tensor: contractions over severeal indices implemented

t.cc

@@ -3316,7 +3316,12 @@ bg.range=n;
 Tensor<double> b(bg);
 b.randomize(1.);
 
-Tensor<double> cc = a.contraction(0,0,b,0,1);
+INDEXLIST il1(1);
+il1[0]={0,0};
+INDEXLIST il2(1);
+il2[0]={0,1};
+Tensor<double> cc = a.contractions(il1,b,il2);
+//Tensor<double> cc = a.contraction(0,0,b,0,1);
 cout <<cc;
 
 INDEXGROUP cga;
@@ -3344,7 +3349,7 @@ for(int i=0; i<n; ++i)
 					{
 					for(int p=0; p<n; ++p)
 						c.lhs(m,l,k,j,i) += a(p,i,j,k) * b(m,p,l);
-					if(abs(c(m,l,k,j,i)-cc(m,l,k,j,i))>1e-13) laerror("internal error in conntraction");
+					if(abs(c(m,l,k,j,i)-cc(m,l,k,j,i))>1e-13) laerror("internal error in contraction");
 					}
 
 //cout <<c;
@@ -3352,4 +3357,32 @@ for(int i=0; i<n; ++i)
 
 //test Tensor apply_permutation_algebra
 
+//test unwind_indices
+if(0)
+{
+int n=5;
+INDEXGROUP g;
+g.number=4;
+g.symmetry= -1;
+g.offset=0;
+g.range=n;
+
+Tensor<double> e(g);
+e.randomize(1.);
+INDEXLIST il(2);
+il[0]= {0,1};
+il[1]= {0,3};
+Tensor<double> eu = e.unwind_indices(il);
+
+for(int i=0; i<n; ++i)
+        for(int j=0; j<n; ++j)
+                for(int k=0; k<n; ++k)
+                        for(int l=0; l<n; ++l)
+                                {
+				if(e(i,j,k,l)!=eu(j,l,i,k)) laerror("error in unwind_indces");
+				}
+cout <<e;
+cout <<eu;
+}
+
 }

tensor.cc

@@ -567,6 +567,22 @@ for(int i=0; i<I.size(); ++i)
 return J;
 }
 
+int flatposition(const INDEX &i, const NRVec<indexgroup> &shape)
+{
+int ii=0;
+for(int g=0; g<i.group; ++g) ii+= shape[g].number;
+ii += i.index;
+return ii;
+}
+
+int flatposition(int group, int index, const NRVec<indexgroup> &shape)
+{
+int ii=0;
+for(int g=0; g<group; ++g) ii+= shape[g].number;
+ii += index;
+return ii;
+}
+
 
 template<typename T>
 static void unwind_callback(const SUPERINDEX &I, T *v)
@@ -648,7 +664,119 @@ return r;
 
