java.lang.Object
dev.nm.algebra.linear.matrix.doubles.matrixtype.dense.triangle.SymmetricMatrix
All Implemented Interfaces:
Matrix, MatrixAccess, MatrixRing, MatrixTable, Densifiable, AbelianGroup<Matrix>, Monoid<Matrix>, Ring<Matrix>, Table, DeepCopyable
Direct Known Subclasses:
BorderedHessian, Hessian, HilbertMatrix

public class SymmetricMatrix extends Object implements Matrix, Densifiable
A symmetric matrix is a square matrix such that its transpose equals to itself, i.e.,
A[i][j] = A[j][i]
See Also:
  • Constructor Details

    • SymmetricMatrix

      public SymmetricMatrix(int dim)
      Construct a symmetric matrix of dimension dim * dim.
      Parameters:
      dim - the matrix dimension
    • SymmetricMatrix

      public SymmetricMatrix(double[][] data)
      Construct a symmetric matrix from a 2D double[][] array. The array specifies only the lower triangular part (main diagonal inclusive) of the whole matrix. For example,
               new double[][]{
                        {1},
                        {2, 3},
                        {4, 5, 6},
                        {7, 8, 9, 10},
                        {11, 12, 13, 14, 15}});
       
      gives \[ \begin{bmatrix} 1 invalid input: '&' 2 invalid input: '&' 4 invalid input: '&' 7 invalid input: '&' 11\\ 2 invalid input: '&' 3 invalid input: '&' 5 invalid input: '&' 8 invalid input: '&' 12\\ 4 invalid input: '&' 5 invalid input: '&' 6 invalid input: '&' 9 invalid input: '&' 13\\ 7 invalid input: '&' 8 invalid input: '&' 9 invalid input: '&' 10 invalid input: '&' 14\\ 11 invalid input: '&' 12 invalid input: '&' 13 invalid input: '&' 14 invalid input: '&' 15 \end{bmatrix} \] This constructor uses lower instead of upper triangular representation for visual reason.
      Parameters:
      data - the lower triangular specification
    • SymmetricMatrix

      public SymmetricMatrix(Matrix A)
      Cast an (almost) symmetric matrix into SymmetricMatrix by averaging A(i,j) and A(j,i).
      Parameters:
      A - an (almost) symmetric matrix
    • SymmetricMatrix

      public SymmetricMatrix(Matrix A, boolean copyLower)
      Cast an (almost) symmetric matrix into SymmetricMatrix.
      Parameters:
      A - an (almost) symmetric matrix
      copyLower - true if the lower triangular portion of A is used; otherwise, the average values of A(i,j) and A(j,i) are used
    • SymmetricMatrix

      public SymmetricMatrix(SymmetricMatrix S)
      Copy constructor.
      Parameters:
      S - a symmetric matrix
  • Method Details

    • nRows

      public int nRows()
      Description copied from interface: Table
      Gets the number of rows. Rows count from 1.
      Specified by:
      nRows in interface Table
      Returns:
      the number of rows
    • nCols

      public int nCols()
      Description copied from interface: Table
      Gets the number of columns. Columns count from 1.
      Specified by:
      nCols in interface Table
      Returns:
      the number of columns
    • deepCopy

      public SymmetricMatrix deepCopy()
      Description copied from interface: DeepCopyable
      The implementation returns an instance created from this by the copy constructor of the class, or just this if the instance itself is immutable.
      Specified by:
      deepCopy in interface DeepCopyable
      Specified by:
      deepCopy in interface Matrix
      Returns:
      an independent (deep) copy of the instance
    • toDense

      public DenseMatrix toDense()
      Description copied from interface: Densifiable
      Densify a matrix, i.e., convert a matrix implementation to the standard dense matrix, DenseMatrix.
      Specified by:
      toDense in interface Densifiable
      Returns:
      a matrix representation in DenseMatrix
    • set

      public void set(int row, int col, double value) throws MatrixAccessException
      Description copied from interface: MatrixAccess
      Set the matrix entry at [i,j] to a value. This is the only method that may change a matrix.
      Specified by:
      set in interface MatrixAccess
      Parameters:
      row - the row index
      col - the column index
      value - the value to set A[i,j] to
      Throws:
      MatrixAccessException - if i or j is out of range
    • get

