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## org.apache.commons.math.linear
Class AbstractRealMatrix

    java.lang.Object
      org.apache.commons.math.linear.AbstractRealMatrix

All Implemented Interfaces:
  AnyMatrix, RealMatrix

Direct Known Subclasses:
  Array2DRowRealMatrix, BlockRealMatrix, OpenMapRealMatrix, RealMatrixImpl

    public abstract class AbstractRealMatrix

extends java.lang.Object
implements RealMatrix

Basic implementation of RealMatrix methods regardless of the underlying storage.

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

Since:
  2.0
Version:
  $Revision: 811833 $ $Date: 2009-09-06 12:27:50 -0400 (Sun, 06 Sep 2009) $

Field Summary
`private DecompositionSolver` | `lu` Deprecated. as of release 2.0, since all methods using this are deprecated

Constructor Summary
`protected` | `AbstractRealMatrix()` Creates a matrix with no data
`protected` | `AbstractRealMatrix(int rowDimension, int columnDimension)` Create a new RealMatrix with the supplied row and column dimensions.

Method Summary
`RealMatrix` | `add(RealMatrix m)` Compute the sum of this and m.
`abstract void` | `addToEntry(int row, int column, double increment)` Change an entry in the specified row and column.
`abstract RealMatrix` | `copy()` Returns a (deep) copy of this.
`void` | `copySubMatrix(int[] selectedRows, int[] selectedColumns, double[][] destination)` Copy a submatrix.
`void` | `copySubMatrix(int startRow, int endRow, int startColumn, int endColumn, double[][] destination)` Copy a submatrix.
`abstract RealMatrix` | `createMatrix(int rowDimension, int columnDimension)` Create a new RealMatrix of the same type as the instance with the supplied row and column dimensions.
`boolean` | `equals(java.lang.Object object)` Returns true iff `object` is a `RealMatrix` instance with the same dimensions as this and all corresponding matrix entries are equal.
`double[]` | `getColumn(int column)` Returns the entries in column number `col` as an array.
`abstract int` | `getColumnDimension()` Returns the number of columns in the matrix.
`RealMatrix` | `getColumnMatrix(int column)` Returns the entries in column number `column` as a column matrix.
`RealVector` | `getColumnVector(int column)` Returns the entries in column number `column` as a vector.
`double[][]` | `getData()` Returns matrix entries as a two-dimensional array.
`double` | `getDeterminant()` Deprecated.
`abstract double` | `getEntry(int row, int column)` Returns the entry in the specified row and column.
`double` | `getFrobeniusNorm()` Returns the Frobenius norm of the matrix.
`double` | `getNorm()` Returns the maximum absolute row sum norm of the matrix.
`double[]` | `getRow(int row)` Returns the entries in row number `row` as an array.
`abstract int` | `getRowDimension()` Returns the number of rows in the matrix.
`RealMatrix` | `getRowMatrix(int row)` Returns the entries in row number `row` as a row matrix.
`RealVector` | `getRowVector(int row)` Returns the entries in row number `row` as a vector.
`RealMatrix` | `getSubMatrix(int[] selectedRows, int[] selectedColumns)` Gets a submatrix.
`RealMatrix` | `getSubMatrix(int startRow, int endRow, int startColumn, int endColumn)` Gets a submatrix.
`double` | `getTrace()` Returns the trace of the matrix (the sum of the elements on the main diagonal).
`int` | `hashCode()` Computes a hashcode for the matrix.
`RealMatrix` | `inverse()` Deprecated.
`boolean` | `isSingular()` Deprecated.
`boolean` | `isSquare()` Is this a square matrix?
`void` | `luDecompose()` Deprecated. as of release 2.0, replaced by `LUDecomposition`
`RealMatrix` | `multiply(RealMatrix m)` Returns the result of postmultiplying this by m.
`abstract void` | `multiplyEntry(int row, int column, double factor)` Change an entry in the specified row and column.
`double[]` | `operate(double[] v)` Returns the result of multiplying this by the vector `v`.
