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exp_lu.m
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exp_lu.m
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function exp_lu()
%% matrix 1
clear all
A = load('data/3-5000/root_P64_cs128.mat');
A = schur_factors(A.A);
u1 = precision('d');
u2 = precision('s');
u3 = precision('h');
u4 = precision('b');
u5 = precision('q52');
u_chain = prec_chain(u1, u2, u3, u4, u5);
depths = [2, 5, 8];
vareps = [1e-14, 1e-12, 1e-10, 1e-08, 1e-06, 1e-04, 1e-02];
n_d = size(depths, 2);
n_eps = size(vareps, 2);
err_back_list1 = zeros(n_eps, n_d);
err_back_list2 = zeros(n_eps, n_d);
err_back_list3 = zeros(n_eps, n_d);
err_bound_list1 = zeros(n_eps, n_d);
err_bound_list2 = zeros(n_eps, n_d);
err_bound_list3 = zeros(n_eps, n_d);
norm_A = norm(A, 'fro');
n_A = size(A, 1);
for i=1:n_eps
for j=1:n_d
eps = vareps(i);
depth = depths(j);
aphA = amphodlr(u_chain, A, depth, 10, 'svd', eps);
[L1, U1] = hlu(aphA, 'hodlr');
norm_L = norm(recover(L1), 'fro');
norm_U = norm(recover(U1), 'fro');
eb1 = lu_err_bound2(depth, eps, norm_A, norm_L, norm_U)/ norm_A;
[L2, U2] = mhlu(aphA, u2, 'hodlr');
norm_L = norm(recover(L2), 'fro');
norm_U = norm(recover(U2), 'fro');
eb2 = lu_err_bound2(depth, eps, norm_A, norm_L, norm_U)/ norm_A;
[L3, U3] = mhlu(aphA, u4, 'hodlr');
norm_L = norm(recover(L3), 'fro');
norm_U = norm(recover(U3), 'fro');
eb3 = lu_err_bound2(depth, eps, norm_A, norm_L, norm_U)/ norm_A;
recover_LU1 = hdot(L1, U1, 'dense');
recover_LU2 = hdot(L2, U2, 'dense');
recover_LU3 = hdot(L3, U3, 'dense');
err_back1 = norm(A - recover_LU1, 'fro') / norm_A;
err_back2 = norm(A - recover_LU2, 'fro') / norm_A;
err_back3 = norm(A - recover_LU3, 'fro') / norm_A;
err_back_list1(i, j) = err_back1;
err_back_list2(i, j) = err_back2;
err_back_list3(i, j) = err_back3;
err_bound_list1(i, j) = eb1;
err_bound_list2(i, j) = eb2;
err_bound_list3(i, j) = eb3;
end
end
save("results/lu1_1.mat", 'err_back_list1');
save("results/lu1_2.mat", 'err_back_list2');
save("results/lu1_3.mat", 'err_back_list3');
save("results/lu1_1_bound.mat", 'err_bound_list1');
save("results/lu1_2_bound.mat", 'err_bound_list2');
save("results/lu1_3_bound.mat", 'err_bound_list3');
%% matrix 2
clear all
A = load('data/3-5000/cavity18.mat');
A = schur_factors(A.Problem.A);
u1 = precision('d');
u2 = precision('s');
u3 = precision('h');
u4 = precision('b');
u5 = precision('q52');
u_chain = prec_chain(u1, u2, u3, u4, u5);
depths = [2, 5, 8];
vareps = [1e-14, 1e-12, 1e-10, 1e-08, 1e-06, 1e-04, 1e-02];
n_d = size(depths, 2);
n_eps = size(vareps, 2);
err_back_list1 = zeros(n_eps, n_d);
err_back_list2 = zeros(n_eps, n_d);
err_back_list3 = zeros(n_eps, n_d);
err_bound_list1 = zeros(n_eps, n_d);
err_bound_list2 = zeros(n_eps, n_d);
