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packtree Class Reference

The packtree object constructs a wavelet packet tree. More...

#include <packtree.h>

Inheritance diagram for packtree::

packtree_base List of all members.

Public Methods

 packtree (const double *vec, const size_t n, liftbase< packcontainer, double > *w)
 Construct a wavelet packet tree from a vector of double values. More...

 ~packtree ()
 destructor does nothing. More...

void prCost ()
 Print the wavelet packet tree cost values in breadth first order. More...

void prBestBasis ()
 Print the wavelet packet tree, showing the nodes that have been selected by the "best basis" algorithm. More...

void bestBasis ()
 Calculate the wavelet packet "best basis". More...

bool bestBasisOK ()
 Return true is be best basis has been calculated properly, return false if the best basis has not been calculated or it was not calculated properly. More...

packdata_list<double> getBestBasisList ()
 Return a list consisting of the best basis packdata values. More...


Private Methods

 packtree (const packtree &rhs)
 disallow the copy constructor. More...

 packtree ()
 disallow the default constructor. More...

double bestBasisWalk (packnode< double > *root)
 Walk the wavelet packet tree and apply the "best basis" algorithm described in Chapter 8 of Ripples in Mathematics. More...

void buildBestBasisList (packnode< double > *root, packdata_list< double > &list)
 Traverse the tree from the top down and add the best basis nodes to the best basis list. More...

void checkBestBasis (packnode< double > *root)
 Recursively traverse the wavelet packet tree and check that the best basis result is correct. More...

void cleanTree (packnode< double > *root, bool removeMark)
 The best basis algorithm selects the nodes nearest the tree root for the best basis set. More...


Private Attributes

bool foundOriginalData
 Found original data marked as part of the best basis. More...

bool foundBestBasisVal
 found a best basis value in the wavelet packet tree. More...


Detailed Description

The packtree object constructs a wavelet packet tree.

The constructor is passed a vector of doubles, the length of the vector (which must be a power of two) and a pointer to a wavelet lifting scheme class that will be used in calculating the wavelet transform step. If the vector passed to the constructor contains N double vaues, the result of the constructor will be a wavelet packet tree with log2(N) levels.

Definition at line 57 of file packtree.h.


Constructor & Destructor Documentation

packtree::packtree ( const packtree & rhs ) [inline, private]
 

disallow the copy constructor.

Definition at line 70 of file packtree.h.

00070 {};

packtree::packtree ( ) [inline, private]
 

disallow the default constructor.

Definition at line 72 of file packtree.h.

00072 {};

packtree::packtree ( const double * vec,
const size_t n,
liftbase< packcontainer, double > * w )
 

Construct a wavelet packet tree from a vector of double values.

The size of the vector, which must be a power of two, is passed in N. A wavelet Lifting Scheme object is passed in w. This object is used to calculate the wavelet transform step which is applied at each level (where level > 0) of the wavelet packet tree.

The first level (level 0) of the wavelet packet tree contains the original data set.

  • vec An array of double values on which the wavelet packet transform is calculated.
  • N The number of elements in the input array
  • w A pointer to the the wavelet transform object to use in calculating the wavelet packet transform.

Definition at line 59 of file packtree.cpp.

00062 {
00063   waveObj = w;
00064 
00065   block_pool mem_pool;
00066   double *vecCopy = (double *)mem_pool.pool_alloc( N * sizeof( double ) );
00067 
00068   for (int i = 0; i < N; i++) {
00069     vecCopy[i] = vec[i];
00070   }
00071 
00072   root = new packnode<double>( vecCopy, N, packnode<double>::OriginalData );
00073   root->mark( true );
00074   newLevel( root, false, false ); 
00075 } // packtree

packtree::~packtree ( ) [inline]
 

destructor does nothing.

Definition at line 90 of file packtree.h.

00090 {}


Member Function Documentation

void packtree::bestBasis ( )
 

Calculate the wavelet packet "best basis".

Definition at line 197 of file packtree.cpp.

Referenced by main().

00198 {
00199   bestBasisWalk( root );
00200 } // bestBasis

bool packtree::bestBasisOK ( )
 

Return true is be best basis has been calculated properly, return false if the best basis has not been calculated or it was not calculated properly.

The best basis is calculated in reference to a particular cost function. A particular cost function will not always result in a data set which differs from the original data set. If this is the case, the "best basis" result will include the original data.

Definition at line 250 of file packtree.cpp.

Referenced by main().

00251 {
00252   foundOriginalData = false;
00253   foundBestBasisVal = false;
00254   checkBestBasis( root );
00255 
00256   bool rslt = (foundBestBasisVal && (!foundOriginalData));
00257 
00258   return rslt;
00259 } // bestBasicOK

double packtree::bestBasisWalk ( packnode< double > * root ) [private]
 

Walk the wavelet packet tree and apply the "best basis" algorithm described in Chapter 8 of Ripples in Mathematics.

Nodes that are "marked" become part of the best basis, which is a minimal representation of the data in terms of the cost function.

Definition at line 153 of file packtree.cpp.

Referenced by bestBasis().

