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Solving equation with two for loops

4 次查看（过去 30 天）
DS
DS 2022-11-15
回答： Walter Roberson 2022-11-18
Ran in:
Hi I would like to find the values of gf for different r and H values. It is obtained by solving the equation S1 which includes gf on both left and right sides. Could you please help me in solving this?
clear all;
close all;
iiy = 1.8;
rho_s = 2160;
rho_w = 997;
M_s = 58.44 * 10^-3;
M_w = 18* 10^-3
M_w = 0.0180
o = 0.072;
H = linspace(0.1,1,100)
H = 1×100
0.1000 0.1091 0.1182 0.1273 0.1364 0.1455 0.1545 0.1636 0.1727 0.1818 0.1909 0.2000 0.2091 0.2182 0.2273 0.2364 0.2455 0.2545 0.2636 0.2727 0.2818 0.2909 0.3000 0.3091 0.3182 0.3273 0.3364 0.3455 0.3545 0.3636
T = 22+273;
Rv = 8.314;
r = 1E-9:100E-9:200E-9;
syms gf
for i = 1:length(H)
for j =1:length(r)
S1 = ( gf -((rho_s/rho_w) *(1 + (M_w/M_s * iiy * H(i)./(( exp(2*o)./(rho_w*Rv*T.*gf*r(j))) - H(i)))))^(1/3));
S(j,i) = vpasolve(S1(j,i)==0,gf, [0 Inf] );
end
end
Error using sub2ind
Out of range subscript.

Error in indexing (line 1074)
R_tilde = sub2ind(size(L), Idx.subs{:});

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采纳的回答

Walter Roberson
Walter Roberson 2022-11-18
Ran in:
I suggest you switch to numeric solutions, and to providing solution hints. Some of the tests I did hinted there might be multiple solutions.
The bumps along the yellow ridge appear to be inherent somehow -- if you zoom in you will see "ribs" on the plot.
iiy = 1.8;
rho_s = 2160;
rho_w = 997;
M_s = 58.44 * 10^-3;
M_w = 18* 10^-3 ;
M_w = 0.0180;
o = 0.072;
H = linspace(0.1,1,100);
T = 22+273;
Rv = 8.314;
r = linspace(1E-9,1000E-9, 50);
numH = length(H);
numr = length(r);
S = NaN(numr, numH);
guess = 1.5;
opt = optimoptions('fsolve','Display','off');
for i = 1:numH
for j = 1:numr
S1 = @(gf) ( gf -((rho_s/rho_w) *(1 + (M_w/M_s * iiy * H(i)./(( exp(2*o)./(rho_w*Rv*T.*gf*r(j))) - H(i)))))^(1/3));
SS = fsolve(S1, guess, opt );
if ~isempty(SS) && imag(SS) == 0
S(j,i) = double(SS);
guess = SS;
end
end
end
surf(H, r, S, 'edgecolor', 'none')
xlabel('H'); ylabel('r'); zlabel('S')
view([57,39])

更多回答（2 个）

Voss
Voss 2022-11-15
Ran in:
S1 is calculated for a given i and j, so it is not correct to index it with i and j on the next line.
That is, use S1==0 instead of S1(j,i) == 0
clear all;
close all;
iiy = 1.8;
rho_s = 2160;
rho_w = 997;
M_s = 58.44 * 10^-3;
M_w = 18* 10^-3
M_w = 0.0180
o = 0.072;
H = linspace(0.1,1,100)
H = 1×100
0.1000 0.1091 0.1182 0.1273 0.1364 0.1455 0.1545 0.1636 0.1727 0.1818 0.1909 0.2000 0.2091 0.2182 0.2273 0.2364 0.2455 0.2545 0.2636 0.2727 0.2818 0.2909 0.3000 0.3091 0.3182 0.3273 0.3364 0.3455 0.3545 0.3636
T = 22+273;
Rv = 8.314;
r = 1E-9:100E-9:200E-9;
syms gf
for i = 1:length(H)
for j =1:length(r)
S1 = ( gf -((rho_s/rho_w) *(1 + (M_w/M_s * iiy * H(i)./(( exp(2*o)./(rho_w*Rv*T.*gf*r(j))) - H(i)))))^(1/3));
% S(j,i) = vpasolve(S1(j,i)==0,gf, [0 Inf] );
S(j,i) = vpasolve(S1==0,gf, [0 Inf] );
end
end
disp(S)
  3 个评论
显示 1更早的评论
Walter Roberson
Walter Roberson 2022-11-15
The implication is that there is a combination of values that vpasolve is not able to find a solution for.
DS
DS 2022-11-15
How can I solve this? Should I use some other functions?

