Use specific variable from index to plot answer of equation
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I have multiple equations using variables that are ranges of values, and some that aren't. Essentially I would like help indexing the variables properly so I can calculate the equations using the full range of variables and then also pull out specific numbers from the range and re-run the equations using those, without having to rewrite the equations.
Ultimately I want to run the calcultion for all possible values of delta_rfO and delta_rfH, but plot only the values that use T=573.15, B=0, and the full range of Q using indexing, for example. Is there a way to set this up with an index so I can choose the values (or ranges of values withing a range) in the plot command?
I tried in this line, specifing the value in Q from row 1 column 9
"plot(delta_rfO(Q(1,9)),delta_rfH(Q(1,9)))" obviously this doesn't work but it is an example of what I would like to do.
clc
clear
T=linspace(573.15,1173.15,100)% Temperatures used in calculation
n1=length(T)
Beta=linspace(0,1,100)%Variable relating cation content of mineral
n2=length(Beta)
delta_winO=0
delta_riO=6
delta_winH=0
delta_riH=-60
Q=linspace(0,3,100)%Ratio value for exponential
n3=length(Q)
f_w=0.2
C_H=0.0045%Concentration value
C_O=0.5%Concentration value
QoH=(f_w+(1-f_w)*C_H)%oxygen concentration
QoO=(f_w+(1-f_w)*C_O)%oxygen concentration
Delta_rwO=(2.91-0.76.*Beta) .* (10^6./T(:,1).^2) - 3.41 - 0.41.*Beta; %Fractionation plag-water
Delta_rwH=9.3 * (10^6./T(:,1).^2) - 61.9;
delta_rfO = Delta_rwO + delta_winO + (delta_riO - Delta_rwO - delta_winO).*exp(-Q./QoO) %rock final
delta_rfH = Delta_rwH + delta_winH + (delta_riH - Delta_rwH - delta_winH).*exp(-Q./QoH) %rock final
plot(delta_rfO,delta_rfH,'b')
plot(delta_rfO(Q(1,9)),delta_rfH(Q(1,9)))
hold on
Delta_rwO=(2.91-0.76.*Beta) .* (10^6./T(:,end).^2) - 3.41 - 0.41.*Beta; %Fractionation plag-water
Delta_rwH=9.3 * (10^6./T(:,end).^2) - 61.9;
delta_rfO = Delta_rwO + delta_winO + (delta_riO - Delta_rwO - delta_winO).*exp(-Q./QoO) %rock final
delta_rfH = Delta_rwH + delta_winH + (delta_riH - Delta_rwH - delta_winH).*exp(-Q./QoH) %rock final
plot(delta_rfO,delta_rfH,'b')
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Accepted Answer
Voss
on 16 Oct 2024
If you want to calculate delta_rfO for all combinations of the specified values of T, Q, and Beta, you can permute (or transpose as the case may be) your T, Q, and Beta vectors appropriately; then the delta_rfO calculation will result in a 3-dimensional array.
Here I've decided to have T correspond to the first dimension of delta_rfO, Q to the second dimension, and Beta to the third dimension, because delta_rfH depends on T and Q only and doesn't depend on Beta. But you can set it up however you like. (Also, I changed some of the lengths of the T, Q, and Beta vectors so that they're all different because it's more clear to see which dimension of the result corresponds to which vector when they're not all the same length.)
