1089 lines
28 KiB
C++
1089 lines
28 KiB
C++
#include <string>
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#include <cmath>
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#include <complex>
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#include <iostream>
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#include "sparsemat.h"
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//////////////////////////////////////////////////////////////////////////////
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//// forced instantization in the corresponding object file
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template SparseMat<double>;
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template SparseMat< complex<double> >;
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#ifdef _GLIBCPP_NO_TEMPLATE_EXPORT
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# define export
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#endif
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export template <class T>
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ostream& operator<<(ostream &s, const SparseMat<T> &x)
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{
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SPMatindex n,m;
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n=x.nrows();
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m=x.ncols();
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s << (int)n << ' ' << (int)m << '\n';
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matel<T> *list=x.getlist();
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while(list)
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{
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s << (int)list->row << ' ' << (int)list->col << ' ' << list->elem << '\n';
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list=list->next;
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}
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s << "-1 -1\n";
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return s;
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}
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export template <class T>
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istream& operator>>(istream &s, SparseMat<T> &x)
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{
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int i,j;
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int n,m;
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matel<T> *l=NULL;
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s >> n >> m;
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x.resize(n,m);
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s >> i >> j;
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while(i>=0 && j>=0)
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{
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matel<T> *ll = l;
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l= new matel<T>;
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l->next= ll;
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l->row=i;
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l->col=j;
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s >> l->elem;
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s >> i >> j;
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}
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x.setlist(l);
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return s;
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}
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//helpers to be used from different functions
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export template <class T>
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void SparseMat<T>::unsort()
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{
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if(symmetric) colsorted=NULL;
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if(colsorted) delete[] colsorted;
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if(rowsorted) delete[] rowsorted;
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colsorted=rowsorted=NULL;
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nonzero=0;
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}
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export template <class T>
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void SparseMat<T>::deletelist()
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{
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if(colsorted||rowsorted) unsort();//prevent obsolete pointers
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if(*count >1) laerror("trying to delete shared list");
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matel<T> *l=list;
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while(l)
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{
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matel<T> *ltmp=l;
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l=l->next;
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delete ltmp;
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}
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list=NULL;
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delete count;
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count=NULL;
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}
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//no checks, not to be public
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export template <class T>
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void SparseMat<T>::copylist(const matel<T> *l)
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{
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list=NULL;
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while(l)
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{
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add(l->row,l->col,l->elem);
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l=l->next;
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}
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}
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export template <class T>
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void SparseMat<T>::copyonwrite()
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{
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if(!count) laerror("probably an assignment to undefined sparse matrix");
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if(*count > 1)
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{
