the (row) vector result of premultiplying this by the vector `v`.
`FieldMatrix<T>`	`scalarAdd(T d)` Increment each entry of this matrix.
`FieldMatrix<T>`	`scalarMultiply(T d)` Multiply each entry by `d`.
`void`	`setColumn(int column, T[] array)` Set the entries in column number `column` as a column matrix.
`void`	`setColumnMatrix(int column, FieldMatrix<T> matrix)` Set the entries in column number `column` as a column matrix.
`void`	`setColumnVector(int column, FieldVector<T> vector)` Set the entries in column number `column` as a vector.
`abstract void`	`setEntry(int row, int column, T value)` Set the entry in the specified row and column.
`void`	`setRow(int row, T[] array)` Set the entries in row number `row` as a row matrix.
`void`	`setRowMatrix(int row, FieldMatrix<T> matrix)` Set the entries in row number `row` as a row matrix.
`void`	`setRowVector(int row, FieldVector<T> vector)` Set the entries in row number `row` as a vector.
`void`	`setSubMatrix(T[][] subMatrix, int row, int column)` Replace the submatrix starting at `(row, column)` using data in the input `subMatrix` array.
`FieldMatrix<T>`	`subtract(FieldMatrix<T> m)` Subtract `m` from this matrix.
`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

- 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)
```
    Create a new FieldMatrix with the supplied row and column dimensions.
    
    Parameters:
    field - Field to which the elements belong.
    rowDimension - Number of rows in the new matrix.
    columnDimension - Number of columns in the new matrix.
    
    Throws:
    
    NotStrictlyPositiveException - if row or column dimension is not positive.
- Method Detail
  - extractField
```
protected static <T extends FieldElement<T>> Field<T> extractField(T[][] d)
```
    Get the elements type from an array.
    
    Type Parameters:
    T - Type of the field elements.
    Parameters:
    d - Data array.
    
    Returns:
    the field to which the array elements belong.
    
    Throws:
    
    NullArgumentException - if the array is null.
    
    NoDataException - if the array is empty.
  - extractField
```
protected static <T extends FieldElement<T>> Field<T> extractField(T[] d)
```
    Get the elements type from an array.
    
    Type Parameters:
    T - Type of the field elements.
    Parameters:
    d - Data array.
    
    Returns:
    the field to which the array elements belong.
    
    Throws:
    
    NoDataException - 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 - 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:
    the type of field elements of the matrix.
  - createMatrix
```
public 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.
    
    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
  - copy
```
public abstract FieldMatrix<T> copy()
```
    Make a (deep) copy of this.
    
    Specified by:
    
    copy in interface FieldMatrix<T extends FieldElement<T>>
    
    Returns:
    a copy of this matrix.
  - add
```
public FieldMatrix<T> add(FieldMatrix<T> m)
```
    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.
  - subtract
```
public FieldMatrix<T> subtract(FieldMatrix<T> m)
```
    Subtract m from this matrix.
    
    Specified by:
    
    subtract in interface FieldMatrix<T extends FieldElement<T>>
    
    Parameters:
    m - Matrix to be subtracted.
    
    Returns:
    this - m.
  - scalarAdd
```
public FieldMatrix<T> scalarAdd(T d)
```
    Increment each entry of this matrix.
    
    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)
```
    Multiply each entry 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)
```
    Postmultiply this matrix by m.
    
    Specified by:
    
    multiply in interface FieldMatrix<T extends FieldElement<T>>
    
    Parameters:
    m - Matrix to postmultiply by.
    
    Returns:
    this * m.
  - preMultiply
```
public FieldMatrix<T> preMultiply(FieldMatrix<T> m)
```
    Premultiply this matrix by m.
    
    Specified by:
    
    preMultiply in interface FieldMatrix<T extends FieldElement<T>>
    
    Parameters:
    m - Matrix to premultiply by.
    
    Returns:
    m * this.
  - power
```
public FieldMatrix<T> power(int p)
```
    Returns the result multiplying this with itself p times. Depending on the type of the field elements, T, instability for high powers might occur.
    
