http://commons.apache.org/proper/commons-math/: The Apache Commons Math project is a library of lightweight, self-contained mathematics and statistics components addressing the most common practical problems not immediately available in the Java programming language or commons-lang. (The Apache Software Foundation)
  • Eldar Agalarov
  • Tim Allison
  • C. Scott Ananian
  • Mark Anderson
  • Peter Andrews
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  • Jared Becksfort
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  • Elliotte Rusty Harold
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  • Curtis Jensen
  • Bruce A Johnson
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  • J. Lewis Muir
  • Venkatesha Murthy
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  • Fredrik Norin
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  • Sujit Pal
  • Todd C. Parnell
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  • Bill Rossi
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  • Jörg Weimar
  • Christian Winter
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  • Albert Davidson Chou
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  • Robert Burrell Donkin
  • Otmar Ertl
  • Luc Maisonobe
  • Tim O'Brien
  • J. Pietschmann
  • Dimitri Pourbaix
  • Gilles Sadowski
  • Greg Sterijevski
  • Brent Worden
  • Thomas Neidhart
  • Evan Ward 
/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

package org.apache.commons.math3.linear;


import org.apache.commons.math3.Field;
import org.apache.commons.math3.FieldElement;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.NoDataException;
import org.apache.commons.math3.exception.NotPositiveException;
import org.apache.commons.math3.exception.NotStrictlyPositiveException;
import org.apache.commons.math3.exception.NullArgumentException;
import org.apache.commons.math3.exception.NumberIsTooSmallException;
import org.apache.commons.math3.exception.OutOfRangeException;


Interface defining field-valued matrix with basic algebraic operations.


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


Type parameters:
  • <T> – the type of the field elements
/**
 * Interface defining field-valued matrix with basic algebraic operations.
 * <p>
 * Matrix element indexing is 0-based -- e.g., <code>getEntry(0, 0)</code>
 * returns the element in the first row, first column of the matrix.</p>
 *
 * @param <T> the type of the field elements
 */
public interface FieldMatrix<T extends FieldElement<T>> extends AnyMatrix {
    
Get the type of field elements of the matrix.

Returns:the type of field elements of the matrix.
/**
     * Get the type of field elements of the matrix.
     *
     * @return the type of field elements of the matrix.
     */
    Field<T> getField();

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

Params:
  • rowDimension –  the number of rows in the new matrix
  • columnDimension –  the number of columns in the new matrix
Throws:
Returns:a new matrix of the same type as the instance
Since:2.0
/**
     * Create a new FieldMatrix<T> of the same type as the instance with
     * the supplied row and column dimensions.
     *
     * @param rowDimension  the number of rows in the new matrix
     * @param columnDimension  the number of columns in the new matrix
     * @return a new matrix of the same type as the instance
     * @throws NotStrictlyPositiveException if row or column dimension is not
     * positive.
     * @since 2.0
     */
    FieldMatrix<T> createMatrix(final int rowDimension, final int columnDimension)
    throws NotStrictlyPositiveException;

    
Make a (deep) copy of this.

Returns:a copy of this matrix.
/**
     * Make a (deep) copy of this.
     *
     * @return a copy of this matrix.
     */
    FieldMatrix<T> copy();

    
Compute the sum of this and m.

Params:
  • m – Matrix to be added.
Throws:
Returns:this + m.
/**
     * Compute the sum of this and m.
     *
     * @param m Matrix to be added.
     * @return {@code this} + {@code m}.
     * @throws MatrixDimensionMismatchException if {@code m} is not the same
     * size as {@code this} matrix.
     */
    FieldMatrix<T> add(FieldMatrix<T> m) throws MatrixDimensionMismatchException;

    
Subtract m from this matrix. 
Params:
  • m – Matrix to be subtracted.
Throws:
Returns:this - m.
/**
     * Subtract {@code m} from this matrix.
     *
     * @param m Matrix to be subtracted.
     * @return {@code this} - {@code m}.
     * @throws MatrixDimensionMismatchException if {@code m} is not the same
     * size as {@code this} matrix.
     */
    FieldMatrix<T> subtract(FieldMatrix<T> m) throws MatrixDimensionMismatchException;

     
Increment each entry of this matrix.

Params:
  • d – Value to be added to each entry.
Returns:d + this.
/**
     * Increment each entry of this matrix.
     *
     * @param d Value to be added to each entry.
     * @return {@code d} + {@code this}.
     */
    FieldMatrix<T> scalarAdd(T d);

    
Multiply each entry by d. 
Params:
  • d – Value to multiply all entries by.
Returns:d * this.
/**
     * Multiply each entry by {@code d}.
     *
     * @param d Value to multiply all entries by.
     * @return {@code d} * {@code this}.
     */
    FieldMatrix<T> scalarMultiply(T d);

    
Postmultiply this matrix by m. 
Params:
  • m –  Matrix to postmultiply by.
Throws:
Returns:this * m.
/**
     * Postmultiply this matrix by {@code m}.
     *
     * @param m  Matrix to postmultiply by.
     * @return {@code this} * {@code m}.
     * @throws DimensionMismatchException if the number of columns of
     * {@code this} matrix is not equal to the number of rows of matrix
     * {@code m}.
     */
    FieldMatrix<T> multiply(FieldMatrix<T> m) throws DimensionMismatchException;

