Double parameter optimisation using optimisation toolbox

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Charles Mitchell-Thurston 2022-5-31

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https://ww2.mathworks.cn/matlabcentral/answers/1730920-double-parameter-optimisation-using-optimisation-toolbox

评论： Charles Mitchell-Thurston 2022-6-1

采纳的回答： Matt J

Hi,

I am wondering if someone could start me off in the right direction.

I have two parameters. P1 ranges from 30:-30 and P2 from 0.00000000000000001:1.

These two parameters can be used to generate a graph. I can then have the X,Y data for that graph.

I have a second graph that i obtain from an experiment and i want to know what values of P1 and P2 will produce that graph(or one that is similar to a fine value).

So i need to sum (experimentalYpoint - generatedYpoint)^2 across all my x points. This will give me a value of how 'similar' the two are. i then optimise P1 and P2 so that the value of my sum gets as close to 0 as it can be.

I think i can use the Optimization Toolbox for this but would someone be able to point me to exactly which part of it that would be useful.

Forry for the long winded question, wanted to try make it clear.

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Charles Mitchell-Thurston 2022-5-31

'given input data xdata, and the observed output ydata, where xdata and ydata are matrices or vectors, and F (x, xdata) is a matrix-valued or vector-valued function of the same size as ydata.'

In this is my xdata P1 and ydata P2?

Torsten 2022-5-31

编辑：Torsten 2022-5-31

xdata = independent variable on which your "experimentalYpoints" depend (e.g. time, length or whatever)

ydata = experimentalYpoints

x = [P1,P2] = vector of parameters to be fitted

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Answer 1

Matt J 2022-5-31

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https://ww2.mathworks.cn/matlabcentral/answers/1730920-double-parameter-optimisation-using-optimisation-toolbox#answer_975195

编辑：Matt J 2022-5-31

In this is my xdata P1 and ydata P2?

xdata, ydata are what you call experimtalX and experimentalY. The unknown parameters that you are trying to solve for go in the vector x, that is x=[P1,P2].

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Charles Mitchell-Thurston 2022-6-1

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Right that makes sense.

I am still a bit unsure on how to set this all up though.

So x=[15,0.5] and this can just be my starting guess as its in the middle of all possible values.

curve_fcn = @(P1P2,x) P1P2(1)*(exp(-(x-P1P2(2)).^2/1e3) + exp(-(x+P1P2(2)).^2/1e3)); Does what my curve function actually is matter?

Using Bjorn's answer as well:

res_fcn = @(P1P2,xdata,ydata,fcn) (y-fcn(P1P2,xdata));

where xdata is xexperimental and ydata is yexperimental

P1P2_lsq = lsqnonlin(@(par) res_fcn(par,xdata,ydata,curve_fcn),x);

So i would need something like

x=[15,0.5]; %standard middle guess
curve_fcn = @(P1P2,x) P1P2(1)*(exp(-(x-P1P2(2)).^2/1e3) + exp(-(x+P1P2(2)).^2/1e3));
xdata = x experimentaldata %extracted from the experimental graph.
ydata = y experimenatldata
%my code that takes in the two parameters and output xdatasimulated and
%ydatasimulated

What i dont get is how i implament my code that gets the generated data into this all nd how i set it up. I have tried reading help lsqcurvefit but i still dont understand

Charles Mitchell-Thurston 2022-6-1

编辑：Charles Mitchell-Thurston 2022-6-1

在 MATLAB Online 中打开

To try help show whats goin on. Below is the part of my code where you take in data. And at the end you end up with inter_y/x Which is the X and Y data for each input that you give it. It is likely ugly code but it does the job.

The input to simpson has to be in the form of a RR.in file which contains all of the parmeters. the part of this that is changed for each parameter is in the code below where it simply inserts P1 and P2 into the .in file.

