tensor: bugfix in unwind_index and linear_transform of single group

davidson.h

@@ -39,6 +39,7 @@ namespace LA {
 //@@@small matrix gdiagonalize - shift complex roots up (option to gdiagonalize?)
 //@@@test gdiagonalize whether it sorts the roots and what for complex ones
 //@@@implement left eigenvectors for nonsymmetric case
+//@@@implement start from larger Krylov space than a single vector - useful for multiroot solutions
 
 
 //Davidson algorithm: J. Comp. Phys. 17:817 (1975) 

lanczos.h

@@ -24,6 +24,10 @@
 #include "nonclass.h"
 #include "auxstorage.h"
 
+//TODO:
+//@@@implement restart when Krylov space is exceeded
+//@@@implement inital guess of more than 1 vector (also in davidson) and block version of the methods
+
 namespace LA {
 
 //Lanczos diagonalization of hermitean matrix 
@@ -36,7 +40,7 @@ namespace LA {
 template <typename T, typename Matrix>
 extern void lanczos(const Matrix &bigmat, NRVec<T> &eivals, NRVec<T> *eivecs, const char *eivecsfile, 
 		int nroots=1,  const bool verbose=0, const double eps=1e-6,
-	 	const bool incore=1, int maxit=100, const int maxkrylov = 500,
+	 	const bool incore=1, int maxit=100, const int maxkrylov = 1000,
 		void (*initguess)(NRVec<T> &)=NULL, const typename LA_traits<T>::normtype *target=NULL)
 {
 if(!bigmat.issymmetric()) laerror("lanczos only for hermitean matrices");
@@ -46,19 +50,16 @@ if ( n!= (int)bigmat.ncols()) laerror("non-square matrix in lanczos");
 if(eivals.size()<nroots) laerror("too small eivals dimension in lanczos");
 
 NRVec<T> vec1(n),vec2(n);
-NRVec<typename LA_traits<T>::normtype> r(maxkrylov);
 NRVec<T> *v0,*v1;
 AuxStorage<T> *s0,*s1;
 
 if(incore)
 	{
 	v0 = new NRVec<T>[maxkrylov];
-	v1 = new NRVec<T>[maxkrylov];
 	}
 else
 	{
 	s0 = new AuxStorage<T>;
-	s1 = new AuxStorage<T>;
 	}
 
 int i,j;
@@ -67,8 +68,6 @@ if(nroots>=maxkrylov) nroots =maxkrylov-1;
 int  nroot=0;
 int oldnroot;
 
-//@@@@@@@@@@
-#if 0
 
 //default guess based on lowest diagonal element of the matrix
 if(initguess) initguess(vec1);
@@ -81,36 +80,96 @@ else
 	vec1[j]=1;
 	}
 
+NRVec<typename LA_traits<T>::normtype> alpha(maxkrylov),beta(maxkrylov-1);
+
 //initial step
 vec1.normalize();
-bigmat.gemv(0,vec2,'n',1,vec1); //avoid bigmat.operator*(vec), since that needs to allocate another n-sized vector
 if(incore) v0[0]=vec1; else s0->put(vec1,0); 
-if(incore) v1[0]=vec2; else s1->put(vec2,0);
+bigmat.gemv(0,vec2,'n',1,vec1); //avoid bigmat.operator*(vec), since that needs to allocate another n-sized vector
-
+{
+T tmp=vec2*vec1;
+alpha[0]= LA_traits<T>::realpart(tmp);
+if(LA_traits<T>::imagpart(tmp)>1e-6) laerror("matrix probably not hermitian in lanczos");
+}
+vec2.axpy(-alpha[0],vec1); 
 