    
Premultiply this matrix by m. 
Params:
  • m – Matrix to premultiply by.
Throws:
Returns:m * this.
/**
     * Premultiply this matrix by {@code m}.
     *
     * @param m Matrix to premultiply by.
     * @return {@code m} * {@code this}.
     * @throws DimensionMismatchException if the number of columns of {@code m}
     * differs from the number of rows of {@code this} matrix.
     */
    FieldMatrix<T> preMultiply(FieldMatrix<T> m) throws DimensionMismatchException;

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

Params:
  • p – raise this to power p
Throws:
Returns:this^p
/**
     * Returns the result multiplying this with itself <code>p</code> times.
     * Depending on the type of the field elements, T, instability for high
     * powers might occur.
     *
     * @param p raise this to power p
     * @return this^p
     * @throws NotPositiveException if {@code p < 0}
     * @throws NonSquareMatrixException if {@code this matrix} is not square
     */
    FieldMatrix<T> power(final int p) throws NonSquareMatrixException,
    NotPositiveException;

    
Returns matrix entries as a two-dimensional array.

Returns:a 2-dimensional array of entries.
/**
     * Returns matrix entries as a two-dimensional array.
     *
     * @return a 2-dimensional array of entries.
     */
    T[][] getData();

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

Params:
  • startRow – Initial row index
  • endRow – Final row index (inclusive)
  • startColumn – Initial column index
  • endColumn – Final column index (inclusive)
Throws:
Returns:the matrix containing the data of the specified rows and columns.
/**
     * Get a submatrix. Rows and columns are indicated
     * counting from 0 to n - 1.
     *
     * @param startRow Initial row index
     * @param endRow Final row index (inclusive)
     * @param startColumn Initial column index
     * @param endColumn Final column index (inclusive)
     * @return the matrix containing the data of the specified rows and columns.
     * @throws NumberIsTooSmallException is {@code endRow < startRow} of
     * {@code endColumn < startColumn}.
     * @throws OutOfRangeException if the indices are not valid.
     */
   FieldMatrix<T> getSubMatrix(int startRow, int endRow, int startColumn, int endColumn)
   throws NumberIsTooSmallException, OutOfRangeException;

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

Params:
  • selectedRows – Array of row indices.
  • selectedColumns – Array of column indices.
Throws:
Returns:the matrix containing the data in the
specified rows and columns.
/**
    * Get a submatrix. Rows and columns are indicated
    * counting from 0 to n - 1.
    *
    * @param selectedRows Array of row indices.
    * @param selectedColumns Array of column indices.
    * @return the matrix containing the data in the
    * specified rows and columns.
    * @throws NoDataException if {@code selectedRows} or
    * {@code selectedColumns} is empty
    * @throws NullArgumentException if {@code selectedRows} or
    * {@code selectedColumns} is {@code null}.
    * @throws OutOfRangeException if row or column selections are not valid.
    */
   FieldMatrix<T> getSubMatrix(int[] selectedRows, int[] selectedColumns)
   throws NoDataException, NullArgumentException, OutOfRangeException;

   
Copy a submatrix. Rows and columns are 0-based. The designated submatrix
is copied into the top left portion of the destination array.

Params:
  • startRow – Initial row index.
  • endRow – Final row index (inclusive).
  • startColumn – Initial column index.
  • endColumn – Final column index (inclusive).
  • destination – The array where the submatrix data should be copied
(if larger than rows/columns counts, only the upper-left part will be modified).
Throws:
/**
    * Copy a submatrix. Rows and columns are 0-based. The designated submatrix
    * is copied into the top left portion of the destination array.
    *
    * @param startRow Initial row index.
    * @param endRow Final row index (inclusive).
    * @param startColumn Initial column index.
    * @param endColumn Final column index (inclusive).
    * @param destination The array where the submatrix data should be copied
    * (if larger than rows/columns counts, only the upper-left part will be modified).
    * @throws MatrixDimensionMismatchException if the dimensions of
    * {@code destination} are not large enough to hold the submatrix.
    * @throws NumberIsTooSmallException if {@code endRow < startRow} or
    * {@code endColumn < startColumn}.
    * @throws OutOfRangeException if the indices are not valid.
    */
    void copySubMatrix(int startRow, int endRow, int startColumn, int endColumn,
                       T[][] destination)
    throws MatrixDimensionMismatchException, NumberIsTooSmallException,
    OutOfRangeException;

