MatrixUtils (Hipparchus 2.2 API)

java.lang.Object
- org.hipparchus.linear.MatrixUtils

```
public class MatrixUtils
extends Object
```
A collection of static methods that operate on or return matrices.

Field Summary

Fields
Modifier and Type	Field and Description
`static RealMatrixFormat`	`DEFAULT_FORMAT` The default format for `RealMatrix` objects.
`static RealMatrixFormat`	`OCTAVE_FORMAT` A format for `RealMatrix` objects compatible with octave.

Method Summary

All Methods Static Methods Concrete Methods
Modifier and Type	Method and Description
`static Array2DRowRealMatrix`	`bigFractionMatrixToRealMatrix(FieldMatrix<BigFraction> m)` Convert a `FieldMatrix`/`BigFraction` matrix to a `RealMatrix`.
`static RealMatrix`	`blockInverse(RealMatrix m, int splitIndex)` Computes the inverse of the given matrix by splitting it into 4 sub-matrices.
`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`	`checkMatrixIndex(AnyMatrix m, int row, int column)` Check if matrix indices are 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`	`checkSameColumnDimension(AnyMatrix left, AnyMatrix right)` Check if matrices have the same number of columns.
`static void`	`checkSameRowDimension(AnyMatrix left, AnyMatrix right)` Check if matrices have the same number of rows.
`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 void`	`checkSymmetric(RealMatrix matrix, double eps)` Checks whether a matrix is symmetric.
`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(Field<T> field, int dimension)` Creates a `FieldVector` with specified dimensions.
`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 RealVector`	`createRealVector(int dimension)` Creates a `RealVector` with specified dimensions.
`static <T extends FieldElement<T>> FieldMatrix<T>`	`createRowFieldMatrix(T[] rowData)` Create a row `FieldMatrix` using the data from the input array.
`static RealMatrix`	`createRowRealMatrix(double[] rowData)` Create a row `RealMatrix` using the data from the input array.
`static void`	`deserializeRealMatrix(Object instance, String fieldName, ObjectInputStream ois)` Deserialize a `RealMatrix` field in a class.
`static void`	`deserializeRealVector(Object instance, String fieldName, ObjectInputStream ois)` Deserialize a `RealVector` field in a class.
`static Array2DRowRealMatrix`	`fractionMatrixToRealMatrix(FieldMatrix<Fraction> m)` Convert a `FieldMatrix`/`Fraction` matrix to a `RealMatrix`.
`static RealMatrix`	`inverse(RealMatrix matrix)` Computes the inverse of the given matrix.
`static RealMatrix`	`inverse(RealMatrix matrix, double threshold)` Computes the inverse of the given matrix.
`static boolean`	`isSymmetric(RealMatrix matrix, double eps)` Checks whether a matrix is symmetric.
`static RealMatrix`	`matrixExponential(RealMatrix rm)` Computes the matrix exponential of the given matrix.
`static <T extends CalculusFieldElement<T>> List<FieldVector<T>>`	`orthonormalize(Field<T> field, List<FieldVector<T>> independent, T threshold, DependentVectorsHandler handler)` Orthonormalize a list of vectors.
`static List<RealVector>`	`orthonormalize(List<RealVector> independent, double threshold, DependentVectorsHandler handler)` Orthonormalize a list of vectors.
`static void`	`serializeRealMatrix(RealMatrix matrix, ObjectOutputStream oos)` Serialize a `RealMatrix`.
`static void`	`serializeRealVector(RealVector vector, ObjectOutputStream oos)` Serialize a `RealVector`.
`static void`	`solveLowerTriangularSystem(RealMatrix rm, RealVector b)` Solve a system of composed of a Lower Triangular Matrix `RealMatrix`.
`static void`	`solveUpperTriangularSystem(RealMatrix rm, RealVector b)` Solver a system composed of an Upper Triangular Matrix `RealMatrix`.

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

- Field Detail
  - DEFAULT_FORMAT
```
public static final RealMatrixFormat DEFAULT_FORMAT
```
    The default format for RealMatrix objects.
  - OCTAVE_FORMAT
```
public static final RealMatrixFormat OCTAVE_FORMAT
```
    A format for RealMatrix objects compatible with octave.
- 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
    
    See Also:
    
    createFieldMatrix(FieldElement[][])
  - createRealMatrix
```
public static RealMatrix createRealMatrix(double[][] data)
                                   throws MathIllegalArgumentException,
                                          NullArgumentException
```
    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:
    
    MathIllegalArgumentException - if data is not rectangular (not all rows have the same length).
    
    MathIllegalArgumentException - if a row or column is empty.
    