 
 template<typename T>
-static void auxmatmult(int nn, int mm, int kk, T *r, T *a, T *b,  T alpha=1, T beta=0, bool conjugate=false) //R(nn,mm) = A * B^T
+Tensor<T> Tensor<T>::unwind_indices(const INDEXLIST &il) const
+{
+if(il.size()==0) return *this;
+if(il.size()==1) return unwind_index(il[0].group,il[0].index);
+
+for(int i=0; i<il.size(); ++i)
+	{
+	if(il[i].group<0||il[i].group>=shape.size()) laerror("wrong group number in unwind_indices");
+	if(il[i].index<0||il[i].index>=shape[il[i].group].number)  laerror("wrong index number in unwind_indices");
+	}
+
+//all indices are solo in their groups - permute groups
+bool sologroups=true;
+int nonsolo=0;
+for(int i=0; i<il.size(); ++i)
+	if(shape[il[i].group].number!=1) {sologroups=false; ++nonsolo;}
+if(sologroups)
+	{
+	NRPerm<int> p(shape.size());
+	bitvector waslisted(shape.size());
+	waslisted.clear();
+	for(int i=0; i<il.size(); ++i) 
+		{
+		p[1+i] = 1+il[i].group;
+		waslisted.set(il[i].group);
+		}
+	int ii=il.size();
+	for(int i=0; i<shape.size(); ++i)
+		{
+		if(!waslisted[i])
+			{
+			waslisted.set(i);
+			p[1+ii] = 1+i;
+			ii++;
+			}
+		}
+
+	if(!p.is_valid()) laerror("internal error in unwind_indices");
+	if(p.is_identity()) return *this;
+	else return permute_index_groups(p);
+	}
+
+
+//general case - recalculate the shape and allocate the new tensor
+NRVec<indexgroup> oldshape(shape); 
+oldshape.copyonwrite();
+NRVec<indexgroup> newshape(shape.size()+nonsolo);
+
+//first the unwound indices as solo groups
+for(int i=0; i<il.size(); ++i)
+	{
+	newshape[i].number=1;
+	newshape[i].symmetry=0;
+	newshape[i].range=shape[il[i].group].range;
+#ifndef LA_TENSOR_ZERO_OFFSET
+	newshape[i].offset = shape[il[i].group].offset;
+#endif
+	oldshape[il[i].group].number --;
+	}
+
+//then the remaining groups with one index removed, if nonempty
+int ii=il.size();
+for(int i=0; i<oldshape.size(); ++i)
+	if(oldshape[i].number>0)
+		{
+		newshape[ii++] = oldshape[i];
+		}
+
+Tensor<T> r(newshape);
+if(r.rank()!=rank()) laerror("internal error 2 in unwind_indces");
+
+//compute the corresponding permutation of FLATINDEX for use in the callback
+NRPerm<int> indexperm(rank());
+bitvector waslisted(rank());
+waslisted.clear();
+//first unwound indices
+ii=0;
+for(int i=0; i<il.size(); ++i)
+	{
+	int pos= flatposition(il[i],shape);
+	indexperm[1+ii] = 1+pos;
+	waslisted.set(pos);
+	++ii;
+	}
+
+//the remaining index groups
+for(int g=0; g<shape.size(); ++g)
+	for(int i=0; i<shape[g].number; ++i)
+		{
+		int pos= flatposition(g,i,shape);
+		if(!waslisted[pos])
+			{
+			waslisted.set(pos);
+			indexperm[1+ii] = 1+pos;
+			++ii;	
+			}
+		}
+
+if(!indexperm.is_valid()) 
+	{
+	std::cout << "indexperm = "<<indexperm<<std::endl;
+	laerror("internal error 3 in unwind_indices");
+	}
+
+//loop recursively and do the unwinding
+help_tt<T> = this;
+help_p = &indexperm;
+r.loopover(unwind_callback);
+return r;
+}
+
+template<typename T>
+static void auxmatmult(int nn, int mm, int kk, T *r, T *a, T *b,  T alpha=1, T beta=0, bool conjugate=false) //R(nn,mm) = A(nn,kk) * B^T(mm,kk)
 {
 for(int i=0; i<nn; ++i) for(int j=0; j<mm; ++j)
 	{
@@ -680,7 +808,7 @@ cblas_zgemm(CblasRowMajor, CblasNoTrans, (conjugate?CblasConjTrans:CblasTrans),
 //The index unwinding is unfortunately a big burden, and in principle could be eliminated in case of non-symmetric indices
 //
 template<typename T>
-void Tensor<T>::addcontraction(const Tensor &rhs1, int group, int index, const Tensor &rhs, int rhsgroup, int rhsindex, T alpha, T beta, bool doresize, bool conjugate)
+void Tensor<T>::addcontraction(const Tensor &rhs1, int group, int index, const Tensor &rhs, int rhsgroup, int rhsindex, T alpha, T beta, bool doresize, bool conjugate1, bool conjugate)
 {
 if(group<0||group>=rhs1.shape.size()) laerror("wrong group number in contraction");
 if(rhsgroup<0||rhsgroup>=rhs.shape.size()) laerror("wrong rhsgroup number in contraction");
@@ -690,6 +818,7 @@ if(rhs1.shape[group].offset != rhs.shape[rhsgroup].offset) laerror("incompatible
 if(rhs1.shape[group].range != rhs.shape[rhsgroup].range) laerror("incompatible index range in contraction");
 
