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optimizeSWMmseBcd.m
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optimizeSWMmseBcd.m
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function X = optimizeSWMmseBcd(K, Q, M, I, J, D, V, L, P)
X = V;
for k = 1 : K
count = 0;
prev = 0;
while true
count = count + 1;
if count > 100
break;
end
T = zeros(Q, 1);
for q = 1 : Q
rowOffset = (k - 1) * Q;
colOffset = (k - 1) * I;
lambdas = L(rowOffset + q, colOffset + 1 : colOffset + I);
[C, A] = cvector(Q, M, I, D, J, X, lambdas, k, q);
for i = 1 : I
if A(i) == 0
rowOffset = (k - 1) * Q * M + (q - 1) * M;
colOffset = (k - 1) * I + i;
X(rowOffset + 1 : rowOffset + M, colOffset) = zeros(M, 1);
end
end
if nnz(A) == 0
T(q) = 0;
continue;
end
rowOffset = (k - 1) * Q * M + (q - 1) * M;
colOffset = (q - 1) * M;
Jkq = J(rowOffset + 1 : rowOffset + M, colOffset + 1 : colOffset + M);
rho = spectralRadius(Jkq);
miuLow = 0;
miuHigh = upperBoundOfMiu(I, P, A, C);
miu = (miuLow + miuHigh) / 2;
delta = zeros(I, 1);
while true
miu = (miuLow + miuHigh) / 2;
deltaLow = zeros(I, 1);
deltaHigh = upperBoundOfDelta(A, C, I, rho, lambdas, miuHigh);
for i = 1 : I
if A(i) == 0
continue;
end
t1 = bisectionTarget(Jkq, C(:, i), deltaLow(i), lambdas(i), miu);
t2 = bisectionTarget(Jkq, C(:, i), deltaHigh(i), lambdas(i), miu);
if (t1 > 1 && t2 > 1) || (t1 < 1 && t2 < 1)
fprintf(2, 'parameter selection error\n');
end
while true
delta(i) = (deltaLow(i) + deltaHigh(i)) / 2;
target = bisectionTarget(Jkq, C(:, i), delta(i), lambdas(i), miu);
if abs(target - 1) < 2e-8
break;
end
if target < 1
deltaLow(i) = delta(i);
else
deltaHigh(i) = delta(i);
end
end
end
power = 0;
for i = 1 : I
if A(i) == 0
continue;
end
power = power + 1 / delta(i)^2;
end
if abs(miuLow - miuHigh) < 2e-10
break;
end
if power < P
miuHigh = miu;
else
miuLow = miu;
end
end
for i = 1 : I
if A(i) == 0
continue;
end
c = C(:, i);
v = (Jkq + (lambdas(i) * delta(i) / 2 + miu) * eye(M)) \ c;
rowOffset = (k - 1) * Q * M + (q - 1) * M;
colOffset = (k - 1) * I + i;
X(rowOffset + 1 : rowOffset + M, colOffset) = v;
end
T(q) = miu;
end
obj = objectiveSubprolem(Q, M, I, V, J, D, L, k);
if abs(obj - prev) < 1e-6
break;
end
prev = obj;
end
end
return
function obj = objectiveSubprolem(Q, M, I, V, J, D, L, k)
obj = 0;
offset = (k - 1) * Q * M;
Jk = J(offset + 1 : offset + Q * M, :);
for i = 1 : I
rowOffset = (k - 1) * Q * M;
colOffset = (k - 1) * I + i;
v = V(rowOffset + 1 : rowOffset + Q * M, colOffset);
obj = obj + real(v' * Jk * v);
offset = (k - 1) * I + i;
d = D(:, offset);
obj = obj - 2 * real(dot(v, d));
for q = 1 : Q
obj = obj + L((k - 1) * Q + q, (k - 1) * I + i) * norm(v((q - 1) * M + 1 : q * M, :));
end
end
return
function y = checkSWMmseConverged(Q, M, I, T, P, V, D, J, L, k)
y = true;
for q = 1 : Q
miu = T(q);
rowOffset = (k - 1) * Q;
colOffset = (k - 1) * I;
lambdas = L(rowOffset + q, colOffset + 1 : colOffset + I);
[C, A] = cvector(Q, M, I, D, J, V, lambdas, k, q);
rowOffset = (k - 1) * Q * M + (q - 1) * M;
colOffset = (q - 1) * M;
Jkq = J(rowOffset + 1 : rowOffset + M, colOffset + 1 : colOffset + M);
for i = 1 : I
rowOffset = (k - 1) * Q * M + (q - 1) * M;
colOffset = (k - 1) * I + i;
v = V(rowOffset + 1 : rowOffset + M, colOffset);
if norm(v) == 0
if norm(C(:, i)) <= lambdas(i) / 2
continue;
else
y = false;
return;
end
else
delta = 1 / norm(v);
target = bisectionTarget(Jkq, C(:, i), delta, lambdas(i), miu);
if abs(target - 1) < 2e-13
continue;
else
y = false;
return;
end
end
end
power = 0;
for i = 1 : I
rowOffset = (k - 1) * Q * M + (q - 1) * M;
colOffset = (k - 1) * I + i;
v = V(rowOffset + 1 : rowOffset + M, colOffset);
power = power + dot(v, v);
end
if abs(miu) < 2e-13 || abs(P - power) < 2e-13
continue;
else
y = false;
return;
end
end
return
function [C, A] = cvector(Q, M, I, D, J, X, lambdas, k, q)
C = zeros(M, I);
for i = 1 : I
rowOffset = (q - 1) * M;
colOffset = (k - 1) * I + i;
d = D(rowOffset + 1 : rowOffset + M, colOffset);
c = d;
for p = 1 : Q
if p == q
continue;
end
rowOffset = (k - 1) * Q * M + (q - 1) * M;
colOffset = (p - 1) * M;
Jkp = J(rowOffset + 1 : rowOffset + M, colOffset + 1 : colOffset + M);
rowOffset = (k - 1) * Q * M + (p - 1) * M;
colOffset = (k - 1) * I + i;
v = X(rowOffset + 1 : rowOffset + M, colOffset);
c = c - Jkp * v;
end
C(:, i) = c;
end
A = zeros(I, 1);
for i = 1 : I
if norm(C(:, i), 2) > lambdas(i) / 2
A(i) = i;
end
end
return
function miuHigh = upperBoundOfMiu(I, P, A, C)
maxc = 0;
nz = 0;
for i = 1 : I
if A(i) == 0
continue;
end
nz = nz + 1;
nc = norm(C(:, i));
if nc > maxc
maxc = nc;
end
end
miuHigh = (P / nz)^(-0.5) * maxc * 1.1;
return
function deltaHigh = upperBoundOfDelta(A, C, I, rho, lambdas, miuHigh)
deltaHigh = zeros(I, 1);
for i = 1 : I
if A(i) == 0
continue;
end
deltaHigh(i) = (rho + miuHigh) / (norm(C(:, i)) - lambdas(i) / 2) * 1.1;
end
return
function rho = spectralRadius(A)
rho = max(abs(eig(A)));
return
function ret = bisectionTarget(Jkq, ciq, delta, lambda, miu)
ret = delta * norm((Jkq + (lambda * delta / 2 + miu) * eye(size(Jkq))) \ ciq);
return