How to attribute vectors from a matrix some proprieties?

I have to create a matrix with 4 columns and with some proprieties.The first column is a ,second b , third c , forth d.Those numbers have to be in an interval ( 1 ,2 ,...,10000) and the conditions are : a>b , (a-c)(b-d)>0, c>d.I've tried to "attach" to a vector a condition that depends on another vector , but i failed,I have to create a matrxi with There are a few rules before creating that matrix:

1. You can't use while.
2. You can't use for.
3. In 1 matrix must appear all of the combinations that verifiy the conditions below.

Does someone know how to apply proprieties to a vector or have any idea how to resolve this problem ? I've tried a few methods but all of them failed.

[Luna]

What have you done so far? Could you please share the code?

[Jan]

I do not understand the question. What is "an interval ( 1 ,2 ,...,10000)"? What did you try to "attach"? Which vector depends on which otehr one? Post, what you have tried so far and an example output.

[Victor Iordache]

Luna , here's what i've done so far ,but I have 1 problem .First i'll give you some explanations, a= first column,b-second ,c-third, 4 -forth.The numbers from every column has to be an integer from 1-10000 , numbers from column a has to be > numbers from column b , same applies to c>d and (a-c)(b-d)>0 "example of a matrix of this kind : A=[4 2 2 1]"

I can't solve one thing now,the last property,that (4-2)(2-1)>0.

%n=input('n=')

-i'll change n with 3 in every randi,first i want to create a matrix by 4x4 with this property , if i can manage this i'll just change 3 with n and it will generate a n x 4 matrix.

a=randi([1,10000],1,3);

b=randi([1,10000],1,3);

c=randi([1,10000],1,3)

d=randi([1,10000],1,3)

%first column

x=max(a,b)

y=reshape(x,3,1)

%

%third column

x1=max(c,d);

y1=reshape(x1,3,1)

%

%second column

x2=min(b,d);

y2=reshape(x2,3,1)

%

%forth column

x3=min(c,d);

y3=reshape(x3,3,1)

T=[y,y2,y1,y3]

[Victor Iordache]

Hello ,Jan.

I have to generate a matrix of n x 4 that has some proprieties.

We'll say that the first column is a , second is b , third is c and forth is d, an example for this kind of matrix is :" A= [ 5 3 2 1]"

The proprieties :

1. a>b ( 5>3)
2. c>d (2>1)
3. (a-c)(b-d)>0 (5-2)(3-1)>0

I need to generate a matrix of n lines with 4 column that has the exact proprieties.All numbers has to be integers from 1 to 10.000.

Answer 1

[Luna]

Hello Victor,

You can try below code. Please read my comments. I hope it helps.

n = 4; 

a = randi(10000,n,1); % creates random a from 1-10000 with n rows
b = arrayfun(@(x) randi(x,1,1),a); % creates random b with n rows. Each element in b is smaller than a's corresponding element (for each row)  

% (a-c)(b-d) > 0 means a>c and b>d at the same time. So the following c and d created by this rule
c = arrayfun(@(x) randi(x,1,1),a); % creates random c with n rows. Each element in c is smaller than a's corresponding element (for each row).
d = arrayfun(@(x) randi(x,1,1),b); % creates random d with n rows. Each element in d is smaller than b's corresponding element (for each row).

T = [a,b,c,d]; % your nx4 matrix

%% checks if the below condition is OK for each row.
% if proof is 1, all rows fit the condition. 
%If proof is zero at least one row in T does not fit the condition. 
proof = any((a-c).*(b-d) > 0);

[Victor Iordache]

Luna , column c must be > column d though..

I've tried it few times and now i've got :

T =

a b c d

6952 862 1880 360

4992 2448 1041 505

5359 4572 3028 4334

4452 3891 2851 320

but 3028<4334

[Victor Iordache]

I've added

n = 4;

a = randi(10000,n,1); % creates random a from 1-10000 with n rows

b = arrayfun(@(x) randi(x,1,1),a); % creates random b with n rows. Each element in b is smaller than a's corresponding element (for each row)

% (a-c)(b-d) > 0 means a>c and b>d at the same time. So the following c and d created by this rule

c = arrayfun(@(x) randi(x,1,1),a); % creates random c with n rows. Each element in c is smaller than a's corresponding element (for each row).

d = arrayfun(@(x) randi(x,1,1),b);% creates random d with n rows. Each element in d is smaller than b's corresponding element (for each row).

e = arrayfun(@(x) randi(x,1,1),c);%creates random e with n rows. Each element in e is smaller than c's

f=min(d,e);

T = [a,b,c,f]% your nx4 matrix

proof = any((a-c).*(b-d) > 0);

is that correct ? I guess ,but i kinda need an approval :))

[Victor Iordache]

And the last thing, that i really don't know how to do. I have to display every combination of this kind o matrix. I don't know how I should be able to do that , is there a command for this ?