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rev_exp_mvprod2.m
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rev_exp_mvprod2.m
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function rev_exp_mvprod2(sfolder, varargin)
mkdir(sfolder);
disp('test 1')
if nargin == 1
min_block_size = 2^6;
DIM = 3;
eps = 1e-06;
n_sample = 1;
elseif nargin == 2
min_block_size = varargin{1};
DIM = 3;
eps = 1e-06;
n_sample = 1;
elseif nargin == 3
min_block_size = varargin{1};
DIM = varargin{2};
eps = 1e-06;
n_sample = 1;
elseif nargin == 4
min_block_size = varargin{1};
DIM = varargin{2};
eps = varargin{3};
n_sample = 1;
else
min_block_size = varargin{1};
DIM = varargin{2};
eps = varargin{3};
n_sample = varargin{4};
end
%% kernel matrix 2
rng(0)
u1 = precision('d').builtin();
u2 = precision('s').builtin();
u3 = precision('h').builtin();
u4 = precision('b');
u5 = precision('q52');
u_chain = prec_chain(u1, u2, u3, u4, u5);
depth = 999;
sizes = [2^9, 2^10, 2^11, 2^12, 2^13, 2^14];
n_size = size(sizes, 2);
err_back_list1 = zeros(n_size, 1);
err_back_list2 = zeros(n_size, 1);
ref_err_back_list = zeros(n_size, 1);
err_bound_list = zeros(n_size, 1);
for i=1:n_size
i_size = sizes(i);
disp(i_size)
x = unifrnd(-1, 1, i_size, DIM);
y = unifrnd(-1, 1, i_size, DIM);
kernel_mat = kernel2(x, y);
aphA = amphodlr(u_chain, kernel_mat, depth, min_block_size, 'svd', eps);
for k=1:n_sample
x = unifrnd(-1, 1, 1, i_size)';
hb1 = mhdot(aphA, x, u2, 'dense');
hb2 = mhdot(aphA, x, u4, 'dense');
rhb = hdot(aphA, x, 'dense');
b = kernel_mat * x;
err_back1 = norm(b - hb1, 'fro') / (norm(b, 'fro') * norm(kernel_mat, 'fro'));
err_back2 = norm(b - hb2, 'fro') / (norm(b, 'fro') * norm(kernel_mat, 'fro'));
ref_err_back = norm(b - rhb, 'fro') / (norm(b, 'fro') * norm(kernel_mat, 'fro'));
err_bound = 2*(sqrt(2)+1)*sqrt(2^(aphA.bottom_level + 1)+2^(aphA.bottom_level-1))*eps;
err_back_list1(i) = err_back_list1(i) + err_back1;
err_back_list2(i) = err_back_list2(i) + err_back2;
ref_err_back_list(i) = ref_err_back_list(i) + ref_err_back;
err_bound_list(i) = err_bound_list(i) + err_bound;
end
end
save(strcat(sfolder, "/rev2_prod2_err_back1.mat"), 'err_back_list1');
save(strcat(sfolder, "/rev2_prod2_err_back2.mat"), 'err_back_list2');
save(strcat(sfolder, "/rev2_prod2_ref_err_back.mat"), 'ref_err_back_list');
save(strcat(sfolder, "/rev2_prod2_bound.mat"), 'err_bound_list');
%% kernel matrix 3
disp('test 2');
rng(0)
u1 = precision('d').builtin();
u2 = precision('s').builtin();
u3 = precision('h').builtin();
u4 = precision('b');
u5 = precision('q52');
u_chain = prec_chain(u1, u2, u3, u4, u5);
depth = 999;
sizes = [2^9, 2^10, 2^11, 2^12, 2^13, 2^14];
n_size = size(sizes, 2);
err_back_list1 = zeros(n_size, 1);
err_back_list2 = zeros(n_size, 1);
ref_err_back_list = zeros(n_size, 1);
err_bound_list = zeros(n_size, 1);
for i=1:n_size
i_size = sizes(i);
