Summation of function handles in cell array

Hi. I have written the following code so far.

par.comp = 2;
par.NT = 9;  
par.P = 1;
par.Asat=[4.92531 4.6543  ];
par.Bsat=[1432.526 1435.264];
par.Csat=[-61.819 -64.848];
ics = [    5.0000    0.2545    0.2545    0.2545    0.2545    0.6295    0.6295    0.6295    5.0000
  4.9810    0.2535    0.2476    0.2289    0.1834    0.3066    0.1780    0.0469    0.0238
  0.0190    0.0010    0.0069    0.0256    0.0711    0.3229    0.4515    0.5826    4.9762]';

for i = 1:par.comp
  Psat{i} = @(T) 10.^(par.Asat(i)-par.Bsat(i)./(par.Csat(i)+T));
  y{i} = @(T,x) x*Psat{i}(T)/par.P;
  end

    xn = bsxfun(@rdivide,ics(:,2:end),ics(:,1));

    for i = 1:par.NT
        T(i) = fzero(@(T) y{1}(T,xn(i,1))+y{2}(T,xn(i,2))-1,300);
    end

The code works as it is supposed to (I think :) ), but I need it to be expandable for a higher value of par.comp. If par. comp is for instance 3 (ics would be 4x9), I need the last for loop to be:

   for i = 1:par.NT
          T(i) = fzero(@(T) y{1}(T,xn(i,1))+y{2}(T,xn(i,2))+y{3}(T,xn(i,3)-1,300);
      end

And so on. Is there any way to do this?

Answer 1

[Guillaume]

To be honest you're probably better off creating an explicit function, but you can achieve the summation with recursive anonymous functions. I have no idea what the impact on performance would be:

%xn = ???? %not sure what it should be when par.comp > 2
assert(all([numel(par.Asat), numel(par.Bsat), numel(par.Csat) >=  par.comp);
assert(size(xn, 2) >= par.comp && size(xn, 1) >= par.NT);

ysum = @(~, ~, ~) -1; %constant -1 for i = 0;
for i = 1:par.comp
  Psat = @(T) 10.^(par.Asat(i)-par.Bsat(i)./(par.Csat(i)+T));
  y = @(T,x) x*Psat(T)/par.P;
  ysum = @(T, xn, j) y(T, xn(j, i)) + ysum(T, xn, j); %call the previously defined anonymous function
end
%at the end of the loop ysum is a massive recursive anonymous function

for i = 1:par.NT
    T(i) = fzero(@(T) ysum(T, xn, i), 300);
end

[Bastian Andersen]

What do you mean about creating an explicit function? I managed to get a solution in a different way as:

xn = bsxfun(@rdivide,ics(:,2:end),ics(:,1));

for i = 1:par.comp
Psat{i} = @(T) 10.^(par.Asat(i)-par.Bsat(i)./(par.Csat(i)+T));
y{i} = @(T,n) xn(n,i)*Psat{i}(T)/par.P;
end

for i = 1:par.NT
T(i) = fzero(@(T) sum(cellfun(@(g) g(T,i),y))-1,300)
end

But your way might be better, as it doesn't use "weird" functions as cell fun or cell arrays, though I'm not sure about what you use j for (and I need Psat and y for later)

[Guillaume]

I meant use a proper m file instead of anonymous function, but actually it may be even more complicated, so forget about it

The j is to distinguish between your two i loops, with the recursive anonymous function you need to pass it the i from the par.NT loop, you can't call it i obviously since it's already used for the par.comp loop. With your solution it's equivalent to:

for i = 1:par.comp
Psat{i} = @(T) 10.^(par.Asat(i)-par.Bsat(i)./(par.Csat(i)+T));
y{i} = @(T,n) xn(n,i)*Psat{i}(T)/par.P;
end

for j = 1:par.NT
T(j) = fzero(@(T) sum(cellfun(@(g) g(T,j),y))-1,300)
end

Your solution and mine are pretty much equivalent in term of weirdness. If anything I'd say the recursive anonymous function is weirder than cellfun. The main difference between the two solutions is that your function does the sum expansion with an explicit loop (that's what cellfun is after all) whereas the sum expansion is already unrolled in my solution. So my solution may be slightly faster.