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(*count)--;
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count = new int; *count=1;
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if(!list) laerror("empty list with count>1");
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unsort();
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copylist(list);
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}
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}
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//global for sort !!! is not thread-safe
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static void *globsorted;
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//global functions cannot be partially specialized in templates, we have to make it a member function
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//!!! gencmp's and genswap are critical for performance, make sure that compiler really inlines them
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template<class T, int type>
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struct gencmp {
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inline static SPMatindexdiff EXEC(register const SPMatindex i, register const SPMatindex j)
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{
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register SPMatindexdiff k;
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register matel<T> *ii,*jj;
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ii=((matel<T> **)globsorted)[i];
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jj=((matel<T> **)globsorted)[j];
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if (k=ii->col-jj->col) return k; else return ii->row-jj->row;}
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};
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template<class T>
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struct gencmp<T,0> {
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inline static SPMatindexdiff EXEC(register const SPMatindex i, register const SPMatindex j)
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{
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register SPMatindexdiff k;
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register matel<T> *ii,*jj;
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ii=((matel<T> **)globsorted)[i];
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jj=((matel<T> **)globsorted)[j];
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if (k=ii->row-jj->row) return k; else return ii->col-jj->col;}
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};
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template<class T>
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inline void genswap(const SPMatindex i,const SPMatindex j)
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{
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SWAP(((matel<T> **)globsorted)[i],((matel<T> **)globsorted)[j]);
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}
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template<class T, int type>
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void genqsort(SPMatindex l,SPMatindex r) /*safer version for worst case*/
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{
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register SPMatindex i,j,piv;
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/* other method for small arrays recommended in NUMREC is not used here
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does not give so large gain for moderate arrays and complicates the
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things, but would be worth trying (cf. profile) */
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if(r<=l) return; /*1 element*/
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if(gencmp<T,type>::EXEC(r,l)<0) genswap<T>(l,r);
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if(r-l==1) return; /*2 elements and preparation for median*/
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piv= (l+r)/2; /*pivoting by median of 3 - safer */
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if(gencmp<T,type>::EXEC(piv,l)<0) genswap<T>(l,piv); /*and change the pivot element implicitly*/
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if(gencmp<T,type>::EXEC(r,piv)<0) genswap<T>(r,piv); /*and change the pivot element implicitly*/
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if(r-l==2) return; /*in the case of 3 elements we are finished too */
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/*general case , l-th r-th already processed*/
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i=l+1; j=r-1;
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do{
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/*important sharp inequality - stops at sentinel element for efficiency*/
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/* this is inefficient if all keys are equal - unnecessary n log n swaps are done, but we assume that it is atypical input*/
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while(gencmp<T,type>::EXEC(i++,piv)<0);
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i--;
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while(gencmp<T,type>::EXEC(j--,piv)>0);
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j++;
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if(i<j)
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{
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/* swap and keep track of position of pivoting element */
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genswap<T>(i,j);
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if(i==piv) piv=j; else if(j==piv) piv=i;
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}
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if(i<=j) {i++; j--;}
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}while(i<=j);
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if(j-l < r-i) /*because of the stack in bad case process first the shorter subarray*/
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{if(l<j) genqsort<T,type>(l,j); if(i<r) genqsort<T,type>(i,r);}
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else
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{if(i<r) genqsort<T,type>(i,r); if(l<j) genqsort<T,type>(l,j);}
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}
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export template <class T>
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unsigned int SparseMat<T>::length() const
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{
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if(nonzero) return nonzero;
