*** empty log message ***
This commit is contained in:
jiri
commit
d7b55e9846
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@ -0,0 +1,28 @@
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# CVS default ignores begin
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tags
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TAGS
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.make.state
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.nse_depinfo
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*~
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\#*
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.#*
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,*
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_$*
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*$
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*.old
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*.bak
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*.BAK
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*.orig
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*.rej
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.del-*
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*.a
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*.olb
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*.o
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*.obj
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*.so
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*.exe
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*.Z
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*.elc
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*.ln
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core
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# CVS default ignores end
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@ -0,0 +1,261 @@
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#ifndef _fourindex_included
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||||
#define _fourindex_included
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||||
|
||||
//element of a linked list, indices in a portable way, no bit shifts and endianity problems any more!
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||||
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||||
template<class I, class T>
|
||||
struct matel4
|
||||
{
|
||||
T elem;
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||||
matel4 *next;
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||||
typedef union {
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I packed[4];
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||||
struct {
|
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I i;
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||||
I j;
|
||||
I k;
|
||||
I l;
|
||||
} indiv;
|
||||
} packedindex;
|
||||
packedindex index;
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||||
};
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||||
|
||||
typedef enum {nosymmetry=0, twoelectronreal=1, twoelectroncomplex=2, twobodyantisym=3} fourindexsymtype; //if twoelectron, only permutation-nonequivalent elements are stored
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||||
|
||||
template <class I, class T>
|
||||
class fourindex {
|
||||
protected:
|
||||
I nn;
|
||||
fourindexsymtype symmetry;
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||||
int *count;
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||||
matel4<I,T> *list;
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||||
private:
|
||||
void deletelist();
|
||||
void copylist(const matel4<I,T> *l);
|
||||
public:
|
||||
//iterator
|
||||
typedef class iterator {
|
||||
private:
|
||||
matel4<I,T> *p;
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||||
public:
|
||||
iterator() {};
|
||||
~iterator() {};
|
||||
iterator(matel4<I,T> *list): p(list) {};
|
||||
bool operator==(const iterator rhs) const {return p==rhs.p;}
|
||||
bool operator!=(const iterator rhs) const {return p!=rhs.p;}
|
||||
iterator operator++() {return p=p->next;}
|
||||
iterator operator++(int) {matel4<I,T> *q=p; p=p->next; return q;}
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||||
matel4<I,T> & operator*() const {return *p;}
|
||||
matel4<I,T> * operator->() const {return p;}
|
||||
};
|
||||
iterator begin() const {return list;}
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iterator end() const {return NULL;}
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||||
|
||||
//constructors etc.
|
||||
inline fourindex() :nn(0),count(NULL),list(NULL) {};
|
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inline fourindex(const I n) :nn(n),count(new int(1)),list(NULL) {};
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fourindex(const fourindex &rhs); //copy constructor
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inline int getcount() const {return count?*count:0;}
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fourindex & operator=(const fourindex &rhs);
|
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fourindex & operator+=(const fourindex &rhs);
|
||||
inline void setsymmetry(fourindexsymtype s) {symmetry=s;}
|
||||
fourindex & join(fourindex &rhs); //more efficient +=, rhs will be emptied
|
||||
inline ~fourindex();
|
||||
inline matel4<I,T> *getlist() const {return list;}
|
||||
inline I size() const {return nn;}
|
||||
void resize(const I n);
|
||||
void copyonwrite();
|
||||
int length() const;
|
||||
inline void add(const I i, const I j, const I k, const I l, const T elem)
|
||||
{matel4<I,T> *ltmp= new matel4<I,T>; ltmp->next=list; list=ltmp; list->index.indiv.i=i;list->index.indiv.j=j;list->index.indiv.k=k;list->index.indiv.l=l; list->elem=elem;}
|
||||
|
||||
inline void add(const typename matel4<I,T>::packedindex &index , const T elem)
|
||||
{matel4<I,T> *ltmp= new matel4<I,T>; ltmp->next=list; list=ltmp; list->index=index; list->elem=elem;}
|
||||
|
||||
inline void add(const I (&index)[4], const T elem)
|
||||
{matel4<I,T> *ltmp= new matel4<I,T>; ltmp->next=list; list=ltmp; memcpy(&list->index.packed, &index, sizeof(typename matel4<I,T>::packedindex)); list->elem=elem;}
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||||
|
||||
|
||||
|
||||
};
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||||
|
||||
|
||||
//destructor
|
||||
template <class I,class T>
|
||||
fourindex<I,T>::~fourindex()
|
||||
{
|
||||
if(!count) return;
|
||||
if(--(*count)<=0)
|
||||
{
|
||||
deletelist();
|
||||
delete count;
|
||||
}
|
||||
}
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||||
|
||||
//copy constructor (sort arrays are not going to be copied)
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||||
template <class I, class T>
|
||||
fourindex<I,T>::fourindex(const fourindex<I,T> &rhs)
|
||||
{
|
||||
#ifdef debug
|
||||
if(! &rhs) laerror("fourindex copy constructor with NULL argument");
|
||||
#endif
|
||||
nn=rhs.nn;
|
||||
if(rhs.list&&!rhs.count) laerror("some inconsistency in fourindex contructors or assignments");
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||||
list=rhs.list;
|
||||
if(list) {count=rhs.count; (*count)++;} else count=new int(1); //make the matrix defined, but empty and not shared
|
