## Vectors and matrices with randomly distributed values

The `breeze.stats.distributions`

package supplements the random number generator that is built into Scala. Scala's default generator just provides the ability to get the random values one by one using the "next" methods. Random number generators in Breeze provide the ability to build vectors and matrices out of these generators. In this recipe, we'll briefly see three of the most common distributions of random numbers.

In this recipe, we will cover at the following sub-recipes:

*Creating vectors with uniformly distributed random values**Creating vectors with normally distributed random values**Creating vectors with random values that have a Poisson distribution**Creating a matrix with uniformly random values**Creating a matrix with normally distributed random values**Creating a matrix with random values that has a Poisson distribution*

### How it works...

Before we delve into how to create the vectors and matrices out of random numbers, let's create instances of the most common random number distribution. All these generators are under the `breeze.stats.distributions`

package:

//Uniform distribution with low being 0 and high being 10 val uniformDist=Uniform(0,10) //Gaussian distribution with mean being 5 and Standard deviation being 1 val gaussianDist=Gaussian(5,1) //Poission distribution with mean being 5 val poissonDist=Poisson(5)

We could actually directly sample from these generators. Given any distribution we created previously, we could sample either a single value or a sequence of values:

//Samples a single value println (uniformDist.sample()) //eg. 9.151191360491392 //Returns a sample vector of size that is passed in as parameter println (uniformDist.sample(2)) //eg. Vector(6.001980062275654, 6.210874664967401)

#### Creating vectors with uniformly distributed random values

With no generator parameter, the `DenseVector.rand`

method accepts a parameter for the length of the vector to be returned. The result is a vector (of length `10`

) with uniformly distributed values between `0`

and `1`

:

val uniformWithoutSize=DenseVector.rand(10)println ("uniformWithoutSize \n"+ uniformWithoutSize)//DenseVector(0.1235038023750481, 0.3120595941786264, 0.3575638744660876, 0.5640844223813524, 0.5336149399548831, 0.1338053814330793, 0.9099684427908603, 0.38690724148973166, 0.22561993631651522, 0.45120359622713657)

The `DenseVector.rand`

method optionally accepts a distribution object and generates random values using that input distribution. The following line generates a vector of `10`

uniformly distributed random values that are within the range `0`

and `10`

:

val uniformDist=Uniform(0,10)val uniformVectInRange=DenseVector.rand(10, uniformDist)println ("uniformVectInRange \n"+uniformVectInRange)//DenseVector(1.5545833905907314, 6.172564377264846, 8.45578509265587, 7.683763574965107, 8.018688137742062, 4.5876187984930406, 3.274758584944064, 2.3873947264259954, 2.139988841403757, 8.314112884416943)

#### Creating vectors with normally distributed random values

In the place of the `uniformDist`

generator, we could also pass the previously created Gaussian generator, which is configured to yield a distribution that has a mean of `5`

and standard deviation of `1`

:

val gaussianVector=DenseVector.rand(10, gaussianDist)println ("gaussianVector \n"+gaussianVector)//DenseVector(4.235655596913547, 5.535011377545014, 6.201428236839494, 6.046289604188366, 4.319709374229152,4.2379652913447154, 2.957868021601233, 3.96371080427211, 4.351274306757224, 5.445022658876723)

#### Creating vectors with random values that have a Poisson distribution

Similarly, by passing the previously created Poisson random number generator, a vector of values that has a mean of `5`

could be generated:

val poissonVector=DenseVector.rand(10, poissonDist)println ("poissonVector \n"+poissonVector)//DenseVector(5, 5, 7, 11, 7, 6, 6, 6, 6, 6)

We saw how easy it is to create a vector of random values. Now, let's proceed to create a matrix of random values. Similar to `DenseVector.rand`

to generate vectors with random values, we'll use the `DenseMatrix.rand`

function to generate a matrix of random values.

#### Creating a matrix with uniformly random values

The `DenseMatrix.rand`

defaults to the uniform distribution and generates a matrix of random values given the row and the column parameter. However, if we would like to have a distribution within a range, then as in vectors, we could use the optional parameter:.

//Uniform distribution, Creates a 3 * 3 Matrix with random values from 0 to 1val uniformMat=DenseMatrix.rand(3, 3)println ("uniformMat \n"+uniformMat)0.4492155777289115 0.9098840386699856 0.82030222529882920.0888975848853315 0.009677790736892788 0.60588859059342370.6201415814136939 0.7017492438727635 0.08404147915159443//Creates a 3 * 3 Matrix with uniformly distributed random values with low being 0 and high being 10val uniformMatrixInRange=DenseMatrix.rand(3,3, uniformDist)println ("uniformMatrixInRange \n"+uniformMatrixInRange)7.592014659345548 8.164652560340933 6.9664452944644018.35949395084735 3.442654641743763 3.67616402409384429.42626645215854 0.23658921372298636 7.327120138868571

#### Creating a matrix with normally distributed random values

Just as in vectors, in place of the `uniformDist`

generator, we could also pass the previously created Gaussian generator to the `rand`

function to generate a matrix of random values that has a mean of `5`

and standard deviation of `1`

:

//Creates a 3 * 3 Matrix with normally distributed random values with mean being 5 and Standard deviation being 1val gaussianMatrix=DenseMatrix.rand(3, 3,gaussianDist)println ("gaussianMatrix \n"+gaussianMatrix)5.724540885605018 5.647051873430568 5.3379061351070986.2228893721489875 4.799561665187845 5.124697794898335.136960834730864 5.176410360757703 5.262707072950913

#### Creating a matrix with random values that has a Poisson distribution

Similarly, by passing the previously created Poisson random number generator, a matrix of random values that has a mean of `5`

could be generated:

//Creates a 3 * 3 Matrix with Poisson distribution with mean being 5val poissonMatrix=DenseMatrix.rand(3, 3,poissonDist)println ("poissonMatrix \n"+poissonMatrix)4 11 36 6 56 4 2