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

Params:
  • selectedRows – Array of row indices.
  • selectedColumns – Array of column indices.
  • destination – Arrays where the submatrix data should be copied
(if larger than rows/columns counts, only the upper-left part will be used)
Throws:
/**
   * Copy a submatrix. Rows and columns are indicated
   * counting from 0 to n - 1.
   *
   * @param selectedRows Array of row indices.
   * @param selectedColumns Array of column indices.
   * @param destination Arrays where the submatrix data should be copied
   * (if larger than rows/columns counts, only the upper-left part will be used)
   * @throws MatrixDimensionMismatchException if the dimensions of
   * {@code destination} do not match those of {@code this}.
   * @throws NoDataException if {@code selectedRows} or
   * {@code selectedColumns} is empty
   * @throws NullArgumentException if {@code selectedRows} or
   * {@code selectedColumns} is {@code null}.
   * @throws OutOfRangeException if the indices are not valid.
   */
  void copySubMatrix(int[] selectedRows, int[] selectedColumns, T[][] destination)
  throws MatrixDimensionMismatchException, NoDataException, NullArgumentException,
  OutOfRangeException;

    
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





Params:
  • 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:
Since:2.0
/**
     * Replace the submatrix starting at {@code (row, column)} using data in the
     * input {@code subMatrix} array. Indexes are 0-based.
     * <p>
     * Example:<br>
     * Starting with
     *
     * <pre>
     * 1  2  3  4
     * 5  6  7  8
     * 9  0  1  2
     * </pre>
     *
     * and <code>subMatrix = {{3, 4} {5,6}}</code>, invoking
     * <code>setSubMatrix(subMatrix,1,1))</code> will result in
     *
     * <pre>
     * 1  2  3  4
     * 5  3  4  8
     * 9  5  6  2
     * </pre>
     *
     * </p>
     *
     * @param subMatrix Array containing the submatrix replacement data.
     * @param row Row coordinate of the top-left element to be replaced.
     * @param column Column coordinate of the top-left element to be replaced.
     * @throws OutOfRangeException if {@code subMatrix} does not fit into this
     * matrix from element in {@code (row, column)}.
     * @throws NoDataException if a row or column of {@code subMatrix} is empty.
     * @throws DimensionMismatchException if {@code subMatrix} is not
     * rectangular (not all rows have the same length).
     * @throws NullArgumentException if {@code subMatrix} is {@code null}.
     * @since 2.0
     */
    void setSubMatrix(T[][] subMatrix, int row, int column)
        throws DimensionMismatchException, OutOfRangeException,
        NoDataException, NullArgumentException;

   
Get the entries in row number row as a row matrix. 
Params:
  • row – Row to be fetched.
Throws:
Returns:a row matrix.
/**
    * Get the entries in row number {@code row}
    * as a row matrix.
    *
    * @param row Row to be fetched.
    * @return a row matrix.
    * @throws OutOfRangeException if the specified row index is invalid.
    */
   FieldMatrix<T> getRowMatrix(int row) throws OutOfRangeException;

   
Set the entries in row number row as a row matrix. 
Params:
  • row – Row to be set.
  • matrix – Row matrix (must have one row and the same number
of columns as the instance).
Throws:
/**
    * Set the entries in row number {@code row}
    * as a row matrix.
    *
    * @param row Row to be set.
    * @param matrix Row matrix (must have one row and the same number
    * of columns as the instance).
    * @throws OutOfRangeException if the specified row index is invalid.
    * @throws MatrixDimensionMismatchException
    * if the matrix dimensions do not match one instance row.
    */
   void setRowMatrix(int row, FieldMatrix<T> matrix)
   throws MatrixDimensionMismatchException, OutOfRangeException;

   
Get the entries in column number column as a column matrix. 
Params:
  • column – Column to be fetched.
Throws:
Returns:a column matrix.
/**
    * Get the entries in column number {@code column}
    * as a column matrix.
    *
    * @param column Column to be fetched.
    * @return a column matrix.
    * @throws OutOfRangeException if the specified column index is invalid.
    */
   FieldMatrix<T> getColumnMatrix(int column) throws OutOfRangeException;

   
Set the entries in column number column as a column matrix. 
Params:
  • column – Column to be set.
  • matrix – column matrix (must have one column and the same
number of rows as the instance).
Throws:
/**
    * Set the entries in column number {@code column}
    * as a column matrix.
    *
    * @param column Column to be set.
    * @param matrix column matrix (must have one column and the same
    * number of rows as the instance).
    * @throws OutOfRangeException if the specified column index is invalid.
    * @throws MatrixDimensionMismatchException if the matrix dimensions do
    * not match one instance column.
    */
   void setColumnMatrix(int column, FieldMatrix<T> matrix)
   throws MatrixDimensionMismatchException, OutOfRangeException;

   
Get the entries in row number row as a vector. 
Params:
  • row – Row to be fetched
Throws:
Returns:a row vector.
/**
    * Get the entries in row number {@code row}
    * as a vector.
    *
    * @param row Row to be fetched
    * @return a row vector.
    * @throws OutOfRangeException if the specified row index is invalid.
    */
   FieldVector<T> getRowVector(int row) throws OutOfRangeException;

   
Set the entries in row number row as a vector. 
Params:
  • row – Row to be set.
  • vector – row vector (must have the same number of columns
as the instance).
Throws:
/**
    * Set the entries in row number {@code row}
    * as a vector.
    *
    * @param row Row to be set.
    * @param vector row vector (must have the same number of columns
    * as the instance).
    * @throws OutOfRangeException if the specified row index is invalid.
    * @throws MatrixDimensionMismatchException if the vector dimension does not
    * match one instance row.
    */
   void setRowVector(int row, FieldVector<T> vector)
   throws MatrixDimensionMismatchException, OutOfRangeException;

