template for general power, power of NRPerm and CyclePerm
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757a76844e
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22
mat.cc
22
mat.cc
@ -28,6 +28,7 @@
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#include <errno.h>
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#include <unistd.h>
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#include <math.h>
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#include "nonclass.h"
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namespace LA {
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@ -3163,12 +3164,13 @@ for(int i=0; i<n; ++i)
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}
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template<typename T>
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NRMat<T>::NRMat(const NRPerm<int> &p, const bool direction)
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NRMat<T>::NRMat(const NRPerm<int> &p, const bool direction, const bool parity)
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{
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int n=p.size();
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resize(n,n);
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clear();
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axpy((T)1,p,direction);
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T alpha= parity? p.parity():1;
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axpy(alpha,p,direction);
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}
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@ -3358,6 +3360,22 @@ copyonwrite();
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template<>
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NRMat<double> NRMat<double>::inverse()
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{
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NRMat<double> tmp(*this);
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return calcinverse(tmp);
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}
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template<>
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NRMat<std::complex<double> > NRMat<std::complex<double> >::inverse()
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{
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NRMat<std::complex<double> > tmp(*this);
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return calcinverse(tmp);
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}
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10
mat.h
10
mat.h
@ -22,6 +22,7 @@
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#define _LA_MAT_H_
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#include "la_traits.h"
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namespace LA {
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//forward declaration
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@ -129,7 +130,7 @@ public:
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void scale_row(const int i, const T f); //in place
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void scale_col(const int i, const T f); //in place
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void axpy(const T alpha, const NRPerm<int> &p, const bool direction);
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explicit NRMat(const NRPerm<int> &p, const bool direction); //permutation matrix
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explicit NRMat(const NRPerm<int> &p, const bool direction, const bool parity=false); //permutation matrix
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/***************************************************************************//**
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@ -155,6 +156,13 @@ public:
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//! assign scalar value to the diagonal elements
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NRMat & operator=(const T &a);
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//! unit matrix for general power
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void identity() {*this = (T)1;}
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//! inverse matrix
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NRMat inverse();
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//! add scalar value to the diagonal elements
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NRMat & operator+=(const T &a);
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//! subtract scalar value to the diagonal elements
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44
nonclass.h
44
nonclass.h
@ -25,6 +25,48 @@
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namespace LA {
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//MISC
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//positive power for a general class
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template<typename T>
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T positive_power(const T &x, const int n)
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{
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if(n<=0) laerror("zero or negative n in positive_power");
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int i=n;
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if(i==1) return x;
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T y,z;
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z=x;
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while(!(i&1))
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{
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z = z*z;
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i >>= 1;
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}
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y=z;
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while((i >>= 1)/*!=0*/)
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{
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z = z*z;
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if(i&1) y = y*z;
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}
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return y;
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}
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//general integer power for a class providing identity() and inverse()
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template<typename T>
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T power(const T &x, const int n)
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{
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int i=n;
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if(i==0) {T r(x); r.identity(); return r;}
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T z;
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if(i>0) z=x;
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else {z=x.inverse(); i= -i;}
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if(i==1) return z;
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return positive_power(z,i);
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}
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template <class T>
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const NRSMat<T> twoside_transform(const NRSMat<T> &S, const NRMat<T> &C, bool transp=0) //calculate C^dagger S C
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{
