com.numericalmethod.suanshu.matrix.doubles.matrixtype.dense.triangle
Class SymmetricMatrix

java.lang.Object
  com.numericalmethod.suanshu.matrix.doubles.matrixtype.MatrixMathImpl<T>
      com.numericalmethod.suanshu.matrix.doubles.matrixtype.MatrixStorageImpl<SymmetricMatrix>
          com.numericalmethod.suanshu.matrix.doubles.matrixtype.dense.triangle.SymmetricMatrix

All Implemented Interfaces:

DeepCopyable, AbelianGroup<Matrix>, Monoid<Matrix>, Ring<Matrix>, Matrix, MatrixAccessor, MatrixRing, Densifiable, MatrixDimension

Direct Known Subclasses:

BorderedHessian, Hessian, HilbertMatrix

public class SymmetricMatrix
extends MatrixStorageImpl<SymmetricMatrix>
implements Densifiable

A symmetric matrix is a square matrix such that its transpose equals to itself, i.e.,

A[i][j] = A[j][i]

We implement this class by storing the data using an lower triangular matrix, e.g., LowerTriangularMatrix. This will reduce the storage cost by almost half compared to DenseMatrix.

We choose to use lower triangular matrix instead of upper triangular matrix for visual reason. A double[] data arrangement resembles a lower triangular matrix.

For example,

         new double[][]{
                  {1},
                  {2, 3},
                  {4, 5, 6},
                  {7, 8, 9, 10},
                  {11, 12, 13, 14, 15}});
 

See Also:

Wikipedia: Symmetric matrix

Field Summary

int	dim dimension; SymmetricMatrix is always square

Constructor Summary

SymmetricMatrix(double[][] data)
Construct a symmetric matrix from a 2D double[][] array.

SymmetricMatrix(int dim)
Construct a symmetric matrix of dimension dim * dim.

SymmetricMatrix(SymmetricMatrix S)
Copy constructor performing a deep copy.

Method Summary

SymmetricMatrix	add(SymmetricMatrix that)
SymmetricMatrix	deepCopy() The implementation can return an instance created from this by the copy constructor of the class, or just this if the instance itself is immutable.
boolean	equals(java.lang.Object obj) Check if two matrices (of different implementations) are equal.
double	get(int row, int col) Get the matrix entry at [row, col].
DenseVector	getColumn(int col) Get a specified column as a vector.
DenseVector	getRow(int row) Get a specified row as a vector.
int	hashCode()
SymmetricMatrix	minus(SymmetricMatrix that)
SymmetricMatrix	ONE() Get an identity matrix that has the same dimension as this matrix.
SymmetricMatrix	scaled(double scalar) scalar * this
void	set(int row, int col, double value) Set the matrix entry at [row, col] to value.
SymmetricMatrix	t() t(A) = A.
DenseMatrix	toDense() Densify a matrix, i.e., convert a matrix implementation to a standard dense matrix, DenseMatrix.
java.lang.String	toString()
SymmetricMatrix	ZERO() The additive element 0 in the group, such that for all elements a in the group, the equation 0 + a = a + 0 = a holds.

Methods inherited from class com.numericalmethod.suanshu.matrix.doubles.matrixtype.MatrixStorageImpl

getMatrixData, setMatrixData

Methods inherited from class com.numericalmethod.suanshu.matrix.doubles.matrixtype.MatrixMathImpl

add, call, getSample, minus, multiply, multiply, nCols, nRows, opposite, setColumn, setColumn, setRow, setRow

Methods inherited from class java.lang.Object

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

Field Detail

dim

public final int dim

dimension; SymmetricMatrix is always square

Constructor Detail

SymmetricMatrix

public SymmetricMatrix(int dim)

Construct a symmetric matrix of dimension dim * dim. Space for the matrix data is not yet allocated.

Parameters:

dim - symmetric matrix dimension, i.e., the number of rows or number of columns

SymmetricMatrix

public SymmetricMatrix(double[][] data)

Construct a symmetric matrix from a 2D double[][] array. The array contains only the lower triangular part (main diagonal inclusive) of the whole matrix.

Parameters:

data - the 2D double[][] array

SymmetricMatrix

public SymmetricMatrix(SymmetricMatrix S)

Copy constructor performing a deep copy.