err_bound_list3 = zeros(n_eps, n_d);
norm_A = norm(A, 'fro');
n_A = size(A, 1);
for i=1:n_eps
for j=1:n_d
eps = vareps(i);
depth = depths(j);
aphA = amphodlr(u_chain, A, depth, 10, 'svd', eps);
[L1, U1] = hlu(aphA, 'hodlr');
norm_L = norm(recover(L1), 'fro');
norm_U = norm(recover(U1), 'fro');
eb1 = lu_err_bound2(depth, eps, norm_A, norm_L, norm_U)/ norm_A;
[L2, U2] = mhlu(aphA, u2, 'hodlr');
norm_L = norm(recover(L2), 'fro');
norm_U = norm(recover(U2), 'fro');
eb2 = lu_err_bound2(depth, eps, norm_A, norm_L, norm_U)/ norm_A;
[L3, U3] = mhlu(aphA, u4, 'hodlr');
norm_L = norm(recover(L3), 'fro');
norm_U = norm(recover(U3), 'fro');
eb3 = lu_err_bound2(depth, eps, norm_A, norm_L, norm_U)/ norm_A;
recover_LU1 = hdot(L1, U1, 'dense');
recover_LU2 = hdot(L2, U2, 'dense');
recover_LU3 = hdot(L3, U3, 'dense');
err_back1 = norm(A - recover_LU1, 'fro') / norm_A;
err_back2 = norm(A - recover_LU2, 'fro') / norm_A;
err_back3 = norm(A - recover_LU3, 'fro') / norm_A;
err_back_list1(i, j) = err_back1;
err_back_list2(i, j) = err_back2;
err_back_list3(i, j) = err_back3;
err_bound_list1(i, j) = eb1;
err_bound_list2(i, j) = eb2;
err_bound_list3(i, j) = eb3;
end
end
save("results/lu2_depth2.mat", 'err_back_list1');
save("results/lu2_depth5.mat", 'err_back_list2');
save("results/lu2_depth8.mat", 'err_back_list3');
save("results/lu2_1_bound.mat", 'err_bound_list1');
save("results/lu2_2_bound.mat", 'err_bound_list2');
save("results/lu2_3_bound.mat", 'err_bound_list3');
%% matrix 3
clear all
A = load('data/3-5000/ex37.mat');
A = schur_factors(A.Problem.A);
u1 = precision('d');
u2 = precision('s');
u3 = precision('h');
u4 = precision('b');
u5 = precision('q52');
u_chain = prec_chain(u1, u2, u3, u4, u5);
depths = [2, 5, 8];
vareps = [1e-14, 1e-12, 1e-10, 1e-08, 1e-06, 1e-04, 1e-02];
n_d = size(depths, 2);
n_eps = size(vareps, 2);
err_back_list1 = zeros(n_eps, n_d);
err_back_list2 = zeros(n_eps, n_d);
err_back_list3 = zeros(n_eps, n_d);
err_bound_list1 = zeros(n_eps, n_d);
err_bound_list2 = zeros(n_eps, n_d);
err_bound_list3 = zeros(n_eps, n_d);
norm_A = norm(A, 'fro');
n_A = size(A, 1);
for i=1:n_eps
for j=1:n_d
eps = vareps(i);
depth = depths(j);
aphA = amphodlr(u_chain, A, depth, 10, 'svd', eps);
[L1, U1] = hlu(aphA, 'hodlr');
norm_L = norm(recover(L1), 'fro');
norm_U = norm(recover(U1), 'fro');
eb1 = lu_err_bound2(depth, eps, norm_A, norm_L, norm_U)/ norm_A;
[L2, U2] = mhlu(aphA, u2, 'hodlr');
norm_L = norm(recover(L2), 'fro');
norm_U = norm(recover(U2), 'fro');
eb2 = lu_err_bound2(depth, eps, norm_A, norm_L, norm_U)/ norm_A;
[L3, U3] = mhlu(aphA, u4, 'hodlr');
norm_L = norm(recover(L3), 'fro');
norm_U = norm(recover(U3), 'fro');
eb3 = lu_err_bound2(depth, eps, norm_A, norm_L, norm_U)/ norm_A;
recover_LU1 = hdot(L1, U1, 'dense');
