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Update PT code in Block RIP

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Ksyer
2024-07-16 15:50:04 +08:00
parent ce60606d82
commit 088f1a82fd
7 changed files with 66 additions and 81 deletions
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Block RIP/Phase transitions/block_phase_transition.m
+29 -12
View File
@@ -1,39 +1,56 @@
function pt = block_phase_transition(N, M)
function [N_b, N_s] = block_phase_transition(N, M)
tau_min = 0;
tau_max = 10;
tau_interval = 0.05;
tau_range = tau_min:tau_interval:tau_max;
K_min = 1;
K_max = 25;
K_max = 15;
K_range = K_min:K_max;
pt = zeros(25, 1);
N_b = zeros(length(K_range), 1);
N_s = zeros(length(K_range), 1);
cache_filename = "I.mat";
cache_filename_1 = "I_2.mat";
cache_filename_2 = "I_" + string(2 * M) + ".mat";
if exist(cache_filename, "file")
load(cache_filename);
if exist(cache_filename_1, "file")
load(cache_filename_1, "I_2");
else
I = zeros(length(tau_range), 0);
I_2 = zeros(length(tau_range), 0);
for tau_idx = 1:length(tau_range)
tau = tau_range(tau_idx);
I(tau_idx) = calc_block_integral(tau, 4);
I_2(tau_idx) = calc_block_integral(tau, 2);
end
save I.mat
save(cache_filename_1, "I_2");
end
if exist(cache_filename_2, "file")
load(cache_filename_2, "I_2M");
else
I_2M = zeros(length(tau_range), 0);
parfor tau_idx = 1:length(tau_range)
tau = tau_range(tau_idx);
I_2M(tau_idx) = calc_block_integral(tau, 2 * M);
end
save(cache_filename_2, "I_2M");
end
for K_idx = 1:length(K_range)
K = K_range(K_idx);
f_set = zeros(length(tau_range), 1);
f_set_1 = zeros(length(tau_range), 1);
f_set_2 = zeros(length(tau_range), 1);
for tau_idx = 1:length(tau_range)
tau = tau_range(tau_idx);
f_set(tau_idx) = 1/2 * (K * (2 * M + tau ^ 2) + (N - K) * I(tau_idx));
f_set_1(tau_idx) = 1/2 * (K * (2 * M + tau ^ 2) + (N - K) * I_2M(tau_idx));
f_set_2(tau_idx) = M/2 * (K * (2 + tau ^ 2) + (N - K) * I_2(tau_idx));
end
pt(K_idx) = min(f_set);
N_b(K_idx) = min(f_set_1);
N_s(K_idx) = min(f_set_2);
end
end
Block RIP/Phase transitions/block_phase_transition_0.m
-40
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@@ -1,40 +0,0 @@
function pt = block_phase_transition_0()
tau_min = 0;
tau_max = 100;
tau_interval = 0.1;
tau_range = tau_min:tau_interval:tau_max;
s_b_min = 1;
s_b_max = 25;
s_b_range = s_b_min:s_b_max;
pt = zeros(25, 1);
cache_filename = "I.mat";
if exist(cache_filename, "file")
load(cache_filename);
else
I = zeros(length(tau_range), 0);
for tau_idx = 1:length(tau_range)
tau = tau_range(tau_idx);
I(tau_idx) = calc_block_integral(tau, 4);
end
end
save I.mat
for s_b_idx = 1:length(s_b_range)
s_b = s_b_range(s_b_idx);
f_set = zeros(length(tau_range), 1);
for tau_idx = 1:length(tau_range)
tau = tau_range(tau_idx);
f_set(tau_idx) = s_b * (1 + tau ^ 2) + (100 - s_b) * I(tau_idx);
end
pt(s_b_idx) = min(f_set);
end
end
Block RIP/Phase transitions/block_phase_transition_2.m
-20
View File
@@ -1,20 +0,0 @@
function pt = block_phase_transition_2(N, M)
K_min = 1;
K_max = 25;
K_range = K_min:K_max;
pt = zeros(25, 1);
d = N;
m = M;
for K_idx = 1:length(K_range)
K = K_range(K_idx);
s = K;
syms t;
syms u;
f = s*(m+t^2)+(d-s)*int((u-t)^2*u^(m-1)*exp(-u^2/2)/(2^(m/2-1)*gamma(m/2)),u,t,inf);
g = diff(f,t);
t1 = solve(g);
n = s*(m+t1^2)+(d-s)*int((u-t1)^2*u^(m-1)*exp(-u^2/2)/(2^(m/2-1)*gamma(m/2)),u,t1,inf);
pt(K_idx) = n;
end
end
Block RIP/Phase transitions/block_phase_transition_formula.m
+22
View File
@@ -0,0 +1,22 @@
function pt = block_phase_transition_formula(N, M)
K_min = 1;
K_max = 25;
K_range = K_min:K_max;
pt = zeros(25, 1);
d = N;
m = M;
for K_idx = 1:length(K_range)
s = K_range(K_idx);
pt(K_idx) = theoretic(m, s, d);
end
end
function n = theoretic(m,s,d)
syms t;
syms u;
f = s*(m+t^2)+(d-s)*int((u-t)^2*u^(m-1)*exp(-u^2/2)/(2^(m/2-1)*gamma(m/2)),u,t,inf);
g = diff(f,t);
t1 = solve(g);
n = s*(m+t1^2)+(d-s)*int((u-t1)^2*u^(m-1)*exp(-u^2/2)/(2^(m/2-1)*gamma(m/2)),u,t1,inf);
end
Block RIP/Phase transitions/draw.m
+2 -1
View File
@@ -29,7 +29,8 @@ ax = gca;
grid(ax, 'on');
set(ax, 'Visible', 'on');
pt = block_phase_transition_2(128, 4);
% pt = block_phase_transition_2(128, 4);
pt = block_phase_transition_2(16*16, 16);
l = line(1:size(pt), pt);
l.Color = "w";
l.LineWidth = 5;
Block RIP/Phase transitions/draw_ft_curve.m
+13
View File
@@ -0,0 +1,13 @@
M = 10;
N = 320 + 160;
epi = 0.02;
[pt_block, pt_sparse] = block_phase_transition(N, M);
plot(pt_sparse);
% hold on;
% plot(pt_sparse);
% xlim([1, 5]);
ylim([1, N]);
xlabel("Sparsity (k)");
ylabel("Number of measurements (n)")
legend("Block sparse recovery", "Sparse recovery");
title("Phase Transition Curve (N = "+string(N)+", M = "+string(M)+")");
Block RIP/Phase transitions/theoretic.m
-8
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@@ -1,8 +0,0 @@
function n = theoretic(m,s,d)
syms t;
syms u;
f = s*(m+t^2)+(d-s)*int((u-t)^2*u^(m-1)*exp(-u^2/2)/(2^(m/2-1)*gamma(m/2)),u,t,inf);
g = diff(f,t);
t1 = solve(g);
n = s*(m+t1^2)+(d-s)*int((u-t1)^2*u^(m-1)*exp(-u^2/2)/(2^(m/2-1)*gamma(m/2)),u,t1,inf);
end