+NRVec<typename LA_traits<T>::normtype> r(1); r[0]=alpha[0];
+NRVec<typename LA_traits<T>::normtype> rold;
+NRMat<typename LA_traits<T>::normtype> smallV;
+int krylovsize=1;
 //iterative Lanczos
 int it=0;
-for(k=2; k<=maxkrylov;++k)
+for(j=1; j<maxkrylov;++j)
 	{
-	diagonalize3(smallV,r,1,1,krylovsize+1,&smallSwork,1); //for symmetric matrix they have already been sorted to ascending order in lapack
+	++it;		
+	if(it>maxit) {std::cout <<"too many interations in lanczos\n"; flag=1; goto finished;}
+	++krylovsize;
+	//extend the Krylov space (last w vector expected in vec2, last v vector in vec1)
+	beta[j-1] = vec2.norm();
+	if(beta[j-1] > 0)
+		{
+		vec2 /= beta[j-1];
+		}
+	else
+		{
+		laerror("zero norm in lanczos");
+		//could generate an arbitrary vector and orthonormalize it
+		}
+	if(incore) v0[j]=vec2; else s0->put(vec2,j);
+	vec1 *= -beta[j-1];
+	bigmat.gemv(1,vec1,'n',1,vec2);
+	{
+	T tmp=vec1*vec2;
+	alpha[j]= LA_traits<T>::realpart(tmp);
+	if(LA_traits<T>::imagpart(tmp)>1e-6) laerror("matrix probably not hermitian in lanczos");
+	}
+	vec1.axpy(-alpha[j],vec2);
+	vec1.swap(vec2); //move new w vector to vec2, new v vector to vec1
+
+	//diagonalize the tridiagonal
+	smallV.resize(j+1,j+1);
+	rold=r;
+	r=alpha.subvector(0,j);
+	NRVec<typename LA_traits<T>::normtype> rr=beta.subvector(0,j-1);
+	diagonalize3(r,rr,&smallV); 
 	if(target) //resort eigenpairs by distance from the target
 		{
-		NRVec<typename LA_traits<T>::normtype> key(krylovsize+1);
+		NRVec<typename LA_traits<T>::normtype> key(j+1);
-		for(int i=0; i<=krylovsize; ++i) key[i] = abs(r[i] - *target);
+		for(int i=0; i<=j; ++i) key[i] = abs(r[i] - *target);
-		NRPerm<int> p(krylovsize+1);
+		NRPerm<int> p(j+1);
 		key.sort(0,p);
 	
-		NRVec<typename LA_traits<T>::normtype> rp(maxkrylov);
+		NRVec<typename LA_traits<T>::normtype> rp(j+1);
-		NRMat<T> smallVp(maxkrylov,maxkrylov);
+		NRMat<typename LA_traits<T>::normtype> smallVp(j+1,j+1);
-		for(int i=0; i<=krylovsize; ++i)
+		for(int i=0; i<=j; ++i)
 			{
 			rp[i]= r[p[i+1]-1];
-			for(int j=0; j<=krylovsize; ++j) smallVp(j,i) = smallV(j,p[i+1]-1);
+			for(int k=0; k<=j; ++k) smallVp(k,i) = smallV(k,p[i+1]-1);
 			}
 		r = rp;
 		smallV = smallVp;
 		}
 
+       	  if(verbose)
+      	    {
+	    for(int iroot=0; iroot<std::min(krylovsize,nroots); ++iroot)
+       	         {
+       	         std::cout <<"Lanczos: iter="<<it <<" dim="<<krylovsize<<" root="<<iroot<<" eigenvalue="<<r[iroot]<<"\n";
+       	         }
+       	   std::cout.flush();
+       	   }
+	//convergence test when we have enough roots even in rold
+	if(krylovsize>nroots)
+		{
+		bool conv=true;
+		for(int  iroot=0; iroot<nroots; ++iroot)
+			if(abs(r[iroot]-rold[iroot])>eps) conv=false;
+		if(conv)
+			{
+			flag=0;
+			goto converged;
+			}
+		}
 	}
 flag=1;
 goto finished;
@@ -125,7 +184,7 @@ for(nroot=0; nroot<nroots; ++nroot)
 	if(eivecs)
 		{
 		vec1=0;
-		for(j=0; j<=krylovsize; ++j )
+		for(j=0; j<krylovsize; ++j )
 			{
             		if(!incore) s0->get(vec2,j);
 			vec1.axpy(smallV(j,nroot),incore?v0[j]:vec2);
@@ -141,12 +200,10 @@ for(nroot=0; nroot<nroots; ++nroot)
 
 if(eivecsfile) delete ev;
 
