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 Details

  • 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:

    • 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:

    • 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:

    • 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:

    • 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

      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:

    • 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

      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:

    • 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