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@ -138,7 +180,7 @@ extern void cholesky(NRMat<std::complex<double> > &a, bool upper=1);
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//inverse by means of linear solve, preserving rhs intact
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template<typename T>
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const NRMat<T> inverse(NRMat<T> a, T *det=0)
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const NRMat<T> calcinverse(NRMat<T> a, T *det=NULL)
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{
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#ifdef DEBUG
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if(a.nrows()!=a.ncols()) laerror("inverse() for non-square matrix");
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@ -569,6 +569,7 @@ for(typename std::list<NRVec_from1<T> >::iterator l=cyclelist.begin(); l!=cyclel
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}
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template <typename T>
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bool CyclePerm<T>::is_valid() const
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{
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@ -641,6 +642,23 @@ NRPerm<T> rr=pp*qq;
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return CyclePerm<T>(rr);
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}
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template <typename T>
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void CyclePerm<T>::simplify(bool keep1)
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{
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int j=0;
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for(int i=1; i<=this->size(); ++i)
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{
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int il= (*this)[i].size();
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if(keep1 && il>0 || il>1 )
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{
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++j;
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if(j!=i) (*this)[j] = (*this)[i]; //keep this
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}
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}
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this->resize(j,true);
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}
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template <typename T>
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int CyclePerm<T>::parity() const
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{
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@ -788,6 +806,57 @@ return s;
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}
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template <typename T>
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CyclePerm<T> CyclePerm<T>::pow(const int n, const bool keep1) const
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{
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#ifdef DEBUG
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if(!this->is_valid()) laerror("power of invalid permutation");
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#endif
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CyclePerm<T> r;
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if(n==0) {r.identity(); return r;}
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//probably negative n will work automatically using the modulo approach
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std::list<NRVec_from1<T> > cyclelist;
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T currentcycle=0;
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//go through all our cycles and compute power of each cycle separately
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for(int i=1; i<=this->size(); ++i)
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{
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int cyclesize = (*this)[i].size();
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if(cyclesize>0 && keep1 || cyclesize>1)
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{
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int modulo = n%cyclesize;
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if(modulo<0) modulo += cyclesize;
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if(modulo==0)
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{
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if(keep1) //keep cycles of length 1 to keep info about the size of the permutation
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{
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for(int j=1; j<=cyclesize; ++j) {NRVec_from1<T> c(1); c[1] = (*this)[i][j]; ++currentcycle; cyclelist.push_back(c);}
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}
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}
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else //the nontrivial case
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{
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int nsplit=gcd(modulo,cyclesize);
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int splitsize=cyclesize/nsplit;
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for(int j=0; j<nsplit; ++j) //loop over split cycles
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{
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NRVec_from1<T> c(splitsize);
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for(int k=1; k<=splitsize; ++k) //fill in the cycle
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{
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c[k] = (*this)[i][((k-1)*modulo)%cyclesize + 1 + j];
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}
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++currentcycle; cyclelist.push_back(c);
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}
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}
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}
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}
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//convert list to NRVec
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r.resize(currentcycle);
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int i=1;
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for(typename std::list<NRVec_from1<T> >::iterator l=cyclelist.begin(); l!=cyclelist.end(); ++l) r[i++] = *l;
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return r;
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}
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///////////////////////////////////////////////////////
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@ -23,6 +23,7 @@
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#include "la_traits.h"
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#include "vec.h"
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#include "polynomial.h"
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#include "nonclass.h"
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typedef unsigned long long PERM_RANK_TYPE;
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@ -30,6 +31,7 @@ typedef unsigned long long PERM_RANK_TYPE;
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namespace LA {
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//forward declaration
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template <typename T> class CyclePerm;
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template <typename T> class Partition;
