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Cosserat_WeakRK_Samples.m
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executable file
·156 lines (153 loc) · 8.36 KB
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%% WeakRK
function [mean_r_all,mean_D_ik_all,D0_ik_all,u0_k_all,v0_k_all,u_k_all,v_k_all,Cu_k_all,Cv_k_all,MSE_all]...
=Cosserat_WeakRK_Samples(R_helix,R_straight,omega_helix,omega_straight,theta_helix_0,theta_straight_0,n_helix,n_straight,s_all,rod_axis_rs,isassigneddir,assigned_dir,helix_cable_strain_all,straight_cable_strain_all,measure_error_level,plot_figure_id,n_substep,n_samples)
n_points=length(s_all);
n_measure=n_helix+n_straight;
D0_ik_all=get_frenet_frame_from_cart(s_all,rod_axis_rs,isassigneddir,assigned_dir);
pD_ik_ps_all=get_partial_D_ik_partial_s(D0_ik_all,s_all);
grad_s=gradient(s_all);
Ys_WeakRK=zeros(12,n_points);
Ys_WeakRK(:,1)=[rod_axis_rs(:,1);D0_ik_all(:,1,1);D0_ik_all(:,2,1);D0_ik_all(:,3,1)];
u0_k_all=zeros(3,n_points);
v0_k_all=zeros(3,n_points);
u_k_all=zeros(3,n_points);
v_k_all=zeros(3,n_points);
MSE_all=zeros(1,n_points);
Cu_k_all=zeros(3,n_measure,n_points);
Cv_k_all=zeros(3,n_measure,n_points);
A_all=zeros(12,12,n_points);
B_all=zeros(n_measure,12,12,n_points);
s_r_all=zeros(n_samples,3,n_points);
s_D_ik_all=zeros(n_samples,3,3,n_points);
s_r_all=repmat(rod_axis_rs,[1,1,n_samples]);
s_r_all=permute(s_r_all,[3,1,2]);
s_D_ik_all=repmat(D0_ik_all,[1,1,1,n_samples]);
s_D_ik_all=permute(s_D_ik_all,[4,1,2,3]);
parfor point=1:n_points
s=s_all(point);
ds=grad_s(point);
epsilon_p_helix=helix_cable_strain_all(:,point);
epsilon_p_straight=straight_cable_strain_all(:,point);
[u0_k,v0_k]=get_ini_darboux_strain_u0_k_and_v0_k(squeeze(D0_ik_all(:,:,point)),squeeze(pD_ik_ps_all(:,:,point)));
u0_k_all(:,point)=u0_k;
v0_k_all(:,point)=v0_k;
[A,B,u_k,v_k,Cu_k,Cv_k]=nonlin_rod_assymbling_matrixs(R_helix,R_straight,omega_helix,omega_straight,theta_helix_0,theta_straight_0,n_helix,n_straight,s,u0_k,v0_k,epsilon_p_helix,epsilon_p_straight,measure_error_level,ds);
u_k_all(:,point)=u_k;
v_k_all(:,point)=v_k;
Cu_k_all(:,:,point)=Cu_k;
Cv_k_all(:,:,point)=Cv_k;
A_all(:,:,point)=A
B_all(:,:,:,point)=B
end
permutedA=permute(A_all,[1,2,3]);
permutedB=permute(B_all,[1,2,3,4]);
spline_A=spline(s_all',permutedA);
spline_B=spline(s_all',permutedB);
helperfunA =@(t) ppval(spline_A,t);
helperfunB =@(t) ppval(spline_B,t);
parfor sample=1:n_samples
disp("now on sample = ")
disp(sample)
Ys_WeakRK=zeros(12,n_points);
