Package org.apache.commons.math3.linear

Class MatrixUtils

java.lang.Object

org.apache.commons.math3.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	Description
static final RealMatrixFormat	DEFAULT_FORMAT	The default format for RealMatrix objects.
static final RealMatrixFormat	OCTAVE_FORMAT	A format for RealMatrix objects compatible with octave.

Method Summary

Modifier and Type	Method	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	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(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 <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 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 Details

DEFAULT_FORMAT

public static final RealMatrixFormat DEFAULT_FORMAT

The default format for RealMatrix objects.

Since:

3.1

OCTAVE_FORMAT

public static final RealMatrixFormat OCTAVE_FORMAT

A format for RealMatrix objects compatible with octave.

Since:

3.1

Method Details

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)
                                   throws NullArgumentException,
DimensionMismatchException,
NoDataException

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:

DimensionMismatchException - if data is not rectangular (not all rows have the same length).

NoDataException - if a row or column is empty.

NullArgumentException - if either data or data[0] is null.

DimensionMismatchException - if data is not rectangular.

See Also:

• createRealMatrix(int, int)

createFieldMatrix

public static <T extends FieldElement<T>>
FieldMatrix<T> createFieldMatrix(T[][] data)
                          throws DimensionMismatchException,
NoDataException,
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:

DimensionMismatchException - if data is not rectangular (not all rows have the same length).

NoDataException - if a row or column is empty.

NullArgumentException - 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:

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:

IllegalArgumentException - if dimension is not positive

Since:

2.0

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

createRealVector

public static RealVector createRealVector(double[] data)
                                   throws NoDataException,
NullArgumentException

Creates a RealVector using the data from the input array.

Parameters:

data - the input data

Returns:

a data.length RealVector

Throws:

NoDataException - if data is empty.

NullArgumentException - if data is null.

createFieldVector

public static <T extends FieldElement<T>>
FieldVector<T> createFieldVector(T[] data)
                          throws NoDataException,
NullArgumentException,
ZeroException

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:

NoDataException - if data is empty.

NullArgumentException - if data is null.

ZeroException - if data has 0 elements

createRowRealMatrix

public static RealMatrix createRowRealMatrix(double[] rowData)
                                      throws NoDataException,
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:

NoDataException - if rowData is empty.

NullArgumentException - if rowData is null.

createRowFieldMatrix

public static <T extends FieldElement<T>>
FieldMatrix<T> createRowFieldMatrix(T[] rowData)
                             throws NoDataException,
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:

NoDataException - if rowData is empty.

NullArgumentException - if rowData is null.

createColumnRealMatrix

public static RealMatrix createColumnRealMatrix(double[] columnData)
                                         throws NoDataException,
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:

NoDataException - if columnData is empty.

NullArgumentException - if columnData is null.

createColumnFieldMatrix

public static <T extends FieldElement<T>>
FieldMatrix<T> createColumnFieldMatrix(T[] columnData)
                                throws NoDataException,
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:

NoDataException - 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:

NonSquareMatrixException - if the matrix is not square.

NonSymmetricMatrixException - if the matrix is not symmetric.

Since:

3.1

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.

Since:

3.1

checkMatrixIndex

public static void checkMatrixIndex(AnyMatrix m,
 int row,
 int column)
                             throws OutOfRangeException

Check if matrix indices are valid.

Parameters:

m - Matrix.

row - Row index to check.

column - Column index to check.

Throws:

OutOfRangeException - if row or column is not a valid index.

checkRowIndex

public static void checkRowIndex(AnyMatrix m,
 int row)
                          throws OutOfRangeException

Check if a row index is valid.

Parameters:

m - Matrix.

row - Row index to check.

Throws:

OutOfRangeException - if row is not a valid index.

checkColumnIndex

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

Check if a column index is valid.

Parameters:

m - Matrix.

column - Column index to check.

Throws:

OutOfRangeException - if column is not a valid index.

checkSubMatrixIndex

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

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:

OutOfRangeException - if the indices are invalid.

NumberIsTooSmallException - if endRow < startRow or endColumn < startColumn.

checkSubMatrixIndex

public static void checkSubMatrixIndex(AnyMatrix m,
 int[] selectedRows,
 int[] selectedColumns)
                                throws NoDataException,
NullArgumentException,
OutOfRangeException

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.

NoDataException - if the row or column selections are empty (zero length).

OutOfRangeException - if row or column selections are not valid.

checkAdditionCompatible

public static void checkAdditionCompatible(AnyMatrix left,
 AnyMatrix right)
                                    throws MatrixDimensionMismatchException

Check if matrices are addition compatible.

Parameters:

left - Left hand side matrix.

right - Right hand side matrix.

Throws:

MatrixDimensionMismatchException - if the matrices are not addition compatible.

checkSubtractionCompatible

public static void checkSubtractionCompatible(AnyMatrix left,
 AnyMatrix right)
                                       throws MatrixDimensionMismatchException

Check if matrices are subtraction compatible

Parameters:

left - Left hand side matrix.

right - Right hand side matrix.

Throws:

MatrixDimensionMismatchException - if the matrices are not addition compatible.

checkMultiplicationCompatible

public static void checkMultiplicationCompatible(AnyMatrix left,
 AnyMatrix right)
                                          throws DimensionMismatchException

Check if matrices are multiplication compatible

Parameters:

left - Left hand side matrix.

right - Right hand side matrix.

Throws:

DimensionMismatchException - 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:

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 DimensionMismatchException,
MathArithmeticException,
NonSquareMatrixException

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:

DimensionMismatchException - if the matrix and vector are not conformable

NonSquareMatrixException - if the matrix rm is not square

MathArithmeticException - 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 DimensionMismatchException,
MathArithmeticException,
NonSquareMatrixException

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:

DimensionMismatchException - if the matrix and vector are not conformable

NonSquareMatrixException - if the matrix rm is not square

MathArithmeticException - 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:

NonSquareMatrixException - if m is not square.

inverse

public static RealMatrix inverse(RealMatrix matrix)
                          throws NullArgumentException,
SingularMatrixException,
NonSquareMatrixException

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

SingularMatrixException - if m is singular

NonSquareMatrixException - if matrix is not square

Since:

3.3

inverse

public static RealMatrix inverse(RealMatrix matrix,
 double threshold)
                          throws NullArgumentException,
SingularMatrixException,
NonSquareMatrixException

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

SingularMatrixException - if matrix is singular

NonSquareMatrixException - if matrix is not square

Since:

3.3