I am currently trying to find the global minimum for a strain-energy-function ("Holzapfel-Model") and I am running into multiple problems:
The SEF has the form
With
We can calculate , where
We want to determine the minimum of the least-square function

My solution was to put all these equations into one long one:
fun = @(x) sum((sigma_11 – (lambda_1.^2 – lambda_2.^2 .* lambda_1.^2).*x(1) + 2 .*lambda_1.^2 .*cos(x(4))^2 .* (2.*x(2).*((lambda_1.^2 .* cos(x(4))^2 + lambda_2.^2 .* sin(x(4))^2) – 1) .* exp(x(2).*((lambda_1.^2 .* cos(x(4))^2 + lambda_2.^2 .* sin(x(4))^2)-1).^2))).^2 + (sigma_22 – (lambda_2.^2 – lambda_2.^2 .* lambda_1.^2).*x(1) + 2 .*lambda_2.^2 .*sin(x(4))^2 .* (2.*x(2).*((lambda_1.^2 .* cos(x(4))^2 + lambda_2.^2 .* sin(x(4))^2) – 1) .* exp(x(2).*((lambda_1.^2 .* cos(x(4))^2 + lambda_2.^2 .* sin(x(4))^2)-1).^2))).^2)

and then use the following parameters
x0 = [15,500,12,0.75*pi];
A = [];
b = [];
Aeq = [];
beq = [];
lb = [0,0,0,0];
ub = [inf, inf, inf, pi];
chi = fmincon(fun, x0,A,b,Aeq,beq,lb,ub,nonlcon)
function [c,ceq] = nonlcon(x,lambda_1,lambda_2)
c =1-(lambda_1.^2 .* cos(x(4)).^2 + lambda_2.^2 * sin(x(4)).^2) ;
ceq = [];
end
With these parameters, I can somewhat get close to my data points.
Now my questions:
I don’t think I understood c,ceq correctly. I used c to account for the constraint on I4, but I’m not sure if this was the right way to do it.
With the initial guess for x0, I can get close but it never seems to approach my curve nearly enough. How do I know if I have a good starting guess, and is fmincon even the right approach for this problem.
I have multiple data sets, for different stretch ratios (lambda_1:lambda_2: 1-1, 1-0.75, 0.75-1, 1-0.5,0.5-1) and since they are the same sample, I would like to use those datas to get one set of parameters for all of them. I tried to put all my data into a single vector, (1:30 would be the first data set, 31:^60 the second,…). This does not seem to work well. Should I find the solution for just one curve and than try to average over the parameters? As you guys can see, I am doing this parameter evaluation thing the first time ever and I would greatly appreciate help.I am currently trying to find the global minimum for a strain-energy-function ("Holzapfel-Model") and I am running into multiple problems:
The SEF has the form
With
We can calculate , where
We want to determine the minimum of the least-square function

My solution was to put all these equations into one long one:
fun = @(x) sum((sigma_11 – (lambda_1.^2 – lambda_2.^2 .* lambda_1.^2).*x(1) + 2 .*lambda_1.^2 .*cos(x(4))^2 .* (2.*x(2).*((lambda_1.^2 .* cos(x(4))^2 + lambda_2.^2 .* sin(x(4))^2) – 1) .* exp(x(2).*((lambda_1.^2 .* cos(x(4))^2 + lambda_2.^2 .* sin(x(4))^2)-1).^2))).^2 + (sigma_22 – (lambda_2.^2 – lambda_2.^2 .* lambda_1.^2).*x(1) + 2 .*lambda_2.^2 .*sin(x(4))^2 .* (2.*x(2).*((lambda_1.^2 .* cos(x(4))^2 + lambda_2.^2 .* sin(x(4))^2) – 1) .* exp(x(2).*((lambda_1.^2 .* cos(x(4))^2 + lambda_2.^2 .* sin(x(4))^2)-1).^2))).^2)