||||
}
|
||||
|
||||
|
||||
|
||||
//assignment operator
|
||||
template <class I, class T>
|
||||
fourindex<I,T> & fourindex<I,T>::operator=(const fourindex<I,T> &rhs)
|
||||
{
|
||||
if (this != &rhs)
|
||||
{
|
||||
if(count)
|
||||
if(--(*count) ==0) {deletelist(); delete count;} // old stuff obsolete
|
||||
list=rhs.list;
|
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nn=rhs.nn;
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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
|
||||
if(count) (*count)++;
|
||||
}
|
||||
return *this;
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||||
}
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||||
|
||||
|
||||
template <class I, class T>
|
||||
fourindex<I,T> & fourindex<I,T>::operator+=(const fourindex<I,T> &rhs)
|
||||
{
|
||||
if(nn!=rhs.nn) laerror("incompatible dimensions for +=");
|
||||
if(!count) {count=new int; *count=1; list=NULL;}
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||||
else copyonwrite();
|
||||
register matel4<I,T> *l=rhs.list;
|
||||
while(l)
|
||||
{
|
||||
add( l->index,l->elem);
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||||
l=l->next;
|
||||
}
|
||||
return *this;
|
||||
}
|
||||
|
||||
template <class I, class T>
|
||||
fourindex<I,T> & fourindex<I,T>::join(fourindex<I,T> &rhs)
|
||||
{
|
||||
if(nn!=rhs.nn) laerror("incompatible dimensions for join");
|
||||
if(*rhs.count!=1) laerror("shared rhs in join()");
|
||||
if(!count) {count=new int; *count=1; list=NULL;}
|
||||
else copyonwrite();
|
||||
matel4<I,T> **last=&list;
|
||||
while(*last) last= &((*last)->next);
|
||||
*last=rhs.list;
|
||||
rhs.list=NULL;
|
||||
return *this;
|
||||
}
|
||||
|
||||
template <class I, class T>
|
||||
void fourindex<I,T>::resize(const I n)
|
||||
{
|
||||
if(n<=0 ) laerror("illegal fourindex dimension");
|
||||
if(count)
|
||||
{
|
||||
if(*count > 1) {(*count)--; count=NULL; list=NULL;} //detach from previous
|
||||
else if(*count==1) deletelist();
|
||||
}
|
||||
nn=n;
|
||||
count=new int(1); //empty but defined matrix
|
||||
list=NULL;
|
||||
}
|
||||
|
||||
|
||||
template <class I, class T>
|
||||
void fourindex<I,T>::deletelist()
|
||||
{
|
||||
if(*count >1) laerror("trying to delete shared list");
|
||||
matel4<I,T> *l=list;
|
||||
while(l)
|
||||
{
|
||||
matel4<I,T> *ltmp=l;
|
||||
l=l->next;
|
||||
delete ltmp;
|
||||
}
|
||||
list=NULL;
|
||||
delete count;
|
||||
count=NULL;
|
||||
}
|
||||
|
||||
template <class I, class T>
|
||||
void fourindex<I,T>::copylist(const matel4<I,T> *l)
|
||||
{
|
||||
list=NULL;
|
||||
while(l)
|
||||
{
|
||||
add(l->index,l->elem);
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||||
l=l->next;
|
||||
}
|
||||
}
|
||||
|
||||
template <class I, class T>
|
||||
void fourindex<I,T>::copyonwrite()
|
||||
{
|
||||
if(!count) laerror("probably an assignment to undefined fourindex");
|
||||
if(*count > 1)
|
||||
{
|
||||
(*count)--;
|
||||
count = new int; *count=1;
|
||||
if(!list) laerror("empty list with count>1");
|
||||
copylist(list);
|
||||
}
|
||||
}
|
||||
|
||||
template <class I, class T>
|
||||
int fourindex<I,T>::length() const
|
||||
{
|
||||
int n=0;
|
||||
matel4<I,T> *l=list;
|
||||
while(l)
|
||||
{
|
||||
++n;
|
||||
l=l->next;
|
||||
}
|
||||
return n;
|
||||
}
|
||||
|
||||
|
||||
template <class I, class T>
|
||||
ostream& operator<<(ostream &s, const fourindex<I,T> &x)
|
||||
{
|
||||
int n;
|
||||
n=x.size();
|
||||
s << n << '\n';
|
||||
typename fourindex<I,T>::iterator it=x.begin();
|
||||
while(it!=x.end())
|
||||
{
|
||||
s << (int)it->index.indiv.i << ' ' << (int)it->index.indiv.j<< ' ' <<(int)it->index.indiv.k << ' ' << (int)it->index.indiv.l << ' ' << it->elem << '\n';
|
||||
++it;
|
||||
}
|
||||
s << "-1 -1 -1 -1\n";
|
||||
return s;
|
||||
}
|
||||
|
||||
template <class I, class T>
|
||||
istream& operator>>(istream &s, fourindex<I,T> &x)
|
||||
{
|
||||
int i,j,k,l;
|
||||
T elem;
|
||||
int n;
|
||||
s >> n ;
|
||||
x.resize(n);
|
||||
s >> i >> j >>k >>l;
|
||||
while(i>=0 && j>=0 &&k>=0 &&l>=0)
|
||||
{
|
||||
s>>elem;
|
||||
x.add(i,j,k,l,elem);
|
||||
s >> i >> j >>k >>ll;
|
||||
}
|
||||
return s;
|
||||
}
|
||||
|
||||
|
||||
#endif /*_fourindex_included*/
|
||||
|
|
@ -0,0 +1,9 @@
|
|||
#ifndef _LA_H_
|
||||
#define _LA_H_
|
||||
|
||||
#include "vec.h"
|
||||
#include "smat.h"
|
||||
#include "mat.h"
|
||||
#include "nonclass.h"
|
||||
|
||||
#endif /* _LA_H_ */
|
||||
|
|
@ -0,0 +1,40 @@
|
|||
////////////////////////////////////////////////////////////////////////////
|
||||
//traits classes
|
||||
|
||||
#ifndef _LA_TRAITS_INCL
|
||||
#define _LA_TRAITS_INCL
|
||||
|
||||
//default one, good for numbers
|
||||
template<class C> struct NRMat_traits {
|
||||
typedef C elementtype;
|
||||
typedef C producttype;
|
||||
static C norm (const C &x) {return abs(x);}
|
||||
static void axpy (C &s, const C &x, const C &c) {s+=x*c;}
|
||||
};
|
||||
|
||||
//specializations
|
||||
template<> struct NRMat_traits<NRMat<double> > {
|
||||
typedef double elementtype;
|
||||
typedef NRMat<double> producttype;
|
||||
static double norm (const NRMat<double> &x) {return x.norm();}
|
||||
static void axpy (NRMat<double>&s, const NRMat<double> &x, const double c) {s.axpy(c,x);}
|
||||
};
|
||||
|
||||
template<> struct NRMat_traits<NRSMat<double> > {
|
||||
typedef double elementtype;
|
||||
typedef NRMat<double> producttype;
|
||||
static const double norm (const NRSMat<double> &x) {return x.norm(0.);}
|
||||
static void axpy (NRSMat<double>&s, const NRSMat<double> &x, const double c) {s.axpy(c,x);}
|
||||
};
|
||||
|
||||
|
||||
template<> struct NRMat_traits<NRMat<complex<double> > > {
|
||||
typedef complex<double> elementtype;
|
||||
typedef NRMat<complex<double> > producttype;
|
||||
static double norm (const NRMat<complex<double> > &x) {return x.norm();}
|
||||
static void axpy (NRMat<complex<double> >&s, const NRMat<complex<double> > &x, const complex<double> c) {s.axpy(c,x);}
|
||||
};
|
||||
|
||||
|
||||
|
||||
#endif
|
||||
|
|
@ -0,0 +1,844 @@
|
|||
#include "mat.h"
|
||||
// TODO :
|
||||
//
|
||||
|
||||
//////////////////////////////////////////////////////////////////////////////
|
||||
//// forced instantization in the corresponding object file
|
||||
template NRMat<double>;
|
||||
template NRMat< complex<double> >;
|
||||
|
||||
|
||||
/*
|
||||
* Templates first, specializations for BLAS next
|
||||
*/
|
||||
|
||||
// dtor
|
||||
template <typename T>
|
||||
NRMat<T>::~NRMat()
|
||||
{
|
||||
if (!count) return;
|
||||
if (--(*count) <= 0) {
|
||||
if (v) {
|
||||
#ifdef MATPTR
|
||||
delete[] (v[0]);
|
||||
#endif
|
||||
delete[] v;
|
||||
}
|
||||
delete count;
|
||||
}
|
||||
}
|
||||
|
||||
// assign NRMat = NRMat
|
||||
template <typename T>
|
||||
NRMat<T> & NRMat<T>::operator=(const NRMat<T> &rhs)
|
||||
{
|
||||
if (this == &rhs) return *this;
|
||||
if (count) {
|
||||
if (--(*count) ==0 ) {
|
||||
#ifdef MATPTR
|
||||
delete[] (v[0]);
|
||||
#endif
|
||||
delete[] v;
|
||||
delete count;
|
||||
}
|
||||
v = rhs.v;
|
||||
nn = rhs.nn;
|
||||
mm = rhs.mm;
|
||||
count = rhs.count;
|
||||
if (count) (*count)--;
|
||||
}
|
||||
return *this;
|
||||
}
|
||||
|
||||
// Assign diagonal
|
||||
template <typename T>
|
||||
NRMat<T> & NRMat<T>::operator=(const T &a)
|
||||
