| Oracle® Complex Event Processing CQL Language Reference 11g Release 1 (11.1.1.4.0) Part Number E12048-04 |
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View PDF |
| Oracle® Complex Event Processing CQL Language Reference 11g Release 1 (11.1.1.4.0) Part Number E12048-04 |
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View PDF |
Oracle CQL provides a variety of built-in single-row functions based on the Colt open source libraries for high performance scientific and technical computing.
For more information, see Section 1.1.11, "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 |
|---|---|
|
A set of basic polynomials, rounding, and calculus functions. |
|
|
A set of Bessel functions. |
|
|
A table with good seeds for pseudo-random number generators. Each sequence in this table has a period of 10**9 numbers. |
|
|
A set of Gamma and Beta functions. |
|
|
A set of probability distributions. |
|
|
A set of non polymorphic, non bounds checking, low level bit-vector functions. |
|
|
A set of hash functions. |
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 CEP that no further input will have a timestamp lesser than the heartbeat value.For more information, see:
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.
This function takes the following arguments:
double1: the x value.
double2: the y value.
For more information, see http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/stat/Gamma.html#beta(double,%20double).
Examples
Consider the query qColt28 in Example 10-1. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-2, the query returns the relation in Example 10-3.
Example 10-1 beta Function Query
<query id="qColt28"><![CDATA[
select beta(c2,c2) from SColtFunc
]]></query>
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.
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 http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/stat/Probability.html#beta(double,%20double,%20double).
Examples
Consider the query qColt35 in Example 10-4. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-5, the query returns the relation in Example 10-6.
Example 10-4 beta1 Function Query
<query id="qColt35"><![CDATA[
select beta1(c2,c2,c2) from SColtFunc
]]></query>
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 in Example 10-7. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-8, the query returns the relation in Example 10-9.
Example 10-7 betaComplemented Function Query
<query id="qColt37"><![CDATA[
select betaComplemented(c2,c2,c2) from SColtFunc
]]></query>
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.
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 |
|---|---|
|
|
0 |
|
|
1 |
|
|
|
|
Any other value of |
Computed binomial coefficient as given in Figure 10-3. |
For more information, see http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/math/Arithmetic.html#binomial(double,%20long).
Examples
Consider the query qColt6 in Example 10-10. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 long) in Example 10-11, the query returns the relation in Example 10-12.
Example 10-10 binomial Function Query
<query id="qColt6"><![CDATA[
select binomial(c2,c3) from SColtFunc
]]></query>
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 |
|---|---|
|
|
0 |
|
|
1 |
|
|
|
|
Any other value of |
Computed binomial coefficient as given in Figure 10-3. |
For more information, see http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/math/Arithmetic.html#binomial(long,%20long).
Examples
Consider the query qColt7 in Example 10-13. Given the data stream SColtFunc with schema (c1 integer, c2 float, c3 long) in Example 10-14, the query returns the relation in Example 10-15.
Example 10-13 binomial1 Function Query
<query id="qColt7"><![CDATA[
select binomial1(c3,c3) from SColtFunc
]]></query>
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.
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 http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/stat/Probability.html#binomial(int,%20int,%20double).
Examples
Consider the query qColt34 in Example 10-16. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-17, the query returns the relation in Example 10-18.
Example 10-16 binomial2 Function Query
<query id="qColt34"><![CDATA[
select binomial2(c1,c1,c2) from SColtFunc
]]></query>
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.
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 http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/stat/Probability.html#binomialComplemented(int,%20int,%20double).
Examples
Consider the query qColt38 in Example 10-19. Given the data stream SColtFunc with schema (integer, c2 double, c3 bigint) in Example 10-20, the query returns the relation in Example 10-21.
Example 10-19 binomialComplemented Function Query
<query id="qColt38"><![CDATA[
select binomialComplemented(c1,c1,c2) from SColtFunc
]]></query>
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 in Example 10-22. Given the data stream SColtFunc with schema (c1 integer, c2 float, c3 bigint) in Example 10-23, the query returns the relation in Example 10-24.
Example 10-22 bitMaskWithBitsSetFromTo Function Query
<query id="qColt53"><![CDATA[
select bitMaskWithBitsSetFromTo(c1,c1) from SColtFunc
]]></query>
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 in Example 10-25. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-26, the query returns the relation in Example 10-27.
