Class BandMatrix

  • All Implemented Interfaces:
    java.lang.Iterable<MatrixEntry>, Matrix

    public class BandMatrix
    extends AbstractMatrix
    Banded matrix. The banded matrix is a useful sparse structure for many kinds of direct computations, however it should only be used if the band is sufficiently narrow as wide bands actually wastes both memory and compute time. The matrix

    a11 a12      
    a21 a22 a23    
    a31 a32 a33 a34  
      a42 a43 a44 a45
        a53 a54 a55

    has two lower diagonals and one upper diagonal. It will be stored in the array

      a11 a21 a31 a21 a22 a32 a42 a23 a33 a43 a53 a34 a44 a54   a45 a55    

    Empty cells are allocated, but never referenced.

    • Constructor Detail

      • BandMatrix

        public BandMatrix​(int n,
                          int kl,
                          int ku)
        Constructor for BandMatrix
        Parameters:
        n - Size of the matrix. Since the matrix must be square, this equals both the number of rows and columns
        kl - Number of bands above the main diagonal (superdiagonals)
        ku - Number of bands below the main diagonal (subdiagonals)
      • BandMatrix

        public BandMatrix​(Matrix A,
                          int kl,
                          int ku)
        Constructor for BandMatrix
        Parameters:
        A - Matrix to copy contents from. Only the parts of A that lie within the allocated band are copied over, the rest is ignored
        kl - Number of bands above the main diagonal (superdiagonals)
        ku - Number of bands below the main diagonal (subdiagonals)
      • BandMatrix

        public BandMatrix​(Matrix A,
                          int kl,
                          int ku,
                          boolean deep)
        Constructor for BandMatrix
        Parameters:
        A - Matrix to copy contents from. Only the parts of A that lie within the allocated band are copied over, the rest is ignored
        kl - Number of bands above the main diagonal (superdiagonals)
        ku - Number of bands below the main diagonal (subdiagonals)
        deep - True for a deep copy. For shallow copies, A must be a banded matrix
    • Method Detail

      • zero

        public Matrix zero()
        Description copied from interface: Matrix
        Zeros all the entries in the matrix, while preserving any underlying structure. Useful for general, unstructured matrices.
        Specified by:
        zero in interface Matrix
        Returns:
        A
      • multAdd

        public Vector multAdd​(double alpha,
                              Vector x,
                              Vector y)
        Description copied from interface: Matrix
        y = alpha*A*x + y
        Specified by:
        multAdd in interface Matrix
        Overrides:
        multAdd in class AbstractMatrix
        x - Vector of size A.numColumns()
        y - Vector of size A.numRows()
        Returns:
        y
      • solve

        public Matrix solve​(Matrix B,
                            Matrix X)
        Description copied from interface: Matrix
        X = A\B. Not all matrices support this operation, those that do not throw UnsupportedOperationException. Note that it is often more efficient to use a matrix decomposition and its associated solver
        Specified by:
        solve in interface Matrix
        Overrides:
        solve in class AbstractMatrix
        Parameters:
        B - Matrix with the same number of rows as A, and the same number of columns as X
        X - Matrix with a number of rows equal A.numColumns(), and the same number of columns as B
        Returns:
        X
      • solve

        public Vector solve​(Vector b,
                            Vector x)
        Description copied from interface: Matrix
        x = A\b. Not all matrices support this operation, those that do not throw UnsupportedOperationException. Note that it is often more efficient to use a matrix decomposition and its associated solver
        Specified by:
        solve in interface Matrix
        Overrides:
        solve in class AbstractMatrix
        Parameters:
        b - Vector of size A.numRows()
        x - Vector of size A.numColumns()
        Returns:
        x
      • transpose

        public Matrix transpose()
        Description copied from interface: Matrix
        Transposes the matrix in-place. In most cases, the matrix must be square for this to work.
        Specified by:
        transpose in interface Matrix
        Overrides:
        transpose in class AbstractMatrix
        Returns:
        This matrix
      • getData

        public double[] getData()
        Returns the matrix contents
      • add

        public void add​(int row,
                        int column,
                        double value)
        Description copied from interface: Matrix
        A(row,column) += value
        Specified by:
        add in interface Matrix
        Overrides:
        add in class AbstractMatrix
      • set

        public void set​(int row,
                        int column,
                        double value)
        Description copied from interface: Matrix
        A(row,column) = value
        Specified by:
        set in interface Matrix
        Overrides:
        set in class AbstractMatrix
      • get

        public double get​(int row,
                          int column)
        Description copied from interface: Matrix
        Returns A(row,column)
        Specified by:
        get in interface Matrix
        Overrides:
        get in class AbstractMatrix
      • numSubDiagonals

        public int numSubDiagonals()
        Returns the number of lower diagonals
      • numSuperDiagonals

        public int numSuperDiagonals()
        Returns the number of upper diagonals