    NullArgumentException - if either data or data[0] is null.
    
    MathIllegalArgumentException - if data is not rectangular.
    
    See Also:
    
    createRealMatrix(int, int)
  - createFieldMatrix
```
public static <T extends FieldElement<T>> FieldMatrix<T> createFieldMatrix(T[][] data)
                                                                    throws MathIllegalArgumentException,
                                                                           NullArgumentException
```
    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:
    
    a matrix containing the values of the array.
    
    Throws:
    
    MathIllegalArgumentException - if data is not rectangular (not all rows have the same length).
    
    MathIllegalArgumentException - if a row or column is empty.
    
    NullArgumentException - if either data or data[0] is null.
    
    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:
    
    IllegalArgumentException - if dimension is not positive
  - 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:
    
    IllegalArgumentException - if dimension is not positive
  - 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
  - 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
  - createRealVector
```
public static RealVector createRealVector(double[] data)
                                   throws MathIllegalArgumentException,
                                          NullArgumentException
```
    Creates a RealVector using the data from the input array.
    
    Parameters:
    
    data - the input data
    
    Returns:
    
    a data.length RealVector
    
    Throws:
    
    MathIllegalArgumentException - if data is empty.
    
    NullArgumentException - if data is null.
  - createRealVector
```
public static RealVector createRealVector(int dimension)
```
    Creates a RealVector with specified dimensions.
    
    Parameters:
    
    dimension - dimension of the vector
    
    Returns:
    
    a new vector
    
    Since:
    
    1.3
  - createFieldVector
```
public static <T extends FieldElement<T>> FieldVector<T> createFieldVector(T[] data)
                                                                    throws MathIllegalArgumentException,
                                                                           NullArgumentException
```
    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:
    
    MathIllegalArgumentException - if data is empty.
    
    NullArgumentException - if data is null.
    
    MathIllegalArgumentException - if data has 0 elements
  - createFieldVector
```
public static <T extends FieldElement<T>> FieldVector<T> createFieldVector(Field<T> field,
                                                                           int dimension)
```
    Creates a FieldVector with specified dimensions.
    
    Type Parameters:
    
    T - the type of the field elements
    
    Parameters:
    
    field - field to which array elements belong
    
    dimension - dimension of the vector
    
    Returns:
    
    a new vector
    
    Since:
    
    1.3
  - createRowRealMatrix
```
public static RealMatrix createRowRealMatrix(double[] rowData)
                                      throws MathIllegalArgumentException,
                                             NullArgumentException
```
    Create a row RealMatrix using the data from the input array.
    
    Parameters:
    
    rowData - the input row data
    
    Returns:
    
    a 1 x rowData.length RealMatrix
    
    Throws:
    
    MathIllegalArgumentException - if rowData is empty.
    
    NullArgumentException - if rowData is null.
  - createRowFieldMatrix
```
public static <T extends FieldElement<T>> FieldMatrix<T> createRowFieldMatrix(T[] rowData)
                                                                       throws MathIllegalArgumentException,
                                                                              NullArgumentException
```
    Create 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:
    
    MathIllegalArgumentException - if rowData is empty.
    
    NullArgumentException - if rowData is null.
  - createColumnRealMatrix
```
public static RealMatrix createColumnRealMatrix(double[] columnData)
                                         throws MathIllegalArgumentException,
                                                NullArgumentException
```
    Creates a column RealMatrix using the data from the input array.
    
    Parameters:
    
    columnData - the input column data
    
    Returns:
    
    a columnData x 1 RealMatrix
    
    Throws:
    
    MathIllegalArgumentException - if columnData is empty.
    
    NullArgumentException - if columnData is null.
  - createColumnFieldMatrix
```
public static <T extends FieldElement<T>> FieldMatrix<T> createColumnFieldMatrix(T[] columnData)
                                                                          throws MathIllegalArgumentException,
                                                                                 NullArgumentException
```
    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:
    
    MathIllegalArgumentException - if data is empty.
    
    NullArgumentException - if columnData is null.
  - checkSymmetric
```
public static void checkSymmetric(RealMatrix matrix,
                                  double eps)
```
    Checks whether a matrix is symmetric.
    
    Parameters:
    
    matrix - Matrix to check.
    
    eps - Relative tolerance.
    
    Throws:
    
    MathIllegalArgumentException - if the matrix is not square.
    
    MathIllegalArgumentException - if the matrix is not symmetric.
  - isSymmetric
```
public static boolean isSymmetric(RealMatrix matrix,
                                  double eps)
```
    Checks whether a matrix is symmetric.
    
