Package org.apache.datasketches.quantiles

Class ItemsSketch<T>

  • Type Parameters:
    T - The sketch data type
    All Implemented Interfaces:
    PartitioningFeature<T>, QuantilesAPI, QuantilesGenericAPI<T>, SketchPartitionLimits
    public final class ItemsSketch<T>
extends Object
implements QuantilesGenericAPI<T>
    This is an implementation of the Low Discrepancy Mergeable Quantiles Sketch, using generic items, described in section 3.2 of the journal version of the paper "Mergeable Summaries" by Agarwal, Cormode, Huang, Phillips, Wei, and Yi:

    Reference:

    A k of 128 produces a normalized, rank error of about 1.7%. For example, the median returned from getQuantile(0.5) will be between the actual quantiles from the hypothetically sorted array of input quantiles at normalized ranks of 0.483 and 0.517, with a confidence of about 99%.

    The size of an ItemsSketch is very dependent on the size of the generic Items input into the sketch, so there is no comparable size table as there is for the DoublesSketch.

    See Also:
    QuantilesAPI

    • Field Detail

      • rand

        public static final Random rand
        Setting the seed makes the results of the sketch deterministic if the input items are received in exactly the same order. This is only useful when performing test comparisons, otherwise, it is not recommended.

    • Method Detail

      • getInstance

        public static <T> ItemsSketch<T> getInstance​(Class<T> clazz,
                                             Comparator<? super T> comparator)
        Obtains a new instance of an ItemsSketch using the DEFAULT_K.
        Type Parameters:
        T - The sketch data type
        Parameters:
        clazz - the given class of T
        comparator - to compare items
        Returns:
        an ItemSketch<T>.

      • getInstance

        public static <T> ItemsSketch<T> getInstance​(Class<T> clazz,
                                             int k,
                                             Comparator<? super T> comparator)
        Obtains a new instance of an ItemsSketch.
        Type Parameters:
        T - The sketch data type
        Parameters:
        clazz - the given class of T
        k - Parameter that controls space usage of sketch and accuracy of estimates. Must be greater than 2 and less than 65536 and a power of 2.
        comparator - to compare items
        Returns:
        an ItemSketch<T>.

      • getInstance

        public static <T> ItemsSketch<T> getInstance​(Class<T> clazz,
                                             org.apache.datasketches.memory.Memory srcMem,
                                             Comparator<? super T> comparator,
                                             ArrayOfItemsSerDe<T> serDe)
        Heapifies the given srcMem, which must be a Memory image of a ItemsSketch
        Type Parameters:
        T - The sketch data type
        Parameters:
        clazz - the given class of T
        srcMem - a Memory image of a sketch. See Memory
        comparator - to compare items
        serDe - an instance of ArrayOfItemsSerDe
        Returns:
        a ItemSketch<T> on the Java heap.

      • getCDF

        public double[] getCDF​(T[] splitPoints,
                       QuantileSearchCriteria searchCrit)
        Description copied from interface: QuantilesGenericAPI
        Returns an approximation to the Cumulative Distribution Function (CDF) of the input stream as a monotonically increasing array of double ranks (or cumulative probabilities) on the interval [0.0, 1.0], given a set of splitPoints.

        The resulting approximations have a probabilistic guarantee that can be obtained from the getNormalizedRankError(false) function.

        Specified by:
        getCDF in interface QuantilesGenericAPI<T>
        Parameters:
        splitPoints - an array of m unique, monotonically increasing items (of the same type as the input items) that divide the item input domain into m+1 overlapping intervals.

        The start of each interval is below the lowest item retained by the sketch corresponding to a zero rank or zero probability, and the end of the interval is the rank or cumulative probability corresponding to the split point.

        The (m+1)th interval represents 100% of the distribution represented by the sketch and consistent with the definition of a cumulative probability distribution, thus the (m+1)th rank or probability in the returned array is always 1.0.

        If a split point exactly equals a retained item of the sketch and the search criterion is:

        • INCLUSIVE, the resulting cumulative probability will include that item.
        • EXCLUSIVE, the resulting cumulative probability will not include the weight of that split point.

