10 Colt Single-Row Functions

This chapter provides a reference to Colt single-row functions included in Oracle Continuous Query Language (Oracle CQL). Colt single-row functions are based on the Colt open source libraries for high performance scientific and technical computing.

For more information, see Functions.

This chapter includes the following section:

Introduction to Oracle CQLBuilt-In Single-Row Colt Functions.

10.1 Introduction to Oracle CQLBuilt-In Single-Row Colt Functions

Table 10-1 lists the built-in single-row Colt functions that Oracle CQL provides.

Table 10-1 Oracle CQL Built-in Single-Row Colt-Based Functions

Colt Package	Function
`cern.jet.math.Arithmetic` A set of basic polynomials, rounding, and calculus functions.	`binomial` `binomial1` `ceil` `factorial` `floor` `log` `log2` `log10` `logFactorial` `longFactorial` `stirlingCorrection`
`cern.jet.math.Bessel` A set of Bessel functions.	`i0` `i0e` `i1` `i1e` `j0` `j1` `jn` `k0` `k0e` `k1` `k1e` `kn` `y0` `y1` `yn`
`cern.jet.random.engine.RandomSeedTable` A table with good seeds for pseudo-random number generators. Each sequence in this table has a period of 10**9 numbers.	`getSeedAtRowColumn`
`cern.jet.stat.Gamma` A set of Gamma and Beta functions.	`beta` `gamma` `incompleteBeta` `incompleteGamma` `incompleteGammaComplement` `logGamma`
`cern.jet.stat.Probability` A set of probability distributions.	`beta1` `betaComplemented` `binomial2` `binomialComplemented` `chiSquare` `chiSquareComplemented` `errorFunction` `errorFunctionComplemented` `gamma1` `gammaComplemented` `negativeBinomial` `negativeBinomialComplemented` `normal` `normal1` `normalInverse` `poisson` `poissonComplemented` `studentT` `studentTInverse`
`cern.colt.bitvector.QuickBitVector` A set of non polymorphic, non bounds checking, low level bit-vector functions.	`bitMaskWithBitsSetFromTo` `leastSignificantBit` `mostSignificantBit`
`cern.colt.map.HashFunctions` A set of hash functions.	`hash` `hash1` `hash2` `hash3`

Note:

Built-in function names are case sensitive and you must use them in the case shown (in lower case).

Note:

In stream input examples, lines beginning with h (such as h 3800) are heartbeat input tuples. These inform Oracle Stream Analytics that no further input will have a timestamp lesser than the heartbeat value.

For more information, see:

10.2 beta

Syntax

Purpose

beta is based on cern.jet.stat.Gamma. It returns the beta function (see Figure 10-1) of the input arguments as a double.

Figure 10-1 cern.jet.stat.Gamma beta

This function takes the following arguments:

double1: the x value.
double2: the y value.

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/random/Beta.html#Beta(double, double, cern.jet.random.engine.RandomEngine).

Examples

Consider the query qColt28. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation .

<query id="qColt28"><![CDATA[ 
    select beta(c2,c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           3.1415927
1000:       +           1.899038
1200:       +           1.251922
2000:       +           4.226169

10.3 beta1

Syntax

Purpose

beta1 is based on cern.jet.stat.Probability. It returns the area P(x) from 0 to x under the beta density function (see Figure 10-2) as a double.

Figure 10-2 cern.jet.stat.Probability beta1

This function takes the following arguments:

double1: the alpha parameter of the beta distribution a.
double2: the beta parameter of the beta distribution b.
double3: the integration end point x.

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/random/Beta.html#Beta(double, double, cern.jet.random.engine.RandomEngine).

Examples

Consider the query qColt35. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt35"><![CDATA[ 
    select beta1(c2,c2,c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           0.5       
1000:       +           0.66235894
1200:       +           0.873397  
2000:       +           0.44519535

10.4 betaComplemented

Syntax

Purpose

betaComplemented is based on cern.jet.stat.Probability. It returns the area under the right hand tail (from x to infinity) of the beta density function (see Figure 10-2) as a double.

This function takes the following arguments:

double1: the alpha parameter of the beta distribution a.
double2: the beta parameter of the beta distribution b.
double3: the integration end point x.

For more information, see:

Examples

Consider the query qColt37. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt37"><![CDATA[ 
    select betaComplemented(c2,c2,c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           0.5       
1000:       +           0.66235894
1200:       +           0.873397  
2000:       +           0.44519535

10.5 binomial

Syntax

Purpose

binomial is based on cern.jet.math.Arithmetic. It returns the binomial coefficient n over k (see Figure 10-3) as a double.

