com.numericalmethod.suanshu.matrix.doubles.matrixtype.dense.diagonal
Class BidiagonalMatrix

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.diagonal.BidiagonalMatrix

All Implemented Interfaces:

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

public class BidiagonalMatrix
extends MatrixStorageImpl<T>

This class represents a matrix with non-zero entries only on the main, and either the super-diagonal or sub-diagonal.

See Also:

Wikipedia: Bidiagonal matrix

Nested Class Summary

static class

BidiagonalMatrix.Type the types of bidiagonal matrices available

Constructor Summary

BidiagonalMatrix(BidiagonalMatrix that)
Copy constructor.

BidiagonalMatrix(double[][] data)
Construct a bidiagonal matrix from a 2D double[][] array.

BidiagonalMatrix(int dim, BidiagonalMatrix.Type type)
Construct a bidiagonal matrix of dimension dim * dim.

Method Summary

BidiagonalMatrix	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	diagonal() Get a copy of the diagonal of the matrix.
boolean	equals(java.lang.Object obj) Check if two matrices (of different implementations) are equal.
DenseVector	getColumn(int col) Get a specified column as a vector.
DenseVector	getRow(int row) Get a specified row as a vector.
int	hashCode()
boolean	isUnreduced(double epsilon) A bidiagonal matrix is unreduced iff it has no 0 on both the super and main diagonals.
Matrix	multiply(Matrix that) this %*% that
BidiagonalMatrix	ONE() Get an identity matrix that has the same dimension as this matrix.
BidiagonalMatrix	scaled(double scalar) scalar * this
DenseVector	subDiagonal() Get a copy of the sub-diagonal of the matrix.
DenseVector	superDiagonal() Get a copy of the super-diagonal of the matrix.
BidiagonalMatrix	t() t(this) Compute the transpose of this matrix.
DenseMatrix	toDense() Densify a matrix, i.e., convert a matrix implementation to a standard dense matrix, DenseMatrix.
java.lang.String	toString()
BidiagonalMatrix.Type	type() Get the type of the bidiagonal matrix.
BidiagonalMatrix	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

get, getMatrixData, set, setMatrixData

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

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

Methods inherited from class java.lang.Object

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

Constructor Detail

BidiagonalMatrix

public BidiagonalMatrix(double[][] data)

Construct a bidiagonal matrix from a 2D double[][] array.

There are two rows. The longer row is the main diagonal and has one more element. If the first row is shorter, it is an upper bidiagonal matrix. If the second row is shorter, it is a lower bidiagonal matrix.

For example,

         new double[][]{
              {2, 5, 8, 11},
              {1, 4, 7, 10, 13}
          }
 

is

              | 1  2  0  0   0  |
              | 0  4  5  0   0  |
              | 0  0  7  8   0  |
              | 0  0  0  10  11 |
              | 0  0  0  0   13 |
 

We allow 'null' input when a diagonal is 0s, except for the main diagonal.

For example,

         new double[][]{
              {1, 4, 7, 10, 13},
              null
          }
 

is

              | 1  0  0  0   0  |
              | 0  4  0  0   0  |
              | 0  0  7  0   0  |
              | 0  0  0  10  0  |
              | 0  0  0  0   13 |
 

The following is not allowed because the dimension cannot be determined.

         new double[][]{
              null,
              null
          }
 

We will treat a diagonal matrix as an upper bidiagonal matrix in this class.

Parameters:

data - the 2D array input

BidiagonalMatrix

public BidiagonalMatrix(int dim,
                        BidiagonalMatrix.Type type)

Construct a bidiagonal matrix of dimension dim * dim.

Parameters:

dim - dimension of the matrix

type - the type of bidiagonal matrix to create

BidiagonalMatrix

public BidiagonalMatrix(BidiagonalMatrix that)

Copy constructor.

Parameters:

that - a BidiagonalMatrix

Method Detail

deepCopy

public BidiagonalMatrix 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.

Returns:

an independent copy of Matrix instance

type

public BidiagonalMatrix.Type type()

Get the type of the bidiagonal matrix.

Returns:

the bidiagonal type of this matrix

t

public BidiagonalMatrix t()

Description copied from interface: MatrixRing

t(this)

Compute the transpose of this matrix. The original matrix does not change. The returned value is independent and can be modified anyhow.

This is the involution on the matrix ring.

Specified by:

t in interface MatrixRing

Overrides:

t in class MatrixMathImpl<BidiagonalMatrix>

Returns:

the transpose of this matrix, of the same type

multiply

public Matrix multiply(Matrix that)

Description copied from interface: MatrixRing

this %*% that

Specified by:

multiply in interface Monoid<Matrix>

Specified by:

multiply in interface MatrixRing

Overrides:

multiply in class MatrixMathImpl<BidiagonalMatrix>

Parameters:

that - another matrix

Returns:

the product of this and that

scaled

public BidiagonalMatrix scaled(double scalar)

Description copied from interface: Matrix

scalar * this

Specified by:

scaled in interface Matrix

Overrides:

scaled in class MatrixMathImpl<BidiagonalMatrix>

Parameters:

scalar - a double

Returns:

scalar * this

ZERO

public BidiagonalMatrix 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.

Returns:

0

ONE

public BidiagonalMatrix 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).

Returns:

an identity matrix

isUnreduced

public boolean isUnreduced(double epsilon)

A bidiagonal matrix is unreduced iff it has no 0 on both the super and main diagonals.

Parameters:

epsilon - a precision parameter: when a number |x| ≤ ε, it is considered 0

Returns:

true iff this is unreduced

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

diagonal

public DenseVector diagonal()

Get a copy of the diagonal of the matrix.

Returns:

a copy of the diagonal

superDiagonal

public DenseVector superDiagonal()

Get a copy of the super-diagonal of the matrix.

Returns:

a copy of the super-diagonal

subDiagonal

public DenseVector subDiagonal()

Get a copy of the sub-diagonal of the matrix.

Returns:

a copy of the sub-diagonal

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<T extends com.numericalmethod.suanshu.matrix.doubles.matrixtype.dense.diagonal.DiagonalDataMatrix>

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<T extends com.numericalmethod.suanshu.matrix.doubles.matrixtype.dense.diagonal.DiagonalDataMatrix>

Parameters:

col - the column index

Returns:

a vector A[, col]

toString

public java.lang.String toString()

Overrides:

toString in class MatrixMathImpl<T extends com.numericalmethod.suanshu.matrix.doubles.matrixtype.dense.diagonal.DiagonalDataMatrix>

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<T extends com.numericalmethod.suanshu.matrix.doubles.matrixtype.dense.diagonal.DiagonalDataMatrix>

Returns:

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

hashCode

public int hashCode()

Overrides:

hashCode in class MatrixStorageImpl<T extends com.numericalmethod.suanshu.matrix.doubles.matrixtype.dense.diagonal.DiagonalDataMatrix>