Package org.jscience.mathematics.vector

Class Matrix<F extends Field<F>>

java.lang.Object
org.jscience.mathematics.vector.Matrix<F>
All Implemented Interfaces:
javolution.lang.Immutable, javolution.lang.Realtime, javolution.lang.ValueType, GroupAdditive<Matrix<F>>, Ring<Matrix<F>>, Structure<Matrix<F>>, VectorSpace<Matrix<F>,F>
Direct Known Subclasses:
ComplexMatrix, DenseMatrix, Float64Matrix, SparseMatrix
public abstract class Matrix<F extends Field<F>> extends Object implements VectorSpace<Matrix<F>,F>, Ring<Matrix<F>>, javolution.lang.ValueType, javolution.lang.Realtime

This class represents a rectangular table of elements of a ring-like algebraic structure.

Instances of this class can be used to resolve system of linear equations involving any kind of Field elements (e.g. Real, Complex, Amount<?>, Function, etc). For example:[code] // Creates a dense matrix (2x2) of Rational numbers. DenseMatrix M = DenseMatrix.valueOf( { Rational.valueOf(23, 45), Rational.valueOf(33, 75) }, { Rational.valueOf(15, 31), Rational.valueOf(-20, 45)}); // Creates a sparse matrix (16x2) of Real numbers. SparseMatrix M = SparseMatrix.valueOf( SparseVector.valueOf(16, Real.ZERO, 0, Real.valueOf(5)), SparseVector.valueOf(16, Real.ZERO, 15, Real.valueOf(-3))); // Creates a floating-point (64 bits) matrix (3x2). Float64Matrix M = Float64Matrix.valueOf( {{ 1.0, 2.0, 3.0}, { 4.0, 5.0, 6.0}}); // Creates a complex single column matrix (1x2). ComplexMatrix M = ComplexMatrix.valueOf( {{ Complex.valueOf(1.0, 2.0), Complex.valueOf(4.0, 5.0)}}).transpose(); // Creates an identity matrix (2x2) for modulo integer. SparseMatrix IDENTITY = SparseMatrix.valueOf( DenseVector.valueOf(ModuloInteger.ONE, ModuloInteger.ONE), ModuloInteger.ZERO); [/code]

Non-commutative field multiplication is supported. Invertible square matrices may form a non-commutative field (also called a division ring). In which case this class may be used to resolve system of linear equations with matrix coefficients.

Implementation Note: Matrices may use StackContext and ConcurrentContext in order to minimize heap allocation and accelerate calculations on multi-core systems.

See Also:

  • Field Summary

    Fields
    Modifier and Type
    Field
    Description
    protected static final javolution.xml.XMLFormat<Matrix>
    XML
    Holds the default XML representation for matrices.

  • Constructor Summary

    Constructors
    Modifier
    Constructor
    Description
    protected
    Matrix()
    Default constructor (for sub-classes).

  • Method Summary

    Modifier and Type
    Method
    Description
    abstract Matrix<F>
    adjoint()
    Returns the adjoint of this matrix.
    abstract F
    cofactor(int i, int j)
    Returns the cofactor of an element in this matrix.
    abstract Matrix<F>
    copy()
    Returns a copy of this matrix allocated by the calling thread (possibly on the stack).
    abstract F
    determinant()
    Returns the determinant of this matrix.
    Matrix<F>
    divide(Matrix<F> that)
    Returns this matrix divided by the one specified.
    boolean
    equals(Object that)
    Indicates if this matrix is strictly equal to the object specified.
    boolean
    equals(Matrix<F> that, Comparator<F> cmp)
    Indicates if this matrix can be considered equals to the one specified using the specified comparator when testing for element equality.
    abstract F
    get(int i, int j)
    Returns a single element from this matrix.
    abstract Vector<F>
    getColumn(int j)
    Returns the column identified by the specified index in this matrix.
    abstract Vector<F>
    getDiagonal()
    Returns the diagonal vector.
    abstract int
    getNumberOfColumns()
    Returns the number of columns n for this matrix.
    abstract int
    getNumberOfRows()
    Returns the number of rows m for this matrix.
    abstract Vector<F>
    getRow(int i)
    Returns the row identified by the specified index in this matrix.
    int
    hashCode()
    Returns a hash code value for this matrix.
    abstract Matrix<F>
    inverse()
    Returns the inverse of this matrix (must be square).
    boolean
    isSquare()
    Indicates if this matrix is square.
    Matrix<F>
    minus(Matrix<F> that)
    Returns the difference between this matrix and the one specified.
    abstract Matrix<F>
    opposite()
    Returns the negation of this matrix.
    abstract Matrix<F>
    plus(Matrix<F> that)
    Returns the sum of this matrix with the one specified.
    Matrix<F>
    pow(int exp)
    Returns this matrix raised at the specified exponent.
    Matrix<F>
    pseudoInverse()
    Returns the inverse or pseudo-inverse if this matrix if not square.
    Matrix<F>
    solve(Matrix<F> y)
    Solves this matrix for the specified matrix (returns x such as this · x = y).
    Vector<F>
    solve(Vector<F> y)
    Solves this matrix for the specified vector (returns x such as this · x = y).
    abstract Matrix<F>
    tensor(Matrix<F> that)
    Returns the linear algebraic matrix tensor product of this matrix and another (Kronecker product).
    abstract Matrix<F>
    times(F k)
    Returns the product of this matrix by the specified factor.
    abstract Matrix<F>
    times(Matrix<F> that)
    Returns the product of this matrix with the one specified.
    abstract Vector<F>
    times(Vector<F> v)
    Returns the product of this matrix by the specified vector.
    final String
    toString()
    Returns the text representation of this matrix as a java.lang.String.
    javolution.text.Text
    toText()
    Returns the text representation of this matrix.
    F
    trace()
    Returns the trace of this matrix.
    abstract Matrix<F>
    transpose()
    Returns the transpose of this matrix.
    abstract Vector<F>
    vectorization()
    Returns the vectorization of this matrix.

