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

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

    public class MatrixUtils

extends java.lang.Object

A collection of static methods that operate on or return matrices.

Version:
  $Revision: 903046 $ $Date: 2010-01-25 21:07:26 -0500 (Mon, 25 Jan 2010) $

Nested Class Summary
`private static class` | `MatrixUtils.BigFractionMatrixConverter` Converter for `FieldMatrix`/`BigFraction`.
`private static class` | `MatrixUtils.FractionMatrixConverter` Converter for `FieldMatrix`/`Fraction`.

Constructor Summary
`private` | `MatrixUtils()` Private constructor.

Method Summary
`static Array2DRowRealMatrix` | `bigFractionMatrixToRealMatrix(FieldMatrix<BigFraction> m)` Convert a `FieldMatrix`/`BigFraction` matrix to a `RealMatrix`.
`static void` | `checkAdditionCompatible(AnyMatrix left, AnyMatrix right)` Check if matrices are addition compatible
`static void` | `checkColumnIndex(AnyMatrix m, int column)` Check if a column index is valid.
`static void` | `checkMultiplicationCompatible(AnyMatrix left, AnyMatrix right)` Check if matrices are multiplication compatible
`static void` | `checkRowIndex(AnyMatrix m, int row)` Check if a row index is valid.
`static void` | `checkSubMatrixIndex(AnyMatrix m, int[] selectedRows, int[] selectedColumns)` Check if submatrix ranges indices are valid.
`static void` | `checkSubMatrixIndex(AnyMatrix m, int startRow, int endRow, int startColumn, int endColumn)` Check if submatrix ranges indices are valid.
`static void` | `checkSubtractionCompatible(AnyMatrix left, AnyMatrix right)` Check if matrices are subtraction compatible
`static BigMatrix` | `createBigIdentityMatrix(int dimension)` Deprecated. since 2.0, replaced by `createFieldIdentityMatrix(Field, int)`
`static BigMatrix` | `createBigMatrix(java.math.BigDecimal[][] data)` Deprecated. since 2.0 replaced by `createFieldMatrix(FieldElement[][])`
`static BigMatrix` | `createBigMatrix(java.math.BigDecimal[][] data, boolean copyArray)` Deprecated. since 2.0 replaced by `createFieldMatrix(FieldElement[][])`
`static BigMatrix` | `createBigMatrix(double[][] data)` Deprecated. since 2.0 replaced by `createFieldMatrix(FieldElement[][])`
`static BigMatrix` | `createBigMatrix(java.lang.String[][] data)` Deprecated. since 2.0 replaced by `createFieldMatrix(FieldElement[][])`
`static BigMatrix` | `createColumnBigMatrix(java.math.BigDecimal[] columnData)` Deprecated. since 2.0 replaced by `createColumnFieldMatrix(FieldElement[])`
`static BigMatrix` | `createColumnBigMatrix(double[] columnData)` Deprecated. since 2.0 replaced by `createColumnFieldMatrix(FieldElement[])`
`static BigMatrix` | `createColumnBigMatrix(java.lang.String[] columnData)` Deprecated. since 2.0 replaced by `createColumnFieldMatrix(FieldElement[])`
`static
`<T extends FieldElement<T>> FieldMatrix<T>`
` | `createColumnFieldMatrix(T[] columnData)` Creates a column `FieldMatrix` using the data from the input array.