%%%%take in data%%%%
H = readmatrix('p1p2values.xlsx');
%%%%creates folder for use%%%%
mkdir RRfiles
%%%%creates .in files%%%%
text = fileread('RR.in');
index = strfind(text, '0p ');
text1 = text(1:index+2);
tempstr = text(index+3:end);
index = strfind(tempstr, ' ');
index = index(2);
text2 = tempstr(index:end);
for i = 1:2 %length(H);
    aniso =H(i,2);
    asym =H(i,3);
    newtext = [text1, num2str(aniso),  'p ',  num2str(asym), text2] ;
    filename = ['RRfiles/RR', num2str(i), '.in'];
    file = fopen(filename,'w');
    fprintf(file,newtext);
    fclose(file);
end
%%%%create fid files%%%%
list=length(H);
for k = 1:2 %list
    command = sprintf('simpson RRfiles/RR%g.in', k);
    status = system(command);
end
zero = 0;
for loop = 1:1000
    for i = 1:2 %list
        QNAN_text=fileread(['RR', num2str(i), '.fid']);
        strfind(QNAN_text, 'QNAN');
        if ans>zero
            fprintf 'Fail'
            command = sprintf('simpson RRfiles/RR%g.in', i);
            status = system(command);
        end
    end
end
fprintf 'all passed'
mkdir Fidfiles
for t = 1:2 %list;
    filename = ['RR', num2str(t), '.fid'];
    movefile ( filename, 'Fidfiles');
end
%%%% create fig files%%%%
fids = uigetdir ('C:\Users\charles\Documents\MATLAB\SIMPSON');
info = dir(fullfile(fids,'*.fid'));
list = {info.name}
%%%% Parameters%%%%
fu=' Hz';
dc = 32;
ls = 0;
wt = 'Gaussian'
wp = 10
zf = 256;
bo = 1;
bp = 32;
%%%% Process%%%%
list = natsortfiles(list);
for i = 1:length(list);
%%%%takes in data%%%%
    raw = importdata( fullfile(fids, list{i}));
    data = raw.data;
    data = data(:,1);
    FID = data;
    num = raw.textdata;
    num = num{3};
    Str = num;
    Str(Str < '0' | Str > '9') = [];
    sw = sscanf(Str, '%d');
    lf=-sw/2; % temporary scale
    hf=sw/2;
    
%%%%processes and plots the figure%%%%
    figure(i);
    f = figure;
    FID=normalize(FID);
    FID=dcOffset(FID,dc);
    FID=leftShift(FID,ls);
    FID=windowFID(FID,sw,wt,wp);
    SPE=FT(FID,zf);
    % SPE=phaseSpectrum0(SPE,-90.);
    SPE=baselineCorrect(SPE,sw,bo,bp);
    FREQ=getFrequency(SPE,lf,hf);
    % [th0,th1,pv]=Phasing(FREQ,SPE);
    %SPE = real(SPE)
    plotSpectrum(gca,FREQ,SPE);
    clear FID FREQ SPE lf hf sw test Str data raw
    savefig( num2str(i) + "hydrogen" );
    close all
end
%%%%Gets data%%%%
data = pwd;
dinfo = dir(fullfile(data,'*gen.fig'));
fignames = {dinfo.name};
numfig = length(fignames);
%%%% creates cells to be filled%%%%
y = cell(numfig, 1);
z = cell(numfig, 1);
inter_y = cell(numfig, 1);
inter_z = cell(numfig, 1);
%%%%code to create variable list for protons iso values%%%%
isofm = H(:,1);
isofm = round(isofm,1)
%%%%code that gets x,y data from sims%%%%
for K = 1 : numfig
  figfile = fignames{K};
  try
    fig = openfig(figfile,'invisible');
    ax = get(fig, 'CurrentAxes');
    if ~isempty(ax)
      hline = get(ax, 'Children');
        y{K} = get(hline,'XData');
        z{K} = get(hline,'YData');
        
        inter_y{K} = y{K}(1,5:124);
        inter_z{K} = abs(z{K}(1,5:124));
    end
    close(fig);
  end
end

Charles Mitchell-Thurston 2022-6-1

在 MATLAB Online 中打开

Yer i just realised that myself as i am trying to top and tail my code with function and end. I have tested the code below and it works for single inputs of P1 and P2 now.

The output of all of this code is inter_z which is a 1x1 cell which contails my 1x120 double which is all of my y values for my plot.

For writing that actual function, function y = TheoreticalY(P1,P2) i assume looks like a start. Do i have to somehow set that 'y' is inter_z? Do i have to clear all variables produced outside of inter_z perhaps?

P1 = 17
P2 = 0.1
%function y = TheoreticalY(P1,P2)
%%%%creates folder for use%%%%
mkdir RRfiles
%%%%creates .in files%%%%
text = fileread('RR.in');
index = strfind(text, '0p ');
text1 = text(1:index+2);
tempstr = text(index+3:end);
index = strfind(tempstr, ' ');
index = index(2);
text2 = tempstr(index:end);
newtext = [text1, num2str(P1),  'p ',  num2str(P2), text2] ;
filename = ['RRfiles/RR.in'];
file = fopen(filename,'w');
fprintf(file,newtext);
fclose(file);
%%%%create fid files%%%%
command = sprintf('simpson RRfiles/RR.in');
status = system(command);
zero = 0;
for loop = 1:1000
    QNAN_text=fileread(['RR.fid']);
    strfind(QNAN_text, 'QNAN');
    if ans>zero
        fprintf 'Fail'
        command = sprintf('simpson RRfiles/RR.in');
        status = system(command);
    end
end
fprintf 'all passed'
mkdir Fidfiles
filename = ['RR.fid'];
movefile ( filename, 'Fidfiles');
%%%% create fig files%%%%
fids = 'C:\Users\charl\Documents\MATLAB stuff\CSA fitting\Fidfiles';
info = dir(fullfile(fids,'*.fid'));
list = {info.name}
%%%% Parameters%%%%
fu=' Hz';
dc = 32;
ls = 0;
wt = 'Gaussian'
wp = 10
zf = 256;
bo = 1;
bp = 32;
%%%% Process%%%%
%%%%takes in data%%%%
    raw = importdata( fullfile(fids, list{1}));
    data = raw.data;
    data = data(:,1);
    FID = data;
    num = raw.textdata;
    num = num{3};
    Str = num;
    Str(Str < '0' | Str > '9') = [];
    sw = sscanf(Str, '%d');
    lf=-sw/2; % temporary scale
    hf=sw/2;
    
