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java.lang.Object cern.jet.stat.tfloat.quantile.FloatQuantileFinderFactory
public class FloatQuantileFinderFactory
Factory constructing exact and approximate quantile finders for both known
and unknown N. Also see QuantileFloatBin1D
,
demonstrating how this package can be used.
The approx. algorithms compute approximate quantiles of large data sequences
in a single pass. The approximation guarantees are explicit, and apply for
arbitrary value distributions and arrival distributions of the data sequence.
The main memory requirements are smaller than for any other known technique
by an order of magnitude.
The approx. algorithms are primarily intended to help applications scale. When faced with a large data sequences, traditional methods either need very large memories or time consuming disk based sorting. In constrast, the approx. algorithms can deal with > 10^10 values without disk based sorting.
All classes can be seen from various angles, for example as
Use methods newXXX(...) to get new instances of one of the following quantile finders.
1. Exact quantile finding algorithm for known and unknown N requiring large main memory.
The folkore algorithm: Keeps all elements in main memory, sorts the list, then picks the quantiles.
2. Approximate quantile finding algorithm for known N requiring only one pass and little main memory.
Needs as input the following parameters:
It is also possible to couple the approximation algorithm with random sampling to further reduce memory requirements. With sampling, the approximation guarantees are explicit but probabilistic, i.e. they apply with respect to a (user controlled) confidence parameter "delta".
After Gurmeet Singh Manku, Sridhar Rajagopalan and Bruce G. Lindsay, Approximate Medians and other Quantiles in One Pass and with Limited Memory, Proc. of the 1998 ACM SIGMOD Int. Conf. on Management of Data, Paper available here.
3. Approximate quantile finding algorithm for unknown N requiring only one pass and little main memory.
This algorithm requires at most two times the memory of a corresponding approx. quantile finder knowing N.Needs as input the following parameters:
It is also possible to couple the approximation algorithm with random sampling to further reduce memory requirements. With sampling, the approximation guarantees are explicit but probabilistic, i.e. they apply with respect to a (user controlled) confidence parameter "delta".
After Gurmeet Singh Manku, Sridhar Rajagopalan and Bruce G. Lindsay, Random Sampling Techniques for Space Efficient Online Computation of Order Statistics of Large Datasets. Proc. of the 1999 ACM SIGMOD Int. Conf. on Management of Data, Paper available here.
Example usage:
_TODO_
KnownFloatQuantileEstimator
,
UnknownFloatQuantileEstimator
Method Summary  

static long[] 
known_N_compute_B_and_K(long N,
float epsilon,
float delta,
int quantiles,
float[] returnSamplingRate)
Computes the number of buffers and number of values per buffer such that quantiles can be determined with an approximation error no more than epsilon with a certain probability. 
static FloatArrayList 
newEquiDepthPhis(int quantiles)
Convenience method that computes phi's for equidepth histograms. 
static FloatQuantileFinder 
newFloatQuantileFinder(boolean known_N,
long N,
float epsilon,
float delta,
int quantiles,
FloatRandomEngine generator)
Returns a quantile finder that minimizes the amount of memory needed under the user provided constraints. 
static long[] 
unknown_N_compute_B_and_K(float epsilon,
float delta,
int quantiles)
Computes the number of buffers and number of values per buffer such that quantiles can be determined with an approximation error no more than epsilon with a certain probability. 
Methods inherited from class java.lang.Object 

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait 
Method Detail 

public static long[] known_N_compute_B_and_K(long N, float epsilon, float delta, int quantiles, float[] returnSamplingRate)
N
 the number of values over which quantiles shall be computed
(e.g 10^6).epsilon
 the approximation error which is guaranteed not to be exceeded
(e.g. 0.001) (0 <= epsilon <= 1). To
get exact result, set epsilon=0.0;delta
 the probability that the approximation error is more than than
epsilon (e.g. 0.0001) (0 <= delta <= 1
). To avoid probabilistic answers, set delta=0.0.quantiles
 the number of quantiles to be computed (e.g. 100) (
quantiles >= 1). If unknown in advance, set this
number large, e.g. quantiles >= 10000.returnSamplingRate
 output parameter, a float[1] where the sampling rate
is to be filled in.
public static FloatQuantileFinder newFloatQuantileFinder(boolean known_N, long N, float epsilon, float delta, int quantiles, FloatRandomEngine generator)
known_N
 specifies whether the number of elements over which quantiles
are to be computed is known or not.N
 if known_N==true, the number of elements over which
quantiles are to be computed. if known_N==false, the
upper limit on the number of elements over which quantiles are
to be computed. If such an upper limit is apriori unknown,
then set N = Long.MAX_VALUE.epsilon
 the approximation error which is guaranteed not to be exceeded
(e.g. 0.001) (0 <= epsilon <= 1). To
get exact result, set epsilon=0.0;delta
 the probability that the approximation error is more than than
epsilon (e.g. 0.0001) (0 <= delta <= 1). To avoid
probabilistic answers, set delta=0.0.quantiles
 the number of quantiles to be computed (e.g. 100) (
quantiles >= 1). If unknown in advance, set this
number large, e.g. quantiles >= 10000.generator
 a uniform random number generator. Set this parameter to
null to use a default generator.
public static FloatArrayList newEquiDepthPhis(int quantiles)
public static long[] unknown_N_compute_B_and_K(float epsilon, float delta, int quantiles)
epsilon
 the approximation error which is guaranteed not to be exceeded
(e.g. 0.001) (0 <= epsilon <= 1). To
get exact results, set epsilon=0.0;delta
 the probability that the approximation error is more than than
epsilon (e.g. 0.0001) (0 <= delta <= 1
). To get exact results, set delta=0.0.quantiles
 the number of quantiles to be computed (e.g. 100) (
quantiles >= 1). If unknown in advance, set this
number large, e.g. quantiles >= 10000.

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