Figure 10-3 Definition of binomial coefficient

This function takes the following arguments:

double1: the n value.
long2: the k value.

Table 10-2 lists the binomial function return values for various values of k.

Table 10-2 cern.jet.math.Arithmetic binomial Return Values

Arguments	Return Value
`k` < 0	0
`k` = 0	1
`k` = 1	`n`
Any other value of `k`	Computed binomial coefficient as given in Figure 10-3.

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/math/Arithmetic.html#binomial(double, long).

Examples

Consider the query qColt6. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 long), the query returns the relation.

<query id="qColt6"><![CDATA[ 
    select binomial(c2,c3) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           -0.013092041 
1000:       +           -0.012374863 
1200:       +           -0.0010145549
2000:       +           -0.0416

10.6 binomial1

Syntax

Purpose

binomial1 is based on cern.jet.math.Arithmetic. It returns the binomial coefficient n over k (see Figure 10-3) as a double.

This function takes the following arguments:

long1: the n value.
long2: the k value.

Table 10-3 lists the BINOMIAL function return values for various values of k.

Table 10-3 cern.jet.math.Arithmetic Binomial1 Return Values

Arguments	Return Value
`k` < 0	0
`k` = 0 \|\| `k` = `n`	1
`k` = 1 \|\| `k` = `n`-1	`n`
Any other value of `k`	Computed binomial coefficient as given in Figure 10-3.

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/random/Binomial.html#Binomial(int, double, cern.jet.random.engine.RandomEngine).

Examples

Consider the query qColt7. Given the data stream SColtFunc with schema (c1 integer, c2 float, c3 long), the query returns the relation.

<query id="qColt7"><![CDATA[ 
    select binomial1(c3,c3) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           1.0
1000:       +           1.0
1200:       +           1.0
2000:       +           1.0

10.7 binomial2

Syntax

Purpose

binomial2 is based on cern.jet.stat.Probability. It returns the sum of the terms 0 through k of the binomial probability density (see Figure 10-4) as a double.

Figure 10-4 cern.jet.stat.Probability binomial2

This function takes the following arguments (all arguments must be positive):

integer1: the end term k.
integer2: the number of trials n.
double3: the probability of success p in (0.0, 1.0).

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/stat/Probability.html#binomial(int, int, double).

Examples

Consider the query qColt34. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt34"><![CDATA[ 
    select binomial2(c1,c1,c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           1.0
1000:       +           1.0
1200:       +           1.0
2000:       +           1.0

10.8 binomialComplemented

Syntax

Purpose

binomialComplemented is based on cern.jet.stat.Probability. It returns the sum of the terms k+1 through n of the binomial probability density (see Figure 10-5) as a double.

Figure 10-5 cern.jet.stat.Probability binomialComplemented

This function takes the following arguments (all arguments must be positive):

integer1: the end term k.
integer2: the number of trials n.
double3: the probability of success p in (0.0, 1.0).

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/stat/Probability.html#binomialComplemented(int, int, double).

Examples

Consider the query qColt38. Given the data stream SColtFunc with schema (integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt38"><![CDATA[ 
    select binomialComplemented(c1,c1,c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           0.0
1000:       +           0.0
1200:       +           0.0
2000:       +           0.0

10.9 bitMaskWithBitsSetFromTo

Syntax

Purpose

bitMaskWithBitsSetFromTo is based on cern.colt.bitvector.QuickBitVector. It returns a 64-bit wide bit mask as a long with bits in the specified range set to 1 and all other bits set to 0.

This function takes the following arguments:

integer1: the from value; index of the start bit (inclusive).
integer2: the to value; index of the end bit (inclusive).

Precondition (not checked): to - from + 1 >= 0 && to - from + 1 <= 64.

If to - from + 1 = 0 then returns a bit mask with all bits set to 0.

For more information, see:

Examples

Consider the query qColt53. Given the data stream SColtFunc with schema (c1 integer, c2 float, c3 bigint), the query returns the relation.

query id="qColt53"><![CDATA[ 
    select bitMaskWithBitsSetFromTo(c1,c1) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           2  
1000:       +           16 
1200:       +           8  
2000:       +           256

10.10 ceil

Syntax

Purpose

ceil is based on cern.jet.math.Arithmetic. It returns the smallest long greater than or equal to its double argument.

This method is safer than using (float) java.lang.Math.ceil(long) because of possible rounding error.