%%%%processes and plots the figure%%%%
    figure(1);
    f = figure;
    FID=normalize(FID);
    FID=dcOffset(FID,dc);
    FID=leftShift(FID,ls);
    FID=windowFID(FID,sw,wt,wp);
    SPE=FT(FID,zf);
    % SPE=phaseSpectrum0(SPE,-90.);
    SPE=baselineCorrect(SPE,sw,bo,bp);
    FREQ=getFrequency(SPE,lf,hf);
    % [th0,th1,pv]=Phasing(FREQ,SPE);
    %SPE = real(SPE)
    plotSpectrum(gca,FREQ,SPE);
    clear FID FREQ SPE lf hf sw test Str data raw
    savefig( num2str(1) + "hydrogen" );
    close all
%%%%Gets data%%%%
data = pwd;
dinfo = dir(fullfile(data,'*gen.fig'));
fignames = {dinfo.name};
numfig = length(fignames);
%%%% creates cells to be filled%%%%
y = cell(numfig, 1);
z = cell(numfig, 1);
inter_y = cell(numfig, 1);
inter_z = cell(numfig, 1);
%%%%code to create variable list for protons iso values%%%%
isofm = P1
isofm = round(isofm,1)
%%%%code that gets x,y data from sims%%%%
for K = 1 : numfig
  figfile = fignames{K};
  try
    fig = openfig(figfile,'invisible');
    ax = get(fig, 'CurrentAxes');
    if ~isempty(ax)
      hline = get(ax, 'Children');
        y{K} = get(hline,'XData');
        z{K} = get(hline,'YData');
        
        inter_y{K} = y{K}(1,5:124);
        inter_z{K} = abs(z{K}(1,5:124));
    end
    close(fig);
  end
end

Charles Mitchell-Thurston 2022-6-1

在 MATLAB Online 中打开

I realised i was still saving it as a live script not a function. I think i have now done the hardest part of my project. Again many thanks to all, there may be another ask on matlab at a later date if i get stuck again but i think the hardest part may be over (he says not knowing the future....)

function y = TheoreticalY(P1,P2)
%%%%creates folder for use%%%%
mkdir RRfiles
%%%%creates .in files%%%%
text = fileread('RR.in');
index = strfind(text, '0p ');
text1 = text(1:index+2);
tempstr = text(index+3:end);
index = strfind(tempstr, ' ');
index = index(2);
text2 = tempstr(index:end);
newtext = [text1, num2str(P1),  'p ',  num2str(P2), text2] ;
filename = ['RRfiles/RR.in'];
file = fopen(filename,'w');
fprintf(file,newtext);
fclose(file);
%%%%create fid files%%%%
command = sprintf('simpson RRfiles/RR.in');
status = system(command);
zero = 0;
for loop = 1:1000
    QNAN_text=fileread(['RR.fid']);
    strfind(QNAN_text, 'QNAN');
    if ans>zero
        fprintf 'Fail'
        command = sprintf('simpson RRfiles/RR.in');
        status = system(command);
    end
end
fprintf 'all passed'
mkdir Fidfiles
filename = ['RR.fid'];
movefile ( filename, 'Fidfiles');
%%%% create fig files%%%%
fids = 'C:\Users\charl\Documents\MATLAB stuff\CSA fitting\Fidfiles';
info = dir(fullfile(fids,'*.fid'));
list = {info.name}
%%%% Parameters%%%%
fu=' Hz';
dc = 32;
ls = 0;
wt = 'Gaussian'
wp = 10
zf = 256;
bo = 1;
bp = 32;
%%%% Process%%%%
%%%%takes in data%%%%
    raw = importdata( fullfile(fids, list{1}));
    data = raw.data;
    data = data(:,1);
    FID = data;
    num = raw.textdata;
    num = num{3};
    Str = num;
    Str(Str < '0' | Str > '9') = [];
    sw = sscanf(Str, '%d');
    lf=-sw/2; % temporary scale
    hf=sw/2;
    