   
Returns the entries in column number column as a vector. 
Params:
  • column – Column to be fetched.
Throws:
Returns:a column vector.
/**
    * Returns the entries in column number {@code column}
    * as a vector.
    *
    * @param column Column to be fetched.
    * @return a column vector.
    * @throws OutOfRangeException if the specified column index is invalid.
    */
   FieldVector<T> getColumnVector(int column) throws OutOfRangeException;

   
Set the entries in column number column as a vector. 
Params:
  • column – Column to be set.
  • vector – Column vector (must have the same number of rows
as the instance).
Throws:
/**
    * Set the entries in column number {@code column}
    * as a vector.
    *
    * @param column Column to be set.
    * @param vector Column vector (must have the same number of rows
    * as the instance).
    * @throws OutOfRangeException if the specified column index is invalid.
    * @throws MatrixDimensionMismatchException if the vector dimension does not
    * match one instance column.
    */
   void setColumnVector(int column, FieldVector<T> vector)
   throws MatrixDimensionMismatchException, OutOfRangeException;

    
Get the entries in row number row as an array. 
Params:
  • row – Row to be fetched.
Throws:
Returns:array of entries in the row.
/**
     * Get the entries in row number {@code row} as an array.
     *
     * @param row Row to be fetched.
     * @return array of entries in the row.
     * @throws OutOfRangeException if the specified row index is not valid.
     */
    T[] getRow(int row) throws OutOfRangeException;

    
Set the entries in row number row as a row matrix. 
Params:
  • row – Row to be set.
  • array – Row matrix (must have the same number of columns as
the instance).
Throws:
/**
     * Set the entries in row number {@code row}
     * as a row matrix.
     *
     * @param row Row to be set.
     * @param array Row matrix (must have the same number of columns as
     * the instance).
     * @throws OutOfRangeException if the specified row index is invalid.
     * @throws MatrixDimensionMismatchException if the array size does not match
     * one instance row.
     */
    void setRow(int row, T[] array) throws MatrixDimensionMismatchException,
    OutOfRangeException;

    
Get the entries in column number col as an array. 
Params:
  • column – the column to be fetched
Throws:
Returns:array of entries in the column
/**
     * Get the entries in column number {@code col} as an array.
     *
     * @param column the column to be fetched
     * @return array of entries in the column
     * @throws OutOfRangeException if the specified column index is not valid.
     */
    T[] getColumn(int column) throws OutOfRangeException;

    
Set the entries in column number column as a column matrix. 
Params:
  • column – the column to be set
  • array – column array (must have the same number of rows as the instance)
Throws:
/**
     * Set the entries in column number {@code column}
     * as a column matrix.
     *
     * @param column the column to be set
     * @param array column array (must have the same number of rows as the instance)
     * @throws OutOfRangeException if the specified column index is invalid.
     * @throws MatrixDimensionMismatchException if the array size does not match
     * one instance column.
     */
    void setColumn(int column, T[] array) throws MatrixDimensionMismatchException,
    OutOfRangeException;

    
Returns the entry in the specified row and column.

Params:
  • row –  row location of entry to be fetched
  • column –  column location of entry to be fetched
Throws:
Returns:matrix entry in row,column
/**
     * Returns the entry in the specified row and column.
     *
     * @param row  row location of entry to be fetched
     * @param column  column location of entry to be fetched
     * @return matrix entry in row,column
     * @throws OutOfRangeException if the row or column index is not valid.
     */
    T getEntry(int row, int column) throws OutOfRangeException;

    
Set the entry in the specified row and column.

Params:
  • 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:
Since:2.0
/**
     * Set the entry in the specified row and column.
     *
     * @param row  row location of entry to be set
     * @param column  column location of entry to be set
     * @param value matrix entry to be set in row,column
     * @throws OutOfRangeException if the row or column index is not valid.
     * @since 2.0
     */
    void setEntry(int row, int column, T value) throws OutOfRangeException;

    
Change an entry in the specified row and column.

Params:
  • 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:
Since:2.0
/**
     * Change an entry in the specified row and column.
     *
     * @param row Row location of entry to be set.
     * @param column Column location of entry to be set.
     * @param increment Value to add to the current matrix entry in
     * {@code (row, column)}.
     * @throws OutOfRangeException if the row or column index is not valid.
     * @since 2.0
     */
    void addToEntry(int row, int column, T increment) throws OutOfRangeException;

    
Change an entry in the specified row and column.

Params:
  • 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:
Since:2.0
/**
     * Change an entry in the specified row and column.
     *
     * @param row Row location of entry to be set.
     * @param column Column location of entry to be set.
     * @param factor Multiplication factor for the current matrix entry
     * in {@code (row,column)}
     * @throws OutOfRangeException if the row or column index is not valid.
     * @since 2.0
     */
    void multiplyEntry(int row, int column, T factor) throws OutOfRangeException;

    
Returns the transpose of this matrix.