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unsigned int n=0;
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matel<T> *l=list;
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while(l)
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{
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++n;
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l=l->next;
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}
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const_cast<SparseMat<T> *>(this)->nonzero=n;
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return n;
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}
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export template <class T>
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unsigned int SparseMat<T>::sort(int type) const //must be const since used from operator* which must be const to be compatible with other stuff, dirty casts here
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{
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if(type==0&&rowsorted || type==1&&colsorted) return nonzero;
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if(!list) return ((SparseMat<T> *)this)->nonzero=0;
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if(type!=2) const_cast<SparseMat<T> *>(this) ->setunsymmetric(); else type=0;//symmetric and sorted not supported simultaneously, type 2 is special just for simplify
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//create array from list, reallocate as necessary
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unsigned int size=3*MAX(nn,mm); //initial guess for a number of nonzero elements
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matel<T> **sorted= new matel<T>* [size];
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((SparseMat<T> *)this)->nonzero=0;
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matel<T> *l = list;
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while(l)
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{
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sorted[(((SparseMat<T> *)this)->nonzero)++]=l;
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if(nonzero >= size ) //reallocate
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{
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size*=2;
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matel<T> **newsorted= new matel<T>* [size];
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memcpy(newsorted,sorted,size/2*sizeof(matel<T>*));
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delete[] sorted;
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sorted=newsorted;
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}
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l= l->next;
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}
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//now sort the array of pointers according to type
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globsorted =sorted;
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if(type==0) {genqsort<T,0>(0,nonzero-1); ((SparseMat<T> *)this)->rowsorted=sorted;} //type handled at compile time for more efficiency
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else {genqsort<T,1>(0,nonzero-1); ((SparseMat<T> *)this)->colsorted=sorted;} //should better be const cast
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//cout <<"sort: nonzero ="<<nonzero<<"\n";
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return nonzero; //number of (in principle) nonzero elements
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}
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export template <class T>
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void SparseMat<T>::simplify()
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{
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unsigned int n;
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if(!list) return;
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copyonwrite();
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if(symmetric)
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{
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unsort();
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matel<T> *p;
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p=list;
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while(p)
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{
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if(p->row>p->col) SWAP(p->row,p->col); //get into one triangle, not OK for complex hermitean
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p=p->next;
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}
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n=sort(2); //sort and further handle like a triangle matrix
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}
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else n=sort(0); //sorts according to row,column
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unsigned int i,j;
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SPMatindex r,c;
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j=0;
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r=rowsorted[j]->row;
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c=rowsorted[j]->col;
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for(i=1; i<n;i++)
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{
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if(r==rowsorted[i]->row && c==rowsorted[i]->col) {rowsorted[j]->elem +=rowsorted[i]->elem; delete rowsorted[i]; rowsorted[i]=NULL;}
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else
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{
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j=i;
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r=rowsorted[j]->row;
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c=rowsorted[j]->col;
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}
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}
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//check if summed to zero
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for(i=0; i<n;i++) if(rowsorted[i] &&
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#ifdef SPARSEEPSILON
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abs(rowsorted[i]->elem)<SPARSEEPSILON
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#else
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! rowsorted[i]->elem
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#endif
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) {delete rowsorted[i]; rowsorted[i]=NULL;}
