sum of all anges is zero

Hi all , Hope all is fine,

I want to generate a n X n matrix of angle but the condition is that sum of all the angles is equal to zero.. my idea is given below but the sum is not zero how i can apply a condition........ Thanks in advance. I have taken 10 by 10 matrix of random angles.........

 angle = (rand(10)-0.5)*360

angle =

-17.8050 -141.6050  -24.6910  127.0912  -29.7839  100.8907  -95.4792   16.9232  154.5789   51.9545
-149.8243  166.2833  147.8331   43.9398 -162.1244  -39.6940  -52.8629  -73.3245   99.2566  -43.7006
-97.5683 -178.3317 -114.5351  -53.6571  144.9778  -92.9911  115.6299   88.0894   -4.7550  112.1690
148.8015   98.9678  -85.0310    4.7698  160.1234  -34.5916 -174.4548 -111.9762  -23.0909   11.8172
-125.1439  114.2292 -127.6060  -35.3491   -3.2889 -145.2764 -164.5114   67.2392  -19.1579  -53.7382
117.2941  132.7301 -131.0153 -152.6520   -3.8691 -132.4896 -119.1636 -113.9360  -69.7142  158.0406
 13.8033 -149.6031  132.9452  -93.6302  -58.4210  159.1382   53.6816  -47.3455    3.0631  135.3394
178.6085  -36.0782   28.6937 -135.6052  144.0194  164.2084   83.4201   45.2227    3.8778   18.0563
-151.8568  -86.4467   17.9497 -113.7932  -47.0712   27.0751   53.1885  100.8819  114.3460   44.0910
-20.6358  108.0247 -127.8163  -93.6171 -139.9670 -158.4794  -17.6675 -150.7947  106.1393   31.3361

>> sum(sum(angle))

ans =

 -676.8780

Answer 1

[Image Analyst]

The usual answer is Roger Stafford's randfixedsum(): http://www.mathworks.com/matlabcentral/fileexchange/9700-random-vectors-with-fixed-sum

Answer 2

[Star Strider]

Subtract the mean rather than 0.5, since there is no guarantee that the mean will be exactly 0.5 with a less-than-infinite sample size:

rm = rand(10);
angle = (rm-mean(rm(:))) * 360;
angle_sum = sum(angle(:))

This produced:

angle_sum =

      -4.1780e-012

which is acceptably close to zero (to me at least).

[John D'Errico]

Suppose the original numbers were sampled from the interval [-180,180] (in degrees.) The problem here is that the result need no longer satisfy that original set of bounds. This may or may not be acceptable. As well, the distribution of those numbers will not be sampled uniformly from the desired set.

Roger's randfixedsum solves all problems, sampling uniformly from the desired distribution.