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@ -65,6 +67,7 @@ public:
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NRVec_from1<T> inversions(const int type, PERM_RANK_TYPE *prank=NULL) const; //inversion tables
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explicit NRPerm(const int type, const NRVec_from1<T> &inversions); //compute permutation from inversions
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explicit NRPerm(const int n, const PERM_RANK_TYPE rank); //compute permutation from its rank
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NRPerm pow(const int n) const {return power(*this,n);};
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};
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extern PERM_RANK_TYPE factorial(const int n);
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@ -90,6 +93,10 @@ public:
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void readfrom(const std::string &line);
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CyclePerm operator*(const CyclePerm q) const; //q is rhs and applied first, this applied second
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PERM_RANK_TYPE order() const; //lcm of cycle lengths
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bool operator==(const CyclePerm &rhs) const {return NRPerm<T>(*this) == NRPerm<T>(rhs);}; //cycle representation is not unique, cannot inherit operator== from NRVec
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void simplify(bool keep1=false); //remove cycles of size 0 or 1
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CyclePerm pow_simple(const int n) const {return CyclePerm(NRPerm<T>(*this).pow(n));}; //do not call power() with our operator*
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CyclePerm pow(const int n, const bool keep1=false) const; //a more efficient algorithm
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};
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@ -144,7 +151,7 @@ public:
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bool is_valid() const {return this->size() == this->sum();}
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explicit CompressedPartition(const Partition<T> &rhs) : NRVec_from1<T>(rhs.size()) {this->clear(); for(int i=1; i<=rhs.size(); ++i) if(!rhs[i]) break; else (*this)[rhs[i]]++; }
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PERM_RANK_TYPE Sn_class_size() const;
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int parity() const; //of a permutation with given cycle lengths
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int parity() const; //of a permutation with given cycle lengths, returns +/- 1
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};
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@ -166,7 +173,7 @@ public:
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PERM_RANK_TYPE Sn_irrep_dim() const;
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PERM_RANK_TYPE Un_irrep_dim(const int n) const;
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PERM_RANK_TYPE generate_all(void (*callback)(const Partition<T>&), int nparts=0); //nparts <0 means at most to -nparts
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int parity() const; //of a permutation with given cycle lengths
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int parity() const; //of a permutation with given cycle lengths, returns +/- 1
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};
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@ -20,6 +20,7 @@
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#include <stdio.h>
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#include <string.h>
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#include <math.h>
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#include "nonclass.h"
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namespace LA {
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@ -224,24 +225,9 @@ return poly_gcd(big,small,thr,d);
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template <typename T>
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Polynomial<T> Polynomial<T>::pow(const int n) const
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{
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int i=n;
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if(i<0) laerror("negative exponent in polynomial::pow");
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if(i==0) {Polynomial<T> r(0); r[0]=(T)1; return r;}
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if(i==1) return *this;
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Polynomial<T>y,z;
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z= *this;
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while(!(i&1))
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{
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z = z*z;
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i >>= 1;
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}
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y=z;
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while((i >>= 1)/*!=0*/)
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{
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z = z*z;
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if(i&1) y = y*z;
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}
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return y;
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if(n<0) laerror("negative exponent in polynomial::pow");
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if(n==0) {Polynomial<T> r(0); r[0]=(T)1; return r;}
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return positive_power(*this,n);
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}
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template <typename T>
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@ -70,6 +70,8 @@ public:
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//compiler generates default copy constructor and assignment operator
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void identity() {q[0]=(T)1; q[1]=q[2]=q[3]=0;};
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//formal indexing
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inline const T operator[](const int i) const {return q[i];};
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inline T& operator[](const int i) {return q[i];};
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6
smat.cc
6
smat.cc
@ -858,6 +858,12 @@ void NRSMat<T>::storesubmatrix(const NRVec<int> &selection, const NRSMat &rhs)
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}
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}
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template<>
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NRSMat<double> NRSMat<double>::inverse() {return NRSMat<double>(NRMat<double>(*this).inverse());}
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template<>
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NRSMat<std::complex<double> > NRSMat<std::complex<double> >::inverse() {return NRSMat<std::complex<double> >(NRMat<std::complex<double> >(*this).inverse());}
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9
smat.h
9
smat.h
@ -93,6 +93,13 @@ public:
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//! assign scalar value to diagonal elements
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NRSMat & operator=(const T &a);