Example 10-25 ceil Function Query
<query id="qColt1"><![CDATA[
select ceil(c2) from SColtFunc
]]></query>
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.
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 http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/stat/Probability.html#chiSquare(double,%20double).
Examples
Consider the query qColt39 in Example 10-28. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-29, the query returns the relation in Example 10-30.
Example 10-28 chiSquare Function Query
<query id="qColt39"><![CDATA[
select chiSquare(c2,c2) from SColtFunc
]]></query>
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 http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/stat/Probability.html#chiSquareComplemented(double,%20double).
Examples
Consider the query qColt40 in Example 10-31. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-32, the query returns the relation in Example 10-33.
Example 10-31 chiSquareComplemented Function Query
<query id="qColt40"><![CDATA[
select chiSquareComplemented(c2,c2) from SColtFunc
]]></query>
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.
For more information, see http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/stat/Probability.html#errorFunction(double).
Examples
Consider the query qColt41 in Example 10-34. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-35, the query returns the relation in Example 10-36.
Example 10-34 errorFunction Function Query
<query id="qColt41"><![CDATA[
select errorFunction(c2) from SColtFunc
]]></query>
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.
For more information, see http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/stat/Probability.html#errorFunctionComplemented(double).
Examples
Consider the query qColt42 in Example 10-37. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-38, the query returns the relation in Example 10-39.
Example 10-37 errorFunctionComplemented Function Query
<query id="qColt42"><![CDATA[
select errorFunctionComplemented(c2) from SColtFunc
]]></query>
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 http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/math/Arithmetic.html#factorial(int).
Examples
Consider the query qColt8 in Example 10-40. Given the data stream SColtFunc with schema (c1 integer, c2 float, c3 bigint) in Example 10-41, the query returns the relation in Example 10-42.
Example 10-40 factorial Function Query
<query id="qColt8"><![CDATA[
select factorial(c1) from SColtFunc
]]></query>
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 in Example 10-43. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-44, the query returns the relation in Example 10-45.
Example 10-43 floor Function Query
<query id="qColt2"><![CDATA[
select floor(c2) from SColtFunc
]]></query>
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 http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/stat/Gamma.html#gamma(double).
Examples
Consider the query qColt29 in Example 10-46. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-47, the query returns the relation in Example 10-48.
Example 10-46 gamma Function Query
<query id="qColt29"><![CDATA[
select gamma(c2) from SColtFunc
]]></query>
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.
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 http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/stat/Probability.html#gamma(double,%20double,%20double).
Examples
Consider the query qColt36 in Example 10-49. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-50, the query returns the relation in Example 10-51.
Example 10-49 gamma1 Function Query
<query id="qColt36"><![CDATA[
select gamma1(c2,c2,c2) from SColtFunc
]]></query>
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.
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 http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/stat/Probability.html#gammaComplemented(double,%20double,%20double).
Examples
Consider the query qColt43 in Example 10-52. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-53, the query returns the relation in Example 10-54.
Example 10-52 gammaComplemented Function Query
<query id="qColt43"><![CDATA[
select gammaComplemented(c2,c2,c2) from SColtFunc
]]></query>
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 http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/random/engine/RandomSeedTable.html#getSeedAtRowColumn(int,%20int).
Examples
Consider the query qColt27 in Example 10-55. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-56, the query returns the relation in Example 10-57.
Example 10-55 getSeedAtRowColumn Function Query
<query id="qColt27"><![CDATA[
select getSeedAtRowColumn(c1,c1) from SColtFunc
]]></query>
Syntax
Purpose
hash is based on cern.colt.map.HashFunctions. It returns an integer hashcode for the specified double value.
For more information, see http://dsd.lbl.gov/~hoschek/colt/api/cern/colt/map/HashFunctions.html#hash(double).
Examples
Consider the query qColt56 in Example 10-58. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-59, the query returns the relation in Example 10-60.
Example 10-58 hash Function Query
<query id="qColt56"><![CDATA[
select hash(c2) from SColtFunc
]]></query>
Syntax
Purpose
hash1 is based on cern.colt.map.HashFunctions. It returns an integer hashcode for the specified float value.
For more information, see http://dsd.lbl.gov/~hoschek/colt/api/cern/colt/map/HashFunctions.html#hash(float).
