SAOS TTS Master curve by Matlab

using least square fit to get the aT and bT for shifting small amplitude oscillatory shear (SAOS) data to a master curve.

Initially I wish to use lsqnonlinear or lscurvefit, but it didn't work out.

now I use 3-D matrix to map a range of aT and bT then from the minimum of square, to find the best fit aT and bT for G' along, or G" along or G' and G" together.

load saos0C.txt

w=saos0C;

load saos0C2.txt

w=saos0C2;

x=w(:,1);

y1=w(:,2);

y2=w(:,3);

lx=log10(x);

ly1=log10(y1);

ly2=log10(y2);

figure(2); plot(lx,ly1,lx,ly2);

load saos-10C.txt

w_shift=saos_10C;

load saos10C.txt

w_shift=saos10C;

load saos20C.txt

w_shift=saos20C;

x_shift=w_shift(:,1);

y1_shift=w_shift(:,2);

y2_shift=w_shift(:,3);

lx_shift=log10(x_shift);

ly1_shift=log10(y1_shift);

ly2_shift=log10(y2_shift);

N0=size(lx,1);

N0=size(lx_shift,1);

N1=sum(ly1_shift>max(ly1))+3;

lx_shift=lx_shift(N0-N1:N0);

ly2_shift=ly2_shift(N0-N1:N0);

ly1_shift=ly1_shift(N0-N1:N0);

N1=sum(ly1_shift<min(ly1))+2;

lx_shift=lx_shift(1:N0-N1);

ly2_shift=ly2_shift(1:N0-N1);

ly1_shift=ly1_shift(1:N0-N1);

figure(8);

plot(lx_shift,ly2_shift,'x',lx_shift,ly1_shift,'x',lx,ly1,lx,ly2);

lp = polyfit(lx,ly1,N0-N1);

l1y = polyval(lp,lx);

lp2 = polyfit(lx,ly2,N0-N1);

l2y = polyval(lp2,lx);

figure(4);

plot(lx,l1y,'x',lx,l2y,'x',lx,ly1,lx,ly2);

axis([-2,1,1.8,2.8])

tts=log10([1.03;4.46]);

tts=log10([0.96986431;0.28729847]);

tts=log10([0.94786000;0.10592537]);

a_shift=linspace(0.5,0.75,100);

b_shift=linspace(0.009,0.015,200);

b_shift=linspace(-0.016,-0.01,200);

a_shift=linspace(-0.4,-0.7,100);

b_shift=linspace(-0.035,-0.021,200);

a_shift=linspace(-1.1,-0.85,100);

temp1=repmat(lx_shift,1,size(a_shift,2));

temp1(:,:,2)=temp1(:,:);

for i=1:size(b_shift,2)

temp1(:,:,i)=temp1(:,:,1);

end

temp2=repmat(ly1_shift,1,size(a_shift,2));

temp2(:,:,2)=temp2(:,:);

for i=2:size(b_shift,2)

temp2(:,:,i)=temp2(:,:,1);

end

temp3=repmat(ly2_shift,1,size(a_shift,2));

temp3(:,:,2)=temp3(:,:);

for i=2:size(b_shift,2)

temp3(:,:,i)=temp3(:,:,1);

end

tempa=repmat(a_shift,size(lx_shift,1),1);

tempa(:,:,2)=tempa(:,:);

for i=2:size(b_shift,2)

tempa(:,:,i)=tempa(:,:,1);

end

tempb=repmat(b_shift,size(lx_shift,1),1);

tempb(:,:,2)=tempb(:,:);

for i=2:size(a_shift,2)

tempb(:,:,i)=tempb(:,:,1);

end

tempk=zeros(size(lx_shift,1),size(a_shift,2),size(b_shift,2));

tempk(:,1,:)=tempb(:,:,1);

for i=2:size(a_shift,2)

tempk(:,i,:)=tempb(:,:,1);

end

tempb(6,40,50)

tempk(6,50,40)

tempb=tempk;

temp6= polyval(lp2,temp1+tempa) - (temp3+tempb);

temp7= polyval(lp,temp1+tempa) - (temp2+tempb);

temp4=temp6.^2;

temp5=sum(temp4,1);

clearvars temp;

temp(:,:)=temp5(1,:,:);

temp8=temp7.^2;

temp9=sum(temp8,1);

clearvars temp0;

temp0(:,:)=temp9(1,:,:);

figure(1);

pcolor(temp);

tempk=temp0+temp;

[a,b]=min(temp);

[c,d]=min(a);

[e,f]=min(temp0);

[g,h]=min(e);

[k,l]=min(tempk);

[m,n]=min(k);

tts_2=[b_shift(d),a_shift(b(d))];

tts_1=[b_shift(h),a_shift(f(h))];

tts=[b_shift(n),a_shift(l(n))];

figure(3);

plot(lx_shift+tts_2(2),ly2_shift+tts_2(1),'x',lx_shift+tts_2(2),ly1_shift+tts_2(1),'x',lx,ly1,lx,ly2);

figure(4);

plot(lx_shift+tts_1(2),ly2_shift+tts_1(1),'x',lx_shift+tts_1(2),ly1_shift+tts_1(1),'x',lx,ly1,lx,ly2);

figure(5);

plot(lx_shift+tts(2),ly2_shift+tts(1),'x',lx_shift+tts(2),ly1_shift+tts(1),'x',lx,ly1,lx,ly2);

etts=10.^tts;

etts_1=10.^tts_1;

etts_2=10.^tts_2;