path: root/src/main/java/org/apache/commons/math3/linear/RealMatrix.java

/*
 * 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.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 a real-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.
 */
public interface RealMatrix extends AnyMatrix {

    /**
     * Create a new RealMatrix 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
     */
    RealMatrix createMatrix(int rowDimension, int columnDimension)
            throws NotStrictlyPositiveException;

    /**
     * Returns a (deep) copy of this.
     *
     * @return matrix copy
     */
    RealMatrix copy();

    /**
     * Returns the sum of {@code this} and {@code m}.
     *
     * @param m matrix to be added
     * @return {@code this + m}
     * @throws MatrixDimensionMismatchException if {@code m} is not the same size as {@code this}.
     */
    RealMatrix add(RealMatrix m) throws MatrixDimensionMismatchException;

    /**
     * Returns {@code this} minus {@code m}.
     *
     * @param m matrix to be subtracted
     * @return {@code this - m}
     * @throws MatrixDimensionMismatchException if {@code m} is not the same size as {@code this}.
     */
    RealMatrix subtract(RealMatrix m) throws MatrixDimensionMismatchException;

    /**
     * Returns the result of adding {@code d} to each entry of {@code this}.
     *
     * @param d value to be added to each entry
     * @return {@code d + this}
     */
    RealMatrix scalarAdd(double d);

    /**
     * Returns the result of multiplying each entry of {@code this} by {@code d}.
     *
     * @param d value to multiply all entries by
     * @return {@code d * this}
     */
    RealMatrix scalarMultiply(double d);

    /**
     * Returns the result of postmultiplying {@code this} by {@code m}.
     *
     * @param m matrix to postmultiply by
     * @return {@code this * m}
     * @throws DimensionMismatchException if {@code columnDimension(this) != rowDimension(m)}
     */
    RealMatrix multiply(RealMatrix m) throws DimensionMismatchException;

    /**
     * Returns the result of premultiplying {@code this} by {@code m}.
     *
     * @param m matrix to premultiply by
     * @return {@code m * this}
     * @throws DimensionMismatchException if {@code rowDimension(this) != columnDimension(m)}
     */
    RealMatrix preMultiply(RealMatrix m) throws DimensionMismatchException;

    /**
     * Returns the result of multiplying {@code this} with itself {@code p} times. Depending on the
     * underlying storage, instability for high powers might occur.
     *
     * @param p raise {@code this} to power {@code p}
     * @return {@code this^p}
     * @throws NotPositiveException if {@code p < 0}
     * @throws NonSquareMatrixException if the matrix is not square
     */
    RealMatrix power(final int p) throws NotPositiveException, NonSquareMatrixException;

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

    /**
     * Returns the <a href="http://mathworld.wolfram.com/MaximumAbsoluteRowSumNorm.html">maximum
     * absolute row sum norm</a> of the matrix.
     *
     * @return norm
     */
    double getNorm();

    /**
     * Returns the <a href="http://mathworld.wolfram.com/FrobeniusNorm.html">Frobenius norm</a> of
     * the matrix.
     *
     * @return norm
     */
    double getFrobeniusNorm();

    /**
     * Gets 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 subMatrix containing the data of the specified rows and columns.
     * @throws OutOfRangeException if the indices are not valid.
     * @throws NumberIsTooSmallException if {@code endRow < startRow} or {@code endColumn <
     *     startColumn}.
     */
    RealMatrix getSubMatrix(int startRow, int endRow, int startColumn, int endColumn)
            throws OutOfRangeException, NumberIsTooSmallException;

    /**
     * Gets 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 subMatrix containing the data in the specified rows and columns
     * @throws NullArgumentException if the row or column selections are {@code null}
     * @throws NoDataException if the row or column selections are empty (zero length).
     * @throws OutOfRangeException if the indices are not valid.
     */
    RealMatrix getSubMatrix(int[] selectedRows, int[] selectedColumns)
            throws NullArgumentException, NoDataException, OutOfRangeException;

    /**
     * Copy 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)
     * @param destination The arrays where the submatrix data should be copied (if larger than
     *     rows/columns counts, only the upper-left part will be used)
     * @throws OutOfRangeException if the indices are not valid.
     * @throws NumberIsTooSmallException if {@code endRow < startRow} or {@code endColumn <
     *     startColumn}.
     * @throws MatrixDimensionMismatchException if the destination array is too small.
     */
    void copySubMatrix(
            int startRow, int endRow, int startColumn, int endColumn, double[][] destination)
            throws OutOfRangeException, NumberIsTooSmallException, MatrixDimensionMismatchException;

