Help with index for maximum value

I have an 2D array of data containing product fractions. The column index is associated with a mix ratio. The row index is associated with the product species. I can find the maximum fraction value for a specific species, but the mix ratio (and index) is wrong.

My code gives:

species max-frac mix-ratio

*H2 0.96220083 0.3

H2O 0.6870072 6.5

*OH 0.12253145 8

*O2 0.098079432 10

*H 0.041959177 10

*O 0.023207462 10

HO2 0.00045286 10

H2O2 6.51818E-05 10

O3 1.13457E-06 10

But the correct answer should be:

species max-frac mix-ratio

*H2 0.96220083 0.3

H2O 0.6870072 8

*OH 0.12253145 10

*O2 0.098079432 10

*H 0.041959177 6.5

*O 0.023207462 10

HO2 0.00045286 10

H2O2 6.51818E-05 10

O3 1.13457E-06 10

Any help sorting this out would be much appreciated.

format long g
fracts()

         species         max-frac        mix-ratio
             *H2    9.6220083e-01    3.0000000e-01
             H2O    6.8700720e-01    6.5000000e+00
             *OH    1.2253145e-01    8.0000000e+00
             *O2    9.8079432e-02    1.0000000e+01
              *H    4.1959177e-02    1.0000000e+01
              *O    2.3207462e-02    1.0000000e+01
             HO2    4.5285974e-04    1.0000000e+01
            H2O2    6.5181832e-05    1.0000000e+01
              O3    1.1345688e-06    1.0000000e+01

[Walter Roberson]

type fracts

of = [0.3 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10];
names = {  '*H2';
            'H2O';
            '*OH';
            '*O2';
            '*H';
            '*O';
            'HO2';
            'H2O2';
            'O3'};
fracs = [   0.96220083253122	0.937001387552033	0.874002714042574	0.810992700049054	0.74780577262337	0.683840005856851	0.618357080450297	0.551422328259094	0.484287900480256	0.418884308578777	0.357182267236621	0.300826351044237	0.250956482728154	0.208114480958745	0.172238875222256	0.142774189736819	0.118866074281767	0.0995650622968137	0.0839741805776359	0.0713232035303872	0.0609871740687707;
            0.0377991674687795	0.0629986124479674	0.125997220790509	0.188994457804212	0.25195480252116	0.314622580031103	0.376181736506199	0.43517993283166	0.489930222331301	0.538953613901196	0.581167160588662	0.615930444659731	0.643073504795639	0.66290507957213	0.676152906227016	0.683821047289943	0.687007202392198	0.686746500964421	0.683921193935693	0.67923402113771	0.673221297606501;
            2.22327976852125e-24	6.85759953134214e-18	1.24360881321903e-10	1.65983550999297e-07	9.48040334378583e-06	0.000128094622628151	0.000771840329195554	0.00279738011490611	0.00723162124064597	0.0148176596665369	0.0257038536127702	0.0393457993900356	0.0546117690529415	0.070076854609197	0.0844073534257148	0.0966629355644787	0.106397607625811	0.11357926910949	0.118432863790443	0.121297320925404	0.122531452149732;
            0	9.21364685054006e-32	5.34174433004885e-19	1.89295142164211e-13	2.68543345763431e-10	3.04085360475654e-08	8.38270610050516e-07	9.54211215508342e-06	6.06164189804761e-05	0.000258760896008051	0.000832935663080812	0.00217119193598601	0.00479493196399169	0.00925026325203391	0.0159515556041904	0.025061794920379	0.0364737499057485	0.0498818174109408	0.06488555384713	0.0810748040992137	0.098079431948234;
            3.34821507154084e-18	2.52865047941693e-13	6.51669170636362e-08	1.26761631833543e-05	0.000229944452125781	0.00140912960718508	0.00468506011821732	0.0105601254956405	0.018335667277251	0.0265638781664281	0.0337757085317884	0.0389383878973618	0.0416222109937517	0.04195917716899	0.0404567590241403	0.0377567111864494	0.0344415242874894	0.0309413222646071	0.0275266078132032	0.024343115131064	0.0214540059464803;
            0	2.09994239128734e-30	7.47501118128108e-18	1.80187954464638e-12	1.86002251374892e-09	1.59473697335477e-07	3.40470296396595e-06	3.03976169384125e-05	0.000152567015120172	0.000516894635128139	0.00132474469856626	0.00275772447439952	0.0048827991380266	0.00759473728588379	0.0106401124308879	0.0137091378038229	0.0165335172395724	0.0189393643993122	0.0208497082710153	0.0222597310944603	0.0232074621430668;
            0	6.15700192926503e-34	5.59172768866557e-21	2.30027012028065e-15	3.46998695200764e-12	4.01572114685042e-10	1.10327080890718e-08	1.22718487457335e-07	7.49217760837377e-07	3.03052602174162e-06	9.13292173694356e-06	2.20669406641223e-05	4.48216072210106e-05	7.9100015422758e-05	0.000124413872247518	0.000178163425558326	0.000236584185151753	0.000295876561847102	0.000352953824076108	0.000405693385509828	0.000452859736165154;
            9.5429764863276e-35	1.63464631004911e-26	3.1311605154588e-17	3.60763856556982e-13	7.52658165719256e-11	2.47087579926888e-09	2.85898094276133e-08	1.70851118629214e-07	6.56018684470211e-07	1.85362990389827e-06	4.19674677437665e-06	8.03365758476776e-06	1.34678983749615e-05	2.02726866956291e-05	2.79423159407678e-05	3.58554678020406e-05	4.34511487430121e-05	5.03319961748204e-05	5.62805544117132e-05	6.12234322683563e-05	6.51818322320969e-05;
            0	0	1.15144522820615e-36	7.42646875633622e-27	2.67068010341209e-21	1.10256114042769e-17	3.76650264552703e-15	2.69148029824262e-13	6.80746887494861e-12	8.43324431369168e-11	6.26559084359002e-10	3.16784106306547e-09	1.18218999340825e-08	3.44509017852597e-08	8.187760648436e-08	1.64604748359476e-07	2.8893351894724e-07	4.54996393304191e-07	6.57386391534331e-07	8.87263983275629e-07	1.13456881751286e-06 ];