    Specified by:
    
    power in interface FieldMatrix<T extends FieldElement<T>>
    
    Parameters:
    p - raise this to power p
    
    Returns:
    this^p
  - getData
```
public T[][] getData()
```
    Returns matrix entries as a two-dimensional array.
    
    Specified by:
    
    getData in interface FieldMatrix<T extends FieldElement<T>>
    
    Returns:
    a 2-dimensional array of entries.
  - getSubMatrix
```
public FieldMatrix<T> getSubMatrix(int startRow,
                          int endRow,
                          int startColumn,
                          int endColumn)
```
    Get 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 matrix containing the data of the specified rows and columns.
  - getSubMatrix
```
public FieldMatrix<T> getSubMatrix(int[] selectedRows,
                          int[] selectedColumns)
```
    Get 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 matrix containing the data in the specified rows and columns.
  - copySubMatrix
```
public void copySubMatrix(int startRow,
                 int endRow,
                 int startColumn,
                 int endColumn,
                 T[][] destination)
```
    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).
  - copySubMatrix
```
public void copySubMatrix(int[] selectedRows,
                 int[] selectedColumns,
                 T[][] destination)
```
    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 - Arrays where the submatrix data should be copied (if larger than rows/columns counts, only the upper-left part will be used)
  - setSubMatrix
```
public void setSubMatrix(T[][] subMatrix,
                int row,
                int column)
```
    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.
  - getRowMatrix
```
public FieldMatrix<T> getRowMatrix(int row)
```
    Get the entries in row number row as a row matrix.
    
    Specified by:
    
    getRowMatrix in interface FieldMatrix<T extends FieldElement<T>>
    
    Parameters:
    row - Row to be fetched.
    
    Returns:
    a row matrix.
  - setRowMatrix
```
public void setRowMatrix(int row,
                FieldMatrix<T> matrix)
```
    Set the entries in row number row as a row matrix.
    
    Specified by:
    
    setRowMatrix in interface FieldMatrix<T extends FieldElement<T>>
    
    Parameters:
    row - Row to be set.
    matrix - Row matrix (must have one row and the same number of columns as the instance).
  - getColumnMatrix
```
public FieldMatrix<T> getColumnMatrix(int column)
```
    Get the entries in column number column as a column matrix.
    
    Specified by:
    
    getColumnMatrix in interface FieldMatrix<T extends FieldElement<T>>
    
    Parameters:
    column - Column to be fetched.
    
    Returns:
    a column matrix.
  - setColumnMatrix
```
public void setColumnMatrix(int column,
                   FieldMatrix<T> matrix)
```
    Set the entries in column number column as a column matrix.
    
    Specified by:
    
    setColumnMatrix in interface FieldMatrix<T extends FieldElement<T>>
    
    Parameters:
    column - Column to be set.
    matrix - column matrix (must have one column and the same number of rows as the instance).
  - getRowVector
```
public FieldVector<T> getRowVector(int row)
```
    Get the entries in row number row as a vector.
    
    Specified by:
    
    getRowVector in interface FieldMatrix<T extends FieldElement<T>>
    
    Parameters:
    row - Row to be fetched
    
    Returns:
    a row vector.
  - setRowVector
```
public void setRowVector(int row,
                FieldVector<T> vector)
```
    Set the entries in row number row as a vector.
    
    Specified by:
    
    setRowVector in interface FieldMatrix<T extends FieldElement<T>>
    
    Parameters:
    row - Row to be set.
    vector - row vector (must have the same number of columns as the instance).
  - getColumnVector
```
public FieldVector<T> getColumnVector(int column)
```
    Returns the entries in column number column as a vector.
    
    Specified by:
    
    getColumnVector in interface FieldMatrix<T extends FieldElement<T>>
    
    Parameters:
    column - Column to be fetched.
    
    Returns:
    a column vector.
  - setColumnVector
```
public void setColumnVector(int column,
                   FieldVector<T> vector)
```
    Set the entries in column number column as a vector.
    
    Specified by:
    
    setColumnVector in interface FieldMatrix<T extends FieldElement<T>>
    
    Parameters:
    column - Column to be set.
    vector - Column vector (must have the same number of rows as the instance).
  - getRow
```
public T[] getRow(int row)
```
    Get the entries in row number row as an array.
    