{
|
||||
copyonwrite();
|
||||
#ifdef DEBUG
|
||||
if (nn != mm) laerror("RMat.operator=scalar on non-square matrix");
|
||||
#endif
|
||||
#ifdef MATPTR
|
||||
for (int i=0; i< nn; i++) v[i][i] = a;
|
||||
#else
|
||||
for (int i=0; i< nn*nn; i+=nn+1) v[i] = a;
|
||||
#endif
|
||||
return *this;
|
||||
}
|
||||
|
||||
// Explicit deep copy of NRmat
|
||||
template <typename T>
|
||||
NRMat<T> & NRMat<T>::operator|=(const NRMat<T> &rhs)
|
||||
{
|
||||
if (this == &rhs) return *this;
|
||||
#ifdef DEBUG
|
||||
if (!rhs.v) laerror("unallocated rhs in Mat operator |=");
|
||||
#endif
|
||||
if (count)
|
||||
if (*count > 1) {
|
||||
--(*count);
|
||||
nn = 0;
|
||||
mm = 0;
|
||||
count = 0;
|
||||
v = 0;
|
||||
}
|
||||
if (nn != rhs.nn || mm != rhs.mm) {
|
||||
if (v) {
|
||||
#ifdef MATPTR
|
||||
delete[] (v[0]);
|
||||
#endif
|
||||
delete[] (v);
|
||||
v = 0;
|
||||
}
|
||||
nn = rhs.nn;
|
||||
mm = rhs.mm;
|
||||
}
|
||||
if (!v) {
|
||||
#ifdef MATPTR
|
||||
v = new T*[nn];
|
||||
v[0] = new T[mm*nn];
|
||||
#else
|
||||
v = new T[mm*nn];
|
||||
#endif
|
||||
}
|
||||
|
||||
#ifdef MATPTR
|
||||
for (int i=1; i< nn; i++) v[i] = v[i-1] + mm;
|
||||
memcpy(v[0], rhs.v[0], nn*mm*sizeof(T));
|
||||
#else
|
||||
memcpy(v, rhs.v, nn*mm*sizeof(T));
|
||||
#endif
|
||||
|
||||
if (!count) count = new int;
|
||||
*count = 1;
|
||||
|
||||
return *this;
|
||||
}
|
||||
|
||||
// M += a
|
||||
template <typename T>
|
||||
NRMat<T> & NRMat<T>::operator+=(const T &a)
|
||||
{
|
||||
copyonwrite();
|
||||
#ifdef DEBUG
|
||||
if (nn != mm) laerror("Mat.operator+=scalar on non-square matrix");
|
||||
#endif
|
||||
#ifdef MATPTR
|
||||
for (int i=0; i< nn; i++) v[i][i] += a;
|
||||
#else
|
||||
for (int i=0; i< nn*nn; i+=nn+1) v[i] += a;
|
||||
#endif
|
||||
return *this;
|
||||
}
|
||||
|
||||
// M -= a
|
||||
template <typename T>
|
||||
NRMat<T> & NRMat<T>::operator-=(const T &a)
|
||||
{
|
||||
copyonwrite();
|
||||
#ifdef DEBUG
|
||||
if (nn != mm) laerror("Mat.operator-=scalar on non-square matrix");
|
||||
#endif
|
||||
#ifdef MATPTR
|
||||
for (int i=0; i< nn; i++) v[i][i] -= a;
|
||||
#else
|
||||
for (int i=0; i< nn*nn; i+=nn+1) v[i] -= a;
|
||||
#endif
|
||||
return *this;
|
||||
}
|
||||
|
||||
// unary minus
|
||||
template <typename T>
|
||||
const NRMat<T> NRMat<T>::operator-() const
|
||||
{
|
||||
NRMat<T> result(nn, mm);
|
||||
#ifdef MATPTR
|
||||
for (int i=0; i<nn*mm; i++) result.v[0][i]= -v[0][i];
|
||||
#else
|
||||
for (int i=0; i<nn*mm; i++) result.v[i]= -v[i];
|
||||
#endif
|
||||
return result;
|
||||
}
|
||||
|
||||
// direct sum
|
||||
template <typename T>
|
||||
const NRMat<T> NRMat<T>::operator&(const NRMat<T> & b) const
|
||||
{
|
||||
NRMat<T> result((T)0, nn+b.nn, mm+b.mm);
|
||||
for (int i=0; i<nn; i++) memcpy(result[i], (*this)[i], sizeof(T)*mm);
|
||||
for (int i=0; i<b.nn; i++) memcpy(result[nn+i]+nn, b[i], sizeof(T)*b.mm);
|
||||
return result;
|
||||
}
|
||||
|
||||
// direct product
|
||||
template <typename T>
|
||||
const NRMat<T> NRMat<T>::operator|(const NRMat<T> &b) const
|
||||
{
|
||||
NRMat<T> result(nn*b.nn, mm*b.mm);
|
||||
for (int i=0; i<nn; i++)
|
||||
for (int j=0; j<mm; j++)
|
||||
for (int k=0; k<b.nn; k++)
|
||||
for (int l=0; l<b.mm; l++)
|
||||
result[i*b.nn+k][j*b.mm+l] = (*this)[i][j]*b[k][l];
|
||||
return result;
|
||||
}
|
||||
|
||||
// sum of columns
|
||||
template <typename T>
|
||||
const NRVec<T> NRMat<T>::csum() const
|
||||
{
|
||||
NRVec<T> result(nn);
|
||||
T sum;
|
||||
|
||||
for (int i=0; i<nn; i++) {
|
||||
sum = (T)0;
|
||||
for(int j=0; j<mm; j++) sum += (*this)[i][j];
|
||||
result[i] = sum;
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
// sum of rows
|
||||
template <typename T>
|
||||
const NRVec<T> NRMat<T>::rsum() const
|
||||
{
|
||||
NRVec<T> result(nn);
|
||||
T sum;
|
||||
|
||||
for (int i=0; i<mm; i++) {
|
||||
sum = (T)0;
|
||||
for(int j=0; j<nn; j++) sum += (*this)[j][i];
|
||||
result[i] = sum;
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
// make detach Mat and make it's own deep copy
|
||||
template <typename T>
|
||||
void NRMat<T>::copyonwrite()
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (!count) laerror("Mat::copyonwrite of undefined matrix");
|
||||
#endif
|
||||
if (*count > 1) {
|
||||
(*count)--;
|
||||
count = new int;
|
||||
*count = 1;
|
||||
#ifdef MATPTR
|
||||
T **newv = new T*[nn];
|
||||
newv[0] = new T[mm*nn];
|
||||
memcpy(newv[0], v[0], mm*nn*sizeof(T));
|
||||
v = newv;
|
||||
for (int i=1; i< nn; i++) v[i] = v[i-1] + mm;
|
||||
#else
|
||||
T *newv = new T[mm*nn];
|
||||
memcpy(newv, v, mm*nn*sizeof(T));
|
||||
v = newv;
|
||||
#endif
|
||||
}
|
||||
}
|
||||
|
||||
template <typename T>
|
||||
void NRMat<T>::resize(const int n, const int m)
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (n<=0 || m<=0) laerror("illegal dimensions in Mat::resize()");
|
||||
#endif
|
||||
if (count)
|
||||
if (*count > 1) {
|
||||
(*count)--;
|
||||
count = 0;
|
||||
v = 0;
|
||||
nn = 0;
|
||||
mm = 0;
|
||||
}
|
||||
if (!count) {
|
||||
count = new int;
|
||||
*count = 1;
|
||||
nn = n;
|
||||
mm = m;
|
||||
#ifdef MATPTR
|
||||
v = new T*[nn];
|
||||
v[0] = new T[m*n];
|
||||
for (int i=1; i< n; i++) v[i] = v[i-1] + m;
|
||||
#else
|
||||
v = new T[m*n];
|
||||
#endif
|
||||
return;
|
||||
}
|
||||
// At this point *count = 1, check if resize is necessary
|
||||
if (n!=nn || m!=mm) {
|
||||
nn = n;
|
||||
mm = m;
|
||||
#ifdef MATPTR
|
||||
delete[] (v[0]);
|
||||
#endif
|
||||
delete[] v;
|
||||
#ifdef MATPTR
|
||||
v = new T*[nn];
|
||||
v[0] = new T[m*n];
|
||||
for (int i=1; i< n; i++) v[i] = v[i-1] + m;
|
||||
#else
|
||||
v = new T[m*n];
|
||||
#endif
|
||||
}
|
||||
}
|
||||
|
||||
// transpose Mat
|
||||
template <typename T>
|
||||
NRMat<T> & NRMat<T>::transposeme()
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (nn != mm) laerror("transpose of non-square Mat");
|
||||
#endif
|
||||
copyonwrite();
|
||||
for(int i=1; i<nn; i++)
|
||||
for(int j=0; j<i; j++) {
|
||||
#ifdef MATPTR
|
||||
T tmp = v[i][j];
|
||||
v[i][j] = v[j][i];
|
||||
v[j][i] = tmp;
|
||||
#else
|
||||
register int a;
|
||||
register int b;
|
||||
a = i*mm+j;
|
||||
b = j*mm+i;
|
||||
T tmp = v[a];
|
||||
v[a] = v[b];
|
||||
v[b] = tmp;
|
||||
#endif
|
||||
}
|
||||
return *this;
|
||||
}
|
||||
|
||||
// Output of Mat
|
||||
template <typename T>
|
||||
void NRMat<T>::fprintf(FILE *file, const char *format, const int modulo) const
|
||||
{
|
||||
lawritemat(file, (const T*)(*this), nn, mm, format, 2, modulo, 0);
|
||||
}
|
||||
|
||||
// Input of Mat
|
||||
template <typename T>
|
||||
void NRMat<T>::fscanf(FILE *f, const char *format)
|
||||
{
|
||||
int n, m;
|
||||
if (std::fscanf(f, "%d %d", &n, &m) != 2)
|
||||
laerror("cannot read matrix dimensions in Mat::fscanf()");
|
||||
resize(n,m);
|
||||
T *p = *this;
|
||||
for(int i=0; i<n; i++)
|
||||
for(int j=0; j<n; j++)
|
||||
if(std::fscanf(f,format,p++) != 1)
|
||||
laerror("cannot read matrix element in Mat::fscanf()");
|
||||
}
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
/*
|
||||
* BLAS specializations for double and complex<double>
|
||||
*/
|
||||
|
||||
// Mat *= a
|
||||
NRMat<double> & NRMat<double>::operator*=(const double &a)
|
||||
{
|
||||
copyonwrite();
|
||||
cblas_dscal(nn*mm, a, *this, 1);