NT = 100;
NQ = 75;
NB = 50;
T = linspace(573.15,1173.15,NT); % Temperatures used in calculation
Beta = linspace(0,1,NB); % Variable relating cation content of mineral
Q = linspace(0,3,NQ); % Ratio value for exponential
T = T.';
Beta = permute(Beta,[1 3 2]);
T is a column vector, Q is a row vector, and Beta is a vector that goes in the third dimension (a "page vector"?):
whos T Beta Q
delta_winO = 0;
delta_riO = 6;
delta_winH = 0;
delta_riH = -60;
f_w = 0.2;
C_H = 0.0045;
C_O = 0.5;
QoH = f_w+(1-f_w)*C_H;
QoO = f_w+(1-f_w)*C_O;
Delta_rwO = (2.91-0.76.*Beta) .* (10^6./T.^2) - 3.41 - 0.41.*Beta; % Fractionation plag-water
Delta_rwH = 9.3 * (10^6./T(:).^2) - 61.9;
delta_rfO = Delta_rwO + delta_winO + (delta_riO - Delta_rwO - delta_winO).*exp(-Q./QoO);
delta_rfH = Delta_rwH + delta_winH + (delta_riH - Delta_rwH - delta_winH).*exp(-Q./QoH);
whos delta_rf*
You can see that delta_rfO is now a 3D array of size NT-by-NQ-by-NB; thus it contains a result for all combinations of the specified T, Q, and Beta values. Similarly delta_rfH is a NT-by-NQ matrix, containing a result for each combination of T and Q (it doesn't depend on Beta).
You can plot slices from these against each other, using indexing. For example:
figure
hold on
plot(delta_rfO(1,:,1), delta_rfH(1,:), 'b','DisplayName',sprintf('T=%g, all Q, Beta=%g',T(1), Beta(1)));
plot(delta_rfO(end,:,1), delta_rfH(end,:),'r','DisplayName',sprintf('T=%g, all Q, Beta=%g',T(end),Beta(1)));
plot(delta_rfO(end,:,end),delta_rfH(end,:),'g','DisplayName',sprintf('T=%g, all Q, Beta=%g',T(end),Beta(end)));
plot(delta_rfO(1,:,end), delta_rfH(1,:), 'k','DisplayName',sprintf('T=%g, all Q, Beta=%g',T(1), Beta(end)));
legend('Location','NorthWest')
xlabel('delta\_rfO')
ylabel('delta\_rfH')
Another example:
figure
hold on
plot(delta_rfO(:,9,1), delta_rfH(:,9), 'b','DisplayName',sprintf('all T, Q=%g, Beta=%g',Q(9), Beta(1)));
plot(delta_rfO(:,end,1), delta_rfH(:,end),'r','DisplayName',sprintf('all T, Q=%g, Beta=%g',Q(end),Beta(1)));
plot(delta_rfO(:,end,end),delta_rfH(:,end),'g','DisplayName',sprintf('all T, Q=%g, Beta=%g',Q(end),Beta(end)));
plot(delta_rfO(:,9,end), delta_rfH(:,9), 'k','DisplayName',sprintf('all T, Q=%g, Beta=%g',Q(9), Beta(end)));
legend('Location','NorthWest')
xlabel('delta\_rfO')
ylabel('delta\_rfH')
If you want to be able to specify a range of values and plot from that - say based on a min and max T and a specific given Beta value - you can do something like:
Tmin = 1080;
Tmax = 1120;
Beta_given = 0.4;
Tidx = find(T >= Tmin & T <= Tmax)
[~,Bidx] = min(abs(Beta-Beta_given))
figure
hold on
for ii = 1:numel(Tidx)
for jj = 1:numel(Bidx)
plot(delta_rfO(Tidx(ii),:,Bidx(jj)),delta_rfH(Tidx(ii),:), ...
'DisplayName',sprintf('T=%g, Beta=%g',T(Tidx(ii)),Beta(Bidx(jj))));
end
end
legend('Location','Best')
xlabel('delta\_rfO')
ylabel('delta\_rfH')
10 Comments
Voss
on 18 Oct 2024
It makes sense to me to modify the plotting function to include creation of the texts. An example is below. Note that I had to include the variable Q as an input to the function. And I made the figure bigger, so the texts don't overlap too much. Adjust as needed.