        It is not recommended to include either the minimum or maximum items of the input stream.

        searchCrit - the desired search criteria.
        Returns:
        a discrete CDF array of m+1 double ranks (or cumulative probabilities) on the interval [0.0, 1.0].

      • getMaxItem

        public T getMaxItem()
        Description copied from interface: QuantilesGenericAPI
        Returns the maximum item of the stream. This may be distinct from the largest item retained by the sketch algorithm.
        Specified by:
        getMaxItem in interface QuantilesGenericAPI<T>
        Returns:
        the maximum item of the stream

      • getMinItem

        public T getMinItem()
        Description copied from interface: QuantilesGenericAPI
        Returns the minimum item of the stream. This may be distinct from the smallest item retained by the sketch algorithm.
        Specified by:
        getMinItem in interface QuantilesGenericAPI<T>
        Returns:
        the minimum item of the stream

      • getPartitionBoundariesFromNumParts

        public GenericPartitionBoundaries<T> getPartitionBoundariesFromNumParts​(int numEquallySizedParts,
                                                                        QuantileSearchCriteria searchCrit)
        Description copied from interface: PartitioningFeature
        This method returns an instance of GenericPartitionBoundaries which provides sufficient information for the user to create the given number of equally sized partitions, where "equally sized" refers to an approximately equal number of items per partition.

        The sketch must not be empty.

        Specified by:
        getPartitionBoundariesFromNumParts in interface PartitioningFeature<T>
        Parameters:
        numEquallySizedParts - an integer that specifies the number of equally sized partitions between getMinItem() and getMaxItem(). This must be a positive integer less than getMaxPartitions()
        • A 1 will return: minItem, maxItem.
        • A 2 will return: minItem, median quantile, maxItem.
        • Etc.
        searchCrit - If INCLUSIVE, all the returned quantiles are the upper boundaries of the equally sized partitions with the exception of the lowest returned quantile, which is the lowest boundary of the lowest ranked partition. If EXCLUSIVE, all the returned quantiles are the lower boundaries of the equally sized partitions with the exception of the highest returned quantile, which is the upper boundary of the highest ranked partition.
        Returns:
        an instance of GenericPartitionBoundaries.

      • getPartitionBoundariesFromPartSize

        public GenericPartitionBoundaries<T> getPartitionBoundariesFromPartSize​(long nominalPartSizeItems,
                                                                        QuantileSearchCriteria searchCrit)
        Description copied from interface: PartitioningFeature
        This method returns an instance of GenericPartitionBoundaries which provides sufficient information for the user to create the given number of equally sized partitions, where "equally sized" refers to an approximately equal number of items per partition.

        The sketch must not be empty.

        Specified by:
        getPartitionBoundariesFromPartSize in interface PartitioningFeature<T>
        Parameters:
        nominalPartSizeItems - an integer that specifies the nominal size, in items, of each target partition. This must be a positive integer greater than getMinPartitionSizeItems().
        searchCrit - If INCLUSIVE, all the returned quantiles are the upper boundaries of the equally sized partitions with the exception of the lowest returned quantile, which is the lowest boundary of the lowest ranked partition. If EXCLUSIVE, all the returned quantiles are the lower boundaries of the equally sized partitions with the exception of the highest returned quantile, which is the upper boundary of the highest ranked partition.
        Returns:
        an instance of GenericPartitionBoundaries.

      • getPMF

        public double[] getPMF​(T[] splitPoints,
                       QuantileSearchCriteria searchCrit)
        Description copied from interface: QuantilesGenericAPI
        Returns an approximation to the Probability Mass Function (PMF) of the input stream as an array of probability masses as doubles on the interval [0.0, 1.0], given a set of splitPoints.

        The resulting approximations have a probabilistic guarantee that can be obtained from the getNormalizedRankError(true) function.

        Specified by:
        getPMF in interface QuantilesGenericAPI<T>
        Parameters:
        splitPoints - an array of m unique, monotonically increasing items (of the same type as the input items) that divide the item input domain into m+1 consecutive, non-overlapping intervals.

        Each interval except for the end intervals starts with a split point and ends with the next split point in sequence.