 Tensor<T> u = rhs1.unwind_index(group,index);
+if(conjugate1) u.conjugateme();
 Tensor<T> rhsu = rhs.unwind_index(rhsgroup,rhsindex);
 
 
@@ -709,7 +838,7 @@ else
 	}
 int nn,mm,kk;
 kk=u.groupsizes[0];
-if(kk!=rhsu.groupsizes[0]) laerror("internal error in contraction");
+if(kk!=rhsu.groupsizes[0]) laerror("internal error in addcontraction");
 nn=1; for(int i=1; i<u.shape.size(); ++i) nn*= u.groupsizes[i];
 mm=1; for(int i=1; i<rhsu.shape.size(); ++i) mm*= rhsu.groupsizes[i];
 data.copyonwrite();
@@ -717,6 +846,59 @@ auxmatmult<T>(nn,mm,kk,&data[0],&u.data[0], &rhsu.data[0],alpha,beta,conjugate);
 }
 
 
+template<typename T>
+void Tensor<T>::addcontractions(const Tensor &rhs1, const INDEXLIST &il1, const Tensor &rhs2, const INDEXLIST &il2,  T alpha, T beta, bool doresize, bool conjugate1, bool conjugate2)
+{
+if(il1.size()==0) laerror("empty contraction - outer product not implemented");
+if(il1.size()!=il2.size()) laerror("mismatch in index lists in addcontractions");
+for(int i=0; i<il1.size(); ++i)
+	{
+	if(il1[i].group<0||il1[i].group>=rhs1.shape.size()) laerror("wrong group1 number in contractions");
+	if(il2[i].group<0||il2[i].group>=rhs2.shape.size()) laerror("wrong group2 number in contractions");
+	if(il1[i].index<0||il1[i].index>=rhs1.shape[il1[i].group].number)  laerror("wrong index1 number in conntractions");
+	if(il2[i].index<0||il2[i].index>=rhs2.shape[il2[i].group].number)  laerror("wrong index2 number in conntractions");
+	if(rhs1.shape[il1[i].group].offset != rhs2.shape[il2[i].group].offset) laerror("incompatible index offset in contractions");
+	if(rhs1.shape[il1[i].group].range  != rhs2.shape[il2[i].group].range) laerror("incompatible index range in contractions");
+	}
+
+Tensor<T> u = rhs1.unwind_indices(il1);
+if(conjugate1) u.conjugateme();
+Tensor<T> rhsu = rhs2.unwind_indices(il2);
+
+
+NRVec<indexgroup> newshape(u.shape.size()+rhsu.shape.size()-2*il1.size());
+int ii=0;
+for(int i=il1.size(); i<rhsu.shape.size(); ++i) newshape[ii++] = rhsu.shape[i];
+for(int i=il1.size(); i<u.shape.size(); ++i) newshape[ii++] = u.shape[i]; //this tensor will have more significant indices than the rhs one
+
+if(doresize)
+	{
+	if(beta!= (T)0) laerror("resize in addcontractions requires beta=0");
+	resize(newshape);
+	}
+else
+	{
+	if(shape!=newshape) laerror("tensor shape mismatch in addcontraction");
+	}
+int nn,mm,kk;
+kk=1;
+int kk2=1;
+for(int i=0; i<il1.size(); ++i)
+	{
+	kk *= u.groupsizes[i];
+	kk2 *= rhsu.groupsizes[i];
+	}
+if(kk!=kk2) laerror("internal error in addcontractions");
+
+nn=1; for(int i=il1.size(); i<u.shape.size(); ++i) nn*= u.groupsizes[i];
+mm=1; for(int i=il1.size(); i<rhsu.shape.size(); ++i) mm*= rhsu.groupsizes[i];
+data.copyonwrite();
+auxmatmult<T>(nn,mm,kk,&data[0],&u.data[0], &rhsu.data[0],alpha,beta,conjugate2);
+}
+
+
+
+
 template<typename T>
 static const PermutationAlgebra<int,T> *help_pa;
 

tensor.h

@@ -36,6 +36,9 @@
 #include "smat.h"
 #include "miscfunc.h"
 
