mp
Class MPBandMatrix

java.lang.Object
  mp.MPDictionary
      mp.MPBandMatrix

public class MPBandMatrix

extends MPDictionary

This class is a band diagonal matrix implementation of the MPDictionary superclass. The dictionary D is represented as an array of column vectors, and for each stored array (column vector) it is also stored how many zeros that preceed this array in the column vector of the matrix. Thus the lengths of the stored column vectors are usualle less than N.

Constructor Summary

MPBandMatrix(int iN, int iK)
Constructs a N×K matrix or dictionary with only zero values.

MPBandMatrix(int iN, int iK, double[] val)
Constructs a N×K matrix or dictionary with values from given one-dimensional array (which represents the matrix).

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	getValue(int n, int k) Returns 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.
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[] col) Replace a column in the dictionary with the given column vector.
void	setValue(int n, int k, double val) Set an entry (a value) in the dictionary.
double	singleInnerProduct(int k1, int k2) Calculates and returns the inner product of two dictionary elements.
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 mp.MPDictionary

getColumn, getColumn, getColumns, getK, getN, getRow, getRow, getRows, isNormalized, setRow

Methods inherited from class java.lang.Object

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

Constructor Detail

MPBandMatrix

public MPBandMatrix(int iN,
                    int iK)

Constructs a N×K matrix or dictionary with only zero values.

Parameters:

iN - length of dictionary elements, i.e. column vectors of the matrix.

iK - number of dictionary elements.

MPBandMatrix

public MPBandMatrix(int iN,
                    int iK,
                    double[] val)

Constructs a N×K matrix or dictionary with values from given one-dimensional array (which represents the matrix). Length of the array should be N*K.

Parameters:

iN - length of dictionary elements, i.e. column vectors of the matrix

iK - number of dictionary elements

val - the values (ordered by column, i.e. by dictionary elements)

Method Detail

getValue

public double getValue(int n,
                       int k)

Returns 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 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 0.0 is returned without error or warning.

Specified by:

getValue in class MPDictionary

Parameters:

n - row number for the returned entry value.

k - column number for the returned entry value.

setValue

public 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 is done.

Specified by:

setValue in class MPDictionary

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.

setColumn

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

Replace a column in the dictionary with the given column vector. The column should be of length N. We should have: 0 <= k < K. If any argument is outside legal dimension or range nothing is done.

Overrides:

setColumn in class MPDictionary

Parameters:

k - column number for the column to be changed.

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

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+factor*D(:,k+1).

Overrides:

addColumn in class MPDictionary

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.

innerProduct

public double innerProduct(int k1,
                           int k2)

Returns the inner product of two dictionary elements, i.e. matrix column vectors. In the current implementation all inner products are calculated (and stored) first time the function is called, subsequent calls to this function just look up in this precalculated table and are thus much faster than first time function was called.
Legal range is 0 <= k1 < K and 0 <= k2 < K.
If k1 or k2 is out of range, 0.0 is returned.

Overrides:

innerProduct in class MPDictionary

Parameters:

k1 - number for the first dictionary element.

k2 - number for the second dictionary element.

singleInnerProduct

public double singleInnerProduct(int k1,
                                 int k2)

Calculates and returns the inner product of two dictionary elements. Just the wanted inner product is calculated and the precalculated table is not used, neither for calculation nor for storing elements.
Legal range is 0 <= k1 < K and 0 <= k2 < K.
If k1 or k2 is out of range, 0.0 is 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.

Overrides:

normalize in class MPDictionary

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.

Overrides:

transposeMultiply in class MPDictionary

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.

Overrides:

transposeMultiply in class MPDictionary

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.

Overrides:

multiply in class MPDictionary

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.

Overrides:

multiply in class MPDictionary

Parameters:

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

x - the results as an array of length N.