# v_randiscr

## PURPOSE

V_RANDISCR Generate discrete random numbers with specified probabiities [X]=(P,N,A)

## SYNOPSIS

function x=v_randiscr(p,n,a)

## DESCRIPTION

```V_RANDISCR Generate discrete random numbers with specified probabiities [X]=(P,N,A)

Usage: (1) v_randiscr([],10)        % generate 10 uniform random binary values
(2) v_randiscr(2:6,10)       % generate 10 random numbers in the range 1:5
with probabilities [2 3 4 5 6]/20
(3) v_randiscr([],10,'abcd') % generate a string of 10 random
characters equiprobable from 'abcd'
(4) v_randiscr([],-3,'abcd') % generate a string of 3 distinct random
characters equiprobable from 'abcd'

Inputs: P  vector or n-D array of probabilities (not necessarily normalized) [default = uniform]
N  number of random values to generate: +ve=with and -ve=without replacement [default = 1]
A  output alphabet [default = 1:length(p) or 0:1 if p is empty]

Outputs: X  vector of not necessarily distinct values taken from alphabet A
If A is omitted and P is a matrix, each row of X(N,M) will contain the M coordinates
of a random element of P.

The vector P is internally normalized by dividing by its sum.```

## CROSS-REFERENCE INFORMATION

This function calls:
This function is called by:
• v_randvec V_RANDVEC Generate real or complex GMM/lognormal random vectors X=(N,M,C,W,MODE)

## SOURCE CODE