    Parameters:
    
    matrix - Matrix to check.
    
    eps - Relative tolerance.
    
    Returns:
    
    true if matrix is symmetric.
  - checkMatrixIndex
```
public static void checkMatrixIndex(AnyMatrix m,
                                    int row,
                                    int column)
                             throws MathIllegalArgumentException
```
    Check if matrix indices are valid.
    
    Parameters:
    
    m - Matrix.
    
    row - Row index to check.
    
    column - Column index to check.
    
    Throws:
    
    MathIllegalArgumentException - if row or column is not a valid index.
  - checkRowIndex
```
public static void checkRowIndex(AnyMatrix m,
                                 int row)
                          throws MathIllegalArgumentException
```
    Check if a row index is valid.
    
    Parameters:
    
    m - Matrix.
    
    row - Row index to check.
    
    Throws:
    
    MathIllegalArgumentException - if row is not a valid index.
  - checkColumnIndex
```
public static void checkColumnIndex(AnyMatrix m,
                                    int column)
                             throws MathIllegalArgumentException
```
    Check if a column index is valid.
    
    Parameters:
    
    m - Matrix.
    
    column - Column index to check.
    
    Throws:
    
    MathIllegalArgumentException - if column is not a valid index.
  - checkSubMatrixIndex
```
public static void checkSubMatrixIndex(AnyMatrix m,
                                       int startRow,
                                       int endRow,
                                       int startColumn,
                                       int endColumn)
                                throws MathIllegalArgumentException
```
    Check if submatrix ranges indices are valid. Rows and columns are indicated counting from 0 to n - 1.
    
    Parameters:
    
    m - Matrix.
    
    startRow - Initial row index.
    
    endRow - Final row index.
    
    startColumn - Initial column index.
    
    endColumn - Final column index.
    
    Throws:
    
    MathIllegalArgumentException - if the indices are invalid.
    
    MathIllegalArgumentException - if endRow < startRow or endColumn < startColumn.
  - checkSubMatrixIndex
```
public static void checkSubMatrixIndex(AnyMatrix m,
                                       int[] selectedRows,
                                       int[] selectedColumns)
                                throws MathIllegalArgumentException,
                                       NullArgumentException
```
    Check if submatrix ranges indices are valid. Rows and columns are indicated counting from 0 to n-1.
    
    Parameters:
    
    m - Matrix.
    
    selectedRows - Array of row indices.
    
    selectedColumns - Array of column indices.
    
    Throws:
    
    NullArgumentException - if selectedRows or selectedColumns are null.
    
    MathIllegalArgumentException - if the row or column selections are empty (zero length).
    
    MathIllegalArgumentException - if row or column selections are not valid.
  - checkAdditionCompatible
```
public static void checkAdditionCompatible(AnyMatrix left,
                                           AnyMatrix right)
                                    throws MathIllegalArgumentException
```
    Check if matrices are addition compatible.
    
    Parameters:
    
    left - Left hand side matrix.
    
    right - Right hand side matrix.
    
    Throws:
    
    MathIllegalArgumentException - if the matrices are not addition compatible.
  - checkSubtractionCompatible
```
public static void checkSubtractionCompatible(AnyMatrix left,
                                              AnyMatrix right)
                                       throws MathIllegalArgumentException
```
    Check if matrices are subtraction compatible
    
    Parameters:
    
    left - Left hand side matrix.
    
    right - Right hand side matrix.
    
    Throws:
    
    MathIllegalArgumentException - if the matrices are not addition compatible.
  - checkMultiplicationCompatible
```
public static void checkMultiplicationCompatible(AnyMatrix left,
                                                 AnyMatrix right)
                                          throws MathIllegalArgumentException
```
    Check if matrices are multiplication compatible
    
    Parameters:
    
    left - Left hand side matrix.
    
    right - Right hand side matrix.
    
    Throws:
    
    MathIllegalArgumentException - if matrices are not multiplication compatible.
  - checkSameColumnDimension
```
public static void checkSameColumnDimension(AnyMatrix left,
                                            AnyMatrix right)
                                     throws MathIllegalArgumentException
```
    Check if matrices have the same number of columns.
    
    Parameters:
    
    left - Left hand side matrix.
    
    right - Right hand side matrix.
    
    Throws:
    
    MathIllegalArgumentException - if matrices don't have the same number of columns.
    
    Since:
    
    1.3
  - checkSameRowDimension
```
public static void checkSameRowDimension(AnyMatrix left,
                                         AnyMatrix right)
                                  throws MathIllegalArgumentException
```
    Check if matrices have the same number of rows.
    
    Parameters:
    
    left - Left hand side matrix.
    
    right - Right hand side matrix.
    