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//restore connectivity
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int nonz=0;
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matel<T> *p,*first,*prev;
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first=NULL;
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prev=NULL;
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for(i=0; i<n;i++) if(p=rowsorted[i])
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{
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++nonz;
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if(!first) first=p;
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if(prev) prev->next=p;
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p->next=NULL;
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prev=p;
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}
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list=first;
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nonzero=nonz;
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unsort(); //since there were NULLs introduced, rowsorted is not dense
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}
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export template <class T>
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void SparseMat<T>::resize(const SPMatindex n, const SPMatindex m)
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{
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if(n<=0 || m<=0) laerror("illegal matrix dimension");
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unsort();
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if(count)
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{
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if(*count > 1) {(*count)--; count=NULL; list=NULL;} //detach from previous
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else if(*count==1) deletelist();
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}
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nn=n;
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mm=m;
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count=new int(1); //empty but defined matrix
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list=NULL;
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symmetric=0;
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colsorted=rowsorted=NULL;
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}
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export template <class T>
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void SparseMat<T>::addsafe(const SPMatindex n, const SPMatindex m, const T elem)
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{
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#ifdef debug
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if(n<0||n>=nn||m<0||m>=mm) laerror("SparseMat out of range");
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#endif
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#ifdef SPARSEEPSILON
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if(abs(elem)<SPARSEEPSILON) return;
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#else
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if(!elem) return;
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#endif
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if(!count) {count=new int; *count=1; list=NULL;} //blank new matrix
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else copyonwrite(); //makes also unsort
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add(n,m,elem);
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}
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//assignment operator
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export template <class T>
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SparseMat<T> & SparseMat<T>::operator=(const SparseMat<T> &rhs)
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{
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if (this != &rhs)
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{
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unsort();
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if(count)
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if(--(*count) ==0) {deletelist(); delete count;} // old stuff obsolete
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list=rhs.list;
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nn=rhs.nn;
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mm=rhs.mm;
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if(list) count=rhs.count; else count= new int(0); //make the matrix defined, but empty and not shared, count will be incremented below
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symmetric=rhs.symmetric;
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if(count) (*count)++;
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}
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return *this;
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}
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export template <class T>
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SparseMat<T> & SparseMat<T>::join(SparseMat<T> &rhs)
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{
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if(symmetric!=rhs.symmetric||nn!=rhs.nn||mm!=rhs.mm) laerror("incompatible matrices in join()");
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if(*rhs.count!=1) laerror("shared rhs in join()");
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if(!count) {count=new int; *count=1; list=NULL;}
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else copyonwrite();
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matel<T> **last=&list;
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while(*last) last= &((*last)->next);
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*last=rhs.list;
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rhs.list=NULL;
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return *this;
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}
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export template <class T>
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SparseMat<T> & SparseMat<T>::addtriangle(const SparseMat &rhs, const bool lower, const char sign)
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{
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if(nn!=rhs.nn||mm!=rhs.mm) laerror("incompatible dimensions for +=");
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if(!count) {count=new int; *count=1; list=NULL;}
