diff --git a/t.cc b/t.cc
index 2a069b5..318a52a 100644
--- a/t.cc
+++ b/t.cc
@@ -4424,7 +4424,7 @@ cout <<z.norm()<<endl;
 
 }
 
-if(1)
+if(0)
 {
 //tucker test order
 int r,n;
@@ -4451,7 +4451,52 @@ cout<<dec;
 Tensor<double> y = x.inverseTucker(dec,inv);
 cout <<"invTucker\n"<<y;
 cout <<"Error = "<<(x0-y).norm()<<endl;
+
+if(inv==false)
+	{
+	Tensor<double> z = x.linear_transform(dec);
+	cout <<"Error2 = "<<(x0-z).norm()<<endl;
+	}
 }
 
 
+if(1)
+{
+//test linear transform
+int r=3;
+int n,sym;
+cin>>n>>sym;
+NRVec<INDEXGROUP> shape(2);
+        {
+        shape[0].number=r;
+        shape[0].symmetry=sym;
+        shape[0].range=n;
+        shape[0].offset=0;
+        shape[1].number=1;
+        shape[1].symmetry=0;
+        shape[1].range=n;
+        shape[1].offset=0;
+
+        }
+Tensor<double> x(shape);
+x.randomize(1.);
+NRVec<NRMat<double> > t(2);
+t[0].resize(n+2,n); t[0].randomize(1.);
+t[1].resize(n+2,n); t[1].randomize(1.);
+
+Tensor<double> xt=x.linear_transform(t);
+shape.copyonwrite();
+shape[0].range=n+2;
+shape[1].range=n+2;
+Tensor<double> y(shape);
+//this is the most stupid way to compute the transform ;-)
+for(int i=0; i<n+2; ++i) for(int j=0; j<n+2; ++j) for(int k=0; k<n+2; ++k) for(int l=0; l<n+2; ++l)
+	{
+	y.lhs(i,j,k,l)=0;
+	for(int ii=0; ii<n; ++ii) for(int jj=0; jj<n; ++jj) for(int kk=0; kk<n; ++kk) for(int ll=0; ll<n; ++ll)
+		y.lhs(i,j,k,l) += x(ii,jj,kk,ll) * t[0](i,ii) * t[0](j,jj) * t[0](k,kk) * t[1](l,ll) ;
+	}
+cout <<"Error = "<<(xt-y).norm()<<endl;
+}
+
 }//main
diff --git a/tensor.cc b/tensor.cc
index a3993d9..88fb736 100644
--- a/tensor.cc
+++ b/tensor.cc
@@ -1785,7 +1785,6 @@ template<typename T>
 Tensor<T> Tensor<T>::inverseTucker(const NRVec<NRMat<T> > &x, bool inverseorder) const
 {
 if(rank()!=x.size()) laerror("input of inverseTucker does not match rank");
-NRVec<INDEXNAME> names_saved = names;
 Tensor<T> tmp(*this);
 Tensor<T> r;
 if(!is_flat()) laerror("inverseTucker only for flat tensors as produced by Tucker");
@@ -1818,14 +1817,60 @@ for(int i=rank()-1; i>=0; --i)
 if(inverseorder)
         {
         NRPerm<int> p(rank()); p.identity();
-        r.names=names_saved.permuted(p.reverse());
+        r.names=names.permuted(p.reverse());
         }
 else
-        r.names=names_saved;
+        r.names=names;
 return r;
 }
 
 
+template<typename T>
+Tensor<T> Tensor<T>::linear_transform(const NRVec<NRMat<T> > &x) const
+{
+if(x.size()!=shape.size()) laerror("wrong number of transformation matrices in linear_transform");
+for(int i=0; i<shape.size(); ++i) if(x[i].ncols()!=shape[i].range) laerror("mismatch of transformation matrix size in linear_transform");
+
+Tensor<T> tmp(*this);
+Tensor<T> r;
+
+//do the groups in reverse order to preserve index ordering
+for(int g=shape.size()-1; g>=0; --g)
+	{
+	Tensor<T> mat(x[g],true); //flat tensor from a matrix
+	for(int i=shape[g].number-1; i>=0; --i) //indices in the group in reverse order
+		{
+		r= tmp.contraction(indexposition(rank()-1,tmp.shape),mat,INDEX(0,0),(T)1,false,false); //always the last index
+		if(i>0)
+                	{
+                	tmp=r;
+                	r.deallocate();
+			}
+		}
+	//the group's indices are now individual ones leftmost in tensor r, restore group size and symmetry
+	if(shape[g].number>1)
+		{
+		INDEXLIST il(shape[g].number);
+		for(int i=0; i<shape[g].number; ++i)
+			{
+			il[i].group=i;
+			il[i].index=0;
+			}
+		r = r.merge_indices(il,shape[g].symmetry);
+		}
+	if(g>0) 
+		{
+		tmp=r;
+                r.deallocate();
+		}
+	}
+
+r.names=names;
+return r;
+}
+
+
+
 template<typename T> 
 int Tensor<T>::findflatindex(const INDEXNAME nam) const
 {
diff --git a/tensor.h b/tensor.h
index e7152f6..29ab57c 100644
--- a/tensor.h
+++ b/tensor.h
@@ -83,6 +83,15 @@ if(LA_traits<T>::is_complex()) //condition known at compile time
 
