Updating .gitignore

.gitignore

@@ -23,9 +23,10 @@ octave-workspace
 
 # coco solution files
 sol*.mat
-coco_log.txt
-coco_scr.txt
-bd.mat
+coco_log*.txt
+coco_scr*.txt
+bd*.mat
+matlab_development/uq/examples/**/data
 
 # Some Mac file
 .DS_Store

archive/demo.m

-% Parameter values
-% p(1) = Period, T
-% p(2) = Forcing Amplitude, A
-% p(3) = Linear Stiffness, k
-% p(4) = Damping, d
-% p(5) = Cubic Stiffness, eps
-p0 = [2*pi; 0.3; 1; 2*0.1; 5];
-u0 = [0; 1; 0];
-
-% Forward Simulation for Starting Guess for Periodic Orbit
-f = @(t,u) duff(u,p0);
-% Long Run Simulation to let transients die out
-[~, u0] = ode45(f, [0, 100*pi], u0);
-% Estimate for steady state solution
-[t0, u0] = ode45(f, [0, p0(1)], u0(end,:));
-
-%%
-% Initialize Boundary Conditions
-data = struct();
-data.fhan = @duff;
-data = per_bc_update(data, [], u0(1,:)', [], p0);
-
-funcs = { @duff @duff_DU @duff_DP };
-pnames = {'T' 'A' 'k' 'd' 'eps'};
-coll_args = {funcs{:} t0 u0 p0};
-bvp_args = { @per_bc, @per_Jbc, data, @per_bc_update };
-
-%%
-prob = coco_prob();
-prob = coco_set(prob, 'coll', 'NTST', 15, 'var', true);
-% prob = coco_set(prob, 'cont', 'NAdapt', 1);
-prob = ode_isol2bvp(prob, '', coll_args{:}, pnames, bvp_args{:});
-
-%%
-[data, uidx] = coco_get_func_data(prob, 'bvp.seg1.coll', 'data', 'uidx');
-
-maps = data.coll_seg.maps;
-
-prob = coco_add_glue(prob, 'glue', uidx(maps.T_idx), uidx(maps.p_idx(1)));
-prob = coco_add_pars(prob, 'x_max', uidx(maps.x0_idx(1)), {'x_max'});
-
-%%
-bd = coco(prob, 'optim', [], 1, {'T','bvp.seg1.coll.T0','x_max'}, [2*pi/1.3, 2*pi/0.7]);
-

archive/demo_coll.m

-% Parameter values
-% p(1) = frequency of oscillation, w
-% p(2) = Forcing Amplitude, A
-% p(3) = Linear Stiffness, k
-% p(4) = Damping, d
-% p(5) = Cubic Stiffness, eps
-% p0 = [2*pi; 0.3; 1; 2*0.1; 5];
-p0 = [1; 0; 1; 0; 0];
-% u0 = [0; 1; 0; 1];
-
-t0 = linspace(0,1,200)';
-u0 = [cos(t0), -sin(t0), sin(t0), cos(t0)];
-
-% % Forward Simulation for Starting Guess for Periodic Orbit
-% f = @(t,u) duff(u,p0);
-% % Long Run Simulation to let transients die out
-% [t0, u0] = ode45(f, [0, 2*pi], u0);
-
-% Estimate for steady state solution
-% [t0, u0] = ode45(f, [0, 2*pi/p0(1)], u0(end,:));
-data = struct();
-data.fhan = @duff;
-data = per_bc_update(data, [], u0(1,:)', [], p0);
-
-prob = coco_prob();
-funcs = { @duff @duff_DU @duff_DP };
-pnames = {'w' 'A' 'k' 'd' 'eps'};
-
-coll_args = {funcs{:}, t0, u0, p0};
-
-bvp_args  = {@per_bc, @per_Jbc, data, @per_bc_update};
-prob = ode_isol2bvp(prob, '', coll_args{:}, pnames, bvp_args{:});
-
-[data, uidx] = coco_get_func_data(prob, 'bvp.seg1.coll', 'data', 'uidx');
-maps = data.coll_seg.maps;
-
-prob = coco_add_glue(prob, 'glue', uidx(maps.T_idx), uidx(maps.p_idx(1)));
-prob = coco_add_glue(prob, 'glue2', uidx(maps.T0_idx), uidx(maps.x0_idx(3)));
-prob = coco_add_pars(prob, 'v0', uidx(maps.x0_idx(2)), 'v0', 'active');
-prob = coco_add_pars(prob, 'x_max', uidx(maps.x0_idx(1)), 'x_max', 'active');
-
-% Start continuation of periodic orbits with updates to the Poincare
-% section before each continuation step.
-
-prob = coco_set(prob, 'cont', 'NAdapt', 10);
-cont_args = { 0, {'w', }};
-
-coco(prob, 'optim', [], cont_args{:});
\ No newline at end of file