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else copyonwrite();
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register matel<T> *l=rhs.list;
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while(l)
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{
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if(rhs.symmetric || lower && l->row <=l->col || !lower && l->row >=l->col)
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#ifdef SPARSEEPSILON
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if(abs(l->elem)>SPARSEEPSILON)
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#endif
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add( l->row,l->col,sign=='+'?l->elem:- l->elem);
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l=l->next;
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}
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return *this;
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}
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export template <class T>
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SparseMat<T> & SparseMat<T>::operator+=(const SparseMat<T> &rhs)
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{
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if(symmetric&&!rhs.symmetric) laerror("cannot add general to symmetric sparse");
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if(nn!=rhs.nn||mm!=rhs.mm) laerror("incompatible dimensions for +=");
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if(!count) {count=new int; *count=1; list=NULL;}
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else copyonwrite();
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bool symmetrize= !symmetric && rhs.symmetric;
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register matel<T> *l=rhs.list;
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if(symmetrize)
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while(l)
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{
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#ifdef SPARSEEPSILON
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if(abs(l->elem)>SPARSEEPSILON)
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#endif
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{add( l->row,l->col,l->elem); if( l->row!=l->col) add( l->col,l->row,l->elem);}
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l=l->next;
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}
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else
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while(l)
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{
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#ifdef SPARSEEPSILON
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if(abs(l->elem)>SPARSEEPSILON)
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#endif
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add( l->row,l->col,l->elem);
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l=l->next;
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}
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return *this;
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}
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export template <class T>
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SparseMat<T> & SparseMat<T>::operator-=(const SparseMat<T> &rhs)
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{
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if(symmetric&&!rhs.symmetric) laerror("cannot add general to symmetric sparse");
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if(nn!=rhs.nn||mm!=rhs.mm) laerror("incompatible dimensions for -=");
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if(!count) {count=new int; *count=1; list=NULL;}
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else copyonwrite();
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bool symmetrize= !symmetric && rhs.symmetric;
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register matel<T> *l=rhs.list;
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if(symmetrize)
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while(l)
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{
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#ifdef SPARSEEPSILON
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if(abs(l->elem)>SPARSEEPSILON)
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#endif
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{add( l->row,l->col,- l->elem); if( l->row!=l->col) add( l->col,l->row,- l->elem);}
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l=l->next;
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}
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else
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while(l)
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{
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#ifdef SPARSEEPSILON
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if(abs(l->elem)>SPARSEEPSILON)
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#endif
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add( l->row,l->col,- l->elem);
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l=l->next;
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}
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return *this;
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}
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//constructor from a dense matrix
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export template <class T>
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SparseMat<T>::SparseMat(const NRMat<T> &rhs)
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{
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nn=rhs.nrows();
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mm=rhs.ncols();
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count=new int;
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*count=1;
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list=NULL;
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symmetric=0;
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colsorted=rowsorted=NULL;
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SPMatindex i,j;
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for(i=0;i<nn;++i)
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for(j=0; j<mm;++j)
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{register T t(rhs(i,j));
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#ifdef SPARSEEPSILON
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if( abs(t)>SPARSEEPSILON)
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#else
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if(t)
