Sorting a matrix with symbolic variables in matlab - matlab

Question

How can i sort or arrange this matrix ? The 10th row is showing up now in the very start while it should follow the sequence and comes at 10th place. Few other elements are also misplaced in the middle. All the variables are symbolic in this case. Thank you.
[ P10_1, P10_10, P10_2, P10_3, P10_4, P10_5, P10_6, P10_7, P10_8, P10_9, P1_1, P1_10, P1_2, P1_3, P1_4, P1_5, P1_6, P1_7, P1_8, P1_9, P2_1, P2_10, P2_2, P2_3, P2_4, P2_5, P2_6, P2_7, P2_8, P2_9, P3_1, P3_10, P3_2, P3_3, P3_4, P3_5, P3_6, P3_7, P3_8, P3_9, P4_1, P4_10, P4_2, P4_3, P4_4, P4_5, P4_6, P4_7, P4_8, P4_9, P5_1, P5_10, P5_2, P5_3, P5_4, P5_5, P5_6, P5_7, P5_8, P5_9, P6_1, P6_10, P6_2, P6_3, P6_4, P6_5, P6_6, P6_7, P6_8, P6_9, P7_1, P7_10, P7_2, P7_3, P7_4, P7_5, P7_6, P7_7, P7_8, P7_9, P8_1, P8_10, P8_2, P8_3, P8_4, P8_5, P8_6, P8_7, P8_8, P8_9, P9_1, P9_10, P9_2, P9_3, P9_4, P9_5, P9_6, P9_7, P9_8, P9_9]
The sort function return this.The 10th row should come in the end but it is appearing in the start.
[ P10_1, P10_2, P10_3, P10_4, P10_5, P10_6, P10_7, P10_8, P10_9, P10_10, P1_1, P1_2, P1_3, P1_4, P1_5, P1_6, P1_7, P1_8, P1_9, P2_1, P2_2, P2_3, P2_4, P2_5, P2_6, P2_7, P2_8, P2_9, P3_1, P3_2, P3_3, P3_4, P3_5, P3_6, P3_7, P3_8, P3_9, P4_1, P4_2, P4_3, P4_4, P4_5, P4_6, P4_7, P4_8, P4_9, P5_1, P5_2, P5_3, P5_4, P5_5, P5_6, P5_7, P5_8, P5_9, P6_1, P6_2, P6_3, P6_4, P6_5, P6_6, P6_7, P6_8, P6_9, P7_1, P7_2, P7_3, P7_4, P7_5, P7_6, P7_7, P7_8, P7_9, P8_1, P8_2, P8_3, P8_4, P8_5, P8_6, P8_7, P8_8, P8_9, P9_1, P9_2, P9_3, P9_4, P9_5, P9_6, P9_7, P9_8, P9_9, P1_10, P2_10, P3_10, P4_10, P5_10, P6_10, P7_10, P8_10, P9_10]

Answer 1

horchler suggested in the comments to create proper variable names to make lexicographic sorting using sort work properly. I think this is a very good idea, but unfortunately the format string he suggests does not work. It always pads a zero, ending up with this:
>> P1 = sym('P0%d_0%d',10)
P =
[ P01_01, P01_02, P01_03, P01_04, P01_05, P01_06, P01_07, P01_08, P01_09, P01_010]
[ P02_01, P02_02, P02_03, P02_04, P02_05, P02_06, P02_07, P02_08, P02_09, P02_010]
[ P03_01, P03_02, P03_03, P03_04, P03_05, P03_06, P03_07, P03_08, P03_09, P03_010]
[ P04_01, P04_02, P04_03, P04_04, P04_05, P04_06, P04_07, P04_08, P04_09, P04_010]
[ P05_01, P05_02, P05_03, P05_04, P05_05, P05_06, P05_07, P05_08, P05_09, P05_010]
[ P06_01, P06_02, P06_03, P06_04, P06_05, P06_06, P06_07, P06_08, P06_09, P06_010]
[ P07_01, P07_02, P07_03, P07_04, P07_05, P07_06, P07_07, P07_08, P07_09, P07_010]
[ P08_01, P08_02, P08_03, P08_04, P08_05, P08_06, P08_07, P08_08, P08_09, P08_010]
[ P09_01, P09_02, P09_03, P09_04, P09_05, P09_06, P09_07, P09_08, P09_09, P09_010]
[ P010_01, P010_02, P010_03, P010_04, P010_05, P010_06, P010_07, P010_08, P010_09, P010_010]
I tried to fix the format string but failed. MATLAB refuses to accept the format string which would be needed:
>> P1 = sym('P%.2d_%.2d',10)
Error using sym>createCharMatrix (line
2172)
Symbolic matrix base name must be a
simple variable name.