        The first interval starts below the lowest item retained by the sketch corresponding to a zero rank or zero probability, and ends with the first split point

        The last (m+1)th interval starts with the last split point and ends after the last item retained by the sketch corresponding to a rank or probability of 1.0.

        The sum of the probability masses of all (m+1) intervals is 1.0.

        If the search criterion is:

        • INCLUSIVE, and the upper split point of an interval equals an item retained by the sketch, the interval will include that item. If the lower split point equals an item retained by the sketch, the interval will exclude that item.
        • EXCLUSIVE, and the upper split point of an interval equals an item retained by the sketch, the interval will exclude that item. If the lower split point equals an item retained by the sketch, the interval will include that item.

        It is not recommended to include either the minimum or maximum items of the input stream.

        searchCrit - the desired search criteria.
        Returns:
        a PMF array of m+1 probability masses as doubles on the interval [0.0, 1.0].

      • getQuantile

        public T getQuantile​(double rank,
                     QuantileSearchCriteria searchCrit)
        Description copied from interface: QuantilesGenericAPI
        Gets the approximate quantile of the given normalized rank and the given search criterion.
        Specified by:
        getQuantile in interface QuantilesGenericAPI<T>
        Parameters:
        rank - the given normalized rank, a double in the range [0.0, 1.0].
        searchCrit - If INCLUSIVE, the given rank includes all quantiles ≤ the quantile directly corresponding to the given rank. If EXCLUSIVE, he given rank includes all quantiles < the quantile directly corresponding to the given rank.
        Returns:
        the approximate quantile given the normalized rank.
        See Also:
        QuantileSearchCriteria

      • getQuantileLowerBound

        public T getQuantileLowerBound​(double rank)
        Description copied from interface: QuantilesGenericAPI
        Gets the lower bound of the quantile confidence interval in which the quantile of the given rank exists.

        Although it is possible to estimate the probability that the true quantile exists within the quantile confidence interval specified by the upper and lower quantile bounds, it is not possible to guarantee the width of the quantile confidence interval as an additive or multiplicative percent of the true quantile.

        Specified by:
        getQuantileLowerBound in interface QuantilesGenericAPI<T>
        Parameters:
        rank - the given normalized rank
        Returns:
        the lower bound of the quantile confidence interval in which the quantile of the given rank exists.

      • getQuantileUpperBound

        public T getQuantileUpperBound​(double rank)
        Description copied from interface: QuantilesGenericAPI
        Gets the upper bound of the quantile confidence interval in which the true quantile of the given rank exists.

        Although it is possible to estimate the probability that the true quantile exists within the quantile confidence interval specified by the upper and lower quantile bounds, it is not possible to guarantee the width of the quantile interval as an additive or multiplicative percent of the true quantile.

        Specified by:
        getQuantileUpperBound in interface QuantilesGenericAPI<T>
        Parameters:
        rank - the given normalized rank
        Returns:
        the upper bound of the quantile confidence interval in which the true quantile of the given rank exists.

      • getQuantiles

        public T[] getQuantiles​(double[] ranks,
                        QuantileSearchCriteria searchCrit)
        Description copied from interface: QuantilesGenericAPI
        Gets an array of quantiles from the given array of normalized ranks.
        Specified by:
        getQuantiles in interface QuantilesGenericAPI<T>
        Parameters:
        ranks - the given array of normalized ranks, each of which must be in the interval [0.0,1.0].
        searchCrit - if INCLUSIVE, the given ranks include all quantiles ≤ the quantile directly corresponding to each rank.
        Returns:
        an array of quantiles corresponding to the given array of normalized ranks.
        See Also:
        QuantileSearchCriteria

      • getRank

        public double getRank​(T quantile,
                      QuantileSearchCriteria searchCrit)
        Description copied from interface: QuantilesGenericAPI
        Gets the normalized rank corresponding to the given a quantile.
        Specified by:
        getRank in interface QuantilesGenericAPI<T>
        Parameters:
        quantile - the given quantile
        searchCrit - if INCLUSIVE the given quantile is included into the rank.
        Returns:
        the normalized rank corresponding to the given quantile.
        See Also:
        QuantileSearchCriteria

      • getRankLowerBound

        public double getRankLowerBound​(double rank)
        Description copied from interface: QuantilesAPI
        Gets the lower bound of the rank confidence interval in which the true rank of the given rank exists.
        Specified by:
        getRankLowerBound in interface QuantilesAPI
        Parameters:
        rank - the given normalized rank.
        Returns:
        the lower bound of the rank confidence interval in which the true rank of the given rank exists.