`RealVector` | `operate(RealVector v)` Returns the result of multiplying this by the vector `v`.
`double[]` | `preMultiply(double[] v)` Returns the (row) vector result of premultiplying this by the vector `v`.
`RealMatrix` | `preMultiply(RealMatrix m)` Returns the result premultiplying this by `m`.
`RealVector` | `preMultiply(RealVector v)` Returns the (row) vector result of premultiplying this by the vector `v`.
`RealMatrix` | `scalarAdd(double d)` Returns the result of adding d to each entry of this.
`RealMatrix` | `scalarMultiply(double d)` Returns the result multiplying each entry of this by d.
`void` | `setColumn(int column, double[] array)` Sets the entries in column number `column` as a column matrix.
`void` | `setColumnMatrix(int column, RealMatrix matrix)` Sets the entries in column number `column` as a column matrix.
`void` | `setColumnVector(int column, RealVector vector)` Sets the entries in column number `column` as a vector.
`abstract void` | `setEntry(int row, int column, double value)` Set the entry in the specified row and column.
`void` | `setRow(int row, double[] array)` Sets the entries in row number `row` as a row matrix.
`void` | `setRowMatrix(int row, RealMatrix matrix)` Sets the entries in row number `row` as a row matrix.
`void` | `setRowVector(int row, RealVector vector)` Sets the entries in row number `row` as a vector.
`void` | `setSubMatrix(double[][] subMatrix, int row, int column)` Replace the submatrix starting at `row, column` using data in the input `subMatrix` array.
`double[]` | `solve(double[] b)` Deprecated.
`RealMatrix` | `solve(RealMatrix b)` Deprecated.
`RealMatrix` | `subtract(RealMatrix m)` Compute this minus m.
`java.lang.String` | `toString()` Get a string representation for this matrix.
`RealMatrix` | `transpose()` Returns the transpose of this matrix.
`double` | `walkInColumnOrder(RealMatrixChangingVisitor visitor)` Visit (and possibly change) all matrix entries in column order.
`double` | `walkInColumnOrder(RealMatrixChangingVisitor visitor, int startRow, int endRow, int startColumn, int endColumn)` Visit (and possibly change) some matrix entries in column order.
`double` | `walkInColumnOrder(RealMatrixPreservingVisitor visitor)` Visit (but don't change) all matrix entries in column order.
`double` | `walkInColumnOrder(RealMatrixPreservingVisitor visitor, int startRow, int endRow, int startColumn, int endColumn)` Visit (but don't change) some matrix entries in column order.
`double` | `walkInOptimizedOrder(RealMatrixChangingVisitor visitor)` Visit (and possibly change) all matrix entries using the fastest possible order.
`double` | `walkInOptimizedOrder(RealMatrixChangingVisitor visitor, int startRow, int endRow, int startColumn, int endColumn)` Visit (and possibly change) some matrix entries using the fastest possible order.
`double` | `walkInOptimizedOrder(RealMatrixPreservingVisitor visitor)` Visit (but don't change) all matrix entries using the fastest possible order.
`double` | `walkInOptimizedOrder(RealMatrixPreservingVisitor visitor, int startRow, int endRow, int startColumn, int endColumn)` Visit (but don't change) some matrix entries using the fastest possible order.
`double` | `walkInRowOrder(RealMatrixChangingVisitor visitor)` Visit (and possibly change) all matrix entries in row order.
`double` | `walkInRowOrder(RealMatrixChangingVisitor visitor, int startRow, int endRow, int startColumn, int endColumn)` Visit (and possibly change) some matrix entries in row order.
`double` | `walkInRowOrder(RealMatrixPreservingVisitor visitor)` Visit (but don't change) all matrix entries in row order.
`double` | `walkInRowOrder(RealMatrixPreservingVisitor visitor, int startRow, int endRow, int startColumn, int endColumn)` Visit (but don't change) some matrix entries in row order.

