(完整版)Matlab各种随机数设置

Matlab

各种随机数设置

randn

（伪随机正态分布数）

Normally distributed pseudorandom numbers

Syntax

r = randn(n)

randn(m,n)

randn([m,n])

randn(m,n,p,...)

randn([m,n,p,...])

randn(size(A))

r = randn(..., 'double')

r = randn(..., 'single')

Description

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.

r = randn(..., 'double') or r = randn(..., 'single') returns an array of normal values of the specified

class.

Note

The size inputs m, n, p, ... should be nonnegative integers. Negative integers are treated

as 0.

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.

Note

In

versions

of

MATLAB

prior

to

7.7

(R2008b),

you

controlled

the

internal

state

of

the

random

number

stream

used

by

randn

by

calling

randn

directly

with

the

'seed'

or

'state'

keywords.

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;

Replace the default stream at MATLAB startup, using a stream whose seed is based on clock,

so that randn will return different values in different MATLAB sessions. It is usually not desirable

to do this more than once per MATLAB session.

aultStream ...

(RandStream('mt 19937ar','seed',sum(100*clock)));

randn(1,5)

Save the current state of the default stream, generate 5 values, restore the state, and repeat

the sequence.

defaultStream = aultStream;

savedState =

z1 = randn(1,5)

= savedState;

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

Normrnd

（随机正态分布数）

Normal random numbers

Syntax

R = normrnd(mu,sigma)

R = normrnd(mu,sigma,m,n,...)

R = normrnd(mu,sigma,[m,n,...])

Description

R

=

normrnd(mu,sigma)

generates

random

numbers

from

the

normal

distribution

with

mean

parameter mu and standard deviation parameter sigma. mu and sigma can be vectors, matrices,

or multidimensional arrays that have the same size, which is also the size of R. A scalar input for

mu or sigma is expanded to a constant array with the same dimensions as the other input.

R

=

normrnd(mu,sigma,m,n,...)

or

R

=

normrnd(mu,sigma,[m,n,...])

generates

an

m

-

by

-

n

-

by

-

...

array. The mu, sigma parameters can each be scalars or arrays of the same size as R.

Examples

n1 = normrnd(1:6,1./(1:6))

n1 =

2.1650

2.3134

3.0250

4.0879

4.8607

6.2827

n2 = normrnd(0,1,[1 5])

n2 =

0.0591

1.7971

0.2641

0.8717

-

1.4462

n3 = normrnd([1 2 3;4 5 6],0.1,2,3)

n3 =

0.9299

1.9361

2.9640

4.1246

5.0577

5.9864

randperm (RandStream)

（区域内的所有整数的随机分布）

Random permutation

randperm(s,n)

Description

randperm(s,n)

generates

a

random

permutation

of

the

integers

from

1

to

n.

For

example,

randperm(s,6) might be [2 4 5 6 1 3]. randperm(s,n) uses random values drawn from the random

number stream s.

betarnd

（贝塔分布）

贝塔分布是一个作为伯 努利分布和二项式分布的共轭先验分布的密度函数

Syntax

R = betarnd(A,B)

R = betarnd(A,B,m,n,...)

R = betarnd(A,B,[m,n,...])

Description

R

=

betarnd(A,B)

generates

random

numbers

from

the

beta

distribution

with

parameters

specified by A and B. A and B can be vectors, matrices, or multidimensional arrays that have the

same size, which is also the size of R. A scalar input for A or B is expanded to a constant array

with the same dimensions as the other input.

R = betarnd(A,B,m,n,...) or R = betarnd(A,B,[m,n,...]) generates an m

-

by

-

n

-

by

-

... array containing

random

numbers

from

the

beta

distribution

with

parameters

A

and

B.

A

and

B

can

each

be

scalars or arrays of the same size as R.

Examples

a = [1 1;2 2];

b = [1 2;1 2];

r = betarnd(a,b)

r =

0.6987

0.6139

0.9102

0.8067

r = betarnd(10,10,[1 5])

r =

0.5974

0.4777

0.5538

0.5465

0.6327

r = betarnd(4,2,2,3)

r =

0.3943

0.6101

0.5768

0.5990

0.2760

0.5474

Binornd

（二项式分布）

二项分布（

binomial distribution

）就是对这类只具有两种互斥结果的离散型随机事件的规

律性进行描 述的一种概率分布。

Syntax

R = binornd(N,P)

R = binornd(N,P

,m,n,...)

R = binornd(N,P

,[m,n,...])

Description

R = binornd(N,P) generates random numbers from the binomial distribution with parameters

specified by the number of trials, N, and probability of success for each trial, P

. N and P can be

vectors, matrices, or multidimensional arrays that have the same size, which is also the size of R.

A scalar input for N or P is expanded to a constant array with the same dimensions as the other

input.

R = binornd(N,P

,m,n,...) or R = binornd(N,P

,[m,n,...]) generates an m

-

by

-

n

-

by

-

.. . array containing

random numbers from the binomial distribution with parameters N and P

. N and P can each be

scalars or arrays of the same size as R.

Algorithm

The binornd function uses the direct method using the definition of the binomial distribution

as a sum of Bernoulli random variables.

Examples

n = 10:10:60;

r1 = binornd(n,1./n)

r1 =

2

1

0

1

1

2

r2 = binornd(n,1./n,[1 6])

r2 =

0

1

2

1

3

1

r3 = binornd(n,1./n,1,6)

r3 =

0

1

1

1

0

3

chi2rnd

（卡方分布）

若

n

个相互独立的随机变量ξ

?

、ξ

?

、……、ξ

n

，均服从标准正态分布，则这

n