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#endif
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add(i,j,t);
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}
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}
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//constructor dense matrix from sparse
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export template <class T>
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NRMat<T>::NRMat(const SparseMat<T> &rhs)
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{
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nn=rhs.nrows();
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mm=rhs.ncols();
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count=new int(1);
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T *p;
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#ifdef MATPTR
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v= new T*[nn];
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p=v[0] = new T[mm*nn];
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for (int i=1; i< nn; i++) v[i] = v[i-1] + mm;
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#else
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p= v = new T[mm*nn];
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#endif
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memset(p,0,nn*mm*sizeof(T));
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matel<T> *l=rhs.getlist();
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bool sym=rhs.issymmetric();
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while(l)
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{
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#ifdef MATPTR
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v[l->row][l->col] +=l->elem;
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if(sym && l->row!=l->col) v[l->col][l->row] +=l->elem;
|
|
#else
|
|
v[l->row*mm+l->col] +=l->elem;
|
|
if(sym && l->row!=l->col) v[l->col*mm+l->row] +=l->elem;
|
|
#endif
|
|
l=l->next;
|
|
}
|
|
}
|
|
|
|
|
|
|
|
|
|
//constructor dense symmetric packed matrix from sparse
|
|
#define nn2 (nn*(nn+1)/2)
|
|
export template <class T>
|
|
NRSMat<T>::NRSMat(const SparseMat<T> &rhs)
|
|
{
|
|
if(!rhs.issymmetric()||rhs.nrows()!=rhs.ncols()) laerror("sparse matrix is not symmetric");
|
|
nn=rhs.nrows();
|
|
count=new int(1);
|
|
v=new T[nn2];
|
|
memset(v,0,nn2*sizeof(T));
|
|
matel<T> *l=rhs.getlist();
|
|
while(l)
|
|
{
|
|
(*this)(l->row,l->col)=l->elem;
|
|
l=l->next;
|
|
}
|
|
}
|
|
#undef nn2
|
|
|
|
//constructor dense vector from sparse
|
|
export template <class T>
|
|
NRVec<T>::NRVec(const SparseMat<T> &rhs)
|
|
{
|
|
if(rhs.nrows()>1 && rhs.ncols()>1) laerror("cannot construct a vector from a sparse matrix with more than one row/column");
|
|
nn=rhs.nrows()>1?rhs.nrows():rhs.ncols();
|
|
v=new T[nn];
|
|
memset(v,0,nn*sizeof(T));
|
|
count=new int(1);
|
|
matel<T> *l=rhs.getlist();
|
|
|
|
if(rhs.nrows()>1) while(l)
|
|
{
|
|
v[l->row]+=l->elem;
|
|
l=l->next;
|
|
}
|
|
else while(l)
|
|
{
|
|
v[l->col]+=l->elem;
|
|
l=l->next;
|
|
}
|
|
}
|
|
|
|
//assignment of a scalar matrix
|
|
export template <class T>
|
|
SparseMat<T> & SparseMat<T>::operator=(const T a)
|
|
{
|
|
if(!count ||nn<=0||mm<=0) laerror("assignment of scalar to undefined sparse matrix");
|
|
if(nn!=mm) laerror("assignment of scalar to non-square sparse matrix");
|
|
resize(nn,mm);//clear
|
|
#ifdef SPARSEEPSILON
|
|
if(abs(a)<SPARSEEPSILON) return *this;
|
|
#else
|
|
if(a==(T)0) return *this;
|
|
#endif
|
|
SPMatindex i;
|
|
for(i=0;i<nn;++i) add(i,i,a);
|
|
return *this;
|
|
}
|
|
|
|
export template <class T>
|
|
SparseMat<T> & SparseMat<T>::operator+=(const T a)
|
|
{
|
|
if(!count ||nn<=0||mm<=0) laerror("assignment of scalar to undefined sparse matrix");
|
|
if(nn!=mm) laerror("assignment of scalar to non-square sparse matrix");
|
|
if(a==(T)0) return *this;
|
|
SPMatindex i;
|
|
for(i=0;i<nn;++i) add(i,i,a);
|
|
return *this;
|
|
}
|
|
|
|
export template <class T>
|
|
SparseMat<T> & SparseMat<T>::operator-=(const T a)
|
|
{
|
|
if(!count ||nn<=0||mm<=0) laerror("assignment of scalar to undefined sparse matrix");
|
|
if(nn!=mm) laerror("assignment of scalar to non-square sparse matrix");
|
|
if(a==(T)0) return *this;
|
|
SPMatindex i;
|
|
for(i=0;i<nn;++i) add(i,i,-a);
|
|
return *this;
|
|
}
|
|
|
|
|
|
|
|
//constructor from a dense symmetric matrix
|
|
export template <class T>
|
|
SparseMat<T>::SparseMat(const NRSMat<T> &rhs)
|
|
{
|
|
nn=rhs.nrows();
|
|
mm=rhs.ncols();
|
|
count=new int;
|
|
*count=1;
|
|
list=NULL;
|
|
symmetric=1;
|
|
colsorted=rowsorted=NULL;
|
|
SPMatindex i,j;
|
|
for(i=0;i<nn;++i)
|
|
for(j=0; j<=i;++j)
|
|
{register T t;
|
|
if(
|
|
#ifdef SPARSEEPSILON
|
|
abs(t=rhs(i,j))>SPARSEEPSILON
|
|
#else
|
|
t=rhs(i,j)
|
|
#endif
|
|
) add(i,j,t);
|
|
}
|
|
}
|
|
|
|
export template <class T>
|
|
void SparseMat<T>::transposeme()
|
|
{
|
|
if(!count) laerror("transposeme on undefined lhs");
|
|
if(symmetric||!list) return;
|
|
copyonwrite();//also unsort
|
|
register matel<T> *l=list;
|
|
while(l)
|
|
{
|
|
SWAP(l->row,l->col);
|
|
l=l->next;
|
|
}
|
|
SWAP(nn,mm);
|
|
}
|
|
|
|
export template <class T>
|
|
void SparseMat<T>::setunsymmetric()
|
|
{
|
|
if(!symmetric) return;
|
|
unsort();
|
|
symmetric=0;
|
|
if(!count) return;
|
|
copyonwrite();
|
|
matel<T> *l=list;
|
|
while(l) //include the mirror picture of elements into the list
|
|
{
|
|
if(
|
|
#ifdef SPARSEEPSILON
|
|
abs(l->elem)>SPARSEEPSILON &&
|
|
#endif
|
|
l->row!=l->col) add(l->col,l->row,l->elem); //not OK for complex-hermitean
|
|
l=l->next;
|
|
}
|
|
}
|
|
|
|
|
|
export template <class T>
|
|
SparseMat<T> & SparseMat<T>::operator*=(const T a)
|
|
{
|
|
if(!count) laerror("operator*= on undefined lhs");
|
|
if(!list||a==(T)1) return *this;
|
|
if(a==(T)0) resize(nn,mm);
|
|
else copyonwrite();
|
|
|
|
register matel<T> *l=list;
|
|
while(l)
|
|
{
|
|
l->elem*=a;
|
|
l=l->next;
|
|
}
|
|
return *this;
|
|
}
|
|
|
|
const double SparseMat<double>::dot(const NRMat<double> &rhs) const
|
|
{
|
|
double r=0;
|
|
matel<double> *l=list;
|
|
while(l)
|
|
{
|
|
r+= l->elem*rhs[l->row][l->col];
|
|
if(symmetric&&l->row!=l->col) r+=l->elem*rhs[l->col][l->row];
|
|
l=l->next;
|
|
}
|
|
return r;
|
|
}
|
|
|
|
|
|
template<class T>
|
|
void NRVec<T>::gemv(const T beta, const SparseMat<T> &a, const char trans, const T alpha, const NRVec<T> &x)
|
|
{
|
|
if((trans=='n'?a.ncols():a.nrows())!= (SPMatindex)x.size()) laerror("incompatible sizes in gemv");
|
|
copyonwrite();
|
|
if(beta!=(T)0) (*this) *= beta;
|
|
else memset(v,0,nn*sizeof(T));
|
|
|
|
bool transp = tolower(trans)!='n'; //not OK for complex
|
|
|
|
matel<T> *l=a.getlist();
