mp
Class MPDictionary

java.lang.Object
  mp.MPDictionary

Direct Known Subclasses:

MPBandMatrix, MPFlexMatrix, MPMatrix, MPSimpleMatrix, MPSparseMatrix

public abstract class MPDictionary

extends java.lang.Object

This abstract class is the superclass for finite real dictionaries used for Matching Pursuit. Note that this class is not related in any way to the util.Dictionary class.
To make a subclass it is necessary to implement the two abstract methods here, i.e. the getValue(..) and setValue(..) functions. It is also needed to implement a constructor.
The rest of the needed functions will then be inherited from the superclass, but often more effective implementations are possible and these should be implemented and override the methods from this superclass.

The dictionary is (here) logically represented as an N×K matrix D, but the actual representation may vary in differnt implementations. It may actually not be stored at all, i.e. be defined from the functions alone. Since its inteded use is in the Matching Pursuit algorithms most effort should be put into making transposeMulitply() and innerProduct() effective.

The dictionary elements are vectors in space matrix RN, i.e. standard Euclidian N-dimensional real space, and the inner product is the standard sum of products with the induced norm as the common 2-norm. The dictionary elements are represented as columns in matrix D.

Constructor Summary

MPDictionary()

Method Summary

void	addColumn(int k, double factor, double[] x) Add a column of the matrix multiplied by a factor to a given vector.
double[]	getColumn(int k) Returns a column of the matrix, i.e. a dictionary element or atom.
void	getColumn(int k, double[] d) Returns, in argument d, a column of the matrix, i.e. a dictionary element or atom.
int	getColumns() Returns number of columns in the matrix, i.e. number of dictionary elements or atoms.
int	getK() Returns number of columns in the matrix, i.e. number of dictionary elements or atoms.
int	getN() Returns number of rows in the matrix, i.e. dimension of the dictionary elements or atoms.
double[]	getRow(int n) Returns a row of the matrix which represents the dictionary.
void	getRow(int n, double[] r) Returns, in argument r, a row of the matrix which represents the dictionary.
int	getRows() Returns number of rows in the matrix, i.e. dimension of the dictionary elements or atoms.
abstract double	getValue(int n, int k) Returns the value of an entry of the matrix, i.e. a single entry of a dictionary element (atom).
double	innerProduct(int k1, int k2) Returns the inner product of two dictionary elements, i.e. matrix column vectors.
boolean	isNormalized() Returns true if the dictionary is normalized, i.e. the 2-norm of all dictionary elements (atoms) is one, else it returns false.
double[]	multiply(double[] y) Multiplies the dictionary D by array y.
void	multiply(double[] y, double[] x) Multiplies the dictionary D by array y.
void	normalize() Normalize the dictionary, i.e. multiply each dictionary element (matrix column vector) by a number (scalar) such that the 2-norm, i.e. sum of squares, will be 1.0.
void	setColumn(int k, double[] d) Set a column of the matrix, i.e. a dictionary element or atom, to values in d.
void	setRow(int n, double[] r) Set a row of the matrix which represents the dictionary to values in r.
abstract void	setValue(int n, int k, double val) Set an entry (a value) in the dictionary.
double[]	transposeMultiply(double[] x) Multiplies the transposed dictionary D' by array x.
void	transposeMultiply(double[] x, double[] y) Multiplies the transposed dictionary D' by array x.

Methods inherited from class java.lang.Object

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

Constructor Detail

MPDictionary

public MPDictionary()

Method Detail

getRows

public int getRows()

Returns number of rows in the matrix, i.e. dimension of the dictionary elements or atoms. The method returns the class variable N.

getColumns

public int getColumns()

Returns number of columns in the matrix, i.e. number of dictionary elements or atoms. The method returns the class variable K.

getN

public int getN()

Returns number of rows in the matrix, i.e. dimension of the dictionary elements or atoms. The method returns the class variable N.

getK

public int getK()

Returns number of columns in the matrix, i.e. number of dictionary elements or atoms. The method returns the class variable K.

isNormalized

public boolean isNormalized()

Returns true if the dictionary is normalized, i.e. the 2-norm of all dictionary elements (atoms) is one, else it returns false. This is the class variable normalized.

getValue

public abstract double getValue(int n,
                                int k)

Returns the value of an entry of the matrix, i.e. a single entry of a dictionary element (atom). Note that the row, i.e. position in the column, is given as first argument, the second argument is the column number i.e. the number of the dictionary atom. We should have: 0 <= n < N and 0 <= k < K. If arguments are outside legal range a zero should be returned without error or warning.

Parameters:

n - row number for the returned entry value.

k - column number for the returned entry value.

setValue

public abstract void setValue(int n,
                              int k,
                              double val)

Set an entry (a value) in the dictionary. Note that the row, i.e. position in the column, is given first, the second argument is the column number i.e. the number of the dictionary atom. We should have: 0 <= n < N and 0 <= k < K. If any argument is outside legal range nothing should be done.