`static RealMatrix` | `createColumnRealMatrix(double[] columnData)` Creates a column `RealMatrix` using the data from the input array.
`static
`<T extends FieldElement<T>> FieldMatrix<T>`
` | `createFieldDiagonalMatrix(T[] diagonal)` Returns a diagonal matrix with specified elements.
`static
`<T extends FieldElement<T>> FieldMatrix<T>`
` | `createFieldIdentityMatrix(Field<T> field, int dimension)` Returns `dimension x dimension` identity matrix.
`static
`<T extends FieldElement<T>> FieldMatrix<T>`
` | `createFieldMatrix(Field<T> field, int rows, int columns)` Returns a `FieldMatrix` with specified dimensions.
`static
`<T extends FieldElement<T>> FieldMatrix<T>`
` | `createFieldMatrix(T[][] data)` Returns a `FieldMatrix` whose entries are the the values in the the input array.
`static
`<T extends FieldElement<T>> FieldVector<T>`
` | `createFieldVector(T[] data)` Creates a `FieldVector` using the data from the input array.
`static RealMatrix` | `createRealDiagonalMatrix(double[] diagonal)` Returns a diagonal matrix with specified elements.
`static RealMatrix` | `createRealIdentityMatrix(int dimension)` Returns `dimension x dimension` identity matrix.
`static RealMatrix` | `createRealMatrix(double[][] data)` Returns a `RealMatrix` whose entries are the the values in the the input array.
`static RealMatrix` | `createRealMatrix(int rows, int columns)` Returns a `RealMatrix` with specified dimensions.
`static RealVector` | `createRealVector(double[] data)` Creates a `RealVector` using the data from the input array.
`static BigMatrix` | `createRowBigMatrix(java.math.BigDecimal[] rowData)` Deprecated. since 2.0 replaced by `createRowFieldMatrix(FieldElement[])`
`static BigMatrix` | `createRowBigMatrix(double[] rowData)` Deprecated. since 2.0 replaced by `createRowFieldMatrix(FieldElement[])`
`static BigMatrix` | `createRowBigMatrix(java.lang.String[] rowData)` Deprecated. since 2.0 replaced by `createRowFieldMatrix(FieldElement[])`
`static
`<T extends FieldElement<T>> FieldMatrix<T>`
` | `createRowFieldMatrix(T[] rowData)` Creates a row `FieldMatrix` using the data from the input array.
`static RealMatrix` | `createRowRealMatrix(double[] rowData)` Creates a row `RealMatrix` using the data from the input array.
`static void` | `deserializeRealMatrix(java.lang.Object instance, java.lang.String fieldName, java.io.ObjectInputStream ois)` Deserialize a `RealMatrix` field in a class.
`static void` | `deserializeRealVector(java.lang.Object instance, java.lang.String fieldName, java.io.ObjectInputStream ois)` Deserialize a `RealVector` field in a class.
`static Array2DRowRealMatrix` | `fractionMatrixToRealMatrix(FieldMatrix<Fraction> m)` Convert a `FieldMatrix`/`Fraction` matrix to a `RealMatrix`.
`static void` | `serializeRealMatrix(RealMatrix matrix, java.io.ObjectOutputStream oos)` Serialize a `RealMatrix`.
`static void` | `serializeRealVector(RealVector vector, java.io.ObjectOutputStream oos)` Serialize a `RealVector`.