    Specified by:
    
    getRow in interface FieldMatrix<T extends FieldElement<T>>
    
    Parameters:
    row - Row to be fetched.
    
    Returns:
    array of entries in the row.
  - setRow
```
public void setRow(int row,
          T[] array)
```
    Set the entries in row number row as a row matrix.
    
    Specified by:
    
    setRow in interface FieldMatrix<T extends FieldElement<T>>
    
    Parameters:
    row - Row to be set.
    array - Row matrix (must have the same number of columns as the instance).
  - getColumn
```
public T[] getColumn(int column)
```
    Get the entries in column number col as an array.
    
    Specified by:
    
    getColumn in interface FieldMatrix<T extends FieldElement<T>>
    
    Parameters:
    column - the column to be fetched
    
    Returns:
    array of entries in the column
  - setColumn
```
public void setColumn(int column,
             T[] array)
```
    Set the entries in column number column as a column matrix.
    
    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)
  - getEntry
```
public abstract T getEntry(int row,
         int column)
```
    Returns the entry in the specified row and column.
    
    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
  - setEntry
```
public abstract void setEntry(int row,
            int column,
            T value)
```
    Set the entry in the specified row and column.
    
    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
  - addToEntry
```
public abstract void addToEntry(int row,
              int column,
              T increment)
```
    Change an entry in the specified row and column.
    
    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).
  - multiplyEntry
```
public abstract void multiplyEntry(int row,
                 int column,
                 T factor)
```
    Change an entry in the specified row and column.
    