Error in sym>convertCharWithOption
(line 2138)
s = createCharMatrix(x,a);
Error in sym>tomupad (line 1871)
S = convertCharWithOption(x,a);
Error in sym (line 109)
S.s = tomupad(x,a);
So I wrote my own function to fix this:
function [ s ] = symMatrix( A,set )
%preallocate an empty matrix to fill it in the loop
s=sym(zeros(set));
%just some math t get the required amount of digits.
digits=ceil(log10(max(set)+1));
%generate format string with required digits. Check documentation of sprintf for details
format=['%s%.',num2str(digits),'d_%.',num2str(digits),'d'];
%finally go through the matrix...
for r=1:set(1)
for c=1:set(2)
%...get the right name for each variable ....
sprintf(format,A,r,c);
%...and create a variable with that name.
s(r,c)=sym(n);
end
end
end
Which produces this result:
>> P2=symMatrix('P',[11,11])
P2 =
[ P01_01, P01_02, P01_03, P01_04, P01_05, P01_06, P01_07, P01_08, P01_09, P01_10, P01_11]
[ P02_01, P02_02, P02_03, P02_04, P02_05, P02_06, P02_07, P02_08, P02_09, P02_10, P02_11]
[ P03_01, P03_02, P03_03, P03_04, P03_05, P03_06, P03_07, P03_08, P03_09, P03_10, P03_11]
[ P04_01, P04_02, P04_03, P04_04, P04_05, P04_06, P04_07, P04_08, P04_09, P04_10, P04_11]
[ P05_01, P05_02, P05_03, P05_04, P05_05, P05_06, P05_07, P05_08, P05_09, P05_10, P05_11]
[ P06_01, P06_02, P06_03, P06_04, P06_05, P06_06, P06_07, P06_08, P06_09, P06_10, P06_11]
[ P07_01, P07_02, P07_03, P07_04, P07_05, P07_06, P07_07, P07_08, P07_09, P07_10, P07_11]
[ P08_01, P08_02, P08_03, P08_04, P08_05, P08_06, P08_07, P08_08, P08_09, P08_10, P08_11]
[ P09_01, P09_02, P09_03, P09_04, P09_05, P09_06, P09_07, P09_08, P09_09, P09_10, P09_11]
[ P10_01, P10_02, P10_03, P10_04, P10_05, P10_06, P10_07, P10_08, P10_09, P10_10, P10_11]
[ P11_01, P11_02, P11_03, P11_04, P11_05, P11_06, P11_07, P11_08, P11_09, P11_10, P11_11]
Finally compare the sorting of all three possibilities:
>> P3=sym('P',[11,11])
P3 =
[ P1_1, P1_2, P1_3, P1_4, P1_5, P1_6, P1_7, P1_8, P1_9, P1_10, P1_11]
[ P2_1, P2_2, P2_3, P2_4, P2_5, P2_6, P2_7, P2_8, P2_9, P2_10, P2_11]
[ P3_1, P3_2, P3_3, P3_4, P3_5, P3_6, P3_7, P3_8, P3_9, P3_10, P3_11]
[ P4_1, P4_2, P4_3, P4_4, P4_5, P4_6, P4_7, P4_8, P4_9, P4_10, P4_11]
[ P5_1, P5_2, P5_3, P5_4, P5_5, P5_6, P5_7, P5_8, P5_9, P5_10, P5_11]