    Throws:
    
    MathIllegalArgumentException - if matrices don't have the same number of rows.
    
    Since:
    
    1.3
  - fractionMatrixToRealMatrix
```
public static Array2DRowRealMatrix fractionMatrixToRealMatrix(FieldMatrix<Fraction> m)
```
    Convert a FieldMatrix/Fraction matrix to a RealMatrix.
    
    Parameters:
    
    m - Matrix to convert.
    
    Returns:
    
    the converted matrix.
  - bigFractionMatrixToRealMatrix
```
public static Array2DRowRealMatrix bigFractionMatrixToRealMatrix(FieldMatrix<BigFraction> m)
```
    Convert a FieldMatrix/BigFraction matrix to a RealMatrix.
    
    Parameters:
    
    m - Matrix to convert.
    
    Returns:
    
    the converted matrix.
  - serializeRealVector
```
public static void serializeRealVector(RealVector vector,
                                       ObjectOutputStream oos)
                                throws 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:
    
    IOException - if object cannot be written to stream
    
    See Also:
    
    deserializeRealVector(Object, String, ObjectInputStream)
  - deserializeRealVector
```
public static void deserializeRealVector(Object instance,
                                         String fieldName,
                                         ObjectInputStream ois)
                                  throws ClassNotFoundException,
                                         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:
    
    ClassNotFoundException - if a class in the stream cannot be found
    
    IOException - if object cannot be read from the stream
    
    See Also:
    
    serializeRealVector(RealVector, ObjectOutputStream)
  - serializeRealMatrix
```
public static void serializeRealMatrix(RealMatrix matrix,
                                       ObjectOutputStream oos)
                                throws 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:
    
    IOException - if object cannot be written to stream
    
    See Also:
    
    deserializeRealMatrix(Object, String, ObjectInputStream)
  - deserializeRealMatrix
```
public static void deserializeRealMatrix(Object instance,
                                         String fieldName,
                                         ObjectInputStream ois)
                                  throws ClassNotFoundException,
                                         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:
    
    ClassNotFoundException - if a class in the stream cannot be found
    
    IOException - if object cannot be read from the stream
    
    See Also:
    
    serializeRealMatrix(RealMatrix, ObjectOutputStream)
  - solveLowerTriangularSystem
```
public static void solveLowerTriangularSystem(RealMatrix rm,
                                              RealVector b)
                                       throws MathIllegalArgumentException,
                                              MathRuntimeException
```
    Solve a system of composed of a Lower Triangular Matrix RealMatrix.
    This method is called to solve systems of equations which are of the lower triangular form. The matrix RealMatrix is assumed, though not checked, to be in lower triangular form. The vector RealVector is overwritten with the solution. The matrix is checked that it is square and its dimensions match the length of the vector.
    
    Parameters:
    
    rm - RealMatrix which is lower triangular
    
    b - RealVector this is overwritten
    
    Throws:
    
    MathIllegalArgumentException - if the matrix and vector are not conformable
    
    MathIllegalArgumentException - if the matrix rm is not square
    
    MathRuntimeException - if the absolute value of one of the diagonal coefficient of rm is lower than Precision.SAFE_MIN
  - solveUpperTriangularSystem
```
public static void solveUpperTriangularSystem(RealMatrix rm,
                                              RealVector b)
                                       throws MathIllegalArgumentException,
                                              MathRuntimeException
```
    Solver a system composed of an Upper Triangular Matrix RealMatrix.
    This method is called to solve systems of equations which are of the lower triangular form. The matrix RealMatrix is assumed, though not checked, to be in upper triangular form. The vector RealVector is overwritten with the solution. The matrix is checked that it is square and its dimensions match the length of the vector.
    
    Parameters:
    
    rm - RealMatrix which is upper triangular
    
    b - RealVector this is overwritten
    
    Throws:
    
    MathIllegalArgumentException - if the matrix and vector are not conformable
    
    MathIllegalArgumentException - if the matrix rm is not square
    
    MathRuntimeException - if the absolute value of one of the diagonal coefficient of rm is lower than Precision.SAFE_MIN
  - blockInverse
```
public static RealMatrix blockInverse(RealMatrix m,
                                      int splitIndex)
```
    Computes the inverse of the given matrix by splitting it into 4 sub-matrices.
    
    Parameters:
    
    m - Matrix whose inverse must be computed.
    
    splitIndex - Index that determines the "split" line and column. The element corresponding to this index will part of the upper-left sub-matrix.
    
    Returns:
    
    the inverse of m.
    