Returns:transpose matrix
/**
     * Returns the transpose of this matrix.
     *
     * @return transpose matrix
     */
    FieldMatrix<T> transpose();

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

Throws:
Returns:trace
/**
     * Returns the <a href="http://mathworld.wolfram.com/MatrixTrace.html">
     * trace</a> of the matrix (the sum of the elements on the main diagonal).
     *
     * @return trace
     * @throws NonSquareMatrixException if the matrix is not square.
     */
    T getTrace() throws NonSquareMatrixException;

    
Returns the result of multiplying this by the vector v. 
Params:
  • v – the vector to operate on
Throws:
Returns:this * v
/**
     * Returns the result of multiplying this by the vector {@code v}.
     *
     * @param v the vector to operate on
     * @return {@code this * v}
     * @throws DimensionMismatchException if the number of columns of
     * {@code this} matrix is not equal to the size of the vector {@code v}.
     */
    T[] operate(T[] v) throws DimensionMismatchException;

    
Returns the result of multiplying this by the vector v. 
Params:
  • v – the vector to operate on
Throws:
Returns:this * v
/**
     * Returns the result of multiplying this by the vector {@code v}.
     *
     * @param v the vector to operate on
     * @return {@code this * v}
     * @throws DimensionMismatchException if the number of columns of
     * {@code this} matrix is not equal to the size of the vector {@code v}.
     */
    FieldVector<T> operate(FieldVector<T> v) throws DimensionMismatchException;

    
Returns the (row) vector result of premultiplying this by the vector v. 
Params:
  • v – the row vector to premultiply by
Throws:
Returns:v * this
/**
     * Returns the (row) vector result of premultiplying this by the vector
     * {@code v}.
     *
     * @param v the row vector to premultiply by
     * @return {@code v * this}
     * @throws DimensionMismatchException if the number of rows of {@code this}
     * matrix is not equal to the size of the vector {@code v}
     */
    T[] preMultiply(T[] v) throws DimensionMismatchException;

    
Returns the (row) vector result of premultiplying this by the vector v. 
Params:
  • v – the row vector to premultiply by
Throws:
Returns:v * this
/**
     * Returns the (row) vector result of premultiplying this by the vector
     * {@code v}.
     *
     * @param v the row vector to premultiply by
     * @return {@code v * this}
     * @throws DimensionMismatchException if the number of rows of {@code this}
     * matrix is not equal to the size of the vector {@code v}
     */
    FieldVector<T> preMultiply(FieldVector<T> v) throws DimensionMismatchException;

    
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.


Params:
  • visitor – visitor used to process all matrix entries
See Also:
Returns:the value returned by FieldMatrixChangingVisitor.end() at the end of the walk
/**
     * Visit (and possibly change) all matrix entries in row order.
     * <p>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.</p>
     * @param visitor visitor used to process all matrix entries
     * @see #walkInRowOrder(FieldMatrixPreservingVisitor)
     * @see #walkInRowOrder(FieldMatrixChangingVisitor, int, int, int, int)
     * @see #walkInRowOrder(FieldMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(FieldMatrixChangingVisitor)
     * @see #walkInColumnOrder(FieldMatrixPreservingVisitor)
     * @see #walkInColumnOrder(FieldMatrixChangingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(FieldMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(FieldMatrixChangingVisitor)
     * @see #walkInOptimizedOrder(FieldMatrixPreservingVisitor)
     * @see #walkInOptimizedOrder(FieldMatrixChangingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(FieldMatrixPreservingVisitor, int, int, int, int)
     * @return the value returned by {@link FieldMatrixChangingVisitor#end()} at the end
     * of the walk
     */
    T walkInRowOrder(FieldMatrixChangingVisitor<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.


Params:
  • visitor – visitor used to process all matrix entries
See Also:
Returns:the value returned by FieldMatrixPreservingVisitor.end() at the end of the walk
/**
     * Visit (but don't change) all matrix entries in row order.
     * <p>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.</p>
     * @param visitor visitor used to process all matrix entries
     * @see #walkInRowOrder(FieldMatrixChangingVisitor)
     * @see #walkInRowOrder(FieldMatrixChangingVisitor, int, int, int, int)
     * @see #walkInRowOrder(FieldMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(FieldMatrixChangingVisitor)
     * @see #walkInColumnOrder(FieldMatrixPreservingVisitor)
     * @see #walkInColumnOrder(FieldMatrixChangingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(FieldMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(FieldMatrixChangingVisitor)
     * @see #walkInOptimizedOrder(FieldMatrixPreservingVisitor)
     * @see #walkInOptimizedOrder(FieldMatrixChangingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(FieldMatrixPreservingVisitor, int, int, int, int)
     * @return the value returned by {@link FieldMatrixPreservingVisitor#end()} at the end
     * of the walk
     */
    T walkInRowOrder(FieldMatrixPreservingVisitor<T> visitor);

    
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.


