SparseMatrix
org.jscience.mathematics.vector

Class SparseMatrix<F extends Field<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>


    public final class SparseMatrix<F extends Field<F>>extends Matrix<F>

    This class represents a matrix made of sparse vectors (as rows). To create a sparse matrix made of column vectors the transpose() method can be used. For example:

            SparseVector<Rational> column0 = SparseVector.valueOf(...);        SparseVector<Rational> column1 = SparseVector.valueOf(...);        SparseMatrix<Rational> M = SparseMatrix.valueOf(column0, column1).transpose();     

    As for any concrete structure, this class is declared final (otherwise most operations would have to be overridden to return the appropriate type). Specialized dense matrix should sub-class Matrix directly. For example:

            // Extension through composition.        final class BandMatrix <F extends Field<F>> extends Matrix<F> {             private SparseMatrix<F> _value;             ...             public BandMatrix opposite() { // Returns the right type.                 return BandMatrix.valueOf(_value.opposite());             }             ...        }

    • Method Detail

      • valueOf

        public static <F extends Field<F>> SparseMatrix<F> valueOf(Vector<F> diagonal,                                           F zero)
        Returns the sparse square matrix having the specified diagonal vector. This method is typically used to create an identity matrix. For example:
              SparseMatrix<Real> IDENTITY = Matrix.valueOf(           DenseVector.valueOf({Real.ONE, Real.ONE, Real.ONE}), Real.ZERO); 
        Parameters:
        diagonal - the diagonal vector.
        zero - value of non-diagonal elements.
        Returns:
        a square matrix with diagonal on the diagonal and zero elsewhere.
      • valueOf

        public static <F extends Field<F>> SparseMatrix<F> valueOf(SparseVector<F>... rows)
        Returns a sparse matrix holding the specified row vectors (column vectors if transposed).
        Parameters:
        rows - the row vectors.
        Returns:
        the matrix having the specified rows.
        Throws:
        DimensionException - if the rows do not have the same dimension.
      • valueOf

        public static <F extends Field<F>> SparseMatrix<F> valueOf(List<SparseVector<F>> rows)
        Returns a sparse matrix holding the row vectors from the specified collection (column vectors if transposed).
        Parameters:
        rows - the list of row vectors.
        Returns:
        the matrix having the specified rows.
        Throws:
        DimensionException - if the rows do not have the same dimension.
      • valueOf

        public static <F extends Field<F>> SparseMatrix<F> valueOf(Matrix<F> that,                                           F zero)
        Returns a sparse matrix equivalent to the specified matrix but with the zero elements removed using the default object equality comparator.
        Parameters:
        that - the matrix to convert.
        zero - the zero element for the sparse vector to return.
        Returns:
        SparseMatrix.valueOf(that, zero, FastComparator.DEFAULT) or a dense matrix holding the same elements
      • valueOf

        public static <F extends Field<F>> SparseMatrix<F> valueOf(Matrix<F> that,                                           F zero,                                           javolution.util.FastComparator<? super F> comparator)
        Returns a sparse matrix equivalent to the specified matrix but with the zero elements removed using the specified object equality comparator.
        Parameters:
        that - the matrix to convert.
        zero - the zero element for the sparse vector to return.
        comparator - the comparator used to determinate zero equality.
        Returns:
        that or a dense matrix holding the same elements as the specified matrix.
      • getZero

        public F getZero()
        Returns the value of the non-set elements for this sparse matrix.
        Returns:
        the element corresponding to zero.
      • getNumberOfRows

        public int getNumberOfRows()
        Description copied from class: Matrix
        Returns the number of rows m for this matrix.
        Specified by:
        getNumberOfRows in class Matrix<F extends Field<F>>
        Returns:
        m, the number of rows.
      • getNumberOfColumns

        public int getNumberOfColumns()
        Description copied from class: Matrix
        Returns the number of columns n for this matrix.
        Specified by:
        getNumberOfColumns in class Matrix<F extends Field<F>>
        Returns:
        n, the number of columns.
      • get