For more information, see:

Examples

Consider the query qColt1. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt1"><![CDATA[ 
    select ceil(c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           1
1000:       +           1
1200:       +           1
2000:       +           1

10.11 chiSquare

Syntax

Purpose

chiSquare is based on cern.jet.stat.Probability. It returns the area under the left hand tail (from 0 to x) of the Chi square probability density function with v degrees of freedom (see Figure 10-6) as a double.

Figure 10-6 cern.jet.stat.Probability chiSquare

This function takes the following arguments (all arguments must be positive):

double1: the degrees of freedom v.
double2: the integration end point x.

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/stat/Probability.html#chiSquare(double, double).

Examples

Consider the query qColt39. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation .

<query id="qColt39"><![CDATA[ 
    select chiSquare(c2,c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           0.0
1000:       +           0.0
1200:       +           0.0
2000:       +           0.0

10.12 chiSquareComplemented

Syntax

Purpose

chiSquareComplemented is based on cern.jet.stat.Probability. It returns the area under the right hand tail (from x to infinity) of the Chi square probability density function with v degrees of freedom (see Figure 10-6) as a double.

This function takes the following arguments (all arguments must be positive):

double1: the degrees of freedom v.
double2: the integration end point x.

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/stat/Probability.html#chiSquareComplemented(double, double).

Examples

Consider the query qColt40. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation .

<query id="qColt40"><![CDATA[ 
    select chiSquareComplemented(c2,c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           0.0
1000:       +           0.0
1200:       +           0.0
2000:       +           0.0

10.13 errorFunction

Syntax

Purpose

errorFunction is based on cern.jet.stat.Probability. It returns the error function of the normal distribution of the double argument as a double, using the integral that Figure 10-7 shows.

Figure 10-7 cern.jet.stat.Probability errorFunction

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/stat/Probability.html#errorFunction(double).

Examples

Consider the query qColt41. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt41"><![CDATA[ 
    select errorFunction(c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           0.5204999 
1000:       +           0.6778012 
1200:       +           0.79184324
2000:       +           0.42839235

10.14 errorFunctionComplemented

Syntax

Purpose

errorFunctionComplemented is based on cern.jet.stat.Probability. It returns the complementary error function of the normal distribution of the double argument as a double, using the integral that Figure 10-8 shows.

Figure 10-8 cern.jet.stat.Probability errorfunctioncompelemented

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/stat/Probability.html#errorFunctionComplemented(double).

Examples

Consider the query qColt42. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt42"><![CDATA[ 
    select errorFunctionComplemented(c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           0.47950011
1000:       +           0.3221988 
1200:       +           0.20815676
2000:       +           0.57160765

10.15 factorial

Syntax

Purpose

factorial is based on cern.jet.math.Arithmetic. It returns the factorial of the positive integer argument as a double.

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/math/Arithmetic.html#factorial(int).

Examples

Consider the query qColt8. Given the data stream SColtFunc with schema (c1 integer, c2 float, c3 bigint), the query returns the relation.

<query id="qColt8"><![CDATA[ 
    select factorial(c1) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +               1.0
1000:       +              24.0
1200:       +               6.0
2000:       +           40320.0

10.16 floor

Syntax

Purpose

floor is based on cern.jet.math.Arithmetic. It returns the largest long value less than or equal to the double argument.

This method is safer than using (double) java.lang.Math.floor(double) because of possible rounding error.

For more information, see:

Examples

Consider the query qColt2. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt2"><![CDATA[ 
    select floor(c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           0
1000:       +           0
1200:       +           0
2000:       +           0

10.17 gamma

Syntax

Purpose

gamma is based on cern.jet.stat.Gamma. It returns the Gamma function of the double argument as a double.

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/stat/Probability.html#gamma(double, double, double).

Examples

Consider the query qColt29. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt29"><![CDATA[ 
    select gamma(c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           1.7724539
1000:       +           1.2980554
1200:       +           1.0768307
2000:       +           2.2181594

10.18 gamma1

Syntax

Purpose

gamma1 is based on cern.jet.stat.Probability. It returns the integral from zero to x of the gamma probability density function (see Figure 10-9) as a double.

Figure 10-9 cern.jet.stat.Probability gamma1

This function takes the following arguments:

double1: the gamma distribution alpha value a
double2: the gamma distribution beta or lambda value b
double3: the integration end point x.

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/random/Gamma.html#Gamma(double, double, cern.jet.random.engine.RandomEngine).