[ P6_1, P6_2, P6_3, P6_4, P6_5, P6_6, P6_7, P6_8, P6_9, P6_10, P6_11]
[ P7_1, P7_2, P7_3, P7_4, P7_5, P7_6, P7_7, P7_8, P7_9, P7_10, P7_11]
[ P8_1, P8_2, P8_3, P8_4, P8_5, P8_6, P8_7, P8_8, P8_9, P8_10, P8_11]
[ P9_1, P9_2, P9_3, P9_4, P9_5, P9_6, P9_7, P9_8, P9_9, P9_10, P9_11]
[ P10_1, P10_2, P10_3, P10_4, P10_5, P10_6, P10_7, P10_8, P10_9, P10_10, P10_11]
[ P11_1, P11_2, P11_3, P11_4, P11_5, P11_6, P11_7, P11_8, P11_9, P11_10, P11_11]
>> sort(P1(:)).' %P1 = sym('P0%d_0%d',10)
ans =
[ P01_01, P01_02, P01_03, P01_04, P01_05, P01_06, P01_07, P01_08, P01_09, P02_01, P02_02, P02_03, P02_04, P02_05, P02_06, P02_07, P02_08, P02_09, P03_01, P03_02, P03_03, P03_04, P03_05, P03_06, P03_07, P03_08, P03_09, P04_01, P04_02, P04_03, P04_04, P04_05, P04_06, P04_07, P04_08, P04_09, P05_01, P05_02, P05_03, P05_04, P05_05, P05_06, P05_07, P05_08, P05_09, P06_01, P06_02, P06_03, P06_04, P06_05, P06_06, P06_07, P06_08, P06_09, P07_01, P07_02, P07_03, P07_04, P07_05, P07_06, P07_07, P07_08, P07_09, P08_01, P08_02, P08_03, P08_04, P08_05, P08_06, P08_07, P08_08, P08_09, P09_01, P09_02, P09_03, P09_04, P09_05, P09_06, P09_07, P09_08, P09_09, P010_01, P010_02, P010_03, P010_04, P010_05, P010_06, P010_07, P010_08, P010_09, P01_010, P02_010, P03_010, P04_010, P05_010, P06_010, P07_010, P08_010, P09_010, P010_010]
>> sort(P2(:)).' %P2=symMatrix('P',[11,11])
ans =
[ P01_01, P01_02, P01_03, P01_04, P01_05, P01_06, P01_07, P01_08, P01_09, P01_10, P01_11, P02_01, P02_02, P02_03, P02_04, P02_05, P02_06, P02_07, P02_08, P02_09, P02_10, P02_11, P03_01, P03_02, P03_03, P03_04, P03_05, P03_06, P03_07, P03_08, P03_09, P03_10, P03_11, P04_01, P04_02, P04_03, P04_04, P04_05, P04_06, P04_07, P04_08, P04_09, P04_10, P04_11, P05_01, P05_02, P05_03, P05_04, P05_05, P05_06, P05_07, P05_08, P05_09, P05_10, P05_11, P06_01, P06_02, P06_03, P06_04, P06_05, P06_06, P06_07, P06_08, P06_09, P06_10, P06_11, P07_01, P07_02, P07_03, P07_04, P07_05, P07_06, P07_07, P07_08, P07_09, P07_10, P07_11, P08_01, P08_02, P08_03, P08_04, P08_05, P08_06, P08_07, P08_08, P08_09, P08_10, P08_11, P09_01, P09_02, P09_03, P09_04, P09_05, P09_06, P09_07, P09_08, P09_09, P09_10, P09_11, P10_01, P10_02, P10_03, P10_04, P10_05, P10_06, P10_07, P10_08, P10_09, P10_10, P10_11, P11_01, P11_02, P11_03, P11_04, P11_05, P11_06, P11_07, P11_08, P11_09, P11_10, P11_11]