Params:
  • 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
Throws:
See Also:
Returns:the value returned by FieldMatrixChangingVisitor.end() at the end of the walk
/**
     * Visit (and possibly change) some matrix entries in row order.
     * <p>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.</p>
     * @param visitor visitor used to process all matrix entries
     * @param startRow Initial row index
     * @param endRow Final row index (inclusive)
     * @param startColumn Initial column index
     * @param endColumn Final column index
     * @throws OutOfRangeException if the indices are not valid.
     * @throws NumberIsTooSmallException if {@code endRow < startRow} or
     * {@code endColumn < startColumn}.
     * @see #walkInRowOrder(FieldMatrixChangingVisitor)
     * @see #walkInRowOrder(FieldMatrixPreservingVisitor)
     * @see #walkInRowOrder(FieldMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(FieldMatrixChangingVisitor)
     * @see #walkInColumnOrder(FieldMatrixPreservingVisitor)
     * @see #walkInColumnOrder(FieldMatrixChangingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(FieldMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(FieldMatrixChangingVisitor)
     * @see #walkInOptimizedOrder(FieldMatrixPreservingVisitor)
     * @see #walkInOptimizedOrder(FieldMatrixChangingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(FieldMatrixPreservingVisitor, int, int, int, int)
     * @return the value returned by {@link FieldMatrixChangingVisitor#end()} at the end
     * of the walk
     */
    T walkInRowOrder(FieldMatrixChangingVisitor<T> visitor,
                     int startRow, int endRow, int startColumn, int endColumn)
    throws OutOfRangeException, NumberIsTooSmallException;

    
Visit (but don't change) some matrix entries in row order.

Row order starts at upper left and iterating through all elements
of a row from left to right before going to the leftmost element
of the next row.


Params:
  • 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
Throws:
See Also:
Returns:the value returned by FieldMatrixPreservingVisitor.end() at the end of the walk
/**
     * Visit (but don't change) some matrix entries in row order.
     * <p>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.</p>
     * @param visitor visitor used to process all matrix entries
     * @param startRow Initial row index
     * @param endRow Final row index (inclusive)
     * @param startColumn Initial column index
     * @param endColumn Final column index
     * @throws OutOfRangeException if the indices are not valid.
     * @throws NumberIsTooSmallException if {@code endRow < startRow} or
     * {@code endColumn < startColumn}.
     * @see #walkInRowOrder(FieldMatrixChangingVisitor)
     * @see #walkInRowOrder(FieldMatrixPreservingVisitor)
     * @see #walkInRowOrder(FieldMatrixChangingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(FieldMatrixChangingVisitor)
     * @see #walkInColumnOrder(FieldMatrixPreservingVisitor)
     * @see #walkInColumnOrder(FieldMatrixChangingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(FieldMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(FieldMatrixChangingVisitor)
     * @see #walkInOptimizedOrder(FieldMatrixPreservingVisitor)
     * @see #walkInOptimizedOrder(FieldMatrixChangingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(FieldMatrixPreservingVisitor, int, int, int, int)
     * @return the value returned by {@link FieldMatrixPreservingVisitor#end()} at the end
     * of the walk
     */
    T walkInRowOrder(FieldMatrixPreservingVisitor<T> visitor,
                     int startRow, int endRow, int startColumn, int endColumn)
    throws OutOfRangeException, NumberIsTooSmallException;

    
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.


Params:
  • visitor – visitor used to process all matrix entries
See Also:
Returns:the value returned by FieldMatrixChangingVisitor.end() at the end of the walk
/**
     * Visit (and possibly change) all matrix entries in column order.
     * <p>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.</p>
     * @param visitor visitor used to process all matrix entries
     * @see #walkInRowOrder(FieldMatrixChangingVisitor)
     * @see #walkInRowOrder(FieldMatrixPreservingVisitor)
     * @see #walkInRowOrder(FieldMatrixChangingVisitor, int, int, int, int)
     * @see #walkInRowOrder(FieldMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(FieldMatrixPreservingVisitor)
     * @see #walkInColumnOrder(FieldMatrixChangingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(FieldMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(FieldMatrixChangingVisitor)
     * @see #walkInOptimizedOrder(FieldMatrixPreservingVisitor)
     * @see #walkInOptimizedOrder(FieldMatrixChangingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(FieldMatrixPreservingVisitor, int, int, int, int)
     * @return the value returned by {@link FieldMatrixChangingVisitor#end()} at the end
     * of the walk
     */
    T walkInColumnOrder(FieldMatrixChangingVisitor<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.


Params:
  • visitor – visitor used to process all matrix entries
See Also:
Returns:the value returned by FieldMatrixPreservingVisitor.end() at the end of the walk
/**
     * Visit (but don't change) all matrix entries in column order.
     * <p>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.</p>
     * @param visitor visitor used to process all matrix entries
     * @see #walkInRowOrder(FieldMatrixChangingVisitor)
     * @see #walkInRowOrder(FieldMatrixPreservingVisitor)
     * @see #walkInRowOrder(FieldMatrixChangingVisitor, int, int, int, int)
     * @see #walkInRowOrder(FieldMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(FieldMatrixChangingVisitor)
     * @see #walkInColumnOrder(FieldMatrixChangingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(FieldMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(FieldMatrixChangingVisitor)
     * @see #walkInOptimizedOrder(FieldMatrixPreservingVisitor)
     * @see #walkInOptimizedOrder(FieldMatrixChangingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(FieldMatrixPreservingVisitor, int, int, int, int)
     * @return the value returned by {@link FieldMatrixPreservingVisitor#end()} at the end
     * of the walk
     */
    T walkInColumnOrder(FieldMatrixPreservingVisitor<T> visitor);

    
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.