and then use the following parameters
x0 = [15,500,12,0.75*pi];
A = [];
b = [];
Aeq = [];
beq = [];
lb = [0,0,0,0];
ub = [inf, inf, inf, pi];
chi = fmincon(fun, x0,A,b,Aeq,beq,lb,ub,nonlcon)
function [c,ceq] = nonlcon(x,lambda_1,lambda_2)
c =1-(lambda_1.^2 .* cos(x(4)).^2 + lambda_2.^2 * sin(x(4)).^2) ;
ceq = [];
end
With these parameters, I can somewhat get close to my data points.
Now my questions:
I don’t think I understood c,ceq correctly. I used c to account for the constraint on I4, but I’m not sure if this was the right way to do it.
With the initial guess for x0, I can get close but it never seems to approach my curve nearly enough. How do I know if I have a good starting guess, and is fmincon even the right approach for this problem.
I have multiple data sets, for different stretch ratios (lambda_1:lambda_2: 1-1, 1-0.75, 0.75-1, 1-0.5,0.5-1) and since they are the same sample, I would like to use those datas to get one set of parameters for all of them. I tried to put all my data into a single vector, (1:30 would be the first data set, 31:^60 the second,…). This does not seem to work well. Should I find the solution for just one curve and than try to average over the parameters? As you guys can see, I am doing this parameter evaluation thing the first time ever and I would greatly appreciate help. I am currently trying to find the global minimum for a strain-energy-function ("Holzapfel-Model") and I am running into multiple problems:
The SEF has the form
With
We can calculate , where
We want to determine the minimum of the least-square function

My solution was to put all these equations into one long one:
fun = @(x) sum((sigma_11 – (lambda_1.^2 – lambda_2.^2 .* lambda_1.^2).*x(1) + 2 .*lambda_1.^2 .*cos(x(4))^2 .* (2.*x(2).*((lambda_1.^2 .* cos(x(4))^2 + lambda_2.^2 .* sin(x(4))^2) – 1) .* exp(x(2).*((lambda_1.^2 .* cos(x(4))^2 + lambda_2.^2 .* sin(x(4))^2)-1).^2))).^2 + (sigma_22 – (lambda_2.^2 – lambda_2.^2 .* lambda_1.^2).*x(1) + 2 .*lambda_2.^2 .*sin(x(4))^2 .* (2.*x(2).*((lambda_1.^2 .* cos(x(4))^2 + lambda_2.^2 .* sin(x(4))^2) – 1) .* exp(x(2).*((lambda_1.^2 .* cos(x(4))^2 + lambda_2.^2 .* sin(x(4))^2)-1).^2))).^2)

and then use the following parameters
x0 = [15,500,12,0.75*pi];
A = [];
b = [];
Aeq = [];
beq = [];
lb = [0,0,0,0];
ub = [inf, inf, inf, pi];
chi = fmincon(fun, x0,A,b,Aeq,beq,lb,ub,nonlcon)
function [c,ceq] = nonlcon(x,lambda_1,lambda_2)
c =1-(lambda_1.^2 .* cos(x(4)).^2 + lambda_2.^2 * sin(x(4)).^2) ;
ceq = [];
end
With these parameters, I can somewhat get close to my data points.
Now my questions:
I don’t think I understood c,ceq correctly. I used c to account for the constraint on I4, but I’m not sure if this was the right way to do it.
With the initial guess for x0, I can get close but it never seems to approach my curve nearly enough. How do I know if I have a good starting guess, and is fmincon even the right approach for this problem.
I have multiple data sets, for different stretch ratios (lambda_1:lambda_2: 1-1, 1-0.75, 0.75-1, 1-0.5,0.5-1) and since they are the same sample, I would like to use those datas to get one set of parameters for all of them. I tried to put all my data into a single vector, (1:30 would be the first data set, 31:^60 the second,…). This does not seem to work well. Should I find the solution for just one curve and than try to average over the parameters? As you guys can see, I am doing this parameter evaluation thing the first time ever and I would greatly appreciate help. fmincon, nonlinear, curve fitting, optimization MATLAB Answers — New Questions

​

Hello,
it should be a ridiculously trivial task, but I have to admit I’ve been stuck on it for a few months. Sadly, I’m not very good at Python either, so I’m coming here.

Assume that I have some circuit like the one below:
I want to read and parse a netlist such that I create a digraph object, which can later be used for testing subgraphs being a spanning tree and alike graph theoretic features. Prsing a netlist posses no difficulty, but it looks like the digraph function does not care about the order in my input cells and when I plot the graph, it is labeled wrongly.
I have spent weeks on it with no result. Can you see a easy solution how to turn it into a graph object and plot it accordingly?
Code below produces obvisouly wrong plot, for instance resistors, while the topoogy seems to be idnetified correctly. Edges/Nodes are mislabeled.