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//! unit matrix for general power
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void identity() {*this = (T)1;}
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//! inverse matrix
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NRSMat inverse();
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//! permute matrix elements
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const NRSMat permuted(const NRPerm<int> &p, const bool inverse=false) const;
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@ -148,7 +155,7 @@ public:
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inline int nrows() const;
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inline int ncols() const;
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inline size_t size() const;
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inline size_t size() const; //NOTE it is the size of data n*(n+1)/2, not nrows
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inline bool transp(const int i, const int j) const {return i>j;} //this can be used for compact storage of matrices, which are actually not symmetric, but one triangle of them is redundant
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const typename LA_traits<T>::normtype norm(const T scalar = (T)0) const;
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@ -82,6 +82,7 @@ public:
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explicit SparseMat(const NRSMat<T> &rhs); //construct from a dense symmetric one
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SparseMat & operator=(const SparseMat &rhs);
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SparseMat & operator=(const T &a); //assign a to diagonal
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void identity() {*this = (T)1;};
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SparseMat & operator+=(const T &a); //assign a to diagonal
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SparseMat & operator-=(const T &a); //assign a to diagonal
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SparseMat & operator*=(const T &a); //multiply by a scalar
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23
t.cc
23
t.cc
@ -899,7 +899,7 @@ a(2,2)=-4;
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a(0,2)=1;
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cout <<a;
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double d;
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NRMat<double> c=inverse(a,&d);
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NRMat<double> c=calcinverse(a,&d);
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cout <<a<<c;
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}
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@ -1442,7 +1442,7 @@ for(int i=0; i<n; ++i) Y(i,i) -= tmp2(i,i);
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cout <<"Y matrix \n"<< Y;
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NRMat<double> vri = inverse(vr);
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NRMat<double> vri = calcinverse(vr);
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NRMat<double> numX = vri * vrd;
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cout <<" numerical X matrix \n"<< numX;
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@ -2087,15 +2087,26 @@ for(i=1; i<=n; ++i) v[i]=10.*i;
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cout <<v.permuted(p);
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}
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if(0)
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if(1)
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{
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int n;
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CyclePerm<int> c;
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cin>>c;
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cin>>c >>n;
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c.simplify();
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cout<<c<<endl;
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NRPerm<int> p(c);
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cout <<p;
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CyclePerm<int> cc(p);
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cout <<cc<<endl;
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NRPerm<int> pp(cc);
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cout <<(p == pp)<<endl;
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cout <<(c == cc)<<endl;
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CyclePerm<int> cc1,cc2;
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cc1=cc.pow_simple(n);
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cc2=cc.pow(n);
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cout<<cc<<endl;
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cout<<cc2<<endl;
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cout <<(cc1 == cc2)<<endl;
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}
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if(0)
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@ -2703,7 +2714,7 @@ diagonalize(d,e);
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//now try similarity transformed H
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NRMat<double> a(n,n);
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a.randomize(1);
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NRMat<double> ainv = inverse(a);
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NRMat<double> ainv = calcinverse(a);
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NRMat<double> atr = a.transpose();
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NRMat<double> ainvtr = ainv.transpose();
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cout <<"error of inverse = "<<(a*ainv).norm(1.)<<endl;
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@ -2748,7 +2759,7 @@ if(0)
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laerror("test exception");
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}
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if(1)
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if(0)
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{
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NRSMat<char> adj;
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cin >>adj;
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@ -114,6 +114,8 @@ public:
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Mat3(void) {};
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Mat3(const T (&a)[3][3]) {memcpy(q,a,3*3*sizeof(T));}
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Mat3(const T x) {memset(q,0,9*sizeof(T)); q[0][0]=q[1][1]=q[2][2]=x;}; //scalar matrix
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Mat3& operator=(const T &x) {memset(q,0,9*sizeof(T)); q[0][0]=q[1][1]=q[2][2]=x; return *this;}; //scalar matrix
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void indentity() {*this = (T)1;};
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Mat3(const T* x) {memcpy(q,x,9*sizeof(T));}
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Mat3(const T x00, const T x01,const T x02,const T x10,const T x11,const T x12,const T x20,const T x21,const T x22)
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{q[0][0]=x00; q[0][1]=x01; q[0][2]=x02; q[1][0]=x10; q[1][1]=x11; q[1][2]=x12; q[2][0]=x20; q[2][1]=x21; q[2][2]=x22;};
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