Degeneration of Array in MATLAB

[pancho_hideboo]

We can get the completely same values in Array but with no repetitions
by using "unique()" in MATLAB.

>> A=[1, 1, 2, 3, 4]

A =

     1     1     2     3     4

>> unique(A)

ans =

     1     2     3     4

Here I would like to relax an euqality condition.
For example, I want to treat 1.0 and 1.001 as same value.
However we can not set tolerance in "unique()".

How can I degenarate Array with finite tolerance in MATLAB ?

>> A=[1.0, 1.001, 2, 3, 4]

A =

    1.0000    1.0010    2.0000    3.0000    4.0000

>> unique(A)

ans =

    1.0000    1.0010    2.0000    3.0000    4.0000

>>

 

[std_match]

You mean rounding?

octave> A=[1.0, 1.001, 2, 3, 4]
A =

   1.0000   1.0010   2.0000   3.0000   4.0000

octave> unique(round(A))
ans =

   1   2   3   4

According to the Matlab manual, you should be able to round to N decimal places by "round(A,N)" but that doesn't work in octave.
To round to 2 decimals in octave, we can do (should also work fine in Matlab)

octave> A=[1.237, 1.242, 2, 3, 4]
A =

   1.2370   1.2420   2.0000   3.0000   4.0000

octave> unique(round(100*A)/100)
ans =

   1.2400   2.0000   3.0000   4.0000

 

[pancho_hideboo]

You mean rounding?

No.
I want to specify relative tolerance.

 

[pancho_hideboo]

function res = main
clear all, close all, clc

tol = 1e-2;
A = [2.0001, -0.001, 1.0001, 1.0, 1.001, 0.0, 2.001, 2, 3.001, 3];

A.'
unique(A).'
my_unique(A, [], tol).'
my_unique(A(end:-1:1), [], tol).'
my_unique(sort(A), [], tol).'

A(1) = 8.6745e-016 + j*1.92803e-008;
A(2) = 8.6746e-016 + j*-1.92804e-008;
A(3) = -5.0306e-016 + j*0.68222;
A(4) = -5.0307e-016 + j*-0.68223;
A(5) = -5.0308e-016 + j*0.68224;
A(6) = -5.0309e-016 + j*-0.68225;
A(7) = 7.11236e-016 + j*0.970492;
A(8) = 7.11237e-016 + j*-0.970493;
A(9) = 7.11238e-016 + j*0.970494;
A(10) = 7.11239e-016 + j*-0.970495;

A.'
unique(A).'
my_unique(A).'
my_unique( A(end:-1:1) ).'
my_unique( sort(A) ).'

function B = my_unique(A, abs_tol, rel_tol)
if nargin <=1
    abs_tol = NaN;
    rel_tol = NaN;
end
if nargin <=2
    rel_tol = NaN;
end

if isempty(abs_tol), abs_tol = NaN; end
if isempty(rel_tol), rel_tol = NaN; end

if isnan(abs_tol) || abs_tol < 0.0, abs_tol = 1e-2; end
if isnan(rel_tol) || rel_tol < 0.0, rel_tol = 1e-4; end

i = 1;
while i <= length(A)
    x0 = A(i);
    k = length(A);
    while k >= i + 1
        x1 = A(k);
        if abs(x0) > abs_tol
            d = abs(x1 - x0) / abs(x0);
            if d < rel_tol, A(k) = []; end
        else
            d = abs(x1 - x0);
            if d < abs_tol, A(k) = []; end
        end
        k = k - 1;
    end
    i = i + 1;
end
B = A;

ans =

    2.0001
   -0.0010
    1.0001
    1.0000
    1.0010
         0
    2.0010
    2.0000
    3.0010
    3.0000


ans =

   -0.0010
         0
    1.0000
    1.0001
    1.0010
    2.0000
    2.0001
    2.0010
    3.0000
    3.0010


ans =

    2.0001
   -0.0010
    1.0001
    3.0010


ans =

    3.0000
    2.0000
         0
    1.0010


ans =

   -0.0010
    1.0000
    2.0000
    3.0000


ans =

   0.0000 + 0.0000i
   0.0000 - 0.0000i
  -0.0000 + 0.6822i
  -0.0000 - 0.6822i
  -0.0000 + 0.6822i
  -0.0000 - 0.6823i
   0.0000 + 0.9705i
   0.0000 - 0.9705i
   0.0000 + 0.9705i
   0.0000 - 0.9705i


ans =

   0.0000 + 0.0000i
   0.0000 - 0.0000i
  -0.0000 + 0.6822i
  -0.0000 - 0.6822i
  -0.0000 + 0.6822i
  -0.0000 - 0.6823i
   0.0000 + 0.9705i
   0.0000 - 0.9705i
   0.0000 + 0.9705i
   0.0000 - 0.9705i


ans =

   0.0000 + 0.0000i
  -0.0000 + 0.6822i
  -0.0000 - 0.6822i
   0.0000 + 0.9705i
   0.0000 - 0.9705i


ans =

   0.0000 - 0.9705i
   0.0000 + 0.9705i
  -0.0000 - 0.6823i
  -0.0000 + 0.6822i
   0.0000 - 0.0000i


ans =

   0.0000 + 0.0000i
  -0.0000 + 0.6822i
  -0.0000 - 0.6822i
   0.0000 + 0.9705i
   0.0000 - 0.9705i

>>