    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)
  - 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()
```
    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
  - operate
```
public T[] operate(T[] v)
```
    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
  - operate
```
public FieldVector<T> operate(FieldVector<T> v)
```
    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
  - preMultiply
```
public T[] preMultiply(T[] v)
```
    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
  - preMultiply
```
public FieldVector<T> preMultiply(FieldVector<T> v)
```
    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
  - walkInRowOrder
```
public T walkInRowOrder(FieldMatrixChangingVisitor<T> visitor)
```
    Visit (and possibly change) all matrix entries in row order.
    Row order starts at upper left and iterating through all elements of a row from left to right before going to the leftmost element of the next row.
    
    Specified by:
    
    walkInRowOrder in interface FieldMatrix<T extends FieldElement<T>>
    
    Parameters:
    visitor - visitor used to process all matrix entries
    
    Returns:
    the value returned by FieldMatrixChangingVisitor.end() at the end of the walk
    See Also:
    FieldMatrix.walkInRowOrder(FieldMatrixPreservingVisitor), FieldMatrix.walkInRowOrder(FieldMatrixChangingVisitor, int, int, int, int), FieldMatrix.walkInRowOrder(FieldMatrixPreservingVisitor, int, int, int, int), FieldMatrix.walkInColumnOrder(FieldMatrixChangingVisitor), FieldMatrix.walkInColumnOrder(FieldMatrixPreservingVisitor), FieldMatrix.walkInColumnOrder(FieldMatrixChangingVisitor, int, int, int, int), FieldMatrix.walkInColumnOrder(FieldMatrixPreservingVisitor, int, int, int, int), FieldMatrix.walkInOptimizedOrder(FieldMatrixChangingVisitor), FieldMatrix.walkInOptimizedOrder(FieldMatrixPreservingVisitor), FieldMatrix.walkInOptimizedOrder(FieldMatrixChangingVisitor, int, int, int, int), FieldMatrix.walkInOptimizedOrder(FieldMatrixPreservingVisitor, int, int, int, int)
  - walkInRowOrder
```
public T walkInRowOrder(FieldMatrixPreservingVisitor<T> visitor)
```
    Visit (but don't change) all matrix entries in row order.
    Row order starts at upper left and iterating through all elements of a row from left to right before going to the leftmost element of the next row.
    
    Specified by:
    
    walkInRowOrder in interface FieldMatrix<T extends FieldElement<T>>
    
    Parameters:
    visitor - visitor used to process all matrix entries
    
    Returns:
    the value returned by FieldMatrixPreservingVisitor.end() at the end of the walk
    See Also:
    FieldMatrix.walkInRowOrder(FieldMatrixChangingVisitor), FieldMatrix.walkInRowOrder(FieldMatrixChangingVisitor, int, int, int, int), FieldMatrix.walkInRowOrder(FieldMatrixPreservingVisitor, int, int, int, int), FieldMatrix.walkInColumnOrder(FieldMatrixChangingVisitor), FieldMatrix.walkInColumnOrder(FieldMatrixPreservingVisitor), FieldMatrix.walkInColumnOrder(FieldMatrixChangingVisitor, int, int, int, int), FieldMatrix.walkInColumnOrder(FieldMatrixPreservingVisitor, int, int, int, int), FieldMatrix.walkInOptimizedOrder(FieldMatrixChangingVisitor), FieldMatrix.walkInOptimizedOrder(FieldMatrixPreservingVisitor), FieldMatrix.walkInOptimizedOrder(FieldMatrixChangingVisitor, int, int, int, int), FieldMatrix.walkInOptimizedOrder(FieldMatrixPreservingVisitor, int, int, int, int)
  - walkInRowOrder
```
public T walkInRowOrder(FieldMatrixChangingVisitor<T> visitor,
               int startRow,
               int endRow,
               int startColumn,
               int endColumn)
```
    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
    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)
```
    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
    See Also:
    FieldMatrix.walkInRowOrder(FieldMatrixChangingVisitor), FieldMatrix.walkInRowOrder(FieldMatrixPreservingVisitor), FieldMatrix.walkInRowOrder(FieldMatrixChangingVisitor, int, int, int, int), FieldMatrix.walkInColumnOrder(FieldMatrixChangingVisitor), FieldMatrix.walkInColumnOrder(FieldMatrixPreservingVisitor), FieldMatrix.walkInColumnOrder(FieldMatrixChangingVisitor, int, int, int, int), FieldMatrix.walkInColumnOrder(FieldMatrixPreservingVisitor, int, int, int, int), FieldMatrix.walkInOptimizedOrder(FieldMatrixChangingVisitor), FieldMatrix.walkInOptimizedOrder(FieldMatrixPreservingVisitor), FieldMatrix.walkInOptimizedOrder(FieldMatrixChangingVisitor, int, int, int, int), FieldMatrix.walkInOptimizedOrder(FieldMatrixPreservingVisitor, int, int, int, int)
  - walkInColumnOrder
```
public T walkInColumnOrder(FieldMatrixChangingVisitor<T> visitor)
```
    Visit (and possibly change) all matrix entries in column order.
    Column order starts at upper left and iterating through all elements of a column from top to bottom before going to the topmost element of the next column.
    
    Specified by:
    
    walkInColumnOrder in interface FieldMatrix<T extends FieldElement<T>>
    
    Parameters:
    visitor - visitor used to process all matrix entries
    
    Returns:
    the value returned by FieldMatrixChangingVisitor.end() at the end of the walk
    See Also:
    FieldMatrix.walkInRowOrder(FieldMatrixChangingVisitor), FieldMatrix.walkInRowOrder(FieldMatrixPreservingVisitor), FieldMatrix.walkInRowOrder(FieldMatrixChangingVisitor, int, int, int, int), FieldMatrix.walkInRowOrder(FieldMatrixPreservingVisitor, int, int, int, int), FieldMatrix.walkInColumnOrder(FieldMatrixPreservingVisitor), FieldMatrix.walkInColumnOrder(FieldMatrixChangingVisitor, int, int, int, int), FieldMatrix.walkInColumnOrder(FieldMatrixPreservingVisitor, int, int, int, int), FieldMatrix.walkInOptimizedOrder(FieldMatrixChangingVisitor), FieldMatrix.walkInOptimizedOrder(FieldMatrixPreservingVisitor), FieldMatrix.walkInOptimizedOrder(FieldMatrixChangingVisitor, int, int, int, int), FieldMatrix.walkInOptimizedOrder(FieldMatrixPreservingVisitor, int, int, int, int)
  - walkInColumnOrder
```
public T walkInColumnOrder(FieldMatrixPreservingVisitor<T> visitor)
```
    Visit (but don't change) all matrix entries in column order.
    Column order starts at upper left and iterating through all elements of a column from top to bottom before going to the topmost element of the next column.
    