|
||||
return *this;
|
||||
}
|
||||
NRMat< complex<double> > &
|
||||
NRMat< complex<double> >::operator*=(const complex<double> &a)
|
||||
{
|
||||
copyonwrite();
|
||||
cblas_zscal(nn*mm, &a, (void *)(*this)[0], 1);
|
||||
return *this;
|
||||
}
|
||||
|
||||
// Mat += Mat
|
||||
NRMat<double> & NRMat<double>::operator+=(const NRMat<double> &rhs)
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (nn != rhs.nn || mm!= rhs.mm)
|
||||
laerror("Mat += Mat of incompatible matrices");
|
||||
#endif
|
||||
copyonwrite();
|
||||
cblas_daxpy(nn*mm, 1.0, rhs, 1, *this, 1);
|
||||
return *this;
|
||||
}
|
||||
NRMat< complex<double> > &
|
||||
NRMat< complex<double> >::operator+=(const NRMat< complex<double> > &rhs)
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (nn != rhs.nn || mm!= rhs.mm)
|
||||
laerror("Mat += Mat of incompatible matrices");
|
||||
#endif
|
||||
copyonwrite();
|
||||
cblas_zaxpy(nn*mm, &CONE, (void *)rhs[0], 1, (void *)(*this)[0], 1);
|
||||
return *this;
|
||||
}
|
||||
|
||||
// Mat -= Mat
|
||||
NRMat<double> & NRMat<double>::operator-=(const NRMat<double> &rhs)
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (nn != rhs.nn || mm!= rhs.mm)
|
||||
laerror("Mat -= Mat of incompatible matrices");
|
||||
#endif
|
||||
copyonwrite();
|
||||
cblas_daxpy(nn*mm, -1.0, rhs, 1, *this, 1);
|
||||
return *this;
|
||||
}
|
||||
NRMat< complex<double> > &
|
||||
NRMat< complex<double> >::operator-=(const NRMat< complex<double> > &rhs)
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (nn != rhs.nn || mm!= rhs.mm)
|
||||
laerror("Mat -= Mat of incompatible matrices");
|
||||
#endif
|
||||
copyonwrite();
|
||||
cblas_zaxpy(nn*mm, &CMONE, (void *)rhs[0], 1, (void *)(*this)[0], 1);
|
||||
return *this;
|
||||
}
|
||||
|
||||
// Mat += SMat
|
||||
NRMat<double> & NRMat<double>::operator+=(const NRSMat<double> &rhs)
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (nn!=mm || nn!=rhs.nrows()) laerror("incompatible matrix size in Mat+=SMat");
|
||||
#endif
|
||||
const double *p = rhs;
|
||||
copyonwrite();
|
||||
for (int i=0; i<nn; i++) {
|
||||
cblas_daxpy(i+1, 1.0, p, 1, (*this)[i], 1);
|
||||
p += i+1;
|
||||
}
|
||||
p = rhs; p++;
|
||||
for (int i=1; i<nn; i++) {
|
||||
cblas_daxpy(i, 1.0, p, 1, (*this)[0]+i, nn);
|
||||
p += i+1;
|
||||
}
|
||||
return *this;
|
||||
}
|
||||
NRMat< complex<double> > &
|
||||
NRMat< complex<double> >::operator+=(const NRSMat< complex<double> > &rhs)
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (nn!=mm || nn!=rhs.nrows()) laerror("incompatible matrix size in Mat+=SMat");
|
||||
#endif
|
||||
const complex<double> *p = rhs;
|
||||
copyonwrite();
|
||||
for (int i=0; i<nn; i++) {
|
||||
cblas_zaxpy(i+1, (void *)&CONE, (void *)p, 1, (void *)(*this)[i], 1);
|
||||
p += i+1;
|
||||
}
|
||||
p = rhs; p++;
|
||||
for (int i=1; i<nn; i++) {
|
||||
cblas_zaxpy(i, (void *)&CONE, (void *)p, 1, (void *)((*this)[i]+i), nn);
|
||||
p += i+1;
|
||||
}
|
||||
return *this;
|
||||
}
|
||||
|
||||
// Mat -= SMat
|
||||
NRMat<double> & NRMat<double>::operator-=(const NRSMat<double> &rhs)
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (nn!=mm || nn!=rhs.nrows()) laerror("incompatible matrix size in Mat-=SMat");
|
||||
#endif
|
||||
const double *p = rhs;
|
||||
copyonwrite();
|
||||
for (int i=0; i<nn; i++) {
|
||||
cblas_daxpy(i+1, -1.0, p, 1, (*this)[i], 1);
|
||||
p += i+1;
|
||||
}
|
||||
p = rhs; p++;
|
||||
for (int i=1; i<nn; i++) {
|
||||
cblas_daxpy(i, -1.0, p, 1, (*this)[0]+i, nn);
|
||||
p += i+1;
|
||||
}
|
||||
return *this;
|
||||
}
|
||||
NRMat< complex<double> > &
|
||||
NRMat< complex<double> >::operator-=(const NRSMat< complex<double> > &rhs)
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (nn!=mm || nn!=rhs.nrows()) laerror("incompatible matrix size in Mat-=SMat");
|
||||
#endif
|
||||
const complex<double> *p = rhs;
|
||||
copyonwrite();
|
||||
for (int i=0; i<nn; i++) {
|
||||
cblas_zaxpy(i+1, (void *)&CMONE, (void *)p, 1, (void *)(*this)[i], 1);
|
||||
p += i+1;
|
||||
}
|
||||
p = rhs; p++;
|
||||
for (int i=1; i<nn; i++) {
|
||||
cblas_zaxpy(i, (void *)&CMONE, (void *)p, 1, (void *)((*this)[i]+i), nn);
|
||||
p += i+1;
|
||||
}
|
||||
return *this;
|
||||
}
|
||||
|
||||
// Mat.Mat - scalar product
|
||||
const double NRMat<double>::dot(const NRMat<double> &rhs) const
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if(nn!=rhs.nn || mm!= rhs.mm) laerror("Mat.Mat incompatible matrices");
|
||||
#endif
|
||||
return cblas_ddot(nn*mm, (*this)[0], 1, rhs[0], 1);
|
||||
}
|
||||
const complex<double>
|
||||
NRMat< complex<double> >::dot(const NRMat< complex<double> > &rhs) const
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if(nn!=rhs.nn || mm!= rhs.mm) laerror("Mat.Mat incompatible matrices");
|
||||
#endif
|
||||
complex<double> dot;
|
||||
cblas_zdotc_sub(nn*mm, (void *)(*this)[0], 1, (void *)rhs[0], 1,
|
||||
(void *)(&dot));
|
||||
return dot;
|
||||
}
|
||||
|
||||
// Mat * Mat
|
||||
const NRMat<double> NRMat<double>::operator*(const NRMat<double> &rhs) const
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (mm != rhs.nn) laerror("product of incompatible matrices");
|
||||
#endif
|
||||
NRMat<double> result(nn, rhs.mm);
|
||||
cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, nn, rhs.mm, mm, 1.0,
|
||||
*this, mm, rhs, rhs.mm, 0.0, result, rhs.mm);
|
||||
return result;
|
||||
}
|
||||
const NRMat< complex<double> >
|
||||
NRMat< complex<double> >::operator*(const NRMat< complex<double> > &rhs) const
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (mm != rhs.nn) laerror("product of incompatible matrices");
|
||||
#endif
|
||||
NRMat< complex<double> > result(nn, rhs.mm);
|
||||
cblas_zgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, nn, rhs.mm, mm,
|
||||
(const void *)(&CONE),(const void *)(*this)[0], mm, (const void *)rhs[0],
|
||||
rhs.mm, (const void *)(&CZERO), (void *)result[0], rhs.mm);
|
||||
return result;
|
||||
}
|
||||
|
||||
// Multiply by diagonal from L
|
||||
void NRMat<double>::diagmultl(const NRVec<double> &rhs)
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (nn != rhs.size()) laerror("incompatible matrix dimension in diagmultl");
|
||||
#endif
|
||||
copyonwrite();
|
||||
for(int i=0; i<nn; i++) cblas_dscal(mm, rhs[i], (*this)[i], 1);
|
||||
}
|
||||
void NRMat< complex<double> >::diagmultl(const NRVec< complex<double> > &rhs)
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (nn != rhs.size()) laerror("incompatible matrix dimension in diagmultl");
|
||||
#endif
|
||||
copyonwrite();
|
||||
for (int i=0; i<nn; i++) cblas_zscal(mm, &rhs[i], (*this)[i], 1);
|
||||
}
|
||||
|
||||
// Multiply by diagonal from R
|
||||
void NRMat<double>::diagmultr(const NRVec<double> &rhs)
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (mm != rhs.size()) laerror("incompatible matrix dimension in diagmultr");
|
||||
#endif
|
||||
copyonwrite();
|
||||
for (int i=0; i<mm; i++) cblas_dscal(nn, rhs[i], (*this)[i], mm);
|
||||
}
|
||||
void NRMat< complex<double> >::diagmultr(const NRVec< complex<double> > &rhs)
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (mm != rhs.size()) laerror("incompatible matrix dimension in diagmultl");
|
||||
#endif
|
||||
copyonwrite();
|
||||
for (int i=0; i<mm; i++) cblas_zscal(nn, &rhs[i], (*this)[i], mm);