      public double get(int i, int j) throws MatrixAccessException
      Description copied from interface: MatrixAccess
      Get the matrix entry at [i,j].
      Specified by:
      get in interface MatrixAccess
      Parameters:
      i - the row index
      j - the column index
      Returns:
      A[i,j]
      Throws:
      MatrixAccessException - if i or j is out of range
    • getRow

      public Vector getRow(int i) throws MatrixAccessException
      Description copied from interface: Matrix
      Get the specified row in the matrix as a vector.
      Specified by:
      getRow in interface Matrix
      Parameters:
      i - the row index
      Returns:
      the vector A[i, ]
      Throws:
      MatrixAccessException - when i < 1, or when i > the number of rows
    • getColumn

      public Vector getColumn(int j) throws MatrixAccessException
      Description copied from interface: Matrix
      Get the specified column in the matrix as a vector.
      Specified by:
      getColumn in interface Matrix
      Parameters:
      j - the column index
      Returns:
      a vector A[, j]
      Throws:
      MatrixAccessException - when j < 1, or when j > the number of columns
    • add

      public Matrix add(Matrix that)
      Description copied from interface: MatrixRing
      this + that
      Specified by:
      add in interface AbelianGroup<Matrix>
      Specified by:
      add in interface MatrixRing
      Parameters:
      that - a matrix
      Returns:
      the sum of this and that
    • minus

      public Matrix minus(Matrix that)
      Description copied from interface: MatrixRing
      this - that
      Specified by:
      minus in interface AbelianGroup<Matrix>
      Specified by:
      minus in interface MatrixRing
      Parameters:
      that - a matrix
      Returns:
      the difference between this and that
    • multiply

      public Matrix multiply(Matrix that)
      Description copied from interface: MatrixRing
      this * that
      Specified by:
      multiply in interface MatrixRing
      Specified by:
      multiply in interface Monoid<Matrix>
      Parameters:
      that - a matrix
      Returns:
      the product ofthis and that
    • t

      public SymmetricMatrix t()
      The transpose of a symmetric matrix is the same as itself.
      Specified by:
      t in interface MatrixRing
      Returns:
      a copy of itself
    • scaled

      public SymmetricMatrix scaled(double scalar)
      Description copied from interface: Matrix
      Scale this matrix, A, by a constant.
      Specified by:
      scaled in interface Matrix
      Parameters:
      scalar - a double
      Returns:
      cA
    • opposite

      public SymmetricMatrix opposite()
      Description copied from interface: MatrixRing
      Get the opposite of this matrix.
      Specified by:
      opposite in interface AbelianGroup<Matrix>
      Specified by:
      opposite in interface MatrixRing
      Returns:
      -this
      See Also:
    • ZERO

      public SymmetricMatrix ZERO()
      Description copied from interface: MatrixRing
      Get a zero matrix that has the same dimension as this matrix.
      Specified by:
      ZERO in interface AbelianGroup<Matrix>
      Specified by:
      ZERO in interface MatrixRing
      Returns:
      the 0 matrix
    • ONE

      public SymmetricMatrix ONE()
      Description copied from interface: MatrixRing
      Get an identity matrix that has the same dimension as this matrix. For a non-square matrix, it zeros out the rows (columns) with index > nCols (nRows).
      Specified by:
      ONE in interface MatrixRing
      Specified by:
      ONE in interface Monoid<Matrix>
      Returns:
      an identity matrix
    • multiply

      public Vector multiply(Vector v)
      Description copied from interface: Matrix
      Right multiply this matrix, A, by a vector.
      Specified by:
      multiply in interface Matrix
      Parameters:
      v - a vector
      Returns:
      Av, a vector
    • toString

      public String toString()
      Overrides:
      toString in class Object
    • equals

      public boolean equals(Object obj)
      Overrides:
      equals in class Object
    • hashCode

      public int hashCode()
      Overrides:
      hashCode in class Object