        public F get(int i,    int j)
        Description copied from class: Matrix
        Returns a single element from this matrix.
        Specified by:
        get in class Matrix<F extends Field<F>>
        Parameters:
        i - the row index (range [0..m[).
        j - the column index (range [0..n[).
        Returns:
        the element read at [i,j].
      • getRow

        public SparseVector<F> getRow(int i)
        Description copied from class: Matrix
        Returns the row identified by the specified index in this matrix.
        Specified by:
        getRow in class Matrix<F extends Field<F>>
        Parameters:
        i - the row index (range [0..m[).
        Returns:
        the vector holding the specified row.
      • getColumn

        public SparseVector<F> getColumn(int j)
        Description copied from class: Matrix
        Returns the column identified by the specified index in this matrix.
        Specified by:
        getColumn in class Matrix<F extends Field<F>>
        Parameters:
        j - the column index (range [0..n[).
        Returns:
        the vector holding the specified column.
      • getDiagonal

        public SparseVector<F> getDiagonal()
        Description copied from class: Matrix
        Returns the diagonal vector.
        Specified by:
        getDiagonal in class Matrix<F extends Field<F>>
        Returns:
        the vector holding the diagonal elements.
      • minus

        public SparseMatrix<F> minus(Matrix<F> that)
        Description copied from class: Matrix
        Returns the difference between this matrix and the one specified.
        Overrides:
        minus in class Matrix<F extends Field<F>>
        Parameters:
        that - the matrix to be subtracted.
        Returns:
        this - that.
      • times

        public SparseVector<F> times(Vector<F> v)
        Description copied from class: Matrix
        Returns the product of this matrix by the specified vector.
        Specified by:
        times in class Matrix<F extends Field<F>>
        Parameters:
        v - the vector.
        Returns:
        this \xc2\xb7 v
      • times

        public SparseMatrix<F> times(Matrix<F> that)
        Description copied from class: Matrix
        Returns the product of this matrix with the one specified.
        Specified by:
        times in interface Ring<Matrix<F extends Field<F>>>
        Specified by:
        times in class Matrix<F extends Field<F>>
        Parameters:
        that - the matrix multiplier.
        Returns:
        this \xc2\xb7 that.
      • inverse

        public SparseMatrix<F> inverse()
        Description copied from class: Matrix
        Returns the inverse of this matrix (must be square).
        Specified by:
        inverse in class Matrix<F extends Field<F>>
        Returns:
        1 / this
      • determinant

        public F determinant()
        Description copied from class: Matrix
        Returns the determinant of this matrix.
        Specified by:
        determinant in class Matrix<F extends Field<F>>
        Returns:
        this matrix determinant.
      • solve

        public Matrix<F> solve(Matrix<F> y)
        Description copied from class: Matrix
        Solves this matrix for the specified matrix (returns x such as this \xc2\xb7 x = y).
        Overrides:
        solve in class Matrix<F extends Field<F>>
        Parameters:
        y - the matrix for which the solution is calculated.
        Returns:
        x such as this \xc2\xb7 x = y
      • cofactor

        public F cofactor(int i,         int j)
        Description copied from class: Matrix
        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.
        Specified by:
        cofactor in class Matrix<F extends Field<F>>
        Parameters:
        i - the row index.
        j - the column index.
        Returns:
        the cofactor of THIS[i,j].
      • adjoint

        public SparseMatrix<F> adjoint()
        Description copied from class: Matrix
        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.
        Specified by:
        adjoint in class Matrix<F extends Field<F>>
        Returns:
        the adjoint of this matrix.
      • vectorization

        public SparseVector<F> vectorization()
        Description copied from class: Matrix
        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.
        Specified by:
        vectorization in class Matrix<F extends Field<F>>
        Returns:
        the vectorization of this matrix.
        See Also:
        Wikipedia: Vectorization.
      • copy

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

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