Ys_WeakRK(:,1)=[rod_axis_rs(:,1);D0_ik_all(:,1,1);D0_ik_all(:,2,1);D0_ik_all(:,3,1)];
for point=2:n_points
ds=grad_s(point-1)/n_substep;
s=s_all(point-1);
Y_update=Ys_WeakRK(:,point-1);
for step=1:n_substep
A=helperfunA(s+step*ds);
B=helperfunB(s+step*ds);
Y=Y_update;
DeltaW_j=rand3p(n_measure,ds);
Upsilon=zeros(12);
plusR=zeros([n_measure,12]);
minusR=zeros([n_measure,12]);
plusU=zeros([n_measure,12]);
minusU=zeros([n_measure,12]);
Vrj=rand2pmat(n_measure,ds);
for p=1:12
Upsilon(p)=Y(p);
for q=1:12
Upsilon(p)=Upsilon(p) +A(p,q)*Y(q)*ds;
for j=1:n_measure
Upsilon(p)=Upsilon(p) +B(j,p,q)*Y(q)*DeltaW_j(j);
end
end
end
for p=1:12
for j=1:n_measure
plusR(j,p)=Y(p);
minusR(j,p)=Y(p);
plusU(j,p)=Y(p);
minusU(j,p)=Y(p);
for q=1:12
plusR(j,p)=plusR(j,p) +A(p,q)*Y(q)*ds+B(j,p,q)*Y(q)*sqrt(ds);
minusR(j,p)=minusR(j,p) +A(p,q)*Y(q)*ds-B(j,p,q)*Y(q)*sqrt(ds);
plusU(j,p)=plusR(j,p) +B(j,p,q)*Y(q)*sqrt(ds);
minusU(j,p)=minusR(j,p)-B(j,p,q)*Y(q)*sqrt(ds);
end
end
end
for p=1:12
for q=1:12
Y_update(p)=Y_update(p)+0.5*A(p,q)*(Y(q)+Upsilon(q))*ds;
for j=1:n_measure
tmp1=zeros(12);
tmp2=zeros(12);
for r=1:n_measure
tmp1(q)=tmp1(q)+(plusU(r,q)+minusU(r,q)-2*Y(q))*(r~=j);
tmp2(q)=tmp1(q)+(plusU(r,q)-minusU(r,q))*(DeltaW_j(j)*DeltaW_j(r)+Vrj(r,j))*(r~=j);
end
Y_update(p)=Y_update(p)+B(j,p,q)*...
0.25*(plusR(j,q)+minusR(j,q)+2*Y(q)+tmp1(q))...
*DeltaW_j(j);
Y_update(p)=Y_update(p)+B(j,p,q)*...
0.25*( ...
(plusR(j,q)-minusR(j,q))*(DeltaW_j(j)^2-ds) ...
+tmp2(q)...
)/sqrt(ds)...
;
end
end
end
end
Ys_WeakRK(:,point)=Y_update;
s_r_all(sample,:,point)=Ys_WeakRK(1:3,point);
s_D_ik_all(sample,:,:,point)=[Ys_WeakRK(4:6,point) Ys_WeakRK(7:9,point) Ys_WeakRK(10:12,point)];
end
end
mean_r_all=squeeze(mean(s_r_all,1));
std_r_all=squeeze(std(s_r_all,0,1));
mean_D_ik_all=squeeze(mean(s_D_ik_all,1));
MSE_all(:)=sqrt(std_r_all(1,:).^2+std_r_all(2,:).^2+std_r_all(3,:).^2);
plotinterval=ceil(n_points/100);
transpancy=0.2;
if plot_figure_id
figure(plot_figure_id)
plot3(squeeze(mean_r_all(1,1:plotinterval:n_points)), squeeze(mean_r_all(2,1:plotinterval:n_points)), squeeze(mean_r_all(3,1:plotinterval:n_points)), 'Color',[0 0 0 1]);
grid on
hold on
figure(plot_figure_id+1)
plot3(squeeze(mean_r_all(1,1:plotinterval:n_points)), squeeze(mean_r_all(2,1:plotinterval:n_points)), squeeze(mean_r_all(3,1:plotinterval:n_points)), 'Color',[0 0 0 1]);
grid on
axis equal
hold on