 }
 
+
+static inline bool ptr_ok(void *ptr)
+{
+#ifdef DEBUG
+if(ptr==NULL) std::cout<<"Warning: write to nonexistent tensor element ignored\n";
+#endif
+return (bool)ptr;
+}
+
 template<typename T>
 class Signedpointer
 {
@@ -91,11 +100,11 @@ int sgn;
 public:
 	Signedpointer(T *p, int s) : ptr(p),sgn(s) {};
 	//dereferencing *ptr  should be ignored for sgn==0
-	const T operator=(const T rhs) {*ptr = signeddata(sgn,rhs); return rhs;}
-	void operator*=(const T rhs) {*ptr *= rhs;}
-	void operator/=(const T rhs) {*ptr /= rhs;}
-	void operator+=(T rhs) {*ptr += signeddata(sgn,rhs);}
-	void operator-=(T rhs) {*ptr -= signeddata(sgn,rhs);}
+	const T operator=(const T rhs) {if(ptr_ok(ptr)) *ptr = signeddata(sgn,rhs); return rhs;}
+	void operator*=(const T rhs) {if(ptr_ok(ptr)) *ptr *= rhs;}
+	void operator/=(const T rhs) {if(ptr_ok(ptr)) *ptr /= rhs;}
+	void operator+=(T rhs) {if(ptr_ok(ptr)) *ptr += signeddata(sgn,rhs);}
+	void operator-=(T rhs) {if(ptr_ok(ptr)) *ptr -= signeddata(sgn,rhs);}
 };
 
 
@@ -182,6 +191,8 @@ struct  INDEX
 int group;
 int index;
 bool operator==(const INDEX &rhs) const {return group==rhs.group && index==rhs.index;};
+	INDEX() {};
+	INDEX(int g, int i): group(g), index(i) {};
 };
 typedef NRVec<INDEX> INDEXLIST; //collection of several indices
 
@@ -223,13 +234,16 @@ public:
 	int myrank;
 	NRVec<LA_largeindex> groupsizes; //group sizes of symmetry index groups (a function of shape but precomputed for efficiency)
 	NRVec<LA_largeindex> cumsizes; //cumulative sizes of symmetry index groups (a function of shape but precomputed for efficiency); always cumsizes[0]=1, index group 0 is the innermost-loop one
-
-public:
 	NRVec<INDEXNAME> names;
+
+	//indexing
 	LA_largeindex index(int *sign, const SUPERINDEX &I) const; //map the tensor indices to the position in data
 	LA_largeindex index(int *sign, const  FLATINDEX &I) const; //map the tensor indices to the position in data
 	LA_largeindex vindex(int *sign, LA_index i1, va_list args) const; //map list of indices  to the position in data
 	SUPERINDEX inverse_index(LA_largeindex s) const; //inefficient, but possible if needed
+	int myflatposition(int group, int index) const {return flatposition(group,index,shape);};
+	int myflatposition(const INDEX &i) const {return flatposition(i,shape);};
+	INDEX myindexposition(int flatindex) const {return indexposition(flatindex,shape);};	
 
 	//constructors
 	Tensor() : myrank(-1) {};
@@ -273,22 +287,16 @@ public:
 	void deallocate() {data.resize(0); shape.resize(0); groupsizes.resize(0); cumsizes.resize(0); names.resize(0);};
 
         inline Signedpointer<T> lhs(const SUPERINDEX &I) {int sign; LA_largeindex i=index(&sign,I);
-#ifdef DEBUG
-				if(sign==0) laerror("l-value pointer to nonexistent tensor element"); 
-#endif
-				 return Signedpointer<T>(&data[i],sign);};
+				if(sign==0)  return Signedpointer<T>(NULL,sign);
+				else return Signedpointer<T>(&data[i],sign);};
 	inline T operator()(const SUPERINDEX &I) const {int sign; LA_largeindex i=index(&sign,I); if(sign==0) return 0; else return signeddata(sign,data[i]);};
         inline Signedpointer<T> lhs(const FLATINDEX &I) {int sign; LA_largeindex i=index(&sign,I); 
-#ifdef DEBUG
-                                if(sign==0) laerror("l-value pointer to nonexistent tensor element");
-#endif
-				return Signedpointer<T>(&data[i],sign);};
+                                if(sign==0) return Signedpointer<T>(NULL,sign);
+				else return Signedpointer<T>(&data[i],sign);};
         inline T operator()(const FLATINDEX &I) const {int sign; LA_largeindex i=index(&sign,I); if(sign==0) return 0; else return signeddata(sign,data[i]);};
         inline Signedpointer<T> lhs(LA_index i1...) {va_list args; int sign; LA_largeindex i; va_start(args,i1); i= vindex(&sign, i1,args);  
-#ifdef DEBUG
-                                if(sign==0) laerror("l-value pointer to nonexistent tensor element");
-#endif
-				return Signedpointer<T>(&data[i],sign); };
+                                if(sign==0) return Signedpointer<T>(NULL,sign);
+				else return Signedpointer<T>(&data[i],sign); };
         inline T operator()(LA_index i1...) const {va_list args; ; int sign; LA_largeindex i; va_start(args,i1);  i= vindex(&sign, i1,args);  if(sign==0) return 0; else return signeddata(sign,data[i]);};
 	
 	inline Tensor& operator=(const Tensor &rhs) {myrank=rhs.myrank; shape=rhs.shape; groupsizes=rhs.groupsizes; cumsizes=rhs.cumsizes; data=rhs.data; names=rhs.names; return *this;};
@@ -406,6 +414,7 @@ public:
 
 	NRVec<NRMat<T> > Tucker(typename LA_traits<T>::normtype thr=1e-12, bool inverseorder=false); //HOSVD-Tucker decomposition, return core tensor in *this, flattened 
 	Tensor inverseTucker(const NRVec<NRMat<T> > &x, bool inverseorder=false) const; //rebuild the original tensor from Tucker
+	Tensor linear_transform(const NRVec<NRMat<T> > &x) const; //linear transform by a different matrix per each index group, preserving group symmetries
 };