00154 {
00155   double cost = 0.0;
00156 
00157   if (top != 0) {
00158     packnode<double> *lhs = top->lhsChild();
00159     packnode<double> *rhs = top->rhsChild();
00160 
00161     if (lhs == 0 && rhs == 0) { // we've reached a leaf
00162       cost = top->cost();
00163     }
00164     else if (lhs != 0 && rhs != 0) {
00165 
00166       double lhsCost = bestBasisWalk( lhs );
00167       double rhsCost = bestBasisWalk( rhs );
00168 
00169       double v1 = top->cost();
00170       double v2 = lhsCost + rhsCost;
00171 
00172       if (v1 <= v2) {
00173         top->mark( true );
00174         lhs->mark( false );
00175         rhs->mark( false );
00176       }
00177       else { // v1 > v2
00178         top->cost( v2 );
00179       }
00180       cost = top->cost();
00181     }
00182     else {
00183       // The tree does not seem to be a full binary tree
00184       // Something has gone badly wrong.
00185       assert( false );
00186     }
00187   }
00188 
00189   return cost;
00190 } // bestBasicWalk

void packtree::buildBestBasisList ( packnode< double > * root,
packdata_list< double > & list ) [private]
 

Traverse the tree from the top down and add the best basis nodes to the best basis list.

Note that the list object is simply a package for a scalar value, the pointer to the head of the list. So it can be passed by value without incurring a cost greater than passing a pointer (e.g., pass by reference).

Definition at line 271 of file packtree.cpp.

Referenced by getBestBasisList().

00273 {
00274   if (top != 0) {
00275     if (top->mark()) {
00276       list.add( top );
00277     }
00278     else {
00279       buildBestBasisList( top->lhsChild(), list );
00280       buildBestBasisList( top->rhsChild(), list );
00281     }
00282   }
00283 } // buildBestBasisList

void packtree::checkBestBasis ( packnode< double > * root ) [private]
 

Recursively traverse the wavelet packet tree and check that the best basis result is correct.

That is, that the best basis has been calculated and that it does not include the orignal data set. The best basis includes the original data set with the packnode ofr the original data set is marked.

This algorithm makes use of two class global variables. There may be a purely recursive, way to do this without these global class variables, but these variables make the algorithm much easier. The variables are initialized by the calling function bestBasisOK().

Definition at line 218 of file packtree.cpp.

Referenced by bestBasisOK().

00219 {
00220   if (top != 0) {
00221     if (top->mark()) {
00222       foundBestBasisVal = true;
00223       if (top->getKind() == packdata<double>::OriginalData) {
00224         foundOriginalData = true;
00225       }
00226     }
00227     if (!foundOriginalData) {
00228       checkBestBasis( top->lhsChild() );
00229     }
00230     if (!foundOriginalData) {
00231       checkBestBasis( top->rhsChild() );
00232     }
00233   }
00234 }  // checkBestBasis

void packtree::cleanTree ( packnode< double > * root,
bool removeMark ) [private]
 

The best basis algorithm selects the nodes nearest the tree root for the best basis set.

These nodes are "marked" true with a boolean flag.

The best basis algorithm outlined in Ripples in Mathematics sets any marks in nodes that are below a marked node in the tree (nodes which are in a subtree of a marked node) to false. However, this is unnecessary when the best basis set is collected, since the algorithm uses top down tree traversal and stops at marked node.

A problem does arise when the entire tree is printed to show the nodes that are marked as part of the best basis set. In this case the result may appear wrong, since child nodes of a best basis node are marked. This function does a top down traversal setting the "marks" on these child nodes to false.

Definition at line 98 of file packtree.cpp.

Referenced by prBestBasis().

00099 {
00100   if (top != 0) {
00101     if (removeMark) {
00102       if (top->mark()) {
00103         top->mark( false );
00104       }
00105     }
00106     else {
00107       // if a mark is found, then set all the "marks" below that
00108       // point to false (e.g., remove the marks).
00109       if (top->mark()) {
00110         removeMark = true;
00111       }
00112     }
00113     cleanTree( top->lhsChild(), removeMark );
00114     cleanTree( top->rhsChild(), removeMark );
00115   }
00116 } // cleanTree

packdata_list< double > packtree::getBestBasisList<double> ( )
 

Return a list consisting of the best basis packdata values.

Definition at line 291 of file packtree.cpp.

Referenced by main().

00292 {
00293   packdata_list<double> list;
00294 
00295   buildBestBasisList( root, list );
00296   return list;
00297 } // getBestBasisList

void packtree::prBestBasis ( )
 

Print the wavelet packet tree, showing the nodes that have been selected by the "best basis" algorithm.

Definition at line 136 of file packtree.cpp.

Referenced by main().

00137 {
00138   if (root != 0) {
00139     cleanTree( root, false );
00140     breadthFirstPrint(printBestBasis);
00141   }
00142 } // prBestBasis

void packtree::prCost ( )
 

Print the wavelet packet tree cost values in breadth first order.

Definition at line 124 of file packtree.cpp.

Referenced by main().

00125 {
00126   if (root != 0) {
00127     breadthFirstPrint(printCost);
00128   }
00129 }


Member Data Documentation

bool packtree::foundBestBasisVal [private]
 

found a best basis value in the wavelet packet tree.

Definition at line 66 of file packtree.h.

bool packtree::foundOriginalData [private]
 

Found original data marked as part of the best basis.

This means that the best basis function failed (or that the original data is the most compact representation relative to the cost function used).

Definition at line 64 of file packtree.h.


The documentation for this class was generated from the following files:
Generated at Tue May 27 21:56:17 2003 for Wavelet compression, determinism and time series forecasting by doxygen1.2.8.1 written by Dimitri van Heesch, © 1997-2001