Parameters:

n - row number for the entry value to be changed.

k - column number for the entry value to be changed.

val - the value to be put into the given entry of the dictionary.

innerProduct

public double innerProduct(int k1,
                           int k2)

Returns the inner product of two dictionary elements, i.e. matrix column vectors. Legal range is 0 <= k1 < K and 0 <= k2 < K. If k1 or k2 are out of range, 0.0 should be returned.

Parameters:

k1 - number for the first dictionary element.

k2 - number for the second dictionary element.

normalize

public void normalize()

Normalize the dictionary, i.e. multiply each dictionary element (matrix column vector) by a number (scalar) such that the 2-norm, i.e. sum of squares, will be 1.0.
This function should set the class variable normalized to true.

getColumn

public double[] getColumn(int k)

Returns a column of the matrix, i.e. a dictionary element or atom. Legal range of the integer argument is 0 <= k < K. If argument is out of range a length N array of zeros should be returned.
The corresponding Matlab expression would be: D(:,k+1).

Parameters:

k - number of the column in dictionary, i.e. matrix D.

getColumn

public void getColumn(int k,
                      double[] d)

Returns, in argument d, a column of the matrix, i.e. a dictionary element or atom. Legal range of the integer argument is 0 <= k < K. If argument is out of range a length N array of zeros should be returned.
The corresponding Matlab expression would be: d = D(:,k+1).

Parameters:

k - number of the column in dictionary, i.e. matrix D.

d - the given column of matrix D.

setColumn

public void setColumn(int k,
                      double[] d)

Set a column of the matrix, i.e. a dictionary element or atom, to values in d. Legal range of the integer argument is 0 <= k < K. If argument is out of range an IllegalArgumentException is thrown.
The corresponding Matlab expression would be: D(:,k+1) = d.

Parameters:

k - number of the column in dictionary, i.e. matrix D.

d - the given column of matrix D.

addColumn

public void addColumn(int k,
                      double factor,
                      double[] x)

Add a column of the matrix multiplied by a factor to a given vector. Legal range of the integer argument is 0 <= k < K.
The corresponding Matlab expression would be: x = x+f*D(:,k+1). Note that this function can not be used from Matlab, use getColumn(k) to get D(:,k+1) and calculate the new x in Matlab.

Parameters:

k - number of the column in dictionary, i.e. matrix D.

factor - a factor to multiply the column vector by.

x - an array of length N.

getRow

public double[] getRow(int n)

Returns a row of the matrix which represents the dictionary. Legal range of the integer argument is 0 <= n < N. If argument is out of range a length K array of zeros should be returned.
The corresponding Matlab expression would be: D(n+1,:).

Parameters:

n - number of the row in dictionary, i.e. matrix D.

getRow

public void getRow(int n,
                   double[] r)

Returns, in argument r, a row of the matrix which represents the dictionary. Legal range of the integer argument is 0 <= n < N. If argument is out of range a length K array of zeros should be returned.
The corresponding Matlab expression would be: r = D(n+1,:).

Parameters:

n - number of the row in dictionary, i.e. matrix D.

r - the given row of matrix D.

setRow

public void setRow(int n,
                   double[] r)

Set a row of the matrix which represents the dictionary to values in r. Legal range of the integer argument is 0 <= n < N. If argument is out of range an IllegalArgumentException is thrown.
The corresponding Matlab expression would be: D(n+1,:) = r.

Parameters:

n - number of the row in dictionary, i.e. matrix D.

r - the given row of matrix D.

transposeMultiply

public double[] transposeMultiply(double[] x)

Multiplies the transposed dictionary D' by array x. D is the matrix representing the dictionary, each column is a dictionary element. An array y is returned.
The dimensions are: D is N×K, x is N×1, and y is K×1.
The corresponding mulitplication in Matlab would be: y = D'*x.

Parameters:

x - the signal (column vector) that is multiplied by the transposed dictionary.

Returns:

the results as an array of length K.

transposeMultiply

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

Multiplies the transposed dictionary D' by array x. D is the matrix representing the dictionary, each column is a dictionary element. An array y is returned.
The dimensions are: D is N×K, x is N×1, and y is K×1.
The corresponding mulitplication in Matlab would be: y = D'*x.

Parameters:

x - the signal (column vector) that is multiplied by the transposed dictionary.

y - the results as an array of length K.

multiply

public double[] multiply(double[] y)

Multiplies the dictionary D by array y. D is the matrix representing the dictionary, each column is a dictionary element. An array x is returned.
The dimensions are: D is N×K, x is N×1, and y is K×1.
The corresponding mulitplication in Matlab would be: x = D*y.

Parameters:

y - the coefficient vector that is multiplied by the dictionary.

Returns:

the results as an array of length N.

multiply

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

Multiplies the dictionary D by array y. D is the matrix representing the dictionary, each column is a dictionary element. An array x is returned.
The dimensions are: D is N×K, x is N×1, and y is K×1.
The corresponding mulitplication in Matlab would be: x = D*y.

Parameters:

y - the coefficient vector that is multiplied by the dictionary.

x - the results as an array of length N.