[玉成]

你好，我使用循环得到m{149}和PP{150,149}关于a的函数表达式，然后在它们等于30时候的根，但是运行太慢，有没有什么好的解决办法。代码如下：

clear

clc

x=[0,0.0810795702470861,0.338893857750972,0.289608984180225,0.373884785059033,0.419305386647289,0.381255405793147,0.387805825669320,0.473950108456370,0.777482062955663,0.899607314986380,0.879732671835855,0.642150284769991,0.686654174145980,0.733665507297614,0.648550239659963,0.792221920178573,0.858663843400142,0.950901518893565,0.908403222771981,0.841901725388123,0.803776648251092,0.685298083103286,0.642201303788118,0.758140400904556,0.497859095240467,0.299720346945175,0.330083731903406,0.399635177673192,0.308616636693337,0.406471800425586,0.596726876476001,0.715214262626168,0.550458743758525,0.492048935650519,0.419049480913983,0.412200268366443,0.364288733652186,0.295831971015213,0.576419028947360,0.574301385466896,0.596020783630510,0.674243062495796,0.498132386268964,0.397725957361996,0.502159675610620,0.592607341674827,0.492748845200838,0.683134575176520,0.723692678801045,0.791615285736084,0.856438696079586,0.838872071129628,0.660231299794271,0.697676532404639,0.554721614799348,0.589892742846681,0.673120226900998,0.756160690500417,0.639809622049692,0.746181259265069,0.654068062590623,0.747902390546003,0.887201993210606,1.15338612214489,0.958977631327466,1.12987192182697,1.17636074235029,1.23483468030576,1.23269555488261,1.33231404505112,1.37060109996512,1.36433302688288,1.36920419311632,1.52115837829399,1.65834482953446,1.87356345706959,1.99647272427397,2.05601842308497,1.99102453480784,2.11084190188162,2.15306161675519,2.26308133401253,2.45670787883561,2.47836705949687,2.50236540231708,2.55557973733006,2.66947127745567,3.01512570503452,2.99371227198361,3.25320110604215,3.31695082167831,3.52252671263044,3.62307908694682,3.64950604277507,3.71171958790155,3.92900862767658,4.18624573833328,4.40580642424208,4.43349562449954,4.37047086316136,4.52217706074632,4.69096186724754,4.47614654427472,4.58321154245995,4.95328125690921,5.03544570887013,5.06096113419815,5.04148762518430,4.92141732190889,4.96950751489138,5.11863558218135,5.10618007179529,5.25124128844036,5.46491228721431,5.50486562885070,5.68312502453605,5.87165380633716,5.98423928608256,6.35071262361604,6.30979036073293,6.46558377293770,6.47035888195859,6.50206243202057,6.68184170578453,6.94508314353340,7.09259966782103,7.38465156007102,7.39499822256765,7.56677221290127,7.62961885234629,7.66481995486628,7.46395102011682,7.69310729809314,8.06425918178358,8.26245926894464,8.57255189453345,8.71701239391423,8.69937525807431,8.72801534449858,8.76648524557879,9.04692602569443,9.12816457617079,9.28273121221453,9.25809977088039,9.37994368599395,9.32028599442426,9.37843566395927,9.62250467915979];

t=[0:0.1:14.8];

r=148

u(1)=0.0001;%初始化量

p(1)=0.0001;

s(1)=0.0001;

Q(1)=0.25;

k=1

for i=2:r

O{i+1}=@(a)(t(i+1)).^a-(t(i)).^a;

O{2}=@(a)t(2).^a-t(1).^a;

m{1}=u(k);

m1{2,1}=m{1}

PP{1,1}=p(k);

PP{2,1}=PP{1,1}+Q(k)

K{2}=@(a)PP{2,1}*O{2}(a)*(((O{2}(a))^2)*PP{2,1}+s(k)*(t(2)-t(1)))^(-1);

m{2}=@(a)m{1}+K{2}(a)*(x(2)-x(1)-m{1}*O{2}(a));

PP{2,2}=@(a)PP{2,1}-O{2}(a)*K{2}(a)*PP{2,1};

PP{3,2}=@(a)PP{2,2}(a)+Q(k);

m1{i+1,i}=@(a)m{i}(a);

PP{i+1,i}=@(a)PP{i,i}(a)+Q(k);

K{i+1}=@(a)PP{i+1,i}(a)*O{i+1}(a)*(((O{i+1}(a))^2)*PP{i+1,i}(a)+s(k)*(t(i+1)-t(i)))^(-1);

m{i+1}=@(a)m{i}(a)+K{i+1}(a)*(x(i+1)-x(i)-m{i}(a)*O{i+1}(a));

PP{i+1,i+1}=@(a)PP{i+1,i}(a)-O{i+1}(a)*K{i+1}(a)*PP{i+1,i}(a);

PP{i+2,i+1}=@(a)PP{i+1,i+1}(a)+Q(k);

end

a=fzero(@(a)PP{150,149}(a)-30,10)

a=fzero(@(a)m{149}(a)-30,10)