matlab\randfun - Random matrices and random streams

Random matrices.

<rand> - Uniformly distributed random numbers.

RAND Uniformly distributed pseudorandom numbers.

R = RAND(N) returns an N-by-N matrix containing pseudorandom values drawn

from the standard uniform distribution on the open interval(0,1). RAND(M,N)

or RAND([M,N]) returns an M-by-N matrix. RAND(M,N,P,...) or

RAND([M,N,P,...]) returns an M-by-N-by-P-by-... array. RAND returns a

scalar. RAND(SIZE(A)) returns an array the same size as A.

Note: The size inputs M, N, P, ... should be nonnegative integers.

Negative integers are treated as 0.

R = RAND(..., 'double') or R = RAND(..., 'single') returns an array of

uniform values of the specified class.

Compatibility Note: In versions of MATLAB prior to 7.7, you controlled

the internal state of the random number stream used by RAND by calling

RAND directly with the 'seed', 'state', or 'twister' keywords. That

syntax is still supported for backwards compatibility, but is deprecated.

Beginning in MATLAB 7.7, use the default stream as described in

RANDSTREAM.

The sequence of numbers produced by RAND is determined by the internal

state of the uniform pseudorandom number generator that underlies RAND,

RANDI, and RANDN. Control that default random number stream using its

properties and methods. See RANDSTREAM for details about the default

stream.

Resetting the default stream to the same fixed state allows computations

to be repeated. Setting the stream to different states leads to unique

computations, however, it does not improve any statistical properties.

Since MATLAB uses the same state each time it starts up, RAND, RANDN, and

RANDI will generate the same sequence of numbers in each session unless

the state is changed.

Examples:

Generate values from the uniform distribution on the interval [a, b].

r = a + (b-a).*rand(100,1);

Use the RANDI function to generate to generate one integer value from the

uniform distribution on the set 1:100.

r = randi(100,1);

Save the current state of the default stream, generate 5 values,

restore the state, and repeat the sequence.

defaultStream = RandStream.getDefaultStream;

savedState = defaultStream.State;

u1 = rand(1,5)

defaultStream.State = savedState;

u2 = rand(1,5) % contains exactly the same values as u1

Replace the default stream with a stream whose seed is based on CLOCK, so

RAND will return different values in different MATLAB sessions. NOTE: It

is usually not desirable to do this more than once per MATLAB session.

RandStream.setDefaultStream(RandStream('mt19937ar','seed',sum(100*clock)));

rand(1,5)

See also randi, randn, RandStream, RandStream/rand, RandStream/getDefaultStream,

sprand, sprandn, randperm.

Overloaded methods:

RandStream/rand

distributed/rand

codistributor2dbc/rand

codistributor1d/rand

codistributed/rand

Reference page in Help browser

doc rand

<randi> - Uniformly distributed random integers.

RANDI Pseudorandom integers from a uniform discrete distribution.

R = RANDI(IMAX,N) returns an N-by-N matrix containing pseudorandom

integer values drawn from the discrete uniform distribution on 1:IMAX.

RANDI(IMAX,M,N) or RANDI(IMAX,[M,N]) returns an M-by-N matrix.

RANDI(IMAX,M,N,P,...) or RANDI(IMAX,[M,N,P,...]) returns an

M-by-N-by-P-by-... array. RANDI(IMAX) returns a scalar.

RANDI(IMAX,SIZE(A)) returns an array the same size as A.

R = RANDI([IMIN,IMAX],...) returns an array containing integer

values drawn from the discrete uniform distribution on IMIN:IMAX.

Note: The size inputs M, N, P, ... should be nonnegative integers.

Negative integers are treated as 0.

R = RANDI(..., CLASSNAME) returns an array of integer values of class

CLASSNAME.

The sequence of numbers produced by RANDI is determined by the internal

state of the uniform pseudorandom number generator that underlies RAND,

RANDI, and RANDN. RANDI uses one uniform value from that default

stream to generate each integer value. Control the default stream using

its properties and methods. See RANDSTREAM for details about the

default stream.

Resetting the default stream to the same fixed state allows computations

to be repeated. Setting the stream to different states leads to unique

computations, however, it does not improve any statistical properties.

Since MATLAB uses the same state each time it starts up, RAND, RANDN, and

RANDI will generate the same sequence of numbers in each session unless

the state is changed.