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

Constructor Detail

### MatrixUtils

    private MatrixUtils()

  Private constructor.

Method Detail

### createRealMatrix

    public static RealMatrix createRealMatrix(int rows,
                                              int columns)

  Returns a `RealMatrix` with specified dimensions.

  The type of matrix returned depends on the dimension. Below 212 elements (i.e. 4096 elements or 64×64 for a square matrix) which can be stored in a 32kB array, a `Array2DRowRealMatrix` instance is built. Above this threshold a `BlockRealMatrix` instance is built.

  The matrix elements are all set to 0.0.

  Parameters:
    `rows` - number of rows of the matrix
    `columns` - number of columns of the matrix
  Returns:
    RealMatrix with specified dimensions
  See Also:
    `createRealMatrix(double[][])`

### createFieldMatrix

    public static <T extends FieldElement<T>> FieldMatrix<T> createFieldMatrix(Field<T> field,
                                                                               int rows,
                                                                               int columns)

  Returns a `FieldMatrix` with specified dimensions.

  The type of matrix returned depends on the dimension. Below 212 elements (i.e. 4096 elements or 64×64 for a square matrix), a `FieldMatrix` instance is built. Above this threshold a `BlockFieldMatrix` instance is built.

  The matrix elements are all set to field.getZero().

  Type Parameters:
    `T` - the type of the field elements
  Parameters:
    `field` - field to which the matrix elements belong
    `rows` - number of rows of the matrix
    `columns` - number of columns of the matrix
  Returns:
    FieldMatrix with specified dimensions
  Since:
    2.0
  See Also:
    `createFieldMatrix(FieldElement[][])`

### createRealMatrix

    public static RealMatrix createRealMatrix(double[][] data)

  Returns a `RealMatrix` whose entries are the the values in the the input array.

  The type of matrix returned depends on the dimension. Below 212 elements (i.e. 4096 elements or 64×64 for a square matrix) which can be stored in a 32kB array, a `Array2DRowRealMatrix` instance is built. Above this threshold a `BlockRealMatrix` instance is built.

  The input array is copied, not referenced.

  Parameters:
    `data` - input array
  Returns:
    RealMatrix containing the values of the array
  Throws:
    `java.lang.IllegalArgumentException` - if `data` is not rectangular (not all rows have the same length) or empty
    `java.lang.NullPointerException` - if either `data` or `data[0]` is null
  See Also:
    `createRealMatrix(int, int)`

### createFieldMatrix

    public static <T extends FieldElement<T>> FieldMatrix<T> createFieldMatrix(T[][] data)

  Returns a `FieldMatrix` whose entries are the the values in the the input array.

  The type of matrix returned depends on the dimension. Below 212 elements (i.e. 4096 elements or 64×64 for a square matrix), a `FieldMatrix` instance is built. Above this threshold a `BlockFieldMatrix` instance is built.

  The input array is copied, not referenced.

  Type Parameters:
    `T` - the type of the field elements
  Parameters:
    `data` - input array
  Returns:
    RealMatrix containing the values of the array
  Throws:
    `java.lang.IllegalArgumentException` - if `data` is not rectangular (not all rows have the same length) or empty
    `java.lang.NullPointerException` - if either `data` or `data[0]` is null
  Since:
    2.0
  See Also:
    `createFieldMatrix(Field, int, int)`

### createRealIdentityMatrix

    public static RealMatrix createRealIdentityMatrix(int dimension)

  Returns `dimension x dimension` identity matrix.

  Parameters:
    `dimension` - dimension of identity matrix to generate
  Returns:
    identity matrix
  Throws:
    `java.lang.IllegalArgumentException` - if dimension is not positive
  Since:
    1.1

### createFieldIdentityMatrix

    public static <T extends FieldElement<T>> FieldMatrix<T> createFieldIdentityMatrix(Field<T> field,
                                                                                       int dimension)

  Returns `dimension x dimension` identity matrix.

  Type Parameters:
    `T` - the type of the field elements
  Parameters:
    `field` - field to which the elements belong
    `dimension` - dimension of identity matrix to generate
  Returns:
    identity matrix
  Throws:
    `java.lang.IllegalArgumentException` - if dimension is not positive
  Since:
    2.0

### createBigIdentityMatrix

    @Deprecated
    public static BigMatrix createBigIdentityMatrix(int dimension)

  Deprecated. since 2.0, replaced by `createFieldIdentityMatrix(Field, int)`

  Returns `dimension x dimension` identity matrix.

  Parameters:
    `dimension` - dimension of identity matrix to generate
  Returns:
    identity matrix
  Throws:
    `java.lang.IllegalArgumentException` - if dimension is not positive
  Since:
    1.1

### createRealDiagonalMatrix

    public static RealMatrix createRealDiagonalMatrix(double[] diagonal)

  Returns a diagonal matrix with specified elements.

  Parameters:
    `diagonal` - diagonal elements of the matrix (the array elements will be copied)
  Returns:
    diagonal matrix
  Since:
    2.0

### createFieldDiagonalMatrix

    public static <T extends FieldElement<T>> FieldMatrix<T> createFieldDiagonalMatrix(T[] diagonal)

  Returns a diagonal matrix with specified elements.