Methods inherited from class java.lang.Object
`clone, finalize, getClass, notify, notifyAll, wait, wait, wait`

Field Detail

### lu

    @Deprecated
    private DecompositionSolver lu

  Deprecated. as of release 2.0, since all methods using this are deprecated
  Cached LU solver.

Constructor Detail

### AbstractRealMatrix

    protected AbstractRealMatrix()

  Creates a matrix with no data

### AbstractRealMatrix

    protected AbstractRealMatrix(int rowDimension,
                                 int columnDimension)
                          throws java.lang.IllegalArgumentException

  Create a new RealMatrix with the supplied row and column dimensions.

  Parameters:
    `rowDimension` - the number of rows in the new matrix
    `columnDimension` - the number of columns in the new matrix
  Throws:
    `java.lang.IllegalArgumentException` - if row or column dimension is not positive

Method Detail

### createMatrix

    public abstract RealMatrix createMatrix(int rowDimension,
                                            int columnDimension)
                                     throws java.lang.IllegalArgumentException

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

  Specified by:
    `createMatrix` in interface `RealMatrix`
  Parameters:
    `rowDimension` - the number of rows in the new matrix
    `columnDimension` - the number of columns in the new matrix
  Returns:
    a new matrix of the same type as the instance
  Throws:
    `java.lang.IllegalArgumentException` - if row or column dimension is not positive

### copy

    public abstract RealMatrix copy()

  Returns a (deep) copy of this.

  Specified by:
    `copy` in interface `RealMatrix`
  Returns:
    matrix copy

### add

    public RealMatrix add(RealMatrix m)
                   throws java.lang.IllegalArgumentException

  Compute the sum of this and m.

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

### subtract

    public RealMatrix subtract(RealMatrix m)
                        throws java.lang.IllegalArgumentException

  Compute this minus m.

  Specified by:
    `subtract` in interface `RealMatrix`
  Parameters:
    `m` - matrix to be subtracted
  Returns:
    this - m
  Throws:
    `java.lang.IllegalArgumentException` - if m is not the same size as this

### scalarAdd

    public RealMatrix scalarAdd(double d)

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

  Specified by:
    `scalarAdd` in interface `RealMatrix`
  Parameters:
    `d` - value to be added to each entry
  Returns:
    d + this

### scalarMultiply

    public RealMatrix scalarMultiply(double d)

  Returns the result multiplying each entry of this by d.

  Specified by:
    `scalarMultiply` in interface `RealMatrix`
  Parameters:
    `d` - value to multiply all entries by
  Returns:
    d * this

### multiply

    public RealMatrix multiply(RealMatrix m)
                        throws java.lang.IllegalArgumentException

  Returns the result of postmultiplying this by m.

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

### preMultiply

    public RealMatrix preMultiply(RealMatrix m)
                           throws java.lang.IllegalArgumentException

  Returns the result premultiplying this by `m`.

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

### getData

    public double[][] getData()

  Returns matrix entries as a two-dimensional array.

  Specified by:
    `getData` in interface `RealMatrix`
  Returns:
    2-dimensional array of entries

### getNorm

    public double getNorm()

  Returns the maximum absolute row sum norm of the matrix.

  Specified by:
    `getNorm` in interface `RealMatrix`
  Returns:
    norm

### getFrobeniusNorm

    public double getFrobeniusNorm()

  Returns the Frobenius norm of the matrix.