|
||||
}
|
||||
|
||||
// Mat * Smat, decomposed to nn x Vec * Smat
|
||||
const NRMat<double>
|
||||
NRMat<double>::operator*(const NRSMat<double> &rhs) const
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (mm != rhs.nrows()) laerror("incompatible dimension in Mat*SMat");
|
||||
#endif
|
||||
NRMat<double> result(nn, rhs.ncols());
|
||||
for (int i=0; i<nn; i++)
|
||||
cblas_dspmv(CblasRowMajor, CblasLower, mm, 1.0, &rhs[0],
|
||||
(*this)[i], 1, 0.0, result[i], 1);
|
||||
return result;
|
||||
}
|
||||
const NRMat< complex<double> >
|
||||
NRMat< complex<double> >::operator*(const NRSMat< complex<double> > &rhs) const
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (mm != rhs.nrows()) laerror("incompatible dimension in Mat*SMat");
|
||||
#endif
|
||||
NRMat< complex<double> > result(nn, rhs.ncols());
|
||||
for (int i=0; i<nn; i++)
|
||||
cblas_zhpmv(CblasRowMajor, CblasLower, mm, (void *)&CONE, (void *)&rhs[0],
|
||||
(void *)(*this)[i], 1, (void *)&CZERO, (void *)result[i], 1);
|
||||
return result;
|
||||
}
|
||||
|
||||
// Mat * Vec
|
||||
const NRVec<double>
|
||||
NRMat<double>::operator*(const NRVec<double> &vec) const
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if(mm != vec.size()) laerror("incompatible sizes in Mat*Vec");
|
||||
#endif
|
||||
NRVec<double> result(nn);
|
||||
cblas_dgemv(CblasRowMajor, CblasNoTrans, nn, mm, 1.0, (*this)[0],
|
||||
mm, &vec[0], 1, 0.0, &result[0], 1);
|
||||
return result;
|
||||
}
|
||||
const NRVec< complex<double> >
|
||||
NRMat< complex<double> >::operator*(const NRVec< complex<double> > &vec) const
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if(mm != vec.size()) laerror("incompatible sizes in Mat*Vec");
|
||||
#endif
|
||||
NRVec< complex<double> > result(nn);
|
||||
cblas_zgemv(CblasRowMajor, CblasNoTrans, nn, mm, (void *)&CONE, (void *)(*this)[0],
|
||||
mm, (void *)&vec[0], 1, (void *)&CZERO, (void *)&result[0], 1);
|
||||
return result;
|
||||
}
|
||||
|
||||
// sum of rows
|
||||
const NRVec<double> NRMat<double>::rsum() const
|
||||
{
|
||||
NRVec<double> result(mm);
|
||||
for (int i=0; i<mm; i++) result[i] = cblas_dasum(nn,(*this)[0]+i,mm);
|
||||
return result;
|
||||
}
|
||||
|
||||
// sum of columns
|
||||
const NRVec<double> NRMat<double>::csum() const
|
||||
{
|
||||
NRVec<double> result(nn);
|
||||
for (int i=0; i<nn; i++) result[i] = cblas_dasum(mm, (*this)[i], 1);
|
||||
return result;
|
||||
}
|
||||
|
||||
// complex conjugate of Mat
|
||||
NRMat<double> &NRMat<double>::conjugateme() {return *this;}
|
||||
|
||||
NRMat< complex<double> > & NRMat< complex<double> >::conjugateme()
|
||||
{
|
||||
copyonwrite();
|
||||
cblas_dscal(mm*nn, -1.0, (double *)((*this)[0])+1, 2);
|
||||
return *this;
|
||||
}
|
||||
|
||||
// transpose and optionally conjugate
|
||||
const NRMat<double> NRMat<double>::transpose(bool conj) const
|
||||
{
|
||||
NRMat<double> result(mm,nn);
|
||||
for(int i=0; i<nn; i++) cblas_dcopy(mm, (*this)[i], 1, result[0]+i, nn);
|
||||
return result;
|
||||
}
|
||||
const NRMat< complex<double> >
|
||||
NRMat< complex<double> >::transpose(bool conj) const
|
||||
{
|
||||
NRMat< complex<double> > result(mm,nn);
|
||||
for (int i=0; i<nn; i++)
|
||||
cblas_zcopy(mm, (void *)(*this)[i], 1, (void *)(result[0]+i), nn);
|
||||
if (conj) cblas_dscal(mm*nn, -1.0, (double *)(result[0])+1, 2);
|
||||
return result;
|
||||
}
|
||||
|
||||
// gemm : this = alpha*op( A )*op( B ) + beta*this
|
||||
void NRMat<double>::gemm(const double &beta, const NRMat<double> &a,
|
||||
const char transa, const NRMat<double> &b, const char transb,
|
||||
const double &alpha)
|
||||
{
|
||||
int l(transa=='n'?a.nn:a.mm);
|
||||
int k(transa=='n'?a.mm:a.nn);
|
||||
int kk(transb=='n'?b.nn:b.mm);
|
||||
int ll(transb=='n'?b.mm:b.nn);
|
||||
|
||||
#ifdef DEBUG
|
||||
if (l!=nn || ll!=mm || k!=kk) laerror("incompatible matrices in Mat:gemm()");
|
||||
#endif
|
||||
if (alpha==0.0 && beta==1.0) return;
|
||||
|
||||
copyonwrite();
|
||||
cblas_dgemm(CblasRowMajor, (transa=='n' ? CblasNoTrans : CblasTrans),
|
||||
(transb=='n' ? CblasNoTrans : CblasTrans), nn, mm, k, alpha, a,
|
||||
a.mm, b , b.mm, beta, *this , mm);
|
||||
}
|
||||
void NRMat< complex<double> >::gemm(const complex<double> & beta,
|
||||
const NRMat< complex<double> > & a, const char transa,
|
||||
const NRMat< complex<double> > & b, const char transb,
|
||||
const complex<double> & alpha)
|
||||
{
|
||||
int l(transa=='n'?a.nn:a.mm);
|
||||
int k(transa=='n'?a.mm:a.nn);
|
||||
int kk(transb=='n'?b.nn:b.mm);
|
||||
int ll(transb=='n'?b.mm:b.nn);
|
||||
|
||||
#ifdef DEBUG
|
||||
if (l!=nn || ll!=mm || k!=kk) laerror("incompatible matrices in Mat:gemm()");
|
||||
#endif
|
||||
if (alpha==CZERO && beta==CONE) return;
|
||||
|
||||
copyonwrite();
|
||||
cblas_zgemm(CblasRowMajor,
|
||||
(transa=='n' ? CblasNoTrans : (transa=='c'?CblasConjTrans:CblasTrans)),
|
||||
(transb=='n' ? CblasNoTrans : (transa=='c'?CblasConjTrans:CblasTrans)),
|
||||
nn, mm, k, &alpha, a , a.mm, b , b.mm, &beta, *this , mm);
|
||||
}
|
||||
|
||||
// norm of Mat
|
||||
const double NRMat<double>::norm(const double scalar) const
|
||||
{
|
||||
if (!scalar) return cblas_dnrm2(nn*mm, (*this)[0], 1);
|
||||
double sum = 0;
|
||||
for (int i=0; i<nn; i++)
|
||||
for (int j=0; j<mm; j++) {
|
||||
register double tmp;
|
||||
#ifdef MATPTR
|
||||
tmp = v[i][j];
|
||||
#else
|
||||
tmp = v[i*mm+j];
|
||||
#endif
|
||||
if (i==j) tmp -= scalar;
|
||||
sum += tmp*tmp;
|
||||
}
|
||||
return sqrt(sum);
|
||||
}
|
||||
const double NRMat< complex<double> >::norm(const complex<double> scalar) const
|
||||
{
|
||||
if (scalar == CZERO) return cblas_dznrm2(nn*mm, (*this)[0], 1);
|
||||
double sum = 0;
|
||||
for (int i=0; i<nn; i++)
|
||||
for (int j=0; j<mm; j++) {
|
||||
register complex<double> tmp;
|
||||
#ifdef MATPTR
|
||||
tmp = v[i][j];
|
||||
#else
|
||||
tmp = v[i*mm+j];
|
||||
#endif
|
||||
if (i==j) tmp -= scalar;
|
||||
sum += tmp.real()*tmp.real()+tmp.imag()*tmp.imag();
|
||||
}
|
||||
return sqrt(sum);
|
||||
}
|
||||
|
||||
// axpy: this = a * Mat
|
||||
void NRMat<double>::axpy(const double alpha, const NRMat<double> &mat)
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (nn!=mat.nn || mm!=mat.mm) laerror("daxpy of incompatible matrices");
|
||||
#endif
|
||||
copyonwrite();
|
||||
cblas_daxpy(nn*mm, alpha, mat, 1, *this, 1);
|
||||
}
|
||||
void NRMat< complex<double> >::axpy(const complex<double> alpha,
|
||||
const NRMat< complex<double> > & mat)
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (nn!=mat.nn || mm!=mat.mm) laerror("zaxpy of incompatible matrices");
|
||||
#endif
|
||||
copyonwrite();
|
||||
cblas_zaxpy(nn*mm, (void *)&alpha, mat, 1, (void *)(*this)[0], 1);
|
||||
}
|
||||
|
||||
// trace of Mat
|
||||
const double NRMat<double>::trace() const
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (nn != mm) laerror("no-square matrix in Mat::trace()");
|
||||
#endif
|
||||
return cblas_dasum(nn, (*this)[0], nn+1);
|
||||
}
|
||||
const complex<double> NRMat< complex<double> >::trace() const
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (nn != mm) laerror("no-square matrix in Mat::trace()");
|
||||
#endif
|
||||
register complex<double> sum = CZERO;
|
||||
for (int i=0; i<nn*nn; i+=(nn+1))
|
||||
#ifdef MATPTR
|
||||
sum += v[0][i];