>> sort(P3(:)).' %P3 = sym('P',10)
ans =
[ P10_1, P10_2, P10_3, P10_4, P10_5, P10_6, P10_7, P10_8, P10_9, P11_1, P11_2, P11_3, P11_4, P11_5, P11_6, P11_7, P11_8, P11_9, P10_10, P10_11, P11_10, P11_11, P1_1, P1_2, P1_3, P1_4, P1_5, P1_6, P1_7, P1_8, P1_9, P2_1, P2_2, P2_3, P2_4, P2_5, P2_6, P2_7, P2_8, P2_9, P3_1, P3_2, P3_3, P3_4, P3_5, P3_6, P3_7, P3_8, P3_9, P4_1, P4_2, P4_3, P4_4, P4_5, P4_6, P4_7, P4_8, P4_9, P5_1, P5_2, P5_3, P5_4, P5_5, P5_6, P5_7, P5_8, P5_9, P6_1, P6_2, P6_3, P6_4, P6_5, P6_6, P6_7, P6_8, P6_9, P7_1, P7_2, P7_3, P7_4, P7_5, P7_6, P7_7, P7_8, P7_9, P8_1, P8_2, P8_3, P8_4, P8_5, P8_6, P8_7, P8_8, P8_9, P9_1, P9_2, P9_3, P9_4, P9_5, P9_6, P9_7, P9_8, P9_9, P1_10, P1_11, P2_10, P2_11, P3_10, P3_11, P4_10, P4_11, P5_10, P5_11, P6_10, P6_11, P7_10, P7_11, P8_10, P8_11, P9_10, P9_11]

Answer 2

I don't know what you mean with "symbolic"? When it's a string, simple parse them as numbers (remove 'P' and replace the underscore '_' with a dot '.').
Finally sort while saving the indices.
this = '[ P10_1, P10_10, P10_2, P10_3, P10_4, P10_5, P10_6, P10_7, P10_8, P10_9, P1_1, P1_10, P1_2, P1_3, P1_4, P1_5, P1_6, P1_7, P1_8, P1_9, P2_1, P2_10, P2_2, P2_3, P2_4, P2_5, P2_6, P2_7, P2_8, P2_9, P3_1, P3_10, P3_2, P3_3, P3_4, P3_5, P3_6, P3_7, P3_8, P3_9, P4_1, P4_10, P4_2, P4_3, P4_4, P4_5, P4_6, P4_7, P4_8, P4_9, P5_1, P5_10, P5_2, P5_3, P5_4, P5_5, P5_6, P5_7, P5_8, P5_9, P6_1, P6_10, P6_2, P6_3, P6_4, P6_5, P6_6, P6_7, P6_8, P6_9, P7_1, P7_10, P7_2, P7_3, P7_4, P7_5, P7_6, P7_7, P7_8, P7_9, P8_1, P8_10, P8_2, P8_3, P8_4, P8_5, P8_6, P8_7, P8_8, P8_9, P9_1, P9_10, P9_2, P9_3, P9_4, P9_5, P9_6, P9_7, P9_8, P9_9]';
% this is the ugly part :)
original = regexp([regexprep(this, {'\[','\]'}, {'',''}) ','], '(.*?),', 'tokens');
m = eval(regexprep(this, {'_', 'P'},{'.',''}));
[s, idx] = sort(m);
original(idx)
As you see, this just works partly, because "symbolic" P10_1 < P10_10, but on numeric level, they're equal. So you just need to figure out to handle it, e.g. ensure you always have two decimal places and complete a leading zero if not.
If it's not a string, ignore this :)