## how to randomly shuffle the row elements of a predefined matrix??

As a variation of my answer above, I'll note that if you want to generate M permutations of N objects (where the N objects are represented by the integers 1-N) you can use:

[~, x] = sort(rand(N, M));

I can generate 100,000 permutations of 52 objects in 0.3 seconds on my machine.

The probability of drawing 3 aces in a 5 card draw can be estimated (using 100,000 dealt hands):

%%%%%%%%%%%%%%%%%

M = 100000; % Number of trials

N = 52; % Number of cards in deck

[~, x] = sort(rand(N, M)); % columns of x are shuffled decks (100,000 shuffled decks)

y = x(1:5,:); % columns of y are the 5 card hands

% N3a is the number of hands containing three Aces out of M (100,000) deals

% I let Aces be cards 1, 14, 27, and 40 (1-13 is one suit, 14-26 is another, etc)

N3a = sum(sum(or(y == 1, y == 14, y == 27, y == 40)) == 3);

P3a = N3a/M

%%%%%%%%%%%%%%%%%

Successive runs of the script gives values of 0.00181, 0.00185, 0.00189, 0.00171.

The theoretical value is 0.001736

## Select a Web Site

### Create Arrays of Random Numbers

MATLAB^{®} uses algorithms to generate *pseudorandom* and *pseudoindependent* numbers. These numbers are not strictly random and independent in the mathematical sense, but they pass various statistical tests of randomness and independence, and their calculation can be repeated for testing or diagnostic purposes.

The , , , and functions are the primary functions for creating arrays of random numbers. The function allows you to control the seed and algorithm that generates random numbers.

### Random Number Functions

There are four fundamental random number functions: , , , and . The function returns floating-point numbers between 0 and 1 that are drawn from a uniform distribution. For example:

The function returns integer values drawn from a discrete uniform distribution. For example,

is a 1000-by-1 column vector containing integer values drawn from a discrete uniform distribution whose range is in the close interval [1, 10]. A histogram of these values is roughly flat, which indicates a fairly uniform sampling of integers between 1 and 10.The function returns arrays of real floating-point numbers that are drawn from a standard normal distribution. For example:

is a 1000-by-1 column vector containing numbers drawn from a standard normal distribution. A histogram of looks like a roughly normal distribution whose mean is 0 and standard deviation is 1.You can use the function to create a array of random integer values that have no repeated values. For example,

is a 1-by-5 array containing integers randomly selected from the range [1, 15]. Unlike , which can return an array containing repeated values, the array returned by has no repeated values.Successive calls to any of these functions return different results. This behavior is useful for creating several different arrays of random values.

### Random Number Generators

MATLAB offers several generator algorithm options, which are summarized in the table.

Value | Generator Name | Generator Keyword |
---|---|---|

Mersenne Twister (used by default stream at MATLAB startup) | mt19937ar | |

SIMD-oriented Fast Mersenne Twister | dsfmt19937 | |

Combined multiple recursive | mrg32k3a | |

Multiplicative Lagged Fibonacci | mlfg6331_64 | |

Philox 4x32 generator with 10 rounds | philox4x32_10 | |

Threefry 4x64 generator with 20 rounds | threefry4x64_20 | |

Legacy MATLAB version 4.0 generator | mcg16807 | |

Legacy MATLAB version 5.0 uniform generator | swb2712 | |

Legacy MATLAB version 5.0 normal generator | shr3cong |

Use the function to set the seed and generator used by the , , , and functions. For example, reset the generator to its default state. To avoid repetition of random number arrays when MATLAB restarts, see Why Do Random Numbers Repeat After Startup?

For more information about controlling the random number generator's state to repeat calculations using the same random numbers, or to guarantee that different random numbers are used in repeated calculations, see Controlling Random Number Generation.

### Random Number Data Types

and functions generate values in double precision by default.

To specify the class as double explicitly:

and can also generate values in single precision.

The values are the same as if you had cast the double precision values from the previous example. The random stream that the functions draw from advances the same way regardless of what class of values is returned.

supports both integer types and single or double precision.

### See Also

| | | |

### Related Topics

## rand

Main Content

### Description

example

returns a single uniformly distributed random number in the interval (0,1).

example

returns an -by- matrix of random numbers.

example

returns an -by-...-by- array of random numbers where indicate the size of each dimension. For example, returns a 3-by-4 matrix.

example

returns an array of random numbers where size vector specifies . For example, returns a 3-by-4 matrix.

example

returns an array of random numbers of data type . The input can be either or . You can use any of the input arguments in the previous syntaxes.

example

returns an array of random numbers like ; that is, of the same object type as . You can specify either or , but not both.

generates numbers from random number stream instead of the default global stream. To create a stream, use . Specify followed by any of the argument combinations in previous syntaxes, except for the ones that involve . This syntax does not support the input.

### Examples

collapse all

### Matrix of Random Numbers

Generate a 5-by-5 matrix of uniformly distributed random numbers between 0 and 1.

*5×5*0.8147 0.0975 0.1576 0.1419 0.6557 0.9058 0.2785 0.9706 0.4218 0.0357 0.1270 0.5469 0.9572 0.9157 0.8491 0.9134 0.9575 0.4854 0.7922 0.9340 0.6324 0.9649 0.8003 0.9595 0.6787

### Random Numbers Within Specified Interval

Generate a 10-by-1 column vector of uniformly distributed numbers in the interval (-5,5).