  Specified by:
    `getFrobeniusNorm` in interface `RealMatrix`
  Returns:
    norm

### getSubMatrix

    public RealMatrix getSubMatrix(int startRow,
                                   int endRow,
                                   int startColumn,
                                   int endColumn)
                            throws MatrixIndexException

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

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

### getSubMatrix

    public RealMatrix getSubMatrix(int[] selectedRows,
                                   int[] selectedColumns)
                            throws MatrixIndexException

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

  Specified by:
    `getSubMatrix` in interface `RealMatrix`
  Parameters:
    `selectedRows` - Array of row indices.
    `selectedColumns` - Array of column indices.
  Returns:
    The subMatrix containing the data in the specified rows and columns
  Throws:
    `MatrixIndexException` - if row or column selections are not valid

### copySubMatrix

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

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

  Specified by:
    `copySubMatrix` in interface `RealMatrix`
  Parameters:
    `startRow` - Initial row index
    `endRow` - Final row index (inclusive)
    `startColumn` - Initial column index
    `endColumn` - Final column index (inclusive)
    `destination` - The arrays where the submatrix data should be copied (if larger than rows/columns counts, only the upper-left part will be used)
  Throws:
    `MatrixIndexException` - if the indices are not valid
    `java.lang.IllegalArgumentException` - if the destination array is too small

### copySubMatrix

    public void copySubMatrix(int[] selectedRows,
                              int[] selectedColumns,
                              double[][] destination)
                       throws MatrixIndexException,
                              java.lang.IllegalArgumentException

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

  Specified by:
    `copySubMatrix` in interface `RealMatrix`
  Parameters:
    `selectedRows` - Array of row indices.
    `selectedColumns` - Array of column indices.
    `destination` - The arrays where the submatrix data should be copied (if larger than rows/columns counts, only the upper-left part will be used)
  Throws:
    `MatrixIndexException` - if the indices are not valid
    `java.lang.IllegalArgumentException` - if the destination array is too small

### setSubMatrix

    public void setSubMatrix(double[][] subMatrix,
                             int row,
                             int column)
                      throws MatrixIndexException

  Replace the submatrix starting at `row, column` using data in the input `subMatrix` array. Indexes are 0-based.

  Example:
  Starting with

       1  2  3  4
       5  6  7  8
       9  0  1  2

  and `subMatrix = {{3, 4} {5,6}}`, invoking `setSubMatrix(subMatrix,1,1))` will result in

       1  2  3  4
       5  3  4  8
       9  5  6  2

  Specified by:
    `setSubMatrix` in interface `RealMatrix`
  Parameters:
    `subMatrix` - array containing the submatrix replacement data
    `row` - row coordinate of the top, left element to be replaced
    `column` - column coordinate of the top, left element to be replaced
  Throws:
    `MatrixIndexException` - if subMatrix does not fit into this matrix from element in (row, column)

### getRowMatrix

    public RealMatrix getRowMatrix(int row)
                            throws MatrixIndexException

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

  Specified by:
    `getRowMatrix` in interface `RealMatrix`
  Parameters:
    `row` - the row to be fetched
  Returns:
    row matrix
  Throws:
    `MatrixIndexException` - if the specified row index is invalid

### setRowMatrix

    public void setRowMatrix(int row,
                             RealMatrix matrix)
                      throws MatrixIndexException,
                             InvalidMatrixException

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

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

### getColumnMatrix

    public RealMatrix getColumnMatrix(int column)
                               throws MatrixIndexException

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

  Specified by:
    `getColumnMatrix` in interface `RealMatrix`
  Parameters:
    `column` - the column to be fetched
  Returns:
    column matrix
  Throws:
    `MatrixIndexException` - if the specified column index is invalid

### setColumnMatrix

    public void setColumnMatrix(int column,
                                RealMatrix matrix)
                         throws MatrixIndexException,
                                InvalidMatrixException

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

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

### getRowVector

    public RealVector getRowVector(int row)
                            throws MatrixIndexException

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

  Specified by:
    `getRowVector` in interface `RealMatrix`
  Parameters:
    `row` - the row to be fetched
  Returns:
    row vector
  Throws:
    `MatrixIndexException` - if the specified row index is invalid

### setRowVector

    public void setRowVector(int row,
                             RealVector vector)
                      throws MatrixIndexException,
                             InvalidMatrixException