|
|
|
|
if(alpha==(T)0 || !l) return;
|
|
T *vec=x.v;
|
|
|
|
if(alpha==(T)1)
|
|
{
|
|
if(a.issymmetric())
|
|
{
|
|
while(l)
|
|
{
|
|
v[l->row]+= l->elem*vec[l->col];
|
|
if(l->row!=l->col) v[l->col]+= l->elem*vec[l->row];
|
|
l=l->next;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
if(transp)
|
|
while(l)
|
|
{
|
|
v[l->col]+= l->elem*vec[l->row];
|
|
l=l->next;
|
|
}
|
|
else
|
|
while(l)
|
|
{
|
|
v[l->row]+= l->elem*vec[l->col];
|
|
l=l->next;
|
|
}
|
|
}
|
|
}
|
|
else
|
|
{
|
|
if(a.issymmetric())
|
|
{
|
|
while(l)
|
|
{
|
|
v[l->row]+= alpha*l->elem*vec[l->col];
|
|
if(l->row!=l->col) v[l->col]+= alpha*l->elem*vec[l->row];
|
|
l=l->next;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
if(transp)
|
|
while(l)
|
|
{
|
|
v[l->col]+= alpha*l->elem*vec[l->row];
|
|
l=l->next;
|
|
}
|
|
else
|
|
while(l)
|
|
{
|
|
v[l->row]+= alpha*l->elem*vec[l->col];
|
|
l=l->next;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
//multiplication with dense vector from both sides
|
|
template <class T>
|
|
const NRVec<T> SparseMat<T>::multiplyvector(const NRVec<T> &vec, const bool transp) const
|
|
{
|
|
if(transp && nn!=(SPMatindex)vec.size() || !transp && mm!=(SPMatindex)vec.size()) laerror("incompatible sizes in sparsemat*vector");
|
|
NRVec<T> result(transp?mm:nn);
|
|
result.gemv((T)0, *this, transp?'t':'n', (T)1., vec);
|
|
return result;
|
|
}
|
|
|
|
|
|
template <class T>
|
|
const NRVec<T> NRVec<T>::operator*(const SparseMat<T> &mat) const
|
|
{
|
|
if(mat.nrows()!= (SPMatindex)size()) laerror("incompatible sizes in vector*sparsemat");
|
|
NRVec<T> result((T)0,mat.ncols());
|
|
matel<T> *l=mat.getlist();
|
|
bool symmetric=mat.issymmetric();
|
|
while(l)
|
|
{
|
|
result.v[l->col]+= l->elem*v[l->row];
|
|
if(symmetric&&l->row!=l->col) result.v[l->row]+= l->elem*v[l->col];
|
|
l=l->next;
|
|
}
|
|
return result;
|
|
|
|
}
|
|
|
|
template<class T>
|
|
const T SparseMat<T>::trace() const
|
|
{
|
|
matel<T> *l=list;
|
|
T sum(0);
|
|
while(l)
|
|
{
|
|
if(l->row==l->col) sum+= l->elem;
|
|
l=l->next;
|
|
}
|
|
return sum;
|
|
}
|
|
|
|
|
|
//not OK for complex hermitean
|
|
template<class T>
|
|
const T SparseMat<T>::norm(const T scalar) const
|
|
{
|
|
if(!list) return T(0);
|
|
const_cast<SparseMat<T> *>(this)->simplify();
|
|
|
|
matel<T> *l=list;
|
|
T sum(0);
|
|
if(scalar!=(T)0)
|
|
{
|
|
if(symmetric)
|
|
while(l)
|
|
{
|
|
T hlp=l->elem;
|
|
bool b=l->row==l->col;
|
|
if(b) hlp-=scalar;
|
|
T tmp=hlp*hlp;
|
|
sum+= tmp;
|
|
if(!b) sum+=tmp;
|
|
l=l->next;
|
|
}
|
|
else
|
|
while(l)
|
|
{
|
|
T hlp=l->elem;
|
|
if(l->row==l->col) hlp-=scalar;
|
|
sum+= hlp*hlp;
|
|
l=l->next;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
if(symmetric)
|
|
while(l)
|
|
{
|
|
T tmp=l->elem*l->elem;
|
|
sum+= tmp;
|
|
if(l->row!=l->col) sum+=tmp;
|
|
l=l->next;
|
|
}
|
|
else
|
|
while(l)
|
|
{
|
|
sum+= l->elem*l->elem;
|
|
l=l->next;
|
|
}
|
|
}
|
|
return sqrt(sum); //not OK for int, would need traits technique
|
|
}
|
|
|
|
|
|
template<class T>
|
|
void SparseMat<T>::axpy(const T alpha, const SparseMat<T> &x, const bool transp)
|
|
{
|
|
if(!transp && (nn!=x.nn||mm!=x.mm) || transp && (mm!=x.nn||nn!=x.mm) ) laerror("incompatible dimensions for axpy");
|
|
if(!count) {count=new int; *count=1; list=NULL;}
|
|
else copyonwrite();
|
|
|
|
if(alpha==(T)0||x.list==NULL) return;
|
|
if(!transp||x.symmetric)
|
|
{
|
|
if(alpha==(T)1) {*this +=x; return;}
|
|
if(alpha==(T)-1) {*this -=x; return;}
|
|
}
|
|
if(symmetric!=x.symmetric) laerror("general axpy not supported for different symmetry types");
|
|
//now does not matter if both are general or both symmetric (transposition will not matter)
|
|
|
|
register matel<T> *l=x.list;
|
|
if(transp)
|
|
while(l)
|
|
{
|
|
register T t=alpha*l->elem;
|
|
#ifdef SPARSEEPSILON
|
|
if(abs(t)>SPARSEEPSILON)
|
|
#endif
|
|
add( l->col,l->row,t);
|
|
l=l->next;
|
|
}
|
|
else
|
|
while(l)
|
|
{
|
|
register T t=alpha*l->elem;
|
|
#ifdef SPARSEEPSILON
|
|
if(abs(t)>SPARSEEPSILON)
|
|
#endif
|
|
add( l->row,l->col,t);
|
|
l=l->next;
|
|
}
|
|
}
|
|
|
|
|
|
template<class T>
|
|
const T SparseMat<T>::dot(const SparseMat<T> &rhs) const //complex conj. not implemented yet
|
|
{
|
|
if(nn!=rhs.nn || mm!=rhs.mm) laerror("dot of incompatible sparse matrices");
|
|
if(symmetric||rhs.symmetric) laerror("dot of symmetric sparse matrices not implemented");
|
|
|
|
T result=0;
|
|
if(list && rhs.list) //both nonzero
|
|
{
|
|
unsigned int na=sort(0);
|
|
unsigned int nb=rhs.sort(0);
|
|
|
|
//now merge the sorted lists
|
|
register unsigned int i,j;
|
|
register SPMatindex ra,ca;
|
|
j=0;
|
|
for(i=0; i<na;i++)
|
|
{
|
|
register SPMatindex rb=0,cb=0;
|
|
ra=rowsorted[i]->row;
|
|
ca=rowsorted[i]->col;
|
|
while(j<nb && (rb=rhs.rowsorted[j]->row) <ra) j++; /*skip in rhs*/
|
|
while(j<nb && (cb=rhs.rowsorted[j]->col) <ca) j++; /*skip in rhs*/
|
|
|
|
if(j==nb) break; //we can exit the i-loop, no suitable element in b any more
|
|
if(ra==rb&&ca==cb)
|
|
{
|
|
T tmp=rowsorted[i]->elem;
|
|
register unsigned int k;
|
|
/*j remembers the position, k forwards in the rhs.rowsorted to find all combinations*/
|
|
k=j;
|
|
do {
|
|
result += tmp*rhs.rowsorted[k]->elem;
|
|
k++;
|
|
} while(k<nb && (rhs.rowsorted[k]->row == ra) && (rhs.rowsorted[k]->col == ca));
|
|
}
|
|
/*else skip in left operand*/
|
|
}
|
|
}
|
|
return result;
|
|
}
|
|
|
|
|
|
|
|
template<class T>
|
|
const SparseMat<T> SparseMat<T>::operator*(const SparseMat<T> &rhs) const
|
|
{
|
|
if(mm!=rhs.nn) laerror("product of incompatible sparse matrices");
|
|
if(symmetric||rhs.symmetric) laerror("product of symmetric sparse matrices not implemented");
|
|
|
|
SparseMat<T> result(nn,rhs.mm);
|
|
if(list && rhs.list) //both nonzero
|
|
{
|
|
unsigned int na=sort(1);
|
|
unsigned int nb=rhs.sort(0);
|
|
|
|
//now merge the sorted lists
|
|
register unsigned int i,j;
|
|
register SPMatindex rb=0,ca;
|
|
j=0;
|
|
for(i=0; i<na;i++)
|
|
{
|
|
ca=colsorted[i]->col;
|
|
while(j<nb && (rb=rhs.rowsorted[j]->row) <ca) j++; /*skip in rhs.rowsorted*/
|
|
if(j==nb) break; //we can exit the i-loop, no suitable element in mb any more
|
|
if(rb==ca)
|
|
{
|
|
T tmp=colsorted[i]->elem;
|
|
register unsigned int k;
|
|
/*j remembers the position, k forwards in the rhs.rowsorted to find all combinations*/
|
|
k=j;
|
|
do {
|
|
result.add(colsorted[i]->row,rhs.rowsorted[k]->col,tmp*rhs.rowsorted[k]->elem);
|
|
k++;
|
|
} while(k<nb && ((rhs.rowsorted[k]->row) == ca));
|
|
}
|
|
/*else skip in left operand*/
|
|
}
|
|
result.simplify();//otherwise number of terms tends to grow exponentially
|
|
}
|
|
return result;
|
|
}
|
|
|
|
|
|
|
|
template <class T>
|
|
void SparseMat<T>::gemm(const T beta, const SparseMat<T> &a, const char transa, const SparseMat<T> &b, const char transb, const T alpha)