archive/demo_po.m

-% Parameter values
-% p(1) = Period, T
-% p(2) = Forcing Amplitude, A
-% p(3) = Linear Stiffness, k
-% p(4) = Damping, d
-% p(5) = Cubic Stiffness, eps
-p0 = [2*pi; 0.3; 1; 2*0.1; 5];
-u0 = [0; 1];
-
-% Forward Simulation for Starting Guess for Periodic Orbit
-f = @(t,u) duffna(t,u,p0);
-
-% Long Run Simulation to let transients die out
-[~, u0] = ode45(f, [0, 100*pi], u0);
-
-% Estimate for steady state solution
-[t0, u0] = ode45(f, [0, p0(1)], u0(end,:)');
-
-funcs = { @duffna @duffna_DU @duffna_DP @duffna_DT};
-pnames = {'T' 'A' 'k' 'd' 'eps'};
-coll_args = {funcs{:} t0 u0 pnames p0};
-prob = coco_prob();
-prob = coco_set(prob, 'ode', 'autonomous', false);
-prob = coco_set(prob, 'coll', 'NTST', 15);
-prob = ode_isol2po(prob, '', coll_args{:});
-
-% Adaptive discretization before each continuation step
-prob = coco_set(prob, 'cont', 'NAdapt', 1);
-
-[data, uidx] = coco_get_func_data(prob, 'po.orb.coll', 'data', 'uidx');
-maps = data.coll_seg.maps;
-
-prob = coco_add_glue(prob, 'glue', uidx(maps.T_idx), uidx(maps.p_idx(1)));
-prob = coco_add_pars(prob, 'v0', uidx(maps.x0_idx(2)), 'v0', 'active');
-
-
-prob = coco_add_pars(prob, 'x_max', uidx(maps.x0_idx(1)), {'x_max'});
-
-bd = coco(prob, 'optim', [], 1, {'po.period', 'T', 'x_max'}, [pi, 4*pi]);
-bd2 = coco_bd_read('optim');
-u = coco_bd_col(bd2, {'T', '||po.orb.x||'});
-plot(2*pi./u(1,:),u(2,:))
-

archive/demo_po_a.m

-% Parameter values
-% p(1) = Period, T
-% p(2) = Forcing Amplitude, A
-% p(3) = Linear Stiffness, k
-% p(4) = Damping, d
-% p(5) = Cubic Stiffness, eps
-p0 = [2*pi; 0.3; 1; 2*0.1; 5];
-u0 = [0; 1; 0];
-
-% Forward Simulation for Starting Guess for Periodic Orbit
-f = @(t,u) duff(u,p0);
-
-% Long Run Simulation to let transients die out
-[~, u0] = ode45(f, [0, 20*pi], u0);
-
-% Estimate for steady state solution
-[t0, u0] = ode45(f, [0, p0(1)], u0(end,:)');
-
-funcs = {@duff @duff_DU @duff_DP};
-pnames = {'T' 'A' 'k' 'd' 'eps'};
-coll_args = {funcs{:} t0 u0 pnames p0};
-
-prob = ode_isol2po(coco_prob(), '', coll_args{:});
-prob = coco_set(prob, 'coll', 'NTST', 15);
-
-% Adaptive discretization before each continuation step
-prob = coco_set(prob, 'cont', 'NAdapt', 1);
-
-[data, uidx] = coco_get_func_data(prob, 'po.orb.coll', 'data', 'uidx');
-maps = data.coll_seg.maps;
-
-prob = coco_add_glue(prob, 'glue', uidx(maps.T_idx), uidx(maps.p_idx(1)));
-prob = coco_add_pars(prob, 'v0', uidx(maps.x0_idx(2)), 'v0', 'active');
-
-
-prob = coco_add_pars(prob, 'x_max', uidx(maps.x0_idx(1)), {'x_max'});
-
-bd = coco(prob, 'optim', [], 1, {'po.period', 'T', 'x_max'}, [pi, 4*pi]);
-bd2 = coco_bd_read('optim');
-u = coco_bd_col(bd2, {'T', '||po.orb.x||'});
-plot(2*pi./u(1,:),u(2,:))
-