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

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

### getColumnVector

    public RealVector getColumnVector(int column)
                               throws MatrixIndexException

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

  Specified by:
    `getColumnVector` in interface `RealMatrix`
  Parameters:
    `column` - the column to be fetched
  Returns:
    column vector
  Throws:
    `MatrixIndexException` - if the specified column index is invalid

### setColumnVector

    public void setColumnVector(int column,
                                RealVector vector)
                         throws MatrixIndexException,
                                InvalidMatrixException

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

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

### getRow

    public double[] getRow(int row)
                    throws MatrixIndexException

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

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

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

### setRow

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

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

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

### getColumn

    public double[] getColumn(int column)
                       throws MatrixIndexException

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

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

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

### setColumn

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

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

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

### getEntry

    public abstract double getEntry(int row,
                                    int column)
                             throws MatrixIndexException

  Returns the entry in the specified row and column.

  Row and column indices start at 0 and must satisfy

  - `0 <= row < rowDimension`
  - `0 <= column < columnDimension`
  otherwise a `MatrixIndexException` is thrown.

  Specified by:
    `getEntry` in interface `RealMatrix`
  Parameters:
    `row` - row location of entry to be fetched
    `column` - column location of entry to be fetched
  Returns:
    matrix entry in row,column
  Throws:
    `MatrixIndexException` - if the row or column index is not valid

### setEntry

    public abstract void setEntry(int row,
                                  int column,
                                  double value)
                           throws MatrixIndexException

  Set the entry in the specified row and column.

  Row and column indices start at 0 and must satisfy

  - `0 <= row < rowDimension`
  - `0 <= column < columnDimension`
  otherwise a `MatrixIndexException` is thrown.

  Specified by:
    `setEntry` in interface `RealMatrix`
  Parameters:
    `row` - row location of entry to be set
    `column` - column location of entry to be set
    `value` - matrix entry to be set in row,column
  Throws:
    `MatrixIndexException` - if the row or column index is not valid

### addToEntry

    public abstract void addToEntry(int row,
                                    int column,
                                    double increment)
                             throws MatrixIndexException

  Change an entry in the specified row and column.

  Row and column indices start at 0 and must satisfy

  - `0 <= row < rowDimension`
  - `0 <= column < columnDimension`
  otherwise a `MatrixIndexException` is thrown.

  Specified by:
    `addToEntry` in interface `RealMatrix`
  Parameters:
    `row` - row location of entry to be set
    `column` - column location of entry to be set
    `increment` - value to add to the current matrix entry in row,column
  Throws:
    `MatrixIndexException` - if the row or column index is not valid

### multiplyEntry

    public abstract void multiplyEntry(int row,
                                       int column,
                                       double factor)
                                throws MatrixIndexException

  Change an entry in the specified row and column.

  Row and column indices start at 0 and must satisfy

  - `0 <= row < rowDimension`
  - `0 <= column < columnDimension`
  otherwise a `MatrixIndexException` is thrown.

  Specified by:
    `multiplyEntry` in interface `RealMatrix`
  Parameters:
    `row` - row location of entry to be set
    `column` - column location of entry to be set
    `factor` - multiplication factor for the current matrix entry in row,column
  Throws:
    `MatrixIndexException` - if the row or column index is not valid

### transpose

    public RealMatrix transpose()

  Returns the transpose of this matrix.

  Specified by:
    `transpose` in interface `RealMatrix`
  Returns:
    transpose matrix

### inverse

    @Deprecated
    public RealMatrix inverse()
                       throws InvalidMatrixException

  Deprecated.

  Returns the inverse of this matrix.

  Specified by:
    `inverse` in interface `RealMatrix`
  Returns:
    inverse matrix
  Throws:
    `InvalidMatrixException` - if this is not invertible

### getDeterminant

    @Deprecated
    public double getDeterminant()
                          throws InvalidMatrixException

  Deprecated.

  Returns the determinant of this matrix.