Examples

Consider the query qColt36. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt36"><![CDATA[ 
    select gamma1(c2,c2,c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           0.5204999 
1000:       +           0.55171627
1200:       +           0.59975785
2000:       +           0.51785487

10.19 gammaComplemented

Syntax

Purpose

gammaComplemented is based on cern.jet.stat.Probability. It returns the integral from x to infinity of the gamma probability density function (see Figure 10-10) as a double.

Figure 10-10 cern.jet.stat.Probability gammaComplemented

This function takes the following arguments:

double1: the gamma distribution alpha value a
double2: the gamma distribution beta or lambda value b
double3: the integration end point x.

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/stat/Probability.html#gammaComplemented(double, double, double).

Examples

Consider the query qColt43. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt43"><![CDATA[ 
    select gammaComplemented(c2,c2,c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           0.47950011
1000:       +           0.44828376
1200:       +           0.40024218
2000:       +           0.48214513

10.20 getSeedAtRowColumn

Syntax

Purpose

getSeedAtRowColumn is based on cern.jet.random.engine.RandomSeedTable. It returns a deterministic seed as an integer from a (seemingly gigantic) matrix of predefined seeds.

This function takes the following arguments:

integer1: the row value; should (but need not) be in [0,Integer.MAX_VALUE].
integer2: the column value; should (but need not) be in [0,1].

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/random/engine/RandomSeedTable.html#getSeedAtRowColumn(int, int).

Examples

Consider the query qColt27. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt27"><![CDATA[ 
    select getSeedAtRowColumn(c1,c1) from SColtFunc
]]></query>

Tmestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           253987020 
1000:       +           1289741558
1200:       +           417696270 
2000:       +           350557787

10.21 hash

Syntax

Purpose

hash is based on cern.colt.map.HashFunctions. It returns an integer hashcode for the specified double value.

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/colt/map/HashFunctions.html#hash(double).

Examples

Consider the query qColt56. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt56"><![CDATA[ 
    select hash(c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +            1071644672
1000:       +            1608935014
1200:       +            2146204385
2000:       +           -1613129319

10.22 hash1

Syntax

Purpose

hash1 is based on cern.colt.map.HashFunctions. It returns an integer hashcode for the specified float value.

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/colt/map/HashFunctions.html#hash(float).

Examples

Consider the query qColt57. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt57"><![CDATA[ 
    select hash1(c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           1302214522
1000:       +           1306362078
1200:       +           1309462552
2000:       +           1300047248

10.23 hash2

Syntax

Purpose

hash2 is based on cern.colt.map.HashFunctions. It returns an integer hashcode for the specified integer value.

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/colt/map/HashFunctions.html#hash(int).

Examples

Consider the query qColt58. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt58"><![CDATA[ 
    select hash2(c1) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           1
1000:       +           4
1200:       +           3
2000:       +           8

10.24 hash3

Syntax

Purpose

hash3 is based on cern.colt.map.HashFunctions. It returns an integer hashcode for the specified long value.

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/colt/map/HashFunctions.html#hash(long).

Examples

Consider the query qColt59. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt59"><![CDATA[ 
    select hash3(c3) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           8
1000:       +           6
1200:       +           12
2000:       +           4

10.25 i0

Syntax

Purpose

i0 is based on cern.jet.math.Bessel. It returns the modified Bessel function of order 0 of the double argument as a double.

The function is defined as i0(x) = j0(ix).

The range is partitioned into the two intervals [0,8] and (8,infinity).

For more information, see:

Examples

Consider the query qColt12. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt12"><![CDATA[ 
    select i0(c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           1.0634834
1000:       +           1.126303 
1200:       +           1.2080469
2000:       +           1.0404018

10.26 i0e

Syntax

Purpose

i0e is based on cern.jet.math.Bessel. It returns the exponentially scaled modified Bessel function of order 0 of the double argument as a double.

The function is defined as: i0e(x) = exp(-|x|) j0(ix).

For more information, see:

Examples

Consider the query qColt13. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt13"><![CDATA[ 
    select i0e(c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           0.64503527
1000:       +           0.55930555
1200:       +           0.4960914 
2000:       +           0.6974022

10.27 i1

Syntax

Purpose

i1 is based on cern.jet.math.Bessel. It returns the modified Bessel function of order 1 of the double argument as a double.

The function is defined as: i1(x) = -i j1(ix).

The range is partitioned into the two intervals [0,8] and (8,infinity). Chebyshev polynomial expansions are employed in each interval.