Params:
  • 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
Throws:
See Also:
Returns:the value returned by FieldMatrixChangingVisitor.end() at the end of the walk
/**
     * Visit (and possibly change) some matrix entries in column order.
     * <p>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.</p>
     * @param visitor visitor used to process all matrix entries
     * @param startRow Initial row index
     * @param endRow Final row index (inclusive)
     * @param startColumn Initial column index
     * @param endColumn Final column index
     * @throws NumberIsTooSmallException if {@code endRow < startRow} or
     * {@code endColumn < startColumn}.
     * @throws OutOfRangeException if the indices are not valid.
     * @see #walkInRowOrder(FieldMatrixChangingVisitor)
     * @see #walkInRowOrder(FieldMatrixPreservingVisitor)
     * @see #walkInRowOrder(FieldMatrixChangingVisitor, int, int, int, int)
     * @see #walkInRowOrder(FieldMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(FieldMatrixChangingVisitor)
     * @see #walkInColumnOrder(FieldMatrixPreservingVisitor)
     * @see #walkInColumnOrder(FieldMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(FieldMatrixChangingVisitor)
     * @see #walkInOptimizedOrder(FieldMatrixPreservingVisitor)
     * @see #walkInOptimizedOrder(FieldMatrixChangingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(FieldMatrixPreservingVisitor, int, int, int, int)
     * @return the value returned by {@link FieldMatrixChangingVisitor#end()} at the end
     * of the walk
     */
    T walkInColumnOrder(FieldMatrixChangingVisitor<T> visitor,
                        int startRow, int endRow, int startColumn, int endColumn)
    throws NumberIsTooSmallException, OutOfRangeException;

    
Visit (but don't change) some matrix entries in column order.

Column order starts at upper left and iterating through all elements
of a column from top to bottom before going to the topmost element
of the next column.


Params:
  • 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
Throws:
See Also:
Returns:the value returned by FieldMatrixPreservingVisitor.end() at the end of the walk
/**
     * Visit (but don't change) some matrix entries in column order.
     * <p>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.</p>
     * @param visitor visitor used to process all matrix entries
     * @param startRow Initial row index
     * @param endRow Final row index (inclusive)
     * @param startColumn Initial column index
     * @param endColumn Final column index
     * @throws NumberIsTooSmallException if {@code endRow < startRow} or
     * {@code endColumn < startColumn}.
     * @throws OutOfRangeException if the indices are not valid.
     * @see #walkInRowOrder(FieldMatrixChangingVisitor)
     * @see #walkInRowOrder(FieldMatrixPreservingVisitor)
     * @see #walkInRowOrder(FieldMatrixChangingVisitor, int, int, int, int)
     * @see #walkInRowOrder(FieldMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(FieldMatrixChangingVisitor)
     * @see #walkInColumnOrder(FieldMatrixPreservingVisitor)
     * @see #walkInColumnOrder(FieldMatrixChangingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(FieldMatrixChangingVisitor)
     * @see #walkInOptimizedOrder(FieldMatrixPreservingVisitor)
     * @see #walkInOptimizedOrder(FieldMatrixChangingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(FieldMatrixPreservingVisitor, int, int, int, int)
     * @return the value returned by {@link FieldMatrixPreservingVisitor#end()} at the end
     * of the walk
     */
    T walkInColumnOrder(FieldMatrixPreservingVisitor<T> visitor,
                        int startRow, int endRow, int startColumn, int endColumn)
    throws NumberIsTooSmallException, OutOfRangeException;

    
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.


Params:
  • visitor – visitor used to process all matrix entries
See Also:
Returns:the value returned by FieldMatrixChangingVisitor.end() at the end of the walk
/**
     * Visit (and possibly change) all matrix entries using the fastest possible order.
     * <p>The fastest walking order depends on the exact matrix class. It may be
     * different from traditional row or column orders.</p>
     * @param visitor visitor used to process all matrix entries
     * @see #walkInRowOrder(FieldMatrixChangingVisitor)
     * @see #walkInRowOrder(FieldMatrixPreservingVisitor)
     * @see #walkInRowOrder(FieldMatrixChangingVisitor, int, int, int, int)
     * @see #walkInRowOrder(FieldMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(FieldMatrixChangingVisitor)
     * @see #walkInColumnOrder(FieldMatrixPreservingVisitor)
     * @see #walkInColumnOrder(FieldMatrixChangingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(FieldMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(FieldMatrixPreservingVisitor)
     * @see #walkInOptimizedOrder(FieldMatrixChangingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(FieldMatrixPreservingVisitor, int, int, int, int)
     * @return the value returned by {@link FieldMatrixChangingVisitor#end()} at the end
     * of the walk
     */
    T walkInOptimizedOrder(FieldMatrixChangingVisitor<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.


