find the max value in an array from a selection of elements corresponding to non unique items in another array

I have two arrays lets call them x and y and if you plot them you can create the following plot for example

As you can see there are some x values that have two corresponding y values. In two arrays of data (Example data below) this would be that there are two occurances of a particular x value (e.g. x = -350) each with two different y values (y = 1.331573626327333 & 43.073736543265510)

How do I:

1) remove all duplicate x data (this I think is the easier part using the unique function I guess). I still want there to be one of these occurances to remain in the arry however at the end

2) find only the max value from the corresponding y data. (i.e from the previous example for x = -350 it should only return y= 43.073736543265510)

In other words how do I remove the duplicate data with the min y value, leaving the max y value and one iteration of the x value behing?

x = [-344.889995378401	-345	-346	-347	-348	-348.790577839601	-349	-350	-351	-352	-352.364199727765	-353	-354	-355	-355.649037035211	-356	-357	-358	-358.675037800818	-359	-360	-361	-361.473920026108	-362	-363	-364	-364.064720071035	-365	-366	-366.456572583127	-367	-368	-368.663505839183	-369	-370	-370.696656851489	-371	-372	-372.565575585720	-373	-374	-374.278385142883	-375	-375.841868323049	-376	-377	-377.261734208111	-378	-378.542802425223	-379	-379.689019976183	-380	-380.703560818727	-381	-381.588917426414	-382	-382.346929864271	-382.978818186504	-383	-383.485197007167	-383.866099638873	-384	-384.120939445921	-384.248508431993	-384.246975028648	-384.113807290917	-384	-383.845642078457	-383.438301912707	-383	-382.886839407149	-382.184796216022	-382	-381.324723768083	-381	-380.297652670582	-380	-379.092744072702	-379	-378	-377.696307208119	-377	-376.092941049423	-376	-375	-374.262056927059	-374	-373	-372.179721696529	-372	-371	-370	-369.814388394383	-369	-368	-367.126138426752	-367	-366	-365	-364.061760966373	-364	-363	-362	-361	-360.547531003596	-360	-359	-358	-357.518863898406	-357	-356	-355	-354.137518769451	-354	-353	-352	-351	-350.304827964543	-350	-349	-348	-347	-346	-345.903207469402	-345	-344	-343	-342	-341	-340.738362769946	-340	-339	-338	-337	-336	-335	-334.470451478080	-334	-333	-332	-331	-330	-329	-328	-327	-326.358673906962	-326	-325	-324	-323	-322	-321	-320	-319	-318	-317	-316	-315	-314.826864645813	-314	-313	-312	-311	-310	-309	-308	-307	-306	-305	-304	-303	-302	-301	-300	-299	-298	-297	-296	-295	-294	-293	-292	-291	-290	-289	-288	-287	-286	-285	-284	-283	-282	-281	-280	-279	-278	-277	-276	-275	-274	-273	-272	-271	-270	-269	-268	-267	-266	-265.485627509798	-265	-264	-263	-262	-261	-260	-259	-258	-257	-256	-255	-254	-253	-252.121489198760	-252	-251	-250	-249	-248	-247	-246	-245	-244	-243	-242.490780588105	-242	-241	-240	-239	-238	-237	-236	-235	-234.195033116041	-234	-233	-232	-231	-230	-229	-228	-227.024343121247	-227	-226	-225	-224	-223	-222	-221	-220.759814889434	-220	-219	-218	-217	-216	-215.160349441984	-215	-214	-213	-212	-211	-210.083517539267	-210	-209	-208	-207	-206	-205.435236196409	-205	-204	-203	-202	-201	-200	-199.792746246760	-199	-198	-197	-196	-195	-194.611481636899	-194	-193	-192	-191	-190	-189.914617322129	-189	-188	-187	-186	-185.638250087510	-185	-184	-183	-182	-181.732061007438	-181	-180	-179	-178.158996830696	-178	-177	-176	-175	-174.889620754774	-174	-173	-172	-171.900243401682	-171	-170	-169.171620462662	-169	-168	-167	-166.687813819363	-166	-165	-164.435590811588	-164	-163	-162.403939292291	-162	-161	-160.583618370755	-160	-159	-158.998264706511	-158	-157.624876721980	-157	-156.439819509359	-156	-155.437922250342	-155	-154.614791184103	-154	-153.966796154046	-153.491067405984	-153.185299106022	-153.047864406426	-153.077703857249	-153.274340321440	-153.637873235383	-154	-154.168982324284	-154.868978248684	-155	-155.739836605355	-156	-156.784186286643	-157	-158	-158.005433020272	-159	-159.408133515186	-160	-161	-161.048957777685	-162	-162.926843921165	-163	-164	-165	-165.020663819739	-166	-167	-167.341769256470	-168	-169	-169.902790859422	-170	-171	-172	-172.720778044628	-173	-174	-175	-175.815150082974	-176	-177	-178	-179	-179.211325317224	-180	-181	-182	-182.940568698066];
