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nufft_table_test.m
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% nufft_table_test.m
% 3D test
if 1, printm '3d'
if 1 || ~isfield(s, 't'), printm 'precompute structure'
% ktype = 'minmax:kb';
ktype = 'kaiser';
Jd = [3 4 3];
Nd = [10 8 9];
Ld = [2^8 2^7 2^7];
Kd = 2 * Nd;
% n_shift = zeros(size(Nd)); printm 'easy: 0 shift'
n_shift = [3 7 2]; % stress it
gam = 2*pi ./ Kd;
k1 = linspace(-2*Kd(1), 2*Kd(1), 21)';
k2 = linspace(-2*Kd(2), 2*Kd(2), 18)';
k3 = linspace(-2*Kd(3), 2*Kd(3), 23)';
[kk1 kk2 kk3] = ndgrid(k1, k2, k3);
om = [gam(1)*kk1(:) gam(2)*kk2(:) gam(3)*kk3(:)];
tic
s.p = nufft_init(om, Nd, Jd, Kd, n_shift, ktype);
printm('pre time init %g', toc)
tic
s.t = nufft_init(om, Nd, Jd, Kd, n_shift, 'table', Ld, ktype);
printm('tab time init %g', toc)
end
% 3D forward direction
if 1, printm '3D forward'
rng(0)
x = rand(Nd);
x = zeros(Nd);
x(4, 2, 3) = 1;
tic
Y.d = dtft(x, om, 'n_shift', n_shift); % exact
printm('dtft3 time %g', toc)
tic
Y.p = nufft(x, s.p);
printm('pre time nufft %g', toc)
printm('pre max%%diff = %g', max_percent_diff(Y.d, Y.p))
tic
Y.t = nufft(x, s.t);
printm('tab time nufft %g', toc)
printm('tab max%%diff = %g', max_percent_diff(Y.d, Y.t))
printm('tab vs pre max%%diff = %g', max_percent_diff(Y.p, Y.t))
if 1
im plc 2 3
im(1, abs(Y.p - Y.d), 'pre - exact'), cbar
im(2, abs(Y.t - Y.d), 'tab - exact'), cbar
im(3, abs(Y.t - Y.p), 'tab - pre'), cbar
end
end
% 3D adjoint
if 1, printm '3D adjoint'
X = [1:s.t.M]' + 1i * ones(s.t.M,1);
tic
c.d = dtft_adj(X, om, Nd, n_shift); % exact
printm('dtft time adj %g', toc)
tic
c.p = nufft_adj(X, s.p);
printm('pre time nufft adj %g', toc)
tic
c.t = nufft_adj(X, s.t);
printm('tab time nufft adj %g', toc)
printm('pre max%%diff = %g', max_percent_diff(c.d, c.p))
printm('tab max%%diff = %g', max_percent_diff(c.d, c.t))
printm('tab vs pre max%%diff = %g', max_percent_diff(c.p, c.t))
if 1
im(4, abs(c.p - c.d), 'pre adj err'), cbar
im(5, abs(c.t - c.d), 'tab adj err'), cbar
im(6, abs(c.t - c.p), 'tab-pre adj'), cbar
end
end
end
% 2D test
if 1
if 1 || ~isfield(s, 't'), printm 'precompute structure'
% ktype = 'minmax:kb';
ktype = 'kaiser';
Jd = [4 5];
Nd = [20 16];
Ld = [2^12 2^13];
Kd = 2 * Nd;
% n_shift = zeros(size(Nd));
n_shift = [3 7]; % stress it
gam = 2*pi ./ Kd;
k1 = linspace(-2*Kd(1), 2*Kd(1), 51)';
k2 = linspace(-2*Kd(2), 2*Kd(2), 81)';
[kk1 kk2] = ndgrid(k1, k2);
om = [gam(1)*kk1(:) gam(2)*kk2(:)];
tic
s.p = nufft_init(om, Nd, Jd, Kd, n_shift, ktype);
printm('pre time init %g', toc)
tic
s.t = nufft_init(om, Nd, Jd, Kd, n_shift, 'table', Ld, ktype);
printm('tab time init %g', toc)
end
% forward direction
if 1, printm 'test forward'
x = [1:Nd(1)]'*abs([1:Nd(2)]-(Nd(2)/2));
tic
Y.d = dtft2(x, om, n_shift); % exact
printm('dtft2 time %g', toc)
tic
Y.p = nufft(x, s.p);
printm('pre time nufft %g', toc)
printm('pre max%%diff = %g', max_percent_diff(Y.d, Y.p))
tic
Y.t = nufft(x, s.t);
printm('tab time nufft %g', toc)