  Type Parameters:
    `T` - the type of the field elements
  Parameters:
    `diagonal` - diagonal elements of the matrix (the array elements will be copied)
  Returns:
    diagonal matrix
  Since:
    2.0

### createBigMatrix

    @Deprecated
    public static BigMatrix createBigMatrix(double[][] data)

  Deprecated. since 2.0 replaced by `createFieldMatrix(FieldElement[][])`

  Returns a `BigMatrix` whose entries are the the values in the the input array. The input array is copied, not referenced.

  Parameters:
    `data` - input array
  Returns:
    RealMatrix containing the values of the array
  Throws:
    `java.lang.IllegalArgumentException` - if `data` is not rectangular (not all rows have the same length) or empty
    `java.lang.NullPointerException` - if data is null

### createBigMatrix

    @Deprecated
    public static BigMatrix createBigMatrix(java.math.BigDecimal[][] data)

  Deprecated. since 2.0 replaced by `createFieldMatrix(FieldElement[][])`

  Returns a `BigMatrix` whose entries are the the values in the the input array. The input array is copied, not referenced.

  Parameters:
    `data` - input array
  Returns:
    RealMatrix containing the values of the array
  Throws:
    `java.lang.IllegalArgumentException` - if `data` is not rectangular (not all rows have the same length) or empty
    `java.lang.NullPointerException` - if data is null

### createBigMatrix

    @Deprecated
    public static BigMatrix createBigMatrix(java.math.BigDecimal[][] data,
                                                       boolean copyArray)

  Deprecated. since 2.0 replaced by `createFieldMatrix(FieldElement[][])`

  Returns a `BigMatrix` whose entries are the the values in the the input array.

  If an array is built specially in order to be embedded in a BigMatrix and not used directly, the `copyArray` may be set to `false`

  Parameters:
    `data` - data for new matrix
    `copyArray` - if true, the input array will be copied, otherwise it will be referenced
  Returns:
    BigMatrix containing the values of the array
  Throws:
    `java.lang.IllegalArgumentException` - if `data` is not rectangular (not all rows have the same length) or empty
    `java.lang.NullPointerException` - if `data` is null
  See Also:
    `createRealMatrix(double[][])`

### createBigMatrix

    @Deprecated
    public static BigMatrix createBigMatrix(java.lang.String[][] data)

  Deprecated. since 2.0 replaced by `createFieldMatrix(FieldElement[][])`

  Returns a `BigMatrix` whose entries are the the values in the the input array. The input array is copied, not referenced.

  Parameters:
    `data` - input array
  Returns:
    RealMatrix containing the values of the array
  Throws:
    `java.lang.IllegalArgumentException` - if `data` is not rectangular (not all rows have the same length) or empty
    `java.lang.NullPointerException` - if data is null

### createRealVector

    public static RealVector createRealVector(double[] data)

  Creates a `RealVector` using the data from the input array.

  Parameters:
    `data` - the input data
  Returns:
    a data.length RealVector
  Throws:
    `java.lang.IllegalArgumentException` - if `data` is empty
    `java.lang.NullPointerException` - if `data`is null

### createFieldVector

    public static <T extends FieldElement<T>> FieldVector<T> createFieldVector(T[] data)

  Creates a `FieldVector` using the data from the input array.

  Type Parameters:
    `T` - the type of the field elements
  Parameters:
    `data` - the input data
  Returns:
    a data.length FieldVector
  Throws:
    `java.lang.IllegalArgumentException` - if `data` is empty
    `java.lang.NullPointerException` - if `data`is null

### createRowRealMatrix

    public static RealMatrix createRowRealMatrix(double[] rowData)

  Creates a row `RealMatrix` using the data from the input array.

  Parameters:
    `rowData` - the input row data
  Returns:
    a 1 x rowData.length RealMatrix
  Throws:
    `java.lang.IllegalArgumentException` - if `rowData` is empty
    `java.lang.NullPointerException` - if `rowData`is null

### createRowFieldMatrix

    public static <T extends FieldElement<T>> FieldMatrix<T> createRowFieldMatrix(T[] rowData)

  Creates a row `FieldMatrix` using the data from the input array.