-//@@@@
-#endif
 
 finished:
-if(incore) {delete[] v0; delete[] v1;}
+if(incore) {delete[] v0;}
-else  {delete s0; delete s1;}
+else  {delete s0;}
 
 if(flag) laerror("no convergence in lanczos");
 }

t.cc

@@ -4502,9 +4502,43 @@ cout <<"Error = "<<(xt-y).norm()<<endl;
 
 if(0)
 {
-//n must not be too small
 int n,m;
-cin>>n >>m;
+bool which;
+cin>>n >>m >>which;
+NRSMat<double> a(n);
+NRVec<double> rr(n);
+
+for(int i=0;i<n;++i) for(int j=0;j<=i;++j)
+        {
+        a(i,j)= RANDDOUBLE();
+	if(i==j) a(i,i)+= .5*(i-n*.5);
+        }
+
+NRSMat<double> aa;
+NRMat<double> vv(n,n);
+aa=a; diagonalize(aa,rr,&vv);
+NRVec<double> r(m);
+NRVec<double> *eivecs = new NRVec<double>[m];
+cout <<"Exact energies " <<rr<<endl;
+
+if(which) lanczos(a,r,eivecs,NULL,m,1,1e-6,1,200,300);
+else davidson(a,r,eivecs,NULL,m,1,1e-6,1,200,300);
+cout <<"Iterative energies " <<r;
+cout <<"Eigenvectors compare:\n";
+for(int i=0; i<m; ++i)
+        {
+        cout <<eivecs[i];
+        for(int j=0; j<n;++j) cout <<vv[j][i]<<" ";
+        cout <<endl;
+        }
+
+}
+
+if(0)
+{
+int n,m;
+bool which;
+cin>>n >>m>>which ;
 NRSMat<complex<double> > a(n);
 a.randomize(.1);
 
@@ -4522,9 +4556,10 @@ cout <<"Exact energies "<<rr;
 
 NRVec<complex<double> > r(m);
 NRVec<complex<double> > *eivecs = new NRVec<complex<double> >[m];
-davidson(a,r,eivecs,NULL,m,true,1e-5,true,10*n,n);
+if(which) lanczos(a,r,eivecs,NULL,m,true,1e-5,true,10*n,n);
+else davidson(a,r,eivecs,NULL,m,true,1e-5,true,10*n,n);
 
-cout <<"Davidson energies " <<r;
+cout <<"Davidson/Lanczos energies " <<r;
 cout <<"Exact energies "<<rr;
 
 cout <<"Eigenvectors compare:\n";
@@ -4539,27 +4574,52 @@ for(int i=0; i<m; ++i)
 
 if(1)
 {
-int n,m;
+int r,n,sym;
-cin>>n >>m;
+cin>>r>>n>>sym;
-NRSMat<double> a(n);
+NRVec<INDEXGROUP> shape(3);
-NRVec<double> rr(n);
+	shape[0].number=2; 
+        shape[0].symmetry=0;
+        shape[0].range=n+1;
+        shape[0].offset=0;
 
-for(int i=0;i<n;++i) for(int j=0;j<=i;++j)
+        shape[1].number=r;
-        {
+        shape[1].symmetry= sym;
-        a(i,j)= RANDDOUBLE();
+        shape[1].range=n;
-	if(i==j) a(i,i)+= .5*(i-n*.5);
+        shape[1].offset=0;
-        }
+
+        shape[2].number=2;
+        shape[2].symmetry=0;
+        shape[2].range=n+2;
+        shape[2].offset=0;
+
+
+Tensor<double> x(shape); x.randomize(1.);
+x.defaultnames();
+cout <<"x= "<<x.shape << " "<<x.names<<endl;
+
+NRVec<INDEXGROUP> yshape(2);
+        yshape[0].number=1; 
+        yshape[0].symmetry=0;
+        yshape[0].range=n;
+        yshape[0].offset=0;
+        
+        yshape[1].number=1; 
+        yshape[1].symmetry= 0;
+        yshape[1].range=n+3;
+        yshape[1].offset=0;
+
+Tensor<double> y(yshape); y.randomize(1.);
+
+INDEX posit(1,0);
+//Tensor<double> z=x.unwind_index(1,1);
+//Tensor<double> z=x.contraction(INDEX(1,1),y,INDEX(0,0),1,false,false);
+Tensor<double> z=x.linear_transform(1,y);
+
+cout <<z.shape;
+
+//check
 