+//@@@todo - outer product
+//@@@permutation of individual indices??? how to treat the symmetry groups
+//@@@todo - index names and contraction by named index list
 
 namespace LA {
 
@@ -98,6 +101,15 @@ class LA_traits<indexgroup> {
 typedef NRVec<LA_index> FLATINDEX; //all indices but in a single vector
 typedef NRVec<NRVec<LA_index> > SUPERINDEX; //all indices in the INDEXGROUP structure
 typedef NRVec<LA_largeindex> GROUPINDEX; //set of indices in the symmetry groups
+struct  INDEX
+{
+int group;
+int index;
+};
+typedef NRVec<INDEX> INDEXLIST; //collection of several indices
+
+int flatposition(const INDEX &i, const NRVec<indexgroup> &shape); //position of that index in FLATINDEX
+int flatposition(const INDEX &i, const NRVec<indexgroup> &shape);
 
 FLATINDEX superindex2flat(const SUPERINDEX &I);
 
@@ -184,8 +196,12 @@ public:
 
 	Tensor permute_index_groups(const NRPerm<int> &p) const; //rearrange the tensor storage permuting index groups as a whole
 	Tensor unwind_index(int group, int index) const; //separate an index from a group and expand it to full range as the least significant one
-	void addcontraction(const Tensor &rhs1, int group, int index, const Tensor &rhs, int rhsgroup, int rhsindex, T alpha=1, T beta=1, bool doresize=false, bool conjugate=false);
+	Tensor unwind_indices(const INDEXLIST &il) const; //the same for a list of indices
-	inline Tensor contraction(int group, int index, const Tensor &rhs, int rhsgroup, int rhsindex, T alpha=1, bool conjugate=false) const {Tensor<T> r; r.addcontraction(*this,group,index,rhs,rhsgroup,rhsindex,alpha,0,true, conjugate); return r; }
+	void addcontraction(const Tensor &rhs1, int group, int index, const Tensor &rhs2, int rhsgroup, int rhsindex, T alpha=1, T beta=1, bool doresize=false, bool conjugate1=false, bool conjugate=false); //rhs1 will have more significant non-contracted indices in the result than rhs2
+	inline Tensor contraction(int group, int index, const Tensor &rhs, int rhsgroup, int rhsindex, T alpha=1, bool conjugate1=false, bool conjugate=false) const {Tensor<T> r; r.addcontraction(*this,group,index,rhs,rhsgroup,rhsindex,alpha,0,true, conjugate1, conjugate); return r; };
+
+	void addcontractions(const Tensor &rhs1, const INDEXLIST &il1, const Tensor &rhs2, const INDEXLIST &il2,  T alpha=1, T beta=1, bool doresize=false, bool conjugate1=false, bool conjugate2=false);
+	inline Tensor contractions( const INDEXLIST &il1, const Tensor &rhs2, const INDEXLIST &il2,  T alpha=1, bool conjugate1=false, bool conjugate2=false) const {Tensor<T> r; r.addcontractions(*this,il1,rhs2,il2,alpha,0,true,conjugate1, conjugate2); return r; };
 
 	void apply_permutation_algebra(const  Tensor &rhs, const PermutationAlgebra<int,T> &pa, bool inverse=false, T alpha=1, T beta=0); //general (not optimally efficient) symmetrizers, antisymmetrizers etc. acting on the flattened index list:
 //								 this *=beta; for I over this: this(I) += alpha * sum_P c_P rhs(P(I))

vec.cc

@@ -909,6 +909,7 @@ void NRVec<T>::storesubvector(const NRVec<int> &selection, const NRVec &rhs)
  ******************************************************************************/
 template<typename T>
 NRVec<T>& NRVec<T>::conjugateme() {
+copyonwrite();
 #ifdef CUDALA
         if(location != cpu) laerror("general conjugation only on CPU");
 #endif