Examples
Consider the query qColt57 in Example 10-61. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-62, the query returns the relation in Example 10-63.
Example 10-61 hash1 Function Query
<query id="qColt57"><![CDATA[
select hash1(c2) from SColtFunc
]]></query>
Syntax
Purpose
hash2 is based on cern.colt.map.HashFunctions. It returns an integer hashcode for the specified integer value.
For more information, see http://dsd.lbl.gov/~hoschek/colt/api/cern/colt/map/HashFunctions.html#hash(int).
Examples
Consider the query qColt58 in Example 10-64. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-65, the query returns the relation in Example 10-66.
Example 10-64 hash2 Function Query
<query id="qColt58"><![CDATA[
select hash2(c1) from SColtFunc
]]></query>
Syntax
Purpose
hash3 is based on cern.colt.map.HashFunctions. It returns an integer hashcode for the specified long value.
For more information, see http://dsd.lbl.gov/~hoschek/colt/api/cern/colt/map/HashFunctions.html#hash(long).
Examples
Consider the query qColt59 in Example 10-67. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-68, the query returns the relation in Example 10-69.
Example 10-67 hash3 Function Query
<query id="qColt59"><![CDATA[
select hash3(c3) from SColtFunc
]]></query>
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 in Example 10-70. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-71, the query returns the relation in Example 10-72.
Example 10-70 i0 Function Query
<query id="qColt12"><![CDATA[
select i0(c2) from SColtFunc
]]></query>
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 in Example 10-73. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-74, the query returns the relation in Example 10-75.
Example 10-73 i0e Function Query
<query id="qColt13"><![CDATA[
select i0e(c2) from SColtFunc
]]></query>
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 in Example 10-76. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-77, the query returns the relation in Example 10-78.
Example 10-76 i1 Function Query
<query id="qColt14"><![CDATA[
select i1(c2) from SColtFunc
]]></query>
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 in Example 10-79. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-80, the query returns the relation in Example 10-81.
Example 10-79 i1e Function Query
<query id="qColt15"><![CDATA[
select i1e(c2) from SColtFunc
]]></query>
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 http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/stat/Gamma.html#incompleteBeta(double,%20double,%20double).
Examples
Consider the query qColt30 in Example 10-82. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-83, the query returns the relation in Example 10-84.
Example 10-82 incompleteBeta Function Query
<query id="qColt30"><![CDATA[
select incompleteBeta(c2,c2,c2) from SColtFunc
]]></query>
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 http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/stat/Gamma.html#incompleteGamma(double,%20double).
Examples
Consider the query qColt31 in Example 10-85. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-86, the query returns the relation in Example 10-87.
Example 10-85 incompleteGamma Function Query
<query id="qColt31"><![CDATA[
select incompleteGamma(c2,c2) from SColtFunc
]]></query>
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 http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/stat/Gamma.html#incompleteGammaComplement(double,%20double).
Examples
Consider the query qColt32 in Example 10-88. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-89, the query returns the relation in Example 10-90.
Example 10-88 incompleteGammaComplement Function Query
<query id="qColt32"><![CDATA[
select incompleteGammaComplement(c2,c2) from SColtFunc
]]></query>
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 http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/math/Bessel.html#j0(double).
Examples
Consider the query qColt16 in Example 10-91. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-92, the query returns the relation in Example 10-93.
Example 10-91 j0 Function Query
<query id="qColt16"><![CDATA[
select j0(c2) from SColtFunc
]]></query>
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 http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/math/Bessel.html#j1(double).
Examples
Consider the query qColt17 in Example 10-94. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-95, the query returns the relation in Example 10-96.
Example 10-94 j1 Function Query
<query id="qColt17"><![CDATA[
select j1(c2) from SColtFunc
]]></query>
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 http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/math/Bessel.html#jn(int,%20double).
Examples
Consider the query qColt18 in Example 10-97. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-98, the query returns the relation in Example 10-99.
Example 10-97 jn Function Query
<query id="qColt18"><![CDATA[
select jn(c1,c2) from SColtFunc
]]></query>
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 http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/math/Bessel.html#k0(double).
Examples
Consider the query qColt19 in Example 10-100. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-101, the query returns the relation in Example 10-102.