maxFracs = max(fracs,[],2);
[~,c] = find(fracs == maxFracs);
ofMaxFracs = of(c)';

fmt = '%16s %16.7e %16.7e\n';
data = [names num2cell(maxFracs) num2cell(ofMaxFracs)].';
var = '\n         species         max-frac        mix-ratio\n';
fprintf(var)
fprintf(fmt,data{:})

%{
code gives this

species	max-frac	mix-ratio
*H2	0.96220083	0.3
H2O	0.6870072	6.5
*OH	0.12253145	8
*O2	0.098079432	10
*H    0.041959177	10
*O    0.023207462	10
HO2	0.00045286	10
H2O2	6.51818E-05	10
O3    1.13457E-06	10
%}

%{
correct answer is

species	max-frac	mix-ratio
*H2	0.96220083	0.3
H2O	0.6870072	8
*OH	0.12253145	10
*O2	0.098079432	10
*H    0.041959177	6.5
*O    0.023207462	10
HO2	0.00045286	10
H2O2	6.51818E-05	10
O3    1.13457E-06	10
%}

[Brantosaurus]

Thank you for the formatting Walter. I'll try better next time!

Answer 1

[Voss]

The easiest way to fix this is to use the second output from max, which tells you the column index in frac of each element of maxFracs.

[maxFracs,c] = max(fracs,[],2);
ofMaxFracs = of(c)';

[Voss]