|
||||
#else
|
||||
sum += v[i];
|
||||
#endif
|
||||
return sum;
|
||||
}
|
||||
|
||||
//////////////////////////////////////////////////////////////////////////////
|
||||
//// forced instantization in the corespoding object file
|
||||
#define INSTANTIZE(T) \
|
||||
template ostream & operator<<(ostream &s, const NRMat< T > &x); \
|
||||
template istream & operator>>(istream &s, NRMat< T > &x); \
|
||||
|
||||
INSTANTIZE(double)
|
||||
INSTANTIZE(complex<double>)
|
||||
|
||||
|
||||
export template <class T>
|
||||
ostream& operator<<(ostream &s, const NRMat<T> &x)
|
||||
{
|
||||
int i,j,n,m;
|
||||
n=x.nrows();
|
||||
m=x.ncols();
|
||||
s << n << ' ' << m << '\n';
|
||||
for(i=0;i<n;i++)
|
||||
{
|
||||
for(j=0; j<m;j++) s << x[i][j] << (j==m-1 ? '\n' : ' '); // endl cannot be used in the conditional expression, since it is an overloaded function
|
||||
}
|
||||
return s;
|
||||
}
|
||||
|
||||
export template <class T>
|
||||
istream& operator>>(istream &s, NRMat<T> &x)
|
||||
{
|
||||
int i,j,n,m;
|
||||
s >> n >> m;
|
||||
x.resize(n,m);
|
||||
for(i=0;i<n;i++) for(j=0; j<m;j++) s>>x[i][j] ;
|
||||
return s;
|
||||
}
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
|
@ -0,0 +1,346 @@
|
|||
#ifndef _LA_MAT_H_
|
||||
#define _LA_MAT_H_
|
||||
|
||||
#include "vec.h"
|
||||
#include "smat.h"
|
||||
|
||||
template <typename T>
|
||||
class NRMat {
|
||||
protected:
|
||||
int nn;
|
||||
int mm;
|
||||
#ifdef MATPTR
|
||||
T **v;
|
||||
#else
|
||||
T *v;
|
||||
#endif
|
||||
int *count;
|
||||
public:
|
||||
friend class NRVec<T>;
|
||||
friend class NRSMat<T>;
|
||||
|
||||
inline NRMat() : nn(0), mm(0), v(0), count(0) {};
|
||||
inline NRMat(const int n, const int m);
|
||||
inline NRMat(const T &a, const int n, const int m);
|
||||
NRMat(const T *a, const int n, const int m);
|
||||
inline NRMat(const NRMat &rhs);
|
||||
explicit NRMat(const NRSMat<T> &rhs);
|
||||
#ifndef MATPTR
|
||||
NRMat(const NRVec<T> &rhs, const int n, const int m);
|
||||
#endif
|
||||
~NRMat();
|
||||
inline int getcount() const {return count?*count:0;}
|
||||
NRMat & operator=(const NRMat &rhs); //assignment
|
||||
NRMat & operator=(const T &a); //assign a to diagonal
|
||||
NRMat & operator|=(const NRMat &rhs); //assignment to a new copy
|
||||
NRMat & operator+=(const T &a); //add diagonal
|
||||
NRMat & operator-=(const T &a); //substract diagonal
|
||||
NRMat & operator*=(const T &a); //multiply by a scalar
|
||||
NRMat & operator+=(const NRMat &rhs);
|
||||
NRMat & operator-=(const NRMat &rhs);
|
||||
NRMat & operator+=(const NRSMat<T> &rhs);
|
||||
NRMat & operator-=(const NRSMat<T> &rhs);
|
||||
const NRMat operator-() const; //unary minus
|
||||
inline const NRMat operator+(const T &a) const;
|
||||
inline const NRMat operator-(const T &a) const;
|
||||
inline const NRMat operator*(const T &a) const;
|
||||
inline const NRMat operator+(const NRMat &rhs) const;
|
||||
inline const NRMat operator-(const NRMat &rhs) const;
|
||||
inline const NRMat operator+(const NRSMat<T> &rhs) const;
|
||||
inline const NRMat operator-(const NRSMat<T> &rhs) const;
|
||||
const T dot(const NRMat &rhs) const; // scalar product of Mat.Mat
|
||||
const NRMat operator*(const NRMat &rhs) const; // Mat * Mat
|
||||
void diagmultl(const NRVec<T> &rhs); //multiply by a diagonal matrix from L
|
||||
void diagmultr(const NRVec<T> &rhs); //multiply by a diagonal matrix from R
|
||||
const NRMat operator*(const NRSMat<T> &rhs) const; // Mat * Smat
|
||||
const NRMat operator&(const NRMat &rhs) const; // direct sum
|
||||
const NRMat operator|(const NRMat<T> &rhs) const; // direct product
|
||||
const NRVec<T> operator*(const NRVec<T> &rhs) const; // Mat * Vec
|
||||
const NRVec<T> rsum() const; //sum of rows
|
||||
const NRVec<T> csum() const; //sum of columns
|
||||
inline T* operator[](const int i); //subscripting: pointer to row i
|
||||
inline const T* operator[](const int i) const;
|
||||
inline T& operator()(const int i, const int j); // (i,j) subscripts
|
||||
inline const T& operator()(const int i, const int j) const;
|
||||
inline int nrows() const;
|
||||
inline int ncols() const;
|
||||
void copyonwrite();
|
||||
void resize(const int n, const int m);
|
||||
inline operator T*(); //get a pointer to the data
|
||||
inline operator const T*() const;
|
||||
NRMat & transposeme(); // square matrices only
|
||||
NRMat & conjugateme(); // square matrices only
|
||||
const NRMat transpose(bool conj=false) const;
|
||||
const NRMat conjugate() const;
|
||||
void gemm(const T &beta, const NRMat &a, const char transa, const NRMat &b,
|
||||
const char transb, const T &alpha);//this = alpha*op( A )*op( B ) + beta*this
|
||||
/*
|
||||
void strassen(const T beta, const NRMat &a, const char transa, const NRMat &b,
|
||||
const char transb, const T alpha);//this := alpha*op( A )*op( B ) + beta*this
|
||||
void s_cutoff(const int,const int,const int,const int) const;
|
||||
*/
|
||||
void fprintf(FILE *f, const char *format, const int modulo) const;
|
||||
void fscanf(FILE *f, const char *format);
|
||||
const double norm(const T scalar=(T)0) const;
|
||||
void axpy(const T alpha, const NRMat &x); // this += a*x
|
||||
inline const T amax() const;
|
||||
const T trace() const;
|
||||
|
||||
//members concerning sparse matrix
|
||||
explicit NRMat(const SparseMat<T> &rhs); // dense from sparse
|
||||
NRMat & operator+=(const SparseMat<T> &rhs);
|
||||
NRMat & operator-=(const SparseMat<T> &rhs);
|
||||
inline void simplify() {}; //just for compatibility with sparse ones
|
||||
|
||||
//Strassen's multiplication (better than n^3, analogous syntax to gemm)
|
||||
void strassen(const T beta, const NRMat &a, const char transa, const NRMat &b, const char transb, const T alpha);//this := alpha*op( A )*op( B ) + beta*this
|
||||
void s_cutoff(const int,const int,const int,const int) const;
|
||||
|
||||
};
|
||||
|
||||
// ctors
|
||||
template <typename T>
|
||||
NRMat<T>::NRMat(const int n, const int m) : nn(n), mm(m), count(new int)
|
||||
{
|
||||
*count = 1;
|
||||
#ifdef MATPTR
|
||||
v = new T*[n];
|
||||
v[0] = new T[m*n];
|
||||
for (int i=1; i<n; i++) v[i] = v[i-1] + m;
|
||||
#else
|
||||
v = new T[m*n];
|
||||
#endif
|
||||
}
|
||||
|
||||
template <typename T>
|
||||
NRMat<T>::NRMat(const T &a, const int n, const int m) : nn(n), mm(m), count(new int)
|
||||
{
|
||||
int i;
|
||||
T *p;
|
||||
*count = 1;
|
||||
#ifdef MATPTR
|
||||
v = new T*[n];
|
||||
p = v[0] = new T[m*n];
|
||||
for (int i=1; i<n; i++) v[i] = v[i-1] + m;
|
||||
#else
|
||||
p = v = new T[m*n];
|
||||
#endif
|
||||
if (a != (T)0)
|
||||
for (i=0; i< n*m; i++) *p++ = a;
|
||||
else
|
||||
memset(p, 0, n*m*sizeof(T));
|
||||
}
|
||||
|
||||
template <typename T>
|
||||
NRMat<T>::NRMat(const T *a, const int n, const int m) : nn(n), mm(m), count(new int)
|
||||
{
|
||||
*count = 1;
|
||||
#ifdef MATPTR
|
||||
v = new T*[n];
|
||||
v[0] = new T[m*n];
|
||||
for (int i=1; i<n; i++) v[i] = v[i-1] + m;
|
||||
memcpy(v[0], a, n*m*sizeof(T));
|
||||
#else
|
||||
v = new T[m*n];
|
||||
memcpy(v, a, n*m*sizeof(T));
|
||||
#endif
|
||||
}
|
||||
|
||||
template <typename T>
|
||||
NRMat<T>::NRMat(const NRMat &rhs)
|
||||
{
|
||||
nn = rhs.nn;
|
||||
mm = rhs.mm;
|
||||
count = rhs.count;
|
||||
v = rhs.v;
|
||||
if (count) ++(*count);