y = [0	0.0272194650481636	0.277667211041931	0.532514056802643	0.791783561400847	1	1.05684019501265	1.33157362632733	1.61101822986139	1.89519567559844	2	2.18919049076846	2.49106573632331	2.79797974637965	3	3.11334931574240	3.44027028255356	3.77255346864151	4	4.11402929910814	4.46902724886179	4.82787908226978	5	5.19975498674158	5.58417032438329	5.97451111232560	6	6.38671247257059	6.80627428865191	7	7.24316435907907	7.69589300518693	8	8.16344613304419	8.65404361736447	9	9.16051123132827	9.69462021996493	10	10.2514461475017	10.8358956023243	11	11.4590770672394	12	12.1105214441594	12.8143840872053	13	13.5745646312312	14	14.3975115697007	15	15.3056046637972	16	16.3341641298170	17	17.5419124747450	18	19	19.0418704364112	20	21	21.5263245578540	22	23	24	25	25.4268397264698	26	27	27.7969847727076	28	29	29.2177462528981	30	30.3202872961235	31	31.2509646326650	32	32.0679034389998	32.7865310672453	33	33.4405799616769	34	34.0521996389837	34.6037917902708	35	35.1294645884743	35.6136417140000	36	36.0785835714883	36.5075819028805	36.9241869322799	37	37.3113507163817	37.6835947011485	38	38.0430382177564	38.3778880260209	38.7032572137306	39	39.0185268065508	39.3130007248546	39.5991579928548	39.8771499173972	40	40.1830422689700	40.5192777579917	40.8462773686695	41	41.1599786300243	41.4612082087638	41.7541181177522	42	42.0379634394675	42.3084492255619	42.5714047817752	42.8269572729572	43	43.0737365432655	43.3101697340312	43.5398685678795	43.7629453495439	43.9795109723238	44	44.1864753289209	44.3870322263417	44.5816329362551	44.7703752566327	44.9533556688765	45	45.1288214088546	45.2982245943236	45.4623250054285	45.6212074568217	45.7749555156692	45.9236514991676	46	46.0666070717566	46.2039131263162	46.3365360895456	46.4645479109286	46.5880193496423	46.7070199716128	46.8216181465068	46.9318810446918	47	47.0375519144161	47.1385085903986	47.2354079480332	47.3283081312105	47.4172661525547	47.5023378923477	47.5835780976915	47.6718792924470	47.7564066942133	47.8372108703701	47.9143413448562	47.9878465951739	48	48.0574711227212	48.1235441947623	48.1861743936172	48.2454031037989	48.3012707352430	48.3538167239141	48.4030795328584	48.4490966537213	48.4919046087505	48.5315389532986	48.5680342788442	48.6014242165427	48.6317414413225	48.6590176765356	48.6832836991738	48.7045693456577	48.7229035182052	48.7383141917832	48.7508284216473	48.7604723514679	48.7672712220438	48.7712493805999	48.7724302906644	48.7708365425201	48.7664898642203	48.7594111331615	48.7496203881993	48.7371368422962	48.7219788956855	48.7041641495352	48.6837094200941	48.6606307533013	48.6349434398378	48.6066620306000	48.5758003525696	48.5535703042663	48.5287210639115	48.5012644662994	48.4712116477520	48.4385730607766	48.4033584891069	48.3655770631041	48.3252372754916	48.2823469973981	48.2369134946827	48.1889434445154	48.1384429521841	48.0854175681021	48.0298723049881	48	47.9718115636930	47.9112390810900	47.8481577341391	47.7825697442610	47.7144768382988	47.6438802685785	47.5707808329560	47.4951788948193	47.4170744030137	47.3364669116620	47.2533555998496	47.1677392911466	47.0796164729409	47	46.9889812545793	46.8957995579050	46.8000928504331	46.7018570703232	46.6010878977656	46.4977807751645	46.3919309269136	46.2835333787455	46.1725829766356	46.0590744052461	46	45.9429364851299	45.8241421246834	45.7027468174559	45.5882964290872	45.4711205683133	45.3512095199400	45.2285534357784	45.1031423530113	45	44.9749122615648	44.8436592146970	44.7095806981797	44.5726645365814	44.4328985420634	44.2902705310962	44.1447683404729	44	43.9963677580251	43.8445527975371	43.6897713580103	43.5320095155122	43.3712534719147	43.2074895678946	43.0407042951559	43	42.8702663159264	42.6965201391615	42.5196388030051	42.3396075906558	42.1564120357951	42	41.9698545760485	41.7790877199458	41.5850244544371	41.3876495413917	41.1869480858613	41	40.9827749606938	40.7737491260170	40.5612465007405	40.3452518983285	40.1257505560649	40	39.9260346433899	39.7537701183348	39.5788214987752	39.4011803265135	39.2208385408334	39.0377884746398	39	38.8525603906248	38.6636342892800	38.4715857330046	38.2764017798323	38.0780699235051	38	37.8741808302773	37.6654370189710	37.4533168838962	37.2378081693135	37.0188991010721	37	36.7918166203136	36.5606492881030	36.3258217285174	36.0873229135416	36	35.8408772973550	35.5881010800979	35.3313597406587	35.0706434384327	35	34.7996974484472	34.5222041878318	34.2404048673906	34	33.9525975512307	33.6512897736333	33.3453020424605	33.0346275583549	33	32.7072211953442	32.3732382950445	32.0341475482132	32	31.6747177910007	31.3080390215111	31	30.9321851442425	30.5330813061153	30.1278465302857	30	29.6983322320471	29.2539081298296	29	28.7882948934346	28.2966780669712	28	27.7805728539791	27.2312628972327	27	26.6419536782021	26.0011222355206	26	25.2755952074750	25	24.4754227121580	24	23.5633366413415	23	22.4699620773531	22	21.0515570260791	21	20	19	18	17	16	15	14.3174544687247	14	13	12.8487603209348	12	11.7494527763937	11	10.8219534165399	10.0044072227190	10	9.28874231909957	9	8.62467937399871	8.02890761546989	8	7.48984573298377	7	6.96447707427975	6.48331753810917	6.00969728657976	6	5.57352625067553	5.14482829921361	5	4.73898259939742	4.34777330518609	4	3.96470024329579	3.60517577581750	3.25136002891266	3	2.90758926505897	2.58039885768803	2.25845522835426	2	1.94404243000721	1.64468881274853	1.35017131473224	1.06048592890052	1	0.783242371444436	0.512542005507627	0.246305822720229	0];