    Methods inherited from class java.lang.Object

    clone, finalize, getClass, notify, notifyAll, wait, wait, wait

  • Field Details

    • XML

      protected static final javolution.xml.XMLFormat<Matrix> XML
      Holds the default XML representation for matrices. For example:[code] [/code]

  • Constructor Details

    • Matrix

      protected Matrix()
      Default constructor (for sub-classes).

  • Method Details

    • getNumberOfRows

      public abstract int getNumberOfRows()
      Returns the number of rows m for this matrix.
      Returns:
      m, the number of rows.

    • getNumberOfColumns

      public abstract int getNumberOfColumns()
      Returns the number of columns n for this matrix.
      Returns:
      n, the number of columns.

    • get

      public abstract F get(int i, int j)
      Returns a single element from this matrix.
      Parameters:
      i - the row index (range [0..m[).
      j - the column index (range [0..n[).
      Returns:
      the element read at [i,j].
      Throws:
      IndexOutOfBoundsException - ((i < 0) || (i >= m)) || ((j < 0) || (j >= n))

    • getRow

      public abstract Vector<F> getRow(int i)
      Returns the row identified by the specified index in this matrix.
      Parameters:
      i - the row index (range [0..m[).
      Returns:
      the vector holding the specified row.
      Throws:
      IndexOutOfBoundsException - (i < 0) || (i >= m)

    • getColumn

      public abstract Vector<F> getColumn(int j)
      Returns the column identified by the specified index in this matrix.
      Parameters:
      j - the column index (range [0..n[).
      Returns:
      the vector holding the specified column.
      Throws:
      IndexOutOfBoundsException - (j < 0) || (j >= n)

    • getDiagonal

      public abstract Vector<F> getDiagonal()
      Returns the diagonal vector.
      Returns:
      the vector holding the diagonal elements.

    • opposite

      public abstract Matrix<F> opposite()
      Returns the negation of this matrix.
      Specified by:
      opposite in interface GroupAdditive<F extends Field<F>>
      Returns:
      -this.

    • plus

      public abstract Matrix<F> plus(Matrix<F> that)
      Returns the sum of this matrix with the one specified.
      Specified by:
      plus in interface GroupAdditive<F extends Field<F>>
      Parameters:
      that - the matrix to be added.
      Returns:
      this + that.
      Throws:
      DimensionException - matrices's dimensions are different.

    • minus

      public Matrix<F> minus(Matrix<F> that)
      Returns the difference between this matrix and the one specified.
      Parameters:
      that - the matrix to be subtracted.
      Returns:
      this - that.
      Throws:
      DimensionException - matrices's dimensions are different.

    • times

      public abstract Matrix<F> times(F k)
      Returns the product of this matrix by the specified factor.
      Specified by:
      times in interface VectorSpace<Matrix<F extends Field<F>>,F extends Field<F>>
      Parameters:
      k - the coefficient multiplier.
      Returns:
      this · k

    • times

      public abstract Vector<F> times(Vector<F> v)
      Returns the product of this matrix by the specified vector.
      Parameters:
      v - the vector.
      Returns:
      this · v
      Throws:
      DimensionException - if v.getDimension() != this.getNumberOfColumns()

    • times

      public abstract Matrix<F> times(Matrix<F> that)
      Returns the product of this matrix with the one specified.
      Specified by:
      times in interface Ring<F extends Field<F>>
      Parameters:
      that - the matrix multiplier.
      Returns:
      this · that.
      Throws:
      DimensionException - if this.getNumberOfColumns() != that.getNumberOfRows().

    • inverse

      public abstract Matrix<F> inverse()
      Returns the inverse of this matrix (must be square).
      Returns:
      1 / this
      Throws:
      DimensionException - if this matrix is not square.

