All Sums 1.0

Distribution of unique sums among all combinations of vectors.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, REPEATEDProbability 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, REPEATEDProbability of the total yielding exactly zero when rolling aA) six-sided die with values [-5:0] ten times, and then aB) ten-sided die with values [-4:5] twenty times.[S,C]=allsums([-5:0],10,[-4:5],20);prob=C(S==0)/sum(C)

Requirements:	No special requirements
Platforms:	Matlab
Keyword:	Dallsumsvec Vec,  Distributions,  Equivalent,  Multiple,  Nsided,  Rolling,  Scenario,  Sided,  Times,  Values
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