%%%%processes and plots the figure%%%%
    figure(1);
    f = figure;
    FID=normalize(FID);
    FID=dcOffset(FID,dc);
    FID=leftShift(FID,ls);
    FID=windowFID(FID,sw,wt,wp);
    SPE=FT(FID,zf);
    % SPE=phaseSpectrum0(SPE,-90.);
    SPE=baselineCorrect(SPE,sw,bo,bp);
    FREQ=getFrequency(SPE,lf,hf);
    % [th0,th1,pv]=Phasing(FREQ,SPE);
    %SPE = real(SPE)
    plotSpectrum(gca,FREQ,SPE);
    clear FID FREQ SPE lf hf sw test Str data raw
    savefig( num2str(1) + "hydrogen" );
    close all
%%%%Gets data%%%%
data = pwd;
dinfo = dir(fullfile(data,'*gen.fig'));
fignames = {dinfo.name};
numfig = length(fignames);
%%%% creates cells to be filled%%%%
y = cell(numfig, 1);
z = cell(numfig, 1);
inter_y = cell(numfig, 1);
inter_z = cell(numfig, 1);
%%%%code to create variable list for protons iso values%%%%
isofm = P1
isofm = round(isofm,1)
%%%%code that gets x,y data from sims%%%%
for K = 1 : numfig
  figfile = fignames{K};
  try
    fig = openfig(figfile,'invisible');
    ax = get(fig, 'CurrentAxes');
    if ~isempty(ax)
      hline = get(ax, 'Children');
        y{K} = get(hline,'XData');
        z{K} = get(hline,'YData');
        
        inter_y{K} = y{K}(1,5:124);
        inter_z{K} = abs(z{K}(1,5:124));
    end
    close(fig);
  end
end
end

Bjorn Gustavsson 2022-6-1

在 MATLAB Online 中打开

Great. In the function you'll have to assign the relevant result to the y-variable.

Perhaps end the function with:

y = cell2mat(inter_y{K});

Charles Mitchell-Thurston 2022-6-1

Loverly

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Answer 2

Bjorn Gustavsson 2022-5-31

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在 MATLAB Online 中打开

The standard fitting method I use is:

% Your curve-function definition (I just mock one up, if you have it defined in a 
% matlab-function you don't need this step)
curve_fcn = @(P1P2,x) P1P2(1)*(exp(-(x-P1P2(2)).^2/1e3) + exp(-(x+P1P2(2)).^2/1e3));
% a sum-of-squares error-function for the fitting
err_fcn = @(P1P2,x,y,fcn) sum((y-fcn(P1P2,x)).^2);
% or a residual between the observed y and your curve-function
res_fcn = @(P1P2,x,y,fcn) (y-fcn(P1P2,x));
P1P2_guess = [1,2]; % Initial guess for the parameters P1 and P2, (adjust to be good values)
% Parameter-fitting with fminsearch
P1P2_fms = fminsearch(@(par) err_fcn(par,x,y,curve_fcn),P1P2_guess);
% Parameter-fitting with lsqnonlin:
P1P2_lsq = lsqnonlin(@(par) res_fcn(par,x,y,curve_fcn),P1P2_guess);

That should give you good parameters for P1 and P2 as the first and second element of P1P2_fms and/or P1P2_lsq.

I find these functions easier to work with since this is more transparend and I know what goes in (old dogs and new tricks are said to not go well...).

HTH

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Matt J 2022-5-31

编辑：Matt J 2022-5-31

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???

But the only difference between your workflow and lsqcurvefit, is that lsqcurvefit takes your curv_fcn directly:

curve_fcn = @(P1P2,x) P1P2(1)*(exp(-(x-P1P2(2)).^2/1e3) + exp(-(x+P1P2(2)).^2/1e3));
P1P2_guess = [1,2]; % Initial guess for the parameters P1 and P2, (adjust to be good values)
P1P2_lsq = lsqcurvefit(curve_fcn,P1P2_guess, x,y);

Moreover, in either workflow, you will inevitably need to provide curve_fcn for when it comes time to plot the fit.

Bjorn Gustavsson 2022-6-1

@Matt J, you're right (again). It is probably only due to habit, I started using fmins/fminsearch (and fminsearchbnd) and lsqnonlin and never bothered starting to use lsqcurvefit because I had gotten used to the setups for the others. You teach me a lot about myself recently, I don't like what I learn but I do appreciate it...

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Double parameter optimisation using optimisation toolbox

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