  Specified by:
    `getDeterminant` in interface `RealMatrix`
  Returns:
    determinant
  Throws:
    `InvalidMatrixException`

### isSquare

    public boolean isSquare()

  Is this a square matrix?

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

### isSingular

    @Deprecated
    public boolean isSingular()

  Deprecated.

  Is this a singular matrix?

  Specified by:
    `isSingular` in interface `RealMatrix`
  Returns:
    true if the matrix is singular

### 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 double getTrace()
                    throws NonSquareMatrixException

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

  Specified by:
    `getTrace` in interface `RealMatrix`
  Returns:
    trace
  Throws:
    `NonSquareMatrixException` - if the matrix is not square

### operate

    public double[] operate(double[] v)
                     throws java.lang.IllegalArgumentException

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

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

### operate

    public RealVector operate(RealVector v)
                       throws java.lang.IllegalArgumentException

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

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

### preMultiply

    public double[] preMultiply(double[] v)
                         throws java.lang.IllegalArgumentException

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

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

### preMultiply

    public RealVector preMultiply(RealVector v)
                           throws java.lang.IllegalArgumentException

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

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

### walkInRowOrder

    public double walkInRowOrder(RealMatrixChangingVisitor visitor)
                          throws MatrixVisitorException

  Visit (and possibly change) all matrix entries in row order.

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

  Specified by:
    `walkInRowOrder` in interface `RealMatrix`
  Parameters:
    `visitor` - visitor used to process all matrix entries
  Returns:
    the value returned by `RealMatrixChangingVisitor.end()` at the end of the walk
  Throws:
    `MatrixVisitorException` - if the visitor cannot process an entry
  See Also:
    `RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInRowOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor, int, int, int, int)`, `RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor, int, int, int, int)`, `RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor, int, int, int, int)`

### walkInRowOrder

    public double walkInRowOrder(RealMatrixPreservingVisitor visitor)
                          throws MatrixVisitorException

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

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

  Specified by:
    `walkInRowOrder` in interface `RealMatrix`
  Parameters:
    `visitor` - visitor used to process all matrix entries
  Returns:
    the value returned by `RealMatrixPreservingVisitor.end()` at the end of the walk
  Throws:
    `MatrixVisitorException` - if the visitor cannot process an entry
  See Also:
    `RealMatrix.walkInRowOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInRowOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor, int, int, int, int)`, `RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor, int, int, int, int)`, `RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor, int, int, int, int)`

### walkInRowOrder

    public double walkInRowOrder(RealMatrixChangingVisitor visitor,
                                 int startRow,
                                 int endRow,
                                 int startColumn,
                                 int endColumn)
                          throws MatrixIndexException,
                                 MatrixVisitorException

  Visit (and possibly change) some matrix entries in row order.

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

  Specified by:
    `walkInRowOrder` in interface `RealMatrix`
  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 `RealMatrixChangingVisitor.end()` at the end of the walk
  Throws:
    `MatrixIndexException` - if the indices are not valid
    `MatrixVisitorException` - if the visitor cannot process an entry
  See Also:
    `RealMatrix.walkInRowOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor, int, int, int, int)`, `RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor, int, int, int, int)`, `RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor, int, int, int, int)`

### walkInRowOrder

    public double walkInRowOrder(RealMatrixPreservingVisitor visitor,
                                 int startRow,
                                 int endRow,
                                 int startColumn,
                                 int endColumn)
                          throws MatrixIndexException,
                                 MatrixVisitorException

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

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

  Specified by:
    `walkInRowOrder` in interface `RealMatrix`
  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 `RealMatrixPreservingVisitor.end()` at the end of the walk
  Throws:
    `MatrixIndexException` - if the indices are not valid
    `MatrixVisitorException` - if the visitor cannot process an entry
  See Also:
    `RealMatrix.walkInRowOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInRowOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor, int, int, int, int)`, `RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor, int, int, int, int)`

### walkInColumnOrder

    public double walkInColumnOrder(RealMatrixChangingVisitor visitor)
                             throws MatrixVisitorException

  Visit (and possibly change) all matrix entries in column order.