quiver3(squeeze(mean_r_all(1,1:plotinterval:n_points)), squeeze(mean_r_all(2,1:plotinterval:n_points)), squeeze(mean_r_all(3,1:plotinterval:n_points)),squeeze(mean_D_ik_all(1,1,1:plotinterval:n_points))', squeeze(mean_D_ik_all(2,1,1:plotinterval:n_points))', squeeze(mean_D_ik_all(3,1,1:plotinterval:n_points))','Color',[1 0 0 1])
quiver3(squeeze(mean_r_all(1,1:plotinterval:n_points)), squeeze(mean_r_all(2,1:plotinterval:n_points)), squeeze(mean_r_all(3,1:plotinterval:n_points)),squeeze(mean_D_ik_all(1,2,1:plotinterval:n_points))', squeeze(mean_D_ik_all(2,2,1:plotinterval:n_points))', squeeze(mean_D_ik_all(3,2,1:plotinterval:n_points))','Color',[0 1 0 1])
quiver3(squeeze(mean_r_all(1,1:plotinterval:n_points)), squeeze(mean_r_all(2,1:plotinterval:n_points)), squeeze(mean_r_all(3,1:plotinterval:n_points)),squeeze(mean_D_ik_all(1,3,1:plotinterval:n_points))', squeeze(mean_D_ik_all(2,3,1:plotinterval:n_points))', squeeze(mean_D_ik_all(3,3,1:plotinterval:n_points))','Color',[0 0 1 1])
for sample=1:n_samples
figure(plot_figure_id)
plot3(squeeze(s_r_all(sample,1,1:plotinterval:n_points)), squeeze(s_r_all(sample,2,1:plotinterval:n_points)), squeeze(s_r_all(sample,3,1:plotinterval:n_points)), 'Color',[0 0 0 transpancy]);
grid on
hold on
figure(plot_figure_id+1)
plot3(squeeze(s_r_all(sample,1,1:plotinterval:n_points)), squeeze(s_r_all(sample,2,1:plotinterval:n_points)), squeeze(s_r_all(sample,3,1:plotinterval:n_points)),'Color',[0 0 0 transpancy]);
grid on
axis equal
hold on
quiver3(squeeze(s_r_all(sample,1,1:plotinterval:n_points)), squeeze(s_r_all(sample,2,1:plotinterval:n_points)), squeeze(s_r_all(sample,3,1:plotinterval:n_points)),squeeze(s_D_ik_all(sample,1,1,1:plotinterval:n_points)), squeeze(s_D_ik_all(sample,2,1,1:plotinterval:n_points)), squeeze(s_D_ik_all(sample,3,1,1:plotinterval:n_points)),'Color',[1 0 0 transpancy])
quiver3(squeeze(s_r_all(sample,1,1:plotinterval:n_points)), squeeze(s_r_all(sample,2,1:plotinterval:n_points)), squeeze(s_r_all(sample,3,1:plotinterval:n_points)),squeeze(s_D_ik_all(sample,1,2,1:plotinterval:n_points)), squeeze(s_D_ik_all(sample,2,2,1:plotinterval:n_points)), squeeze(s_D_ik_all(sample,3,2,1:plotinterval:n_points)),'Color',[0 1 0 transpancy])
quiver3(squeeze(s_r_all(sample,1,1:plotinterval:n_points)), squeeze(s_r_all(sample,2,1:plotinterval:n_points)), squeeze(s_r_all(sample,3,1:plotinterval:n_points)),squeeze(s_D_ik_all(sample,1,3,1:plotinterval:n_points)), squeeze(s_D_ik_all(sample,2,3,1:plotinterval:n_points)), squeeze(s_D_ik_all(sample,3,3,1:plotinterval:n_points)),'Color',[0 0 1 transpancy])
end
end
end