    /**
     * 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 The arrays where the submatrix data should be copied (if larger than
     *     rows/columns counts, only the upper-left part will be used)
     * @throws NullArgumentException if the row or column selections are {@code null}
     * @throws NoDataException if the row or column selections are empty (zero length).
     * @throws OutOfRangeException if the indices are not valid.
     * @throws MatrixDimensionMismatchException if the destination array is too small.
     */
    void copySubMatrix(int[] selectedRows, int[] selectedColumns, double[][] destination)
            throws OutOfRangeException,
                    NullArgumentException,
                    NoDataException,
                    MatrixDimensionMismatchException;

    /**
     * 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))}
     * will result in
     *
     * <pre>
     * 1  2  3  4
     * 5  3  4  8
     * 9  5  6  2
     * </pre>
     *
     * @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 NoDataException if {@code subMatrix} is empty.
     * @throws OutOfRangeException if {@code subMatrix} does not fit into this matrix from element
     *     in {@code (row, column)}.
     * @throws DimensionMismatchException if {@code subMatrix} is not rectangular (not all rows have
     *     the same length) or empty.
     * @throws NullArgumentException if {@code subMatrix} is {@code null}.
     * @since 2.0
     */
    void setSubMatrix(double[][] subMatrix, int row, int column)
            throws NoDataException,
                    OutOfRangeException,
                    DimensionMismatchException,
                    NullArgumentException;

    /**
     * Get the entries at the given row index as a row matrix. Row indices start at 0.
     *
     * @param row Row to be fetched.
     * @return row Matrix.
     * @throws OutOfRangeException if the specified row index is invalid.
     */
    RealMatrix getRowMatrix(int row) throws OutOfRangeException;

    /**
     * Sets the specified {@code row} of {@code this} matrix to the entries of the specified row
     * {@code matrix}. Row indices start at 0.
     *
     * @param row Row to be set.
     * @param matrix Row matrix to be copied (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 row dimension of the {@code matrix} is not
     *     {@code 1}, or the column dimensions of {@code this} and {@code matrix} do not match.
     */
    void setRowMatrix(int row, RealMatrix matrix)
            throws OutOfRangeException, MatrixDimensionMismatchException;

    /**
     * Get the entries at the given column index as a column matrix. Column indices start at 0.
     *
     * @param column Column to be fetched.
     * @return column Matrix.
     * @throws OutOfRangeException if the specified column index is invalid.
     */
    RealMatrix getColumnMatrix(int column) throws OutOfRangeException;

    /**
     * Sets the specified {@code column} of {@code this} matrix to the entries of the specified
     * column {@code matrix}. Column indices start at 0.
     *
     * @param column Column to be set.
     * @param matrix Column matrix to be copied (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 column dimension of the {@code matrix} is not
     *     {@code 1}, or the row dimensions of {@code this} and {@code matrix} do not match.
     */
    void setColumnMatrix(int column, RealMatrix matrix)
            throws OutOfRangeException, MatrixDimensionMismatchException;

    /**
     * Returns the entries in row number {@code row} as a vector. Row indices start at 0.
     *
     * @param row Row to be fetched.
     * @return a row vector.
     * @throws OutOfRangeException if the specified row index is invalid.
     */
    RealVector getRowVector(int row) throws OutOfRangeException;

    /**
     * Sets the specified {@code row} of {@code this} matrix to the entries of the specified {@code
     * vector}. Row indices start at 0.
     *
     * @param row Row to be set.
     * @param vector row vector to be copied (must have the same number of column as the instance).
     * @throws OutOfRangeException if the specified row index is invalid.
     * @throws MatrixDimensionMismatchException if the {@code vector} dimension does not match the
     *     column dimension of {@code this} matrix.
     */
    void setRowVector(int row, RealVector vector)
            throws OutOfRangeException, MatrixDimensionMismatchException;

    /**
     * Get the entries at the given column index as a vector. Column indices start at 0.
     *
     * @param column Column to be fetched.
     * @return a column vector.
     * @throws OutOfRangeException if the specified column index is invalid
     */
    RealVector getColumnVector(int column) throws OutOfRangeException;