      • getRankUpperBound

        public double getRankUpperBound​(double rank)
        Description copied from interface: QuantilesAPI
        Gets the upper bound of the rank confidence interval in which the true rank of the given rank exists.
        Specified by:
        getRankUpperBound in interface QuantilesAPI
        Parameters:
        rank - the given normalized rank.
        Returns:
        the upper bound of the rank confidence interval in which the true rank of the given rank exists.

      • getRanks

        public double[] getRanks​(T[] quantiles,
                         QuantileSearchCriteria searchCrit)
        Description copied from interface: QuantilesGenericAPI
        Gets an array of normalized ranks corresponding to the given array of quantiles and the given search criterion.
        Specified by:
        getRanks in interface QuantilesGenericAPI<T>
        Parameters:
        quantiles - the given array of quantiles
        searchCrit - if INCLUSIVE, the given quantiles include the rank directly corresponding to each quantile.
        Returns:
        an array of normalized ranks corresponding to the given array of quantiles.
        See Also:
        QuantileSearchCriteria

      • getK

        public int getK()
        Description copied from interface: QuantilesAPI
        Gets the user configured parameter k, which controls the accuracy of the sketch and its memory space usage.
        Specified by:
        getK in interface QuantilesAPI
        Returns:
        the user configured parameter k, which controls the accuracy of the sketch and its memory space usage.

      • getN

        public long getN()
        Description copied from interface: QuantilesAPI
        Gets the length of the input stream offered to the sketch..
        Specified by:
        getN in interface QuantilesAPI
        Specified by:
        getN in interface SketchPartitionLimits
        Returns:
        the length of the input stream offered to the sketch.

      • getNormalizedRankError

        public double getNormalizedRankError​(boolean pmf)
        Description copied from interface: QuantilesAPI
        Gets the approximate rank error of this sketch normalized as a fraction between zero and one. The epsilon returned is a best fit to 99 percent confidence empirically measured max error in thousands of trials.
        Specified by:
        getNormalizedRankError in interface QuantilesAPI
        Parameters:
        pmf - if true, returns the "double-sided" normalized rank error for the getPMF() function. Otherwise, it is the "single-sided" normalized rank error for all the other queries.
        Returns:
        if pmf is true, returns the "double-sided" normalized rank error for the getPMF() function. Otherwise, it is the "single-sided" normalized rank error for all the other queries.

      • getNormalizedRankError

        public static double getNormalizedRankError​(int k,
                                            boolean pmf)
        Gets the normalized rank error given k and pmf. Static method version of the getNormalizedRankError(boolean).
        Parameters:
        k - the configuration parameter
        pmf - if true, returns the "double-sided" normalized rank error for the getPMF() function. Otherwise, it is the "single-sided" normalized rank error for all the other queries.
        Returns:
        if pmf is true, the normalized rank error for the getPMF() function. Otherwise, it is the "single-sided" normalized rank error for all the other queries.

      • getKFromEpsilon

        public static int getKFromEpsilon​(double epsilon,
                                  boolean pmf)
        Gets the approximate k to use given epsilon, the normalized rank error.
        Parameters:
        epsilon - the normalized rank error between zero and one.
        pmf - if true, this function returns k assuming the input epsilon is the desired "double-sided" epsilon for the getPMF() function. Otherwise, this function returns k assuming the input epsilon is the desired "single-sided" epsilon for all the other queries.
        Returns:
        k given epsilon.

      • hasMemory

        public boolean hasMemory()
        Description copied from interface: QuantilesAPI
        Returns true if this sketch's data structure is backed by Memory or WritableMemory.
        Specified by:
        hasMemory in interface QuantilesAPI
        Returns:
        true if this sketch's data structure is backed by Memory or WritableMemory.

      • isEmpty

        public boolean isEmpty()
        Description copied from interface: QuantilesAPI
        Returns true if this sketch is empty.
        Specified by:
        isEmpty in interface QuantilesAPI
        Returns:
        true if this sketch is empty.