%Setting up arrays
NT = 100;
NQ = 75;
NB = 50;
T = linspace(573.15,1173.15,NT); % Temperatures used in calculation
Q = linspace(0,3,NQ); % Variable relating cation content of mineral
Beta = linspace(0,1,NB);% Ratio value for exponential
T = T.';
Beta = permute(Beta,[1 3 2]);
delta_winO = -4.5;
delta_riO = 6;
delta_winH = -26;
delta_riH = -85;
f_w = 0.2;
C_H = 0.0045;
C_O = 0.5;
QoH = f_w+(1-f_w)*C_H;
QoO = f_w+(1-f_w)*C_O;
Delta_rwO = (2.91-0.76.*Beta) .* (10^6./T.^2) - 3.41 - 0.41.*Beta; % Fractionation plag-water
Delta_rwH = 9.3 * (10^6./T.^2) - 61.9;
delta_rfO = Delta_rwO + delta_winO + (delta_riO - Delta_rwO - delta_winO).*exp(-Q./QoO);
delta_rfH = Delta_rwH + delta_winH + (delta_riH - Delta_rwH - delta_winH).*exp(-Q./QoH);
figure('Position',[10 10 1000 1000])
hold on
% plot stuff:
plot_stuff(delta_rfO,delta_rfH,Q)
% change some variables:
delta_winO = 0;
delta_riO = 6;
delta_winH = 0;
delta_riH = -50;
% recalculate only what needs to be recalculated:
delta_rfO = Delta_rwO + delta_winO + (delta_riO - Delta_rwO - delta_winO).*exp(-Q./QoO);
delta_rfH = Delta_rwH + delta_winH + (delta_riH - Delta_rwH - delta_winH).*exp(-Q./QoH);
% plot the new results too:
plot_stuff(delta_rfO,delta_rfH,Q)
xlabel('\Delta_{rf}^O','fontweight','bold','fontsize',20)
ylabel('\Delta_{rf}^H','fontweight','bold','fontsize',20)
box on
function plot_stuff(delta_rfO,delta_rfH,Q)
fill( ...
[delta_rfO(1,:,end) delta_rfO([1 end],end,end).' delta_rfO(end,end:-1:1,end)], ...
[delta_rfH(1,:) delta_rfH([1 end],end).' delta_rfH(end,end:-1:1)], ...
'r','EdgeColor','r','FaceAlpha',0.25)
fill( ...
[delta_rfO(1,:,1) delta_rfO([1 end],end,1).' delta_rfO(end,end:-1:1,1)], ...
[delta_rfH(1,:) delta_rfH([1 end],end).' delta_rfH(end,end:-1:1)], ...
'b','EdgeColor','b','FaceAlpha',0.25)
idx = [4 7 13 26];
%Contouring Water-Rock Ratios
%Q=0.125,0.25,0.5,1,infinity
for ii = 1:numel(idx)
plot(delta_rfO([1 end],idx(ii),1),delta_rfH([1 end],idx(ii)),'b', LineStyle=':' ,LineWidth=1)
text(delta_rfO(end,idx(ii),1),delta_rfH(end,idx(ii)),sprintf('Q=%0.3f',Q(idx(ii))),'Color','b','HorizontalAlignment','center')
end
text(delta_rfO(end,end,1),delta_rfH(end,end),'Q=Inf','Color','b','HorizontalAlignment','center')
%Contouring Water-Rock Ratios
%Q=0.125,0.25,0.5,1,infinity
for ii = 1:numel(idx)
plot(delta_rfO([1 end],idx(ii),end),delta_rfH([1 end],idx(ii)),'r', LineStyle=':' ,LineWidth=1)
text(delta_rfO(1,idx(ii),end),delta_rfH(1,idx(ii)),sprintf('Q=%0.3f',Q(idx(ii))),'Color','r','HorizontalAlignment','center')
end
text(delta_rfO(1,end,end),delta_rfH(1,end),'Q=Inf','Color','r','HorizontalAlignment','right')
end
More Answers (1)
Walter Roberson
on 16 Oct 2024
plot(delta_rfO(Q(1,9)),delta_rfH(Q(1,9)))
You are trying to use Q(1,9) as a subscript to delta_rf0 but Q(1,9) does not happen to be a positive integer.
Probably what you want is
plot(delta_rfO(1,9),delta_rfH(1,9), 'o')
The 'o' will cause a 'o' marker to be drawn at the single point designated. Without the 'o' option, plot() will only draw lines when there are two adjacent finite points, and since you are only drawing a single point there are no two adjacent finite points so no line would be drawn.
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