disp(i_size)
x = unifrnd(-1, 1, i_size, DIM);
y = unifrnd(-1, 1, i_size, DIM);
kernel_mat = kernel3(x, y);
aphA = amphodlr(u_chain, kernel_mat, depth, min_block_size, 'svd', eps);
for k=1:n_sample
x = unifrnd(-1, 1, 1, i_size)';
hb1 = mhdot(aphA, x, u2, 'dense');
hb2 = mhdot(aphA, x, u4, 'dense');
rhb = hdot(aphA, x, 'dense');
b = kernel_mat * x;
err_back1 = norm(b - hb1, 'fro') / (norm(b, 'fro') * norm(kernel_mat, 'fro'));
err_back2 = norm(b - hb2, 'fro') / (norm(b, 'fro') * norm(kernel_mat, 'fro'));
ref_err_back = norm(b - rhb, 'fro') / (norm(b, 'fro') * norm(kernel_mat, 'fro'));
err_bound = 2*(sqrt(2)+1)*sqrt(2^(aphA.bottom_level + 1)+2^(aphA.bottom_level-1))*eps;
err_back_list1(i) = err_back_list1(i) + err_back1;
err_back_list2(i) = err_back_list2(i) + err_back2;
ref_err_back_list(i) = ref_err_back_list(i) + ref_err_back;
err_bound_list(i) = err_bound_list(i) + err_bound;
end
end
save(strcat(sfolder, "/rev2_prod3_err_back1.mat"), 'err_back_list1');
save(strcat(sfolder, "/rev2_prod3_err_back2.mat"), 'err_back_list2');
save(strcat(sfolder, "/rev2_prod3_ref_err_back.mat"), 'ref_err_back_list');
save(strcat(sfolder, "/rev2_prod3_bound.mat"), 'err_bound_list');
%% kernel matrix 4
disp("test 3")
rng(0)
u1 = precision('d').builtin();
u2 = precision('s').builtin();
u3 = precision('h').builtin();
u4 = precision('b');
u5 = precision('q52');
u_chain = prec_chain(u1, u2, u3, u4, u5);
depth = 999;
sizes = [2^9, 2^10, 2^11, 2^12, 2^13, 2^14];
n_size = size(sizes, 2);
err_back_list1 = zeros(n_size, 1);
err_back_list2 = zeros(n_size, 1);
ref_err_back_list = zeros(n_size, 1);
err_bound_list = zeros(n_size, 1);
for i=1:n_size
i_size = sizes(i);
disp(i_size)
x = unifrnd(-1, 1, i_size, DIM);
y = unifrnd(-1, 1, i_size, DIM);
kernel_mat = kernel4(x, y);
aphA = amphodlr(u_chain, kernel_mat, depth, min_block_size, 'svd', eps);
for k=1:n_sample
x = unifrnd(-1, 1, 1, i_size)';
hb1 = mhdot(aphA, x, u2, 'dense');
hb2 = mhdot(aphA, x, u4, 'dense');
rhb = hdot(aphA, x, 'dense');
b = kernel_mat * x;
err_back1 = norm(b - hb1, 'fro') / (norm(b, 'fro') * norm(kernel_mat, 'fro'));
err_back2 = norm(b - hb2, 'fro') / (norm(b, 'fro') * norm(kernel_mat, 'fro'));
ref_err_back = norm(b - rhb, 'fro') / (norm(b, 'fro') * norm(kernel_mat, 'fro'));
err_bound = 2*(sqrt(2)+1)*sqrt(2^(aphA.bottom_level + 1)+2^(aphA.bottom_level-1))*eps;
err_back_list1(i) = err_back_list1(i) + err_back1;
err_back_list2(i) = err_back_list2(i) + err_back2;
ref_err_back_list(i) = ref_err_back_list(i) + ref_err_back;
err_bound_list(i) = err_bound_list(i) + err_bound;
end
end
save(strcat(sfolder, "/rev2_prod4_err_back1.mat"), 'err_back_list1');
save(strcat(sfolder, "/rev2_prod4_err_back2.mat"), 'err_back_list2');
save(strcat(sfolder, "/rev2_prod4_ref_err_back.mat"), 'ref_err_back_list');
save(strcat(sfolder, "/rev2_prod4_bound.mat"), 'err_bound_list');
end