  Type Parameters:
    `T` - the type of the field elements
  Parameters:
    `rowData` - the input row data
  Returns:
    a 1 x rowData.length FieldMatrix
  Throws:
    `java.lang.IllegalArgumentException` - if `rowData` is empty
    `java.lang.NullPointerException` - if `rowData`is null

### createRowBigMatrix

    @Deprecated
    public static BigMatrix createRowBigMatrix(double[] rowData)

  Deprecated. since 2.0 replaced by `createRowFieldMatrix(FieldElement[])`

  Creates a row `BigMatrix` using the data from the input array.

  Parameters:
    `rowData` - the input row data
  Returns:
    a 1 x rowData.length BigMatrix
  Throws:
    `java.lang.IllegalArgumentException` - if `rowData` is empty
    `java.lang.NullPointerException` - if `rowData`is null

### createRowBigMatrix

    @Deprecated
    public static BigMatrix createRowBigMatrix(java.math.BigDecimal[] rowData)

  Deprecated. since 2.0 replaced by `createRowFieldMatrix(FieldElement[])`

  Creates a row `BigMatrix` using the data from the input array.

  Parameters:
    `rowData` - the input row data
  Returns:
    a 1 x rowData.length BigMatrix
  Throws:
    `java.lang.IllegalArgumentException` - if `rowData` is empty
    `java.lang.NullPointerException` - if `rowData`is null

### createRowBigMatrix

    @Deprecated
    public static BigMatrix createRowBigMatrix(java.lang.String[] rowData)

  Deprecated. since 2.0 replaced by `createRowFieldMatrix(FieldElement[])`

  Creates a row `BigMatrix` using the data from the input array.

  Parameters:
    `rowData` - the input row data
  Returns:
    a 1 x rowData.length BigMatrix
  Throws:
    `java.lang.IllegalArgumentException` - if `rowData` is empty
    `java.lang.NullPointerException` - if `rowData`is null

### createColumnRealMatrix

    public static RealMatrix createColumnRealMatrix(double[] columnData)

  Creates a column `RealMatrix` using the data from the input array.

  Parameters:
    `columnData` - the input column data
  Returns:
    a columnData x 1 RealMatrix
  Throws:
    `java.lang.IllegalArgumentException` - if `columnData` is empty
    `java.lang.NullPointerException` - if `columnData`is null

### createColumnFieldMatrix

    public static <T extends FieldElement<T>> FieldMatrix<T> createColumnFieldMatrix(T[] columnData)

  Creates a column `FieldMatrix` using the data from the input array.

  Type Parameters:
    `T` - the type of the field elements
  Parameters:
    `columnData` - the input column data
  Returns:
    a columnData x 1 FieldMatrix
  Throws:
    `java.lang.IllegalArgumentException` - if `columnData` is empty
    `java.lang.NullPointerException` - if `columnData`is null

### createColumnBigMatrix

    @Deprecated
    public static BigMatrix createColumnBigMatrix(double[] columnData)

  Deprecated. since 2.0 replaced by `createColumnFieldMatrix(FieldElement[])`

  Creates a column `BigMatrix` using the data from the input array.

  Parameters:
    `columnData` - the input column data
  Returns:
    a columnData x 1 BigMatrix
  Throws:
    `java.lang.IllegalArgumentException` - if `columnData` is empty
    `java.lang.NullPointerException` - if `columnData`is null

### createColumnBigMatrix

    @Deprecated
    public static BigMatrix createColumnBigMatrix(java.math.BigDecimal[] columnData)

  Deprecated. since 2.0 replaced by `createColumnFieldMatrix(FieldElement[])`

  Creates a column `BigMatrix` using the data from the input array.

  Parameters:
    `columnData` - the input column data
  Returns:
    a columnData x 1 BigMatrix
  Throws:
    `java.lang.IllegalArgumentException` - if `columnData` is empty
    `java.lang.NullPointerException` - if `columnData`is null

### createColumnBigMatrix

    @Deprecated
    public static BigMatrix createColumnBigMatrix(java.lang.String[] columnData)

  Deprecated. since 2.0 replaced by `createColumnFieldMatrix(FieldElement[])`

  Creates a column `BigMatrix` using the data from the input array.