archive/duff.m

-function y = duff(u,p)
-
-% Autonomous, Vectorized encoding of the Duffing oscillator
-% x'' + d*x' + k*x + eps*x^3 = A*cos(2*pi*t/T)
-% u1 = x
-% u2 = x'
-% u3 = sin(wt)
-% u4 = cos(wt)
-
-w = p(1,:);
-A = p(2,:);
-k = p(3,:);
-d = p(4,:);
-eps = p(5,:);
-
-u1 = u(1,:); % Position
-u2 = u(2,:); % Velocity
-u3 = u(3,:); % sin(wt)
-u4 = u(4,:); % cos(wt)
-
-y(1,:) = u2;
-y(2,:) = A.*u4 - d.*u2- k.*u1 - eps.*u1.^3;
-% Solution to u3 and u4 is u3 = sin(wt), u4 = cos(wt)
-% Therefore, this is an autonomous way to encode the non-autonomous forcing
-% function.  See Mehdi RSPA paper, reference ~47 (the one about
-% continuation in a finite element model)
-y(3,:) = u3 + w.*u4 - u3.*(u3.^2 + u4.^2);
-y(4,:) = u4 - w.*u3 - u4.*(u3.^2 + u4.^2);
-
-end
\ No newline at end of file

archive/duff_DP.m

-function J = duff_DP(u,p)
-
-u1 = u(1,:);
-u2 = u(2,:);
-u3 = u(3,:);
-u4 = u(4,:);
-
-J = zeros(4,size(p,1),size(u,2));
-
-J(2,2,:) = u4;
-J(2,3,:) = -u1;
-J(2,4,:) = -u2;
-J(2,5,:) = -u1.^3;
-J(3,1,:) = u4;
-J(4,1,:) = -u3;
-
-end
\ No newline at end of file

archive/duff_DU.m

-function J = duff_DU(u,p)
-
-u1 = u(1,:);
-u3 = u(3,:);
-u4 = u(4,:);
-w = p(1,:);
-A = p(2,:);
-k = p(3,:);
-d = p(4,:);
-eps = p(5,:);
-
-J = zeros(4,4,numel(u1));
-
-J(1,2,:) = 1;
-J(2,1,:) = -k - 3*eps.*u1.^2;
-J(2,2,:) = -d;
-J(2,4,:) = A;
-J(3,3,:) = 1 - 3*u3.^2 - u4.^2;
-J(3,4,:) = w - 2*u3.*u4;
-J(4,3,:) = -w - 2*u3.*u4;
-J(4,4,:) = 1 - u3.^2 - 3*u4.^2;
-
-end
\ No newline at end of file

archive/duffna.m

-function y = duffna(t,u,p)
-
-% non-Autonomous, Vectorized encoding of the Duffing oscillator
-% x'' + d*x' + k*x + eps*x^3 = A*cos(2*pi*t/T)
-% u1 = x
-% u2 = x'
-
-T = p(1,:);
-A = p(2,:);
-k = p(3,:);
-d = p(4,:);
-eps = p(5,:);
-
-u1 = u(1,:); % Position
-u2 = u(2,:); % Velocity
-
-y(1,:) = u2;
-y(2,:) = A.*cos((2*pi./T).*t) - d.*u2- k.*u1 - eps.*u1.^3;
-
-end
\ No newline at end of file

archive/duffna_DP.m

-function J = duffna_DP(t,u,p)
-
-T = p(1,:);
-A = p(2,:);
-
-u1 = u(1,:);
-u2 = u(2,:);
-
-J = zeros(2,numel(p(:,1)),numel(u1));
-
-J(2,1,:) = (2*pi*A.*t./(T.^2)).*sin((2*pi./T).*t);
-J(2,2,:) = cos(2*pi./T.*t);
-J(2,3,:) = -u1;
-J(2,4,:) = -u2;
-J(2,5,:) = -u1.^3;
-
-end
\ No newline at end of file

archive/duffna_DT.m

-function Jt = duffna_DT(t,u,p)
-
-T = p(1,:);
-A = p(2,:);
-
-Jt = zeros(2,numel(t));
-Jt(2,:) = -(2*pi./T).*A.*sin((2*pi./T).*t);
-
-end
\ No newline at end of file