Params:
  • visitor – visitor used to process all matrix entries
See Also:
Returns:the value returned by FieldMatrixPreservingVisitor.end() at the end of the walk
/**
     * Visit (but don't change) all matrix entries using the fastest possible order.
     * <p>The fastest walking order depends on the exact matrix class. It may be
     * different from traditional row or column orders.</p>
     * @param visitor visitor used to process all matrix entries
     * @see #walkInRowOrder(FieldMatrixChangingVisitor)
     * @see #walkInRowOrder(FieldMatrixPreservingVisitor)
     * @see #walkInRowOrder(FieldMatrixChangingVisitor, int, int, int, int)
     * @see #walkInRowOrder(FieldMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(FieldMatrixChangingVisitor)
     * @see #walkInColumnOrder(FieldMatrixPreservingVisitor)
     * @see #walkInColumnOrder(FieldMatrixChangingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(FieldMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(FieldMatrixChangingVisitor)
     * @see #walkInOptimizedOrder(FieldMatrixChangingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(FieldMatrixPreservingVisitor, int, int, int, int)
     * @return the value returned by {@link FieldMatrixPreservingVisitor#end()} at the end
     * of the walk
     */
    T walkInOptimizedOrder(FieldMatrixPreservingVisitor<T> visitor);

    
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.


Params:
  • 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)
Throws:
See Also:
Returns:the value returned by FieldMatrixChangingVisitor.end() at the end of the walk
/**
     * Visit (and possibly change) some matrix entries using the fastest possible order.
     * <p>The fastest walking order depends on the exact matrix class. It may be
     * different from traditional row or column orders.</p>
     * @param visitor visitor used to process all matrix entries
     * @param startRow Initial row index
     * @param endRow Final row index (inclusive)
     * @param startColumn Initial column index
     * @param endColumn Final column index (inclusive)
     * @throws NumberIsTooSmallException if {@code endRow < startRow} or
     * {@code endColumn < startColumn}.
     * @throws OutOfRangeException if the indices are not valid.
     * @see #walkInRowOrder(FieldMatrixChangingVisitor)
     * @see #walkInRowOrder(FieldMatrixPreservingVisitor)
     * @see #walkInRowOrder(FieldMatrixChangingVisitor, int, int, int, int)
     * @see #walkInRowOrder(FieldMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(FieldMatrixChangingVisitor)
     * @see #walkInColumnOrder(FieldMatrixPreservingVisitor)
     * @see #walkInColumnOrder(FieldMatrixChangingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(FieldMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(FieldMatrixChangingVisitor)
     * @see #walkInOptimizedOrder(FieldMatrixPreservingVisitor)
     * @see #walkInOptimizedOrder(FieldMatrixPreservingVisitor, int, int, int, int)
     * @return the value returned by {@link FieldMatrixChangingVisitor#end()} at the end
     * of the walk
     */
    T walkInOptimizedOrder(FieldMatrixChangingVisitor<T> visitor,
                           int startRow, int endRow, int startColumn, int endColumn)
    throws NumberIsTooSmallException, OutOfRangeException;

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

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


Params:
  • 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)
Throws:
See Also:
Returns:the value returned by FieldMatrixPreservingVisitor.end() at the end of the walk
/**
     * Visit (but don't change) some matrix entries using the fastest possible order.
     * <p>The fastest walking order depends on the exact matrix class. It may be
     * different from traditional row or column orders.</p>
     * @param visitor visitor used to process all matrix entries
     * @param startRow Initial row index
     * @param endRow Final row index (inclusive)
     * @param startColumn Initial column index
     * @param endColumn Final column index (inclusive)
     * @throws NumberIsTooSmallException if {@code endRow < startRow} or
     * {@code endColumn < startColumn}.
     * @throws OutOfRangeException if the indices are not valid.
     * @see #walkInRowOrder(FieldMatrixChangingVisitor)
     * @see #walkInRowOrder(FieldMatrixPreservingVisitor)
     * @see #walkInRowOrder(FieldMatrixChangingVisitor, int, int, int, int)
     * @see #walkInRowOrder(FieldMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(FieldMatrixChangingVisitor)
     * @see #walkInColumnOrder(FieldMatrixPreservingVisitor)
     * @see #walkInColumnOrder(FieldMatrixChangingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(FieldMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(FieldMatrixChangingVisitor)
     * @see #walkInOptimizedOrder(FieldMatrixPreservingVisitor)
     * @see #walkInOptimizedOrder(FieldMatrixChangingVisitor, int, int, int, int)
     * @return the value returned by {@link FieldMatrixPreservingVisitor#end()} at the end
     * of the walk
     */
    T walkInOptimizedOrder(FieldMatrixPreservingVisitor<T> visitor,
                           int startRow, int endRow, int startColumn, int endColumn)
    throws NumberIsTooSmallException, OutOfRangeException;
}