  Parameters:
    `columnData` - the input column data
  Returns:
    a columnData x 1 BigMatrix
  Throws:
    `java.lang.IllegalArgumentException` - if `columnData` is empty
    `java.lang.NullPointerException` - if `columnData`is null

### checkRowIndex

    public static void checkRowIndex(AnyMatrix m,
                                     int row)

  Check if a row index is valid.

  Parameters:
    `m` - matrix containing the submatrix
    `row` - row index to check
  Throws:
    `MatrixIndexException` - if index is not valid

### checkColumnIndex

    public static void checkColumnIndex(AnyMatrix m,
                                        int column)
                                 throws MatrixIndexException

  Check if a column index is valid.

  Parameters:
    `m` - matrix containing the submatrix
    `column` - column index to check
  Throws:
    `MatrixIndexException` - if index is not valid

### checkSubMatrixIndex

    public static void checkSubMatrixIndex(AnyMatrix m,
                                           int startRow,
                                           int endRow,
                                           int startColumn,
                                           int endColumn)

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

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

### checkSubMatrixIndex

    public static void checkSubMatrixIndex(AnyMatrix m,
                                           int[] selectedRows,
                                           int[] selectedColumns)
                                    throws MatrixIndexException

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

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

### checkAdditionCompatible

    public static void checkAdditionCompatible(AnyMatrix left,
                                               AnyMatrix right)
                                        throws java.lang.IllegalArgumentException

  Check if matrices are addition compatible

  Parameters:
    `left` - left hand side matrix
    `right` - right hand side matrix
  Throws:
    `java.lang.IllegalArgumentException` - if matrices are not addition compatible

### checkSubtractionCompatible

    public static void checkSubtractionCompatible(AnyMatrix left,
                                                  AnyMatrix right)
                                           throws java.lang.IllegalArgumentException

  Check if matrices are subtraction compatible

  Parameters:
    `left` - left hand side matrix
    `right` - right hand side matrix
  Throws:
    `java.lang.IllegalArgumentException` - if matrices are not subtraction compatible

### checkMultiplicationCompatible

    public static void checkMultiplicationCompatible(AnyMatrix left,
                                                     AnyMatrix right)
                                              throws java.lang.IllegalArgumentException

  Check if matrices are multiplication compatible

  Parameters:
    `left` - left hand side matrix
    `right` - right hand side matrix
  Throws:
    `java.lang.IllegalArgumentException` - if matrices are not multiplication compatible

### fractionMatrixToRealMatrix

    public static Array2DRowRealMatrix fractionMatrixToRealMatrix(FieldMatrix<Fraction> m)

  Convert a `FieldMatrix`/`Fraction` matrix to a `RealMatrix`.

  Parameters:
    `m` - matrix to convert
  Returns:
    converted matrix

### bigFractionMatrixToRealMatrix

    public static Array2DRowRealMatrix bigFractionMatrixToRealMatrix(FieldMatrix<BigFraction> m)

  Convert a `FieldMatrix`/`BigFraction` matrix to a `RealMatrix`.

  Parameters:
    `m` - matrix to convert
  Returns:
    converted matrix

### serializeRealVector

    public static void serializeRealVector(RealVector vector,
                                           java.io.ObjectOutputStream oos)
                                    throws java.io.IOException

  Serialize a `RealVector`.

  This method is intended to be called from within a private `writeObject` method (after a call to `oos.defaultWriteObject()`) in a class that has a `RealVector` field, which should be declared `transient`. This way, the default handling does not serialize the vector (the `RealVector` interface is not serializable by default) but this method does serialize it specifically.

