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

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

All Implemented Interfaces:

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

public class UpperTriangularMatrix
extends TriangularMatrix<UpperTriangularMatrix>
implements Densifiable

This class implements upper triangular matrix, which has 0 entries whenever row index > column index.

This implementation saves about half of the data cost (except for the diagonal) when compared to the implementation of DenseMatrix. Users may use this class instead of DenseMatrix when they know that the matrix is upper triangular.

Upper triangular matrices are always square.

Constructor Summary

UpperTriangularMatrix(double[][] data)
Construct an upper triangular matrix from a 2D double[][] array.

UpperTriangularMatrix(int dim)
Construct an upper triangular matrix of dimension dim * dim.

UpperTriangularMatrix(Matrix U)
Copy constructor performing a deep copy of a matrix.

UpperTriangularMatrix(UpperTriangularMatrix U)
Copy constructor performing a deep copy.

Method Summary

UpperTriangularMatrix	add(UpperTriangularMatrix that)
UpperTriangularMatrix	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.
DenseVector	getColumn(int col) Get a specified column as a vector.
DenseVector	getRow(int row) Get a specified row as a vector.
UpperTriangularMatrix	minus(UpperTriangularMatrix that)
UpperTriangularMatrix	multiply(UpperTriangularMatrix that)
UpperTriangularMatrix	ONE() Get an identity matrix that has the same dimension as this matrix.
UpperTriangularMatrix	scaled(double scalar) scalar * this
LowerTriangularMatrix	t() t(A)
DenseMatrix	toDense() Densify a matrix, i.e., convert a matrix implementation to a standard dense matrix, DenseMatrix.
UpperTriangularMatrix	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.dense.triangle.TriangularMatrix

dim, getMatrixData

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

equals, get, hashCode, set, 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, toString

Methods inherited from class java.lang.Object

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

Constructor Detail

UpperTriangularMatrix

public UpperTriangularMatrix(int dim)

Construct an upper triangular matrix of dimension dim * dim. Space for the matrix data is not yet allocated.

Parameters:

dim - dimension; for a square matrix, it is the number of rows or columns

UpperTriangularMatrix

public UpperTriangularMatrix(double[][] data)

Construct an upper triangular matrix from a 2D double[][] array.

Parameters:

data - the 2D array input

Throws:

java.lang.IllegalArgumentException - if data is not upper triangular

UpperTriangularMatrix

public UpperTriangularMatrix(Matrix U)

Copy constructor performing a deep copy of a matrix.

Parameters:

U - a matrix

Throws:

java.lang.IllegalArgumentException - when A is not square, or when A is not upper triangular

UpperTriangularMatrix

public UpperTriangularMatrix(UpperTriangularMatrix U)

Copy constructor performing a deep copy.

Parameters:

U - an UpperTriangularMatrix

Method Detail

deepCopy

public UpperTriangularMatrix 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

getRow

public DenseVector getRow(int row)

Description copied from interface: MatrixAccessor

Get a specified row as a vector.

Specified by:

getRow in interface MatrixAccessor

Overrides:

getRow in class MatrixMathImpl<UpperTriangularMatrix>

Parameters:

row - the row index

Returns:

a vector A[row, ]

getColumn

public DenseVector getColumn(int col)

Description copied from interface: MatrixAccessor

Get a specified column as a vector.

Specified by:

getColumn in interface MatrixAccessor

Overrides:

getColumn in class MatrixMathImpl<UpperTriangularMatrix>

Parameters:

col - the column index

Returns:

a vector A[, col]

add

public UpperTriangularMatrix add(UpperTriangularMatrix that)

minus

public UpperTriangularMatrix minus(UpperTriangularMatrix that)

multiply

public UpperTriangularMatrix multiply(UpperTriangularMatrix that)

ZERO

public UpperTriangularMatrix 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 UpperTriangularMatrix 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 LowerTriangularMatrix t()

t(A)

Specified by:

t in interface MatrixRing

Overrides:

t in class MatrixMathImpl<UpperTriangularMatrix>

Returns:

a lower triangular matrix which is the transpose of this

scaled

public UpperTriangularMatrix scaled(double scalar)

Description copied from interface: Matrix

scalar * this

Specified by:

scaled in interface Matrix

Overrides:

scaled in class MatrixMathImpl<UpperTriangularMatrix>

Parameters:

scalar - a double

Returns:

scalar * this