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Walter Roberson
Walter Roberson 2022-11-15
Ran in:
iiy = 1.8;
rho_s = 2160;
rho_w = 997;
M_s = 58.44 * 10^-3;
M_w = 18* 10^-3
M_w = 0.0180
o = 0.072;
H = linspace(0.1,1,100)
H = 1×100
0.1000 0.1091 0.1182 0.1273 0.1364 0.1455 0.1545 0.1636 0.1727 0.1818 0.1909 0.2000 0.2091 0.2182 0.2273 0.2364 0.2455 0.2545 0.2636 0.2727 0.2818 0.2909 0.3000 0.3091 0.3182 0.3273 0.3364 0.3455 0.3545 0.3636
T = 22+273;
Rv = 8.314;
r = 1E-9:100E-9:200E-9;
syms gf
numH = length(H);
numr = length(r);
S = zeros(numr, numH);
for i = 1:numH
for j = 1:numr
S1 = ( gf -((rho_s/rho_w) *(1 + (M_w/M_s * iiy * H(i)./(( exp(2*o)./(rho_w*Rv*T.*gf*r(j))) - H(i)))))^(1/3));
S(j,i) = vpasolve(S1==0, gf, [0 Inf] );
end
end
format long g
S
S = 2×100
1.29402159925611 1.29402755858776 1.2940335182164 1.29403947814207 1.29404543836478 1.29405139888457 1.29405735970146 1.29406332081548 1.29406928222665 1.294075243935 1.29408120594055 1.29408716824334 1.29409313084338 1.29409909374071 1.29410505693534 1.29411102042732 1.29411698421665 1.29412294830337 1.2941289126875 1.29413487736908 1.29414084234812 1.29414680762465 1.2941527731987 1.2941587390703 1.29416470523946 1.29417067170622 1.29417663847061 1.29418260553264 1.29418857289235 1.29419454054976 1.30076236019233 1.30140057925328 1.3020421735055 1.30268717464784 1.30333561482099 1.30398752661578 1.30464294308161 1.30530189773512 1.3059644245691 1.30663055806151 1.30730033318485 1.30797378541565 1.3086509507442 21.4298073297381 1.31001656728512 1.31070509313834 1.31139748139228 1.31209377076126 1.31279400053724 1.31349821060138 1.31420644143594 1.31491873413649 1.31563513042437 1.31635567265952 1.31708040385366 1.31780936768376 1.31854260850588 1.31928017136941 1.32002210203163 1.32076844697273
  3 个评论
显示 1更早的评论
DS
DS 2022-11-15
Unable to perform assignment because the size of the left side is 1-by-1 and the size of
the right side is 0-by-1.
I still got this error. Could you please help me what should I do?
Torsten
Torsten 2022-11-15
编辑：Torsten 2022-11-15
Your equation might have no solution or vpasolve might fail to compute it ...
iiy = 1.8;
rho_s = 2160;
rho_w = 997;
M_s = 58.44 * 10^-3;
M_w = 18* 10^-3
M_w = 0.0180
o = 0.072;
H = linspace(0.1,1,100)
T = 22+273;
Rv = 8.314;
r = linspace(1E-9,1000E-9, 20);
syms gf
numH = length(H);
numr = length(r);
S = NaN(numr, numH);
for i = 1:numH
for j = 1:numr
S1 = ( gf -((rho_s/rho_w) *(1 + (M_w/M_s * iiy * H(i)./(( exp(2*o)./(rho_w*Rv*T.*gf*r(j))) - H(i)))))^(1/3));
SS = vpasolve(S1==0, gf, [0 Inf] );
if ~isempty(SS)
S(j,i) = double(SS);
end
end
end
format long g
S

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