    /**
     * Sets the specified {@code column} of {@code this} matrix to the entries of the specified
     * {@code vector}. Column indices start at 0.
     *
     * @param column Column to be set.
     * @param vector column vector to be copied (must have the same number of rows as the instance).
     * @throws OutOfRangeException if the specified column index is invalid.
     * @throws MatrixDimensionMismatchException if the {@code vector} dimension does not match the
     *     row dimension of {@code this} matrix.
     */
    void setColumnVector(int column, RealVector vector)
            throws OutOfRangeException, MatrixDimensionMismatchException;

    /**
     * Get the entries at the given row index. Row indices start at 0.
     *
     * @param row Row to be fetched.
     * @return the array of entries in the row.
     * @throws OutOfRangeException if the specified row index is not valid.
     */
    double[] getRow(int row) throws OutOfRangeException;

    /**
     * Sets the specified {@code row} of {@code this} matrix to the entries of the specified {@code
     * array}. Row indices start at 0.
     *
     * @param row Row to be set.
     * @param array Row matrix to be copied (must have the same number of columns as the instance)
     * @throws OutOfRangeException if the specified row index is invalid.
     * @throws MatrixDimensionMismatchException if the {@code array} length does not match the
     *     column dimension of {@code this} matrix.
     */
    void setRow(int row, double[] array)
            throws OutOfRangeException, MatrixDimensionMismatchException;

    /**
     * Get the entries at the given column index as an array. Column indices start at 0.
     *
     * @param column Column to be fetched.
     * @return the array of entries in the column.
     * @throws OutOfRangeException if the specified column index is not valid.
     */
    double[] getColumn(int column) throws OutOfRangeException;

    /**
     * Sets the specified {@code column} of {@code this} matrix to the entries of the specified
     * {@code array}. Column indices start at 0.
     *
     * @param column Column to be set.
     * @param array Column array to be copied (must have the same number of rows as the instance).
     * @throws OutOfRangeException if the specified column index is invalid.
     * @throws MatrixDimensionMismatchException if the {@code array} length does not match the row
     *     dimension of {@code this} matrix.
     */
    void setColumn(int column, double[] array)
            throws OutOfRangeException, MatrixDimensionMismatchException;

    /**
     * Get the entry in the specified row and column. Row and column indices start at 0.
     *
     * @param row Row index of entry to be fetched.
     * @param column Column index of entry to be fetched.
     * @return the matrix entry at {@code (row, column)}.
     * @throws OutOfRangeException if the row or column index is not valid.
     */
    double getEntry(int row, int column) throws OutOfRangeException;

    /**
     * Set the entry in the specified row and column. Row and column indices start at 0.
     *
     * @param row Row index of entry to be set.
     * @param column Column index of entry to be set.
     * @param value the new value of the entry.
     * @throws OutOfRangeException if the row or column index is not valid
     * @since 2.0
     */
    void setEntry(int row, int column, double value) throws OutOfRangeException;

    /**
     * Adds (in place) the specified value to the specified entry of {@code this} matrix. Row and
     * column indices start at 0.
     *
     * @param row Row index of the entry to be modified.
     * @param column Column index of the entry to be modified.
     * @param increment value to add to the matrix entry.
     * @throws OutOfRangeException if the row or column index is not valid.
     * @since 2.0
     */
    void addToEntry(int row, int column, double increment) throws OutOfRangeException;

    /**
     * Multiplies (in place) the specified entry of {@code this} matrix by the specified value. Row
     * and column indices start at 0.
     *
     * @param row Row index of the entry to be modified.
     * @param column Column index of the entry to be modified.
     * @param factor Multiplication factor for the matrix entry.
     * @throws OutOfRangeException if the row or column index is not valid.
     * @since 2.0
     */
    void multiplyEntry(int row, int column, double factor) throws OutOfRangeException;

    /**
     * Returns the transpose of this matrix.
     *
     * @return transpose matrix
     */
    RealMatrix transpose();

    /**
     * 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 the trace.
     * @throws NonSquareMatrixException if the matrix is not square.
     */
    double getTrace() throws NonSquareMatrixException;