When you use find, the order returned indices are in column-major order

of = [0.3 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10];
names = {  '*H2';
            'H2O';
            '*OH';
            '*O2';
            '*H';
            '*O';
            'HO2';
            'H2O2';
            'O3'};
fracs = [   0.96220083253122	0.937001387552033	0.874002714042574	0.810992700049054	0.74780577262337	0.683840005856851	0.618357080450297	0.551422328259094	0.484287900480256	0.418884308578777	0.357182267236621	0.300826351044237	0.250956482728154	0.208114480958745	0.172238875222256	0.142774189736819	0.118866074281767	0.0995650622968137	0.0839741805776359	0.0713232035303872	0.0609871740687707;
            0.0377991674687795	0.0629986124479674	0.125997220790509	0.188994457804212	0.25195480252116	0.314622580031103	0.376181736506199	0.43517993283166	0.489930222331301	0.538953613901196	0.581167160588662	0.615930444659731	0.643073504795639	0.66290507957213	0.676152906227016	0.683821047289943	0.687007202392198	0.686746500964421	0.683921193935693	0.67923402113771	0.673221297606501;
            2.22327976852125e-24	6.85759953134214e-18	1.24360881321903e-10	1.65983550999297e-07	9.48040334378583e-06	0.000128094622628151	0.000771840329195554	0.00279738011490611	0.00723162124064597	0.0148176596665369	0.0257038536127702	0.0393457993900356	0.0546117690529415	0.070076854609197	0.0844073534257148	0.0966629355644787	0.106397607625811	0.11357926910949	0.118432863790443	0.121297320925404	0.122531452149732;
            0	9.21364685054006e-32	5.34174433004885e-19	1.89295142164211e-13	2.68543345763431e-10	3.04085360475654e-08	8.38270610050516e-07	9.54211215508342e-06	6.06164189804761e-05	0.000258760896008051	0.000832935663080812	0.00217119193598601	0.00479493196399169	0.00925026325203391	0.0159515556041904	0.025061794920379	0.0364737499057485	0.0498818174109408	0.06488555384713	0.0810748040992137	0.098079431948234;
            3.34821507154084e-18	2.52865047941693e-13	6.51669170636362e-08	1.26761631833543e-05	0.000229944452125781	0.00140912960718508	0.00468506011821732	0.0105601254956405	0.018335667277251	0.0265638781664281	0.0337757085317884	0.0389383878973618	0.0416222109937517	0.04195917716899	0.0404567590241403	0.0377567111864494	0.0344415242874894	0.0309413222646071	0.0275266078132032	0.024343115131064	0.0214540059464803;
            0	2.09994239128734e-30	7.47501118128108e-18	1.80187954464638e-12	1.86002251374892e-09	1.59473697335477e-07	3.40470296396595e-06	3.03976169384125e-05	0.000152567015120172	0.000516894635128139	0.00132474469856626	0.00275772447439952	0.0048827991380266	0.00759473728588379	0.0106401124308879	0.0137091378038229	0.0165335172395724	0.0189393643993122	0.0208497082710153	0.0222597310944603	0.0232074621430668;
            0	6.15700192926503e-34	5.59172768866557e-21	2.30027012028065e-15	3.46998695200764e-12	4.01572114685042e-10	1.10327080890718e-08	1.22718487457335e-07	7.49217760837377e-07	3.03052602174162e-06	9.13292173694356e-06	2.20669406641223e-05	4.48216072210106e-05	7.9100015422758e-05	0.000124413872247518	0.000178163425558326	0.000236584185151753	0.000295876561847102	0.000352953824076108	0.000405693385509828	0.000452859736165154;
            9.5429764863276e-35	1.63464631004911e-26	3.1311605154588e-17	3.60763856556982e-13	7.52658165719256e-11	2.47087579926888e-09	2.85898094276133e-08	1.70851118629214e-07	6.56018684470211e-07	1.85362990389827e-06	4.19674677437665e-06	8.03365758476776e-06	1.34678983749615e-05	2.02726866956291e-05	2.79423159407678e-05	3.58554678020406e-05	4.34511487430121e-05	5.03319961748204e-05	5.62805544117132e-05	6.12234322683563e-05	6.51818322320969e-05;
            0	0	1.15144522820615e-36	7.42646875633622e-27	2.67068010341209e-21	1.10256114042769e-17	3.76650264552703e-15	2.69148029824262e-13	6.80746887494861e-12	8.43324431369168e-11	6.26559084359002e-10	3.16784106306547e-09	1.18218999340825e-08	3.44509017852597e-08	8.187760648436e-08	1.64604748359476e-07	2.8893351894724e-07	4.54996393304191e-07	6.57386391534331e-07	8.87263983275629e-07	1.13456881751286e-06 ];

maxFracs = max(fracs,[],2);

temp = fracs == maxFracs

temp = 9×21 logical array
   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0
   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1
   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1
   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0   0   0
   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1
   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1
   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1
   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1

[~,c] = find(temp)

c = 9×1

1 14 17 21 21 21 21 21 21

So, e.g., the second element of c is 14, indicating that the second element where temp is true is in the 14th column of maxFracs, but it would be a mistake to assume that that element is in the 2nd row of temp; in fact it's in the 5th row, which you could see if you kept the row indices returned by find.

[r,c] = find(temp)

r = 9×1

1 5 2 3 4 6 7 8 9

c = 9×1

1 14 17 21 21 21 21 21 21

To do this properly using find, you'd need to keep those row indices and sort them along with the column indices.

[r,c] = find(fracs == maxFracs);
[~,sort_idx] = sort(r);
c = c(sort_idx);
ofMaxFracs = of(c)'

ofMaxFracs = 9×1

0.3000 8.0000 10.0000 10.0000 6.5000 10.0000 10.0000 10.0000 10.0000

But, again, just using the second output from max is easier:

[maxFracs,c] = max(fracs,[],2);
ofMaxFracs = of(c)'

ofMaxFracs = 9×1

0.3000 8.0000 10.0000 10.0000 6.5000 10.0000 10.0000 10.0000 10.0000

[Brantosaurus]

That did the trick!

Many thanks for the answer.

I missed the wood for the trees!

[Voss]

You're welcome!

[Brantosaurus]

Also thanks for your help explaining my mistake. Very valuable. I'll keep that for reference.