|
||||
}
|
||||
|
||||
template <typename T>
|
||||
NRMat<T>::NRMat(const NRSMat<T> &rhs)
|
||||
{
|
||||
int i;
|
||||
nn = mm = rhs.nrows();
|
||||
count = new int;
|
||||
*count = 1;
|
||||
#ifdef MATPTR
|
||||
v = new T*[nn];
|
||||
v[0] = new T[mm*nn];
|
||||
for (int i=1; i<nn; i++) v[i] = v[i-1] + mm;
|
||||
#else
|
||||
v = new T[mm*nn];
|
||||
#endif
|
||||
|
||||
int j, k = 0;
|
||||
#ifdef MATPTR
|
||||
for (i=0; i<nn; i++)
|
||||
for (j=0; j<=i; j++) v[i][j] = v[j][i] = rhs[k++];
|
||||
#else
|
||||
for (i=0; i<nn; i++)
|
||||
for (j=0; j<=i; j++) v[i*nn+j] = v[j*nn+i] = rhs[k++];
|
||||
#endif
|
||||
}
|
||||
|
||||
#ifndef MATPTR
|
||||
template <typename T>
|
||||
NRMat<T>::NRMat(const NRVec<T> &rhs, const int n, const int m)
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (n*m != rhs.nn) laerror("matrix dimensions incompatible with vector length");
|
||||
#endif
|
||||
nn = n;
|
||||
mm = m;
|
||||
count = rhs.count;
|
||||
v = rhs.v;
|
||||
(*count)++;
|
||||
}
|
||||
#endif
|
||||
|
||||
// Mat + Smat
|
||||
template <typename T>
|
||||
inline const NRMat<T> NRMat<T>::operator+(const NRSMat<T> &rhs) const
|
||||
{
|
||||
return NRMat<T>(*this) += rhs;
|
||||
}
|
||||
|
||||
// Mat - Smat
|
||||
template <typename T>
|
||||
inline const NRMat<T> NRMat<T>::operator-(const NRSMat<T> &rhs) const
|
||||
{
|
||||
return NRMat<T>(*this) -= rhs;
|
||||
}
|
||||
|
||||
// Mat[i] : pointer to the first element of i-th row
|
||||
template <typename T>
|
||||
inline T* NRMat<T>::operator[](const int i)
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (*count != 1) laerror("Mat lval use of [] with count > 1");
|
||||
if (i<0 || i>=nn) laerror("Mat [] out of range");
|
||||
if (!v) laerror("[] for unallocated Mat");
|
||||
#endif
|
||||
#ifdef MATPTR
|
||||
return v[i];
|
||||
#else
|
||||
return v+i*mm;
|
||||
#endif
|
||||
}
|
||||
template <typename T>
|
||||
inline const T* NRMat<T>::operator[](const int i) const
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (i<0 || i>=nn) laerror("Mat [] out of range");
|
||||
if (!v) laerror("[] for unallocated Mat");
|
||||
#endif
|
||||
#ifdef MATPTR
|
||||
return v[i];
|
||||
#else
|
||||
return v+i*mm;
|
||||
#endif
|
||||
}
|
||||
|
||||
// Mat(i,j) reference to the matrix element M_{ij}
|
||||
template <typename T>
|
||||
inline T & NRMat<T>::operator()(const int i, const int j)
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (*count != 1) laerror("Mat lval use of (,) with count > 1");
|
||||
if (i<0 || i>=nn || j<0 || j>mm) laerror("Mat (,) out of range");
|
||||
if (!v) laerror("(,) for unallocated Mat");
|
||||
#endif
|
||||
#ifdef MATPTR
|
||||
return v[i][j];
|
||||
#else
|
||||
return v[i*mm+j];
|
||||
#endif
|
||||
}
|
||||
template <typename T>
|
||||
inline const T & NRMat<T>::operator()(const int i, const int j) const
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (i<0 || i>=nn || j<0 || j>mm) laerror("Mat (,) out of range");
|
||||
if (!v) laerror("(,) for unallocated Mat");
|
||||
#endif
|
||||
#ifdef MATPTR
|
||||
return v[i][j];
|
||||
#else
|
||||
return v[i*mm+j];
|
||||
#endif
|
||||
}
|
||||
|
||||
// number of rows
|
||||
template <typename T>
|
||||
inline int NRMat<T>::nrows() const
|
||||
{
|
||||
return nn;
|
||||
}
|
||||
|
||||
// number of columns
|
||||
template <typename T>
|
||||
inline int NRMat<T>::ncols() const
|
||||
{
|
||||
return mm;
|
||||
}
|
||||
|
||||
// reference pointer to Mat
|
||||
template <typename T>
|
||||
inline NRMat<T>::operator T* ()
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (!v) laerror("unallocated Mat in operator T*");
|
||||
#endif
|
||||
#ifdef MATPTR
|
||||
return v[0];
|
||||
#else
|
||||
return v;
|
||||
#endif
|
||||
}
|
||||
template <typename T>
|
||||
inline NRMat<T>::operator const T* () const
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (!v) laerror("unallocated Mat in operator T*");
|
||||
#endif
|
||||
#ifdef MATPTR
|
||||
return v[0];
|
||||
#else
|
||||
return v;
|
||||
#endif
|
||||
}
|
||||
|
||||
// max element of Mat
|
||||
inline const double NRMat<double>::amax() const
|
||||
{
|
||||
#ifdef MATPTR
|
||||
return v[0][cblas_idamax(nn*mm, v[0], 1)];
|
||||
#else
|
||||
return v[cblas_idamax(nn*mm, v, 1)];
|
||||
#endif
|
||||
}
|
||||
inline const complex<double> NRMat< complex<double> >::amax() const
|
||||
{
|
||||
#ifdef MATPTR
|
||||
return v[0][cblas_izamax(nn*mm, (void *)v[0], 1)];
|
||||
#else
|
||||
return v[cblas_izamax(nn*mm, (void *)v, 1)];
|
||||
#endif
|
||||
}
|
||||
|
||||
|
||||
// I/O
|
||||
template <typename T> extern ostream& operator<<(ostream &s, const NRMat<T> &x);
|
||||
template <typename T> extern istream& operator>>(istream &s, NRMat<T> &x);
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
// generate operators: Mat + a, a + Mat, Mat * a
|
||||
NRVECMAT_OPER(Mat,+)
|
||||
NRVECMAT_OPER(Mat,-)
|
||||
NRVECMAT_OPER(Mat,*)
|
||||
// generate Mat + Mat, Mat - Mat
|
||||
NRVECMAT_OPER2(Mat,+)
|
||||
NRVECMAT_OPER2(Mat,-)
|
||||
|
||||
#endif /* _LA_MAT_H_ */
|
||||
|
|
@ -0,0 +1,259 @@
|
|||
//general routine for polynomial of a matrix, tuned to minimize the number
|
||||
//of matrix-matrix multiplications on cost of additions and memory
|
||||
// the polynom and exp routines will work on any type, for which traits class
|
||||
// is defined containing definition of an element type, norm and axpy operation
|
||||
|
||||
#include "la_traits.h"
|
||||
#include "sparsemat_traits.h"
|
||||
|
||||
template<class T,class R>
|
||||
const T polynom2(const T &x, const NRVec<R> &c)
|
||||
{
|
||||
int order=c.size()-1;
|
||||
T z,y;
|
||||
|
||||
//trivial reference implementation by horner scheme
|
||||
if(order==0) {y=x; y=c[0];} //to avoid the problem: we do not know the size of the matrix to contruct a scalar one
|
||||
else
|
||||
{
|
||||
int i;
|
||||
z=x*c[order];
|
||||
for(i=order-1; i>=0; i--)
|
||||
{
|
||||
if(i<order-1) z=y*x;
|
||||
y=z+c[i];
|
||||
}
|
||||
}
|
||||
|
||||
return y;
|
||||
}
|
||||
|
||||
|
||||
template<class T,class R>
|
||||
const T polynom(const T &x, const NRVec<R> &c)
|
||||
{
|
||||
int n=c.size()-1;
|
||||
int i,j,k,m=0,t;
|
||||
|
||||
if(n<=4) return polynom2(x,c); //here the horner scheme is optimal
|
||||
|
||||
//first find m which minimizes the number of multiplications
|
||||
j=10*n;
|
||||
for(i=2;i<=n+1;i++)
|
||||
{
|
||||
t=i-2+2*(n/i)-(n%i)?0:1;
|
||||
if(t<j)
|
||||
{
|
||||
j=t;
|
||||
m=i;
|
||||
}
|
||||
}
|
||||
|
||||
//allocate array for powers up to m
|
||||
T *xpows = new T[m];
|
||||
xpows[0]=x;
|
||||
for(i=1;i<m;i++) xpows[i]=xpows[i-1]*x;
|
||||
|
||||
|
||||
//run the summation loop
|
||||
T r,s,f;
|
||||
k= -1;
|
||||
for(i=0; i<=n/m;i++)
|
||||
{
|
||||
for(j=0;j<m;j++)
|
||||
{
|
||||
k++;
|
||||
if(k>n) break;
|
||||
if(j==0) {if(i==0) s=x; /*just to get the dimensions of the matrix*/ s=c[k]; /*create diagonal matrix*/}
|
||||
else
|
||||
NRMat_traits<T>::axpy(s,xpows[j-1],c[k]); //general s+=xpows[j-1]*c[k]; but more efficient for matrices
|
||||
}
|
||||
|
||||
if(i==0) {r=s; f=xpows[m-1];}
|
||||
else
|
||||
{
|
||||
r+= s*f;
|
||||
f=f*xpows[m-1];
|
||||
}
|
||||
}
|
||||
|
||||
delete[] xpows;
|
||||
return r;
|
||||
}
|
||||
|
||||
|
||||
//for general objects
|
||||
template<class T>
|
||||