```0001 function x=v_randiscr(p,n,a)
0002 %V_RANDISCR Generate discrete random numbers with specified probabiities [X]=(P,N,A)
0003 %
0004 % Usage: (1) v_randiscr([],10)        % generate 10 uniform random binary values
0005 %        (2) v_randiscr(2:6,10)       % generate 10 random numbers in the range 1:5
0006 %                                       with probabilities [2 3 4 5 6]/20
0007 %        (3) v_randiscr([],10,'abcd') % generate a string of 10 random
0008 %                                       characters equiprobable from 'abcd'
0009 %        (4) v_randiscr([],-3,'abcd') % generate a string of 3 distinct random
0010 %                                       characters equiprobable from 'abcd'
0011 %
0012 % Inputs: P  vector or n-D array of probabilities (not necessarily normalized) [default = uniform]
0013 %         N  number of random values to generate: +ve=with and -ve=without replacement [default = 1]
0014 %         A  output alphabet [default = 1:length(p) or 0:1 if p is empty]
0015 %
0016 % Outputs: X  vector of not necessarily distinct values taken from alphabet A
0017 %             If A is omitted and P is a matrix, each row of X(N,M) will contain the M coordinates
0018 %             of a random element of P.
0019 %
0020 % The vector P is internally normalized by dividing by its sum.
0021
0022 % Somewhat similar in function to RANDSRC in the comms toolbox
0023
0024 % Revisions:
0025 %   2020-08-01 Fixed error when n=-(alphabet size)
0026 %   2020-11-03 Clarified comments and speeded up non-replacement sampling
0027 %              with uniform probabilities
0028 %
0029 %   Copyright (c) 2005-2012 Mike Brookes,  mike.brookes@ic.ac.uk
0030 %      Version: \$Id: v_randiscr.m 10865 2018-09-21 17:22:45Z dmb \$
0031 %
0032 %   VOICEBOX is a MATLAB toolbox for speech processing.
0034 %
0035 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0036 %   This program is free software; you can redistribute it and/or modify
0037 %   it under the terms of the GNU General Public License as published by
0038 %   the Free Software Foundation; either version 2 of the License, or
0039 %   (at your option) any later version.
0040 %
0041 %   This program is distributed in the hope that it will be useful,
0042 %   but WITHOUT ANY WARRANTY; without even the implied warranty of
0043 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
0044 %   GNU General Public License for more details.
0045 %
0046 %   You can obtain a copy of the GNU General Public License from
0047 %   http://www.gnu.org/copyleft/gpl.html or by writing to
0048 %   Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA.
0049 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0050 gota=nargin>2;
0051 if nargin<1 || ~numel(p)
0052     if gota
0053         p=ones(1,length(a));
0054     else
0055         p=ones(1,2);
0056         a=(0:1)';
0057         gota=1;
0058     end
0059 end
0060 if nargin<2 || ~numel(n)
0061     n=1;
0062 end
0063 q=p(:);
0064 d=length(q);                    % size of output alphabet
0065 if gota && d~=numel(a)
0066     error('sizes of alphabet and probability vector/matrix must match');
0067 end
0068 if n>1                          % sample with replacement
0069     dn=d+n-1;
0070     z=zeros(dn,1);                % array to hold random numbers
0071     z(1:d)=cumsum(q/sum(q));       % last value is overwritten in the next line
0072     z(d:end)=rand(n,1);         % create a random number for each sample
0073     [y,iy]=sort(z);             % the original entries z(1:d-1) now divide the samples into bins for each possible value
0074     y(iy)=(1:dn)';                 % create inverse index
0075     m=zeros(dn,1);
0076     m(y(1:d-1))=1;                 % set original initial d-1 values to 1
0077     m(1)=m(1)+1;                % and also the first value
0078     m=cumsum(m);                % label each of the random nuumbers with its corresponding value in 1:d
0079     x=m(y(d:dn));               % find the partitions of the n random numbers
0080 else                            % sample without replacement
0081     n=abs(n);                   % number of samples needed
0082     if n>d
0083         error('Number of output samples exceeds alphabet size');
0084     end
0085     if all(q==q(1))             % if all probabilities are equal
0086         [y,iy]=sort(rand(d,1)); % iy is a random permutation of 1:d
0087         x=iy(1:n);              % select the first n values
0088     else
0089         f=(1:d)';               % initialize the alphabet to 1:d
0090         x=zeros(n,1);           % space for the output samples
0091         nn=n;                   % number of samples remaining
0092         while nn>0              % number of samples remaining
0093             dd=numel(f);        % alphabet size (always >=nn)
0094             if dd==1            % singleton alphabet
0095                 x(n)=f;         % set remaining sample to the only remaining value
0096                 nn=0;           % and set remaining value count to zero
0097             else
0098                 qq=q(f);                        % remaiing alphabet probabilities
0099                 dn=dd+nn-1;
0100                 z=zeros(dn,1);                  % array to hold random numbers
0101                 z(1:dd)=cumsum(qq/sum(qq));     % last value is overwritten in the next line
0102                 z(dd:dn)=rand(nn,1);            % create a random number for each sample
0103                 [y,iy]=sort(z);                 % the original entries z(1:dd-1) now divide the samples into bins for each possible value
0104                 y(iy)=(1:dn)';                  % create inverse index
0105                 m=zeros(dn,1);
0106                 m(y(1:dd-1))=1;                   % set original initial dd-1 values to 1
0107                 m(1)=m(1)+1;                    % and also the first value
0108                 m=cumsum(m);                    % label each of the random nuumbers with its corresponding value in 1:dd
0109                 z=m(y(dd:dn));                  % find the partitions of the nn random numbers
0110                 [y,iy]=sort(z);                 % sorts the positions within each partition
0111                 z(iy(1+find(y(1:nn-1)==y(2:nn))))=[];          % keep only the first sample from each partition
0112                 k=numel(z);                     % number of new samples
0113                 x(n-nn+1:n-nn+k)=f(z);          % add new samples into output array
0114                 nn=nn-k;                        % number of remaining samples
0115                 f(z)=[];                        % remove used entries from alphabet
0116             end
0117         end
0118     end
0119 end
0120 if gota
0121     x=a(x);                                     % select from output alphabet
0122 elseif length(q)>length(p)                      % need multiple dimensions
0123     v=x-1;
0124     s=cumprod(size(p));
0125     m=length(s);
0126     s(2:end)=s(1:end-1);
0127     s(1)=1;
0128     x=zeros(n,m);
0129     for i=m:-1:1
0130         x(:,i)=1+floor(v/s(i));                 % find indices starting with the last
0131         v=rem(v,s(i));
0132     end
0133 end```

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