For more information, see:

Examples

Consider the query qColt14. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt14"><![CDATA[ 
    select i1(c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           0.2578943 
1000:       +           0.37187967
1200:       +           0.49053898
2000:       +           0.20402676

10.28 i1e

Syntax

Purpose

i1e is based on cern.jet.math.Bessel. It returns the exponentially scaled modified Bessel function of order 1 of the double argument as a double.

The function is defined as i1(x) = -i exp(-|x|) j1(ix).

For more information, see

Examples

Consider the query qColt15. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt15"><![CDATA[ 
    select i1e(c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           0.1564208 
1000:       +           0.18466999
1200:       +           0.20144266
2000:       +           0.13676323

10.29 incompleteBeta

Syntax

Purpose

incompleteBeta is based on cern.jet.stat.Gamma. It returns the Incomplete Beta Function evaluated from zero to x as a double.

This function takes the following arguments:

double1: the beta distribution alpha value a
double2: the beta distribution beta value b
double3: the integration end point x.

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/stat/Gamma.html#incompleteBeta(double, double, double).

Examples

Consider the query qColt30. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt30"><![CDATA[ 
    select incompleteBeta(c2,c2,c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           0.5       
1000:       +           0.66235894
1200:       +           0.873397  
2000:       +           0.44519535

10.30 incompleteGamma

Syntax

Purpose

incompleteGamma is based on cern.jet.stat.Gamma. It returns the Incomplete Gamma function of the arguments as a double.

This function takes the following arguments:

double1: the gamma distribution alpha value a.
double2: the integration end point x.

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/stat/Gamma.html#incompleteGamma(double, double).

Examples

Consider the query qColt31. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt31"><![CDATA[ 
    select incompleteGamma(c2,c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           0.6826895
1000:       +           0.6565891
1200:       +           0.6397422
2000:       +           0.7014413

10.31 incompleteGammaComplement

Syntax

Purpose

incompleteGammaComplement is based on cern.jet.stat.Gamma. It returns the Complemented Incomplete Gamma function of the arguments as a double.

This function takes the following arguments:

double1: the gamma distribution alpha value a.
double2: the integration start point x.

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/stat/Gamma.html#incompleteGammaComplement(double, double).

Examples

Consider the query qColt32. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt32"><![CDATA[ 
    select incompleteGammaComplement(c2,c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           0.3173105 
1000:       +           0.34341094
1200:       +           0.3602578 
2000:       +           0.29855874

10.32 j0

Syntax

Purpose

j0 is based on cern.jet.math.Bessel. It returns the Bessel function of the first kind of order 0 of the double argument as a double.

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/math/Bessel.html#j0(double).

Examples

Consider the query qColt16. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt16"><![CDATA[ 
    select j0(c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           0.9384698
1000:       +           0.8812009
1200:       +           0.8115654
2000:       +           0.9603982

10.33 j1

Syntax

Purpose

j1 is based on cern.jet.math.Bessel. It returns the Bessel function of the first kind of order 1 of the double argument as a double.

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/math/Bessel.html#j1(double).

Examples

Consider the query qColt17. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt17"><![CDATA[ 
    select j1(c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           0.24226846
1000:       +           0.32899573
1200:       +           0.40236986
2000:       +           0.19602658

10.34 jn

Syntax

Purpose

jn is based on cern.jet.math.Bessel. It returns the Bessel function of the first kind of order n of the argument as a double.

This function takes the following arguments:

integer1: the order of the Bessel function n.
double2: the value to compute the bessel function of x.

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/math/Bessel.html#jn(int, double).

Examples

Consider the query qColt18. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt18"><![CDATA[ 
    select jn(c1,c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           0.24226846  
1000:       +           6.1009696E-4
1200:       +           0.0139740035
2000:       +           6.321045E-11

10.35 k0

Syntax

Purpose

k0 is based on cern.jet.math.Bessel. It returns the modified Bessel function of the third kind of order 0 of the double argument as a double.

The range is partitioned into the two intervals [0,8] and (8, infinity). Chebyshev polynomial expansions are employed in each interval.

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/math/Bessel.html#k0(double).

Examples

Consider the query qColt19. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt19"><![CDATA[ 
    select k0(c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           0.92441905
1000:       +           0.6605199 
1200:       +           0.49396032
2000:       +           1.1145291

10.36 k0e

Syntax

Purpose

k0e is based on cern.jet.math.Bessel. It returns the exponentially scaled modified Bessel function of the third kind of order 0 of the double argument as a double.

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/math/Bessel.html#k0e(double).