|
|
{
|
|
SPMatindex l(transa=='n'?a.nn:a.mm);
|
|
SPMatindex k(transa=='n'?a.mm:a.nn);
|
|
SPMatindex kk(transb=='n'?b.nn:b.mm);
|
|
SPMatindex ll(transb=='n'?b.mm:b.nn);
|
|
if(a.symmetric||b.symmetric) laerror("symmetric sparse matrices not supported in gemm");
|
|
|
|
if(beta==(T)0) resize(l,ll); //empty matrix
|
|
else *this *= beta; //takes care about beta=1
|
|
if(l!=nn|| ll!=mm||k!=kk) laerror("incompatible sparse matrices in gemm");
|
|
|
|
if(alpha==(T)0 || !a.list ||!b.list) return;
|
|
copyonwrite();
|
|
|
|
//regular case, specialize for transpositions
|
|
matel<T> **ma,**mb;
|
|
unsigned int na,nb;
|
|
bool tra= transa!='n';
|
|
bool trb= transb!='n';
|
|
if(!tra) {na=a.sort(1); ma=a.colsorted;} else {na=a.sort(0); ma=a.rowsorted;}
|
|
if(!trb) {nb=b.sort(0); mb=b.rowsorted;} else {nb=b.sort(1); mb=b.colsorted;}
|
|
|
|
//now merge the sorted lists
|
|
register unsigned int i,j;
|
|
register SPMatindex rb=0,ca,row;
|
|
j=0;
|
|
for(i=0; i<na;i++)
|
|
{
|
|
ca=tra?ma[i]->row:ma[i]->col;
|
|
row=tra?ma[i]->col:ma[i]->row;
|
|
while(j<nb && (rb=trb?mb[j]->col:mb[j]->row) <ca) j++; /*skip in mb*/
|
|
if(j==nb) break; //we can exit the i-loop, no suitable element in mb any more
|
|
if(rb==ca)
|
|
{
|
|
T tmp=alpha * ma[i]->elem;
|
|
register unsigned int k;
|
|
/*j remembers the position, k forwards in the mb to find all combinations*/
|
|
k=j;
|
|
do {
|
|
register SPMatindex col;
|
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col=trb?mb[k]->row:mb[k]->col;
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if(!symmetric||row<=col) add(row,col,tmp*mb[k]->elem);
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k++;
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} while(k<nb && ((trb?mb[k]->col:mb[k]->row) == ca));
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}
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/*else skip in ma*/
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}
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simplify();
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}
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#ifdef _GLIBCPP_NO_TEMPLATE_EXPORT
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#define INSTANTIZE(T) \
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template ostream& operator<<(ostream &s, const SparseMat<T> &x); \
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template istream& operator>>(istream &s, SparseMat<T> &x); \
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template void SparseMat<T>::copyonwrite(); \
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template void SparseMat<T>::resize(const SPMatindex n, const SPMatindex m); \
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template void SparseMat<T>::unsort(); \
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template unsigned int SparseMat<T>::sort(int type) const; \
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template unsigned int SparseMat<T>::length() const; \
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template void SparseMat<T>::deletelist(); \
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template void SparseMat<T>::simplify(); \
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template void SparseMat<T>::copylist(const matel<T> *l); \
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template void SparseMat<T>::add(const SPMatindex n, const SPMatindex m, const T elem); \
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template SparseMat<T> & SparseMat<T>::operator=(const SparseMat<T> &rhs); \
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template SparseMat<T> & SparseMat<T>::operator+=(const SparseMat<T> &rhs); \
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template SparseMat<T> & SparseMat<T>::operator-=(const SparseMat<T> &rhs); \
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template SparseMat<T>::SparseMat(const NRMat<T> &rhs); \
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template SparseMat<T>::SparseMat(const NRSMat<T> &rhs); \
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template void SparseMat<T>::transposeme(); \
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template SparseMat<T> & SparseMat<T>::operator*=(const T a); \
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template void SparseMat<T>::setunsymmetric(); \
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template SparseMat<T> & SparseMat<T>::operator=(const T a); \
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template SparseMat<T> & SparseMat<T>::operator+=(const T a); \
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template SparseMat<T> & SparseMat<T>::operator-=(const T a); \
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template NRMat<T>::NRMat(const SparseMat<T> &rhs); \
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template NRSMat<T>::NRSMat(const SparseMat<T> &rhs); \
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template NRVec<T>::NRVec(const SparseMat<T> &rhs); \
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template const NRVec<T> SparseMat<T>::operator*(const NRVec<T> &vec) const; \
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template const NRVec<T> NRVec<T>::operator*(const SparseMat<T> &mat) const; \
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template SparseMat<T> & SparseMat<T>::join(SparseMat<T> &rhs); \
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template const T SparseMat<T>::trace() const; \
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template const T SparseMat<T>::norm(const T scalar) const; \
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template void SparseMat<T>::axpy(const T alpha, const SparseMat<T> &x, const bool transp); \
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template const SparseMat<T> SparseMat<T>::operator*(const SparseMat<T> &rhs) const; \
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template const T SparseMat<T>::dot(const SparseMat<T> &rhs) const; \
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template void SparseMat<T>::gemm(const T beta, const SparseMat<T> &a, const char transa, const SparseMat<T> &b, const char transb, const T alpha); \
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template void NRVec<T>::gemv(const T beta, const SparseMat<T> &a, const char trans, const T alpha, const NRVec<T> &x);\
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INSTANTIZE(double)
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// some functions are not OK for hermitean! INSTANTIZE(complex<double>)
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#endif
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