Examples:

Generate integer values from the uniform distribution on the set 1:10.

r = randi(10,100,1);

Generate an integer array of integers drawn uniformly from 1:10.

r = randi(10,100,1,'uint32');

Generate integer values drawn uniformly from -10:10.

r = randi([-10 10],100,1);

Save the current state of the default stream, generate 5 integer

values, restore the state, and repeat the sequence.

defaultStream = RandStream.getDefaultStream;

savedState = defaultStream.State;

i1 = randi(10,1,5)

defaultStream.State = savedState;

i2 = randi(10,1,5) % contains exactly the same values as i1

Replace the default stream with a stream whose seed is based on CLOCK, so

RANDI will return different values in different MATLAB sessions. NOTE: It

is usually not desirable to do this more than once per MATLAB session.

RandStream.setDefaultStream(RandStream('mt19937ar','seed',sum(100*clock)));

randi(10,1,5)

See also rand, randn, RandStream, RandStream/randi, RandStream/getDefaultStream.

Overloaded methods:

RandStream/randi

Reference page in Help browser

doc randi

<randn> - Normally distributed random numbers.

RANDN Normally distributed pseudorandom numbers.

R = RANDN(N) returns an N-by-N matrix containing pseudorandom values drawn

from the standard normal distribution. RANDN(M,N) or RANDN([M,N]) returns

an M-by-N matrix. RANDN(M,N,P,...) or RANDN([M,N,P,...]) returns an

M-by-N-by-P-by-... array. RANDN returns a scalar. RANDN(SIZE(A)) returns

an array the same size as A.

Note: The size inputs M, N, P, ... should be nonnegative integers.

Negative integers are treated as 0.

R = RANDN(..., 'double') or R = RANDN(..., 'single') returns an array of

normal values of the specified class.

Compatibility Note: In versions of MATLAB prior to 7.7, you controlled

the internal state of the random number stream used by RANDN by calling

RANDN directly with the 'seed' or 'state' keywords. That syntax is

still supported for backwards compatibility, but is deprecated. Beginning

In matlab 7.7, use the default stream as described in randstream.

The sequence of numbers produced by RANDN is determined by the internal

state of the uniform pseudorandom number generator that underlies RAND,

RANDI, and RANDN. RANDN uses one or more uniform values from that

default stream to generate each normal value. Control the default

stream using its properties and methods. See RANDSTREAM for details

about the default stream.

Resetting the default stream to the same fixed state allows computations

to be repeated. Setting the stream to different states leads to unique

computations, however, it does not improve any statistical properties.

Since MATLAB uses the same state each time it starts up, RAND, RANDN, and

RANDI will generate the same sequence of numbers in each session unless

the state is changed.

Examples:

Generate values from a normal distribution with mean 1 and standard

deviation 2.

r = 1 + 2.*randn(100,1);

Generate values from a bivariate normal distribution with specified mean

Vector and covariance matrix.

mu = [1 2];

Sigma = [1 .5; .5 2]; R = chol(Sigma);

z = repmat(mu,100,1) + randn(100,2)*R;

Save the current state of the default stream, generate 5 values,

restore the state, and repeat the sequence.

defaultStream = RandStream.getDefaultStream;

savedState = defaultStream.State;

z1 = randn(1,5)

defaultStream.State = savedState;

z2 = randn(1,5) % contains exactly the same values as z1

Replace the default stream with a stream whose seed is based on CLOCK, so

RANDN will return different values in different MATLAB sessions. NOTE: It

Is usually not desirable to do this more than once per matlab session.

RandStream.setDefaultStream(RandStream('mt19937ar','seed',sum(100*clock)));

randn(1,5)

See also rand, randi, RandStream, RandStream/randn, RandStream/getDefaultStream.

Overloaded methods:

RandStream/randn

distributed/randn

codistributor2dbc/randn

codistributor1d/randn

codistributed/randn

Reference page in Help browser

doc randn

Random reordering.

<randperm> - Random permutation.

RANDPERM Random permutation.

RANDPERM(n) is a random permutation of the integers from 1 to n.

For example, RANDPERM(6) might be [2 4 5 6 1 3].

Note that RANDPERM calls RAND and therefore changes RAND's state.

See also permute.

Overloaded methods:

RandStream/randperm

Reference page in Help browser

doc randperm

Random Streams

<RandStream> - Create a random number stream.

RANDSTREAM Random number stream.

(Pseudo)random numbers in MATLAB come from one or more random number

streams. The simplest way to generate arrays of random numbers is to use

RAND, RANDN, or RANDI. These functions all rely on the same stream of

uniform random numbers, known as the default stream. You can create other

streams that act separately from the default stream, and you can use their

RAND, RANDN, or RANDI methods to generate arrays of random numbers. You can

also create a random number stream and make it the default stream.

To create a single random number stream, use either the RandStream

constructor or the RandStream.CREATE factory method. To create multiple