recover_LU2 = hdot(L2, U2, 'dense');
recover_LU3 = hdot(L3, U3, 'dense');
err_back1 = norm(A - recover_LU1, 'fro') / norm_A;
err_back2 = norm(A - recover_LU2, 'fro') / norm_A;
err_back3 = norm(A - recover_LU3, 'fro') / norm_A;
err_back_list1(i, j) = err_back1;
err_back_list2(i, j) = err_back2;
err_back_list3(i, j) = err_back3;
err_bound_list1(i, j) = eb1;
err_bound_list2(i, j) = eb2;
err_bound_list3(i, j) = eb3;
end
end
save("results/lu3_depth2.mat", 'err_back_list1');
save("results/lu3_depth5.mat", 'err_back_list2');
save("results/lu3_depth8.mat", 'err_back_list3');
save("results/lu3_1_bound.mat", 'err_bound_list1');
save("results/lu3_2_bound.mat", 'err_bound_list2');
save("results/lu3_3_bound.mat", 'err_bound_list3');
%% matrix 4
clear all
A = load('data/3-5000/psmigr_1.mat');
A = schur_factors(A.Problem.A);
u1 = precision('d');
u2 = precision('s');
u3 = precision('h');
u4 = precision('b');
u5 = precision('q52');
u_chain = prec_chain(u1, u2, u3, u4, u5);
depths = [2, 5, 8];
vareps = [1e-14, 1e-12, 1e-10, 1e-08, 1e-06, 1e-04, 1e-02];
n_d = size(depths, 2);
n_eps = size(vareps, 2);
err_back_list1 = zeros(n_eps, n_d);
err_back_list2 = zeros(n_eps, n_d);
err_back_list3 = zeros(n_eps, n_d);
err_bound_list1 = zeros(n_eps, n_d);
err_bound_list2 = zeros(n_eps, n_d);
err_bound_list3 = zeros(n_eps, n_d);
norm_A = norm(A, 'fro');
n_A = size(A, 1);
for i=1:n_eps
for j=1:n_d
eps = vareps(i);
depth = depths(j);
aphA = amphodlr(u_chain, A, depth, 10, 'svd', eps);
[L1, U1] = hlu(aphA, 'hodlr');
norm_L = norm(recover(L1), 'fro');
norm_U = norm(recover(U1), 'fro');
eb1 = lu_err_bound2(depth, eps, norm_A, norm_L, norm_U)/ norm_A;
[L2, U2] = mhlu(aphA, u2, 'hodlr');
norm_L = norm(recover(L2), 'fro');
norm_U = norm(recover(U2), 'fro');
eb2 = lu_err_bound2(depth, eps, norm_A, norm_L, norm_U)/ norm_A;
[L3, U3] = mhlu(aphA, u4, 'hodlr');
norm_L = norm(recover(L3), 'fro');
norm_U = norm(recover(U3), 'fro');
eb3 = lu_err_bound2(depth, eps, norm_A, norm_L, norm_U)/ norm_A;
recover_LU1 = hdot(L1, U1, 'dense');
recover_LU2 = hdot(L2, U2, 'dense');
recover_LU3 = hdot(L3, U3, 'dense');
err_back1 = norm(A - recover_LU1, 'fro') / norm_A;
err_back2 = norm(A - recover_LU2, 'fro') / norm_A;
err_back3 = norm(A - recover_LU3, 'fro') / norm_A;
err_back_list1(i, j) = err_back1;
err_back_list2(i, j) = err_back2;
err_back_list3(i, j) = err_back3;
err_bound_list1(i, j) = eb1;
err_bound_list2(i, j) = eb2;
err_bound_list3(i, j) = eb3;
end
end
save("results/lu4_depth2.mat", 'err_back_list1');
save("results/lu4_depth5.mat", 'err_back_list2');
save("results/lu4_depth8.mat", 'err_back_list3');
save("results/lu4_1_bound.mat", 'err_bound_list1');
save("results/lu4_2_bound.mat", 'err_bound_list2');
save("results/lu4_3_bound.mat", 'err_bound_list3');
end