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

  Specified by:
    `walkInColumnOrder` in interface `RealMatrix`
  Parameters:
    `visitor` - visitor used to process all matrix entries
  Returns:
    the value returned by `RealMatrixChangingVisitor.end()` at the end of the walk
  Throws:
    `MatrixVisitorException` - if the visitor cannot process an entry
  See Also:
    `RealMatrix.walkInRowOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInRowOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor, int, int, int, int)`, `RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor, int, int, int, int)`, `RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor, int, int, int, int)`

### walkInColumnOrder

    public double walkInColumnOrder(RealMatrixPreservingVisitor visitor)
                             throws MatrixVisitorException

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

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

  Specified by:
    `walkInColumnOrder` in interface `RealMatrix`
  Parameters:
    `visitor` - visitor used to process all matrix entries
  Returns:
    the value returned by `RealMatrixPreservingVisitor.end()` at the end of the walk
  Throws:
    `MatrixVisitorException` - if the visitor cannot process an entry
  See Also:
    `RealMatrix.walkInRowOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInRowOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor, int, int, int, int)`, `RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor, int, int, int, int)`, `RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor, int, int, int, int)`

### walkInColumnOrder

    public double walkInColumnOrder(RealMatrixChangingVisitor visitor,
                                    int startRow,
                                    int endRow,
                                    int startColumn,
                                    int endColumn)
                             throws MatrixIndexException,
                                    MatrixVisitorException

  Visit (and possibly change) some matrix entries in column order.

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

  Specified by:
    `walkInColumnOrder` in interface `RealMatrix`
  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 `RealMatrixChangingVisitor.end()` at the end of the walk
  Throws:
    `MatrixIndexException` - if the indices are not valid
    `MatrixVisitorException` - if the visitor cannot process an entry
  See Also:
    `RealMatrix.walkInRowOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInRowOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor, int, int, int, int)`, `RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor, int, int, int, int)`, `RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor, int, int, int, int)`

### walkInColumnOrder

    public double walkInColumnOrder(RealMatrixPreservingVisitor visitor,
                                    int startRow,
                                    int endRow,
                                    int startColumn,
                                    int endColumn)
                             throws MatrixIndexException,
                                    MatrixVisitorException

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

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

  Specified by:
    `walkInColumnOrder` in interface `RealMatrix`
  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 `RealMatrixPreservingVisitor.end()` at the end of the walk
  Throws:
    `MatrixIndexException` - if the indices are not valid
    `MatrixVisitorException` - if the visitor cannot process an entry
  See Also:
    `RealMatrix.walkInRowOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInRowOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor, int, int, int, int)`, `RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor, int, int, int, int)`

### walkInOptimizedOrder

    public double walkInOptimizedOrder(RealMatrixChangingVisitor visitor)
                                throws MatrixVisitorException

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

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

  Specified by:
    `walkInOptimizedOrder` in interface `RealMatrix`
  Parameters:
    `visitor` - visitor used to process all matrix entries
  Returns:
    the value returned by `RealMatrixChangingVisitor.end()` at the end of the walk
  Throws:
    `MatrixVisitorException` - if the visitor cannot process an entry
  See Also:
    `RealMatrix.walkInRowOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInRowOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor, int, int, int, int)`, `RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor, int, int, int, int)`, `RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor, int, int, int, int)`

### walkInOptimizedOrder

    public double walkInOptimizedOrder(RealMatrixPreservingVisitor visitor)
                                throws MatrixVisitorException

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

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

  Specified by:
    `walkInOptimizedOrder` in interface `RealMatrix`
  Parameters:
    `visitor` - visitor used to process all matrix entries
  Returns:
    the value returned by `RealMatrixPreservingVisitor.end()` at the end of the walk
  Throws:
    `MatrixVisitorException` - if the visitor cannot process an entry
  See Also:
    `RealMatrix.walkInRowOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInRowOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor, int, int, int, int)`, `RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor, int, int, int, int)`, `RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor, int, int, int, int)`