archive/duffna_DU.m

-function J = duffna_DU(t,u,p)
-
-u1 = u(1,:);
-T = p(1,:);
-A = p(2,:);
-k = p(3,:);
-d = p(4,:);
-eps = p(5,:);
-
-J = zeros(2,2,numel(u1));
-
-J(1,2,:) = 1;
-J(2,1,:) = -k - 3*eps.*u1.^2;
-J(2,2,:) = -d;
-
-end
\ No newline at end of file

archive/per_Jbc.m

-function  Jbc = per_Jbc(data, T, x0, x1, p)
-
-Jbc = data.J;
-
-
-end
\ No newline at end of file

archive/per_bc.m

-function [data, y] = per_bc(T, u0, u1, p)
-
-% Boundary Conditions for the oscillator
-% 1. u1(0) - u1(T) = 0 -----| Initial Postion = Final Position
-% 2. u2(0) - u2(T) = 0 -----| Initial Velocity = Final Velocity
-% 3. u3(0) - u3(1) = 0 -----| 
-% 4. u4(0) - u4(1) = 0 -----|
-% 4. u2(0) = 0 -------------| Phase Condition: Start orbit where the Velocity 
-%                           |                  is zero (max Amplitude).
-
-u01 = u0(1,:); % Initial Position
-u02 = u0(2,:); % Initial Velocity
-u03 = u0(3,:);
-u04 = u0(4,:);
-
-u11 = u1(1,:); % Final Position
-u12 = u1(2,:); % Final Velocity
-u13 = u1(3,:); 
-u14 = u1(4,:); 
-
-y(1,:) = u01 - u11;       % Periodic Position BC
-y(2,:) = u02 - u12;       % Periodic Velocity BC
-y(3,:) = u03 - u13;
-y(4,:) = u04 - u14;
-y(5,:) = u02;             % Poincare Section
-
-end
\ No newline at end of file

archive/per_bc_update.m

-function data = per_bc_update(data, T, u0, u1, p)
-
-% Update Function for the boundary conditions
-
-n = numel(u0);
-q = numel(p);
-
-pmat = sparse(n,q);
-pmat(n,1) = 1;
-
-% Jacobian for Poincare Section at u2 = 0
-data.J = [ sparse(n,1), speye(n,n),                -speye(n,n),  pmat;
-           sparse(1,1), sparse([0 1 zeros(1,n-2)]), sparse(1,n), sparse(1,q)];
-
-end
\ No newline at end of file

coco_example_runs/duff/F.m

-function y = F(u,p)
-
-% State Vector Assignment
-u1 = u(1,:);        % Position
-u2 = u(2,:);        % Velocity
-u3 = u(3,:);        % time
-
-% Parameter Assignment
-A = p(1,:);         % Forcing function amplitude
-k = p(2,:);         % Linear Stiffness
-d = p(3,:);         % Linear Damping
-w = p(4,:);         % Forcing function frequency
-eps = p(5,:);       % Nonlinear Stiffness
-
-y(1,:) = u2;
-y(2,:) = A.*cos(w.*u3) - d.*u2-k.*u1 - eps.*u1.^3;
-y(3,:) = 1;
-
-end
\ No newline at end of file

coco_example_runs/duff/F_dP.m

-function J = F_dP(u,p)
-
-% State Vector Assignment
-u1 = u(1,:);        % Position
-u2 = u(2,:);        % Velocity
-u3 = u(3,:);        % time
-
-A = p(1,:);
-w = p(4,:);
-
-J = zeros(3,5,numel(u1));
-J(2,1,:) = cos(w.*u3);
-J(2,2,:) = -u1;
-J(2,3,:) = -u2;
-J(2,4,:) = -A.*u3.*sin(w.*u3);
-J(2,5,:) = -u1.^3;
-
-end
\ No newline at end of file

coco_example_runs/duff/F_dU.m

-function J = F_dU(u,p)
-
-% State Vector Assignment
-u1 = u(1,:);        % Position
-u3 = u(3,:);        % Position
-
-% Parameter Assignment
-A = p(1,:);         % Forcing function amplitude
-k = p(2,:);         % Linear Stiffness
-d = p(3,:);         % Linear Damping
-w = p(4,:);         % Forcing function frequency
-eps = p(5,:);       % Nonlinear Stiffness
-
-% Assign Jacobian Terms
-J = zeros(3,3,numel(u1));
-
-J(1,2,:) = 1;
-J(2,1,:) = -k - 3*eps.*u1.^2;
-J(2,2,:) = -d;
-J(2,3,:) = -A.*w.*sin(w.*u3);
-
-end
\ No newline at end of file