[Bhaskar R]

 [vals_x,loc,~] = unique(x);
 vals_y = y(loc);
 plot(vals_x, vals_y);

Hope I understood your query, if not comment back

[darova]

You want to remove y values after xmax/xmin. Is it correct?

[Nick Turton]

This has partially done what I need it to do as it is reloving duplicates but doesn't appear to remove the duplicates I want to remove.

I want to remove y values after xmax/xmin but only the duplicated values with the minimum value of y.

If I was to try this for the example data above and then search for the corresponding value of y for x = -350 it would now return y = 1.331573626327333, not the y = 43.073736543265510 which I desire

vals_y(find(vals_x==-350))

Answer 1

[Guillaume]

Note: For such large arrays, it is better to attach your data as a mat file rather than copy/pasting the content in the question. In particular, by pasting the data as text, you inevitably introduce some rounding of the values which may have important implication to what you want.

Your x data is made up of floating-point values. You always have to be very careful when you say that two values are equal in an array of floating-point numbers. For example:

>> x = [0.1+0.1+0.1, 0.3]
x =
          0.3          0.3

Are the two values in x the same? You'd think so

>> x(1) == x(2)
ans =
  logical
   0

but actually, they aren't.

>> x(1)-x(2)
ans =
   5.5511e-17

They differ by a very small amount. The same might be the case for your duplicate values. For that reason, comparison with floating point numbers should always be done by comparing their difference relative to a small tolerance. Fortunately, for you, matlab has uniquetol that simplifies this.

So, to answer your question:

   tol = 3e-3;   %seems to work fairly well with your data
   [xvals, ~, loc] = uniquetol(x);  %get unique values of x and their location
   yvals = accumarray(loc, (1:numel(y))', [], @(locs) max(y(locs)));  %get max y at corresponding locations

Note that if you reduce the tolerance, eg.

tol = 1e-5;
[xvals, ~, loc] = uniquetol(x, tol);  
yvals = accumarray(loc, (1:numel(y))', [], @(locs) max(y(locs)));
plot(x, y, xvals, yvals)

then you get

that's because some x elements are not actually duplicate as I explained, and some of these unique values correspond to the 'bottom' part of your graph.

Perhaps, a better solution is to go back to the equation that generated your data and limit the range before computing the result.

[Nick Turton]

Thanks everyone for your responses. I'll take your comments on board for furure reference.

BTW I have found a hacky workaround to my issue for this occasion

[val_x_min, loc_x_min] = min(x);
y_at_xmin = y(loc_x_min);
[val_x_max, loc_x_max] = max(x);
y_at_xmax = y(loc_x_max);

y_linear = (y_at_xmin-y_at_xmax)/(val_x_min-val_x_max).*(x-val_x_min) + y_at_xmin;
y2= y-y_linear;

D= [x;y2];
D(:, D(2,:) < 0) = [];

D(2,:) = D(2,:) +(y_at_xmin-y_at_xmax)/(val_x_min-val_x_max).*(D(1,:)-val_x_min) + y_at_xmin;

plot(x,y,D(1,:),D(2,:),'lineWidth',2)