### walkInOptimizedOrder

    public double walkInOptimizedOrder(RealMatrixChangingVisitor visitor,
                                       int startRow,
                                       int endRow,
                                       int startColumn,
                                       int endColumn)
                                throws MatrixIndexException,
                                       MatrixVisitorException

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

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

  Specified by:
    `walkInOptimizedOrder` in interface `RealMatrix`
  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 `RealMatrixChangingVisitor.end()` at the end of the walk
  Throws:
    `MatrixIndexException` - if the indices are not valid
    `MatrixVisitorException` - if the visitor cannot process an entry
  See Also:
    `RealMatrix.walkInRowOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInRowOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor, int, int, int, int)`, `RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor, int, int, int, int)`, `RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor, int, int, int, int)`

### walkInOptimizedOrder

    public double walkInOptimizedOrder(RealMatrixPreservingVisitor visitor,
                                       int startRow,
                                       int endRow,
                                       int startColumn,
                                       int endColumn)
                                throws MatrixIndexException,
                                       MatrixVisitorException

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

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

  Specified by:
    `walkInOptimizedOrder` in interface `RealMatrix`
  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 `RealMatrixPreservingVisitor.end()` at the end of the walk
  Throws:
    `MatrixIndexException` - if the indices are not valid
    `MatrixVisitorException` - if the visitor cannot process an entry
  See Also:
    `RealMatrix.walkInRowOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInRowOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor, int, int, int, int)`, `RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor, int, int, int, int)`, `RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor, int, int, int, int)`, `RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor)`, `RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor)`, `RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor, int, int, int, int)`

### solve

    @Deprecated
    public double[] solve(double[] b)
                   throws java.lang.IllegalArgumentException,
                          InvalidMatrixException

  Deprecated.

  Returns the solution vector for a linear system with coefficient matrix = this and constant vector = `b`.

  Specified by:
    `solve` in interface `RealMatrix`
  Parameters:
    `b` - constant vector
  Returns:
    vector of solution values to AX = b, where A is *this
  Throws:
    `java.lang.IllegalArgumentException` - if this.rowDimension != b.length
    `InvalidMatrixException` - if this matrix is not square or is singular

### solve

    @Deprecated
    public RealMatrix solve(RealMatrix b)
                     throws java.lang.IllegalArgumentException,
                            InvalidMatrixException

  Deprecated.

  Returns a matrix of (column) solution vectors for linear systems with coefficient matrix = this and constant vectors = columns of `b`.

  Specified by:
    `solve` in interface `RealMatrix`
  Parameters:
    `b` - matrix of constant vectors forming RHS of linear systems to to solve
  Returns:
    matrix of solution vectors
  Throws:
    `java.lang.IllegalArgumentException` - if this.rowDimension != row dimension
    `InvalidMatrixException` - if this matrix is not square or is singular

### luDecompose

    @Deprecated
    public void luDecompose()
                     throws InvalidMatrixException

  Deprecated. as of release 2.0, replaced by `LUDecomposition`

  Computes a new LU decomposition for this matrix, storing the result for use by other methods.

  Implementation Note:
  Uses Crout's algorithm, with partial pivoting.

  Usage Note:
  This method should rarely be invoked directly. Its only use is to force recomputation of the LU decomposition when changes have been made to the underlying data using direct array references. Changes made using setXxx methods will trigger recomputation when needed automatically.

  Throws:
    `InvalidMatrixException` - if the matrix is non-square or singular.

### toString

    public java.lang.String toString()

  Get a string representation for this matrix.

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

### equals

    public boolean equals(java.lang.Object object)

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

  Overrides:
    `equals` in class `java.lang.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 `java.lang.Object`
  Returns:
    hashcode for matrix

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