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All Sums

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All Sums

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26 Oct 2011 (Updated )

Distribution of unique sums among all combinations of vectors.

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ALLSUMS Distribution of unique sums among all combinations of vectors.

[S,C]=ALLSUMS(IN) depending on input IN, will do one of two different procedures for calculating all unique combinations of sums.
 
The output vectors, S and C, are respectively the list of unique sums, and the count distribution for those sums among all combinations.
 
 
SINGLE INPUT:
 
[S,C]=ALLSUMS(VEC) for a single input vector of length N, returns the distribution of unique sums among the (2^N)-1 combinations of non-empty subsets of elements within VEC.
 
EXAMPLE:
Number of ways to have a total of 250 using only the odd numbers from 1 to 100.
[S,C]=allsums(1:2:100);
num=C(S==250)
 
 
MULTIPLE INPUTS:
 
[S,C]=ALLSUMS(VEC,K) with vector VEC of length N, assumes theequivalent scenario of rolling a N-sided die, with values VEC, K times and returns the distributions of unique sums among all N^K combinations of values.
 
[S,C]=ALLSUMS(VEC1,K1,VEC2,K2,...) with vectors of length N1, N2, ... assumes the equivalent scenario of rolling a N1-sided die, with values VEC1, K1 times; then rolling a N2-sided dice, with values VEC2, K2 times; etc. and returns the distribution of unique sums among all (N1^K1)*(N2^K2)*... combinations of values
 
SINGLE VECTOR, REPEATED
Probability distribution of rolling a regular 6-sided die 100 times
[S,C]=allsums(1:6,100);
plot(S,C./sum(C)), grid on
 
MULTIPLE VECTORS, REPEATED
Probability of the total yielding exactly zero when rolling a
A) six-sided die with values [-5:0] ten times, and then a
B) ten-sided die with values [-4:5] twenty times.
[S,C]=allsums([-5:0],10,[-4:5],20);
prob=C(S==0)/sum(C)

Acknowledgements

This file inspired Sum Of Probability Distributions and Apply A Function To A Set Of Probability Distributions.

MATLAB release MATLAB 7.12 (R2011a)
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Comments and Ratings (2)
08 Dec 2011 Mike Sheppard

For unequal probabilities see "Sum of probability distributions" #34082

31 Oct 2011 Jonathan Sullivan  
Updates
27 Oct 2011

Generalized for multiple inputs, and across different vectors.

28 Oct 2011

Generalized to multiple inputs, fixed error checking and modified code for performance.

02 Nov 2011

Rephrased examples and summary

04 Apr 2012

Updated help section

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