      • isDirect

        public boolean isDirect()
        Description copied from interface: QuantilesAPI
        Returns true if this sketch's data structure is off-heap (a.k.a., Direct or Native memory).
        Specified by:
        isDirect in interface QuantilesAPI
        Returns:
        true if this sketch's data structure is off-heap (a.k.a., Direct or Native memory).

      • isEstimationMode

        public boolean isEstimationMode()
        Description copied from interface: QuantilesAPI
        Returns true if this sketch is in estimation mode.
        Specified by:
        isEstimationMode in interface QuantilesAPI
        Returns:
        true if this sketch is in estimation mode.

      • isReadOnly

        public boolean isReadOnly()
        Description copied from interface: QuantilesAPI
        Returns true if this sketch is read only.
        Specified by:
        isReadOnly in interface QuantilesAPI
        Returns:
        true if this sketch is read only.

      • reset

        public void reset()
        Description copied from interface: QuantilesAPI
        Resets this sketch to the empty state. If the sketch is read only this does nothing.

        The parameter k will not change.

        Specified by:
        reset in interface QuantilesAPI

      • toByteArray

        public byte[] toByteArray​(ArrayOfItemsSerDe<T> serDe)
        Serialize this sketch to a byte array form.
        Parameters:
        serDe - an instance of ArrayOfItemsSerDe
        Returns:
        byte array of this sketch

      • toByteArray

        public byte[] toByteArray​(boolean ordered,
                          ArrayOfItemsSerDe<T> serDe)
        Serialize this sketch to a byte array form.
        Parameters:
        ordered - if true the base buffer will be ordered (default == false).
        serDe - an instance of ArrayOfItemsSerDe
        Returns:
        this sketch in a byte array form.

      • toString

        public String toString()
        Returns human readable summary information about this sketch. Used for debugging.
        Specified by:
        toString in interface QuantilesAPI
        Overrides:
        toString in class Object
        Returns:
        a summary of the key parameters of the sketch.

      • toString

        public String toString​(boolean withLevels,
                       boolean withLevelsAndItems)
        Returns human readable summary information about this sketch. Used for debugging.
        Parameters:
        withLevels - if true includes sketch levels array summary information
        withLevelsAndItems - if true include detail of levels array and items array together
        Returns:
        human readable summary information about this sketch.

      • toString

        public static String toString​(byte[] byteArr)
        Returns a human readable string of the preamble of a byte array image of an ItemsSketch. Used for debugging.
        Parameters:
        byteArr - the given byte array
        Returns:
        a human readable string of the preamble of a byte array image of an ItemsSketch.

      • toString

        public static String toString​(org.apache.datasketches.memory.Memory mem)
        Returns a human readable string of the preamble of a Memory image of an ItemsSketch. Used for debugging.
        Parameters:
        mem - the given Memory
        Returns:
        a human readable string of the preamble of a Memory image of an ItemsSketch.

      • downSample

        public ItemsSketch<T> downSample​(int newK)
        From an existing sketch, this creates a new sketch that can have a smaller K. The original sketch is not modified.
        Parameters:
        newK - the new K that must be smaller than current K. It is required that this.getK() = newK * 2^(nonnegative integer).
        Returns:
        the new sketch.

      • getNumRetained

        public int getNumRetained()
        Description copied from interface: QuantilesAPI
        Gets the number of quantiles retained by the sketch.
        Specified by:
        getNumRetained in interface QuantilesAPI
        Returns:
        the number of quantiles retained by the sketch

      • putMemory

        public void putMemory​(org.apache.datasketches.memory.WritableMemory dstMem,
                      ArrayOfItemsSerDe<T> serDe)
        Puts the current sketch into the given Memory if there is sufficient space. Otherwise, throws an error.
        Parameters:
        dstMem - the given memory.
        serDe - an instance of ArrayOfItemsSerDe

      • update

        public void update​(T item)
        Description copied from interface: QuantilesGenericAPI
        Updates this sketch with the given item.
        Specified by:
        update in interface QuantilesGenericAPI<T>
        Parameters:
        item - from a stream of items. Nulls are ignored.