    Specified by:
    
    walkInColumnOrder in interface FieldMatrix<T extends FieldElement<T>>
    
    Parameters:
    visitor - visitor used to process all matrix entries
    
    Returns:
    the value returned by FieldMatrixPreservingVisitor.end() at the end of the walk
    See Also:
    FieldMatrix.walkInRowOrder(FieldMatrixChangingVisitor), FieldMatrix.walkInRowOrder(FieldMatrixPreservingVisitor), FieldMatrix.walkInRowOrder(FieldMatrixChangingVisitor, int, int, int, int), FieldMatrix.walkInRowOrder(FieldMatrixPreservingVisitor, int, int, int, int), FieldMatrix.walkInColumnOrder(FieldMatrixChangingVisitor), FieldMatrix.walkInColumnOrder(FieldMatrixChangingVisitor, int, int, int, int), FieldMatrix.walkInColumnOrder(FieldMatrixPreservingVisitor, int, int, int, int), FieldMatrix.walkInOptimizedOrder(FieldMatrixChangingVisitor), FieldMatrix.walkInOptimizedOrder(FieldMatrixPreservingVisitor), FieldMatrix.walkInOptimizedOrder(FieldMatrixChangingVisitor, int, int, int, int), FieldMatrix.walkInOptimizedOrder(FieldMatrixPreservingVisitor, int, int, int, int)
  - walkInColumnOrder
```
public T walkInColumnOrder(FieldMatrixChangingVisitor<T> visitor,
                  int startRow,
                  int endRow,
                  int startColumn,
                  int endColumn)
```
    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
    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)
```
    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
    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)
```
    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
    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)
```
    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
    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)
```
    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
    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)
```
    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
    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:
    
    OutOfRangeException - if index is not valid.
  - checkColumnIndex
```
protected void checkColumnIndex(int column)
```
    Check if a column index is valid.
    
    Parameters:
    column - Column index to check.
    
    Throws:
    
    OutOfRangeException - 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:
    
    OutOfRangeException - if the indices are not valid.
    
    NumberIsTooSmallException - if endRow < startRow or endColumn < startColumn.
  - 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:
    
    NullArgumentException - if the arrays are null.
    
    NoDataException - if the arrays have zero length.
    
    OutOfRangeException - 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:
    
    MatrixDimensionMismatchException - if the 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:
    
    MatrixDimensionMismatchException - if the 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:
    
    DimensionMismatchException - if the matrix is not multiplication-compatible with instance.

Class AbstractFieldMatrix<T extends FieldElement<T>>

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

AbstractFieldMatrix

AbstractFieldMatrix

AbstractFieldMatrix

Method Detail

extractField

extractField

buildArray

buildArray

getField

createMatrix

copy

add

subtract

scalarAdd

scalarMultiply

multiply

preMultiply

power

getData

getSubMatrix

getSubMatrix

copySubMatrix

copySubMatrix

setSubMatrix

getRowMatrix

setRowMatrix

getColumnMatrix

setColumnMatrix

getRowVector

setRowVector

getColumnVector

setColumnVector

getRow

setRow

getColumn

setColumn

getEntry

setEntry

addToEntry

multiplyEntry

transpose

isSquare

getRowDimension

getColumnDimension

getTrace

operate

operate

preMultiply

preMultiply

walkInRowOrder

walkInRowOrder

walkInRowOrder

walkInRowOrder

walkInColumnOrder

walkInColumnOrder

walkInColumnOrder

walkInColumnOrder

walkInOptimizedOrder

walkInOptimizedOrder

walkInOptimizedOrder

walkInOptimizedOrder

toString

equals

hashCode

checkRowIndex

checkColumnIndex

checkSubMatrixIndex

checkSubMatrixIndex

checkAdditionCompatible

checkSubtractionCompatible

checkMultiplicationCompatible