added gram-schmidt

common/gsog.m

@@ -0,0 +1,13 @@
+function [Q, R] = gsog(X)
+% Gram-Schmidt orthogonalization
+[d,n] = size(X);
+m = min(d,n);
+R = eye(m,n);
+Q = zeros(d,m);
+D = zeros(1,m);
+for i = 1:m
+    R(1:i-1,i) = bsxfun(@times,Q(:,1:i-1),1./D(1:i-1))'*X(:,i);
+    Q(:,i) = X(:,i)-Q(:,1:i-1)*R(1:i-1,i);
+    D(i) = dot(Q(:,i),Q(:,i));
+end
+R(:,m+1:n) = bsxfun(@times,Q,1./D)'*X(:,m+1:n);

common/gson.m

@@ -0,0 +1,13 @@
+function [Q, R] = gson(X)
+% Gram-Schmidt orthonormalization which produces the same result as [Q,R]=qr(X,0)
+[d,n] = size(X);
+m = min(d,n);
+R = zeros(m,n);
+Q = zeros(d,m);
+for i = 1:m
+    R(1:i-1,i) = Q(:,1:i-1)'*X(:,i);
+    v = X(:,i)-Q(:,1:i-1)*R(1:i-1,i);
+    R(i,i) = norm(v);
+    Q(:,i) = v/R(i,i);
+end
+R(:,m+1:n) = Q'*X(:,m+1:n);

common/mgsog.m

@@ -0,0 +1,17 @@
+function [Q, R] = mgsog(X)
+% Modified Gram-Schmidt orthogonalization
+[d,n] = size(X);
+m = min(d,n);
+R = eye(m,n);
+Q = zeros(d,m);
+D = zeros(1,m);
+for i = 1:m
+    v = X(:,i);
+    for j = 1:i-1
+        R(j,i) = Q(:,j)'*v/D(j);
+        v = v-R(j,i)*Q(:,j);
+    end
+    Q(:,i) = v;
+    D(i) = dot(Q(:,i),Q(:,i));
+end
+R(:,m+1:n) = bsxfun(@times,Q,1./D)'*X(:,m+1:n);

common/mgson.m

@@ -0,0 +1,17 @@
+function [Q, R] = mgson(X)
+% Modified Gram-Schmidt orthonormalization (numerical stable version of Gram-Schmidt algorithm) 
+% which produces the same result as [Q,R]=qr(X,0)
+[d,n] = size(X);
+m = min(d,n);
+R = zeros(m,n);
+Q = zeros(d,m);
+for i = 1:m
+    v = X(:,i);
+    for j = 1:i-1
+        R(j,i) = Q(:,j)'*v;
+        v = v-R(j,i)*Q(:,j);
+    end
+    R(i,i) = norm(v);
+    Q(:,i) = v/R(i,i);
+end
+R(:,m+1:n) = Q'*X(:,m+1:n);

common/unitize.m

@@ -7,5 +7,5 @@
     dim = find(size(X)~=1,1);
     if isempty(dim), dim = 1; end
 end
-s = sqrt(sum(X.^2,dim));
+s = sqrt(dot(X,X,dim));
 Y = bsxfun(@times,X,1./s);