Example 10-100 k0 Function Query
<query id="qColt19"><![CDATA[
select k0(c2) from SColtFunc
]]></query>
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 http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/math/Bessel.html#k0e(double).
Examples
Consider the query qColt20 in Example 10-103. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-104, the query returns the relation in Example 10-105.
Example 10-103 k0e Function Query
<query id="qColt20"><![CDATA[
select k0e(c2) from SColtFunc
]]></query>
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 http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/math/Bessel.html#k1(double).
Examples
Consider the query qColt21 in Example 10-106. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-107, the query returns the relation in Example 10-108.
Example 10-106 k1 Function Query
<query id="qColt21"><![CDATA[
select k1(c2) from SColtFunc
]]></query>
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 in Example 10-109. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-110, the query returns the relation in Example 10-111.
Example 10-109 k1e Function Query
<query id="qColt22"><![CDATA[
select k1e(c2) from SColtFunc
]]></query>
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 http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/math/Bessel.html#kn(int,%20double).
Examples
Consider the query qColt23 in Example 10-112. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-113, the query returns the relation in Example 10-114.
Example 10-112 kn Function Query
<query id="qColt23"><![CDATA[
select kn(c1,c2) from SColtFunc
]]></query>
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 in Example 10-115. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-116, the query returns the relation in Example 10-117.
Example 10-115 leastSignificantBit Function Query
<query id="qColt54"><![CDATA[
select leastSignificantBit(c1) from SColtFunc
]]></query>
Syntax
Purpose
log is based on cern.jet.math.Arithmetic. It returns the computation that Figure 10-11 shows as a double.
This function takes the following arguments:
double1: the base.
double2: the value.
For more information, see http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/math/Arithmetic.html#log(double,%20double).
Examples
Consider the query qColt3 in Example 10-118. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-119, the query returns the relation in Example 10-120.
Example 10-118 log Function Query
<query id="qColt3"><![CDATA[
select log(c2,c2) from SColtFunc
]]></query>
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 http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/math/Arithmetic.html#log10(double).
Examples
Consider the query qColt4 in Example 10-121. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-122, the query returns the relation in Example 10-123.
Example 10-121 log10 Function Query
<query id="qColt4"><![CDATA[
select log10(c2) from SColtFunc
]]></query>
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 http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/math/Arithmetic.html#log2(double).
Examples
Consider the query qColt9 in Example 10-124. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-125, the query returns the relation in Example 10-126.
Example 10-124 log2 Function Query
<query id="qColt9"><![CDATA[
select log2(c2) from SColtFunc
]]></query>
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 http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/math/Arithmetic.html#logFactorial(int).
Examples
Consider the query qColt10 in Example 10-127. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-128, the query returns the relation in Example 10-129.
Example 10-127 logFactorial Function Query
<query id="qColt10"><![CDATA[
select logFactorial(c1) from SColtFunc
]]></query>
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 http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/stat/Gamma.html#logGamma(double).
Examples
Consider the query qColt33 in Example 10-130. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-131, the query returns the relation in Example 10-132.
Example 10-130 logGamma Function Query
<query id="qColt33"><![CDATA[
select logGamma(c2) from SColtFunc
]]></query>
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 http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/math/Arithmetic.html#longFactorial(int).
Examples
Consider the query qColt11 in Example 10-133. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-134, the query returns the relation in Example 10-135.
Example 10-133 longFactorial Function Query
<query id="qColt11"><![CDATA[
select longFactorial(c1) from SColtFunc
]]></query>
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:
http://dsd.lbl.gov/~hoschek/colt/api/cern/colt/bitvector/QuickBitVector.html#mostSignificantBit(int)
Examples
Consider the query qColt55 in Example 10-136. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-137, the query returns the relation in Example 10-138.
Example 10-136 mostSignificantBit Function Query
<query id="qColt55"><![CDATA[
select mostSignificantBit(c1) from SColtFunc
]]></view>
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.
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 http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/stat/Probability.html#negativeBinomial(int,%20int,%20double).
Examples
Consider the query qColt44 in Example 10-139. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-140, the query returns the relation in Example 10-141.
Example 10-139 negativeBinomial Function Query
<query id="qColt44"><![CDATA[
select negativeBinomial(c1,c1,c2) from SColtFunc
]]></query>
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.
