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java.lang.Object umontreal.iro.lecuyer.stat.list.ListOfStatProbes<E> umontreal.iro.lecuyer.stat.list.ListOfTallies<E> umontreal.iro.lecuyer.stat.list.ListOfTalliesWithCovariance<E>
public class ListOfTalliesWithCovariance<E extends Tally>
Extends ListOfTallies
to add support for the computation
of the sample covariance between each pair of elements
in a list, without storing all observations.
This list of tallies contains internal structures to keep track of
bar(X)_{n, i} for
i = 0,…, d  1, and
∑_{k=0}^{n1}(X_{i, k}  bar(X)_{k, i})(X_{j, k}  bar(X)_{k, j})/n, for
i = 0,…, d  2 and
j = 1,…, d  1, with j > i.
Here,
bar(X)_{n, i} is the ith component of
bar(X)_{n}, the average vector,
and
bar(X)_{0, i} = 0 for
i = 0,…, d  1.
The value X_{i, k} corresponds to the ith component of the kth observation
X_{k}.
These sums are updated every time a vector is added to this list, and
are used to estimate the covariances.
Note: the size of the list of tallies must remain fixed because of the data structures used for computing sample covariances. As a result, the first call to init makes this list unmodifiable.
Note: for the sample covariance to be computed between a pair
of tallies, the number of observations in each tally
should be the same. It is therefore recommended to always
add complete vectors of observations to this list.
Moreover, one must use
the add
method in this class to add vectors of observations for
the sums used for covariance estimation to be updated correctly.
Failure to use this method, e.g., adding observations
to each individual tally in the list, will result in an incorrect
estimate of the covariances, unless the tallies
in the list can store observations.
For example, the following code, which adds the vector v in
the list of tallies list, works correctly only if the list
contains instances of TallyStore
:
Constructor Summary  

ListOfTalliesWithCovariance()
Creates an empty list of tallies with covariance support. 

ListOfTalliesWithCovariance(String name)
Creates an empty list of tallies with covariance support and name name. 
Method Summary  

void 
add(double[] x)
Adds a new vector of observations x to this list of tallies, and updates the internal data structures computing averages, and sums of products. 
void 
add(cern.colt.matrix.DoubleMatrix1D x)

ListOfTalliesWithCovariance<E> 
clone()
Clones this object. 
double 
covariance(int i,
int j)
Returns the empirical covariance of the observations in tallies with indices i and j. 
static ListOfTalliesWithCovariance<Tally> 
createWithTally(int size)
This factory method constructs and returns a list of tallies with size instances of Tally . 
static ListOfTalliesWithCovariance<TallyStore> 
createWithTallyStore(int size)
This factory method constructs and returns a list of tallies with size instances of TallyStore . 
void 
init()
Initializes this list of statistical probes by calling init on each element. 
Methods inherited from class umontreal.iro.lecuyer.stat.list.ListOfTallies 

areAllNumberObsEqual, average, correlation, correlation, covariance, numberObs, standardDeviation, variance 
Methods inherited from class umontreal.iro.lecuyer.stat.list.ListOfStatProbes 

add, add, addAll, addAll, addArrayOfObservationListener, clear, clearArrayOfObservationListeners, contains, containsAll, equals, get, getName, hashCode, indexOf, isBroadcasting, isCollecting, isEmpty, isModifiable, iterator, lastIndexOf, listIterator, listIterator, notifyListeners, remove, remove, removeAll, removeArrayOfObservationListener, report, retainAll, set, setBroadcasting, setCollecting, setName, setUnmodifiable, size, subList, sum, toArray, toArray 
Methods inherited from class java.lang.Object 

getClass, notify, notifyAll, toString, wait, wait, wait 
Constructor Detail 

public ListOfTalliesWithCovariance()
init
before
adding any observation.
public ListOfTalliesWithCovariance(String name)
init
before
adding any observation.
name
 the name of the new list.Method Detail 

public static ListOfTalliesWithCovariance<Tally> createWithTally(int size)
Tally
.
size
 the size of the list.
public static ListOfTalliesWithCovariance<TallyStore> createWithTallyStore(int size)
TallyStore
.
size
 the size of the list.
public void init()
ListOfStatProbes
init
on each element.
init
in class ListOfStatProbes<E extends Tally>
public void add(double[] x)
add
in class ListOfTallies<E extends Tally>
x
 the new vector of observations.public void add(cern.colt.matrix.DoubleMatrix1D x)
public double covariance(int i, int j)
ListOfTallies
ListOfTalliesWithCovariance
subclass provides an alternative implementation
of this method which does not require the
observations to be stored.
covariance
in class ListOfTallies<E extends Tally>
i
 the index of the first tally.j
 the index of the second tally.
public ListOfTalliesWithCovariance<E> clone()
clone
in class ListOfTallies<E extends Tally>

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