clear
close all
clc

netlist = {
‘R1 N001 0 R’;
‘R2 N002 N001 R’;
‘R3 0 N002 R’;
‘C1 N002 N001 C’;
‘C2 N001 0 C’;
‘C3 N002 0 C’;
‘L1 N002 N001 L’;
‘L2 0 N001 L’;
‘L3 0 N002 L’
};
elements = {};
sourceNodes = {};
targetNodes = {};
labels = {};
for i = 1:length(netlist)
parts = strsplit(netlist{i});
elements{end+1} = parts{1};
sourceNodes{end+1} = parts{2};
targetNodes{end+1} = parts{3};
labels{end+1} = [parts{4} ‘ – ‘ parts{1}];
end
edgeTable = table(sourceNodes’, targetNodes’, labels’, ‘VariableNames’, {‘EndNodes’, ‘EndNodes2’, ‘Label’});
G = digraph(edgeTable.EndNodes, edgeTable.EndNodes2);
G.Edges.Label = edgeTable.Label;
h = plot(G, ‘EdgeLabel’, G.Edges.Label, ‘NodeLabel’, G.Nodes.Name, ‘Layout’, ‘force’);Hello,
it should be a ridiculously trivial task, but I have to admit I’ve been stuck on it for a few months. Sadly, I’m not very good at Python either, so I’m coming here.

Assume that I have some circuit like the one below:
I want to read and parse a netlist such that I create a digraph object, which can later be used for testing subgraphs being a spanning tree and alike graph theoretic features. Prsing a netlist posses no difficulty, but it looks like the digraph function does not care about the order in my input cells and when I plot the graph, it is labeled wrongly.
I have spent weeks on it with no result. Can you see a easy solution how to turn it into a graph object and plot it accordingly?
Code below produces obvisouly wrong plot, for instance resistors, while the topoogy seems to be idnetified correctly. Edges/Nodes are mislabeled.

clear
close all
clc

netlist = {
‘R1 N001 0 R’;
‘R2 N002 N001 R’;
‘R3 0 N002 R’;
‘C1 N002 N001 C’;
‘C2 N001 0 C’;
‘C3 N002 0 C’;
‘L1 N002 N001 L’;
‘L2 0 N001 L’;
‘L3 0 N002 L’
};
elements = {};
sourceNodes = {};
targetNodes = {};
labels = {};
for i = 1:length(netlist)
parts = strsplit(netlist{i});
elements{end+1} = parts{1};
sourceNodes{end+1} = parts{2};
targetNodes{end+1} = parts{3};
labels{end+1} = [parts{4} ‘ – ‘ parts{1}];
end
edgeTable = table(sourceNodes’, targetNodes’, labels’, ‘VariableNames’, {‘EndNodes’, ‘EndNodes2’, ‘Label’});
G = digraph(edgeTable.EndNodes, edgeTable.EndNodes2);
G.Edges.Label = edgeTable.Label;
h = plot(G, ‘EdgeLabel’, G.Edges.Label, ‘NodeLabel’, G.Nodes.Name, ‘Layout’, ‘force’); Hello,
it should be a ridiculously trivial task, but I have to admit I’ve been stuck on it for a few months. Sadly, I’m not very good at Python either, so I’m coming here.

Assume that I have some circuit like the one below:
I want to read and parse a netlist such that I create a digraph object, which can later be used for testing subgraphs being a spanning tree and alike graph theoretic features. Prsing a netlist posses no difficulty, but it looks like the digraph function does not care about the order in my input cells and when I plot the graph, it is labeled wrongly.
I have spent weeks on it with no result. Can you see a easy solution how to turn it into a graph object and plot it accordingly?
Code below produces obvisouly wrong plot, for instance resistors, while the topoogy seems to be idnetified correctly. Edges/Nodes are mislabeled.

clear
close all
clc

netlist = {
‘R1 N001 0 R’;
‘R2 N002 N001 R’;
‘R3 0 N002 R’;
‘C1 N002 N001 C’;
‘C2 N001 0 C’;
‘C3 N002 0 C’;
‘L1 N002 N001 L’;
‘L2 0 N001 L’;
‘L3 0 N002 L’
};
elements = {};
sourceNodes = {};
targetNodes = {};
labels = {};
for i = 1:length(netlist)
parts = strsplit(netlist{i});
elements{end+1} = parts{1};
sourceNodes{end+1} = parts{2};
targetNodes{end+1} = parts{3};
labels{end+1} = [parts{4} ‘ – ‘ parts{1}];
end
edgeTable = table(sourceNodes’, targetNodes’, labels’, ‘VariableNames’, {‘EndNodes’, ‘EndNodes2’, ‘Label’});
G = digraph(edgeTable.EndNodes, edgeTable.EndNodes2);
G.Edges.Label = edgeTable.Label;
h = plot(G, ‘EdgeLabel’, G.Edges.Label, ‘NodeLabel’, G.Nodes.Name, ‘Layout’, ‘force’); digraph, circuit, netlist, spanning tree, graph plotting, spice MATLAB Answers — New Questions

