mpv2
Class PermutationMatrix

java.lang.Object
  mpv2.AllMatrices
      mpv2.PermutationMatrix

All Implemented Interfaces:

java.io.Serializable, java.lang.Cloneable

public class PermutationMatrix
extends AllMatrices
implements java.lang.Cloneable, java.io.Serializable

This is a permutation matrix class made by implementing AllMatrices.

See Also:

Serialized Form

Field Summary

Fields inherited from class mpv2.AllMatrices

K, N

Constructor Summary

PermutationMatrix(double[] ord)
Construct an n-by-n permutation matrix which will make the given array when the matrix is applied to the sorted sequence, ord = A*ascending(ord).

PermutationMatrix(int n)
Construct an n-by-n permutation matrix with ones on the diagonal, i.e. identity matrix.

PermutationMatrix(int[] p)
Construct an N-by-N permutation matrix from a vector p, A(n,k)==1 <=> p[n]==k.

Method Summary

java.lang.Object	clone() Clone the Matrix object.
double	cond() Matrix condition (2 norm)
PermutationMatrix	copy() Make a deep copy of a matrix
double	det() Matrix determinant
double	get(int n, int k) Get a single element, A(n,k).
int[]	getPos() Access the internal array pos, we have A(n,k)==1 <=> pos[n]==k.
static PermutationMatrix	identity(int n) Generate identity matrix
double	innerProduct(int k1, int k2) Returns the inner product of two matrix column vectors, which for a diagonal matrix is zero.
double	norm2() Two norm
double	normF() Frobenius norm
static PermutationMatrix	perfectShuffle(int n, int s) Generate perfect shuffle (stride) permutation matrix.
static PermutationMatrix	random(int n) Generate randon permutation matrix
int	rank() Matrix rank
static PermutationMatrix	reverse(int n) Generate reverse matrix
void	set(int n, int k, double s) Set a single element, A(n,k)=s, this is not allowed som method just return.
void	times(double[] y, double[] x) Multiplies the matrix by an array, x = A*y.
void	transposeTimes(double[] x, double[] y) Multiplies the transposed matrix by an array, y = A'*x.

Methods inherited from class mpv2.AllMatrices

addColumn, chol, columnNorm0, columnNorm1, columnNorm2, columnNormInf, eig, eqConstant, eqCopy, eqCopy, eqCopy, eqCopy, eqCopy, eqDifference, eqEProduct, eqEQuotient, eqIdentity, eqInverse, eqIProduct, eqNegate, eqOnes, eqPermuteColumns, eqPermuteRows, eqProduct, eqProduct, eqRandom, eqScaleColumns, eqScaleRows, eqSum, eqTProduct, eqTranspose, eqZeros, getAll, getAll, getColumn, getColumn, getColumnDimension, getK, getN, getRow, getRow, getRowDimension, getSubMatrix, getSubMatrix, getSubMatrix, getSubMatrix, getValue, lu, lup, norm1, normInf, pluseqOuterProduct, print, print, print, print, qr, setAll, setColumn, setRow, setValue, sumAll, svd, times, times, times, trace, transposeTimes, transposeTimes, transposeTimes

Methods inherited from class java.lang.Object

equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

PermutationMatrix

public PermutationMatrix(int n)

Construct an n-by-n permutation matrix with ones on the diagonal, i.e. identity matrix.

Parameters:

n - Number of rows and columns

PermutationMatrix

public PermutationMatrix(int[] p)

Construct an N-by-N permutation matrix from a vector p, A(n,k)==1 <=> p[n]==k. p must be a permutation of the integers from 0 to (N-1).

Parameters:

p - the vector that gives p.

Throws:

java.lang.IllegalArgumentException

PermutationMatrix

public PermutationMatrix(double[] ord)

Construct an n-by-n permutation matrix which will make the given array when the matrix is applied to the sorted sequence, ord = A*ascending(ord). Note that A'*ord will give an ordered sequence, i.e. ascending(ord).

Parameters:

ord - the sequence that the permutation matrix will put the ordered sequence into

Method Detail

random

public static PermutationMatrix random(int n)

Generate randon permutation matrix

Parameters:

n - Number of rows and colums.

Returns:

An n-by-n permutation matrix

identity

public static PermutationMatrix identity(int n)

Generate identity matrix

Parameters:

n - Number of rows and colums.

Returns:

An n-by-n identity matrix

reverse

public static PermutationMatrix reverse(int n)

Generate reverse matrix

Parameters:

n - Number of rows and colums.

Returns:

An n-by-n reverse matrix

perfectShuffle

public static PermutationMatrix perfectShuffle(int n,
                                               int s)

Generate perfect shuffle (stride) permutation matrix. This permutation always start with the first element, i.e. P(0,0)=1. The next element is found by going s positions forward (mod n), and if that element is already used go forward until next unused ek\lement is found.

Parameters:

n - Number of rows and colums.

s - The stride, how many elements to go forward on each, normally a factor of n.

Returns:

An n-by-n perfect shuffle (stride) permutation matrix

copy

public PermutationMatrix copy()

Make a deep copy of a matrix

clone

public java.lang.Object clone()

Clone the Matrix object.

Overrides:

clone in class java.lang.Object

get

public double get(int n,
                  int k)

Get a single element, A(n,k).

Specified by:

get in class AllMatrices

Parameters:

n - Row index.

k - Column index.

Returns:

A(n,k)

Throws:

java.lang.ArrayIndexOutOfBoundsException

getPos

public int[] getPos()

Access the internal array pos, we have A(n,k)==1 <=> pos[n]==k.

Returns:

Pointer to the one-dimensional array of column numbers.

set

public void set(int n,
                int k,
                double s)

Set a single element, A(n,k)=s, this is not allowed som method just return.

Specified by:

set in class AllMatrices

Parameters:

n - Row index.

k - Column index.

s - A(n,k).

Throws:

java.lang.ArrayIndexOutOfBoundsException

normF

public double normF()

Frobenius norm

Overrides:

normF in class AllMatrices

Returns:

sqrt of sum of squares of all elements.

det

public double det()

Matrix determinant

Overrides:

det in class AllMatrices

Returns:

determinant

rank

public int rank()

Matrix rank

Overrides:

rank in class AllMatrices

Returns:

effective numerical rank, obtained from SVD.

cond

public double cond()

Matrix condition (2 norm)

Overrides:

cond in class AllMatrices

Returns:

ratio of largest to smallest singular value.

norm2

public double norm2()

Two norm

Overrides:

norm2 in class AllMatrices

Returns:

maximum singular value.

innerProduct

public double innerProduct(int k1,
                           int k2)

Returns the inner product of two matrix column vectors, which for a diagonal matrix is zero.

Overrides:

innerProduct in class AllMatrices

Parameters:

k1 - number for the first dictionary element.

k2 - number for the second dictionary element.

times

public void times(double[] y,
                  double[] x)

Multiplies the matrix by an array, x = A*y.

Overrides:

times in class AllMatrices

Parameters:

y - the input array

x - the results as an array of length N.

transposeTimes

public void transposeTimes(double[] x,
                           double[] y)

Multiplies the transposed matrix by an array, y = A'*x. Note that the transposed of a permutation matrix is its inverse.

Overrides:

transposeTimes in class AllMatrices

Parameters:

x - the input array

y - the results as an array of length K.