    /**
     * 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 length of {@code v} does not match the column
     *     dimension of {@code this}.
     */
    double[] operate(double[] v) throws DimensionMismatchException;

    /**
     * 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 dimension of {@code v} does not match the column
     *     dimension of {@code this}.
     */
    RealVector operate(RealVector v) throws DimensionMismatchException;

    /**
     * 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 length of {@code v} does not match the row
     *     dimension of {@code this}.
     */
    double[] preMultiply(double[] v) throws DimensionMismatchException;

    /**
     * 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 dimension of {@code v} does not match the row
     *     dimension of {@code this}.
     */
    RealVector preMultiply(RealVector v) throws DimensionMismatchException;

    /**
     * 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.
     *
     * @param visitor visitor used to process all matrix entries
     * @see #walkInRowOrder(RealMatrixPreservingVisitor)
     * @see #walkInRowOrder(RealMatrixChangingVisitor, int, int, int, int)
     * @see #walkInRowOrder(RealMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(RealMatrixChangingVisitor)
     * @see #walkInColumnOrder(RealMatrixPreservingVisitor)
     * @see #walkInColumnOrder(RealMatrixChangingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(RealMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(RealMatrixChangingVisitor)
     * @see #walkInOptimizedOrder(RealMatrixPreservingVisitor)
     * @see #walkInOptimizedOrder(RealMatrixChangingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(RealMatrixPreservingVisitor, int, int, int, int)
     * @return the value returned by {@link RealMatrixChangingVisitor#end()} at the end of the walk
     */
    double walkInRowOrder(RealMatrixChangingVisitor visitor);

    /**
     * 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.
     *
     * @param visitor visitor used to process all matrix entries
     * @see #walkInRowOrder(RealMatrixChangingVisitor)
     * @see #walkInRowOrder(RealMatrixChangingVisitor, int, int, int, int)
     * @see #walkInRowOrder(RealMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(RealMatrixChangingVisitor)
     * @see #walkInColumnOrder(RealMatrixPreservingVisitor)
     * @see #walkInColumnOrder(RealMatrixChangingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(RealMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(RealMatrixChangingVisitor)
     * @see #walkInOptimizedOrder(RealMatrixPreservingVisitor)
     * @see #walkInOptimizedOrder(RealMatrixChangingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(RealMatrixPreservingVisitor, int, int, int, int)
     * @return the value returned by {@link RealMatrixPreservingVisitor#end()} at the end of the
     *     walk
     */
    double walkInRowOrder(RealMatrixPreservingVisitor visitor);

    /**
     * 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.
     *
     * @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(RealMatrixChangingVisitor)
     * @see #walkInRowOrder(RealMatrixPreservingVisitor)
     * @see #walkInRowOrder(RealMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(RealMatrixChangingVisitor)
     * @see #walkInColumnOrder(RealMatrixPreservingVisitor)
     * @see #walkInColumnOrder(RealMatrixChangingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(RealMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(RealMatrixChangingVisitor)
     * @see #walkInOptimizedOrder(RealMatrixPreservingVisitor)
     * @see #walkInOptimizedOrder(RealMatrixChangingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(RealMatrixPreservingVisitor, int, int, int, int)
     * @return the value returned by {@link RealMatrixChangingVisitor#end()} at the end of the walk
     */
    double walkInRowOrder(
            RealMatrixChangingVisitor visitor,
            int startRow,
            int endRow,
            int startColumn,
            int endColumn)
            throws OutOfRangeException, NumberIsTooSmallException;

    /**
     * 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.
     *
     * @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(RealMatrixChangingVisitor)
     * @see #walkInRowOrder(RealMatrixPreservingVisitor)
     * @see #walkInRowOrder(RealMatrixChangingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(RealMatrixChangingVisitor)
     * @see #walkInColumnOrder(RealMatrixPreservingVisitor)
     * @see #walkInColumnOrder(RealMatrixChangingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(RealMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(RealMatrixChangingVisitor)
     * @see #walkInOptimizedOrder(RealMatrixPreservingVisitor)
     * @see #walkInOptimizedOrder(RealMatrixChangingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(RealMatrixPreservingVisitor, int, int, int, int)
     * @return the value returned by {@link RealMatrixPreservingVisitor#end()} at the end of the
     *     walk
     */
    double walkInRowOrder(
            RealMatrixPreservingVisitor visitor,
            int startRow,
            int endRow,
            int startColumn,
            int endColumn)
            throws OutOfRangeException, NumberIsTooSmallException;