    Throws:
    
    MathIllegalArgumentException - if m is not square.
  - inverse
```
public static RealMatrix inverse(RealMatrix matrix)
                          throws MathIllegalArgumentException,
                                 NullArgumentException
```
    Computes the inverse of the given matrix.
    By default, the inverse of the matrix is computed using the QR-decomposition, unless a more efficient method can be determined for the input matrix.
    Note: this method will use a singularity threshold of 0, use inverse(RealMatrix, double) if a different threshold is needed.
    
    Parameters:
    
    matrix - Matrix whose inverse shall be computed
    
    Returns:
    
    the inverse of matrix
    
    Throws:
    
    NullArgumentException - if matrix is null
    
    MathIllegalArgumentException - if m is singular
    
    MathIllegalArgumentException - if matrix is not square
  - inverse
```
public static RealMatrix inverse(RealMatrix matrix,
                                 double threshold)
                          throws MathIllegalArgumentException,
                                 NullArgumentException
```
    Computes the inverse of the given matrix.
    By default, the inverse of the matrix is computed using the QR-decomposition, unless a more efficient method can be determined for the input matrix.
    
    Parameters:
    
    matrix - Matrix whose inverse shall be computed
    
    threshold - Singularity threshold
    
    Returns:
    
    the inverse of m
    
    Throws:
    
    NullArgumentException - if matrix is null
    
    MathIllegalArgumentException - if matrix is singular
    
    MathIllegalArgumentException - if matrix is not square
  - matrixExponential
```
public static RealMatrix matrixExponential(RealMatrix rm)
```
    Computes the matrix exponential of the given matrix. The algorithm implementation follows the Pade approximant method of
    Higham, Nicholas J. “The Scaling and Squaring Method for the Matrix Exponential Revisited.” SIAM Journal on Matrix Analysis and Applications 26, no. 4 (January 2005): 1179–93.
    
    Parameters:
    
    rm - RealMatrix whose inverse shall be computed
    
    Returns:
    
    The inverse of rm
    
    Throws:
    
    MathIllegalArgumentException - if matrix is not square
  - orthonormalize
```
public static List<RealVector> orthonormalize(List<RealVector> independent,
                                              double threshold,
                                              DependentVectorsHandler handler)
```
    Orthonormalize a list of vectors.
    Orthonormalization is performed by using the Modified Gram-Schmidt process.
    
    Parameters:
    
    independent - list of independent vectors
    
    threshold - projected vectors with a norm less than or equal to this threshold are considered to have zero norm, hence the vectors they come from are not independent from previous vectors
    
    handler - handler for dependent vectors
    
    Returns:
    
    orthonormal basis having the same span as independent
    
    Since:
    
    2.1
  - orthonormalize
```
public static <T extends CalculusFieldElement<T>> List<FieldVector<T>> orthonormalize(Field<T> field,
                                                                                      List<FieldVector<T>> independent,
                                                                                      T threshold,
                                                                                      DependentVectorsHandler handler)
```
    Orthonormalize a list of vectors.
    Orthonormalization is performed by using the Modified Gram-Schmidt process.
    
    Type Parameters:
    
    T - type of the field elements
    
    Parameters:
    
    independent - list of independent vectors
    
    threshold - projected vectors with a norm less than or equal to this threshold are considered to have zero norm, hence the vectors they come from are not independent from previous vectors
    
    field - type of the files elements
    
    handler - handler for dependent vectors
    
    Returns:
    
    orthonormal basis having the same span as independent
    
    Since:
    
    2.1

Class MatrixUtils

Field Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

DEFAULT_FORMAT

OCTAVE_FORMAT

Method Detail

createRealMatrix

createFieldMatrix

createRealMatrix

createFieldMatrix

createRealIdentityMatrix

createFieldIdentityMatrix

createRealDiagonalMatrix

createFieldDiagonalMatrix

createRealVector

createRealVector

createFieldVector

createFieldVector

createRowRealMatrix

createRowFieldMatrix

createColumnRealMatrix

createColumnFieldMatrix

checkSymmetric

isSymmetric

checkMatrixIndex

checkRowIndex

checkColumnIndex

checkSubMatrixIndex

checkSubMatrixIndex

checkAdditionCompatible

checkSubtractionCompatible

checkMultiplicationCompatible

checkSameColumnDimension

checkSameRowDimension

fractionMatrixToRealMatrix

bigFractionMatrixToRealMatrix

serializeRealVector

deserializeRealVector

serializeRealMatrix

deserializeRealMatrix

solveLowerTriangularSystem

solveUpperTriangularSystem

blockInverse

inverse

inverse

matrixExponential

orthonormalize

orthonormalize