Examples

Consider the query qColt20. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt20"><![CDATA[ 
    select k0e(c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           1.5241094
1000:       +           1.3301237
1200:       +           1.2028574
2000:       +           1.662682

10.37 k1

Syntax

Purpose

k1 is based on cern.jet.math.Bessel. It returns the modified Bessel function of the third kind of order 1 of the double argument as a double.

The range is partitioned into the two intervals [0,2] and (2, infinity). Chebyshev polynomial expansions are employed in each interval.

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/math/Bessel.html#k1(double).

Examples

Consider the query qColt21. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt21"><![CDATA[ 
    select k1(c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           1.6564411
1000:       +           1.0502836
1200:       +           0.7295154
2000:       +           2.1843543

10.38 k1e

Syntax

Purpose

k1e is based on cern.jet.math.Bessel. It returns the exponentially scaled modified Bessel function of the third kind of order 1 of the double argument as a double.

The function is defined as: k1e(x) = exp(x) * k1(x).

For more information, see:

Examples

Consider the query qColt22. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt22"><![CDATA[ 
    select k1e(c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           2.7310097
1000:       +           2.1150115
1200:       +           1.7764645
2000:       +           3.258674

10.39 kn

Syntax

Purpose

kn is based on cern.jet.math.Bessel. It returns the modified Bessel function of the third kind of order n of the argument as a double.

This function takes the following arguments:

integer1: the n value order of the Bessel function.
double2: the x value to compute the bessel function of.

The range is partitioned into the two intervals [0,9.55] and (9.55, infinity). An ascending power series is used in the low range, and an asymptotic expansion in the high range.

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/math/Bessel.html#kn(int, double).

Examples

Consider the query qColt23. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt23"><![CDATA[ 
    select kn(c1,c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +             1.6564411  
1000:       +           191.99422    
1200:       +            10.317473   
2000:       +             9.7876858E8

10.40 leastSignificantBit

Syntax

Purpose

leastSignificantBit is based on cern.colt.bitvector.QuickBitVector. It returns the index (as an integer) of the least significant bit in state true of the integer argument. Returns 32 if no bit is in state true.

For more information, see:

Examples

Consider the query qColt54. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt54"><![CDATA[ 
    select leastSignificantBit(c1) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           0
1000:       +           2
1200:       +           0
2000:       +           3

10.41 log

Syntax

Purpose

log is based on cern.jet.math.Arithmetic. It returns the computation that Figure 10-11 shows as a double.

Figure 10-11 cern.jet.math.Arithmetic log

This function takes the following arguments:

double1: the base.
double2: the value.

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/math/Arithmetic.html#log(double, double).

Examples

Consider the query qColt3. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt3"><![CDATA[ 
    select log(c2,c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           1.0
1000:       +           1.0
1200:       +           1.0
2000:       +           1.0

10.42 log10

Syntax

Purpose

log10 is based on cern.jet.math.Arithmetic. It returns the base 10 logarithm of a double value as a double.

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/math/Arithmetic.html#log10(double).

Examples

Consider the query qColt4. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt4"><![CDATA[ 
    select log10(c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           -0.30103    
1000:       +           -0.15490197 
1200:       +           -0.050610002
2000:       +           -0.39794

10.43 log2

Syntax

Purpose

log2 is based on cern.jet.math.Arithmetic. It returns the base 2 logarithm of a double value as a double.

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/math/Arithmetic.html#log2(double).

Examples

Consider the query qColt9. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt9"><![CDATA[ 
    select log2(c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           -1.0       
1000:       +           -0.5145732 
1200:       +           -0.16812278
2000:       +           -1.321928

10.44 logFactorial

Syntax

Purpose

logFactorial is based on cern.jet.math.Arithmetic. It returns the natural logarithm (base e) of the factorial of its integer argument as a double

For argument values k<30, the function looks up the result in a table in O(1). For argument values k>=30, the function uses Stirlings approximation.

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/math/Arithmetic.html#logFactorial(int).

Examples

Consider the query qColt10. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt10"><![CDATA[ 
    select logFactorial(c1) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +            0.0      
1000:       +            3.1780539
1200:       +            1.7917595
2000:       +           10.604603

10.45 logGamma

Syntax

Purpose

logGamma is based on cern.jet.stat.Gamma. It returns the natural logarithm (base e) of the gamma function of the double argument as a double.

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/stat/Gamma.html#logGamma(double).

Examples

Consider the query qColt33. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt33"><![CDATA[ 
    select logGamma(c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           0.5723649 
1000:       +           0.26086727
1200:       +           0.07402218
2000:       +           0.7966778

10.46 longFactorial

Syntax

Purpose

longFactorial is based on cern.jet.math.Arithmetic. It returns the factorial of its integer argument (in the range k >= 0 && k < 21) as a long.