    • divide

      public Matrix<F> divide(Matrix<F> that)
      Returns this matrix divided by the one specified.
      Parameters:
      that - the matrix divisor.
      Returns:
      this / that.
      Throws:
      DimensionException - if that matrix is not square or dimensions do not match.

    • pseudoInverse

      public Matrix<F> pseudoInverse()
      Returns the inverse or pseudo-inverse if this matrix if not square.

      Note: To resolve the equation A * X = B, it is usually faster to calculate A.lu().solve(B) rather than A.inverse().times(B).

      Returns:
      the inverse or pseudo-inverse of this matrix.

    • determinant

      public abstract F determinant()
      Returns the determinant of this matrix.
      Returns:
      this matrix determinant.
      Throws:
      DimensionException - if this matrix is not square.

    • transpose

      public abstract Matrix<F> transpose()
      Returns the transpose of this matrix.
      Returns:
      A'.

    • cofactor

      public abstract F cofactor(int i, int j)
      Returns the cofactor of an element in this matrix. It is the value obtained by evaluating the determinant formed by the elements not in that particular row or column.
      Parameters:
      i - the row index.
      j - the column index.
      Returns:
      the cofactor of THIS[i,j].
      Throws:
      DimensionException - matrix is not square or its dimension is less than 2.

    • adjoint

      public abstract Matrix<F> adjoint()
      Returns the adjoint of this matrix. It is obtained by replacing each element in this matrix with its cofactor and applying a + or - sign according (-1)**(i+j), and then finding the transpose of the resulting matrix.
      Returns:
      the adjoint of this matrix.
      Throws:
      DimensionException - if this matrix is not square or if its dimension is less than 2.

    • isSquare

      public boolean isSquare()
      Indicates if this matrix is square.
      Returns:
      getNumberOfRows() == getNumberOfColumns()

    • solve

      public Vector<F> solve(Vector<F> y)
      Solves this matrix for the specified vector (returns x such as this · x = y).
      Parameters:
      y - the vector for which the solution is calculated.
      Returns:
      x such as this · x = y
      Throws:
      DimensionException - if that matrix is not square or dimensions do not match.

    • solve

      public Matrix<F> solve(Matrix<F> y)
      Solves this matrix for the specified matrix (returns x such as this · x = y).
      Parameters:
      y - the matrix for which the solution is calculated.
      Returns:
      x such as this · x = y
      Throws:
      DimensionException - if that matrix is not square or dimensions do not match.

    • pow

      public Matrix<F> pow(int exp)
      Returns this matrix raised at the specified exponent.
      Parameters:
      exp - the exponent.
      Returns:
      thisexp
      Throws:
      DimensionException - if this matrix is not square.

    • trace

      public F trace()
      Returns the trace of this matrix.
      Returns:
      the sum of the diagonal elements.

    • tensor

      public abstract Matrix<F> tensor(Matrix<F> that)
      Returns the linear algebraic matrix tensor product of this matrix and another (Kronecker product). The default implementation returns a DenseMatrix.
      Parameters:
      that - the second matrix.
      Returns:
      this ⊗ that
      See Also:

    • vectorization

      public abstract Vector<F> vectorization()
      Returns the vectorization of this matrix. The vectorization of a matrix is the column vector obtain by stacking the columns of the matrix on top of one another. The default implementation returns a DenseVector.
      Returns:
      the vectorization of this matrix.
      See Also:

    • toText

      public javolution.text.Text toText()
      Returns the text representation of this matrix.
      Specified by:
      toText in interface javolution.lang.Realtime
      Returns:
      the text representation of this matrix.

    • toString

      public final String toString()
      Returns the text representation of this matrix as a java.lang.String.
      Overrides:
      toString in class Object
      Returns:
      toText().toString()

    • equals

      public boolean equals(Matrix<F> that, Comparator<F> cmp)
      Indicates if this matrix can be considered equals to the one specified using the specified comparator when testing for element equality. The specified comparator may allow for some tolerance in the difference between the matrix elements.
      Parameters:
      that - the matrix to compare for equality.
      cmp - the comparator to use when testing for element equality.
      Returns:
      true if this matrix and the specified matrix are both matrices with equal elements according to the specified comparator; false otherwise.

    • equals

      public boolean equals(Object that)
      Indicates if this matrix is strictly equal to the object specified.
      Overrides:
      equals in class Object
      Parameters:
      that - the object to compare for equality.
      Returns:
      true if this matrix and the specified object are both matrices with equal elements; false otherwise.
      See Also:

    • hashCode

      public int hashCode()
      Returns a hash code value for this matrix. Equals objects have equal hash codes.
      Overrides:
      hashCode in class Object
      Returns:
      this matrix hash code value.
      See Also:

    • copy

      public abstract Matrix<F> copy()
      Returns a copy of this matrix allocated by the calling thread (possibly on the stack).
      Specified by:
      copy in interface javolution.lang.ValueType
      Returns:
      an identical and independant copy of this matrix.