*10×1*3.1472 4.0579 -3.7301 4.1338 1.3236 -4.0246 -2.2150 0.4688 4.5751 4.6489

In general, you can generate random numbers in the interval (a,b) with the formula .

### Random Integers

Use the function (instead of ) to generate 5 random integers from the uniform distribution between 10 and 50.

### Random Complex Numbers

Generate a single random complex number with real and imaginary parts in the interval (0,1).

### Reset Random Number Generator

Save the current state of the random number generator and create a 1-by-5 vector of random numbers.

*1×5*0.8147 0.9058 0.1270 0.9134 0.6324

Restore the state of the random number generator to , and then create a new 1-by-5 vector of random numbers. The values are the same as before.

*1×5*0.8147 0.9058 0.1270 0.9134 0.6324

Always use the function (rather than the or functions) to specify the settings of the random number generator. For more information, see Replace Discouraged Syntaxes of rand and randn.

### 3-D Array of Random Numbers

Create a 3-by-2-by-3 array of random numbers.

### Specify Data Type of Random Numbers

Create a 1-by-4 vector of random numbers whose elements are single precision.

*1x4 single row vector*0.8147 0.9058 0.1270 0.9134

### Clone Size from Existing Array

Create a matrix of random numbers with the same size as an existing array.

*2×2*0.8147 0.1270 0.9058 0.9134

It is a common pattern to combine the previous two lines of code into a single line:

### Clone Size and Data Type from Existing Array

Create a 2-by-2 matrix of single precision random numbers.

Create an array of random numbers that is the same size and data type as .

*2x2 single matrix*0.8147 0.1270 0.9058 0.9134

### Clone Distributed Array

If you have Parallel Computing Toolbox™, create a 1000-by-1000 distributed array of random numbers with underlying data type . For the data type, the syntax clones the underlying data type in addition to the primary data type.

Create an array of random numbers that is the same size, primary data type, and underlying data type as .

### Input Arguments

collapse all

### — Size of square matrix

integer value

Size of square matrix, specified as an integer value.

If is , then is an empty matrix.

If is negative, then it is treated as .

**Data Types: ** | | | | | | | | |

### — Size of each dimension (as separate arguments)

integer values

Size of each dimension, specified as separate arguments of integer values.

If the size of any dimension is , then is an empty array.

If the size of any dimension is negative, then it is treated as .

Beyond the second dimension, ignores trailing dimensions with a size of 1. For example, produces a 3-by-1 vector of random numbers.

**Data Types: ** | | | | | | | | |

### — Size of each dimension (as a row vector)

integer values

Size of each dimension, specified as a row vector of integer values. Each element of this vector indicates the size of the corresponding dimension:

If the size of any dimension is , then is an empty array.

If the size of any dimension is negative, then it is treated as .

Beyond the second dimension, ignores trailing dimensions with a size of 1. For example, produces a 3-by-1 vector of random numbers.

**Example: ** creates a 2-by-3-by-4 array.

**Data Types: ** | | | | | | | | |

### — Data type (class) to create

(default) |

Data type (class) to create, specified as , , or the name of another class that provides support.

**Example: **

### — Prototype of array to create

numeric array

Prototype of array to create, specified as a numeric array.

**Example: **

**Data Types: ** | **Complex Number Support: **Yes

### — Random number stream

object

Random number stream, specified as a object.

**Example: **

### Tips

The sequence of numbers produced by is determined by the internal settings of the uniform pseudorandom number generator that underlies , , and . You can control that shared random number generator using .

### Extended Capabilities

### C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

The data type (class) must be a built-in MATLAB

^{®}numeric type. For other classes, the static method is not invoked. For example, does not invoke .Size arguments must have a fixed size.

See Variable-Sizing Restrictions for Code Generation of Toolbox Functions (MATLAB Coder).

If extrinsic calls are enabled and is not called from inside a loop, generated MEX files use the same random number state as MATLAB in serial code. Otherwise, the generated MEX code and standalone code maintain their own random number state that is initialized to the same state as MATLAB.

### Thread-Based Environment

Run code in the background using MATLAB® or accelerate code with Parallel Computing Toolbox™ .

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

### GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Usage notes and limitations:

The stream syntax is not supported on a GPU.

You can specify as . If you specify as , the default underlying type of the array is .

To create a GPU array with underlying type , specify the underlying type as an additional argument before . For example, creates a 3-by-3 GPU array of random numbers with underlying type .

You can specify the underlying type as one of these options:

You can also specify the numeric variable as a .

If you specify as a , the underlying type of the returned array is the same as .

For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

### Distributed Arrays

Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

Usage notes and limitations:

The stream syntax is not supported for or arrays.

You can specify as or . If you specify as or , the default underlying type of the returned array is .

To create a distributed or codistributed array with underlying type , specify the underlying type as an additional argument before . For example, creates a 3-by-3 distributed matrix of random numbers with underlying type .

You can specify the underlying type as one of these options:

You can also specify as a or array.

If you specify as a or array, the underlying type of the returned array is the same as .

For additional syntaxes, see (Parallel Computing Toolbox).

For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).

**Introduced before R2006a**

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You moron?!!. Yes, I. yes, I did you.

## Array matlab randomize

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Random Numbers in MatlabHe only asked her one question before his fingers tugged at the zipper of her red pencil dress she wore that day. Are you sure. He asked. Of course. of course she was sure.

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