output for different changing variables - matlab

Question

I have 4 variables a,b,c,d. a can vary 1,2 i.e. a=1,2, b=1,2,3, c=1,2,3,4, d=1,2,3,4,5 so by varying each element I want to make output value i.e.
a b c d output
1 1 1 1 1
1 1 1 2 2
1 1 1 3 3
1 1 1 4 4
1 1 1 5 5
now varying c with 1 value and d with all values i.e.
a b c d output
1 1 2 1 6
1 1 2 2 7
1 1 2 3 8
1 1 2 4 9
1 1 2 5 10
now change c to 3 and doing above so getting output as 11,12,13,14,15. when c reaches max varying limit then change b i.e.
a b c d output
1 2 1 1 16
1 2 1 2 17
1 2 1 3 18
1 2 1 4 19
1 2 1 5 20
then
a b c d output
1 2 2 1 21
1 2 2 2 22
1 2 2 3 23
1 2 2 4 24
1 2 2 5 25
so like this I want to proceed and want output for all conditions of a,b,c,d. so how to do it or any equation to do this in matlab. in above a,b,c,d vary 2,3,4,5 i.e in increasing order but in general case they can vary without increasing order e.g. a,b,c,d can vary 7,4,9,13.

Answer 1

A possible algorithm could be to buil the combinations column by column considering the number of times eache value has to be repeted starting form the array d
Defined:
len_a the length of the arraya
len_b the length of the arrayb
len_c the length of the arrayc
len_d the length of the arrayd
you need to replicate the d array len_a * len_b * len_c times.
The array c needs to be replicated len_c * len_d times to cover the "right side" combination, the this set of data have to be replicated len_a * len_b times to account for the "left side" to come.
Similar approach applies for the definiton of the array a and b.
To have the set of combinations in a "random" sequence, is sufficient to
use the randperm function.
% Define the input arrays
a=1:2;
len_a=length(a);
b=1:3;
len_b=length(b);
c=1:4;
len_c=length(c);
d=1:5;
len_d=length(d);
% Generate the fourth column of the table
%
d1=repmat(d',len_a*len_b*len_c,1)
%
% Generate the third column of the table
c1=repmat(reshape(bsxfun(#plus,zeros(len_d,1),[1:len_c]),len_c*len_d,1),len_a*len_b,1)
%
% Generate the second column of the table
b1=repmat(reshape(bsxfun(#plus,zeros(len_c*len_d,1),[1:len_b]),len_b*len_c*len_d,1),len_a,1)
%
% Generate the first column of the table
a1=reshape(bsxfun(#plus,zeros(len_b*len_c*len_d,1),[1:len_a]),len_a*len_b*len_c*len_d,1)
%
% Merge the colums and add the counter in the fifth column
combination_set_1=[a1 b1 c1 d1 (1:len_a*len_b*len_c*len_d)']
% Randomize the rows
combination_set_2=combination_set_1(randperm(len_a*len_b*len_c*len_d),:)
Output:
1 1 1 1 1
1 1 1 2 2
1 1 1 3 3
1 1 1 4 4
1 1 1 5 5
1 1 2 1 6
1 1 2 2 7
1 1 2 3 8
1 1 2 4 9
1 1 2 5 10
1 1 3 1 11
1 1 3 2 12
1 1 3 3 13
1 1 3 4 14
1 1 3 5 15
1 1 4 1 16
1 1 4 2 17
1 1 4 3 18
1 1 4 4 19
1 1 4 5 20
1 2 1 1 21
1 2 1 2 22
1 2 1 3 23
1 2 1 4 24
1 2 1 5 25
1 2 2 1 26
1 2 2 2 27
1 2 2 3 28
1 2 2 4 29
1 2 2 5 30
1 2 3 1 31
1 2 3 2 32
1 2 3 3 33
1 2 3 4 34
1 2 3 5 35
1 2 4 1 36
1 2 4 2 37
1 2 4 3 38
1 2 4 4 39
1 2 4 5 40
1 3 1 1 41
1 3 1 2 42
1 3 1 3 43
1 3 1 4 44
1 3 1 5 45
1 3 2 1 46
1 3 2 2 47
1 3 2 3 48
1 3 2 4 49
1 3 2 5 50
1 3 3 1 51
1 3 3 2 52
1 3 3 3 53
1 3 3 4 54
1 3 3 5 55
1 3 4 1 56
1 3 4 2 57
1 3 4 3 58
1 3 4 4 59
1 3 4 5 60
2 1 1 1 61
2 1 1 2 62
2 1 1 3 63
2 1 1 4 64
2 1 1 5 65
2 1 2 1 66
2 1 2 2 67
2 1 2 3 68
2 1 2 4 69
2 1 2 5 70
2 1 3 1 71
2 1 3 2 72
2 1 3 3 73
2 1 3 4 74
2 1 3 5 75
2 1 4 1 76
2 1 4 2 77
2 1 4 3 78
2 1 4 4 79
2 1 4 5 80
2 2 1 1 81
2 2 1 2 82
2 2 1 3 83
2 2 1 4 84
2 2 1 5 85
2 2 2 1 86
2 2 2 2 87
2 2 2 3 88
2 2 2 4 89
2 2 2 5 90
2 2 3 1 91
2 2 3 2 92
2 2 3 3 93
2 2 3 4 94
2 2 3 5 95
2 2 4 1 96
2 2 4 2 97
2 2 4 3 98
2 2 4 4 99
2 2 4 5 100
2 3 1 1 101
2 3 1 2 102
2 3 1 3 103
2 3 1 4 104
2 3 1 5 105
2 3 2 1 106
2 3 2 2 107
2 3 2 3 108
2 3 2 4 109
2 3 2 5 110
2 3 3 1 111
2 3 3 2 112
2 3 3 3 113
2 3 3 4 114
2 3 3 5 115
2 3 4 1 116
2 3 4 2 117
2 3 4 3 118
2 3 4 4 119
2 3 4 5 120
Hope this helps.
Qapla'