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/math/Arithmetic.html#longFactorial(int).

Examples

Consider the query qColt11. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt11"><![CDATA[ 
    select longFactorial(c1) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           1
1000:       +           24
1200:       +           6
2000:       +           40320

10.47 mostSignificantBit

Syntax

Purpose

mostSignificantBit is based on cern.colt.bitvector.QuickBitVector. It returns the index (as an integer) of the most significant bit in state true of the integer argument. Returns -1 if no bit is in state true.

For more information, see:

Examples

Consider the query qColt55. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt55"><![CDATA[ 
    select mostSignificantBit(c1) from SColtFunc
]]></view>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           0
1000:       +           2
1200:       +           1
2000:       +           3

10.48 negativeBinomial

Syntax

Purpose

negativeBinomial is based on cern.jet.stat.Probability. It returns the sum of the terms 0 through k of the Negative Binomial Distribution (see Figure 10-12) as a double.

Figure 10-12 cern.jet.stat.Probability negativeBinomial

This function takes the following arguments:

integer1: the end term k.
integer2: the number of trials n.
double3: the probability of success p in (0.0,1.0).

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/stat/Probability.html#negativeBinomial(int, int, double).

Examples

Consider the query qColt44. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt44"><![CDATA[ 
    select negativeBinomial(c1,c1,c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           0.75      
1000:       +           0.94203234
1200:       +           0.99817264
2000:       +           0.28393665

10.49 negativeBinomialComplemented

Syntax

Purpose

negativeBinomialComplemented is based on cern.jet.stat.Probability. It returns the sum of the terms k+1 to infinity of the Negative Binomial distribution (see Figure 10-13) as a double.

Figure 10-13 cern.jet.stat.Probability negativeBinomialComplemented

This function takes the following arguments:

integer1: the end term k.
integer2: the number of trials n.
double3: the probability of success p in (0.0,1.0).

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/stat/Probability.html#negativeBinomialComplemented(int, int, double).

Examples

Consider the query qColt45. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt45"><![CDATA[ 
    select negativeBinomialComplemented(c1,c1,c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           0.25        
1000:       +           0.05796766  
1200:       +           0.0018273441
2000:       +           0.7160633

10.50 normal

Syntax

Purpose

normal is based on cern.jet.stat.Probability. It returns the area under the Normal (Gaussian) probability density function, integrated from minus infinity to the double argument x (see Figure 10-14) as a double.

Figure 10-14 cern.jet.stat.Probability normal

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/stat/Probability.html#normal(double).

Examples

Consider the query qColt46. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt46"><![CDATA[ 
    select normal(c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           0.69146246
1000:       +           0.7580363 
1200:       +           0.81326705
2000:       +           0.65542173

10.51 normal1

Syntax

Purpose

normal1 is based on cern.jet.stat.Probability. It returns the area under the Normal (Gaussian) probability density function, integrated from minus infinity to x (see Figure 10-15) as a double.

Figure 10-15 cern.jet.stat.Probability normal1

This function takes the following arguments:

double1: the normal distribution mean.
double2: the variance of the normal distribution v.
double3: the integration limit x.

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/stat/Probability.html#normal(double, double, double).

Examples

Consider the query qColt47. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt47"><![CDATA[ 
    select normal1(c2,c2,c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           0.5
1000:       +           0.5
1200:       +           0.5
2000:       +           0.5

10.52 normalInverse

Syntax

Purpose

normalInverse is based on cern.jet.stat.Probability. It returns the double value, x, for which the area under the Normal (Gaussian) probability density function (integrated from minus infinity to x) equals the double argument y (assumes mean is zero and variance is one).

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/stat/Probability.html#normalInverse(double).

Examples

Consider the query qColt48. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt48"><![CDATA[ 
    select normalInverse(c2) from SColtFunc
]]></view>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           0.0      
1000:       +           0.5244005
1200:       +           1.226528 
2000:       +           0.2533471

10.53 poisson

Syntax

Purpose

poisson is based on cern.jet.stat.Probability. It returns the sum of the first k terms of the Poisson distribution (see Figure 10-16) as a double.

Figure 10-16 cern.jet.stat.Probability poisson

This function takes the following arguments:

integer1: the number of terms k.
double2: the mean of the Poisson distribution m.

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/stat/Probability.html#poisson(int, double).