Parameters:

S - the matrix to be copied

Method Detail

deepCopy

public SymmetricMatrix deepCopy()

Description copied from interface: Matrix

The implementation can return an instance created from this by the copy constructor of the class, or just this if the instance itself is immutable.

Override the return type.

Specified by:

deepCopy in interface DeepCopyable

Specified by:

deepCopy in interface Matrix

Returns:

an independent copy of Matrix instance

toDense

public DenseMatrix toDense()

Description copied from interface: Densifiable

Densify a matrix, i.e., convert a matrix implementation to a standard dense matrix, DenseMatrix.

This is equivalent to

new DenseMatrix(Matrix A)

Individual matrix implementation may optimize the conversion by taking advantage of having access to the class' private members. In other words, toDense() is in general more efficient than explicit copy construction.

As an example, for some long matrix computations, we may not be sure about the return type. We can always cast it to the standard matrix. That is,

DenseMatrix A = B.multiply(C).add(D).minus(E).toDense();

This statement always works regardless of the types of B, C, D, and E.

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: MatrixAccessor

Set the matrix entry at [row, col] to value.

This is the only method that may change the entries of a matrix.

Specified by:

set in interface MatrixAccessor

Overrides:

set in class MatrixStorageImpl<SymmetricMatrix>

Parameters:

row - the row index

col - the column index

value - the value to set A[row, col] to

Throws:

MatrixAccessException - if row or col is out of range

get

public double get(int row,
                  int col)
           throws MatrixAccessException

Description copied from interface: MatrixAccessor

Get the matrix entry at [row, col].

Specified by:

get in interface MatrixAccessor

Overrides:

get in class MatrixStorageImpl<SymmetricMatrix>

Parameters:

row - the row index

col - the column index

Returns:

A[row, col]

Throws:

MatrixAccessException - if row or col is out of range

getRow

public DenseVector getRow(int row)
                   throws MatrixAccessException

Description copied from interface: MatrixAccessor

Get a specified row as a vector.

Specified by:

getRow in interface MatrixAccessor

Overrides:

getRow in class MatrixMathImpl<SymmetricMatrix>

Parameters:

row - the row index

Returns:

a vector A[row, ]

Throws:

MatrixAccessException - when row < 1, or when row > number of rows

getColumn

public DenseVector getColumn(int col)
                      throws MatrixAccessException

Description copied from interface: MatrixAccessor

Get a specified column as a vector.

Specified by:

getColumn in interface MatrixAccessor

Overrides:

getColumn in class MatrixMathImpl<SymmetricMatrix>

Parameters:

col - the column index

Returns:

a vector A[, col]

Throws:

MatrixAccessException - when col < 1, or when col > number of columns

add

public SymmetricMatrix add(SymmetricMatrix that)

minus

public SymmetricMatrix minus(SymmetricMatrix that)

ZERO

public SymmetricMatrix ZERO()

Description copied from interface: AbelianGroup

The additive element 0 in the group, such that for all elements a in the group, the equation

0 + a = a + 0 = a

holds.

Specified by:

ZERO in interface AbelianGroup<Matrix>

Specified by:

ZERO in interface MatrixRing

Returns:

0

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 Monoid<Matrix>

Specified by:

ONE in interface MatrixRing

Returns:

an identity matrix

t

public SymmetricMatrix t()

t(A) = A.

Specified by:

t in interface MatrixRing

Overrides:

t in class MatrixMathImpl<SymmetricMatrix>

Returns:

itself

scaled

public SymmetricMatrix scaled(double scalar)

Description copied from interface: Matrix

scalar * this

Specified by:

scaled in interface Matrix

Overrides:

scaled in class MatrixMathImpl<SymmetricMatrix>

Parameters:

scalar - a double

Returns:

scalar * this

toString

public java.lang.String toString()

Overrides:

toString in class MatrixMathImpl<SymmetricMatrix>

equals

public boolean equals(java.lang.Object obj)

Description copied from class: MatrixStorageImpl

Check if two matrices (of different implementations) are equal. They are equal iff two matrices have the same values, entry-by-entry.

Overrides:

equals in class MatrixStorageImpl<SymmetricMatrix>

Returns:

true iff two matrices have the same values, entry-by-entry

hashCode

public int hashCode()

Overrides:

hashCode in class MatrixStorageImpl<SymmetricMatrix>