-NRSMat<double> aa;
-NRMat<double> vv(n,n);
-aa=a; diagonalize(aa,rr,&vv);
-NRVec<double> r(m);
-NRVec<double> *eivecs = new NRVec<double>[m];
-double target= 0;
-cout <<"Exact energies " <<rr<<endl;
 
-davidson(a,r,eivecs,NULL,m,1,1e-6,1,200,300,(void (*)(LA::NRVec<double>&))NULL,&target);
-cout <<"Davidson energies " <<r;
 }
 
 }//main

tensor.cc

@@ -713,6 +713,9 @@ return q;
 template<typename T>
 Tensor<T> Tensor<T>::permute_index_groups(const NRPerm<int> &p) const
 {
+if(p.size()!=shape.size()) laerror("permutation size mismatch in permute_index_groups");
+if(p.is_identity()) return *this;
+
 //std::cout <<"permute_index_groups permutation = "<<p<<std::endl;
 NRVec<INDEXGROUP> newshape=shape.permuted(p,true);
 //std::cout <<"permute_index_groups newshape = "<<newshape<<std::endl;
@@ -836,6 +839,7 @@ if(group==0 && index==0 && shape[0].symmetry==0) //formal split of 1 index witho
 	}
 if(shape[group].number==1) return unwind_index_group(group); //single index in the group
 
+
 //general case - recalculate the shape and allocate the new tensor
 NRVec<INDEXGROUP> newshape(shape.size()+1);
 newshape[0].number=1;
@@ -856,7 +860,10 @@ for(int i=0; i<shape.size(); ++i)
 		--newshape[i+1].number;
 		flatindex += index;
 		}
-	else flatindex += shape[i].number;
+	else 
+		{
+		if(i<group) flatindex += shape[i].number;
+		}
 	}
 
 
@@ -1840,6 +1847,10 @@ 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
 		{
+#ifdef LA_TENSOR_INDEXPOSITION
+		//what should we do with index position?
+		//either set upperindex of mat appropriately, or request ignoring that in contractions?
+#endif
 		r= tmp.contraction(indexposition(rank()-1,tmp.shape),mat,INDEX(0,0),(T)1,false,false); //always the last index
 		if(i>0)
                 	{
@@ -1870,6 +1881,59 @@ return r;
 }
 
 
+template<typename T>
+Tensor<T> Tensor<T>::linear_transform(const int g, const Tensor<T> &x) const
+{
+if(g<0||g>=shape.size()) laerror("wrong index group number in linear_transform");
+if(x.rank()!=2 || x.shape.size()!=2 || x.shape[0].number!=1||x.shape[1].number!=1) laerror("wrong tensor shape for linear_transform");
+if(x.shape[0].range!=shape[g].range) laerror("index range mismatch in linear_transform");
+
+Tensor<T> tmp(*this);
+Tensor<T> r;
+
+
+//contract all indices in the reverse order
+	int gnow=g;
+	for(int i=shape[g].number-1; i>=0; --i) //indices in the group in reverse order
+		{
+		r= tmp.contraction(INDEX(gnow,i),x,INDEX(0,0),(T)1,false,false);
+		++gnow; //new group number in r, one index was added left
+		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);
+		}
+
+//permute the group (now 0) to its original position
+if(g!=0)
+	{
+	NRPerm<int> p(r.shape.size());
+	for(int i=0; i<g; ++i) p[i+1] = (i+1)+1;
+	p[g+1]=1;
+	for(int i=g+1; i<r.shape.size();++i) p[i+1] = i+1;
+	//std::cout<<"perm "<<p;
+	r=r.permute_index_groups(p);
+	}
+
+//preserve names
+r.names=names;
+
+return r;
+}
+
+
 
 template<typename T> 
 int Tensor<T>::findflatindex(const INDEXNAME nam) const

tensor.h

@@ -421,6 +421,8 @@ 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
+	Tensor linear_transform(const int g, const Tensor<T> &x) const; //linear transform a single group, preserve its position and symmetry, x must be rank-2 flat tensor (this is useful for raising/lowering indices)
+	Tensor linear_transform(const int g, const NRMat<T> &x) const {Tensor<T> mat(x,true); return linear_transform(g,mat);}; //linear transform a single group, preserve its position and symmetry
 };