Optimize matrix operations in optimizeMu()

Remove some unnecessary copy operations to speed up runtime when D is large.

@MoDT/optimizeMu.m

@@ -30,8 +30,8 @@
 % some structural information that will be useful for our call to sparse()
 % later. We don't need this for the MEX version, which uses this banded storage
 % format directly.
+nSuperDiag = (size(B_Q,1) - 1) / 2;
 if ~self.use_mex
-    nSuperDiag = (size(B_Q,1) - 1) / 2;
     H_i = bsxfun(@plus, (-nSuperDiag:nSuperDiag)', 1:D*T);
     H_j = repmat(1:D*T, 2*nSuperDiag+1, 1);
     H_mask = (H_i > 0) & (H_i <= D*T);
@@ -49,11 +49,9 @@
     % Make H = Qinv_matrix + Cinv_matrix
     % Get the observation information matrix
     C_k = C(:,:,k);
-    B_C = make_Cinv_matrix( C_k, sum_wzu(:,k) );
+    B_C = make_Cinv_matrix( C_k, sum_wzu(:,k), nSuperDiag );
     % Add the two matrices together to get H
-    B = B_Q;
-    offset = (size(B_Q,1) - size(B_C,1)) / 2;
-    B(offset+1:end-offset,:) = B(offset+1:end-offset,:) + B_C;
+    B = B_Q + B_C;
 
     % Calculate b = C_k \ wzuY(:,:,k)
     b = C_k \ wzuY(:,:,k);
@@ -215,15 +213,16 @@
 end
 
 
-function B = make_Cinv_matrix( C, wzu )
+function B = make_Cinv_matrix( C, wzu, kd )
 % Construct the banded representation of the observation information matrix
-%   B = make_Cinv_matrix( C, wzu )
+%   B = make_Cinv_matrix( C, wzu, kd )
 %
 % Returns:
-%   B       [2*D-1 x D*T] column-major banded storage of a [D*T x D*T] matrix
+%   B       [2*kd+1 x D*T] column-major banded storage of a [D*T x D*T] matrix
 % Required arguments:
 %   C       [D x D] Observation covariance matrix
 %   wzu     [T x 1] weight for each time frame
+%   kd      Number of super-diagonals for the output matrix
 %
 % This represents the [D*T x D*t] observation matrix:
 %   [ wzu(1)*C^-1                                     ]
@@ -241,9 +240,9 @@
 Cinv = (Cinv + Cinv')/2; % Enforce symmetry
 % Convert the [D x D] full format into a [2*D-1 x D] banded format
 D = size(C,1);
-B1 = zeros(2*D-1, D);
-idx = bsxfun(@plus, (1:D)', (D-1:-1:0) + (0:D-1)*size(B1,1));
+B1 = zeros(2*kd+1, D);
+idx = bsxfun(@plus, (1:D)', kd + 1-(1:D) + (0:D-1)*size(B1,1));
 B1(idx) = Cinv(:);
 % Repeat and scale by wzu
-B = kron(wzu', B1);
+B = reshape(B1(:)*wzu', [2*kd+1, D*length(wzu)]);
 end