Problem in sorting the elements of a complex column vetor in descending order.

I am trying to sort the elements of a complex column vetor in descending order. The vector V is,

0.00192283028876372 + 2.81043109217511e-19i

0.00190176141109370 + 2.84699448762080e-19i

0.00147928037481547 - 2.74849838261212e-20i

0.00142769822781175 + 5.39004850343165e-20i

0.00117784972186107 + 2.08922253853130e-19i

0.00107796253204560 - 4.70645642035523e-20i

0.000800293022988111 + 1.22052572461947e-20i

0.000269899528923458 - 6.15654463989809e-20i

6.30592283269993e-05 - 7.50552502780072e-20i

2.23684164933882e-05 + 4.04939694038624e-21i

2.20073577954736e-05 - 5.80181618012595e-21i

1.95849840201760e-05 + 1.48445834874224e-20i

1.71925856406516e-05 - 1.15719050036467e-20i

1.28038961421133e-05 + 7.36148671834500e-20i

8.73059513582096e-06 + 1.23064435626381e-20i

6.28618594970652e-06 - 5.04267327744353e-20i

6.99991469893008e-08 - 1.02450891500650e-20i

2.80343931756963e-08 + 1.23048032017686e-20i

4.29713831923512e-09 + 3.73908633968205e-21i

2.28802604174547e-09 + 1.73500648980058e-20i

3.50507467296844e-10 - 1.10159115820306e-21i

7.32973689738923e-11 - 4.65099992985255e-21i

2.07808170074765e-11 - 2.84966374048803e-22i

4.68510672896002e-12 - 2.29503200085301e-21i

2.99051403313190e-12 + 3.62505072381834e-21i

1.32399364803625e-12 - 4.30261778360293e-21i

6.07212915777181e-13 + 2.79063028387683e-22i

1.23086553364893e-13 + 8.26560004261648e-21i

1.72392520759381e-14 + 1.86019192086409e-21i

1.01989680354965e-14 + 3.46136359467220e-21i

-8.05918955245067e-21 + 8.23317408693105e-22i

1.36822909718840e-15 - 1.33221528989010e-21i

I code as below,

% sort the variances in decreasing order

[junk, rindices] = sort(-1*V);

% V1=[2;6;4;3;1;8];

% [junk1, rindices1] = sort(-1*V1);

V = V(rindices);

However, after sorting, V became,

-8.05918955245067e-21 + 8.23317408693105e-22i

1.36822909718840e-15 - 1.33221528989010e-21i

1.01989680354965e-14 + 3.46136359467220e-21i

1.72392520759381e-14 + 1.86019192086409e-21i

1.23086553364893e-13 + 8.26560004261648e-21i

6.07212915777181e-13 + 2.79063028387683e-22i

1.32399364803625e-12 - 4.30261778360293e-21i

2.99051403313190e-12 + 3.62505072381834e-21i

4.68510672896002e-12 - 2.29503200085301e-21i

2.07808170074765e-11 - 2.84966374048803e-22i

7.32973689738923e-11 - 4.65099992985255e-21i

3.50507467296844e-10 - 1.10159115820306e-21i

2.28802604174547e-09 + 1.73500648980058e-20i

4.29713831923512e-09 + 3.73908633968205e-21i

2.80343931756963e-08 + 1.23048032017686e-20i

6.99991469893008e-08 - 1.02450891500650e-20i

6.28618594970652e-06 - 5.04267327744353e-20i

8.73059513582096e-06 + 1.23064435626381e-20i

1.28038961421133e-05 + 7.36148671834500e-20i

1.71925856406516e-05 - 1.15719050036467e-20i

1.95849840201760e-05 + 1.48445834874224e-20i

2.20073577954736e-05 - 5.80181618012595e-21i

2.23684164933882e-05 + 4.04939694038624e-21i

6.30592283269993e-05 - 7.50552502780072e-20i

0.000269899528923458 - 6.15654463989809e-20i

0.000800293022988111 + 1.22052572461947e-20i

0.00107796253204560 - 4.70645642035523e-20i

0.00117784972186107 + 2.08922253853130e-19i

0.00142769822781175 + 5.39004850343165e-20i

0.00147928037481547 - 2.74849838261212e-20i

0.00190176141109370 + 2.84699448762080e-19i

0.00192283028876372 + 2.81043109217511e-19i

which is defintely not in descending order.

I also tried on positive real numbers,

V1=[2;6;4;3;1;8];

[junk1, rindices1] = sort(-1*V1);

and the consequence is correct.

I don't know why the sorting of the complex numbers seems wrong.

Answer 1

[Cris LaPierre]

Just specify 'descend' for your sort order.