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 http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/stat/Probability.html#negativeBinomialComplemented(int,%20int,%20double).
Examples
Consider the query qColt45 in Example 10-142. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-143, the query returns the relation in Example 10-144.
Example 10-142 negativeBinomialComplemented Function Query
<query id="qColt45"><![CDATA[
select negativeBinomialComplemented(c1,c1,c2) from SColtFunc
]]></query>
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.
For more information, see http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/stat/Probability.html#normal(double).
Examples
Consider the query qColt46 in Example 10-145. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-146, the query returns the relation in Example 10-147.
Example 10-145 normal Function Query
<query id="qColt46"><![CDATA[
select normal(c2) from SColtFunc
]]></query>
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.
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 http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/stat/Probability.html#normal(double,%20double,%20double).
Examples
Consider the query qColt47 in Example 10-148. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-149, the query returns the relation in Example 10-150.
Example 10-148 normal1 Function Query
<query id="qColt47"><![CDATA[
select normal1(c2,c2,c2) from SColtFunc
]]></query>
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 http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/stat/Probability.html#normalInverse(double).
Examples
Consider the query qColt48 in Example 10-151. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-152, the query returns the relation in Example 10-153.
Example 10-151 normalInverse Function Query
<query id="qColt48"><![CDATA[
select normalInverse(c2) from SColtFunc
]]></view>
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.
This function takes the following arguments:
integer1: the number of terms k.
double2: the mean of the Poisson distribution m.
For more information, see http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/stat/Probability.html#poisson(int,%20double).
Examples
Consider the query qColt49 in Example 10-154. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-155, the query returns the relation in Example 10-156.
Example 10-154 poisson Function Query
<query id="qColt49"><![CDATA[
select poisson(c1,c2) from SColtFunc
]]></query>
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.
This function takes the following arguments:
integer1: the start term k.
double2: the mean of the Poisson distribution m.
For more information, see http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/stat/Probability.html#poissonComplemented(int,%20double).
Examples
Consider the query qColt50 in Example 10-157. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-158, the query returns the relation in Example 10-159.
Example 10-157 poissonComplemented Function Query
<query id="qColt50"><![CDATA[
select poissonComplemented(c1,c2) from SColtFunc
]]></query>
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.
For more information, see http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/math/Arithmetic.html#stirlingCorrection(int).
Examples
Consider the query qColt5 in Example 10-160. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-161, the query returns the relation in Example 10-162.
Example 10-160 stirlingCorrection Function Query
<query id="qColt5"><![CDATA[
select stirlingCorrection(c1) from SColtFunc
]]></query>
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.
This function takes the following arguments:
double1: the degrees of freedom k.
double2: the integration end point t.
For more information, see http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/stat/Probability.html#studentT(double,%20double).
Examples
Consider the query qColt51 in Example 10-163. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-164, the query returns the relation in Example 10-165.
Example 10-163 studentT Function Query
<query id="qColt51"><![CDATA[
select studentT(c2,c2) from SColtFunc
]]></query>
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 in Example 10-166. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-167, the query returns the relation in Example 10-168.
Example 10-166 studentTInverse Function Query
<query id="qColt52"><![CDATA[
select studentTInverse(c2,c1) from SColtFunc
]]></query>
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 http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/math/Bessel.html#y0(double).
Examples
Consider the query qColt24 in Example 10-169. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-170, the query returns the relation in Example 10-171.
Example 10-169 y0 Function Query
<query id="qColt24"><![CDATA[
select y0(c2) from SColtFunc
]]></query>
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 http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/math/Bessel.html#y1(double).
Examples
Consider the query qColt25 in Example 10-172. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-173, the query returns the relation in Example 10-174.
Example 10-172 y1 Function Query
<query id="qColt25"><![CDATA[
select y1(c2) from SColtFunc
]]></query>
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 http://dsd.lbl.gov/~hoschek/colt/api/cern/jet/math/Bessel.html#yn(int,%20double).
Examples
Consider the query qColt26 in Example 10-175. Given the data stream SColtFunc with schema (c1 integer, c2 double, c3 bigint) in Example 10-176, the query returns the relation in Example 10-177.
Example 10-175 yn Function Query
<query id="qColt26"><![CDATA[
select yn(c1,c2) from SColtFunc
]]></query>
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