    /**
     * 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.
     *
     * @param visitor visitor used to process all matrix entries
     * @see #walkInRowOrder(RealMatrixChangingVisitor)
     * @see #walkInRowOrder(RealMatrixPreservingVisitor)
     * @see #walkInRowOrder(RealMatrixChangingVisitor, int, int, int, int)
     * @see #walkInRowOrder(RealMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(RealMatrixPreservingVisitor)
     * @see #walkInColumnOrder(RealMatrixChangingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(RealMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(RealMatrixChangingVisitor)
     * @see #walkInOptimizedOrder(RealMatrixPreservingVisitor)
     * @see #walkInOptimizedOrder(RealMatrixChangingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(RealMatrixPreservingVisitor, int, int, int, int)
     * @return the value returned by {@link RealMatrixChangingVisitor#end()} at the end of the walk
     */
    double walkInColumnOrder(RealMatrixChangingVisitor visitor);

    /**
     * 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.
     *
     * @param visitor visitor used to process all matrix entries
     * @see #walkInRowOrder(RealMatrixChangingVisitor)
     * @see #walkInRowOrder(RealMatrixPreservingVisitor)
     * @see #walkInRowOrder(RealMatrixChangingVisitor, int, int, int, int)
     * @see #walkInRowOrder(RealMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(RealMatrixChangingVisitor)
     * @see #walkInColumnOrder(RealMatrixChangingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(RealMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(RealMatrixChangingVisitor)
     * @see #walkInOptimizedOrder(RealMatrixPreservingVisitor)
     * @see #walkInOptimizedOrder(RealMatrixChangingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(RealMatrixPreservingVisitor, int, int, int, int)
     * @return the value returned by {@link RealMatrixPreservingVisitor#end()} at the end of the
     *     walk
     */
    double walkInColumnOrder(RealMatrixPreservingVisitor visitor);

    /**
     * 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.
     *
     * @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(RealMatrixChangingVisitor)
     * @see #walkInRowOrder(RealMatrixPreservingVisitor)
     * @see #walkInRowOrder(RealMatrixChangingVisitor, int, int, int, int)
     * @see #walkInRowOrder(RealMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(RealMatrixChangingVisitor)
     * @see #walkInColumnOrder(RealMatrixPreservingVisitor)
     * @see #walkInColumnOrder(RealMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(RealMatrixChangingVisitor)
     * @see #walkInOptimizedOrder(RealMatrixPreservingVisitor)
     * @see #walkInOptimizedOrder(RealMatrixChangingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(RealMatrixPreservingVisitor, int, int, int, int)
     * @return the value returned by {@link RealMatrixChangingVisitor#end()} at the end of the walk
     */
    double walkInColumnOrder(
            RealMatrixChangingVisitor visitor,
            int startRow,
            int endRow,
            int startColumn,
            int endColumn)
            throws OutOfRangeException, NumberIsTooSmallException;

    /**
     * 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.
     *
     * @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(RealMatrixChangingVisitor)
     * @see #walkInRowOrder(RealMatrixPreservingVisitor)
     * @see #walkInRowOrder(RealMatrixChangingVisitor, int, int, int, int)
     * @see #walkInRowOrder(RealMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(RealMatrixChangingVisitor)
     * @see #walkInColumnOrder(RealMatrixPreservingVisitor)
     * @see #walkInColumnOrder(RealMatrixChangingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(RealMatrixChangingVisitor)
     * @see #walkInOptimizedOrder(RealMatrixPreservingVisitor)
     * @see #walkInOptimizedOrder(RealMatrixChangingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(RealMatrixPreservingVisitor, int, int, int, int)
     * @return the value returned by {@link RealMatrixPreservingVisitor#end()} at the end of the
     *     walk
     */
    double walkInColumnOrder(
            RealMatrixPreservingVisitor visitor,
            int startRow,
            int endRow,
            int startColumn,
            int endColumn)
            throws OutOfRangeException, NumberIsTooSmallException;