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I want to solve PEB minimization problem in sort of RIS problem. So I have formulated SDP problem via ‘CVX’ and at the end of the CVX formulation, using built-in svd(or svds) function to extract RIS phase profile matrix F(with size M times T, M=# of RIS elements and T is # of transmissions). Optimal solution of CVX is X which has size M by M. And X is FF^H. From X F is extracted by using svds as size of M by T.
The code is below,

M = signal.M;
T = signal.T;
% k-th column of identity matrix
e1 = [1; 0; 0];
e2 = [0; 1; 0];
e3 = [0; 0; 1];

% define optimization problem
cvx_begin sdp
variable X(M, M) hermitian
variable u(3, 1)

minimize(sum(u))

subject to
[J_car(1:3, 1:3), e1; e1′, u(1)] >= 0;
[J_car(1:3, 1:3), e2; e2′, u(2)] >= 0;
[J_car(1:3, 1:3), e3; e3′, u(3)] >= 0;
trace(X) == M * T;
X >= 0;

cvx_end

optimX = X;
[U, S, V] = svds(optimX, T);

num_singular_values = min(size(S, 1), T);
optimF = U(:, 1:num_singular_values) * sqrt(S(1:num_singular_values, 1:num_singular_values));
end

and the optimization problem is:

Then my questions are:
Is it correct method using ‘svd’ to extract F(size M by T) from optimal solution X?
If not, what method can I try to? If possible, comment breif code for it.
It is not programming issue, but about mathematical, Is sum of all elements in auxiliary variable(objective for (12)) same as objective for (11)?I want to solve PEB minimization problem in sort of RIS problem. So I have formulated SDP problem via ‘CVX’ and at the end of the CVX formulation, using built-in svd(or svds) function to extract RIS phase profile matrix F(with size M times T, M=# of RIS elements and T is # of transmissions). Optimal solution of CVX is X which has size M by M. And X is FF^H. From X F is extracted by using svds as size of M by T.
The code is below,

M = signal.M;
T = signal.T;
% k-th column of identity matrix
e1 = [1; 0; 0];
e2 = [0; 1; 0];
e3 = [0; 0; 1];

% define optimization problem
cvx_begin sdp
variable X(M, M) hermitian
variable u(3, 1)

minimize(sum(u))

subject to
[J_car(1:3, 1:3), e1; e1′, u(1)] >= 0;
[J_car(1:3, 1:3), e2; e2′, u(2)] >= 0;
[J_car(1:3, 1:3), e3; e3′, u(3)] >= 0;
trace(X) == M * T;
X >= 0;

cvx_end

optimX = X;
[U, S, V] = svds(optimX, T);

num_singular_values = min(size(S, 1), T);
optimF = U(:, 1:num_singular_values) * sqrt(S(1:num_singular_values, 1:num_singular_values));
end

and the optimization problem is:

Then my questions are:
Is it correct method using ‘svd’ to extract F(size M by T) from optimal solution X?
If not, what method can I try to? If possible, comment breif code for it.
It is not programming issue, but about mathematical, Is sum of all elements in auxiliary variable(objective for (12)) same as objective for (11)? I want to solve PEB minimization problem in sort of RIS problem. So I have formulated SDP problem via ‘CVX’ and at the end of the CVX formulation, using built-in svd(or svds) function to extract RIS phase profile matrix F(with size M times T, M=# of RIS elements and T is # of transmissions). Optimal solution of CVX is X which has size M by M. And X is FF^H. From X F is extracted by using svds as size of M by T.
The code is below,

M = signal.M;
T = signal.T;
% k-th column of identity matrix
e1 = [1; 0; 0];
e2 = [0; 1; 0];
e3 = [0; 0; 1];

% define optimization problem
cvx_begin sdp
variable X(M, M) hermitian
variable u(3, 1)

minimize(sum(u))

subject to
[J_car(1:3, 1:3), e1; e1′, u(1)] >= 0;
[J_car(1:3, 1:3), e2; e2′, u(2)] >= 0;
[J_car(1:3, 1:3), e3; e3′, u(3)] >= 0;
trace(X) == M * T;
X >= 0;

cvx_end

optimX = X;
[U, S, V] = svds(optimX, T);

num_singular_values = min(size(S, 1), T);
optimF = U(:, 1:num_singular_values) * sqrt(S(1:num_singular_values, 1:num_singular_values));
end

and the optimization problem is:

Then my questions are:
Is it correct method using ‘svd’ to extract F(size M by T) from optimal solution X?
If not, what method can I try to? If possible, comment breif code for it.
It is not programming issue, but about mathematical, Is sum of all elements in auxiliary variable(objective for (12)) same as objective for (11)? svd, ris, mimo, cvx, optim MATLAB Answers — New Questions

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