B = sort(___,direction)

format longE
V=[0.00192283028876372 + 2.81043109217511e-19i
0.00190176141109370 + 2.84699448762080e-19i
0.00147928037481547 - 2.74849838261212e-20i
0.00142769822781175 + 5.39004850343165e-20i
0.00117784972186107 + 2.08922253853130e-19i
0.00107796253204560 - 4.70645642035523e-20i
0.000800293022988111 + 1.22052572461947e-20i
0.000269899528923458 - 6.15654463989809e-20i
6.30592283269993e-05 - 7.50552502780072e-20i
2.23684164933882e-05 + 4.04939694038624e-21i
2.20073577954736e-05 - 5.80181618012595e-21i
1.95849840201760e-05 + 1.48445834874224e-20i
1.71925856406516e-05 - 1.15719050036467e-20i
1.28038961421133e-05 + 7.36148671834500e-20i
8.73059513582096e-06 + 1.23064435626381e-20i
6.28618594970652e-06 - 5.04267327744353e-20i
6.99991469893008e-08 - 1.02450891500650e-20i
2.80343931756963e-08 + 1.23048032017686e-20i
4.29713831923512e-09 + 3.73908633968205e-21i
2.28802604174547e-09 + 1.73500648980058e-20i
3.50507467296844e-10 - 1.10159115820306e-21i
7.32973689738923e-11 - 4.65099992985255e-21i
2.07808170074765e-11 - 2.84966374048803e-22i
4.68510672896002e-12 - 2.29503200085301e-21i
2.99051403313190e-12 + 3.62505072381834e-21i
1.32399364803625e-12 - 4.30261778360293e-21i
6.07212915777181e-13 + 2.79063028387683e-22i
1.23086553364893e-13 + 8.26560004261648e-21i
1.72392520759381e-14 + 1.86019192086409e-21i
1.01989680354965e-14 + 3.46136359467220e-21i
-8.05918955245067e-21 + 8.23317408693105e-22i
1.36822909718840e-15 - 1.33221528989010e-21i];

newV = sort(V,'descend')

newV = 
      1.922830288763720e-03 + 2.810431092175110e-19i
      1.901761411093700e-03 + 2.846994487620800e-19i
      1.479280374815470e-03 - 2.748498382612120e-20i
      1.427698227811750e-03 + 5.390048503431650e-20i
      1.177849721861070e-03 + 2.089222538531300e-19i
      1.077962532045600e-03 - 4.706456420355230e-20i
      8.002930229881110e-04 + 1.220525724619470e-20i
      2.698995289234580e-04 - 6.156544639898089e-20i
      6.305922832699930e-05 - 7.505525027800721e-20i
      2.236841649338820e-05 + 4.049396940386240e-21i
      2.200735779547360e-05 - 5.801816180125950e-21i
      1.958498402017600e-05 + 1.484458348742240e-20i
      1.719258564065160e-05 - 1.157190500364670e-20i
      1.280389614211330e-05 + 7.361486718345000e-20i
      8.730595135820959e-06 + 1.230644356263810e-20i
      6.286185949706520e-06 - 5.042673277443530e-20i
      6.999914698930080e-08 - 1.024508915006500e-20i
      2.803439317569630e-08 + 1.230480320176860e-20i
      4.297138319235120e-09 + 3.739086339682050e-21i
      2.288026041745470e-09 + 1.735006489800580e-20i
      3.505074672968440e-10 - 1.101591158203060e-21i
      7.329736897389230e-11 - 4.650999929852550e-21i
      2.078081700747650e-11 - 2.849663740488030e-22i
      4.685106728960020e-12 - 2.295032000853010e-21i
      2.990514033131900e-12 + 3.625050723818340e-21i
      1.323993648036250e-12 - 4.302617783602930e-21i
      6.072129157771810e-13 + 2.790630283876830e-22i
      1.230865533648930e-13 + 8.265600042616479e-21i
      1.723925207593810e-14 + 1.860191920864090e-21i
      1.019896803549650e-14 + 3.461363594672200e-21i
      1.368229097188400e-15 - 1.332215289890100e-21i
     -8.059189552450671e-21 + 8.233174086931050e-22i

[奥 刘]

Thanks! But I just can't figure out why I use

[junk, rindices] = sort(-1*V);

didn't give the same answer. I think they are the same.

[Cris LaPierre]

That is because your numbers are complex. You can find details here. By default, the sort function sorts complex values by their magnitude, and breaks ties using phase angles.

The magnitude is always positive. So while negating real numbers flips their order, that does not work for complex numbers because it doesn't change the sign of their magnitude.

[奥 刘]

@Cris LaPierre Thanks！