    /**
     * 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.
     *
     * @param visitor visitor used to process all matrix entries
     * @see #walkInRowOrder(RealMatrixChangingVisitor)
     * @see #walkInRowOrder(RealMatrixPreservingVisitor)
     * @see #walkInRowOrder(RealMatrixChangingVisitor, int, int, int, int)
     * @see #walkInRowOrder(RealMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(RealMatrixChangingVisitor)
     * @see #walkInColumnOrder(RealMatrixPreservingVisitor)
     * @see #walkInColumnOrder(RealMatrixChangingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(RealMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(RealMatrixPreservingVisitor)
     * @see #walkInOptimizedOrder(RealMatrixChangingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(RealMatrixPreservingVisitor, int, int, int, int)
     * @return the value returned by {@link RealMatrixChangingVisitor#end()} at the end of the walk
     */
    double walkInOptimizedOrder(RealMatrixChangingVisitor visitor);

    /**
     * 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.
     *
     * @param visitor visitor used to process all matrix entries
     * @see #walkInRowOrder(RealMatrixChangingVisitor)
     * @see #walkInRowOrder(RealMatrixPreservingVisitor)
     * @see #walkInRowOrder(RealMatrixChangingVisitor, int, int, int, int)
     * @see #walkInRowOrder(RealMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(RealMatrixChangingVisitor)
     * @see #walkInColumnOrder(RealMatrixPreservingVisitor)
     * @see #walkInColumnOrder(RealMatrixChangingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(RealMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(RealMatrixChangingVisitor)
     * @see #walkInOptimizedOrder(RealMatrixChangingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(RealMatrixPreservingVisitor, int, int, int, int)
     * @return the value returned by {@link RealMatrixPreservingVisitor#end()} at the end of the
     *     walk
     */
    double walkInOptimizedOrder(RealMatrixPreservingVisitor visitor);

    /**
     * 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.
     *
     * @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 OutOfRangeException if the indices are not valid.
     * @throws NumberIsTooSmallException if {@code endRow < startRow} or {@code endColumn <
     *     startColumn}.
     * @see #walkInRowOrder(RealMatrixChangingVisitor)
     * @see #walkInRowOrder(RealMatrixPreservingVisitor)
     * @see #walkInRowOrder(RealMatrixChangingVisitor, int, int, int, int)
     * @see #walkInRowOrder(RealMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(RealMatrixChangingVisitor)
     * @see #walkInColumnOrder(RealMatrixPreservingVisitor)
     * @see #walkInColumnOrder(RealMatrixChangingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(RealMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(RealMatrixChangingVisitor)
     * @see #walkInOptimizedOrder(RealMatrixPreservingVisitor)
     * @see #walkInOptimizedOrder(RealMatrixPreservingVisitor, int, int, int, int)
     * @return the value returned by {@link RealMatrixChangingVisitor#end()} at the end of the walk
     */
    double walkInOptimizedOrder(
            RealMatrixChangingVisitor visitor,
            int startRow,
            int endRow,
            int startColumn,
            int endColumn)
            throws OutOfRangeException, NumberIsTooSmallException;

    /**
     * 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.
     *
     * @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 OutOfRangeException if the indices are not valid.
     * @throws NumberIsTooSmallException if {@code endRow < startRow} or {@code endColumn <
     *     startColumn}.
     * @see #walkInRowOrder(RealMatrixChangingVisitor)
     * @see #walkInRowOrder(RealMatrixPreservingVisitor)
     * @see #walkInRowOrder(RealMatrixChangingVisitor, int, int, int, int)
     * @see #walkInRowOrder(RealMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(RealMatrixChangingVisitor)
     * @see #walkInColumnOrder(RealMatrixPreservingVisitor)
     * @see #walkInColumnOrder(RealMatrixChangingVisitor, int, int, int, int)
     * @see #walkInColumnOrder(RealMatrixPreservingVisitor, int, int, int, int)
     * @see #walkInOptimizedOrder(RealMatrixChangingVisitor)
     * @see #walkInOptimizedOrder(RealMatrixPreservingVisitor)
     * @see #walkInOptimizedOrder(RealMatrixChangingVisitor, int, int, int, int)
     * @return the value returned by {@link RealMatrixPreservingVisitor#end()} at the end of the
     *     walk
     */
    double walkInOptimizedOrder(
            RealMatrixPreservingVisitor visitor,
            int startRow,
            int endRow,
            int startColumn,
            int endColumn)
            throws OutOfRangeException, NumberIsTooSmallException;
}