Examples

Consider the query qColt49. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt49"><![CDATA[ 
    select poisson(c1,c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           0.909796 
1000:       +           0.9992145
1200:       +           0.9870295
2000:       +           1.0

10.54 poissonComplemented

Syntax

Purpose

poissonComplemented is based on cern.jet.stat.Probability. It returns the sum of the terms k+1 to Infinity of the Poisson distribution (see Figure 10-17) as a double.

Figure 10-17 cern.jet.stat.Probability poissonComplemented

This function takes the following arguments:

integer1: the start term k.
double2: the mean of the Poisson distribution m.

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/stat/Probability.html#poissonComplemented(int, double).

Examples

Consider the query qColt50. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt50"><![CDATA[ 
    select poissonComplemented(c1,c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           0.09020401  
1000:       +           7.855354E-4 
1200:       +           0.012970487 
2000:       +           5.043364E-10

10.55 stirlingCorrection

Syntax

Purpose

stirlingCorrection is based on cern.jet.math.Arithmetic. It returns the correction term of the Stirling approximation of the natural logarithm (base e) of the factorial of the integer argument (see Figure 10-18) as a double.

Figure 10-18 cern.jet.math.Arithmetic stirlingCorrection

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/math/Arithmetic.html#stirlingCorrection(int).

Examples

Consider the query qColt5. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt5"><![CDATA[ 
    select stirlingCorrection(c1) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           0.08106147 
1000:       +           0.020790672
1200:       +           0.027677925
2000:       +           0.010411265

10.56 studentT

Syntax

Purpose

studentT is based on cern.jet.stat.Probability. It returns the integral from minus infinity to t of the Student-t distribution with k > 0 degrees of freedom (see Figure 10-19) as a double.

Figure 10-19 cern.jet.stat.Probability studentT

This function takes the following arguments:

double1: the degrees of freedom k.
double2: the integration end point t.

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/stat/Probability.html#studentT(double, double).

Examples

Consider the query qColt51. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt51"><![CDATA[ 
    select studentT(c2,c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           0.621341  
1000:       +           0.67624015
1200:       +           0.7243568 
2000:       +           0.5930112

10.57 studentTInverse

Syntax

Purpose

studentTInverse is based on cern.jet.stat.Probability. It returns the double value, t, for which the area under the Student-t probability density function (integrated from minus infinity to t) equals 1-alpha/2. The value returned corresponds to the usual Student t-distribution lookup table for talpha[size]. This function uses the studentt function to determine the return value iteratively.

This function takes the following arguments:

double1: the probability alpha.
integer2: the data set size.

For more information, see:

Examples

Consider the query qColt52. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt52"><![CDATA[ 
    select studentTInverse(c2,c1) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           1.0       
1000:       +           0.4141633 
1200:       +           0.15038916
2000:       +           0.8888911

10.58 y0

Syntax

Purpose

y0 is based on cern.jet.math.Bessel. It returns the Bessel function of the second kind of order 0 of the double argument as a double.

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/math/Bessel.html#y0(double).

Examples

Consider the query qColt24. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt24"><![CDATA[ 
    select y0(c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           -0.44451874  
1000:       +           -0.19066493  
1200:       +           -0.0031519707
2000:       +           -0.60602456

10.59 y1

Syntax

Purpose

y1 is based on cern.jet.math.Bessel. It returns the Bessel function of the second kind of order 1 of the float argument as a double.

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/math/Bessel.html#y1(double).

Examples

Consider the query qColt25. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt25"><![CDATA[ 
    select y1(c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +           -1.4714724 
1000:       +           -1.1032499 
1200:       +           -0.88294965
2000:       +           -1.780872

10.60 yn

Syntax

Purpose

yn is based on cern.jet.math.Bessel. It returns the Bessel function of the second kind of order n of the double argument as a double.

This function takes the following arguments:

integer1: the n value order of the Bessel function.
double2: the x value to compute the Bessel function of.

For more information, see https://dst.lbl.gov/ACSSoftware/colt/api/cern/jet/math/Bessel.html#yn(int, double).

Examples

Consider the query qColt26. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint), the query returns the relation.

<query id="qColt26"><![CDATA[ 
    select yn(c1,c2) from SColtFunc
]]></query>

Timestamp   Tuple
  10        1,0.5,8
1000        4,0.7,6
1200        3,0.89,12
2000        8,0.4,4

Timestamp   Tuple Kind  Tuple
  10:       +             -1.4714724  
1000:       +           -132.63406    
1200:       +             -8.020442   
2000:       +             -6.3026547E8