  The following example shows how a simple class with a name and a real vector should be written:

       public class NamedVector implements Serializable {

           private final String name;
           private final transient RealVector coefficients;

           // omitted constructors, getters ...

           private void writeObject(ObjectOutputStream oos) throws IOException {
               oos.defaultWriteObject();  // takes care of name field
               MatrixUtils.serializeRealVector(coefficients, oos);
           }

           private void readObject(ObjectInputStream ois) throws ClassNotFoundException, IOException {
               ois.defaultReadObject();  // takes care of name field
               MatrixUtils.deserializeRealVector(this, "coefficients", ois);
           }

       }

  Parameters:
    `vector` - real vector to serialize
    `oos` - stream where the real vector should be written
  Throws:
    `java.io.IOException` - if object cannot be written to stream
  See Also:
    `deserializeRealVector(Object, String, ObjectInputStream)`

### deserializeRealVector

    public static void deserializeRealVector(java.lang.Object instance,
                                             java.lang.String fieldName,
                                             java.io.ObjectInputStream ois)
                                      throws java.lang.ClassNotFoundException,
                                             java.io.IOException

  Deserialize a `RealVector` field in a class.

  This method is intended to be called from within a private `readObject` method (after a call to `ois.defaultReadObject()`) in a class that has a `RealVector` field, which should be declared `transient`. This way, the default handling does not deserialize the vector (the `RealVector` interface is not serializable by default) but this method does deserialize it specifically.

  Parameters:
    `instance` - instance in which the field must be set up
    `fieldName` - name of the field within the class (may be private and final)
    `ois` - stream from which the real vector should be read
  Throws:
    `java.lang.ClassNotFoundException` - if a class in the stream cannot be found
    `java.io.IOException` - if object cannot be read from the stream
  See Also:
    `serializeRealVector(RealVector, ObjectOutputStream)`

### serializeRealMatrix

    public static void serializeRealMatrix(RealMatrix matrix,
                                           java.io.ObjectOutputStream oos)
                                    throws java.io.IOException

  Serialize a `RealMatrix`.

  This method is intended to be called from within a private `writeObject` method (after a call to `oos.defaultWriteObject()`) in a class that has a `RealMatrix` field, which should be declared `transient`. This way, the default handling does not serialize the matrix (the `RealMatrix` interface is not serializable by default) but this method does serialize it specifically.

  The following example shows how a simple class with a name and a real matrix should be written:

       public class NamedMatrix implements Serializable {

           private final String name;
           private final transient RealMatrix coefficients;

           // omitted constructors, getters ...

           private void writeObject(ObjectOutputStream oos) throws IOException {
               oos.defaultWriteObject();  // takes care of name field
               MatrixUtils.serializeRealMatrix(coefficients, oos);
           }

           private void readObject(ObjectInputStream ois) throws ClassNotFoundException, IOException {
               ois.defaultReadObject();  // takes care of name field
               MatrixUtils.deserializeRealMatrix(this, "coefficients", ois);
           }

       }

  Parameters:
    `matrix` - real matrix to serialize
    `oos` - stream where the real matrix should be written
  Throws:
    `java.io.IOException` - if object cannot be written to stream
  See Also:
    `deserializeRealMatrix(Object, String, ObjectInputStream)`

### deserializeRealMatrix

    public static void deserializeRealMatrix(java.lang.Object instance,
                                             java.lang.String fieldName,
                                             java.io.ObjectInputStream ois)
                                      throws java.lang.ClassNotFoundException,
                                             java.io.IOException

  Deserialize a `RealMatrix` field in a class.

  This method is intended to be called from within a private `readObject` method (after a call to `ois.defaultReadObject()`) in a class that has a `RealMatrix` field, which should be declared `transient`. This way, the default handling does not deserialize the matrix (the `RealMatrix` interface is not serializable by default) but this method does deserialize it specifically.

  Parameters:
    `instance` - instance in which the field must be set up
    `fieldName` - name of the field within the class (may be private and final)
    `ois` - stream from which the real matrix should be read
  Throws:
    `java.lang.ClassNotFoundException` - if a class in the stream cannot be found
    `java.io.IOException` - if object cannot be read from the stream
  See Also:
    `serializeRealMatrix(RealMatrix, ObjectOutputStream)`

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