printm('tab max%%diff = %g', max_percent_diff(Y.d, Y.t))
printm('tab vs pre max%%diff = %g', max_percent_diff(Y.p, Y.t))
im plc 2 3
re = @(t) reshape(abs(t), length(k1), length(k2));
im(1, k1, k2, re(Y.p - Y.d), 'pre'), cbar
im(2, k1, k2, re(Y.t - Y.d), 'tab'), cbar
im(3, k1, k2, re(Y.t - Y.p), 'tab-pre'), cbar
end
% 2D adjoint
if 1, printm '2D adjoint'
X = [1:s.t.M]' + 1i * ones(s.t.M,1);
tic
c.d = dtft2_adj(X, om, Nd(1), Nd(2), n_shift); % exact
printm('dtft2 time adj %g', toc)
tic
c.p = nufft_adj(X, s.p);
printm('pre time nufft adj %g', toc)
tic
c.t = nufft_adj(X, s.t);
printm('tab time nufft adj %g', toc)
printm('pre max%%diff = %g', max_percent_diff(c.d, c.p))
printm('tab max%%diff = %g', max_percent_diff(c.d, c.t))
printm('tab vs pre max%%diff = %g', max_percent_diff(c.p, c.t))
im(4, abs(c.p - c.d), 'pre adj err'), cbar
im(5, abs(c.t - c.d), 'tab adj err'), cbar
im(6, abs(c.t - c.p), 'tab-pre adj'), cbar
end
end
% 1D test
if 1 || ~isfield(s, 't'), printm '1d'
% ktype = 'minmax:kb';
ktype = 'kaiser';
Jd = 4;
Nd = 32;
Ld = 2^14; % table over-sampling
Kd = 2 * Nd;
n_shift = zeros(size(Nd));
% n_shift = Nd/2;
gam = 2*pi ./ Kd;
kv = 2*Kd;
kv = linspace(-kv, kv, 1001)';
om = gam * kv;
tic
s.p = nufft_init(om, Nd, Jd, Kd, n_shift, ktype);
printm('pre time init %g', toc)
tic
s.t = nufft_init(om, Nd, Jd, Kd, n_shift, 'table', Ld, ktype);
printm('tab time init %g', toc)
end
if 0
ramp = [1:Nd]';
Y.dr = dtft(ramp, om, 'n_shift', n_shift);
Y.de = dtft(eye(Nd), om, 'n_shift', n_shift);
printm('dtft max%%diff = %g', max_percent_diff(Y.dr,Y.de*ramp))
Y.pr = nufft(ramp, s.p);
Y.pe = nufft(eye(Nd), s.p);
printm('pre max%%diff = %g', max_percent_diff(Y.pr,Y.pe*ramp))
printm('max%%diff = %g', max_percent_diff(Y.dr,Y.pr))
printm('max%%diff = %g', max_percent_diff(Y.de,Y.pe))
e = Y.pr - Y.dr;
if im
clf, plot(kv, abs(e), 'c-')
% clf, plot(kv, sum(abs(e),2), 'c-')
end
end
% forward direction
if 1, printm '1d forward'
x = [1:Nd]';
% x = unitv(Nd, ii);
Y.d = dtft(x, om, 'n_shift', n_shift); % exact
cpu etic
Y.p = nufft(x, s.p);
cpu etoc 'pre time nufft'
printm('pre max%%diff = %g', max_percent_diff(Y.d,Y.p))
tic
Y.t = nufft(x, s.t);
printm('tab time nufft %g', toc)
printm('tab max%%diff = %g', max_percent_diff(Y.d, Y.t))
if im
clf
subplot(211)
plot(kv, abs(Y.p - Y.d), 'c-'), title 'pre'
subplot(212)
plot(kv, abs(Y.t - Y.d), 'y-'), title 'tab'
end
prompt
end
% adjoint
if 1, printm '1d adj'
X = [1:s.t.M]' + 1i * ones(size(om));
c.d = dtft2_adj(X, [om 0*om], Nd(1), 1, [n_shift 0]); % exact
tic
c.p = nufft_adj(X, s.p);
printm('pre time nufft adj %g', toc)
tic
c.t = nufft_adj(X, s.t);
printm('tab time nufft adj %g', toc)
printm('pre nufft adj vs dtft adj max%%diff = %g', max_percent_diff(c.d,c.p))
printm('tab nufft adj vs dtft adj max%%diff = %g', max_percent_diff(c.d,c.t))
if im
clf
nn = 0:Nd(1)-1;
subplot(211)
plot(nn, abs(c.p - c.d) / mean(abs(c.d)), 'c-'), title 'pre'
subplot(212)
plot(nn, abs(c.t - c.d) / mean(abs(c.d)), 'y-'), title 'tab'
end
end