const T ncommutator ( const T &x, const T &y, int nest=1, const bool right=1)
|
||||
{
|
||||
T z;
|
||||
if(right) {z=x; while(--nest>=0) z=z*y-y*z;}
|
||||
else {z=y; while(--nest>=0) z=x*z-z*x;}
|
||||
return z;
|
||||
}
|
||||
|
||||
template<class T>
|
||||
const T nanticommutator ( const T &x, const T &y, int nest=1, const bool right=1)
|
||||
{
|
||||
T z;
|
||||
if(right) {z=x; while(--nest>=0) z=z*y+y*z;}
|
||||
else {z=y; while(--nest>=0) z=x*z+z*x;}
|
||||
return z;
|
||||
}
|
||||
|
||||
//general BCH expansion (can be written more efficiently in a specialization for matrices)
|
||||
template<class T>
|
||||
const T BCHexpansion (const T &h, const T &t, const int n, const bool verbose=1)\
|
||||
{
|
||||
T result=h;
|
||||
double factor=1.;
|
||||
T z=h;
|
||||
for(int i=1; i<=n; ++i)
|
||||
{
|
||||
factor/=i;
|
||||
z= z*t-t*z;
|
||||
if(verbose) cerr << "BCH contribution at order "<<i<<" : "<<z.norm()<<endl;
|
||||
result+= z*factor;
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
|
||||
template<class T>
|
||||
const T ipow( const T &x, int i)
|
||||
{
|
||||
if(i<0) laerror("negative exponent in ipow");
|
||||
if(i==0) {T r=x; r=1.; return r;}//trick for matrix dimension
|
||||
if(i==1) return x;
|
||||
T y,z;
|
||||
z=x;
|
||||
while(!(i&1))
|
||||
{
|
||||
z = z*z;
|
||||
i >>= 1;
|
||||
}
|
||||
y=z;
|
||||
while((i >>= 1)/*!=0*/)
|
||||
{
|
||||
z = z*z;
|
||||
if(i&1) y = y*z;
|
||||
}
|
||||
return y;
|
||||
}
|
||||
|
||||
inline int nextpow2(const double n)
|
||||
{
|
||||
const double log2=log(2.);
|
||||
if(n<=.75) return 0; //try to keep the taylor expansion short
|
||||
if(n<=1.) return 1;
|
||||
return int(ceil(log(n)/log2-log(.75)));
|
||||
}
|
||||
|
||||
|
||||
template<class T>
|
||||
NRVec<typename NRMat_traits<T>::elementtype> exp_aux(const T &x, int &power)
|
||||
{
|
||||
//should better be computed by mathematica to have accurate last digits, chebyshev instead, see exp in glibc
|
||||
static double exptaylor[]={
|
||||
1.,
|
||||
1.,
|
||||
0.5,
|
||||
0.1666666666666666666666,
|
||||
0.0416666666666666666666,
|
||||
0.0083333333333333333333,
|
||||
0.0013888888888888888888,
|
||||
0.00019841269841269841253,
|
||||
2.4801587301587301566e-05,
|
||||
2.7557319223985892511e-06,
|
||||
2.7557319223985888276e-07,
|
||||
2.5052108385441720224e-08,
|
||||
2.0876756987868100187e-09,
|
||||
1.6059043836821613341e-10,
|
||||
1.1470745597729724507e-11,
|
||||
7.6471637318198164055e-13,
|
||||
4.7794773323873852534e-14,
|
||||
2.8114572543455205981e-15,
|
||||
1.5619206968586225271e-16,
|
||||
8.2206352466243294955e-18,
|
||||
4.1103176233121648441e-19,
|
||||
0.};
|
||||
double mnorm= NRMat_traits<T>::norm(x);
|
||||
power=nextpow2(mnorm);
|
||||
double scale=exp(-log(2.)*power);
|
||||
|
||||
|
||||
//find how long taylor expansion will be necessary
|
||||
const double precision=1e-16;
|
||||
double s,t;
|
||||
s=mnorm*scale;
|
||||
int n=0;
|
||||
t=1.;
|
||||
do {
|
||||
n++;
|
||||
t*=s;
|
||||
}
|
||||
while(t*exptaylor[n]>precision);//taylor 0 will terminate in any case
|
||||
|
||||
|
||||
int i; //adjust the coefficients in order to avoid scaling the argument
|
||||
NRVec<typename NRMat_traits<T>::elementtype> taylor2(n+1);
|
||||
for(i=0,t=1.;i<=n;i++)
|
||||
{
|
||||
taylor2[i]=exptaylor[i]*t;
|
||||
t*=scale;
|
||||
}
|
||||
return taylor2;
|
||||
}
|
||||
|
||||
|
||||
|
||||
template<class T>
|
||||
const T exp(const T &x)
|
||||
{
|
||||
int power;
|
||||
|
||||
//prepare the polynom of and effectively scale T
|
||||
NRVec<typename NRMat_traits<T>::elementtype> taylor2=exp_aux(x,power);
|
||||
|
||||
T r=polynom(x,taylor2); //for accuracy summing from the smallest terms up would be better, but this is more efficient for matrices
|
||||
|
||||
//power the result back
|
||||
for(int i=0; i<power; i++) r=r*r;
|
||||
return r;
|
||||
}
|
||||
|
||||
|
||||
template<class MAT>
|
||||
const typename NRMat_traits<MAT>::elementtype determinant(MAT a)//again passed by value
|
||||
{
|
||||
typename NRMat_traits<MAT>::elementtype det;
|
||||
if(a.nrows()!=a.ncols()) laerror("determinant of non-square matrix");
|
||||
linear_solve(a,NULL,&det);
|
||||
return det;
|
||||
}
|
||||
|
||||
|
||||
template<class M, class V>
|
||||
const V exptimes(const M &mat, V vec) //uses just matrix vector multiplication
|
||||
{
|
||||
if(mat.nrows()!=mat.ncols()||(unsigned int) mat.nrows() != (unsigned int)vec.size()) laerror("inappropriate sizes in exptimes");
|
||||
int power;
|
||||
//prepare the polynom of and effectively scale the matrix
|
||||
NRVec<typename NRMat_traits<M>::elementtype> taylor2=exp_aux(mat,power);
|
||||
|
||||
V result(mat.nrows());
|
||||
for(int i=1; i<=(1<<power); ++i) //unfortunatelly, here we have to repeat it many times, unlike if the matrix is stored explicitly
|
||||
{
|
||||
if(i>1) vec=result; //apply again to the result of previous application
|
||||
//apply polynom of the matrix to the vector iteratively
|
||||
V y=vec;
|
||||
result=y*taylor2[0];
|
||||
for(int j=1; j<taylor2.size(); ++j)
|
||||
{
|
||||
y=mat*y;
|
||||
result.axpy(taylor2[j],y);
|
||||
}
|
||||
}
|
||||
|
||||
return result;
|
||||
}
|
||||
|
|
@ -0,0 +1,524 @@
|
|||
extern "C" {
|
||||
#include "atlas_enum.h"
|
||||
#include "clapack.h"
|
||||
}
|
||||
#include "la.h"
|
||||
|
||||
#ifdef FORTRAN_
|
||||
#define FORNAME(x) x##_
|
||||
#else
|
||||
#define FORNAME(x) x
|
||||
#endif
|
||||
|
||||
#define INSTANTIZE(T) \
|
||||
template void lawritemat(FILE *file,const T *a,int r,int c,const char *form0, \
|
||||
int nodim,int modulo, int issym);
|
||||
INSTANTIZE(double)
|
||||
INSTANTIZE(complex<double>)
|
||||
|
||||
template <typename T>
|
||||
void lawritemat(FILE *file,const T *a,int r,int c,const char *form0,
|
||||
int nodim,int modulo, int issym)
|
||||
{
|
||||
int i,j;
|
||||
const char *f;
|
||||
|
||||
/*print out title before %*/
|
||||
f=form0;
|
||||
skiptext:
|
||||
while (*f && *f !='%' ) {fputc(*f++,file);}
|
||||
if (*f=='%' && f[1]=='%') {
|
||||
fputc(*f,file); f+=2;
|
||||
goto skiptext;
|
||||
}
|
||||
/* this has to be avoided when const arguments should be allowed *f=0; */
|
||||
/*use the rest as a format for numbers*/
|
||||
|
||||
if (modulo) nodim=0;
|
||||
if (nodim==2) fprintf(file,"%d %d\n",r,c);
|
||||
if (nodim==1) fprintf(file,"%d\n",c);
|
||||
if (modulo) {
|
||||
int n1, n2, l, m;
|
||||
char ff[32];
|
||||
/* prepare integer format for column numbering */
|
||||
if (sscanf(f+1,"%d",&l) != 1) l=128/modulo;
|
||||
l -= 2;
|
||||
m = l/2;
|
||||
l = l-m;
|
||||
sprintf(ff,"%%%ds%%3d%%%ds", l, m);
|
||||
n1 = 1;
|
||||
while(n1 <= c) {
|
||||
n2=n1+modulo-1;
|
||||
if (n2 > c) n2 = c;
|
||||
|
||||
/*write block between columns n1 and n2 */
|
||||
fprintf(file,"\n ");
|
||||
for (i=n1; i<=n2; i++) fprintf(file,ff," ",i," ");
|
||||
fprintf(file,"\n\n");
|
||||
|
||||
for (i=1; i<=r; i++) {
|
||||
fprintf(file, "%3d ", i);
|
||||
for (j=n1; j<=n2; j++) {
|
||||
if(issym) {
|
||||
int ii,jj;
|
||||
if (i >= j) {
|
||||
ii=i;
|
||||
jj=j;
|
||||
} else {
|
||||
ii=j;
|
||||
jj=i;
|
||||
}
|
||||
fprintf(file, f, ((complex<double>)a[ii*(ii+1)/2+jj]).real(), ((complex<double>)a[ii*(ii+1)/2+jj]).imag());
|
||||
} else fprintf(file, f, ((complex<double>)a[(i-1)*c+j-1]).real(), ((complex<double>)a[(i-1)*c+j-1]).imag());
|
||||
if (j < n2) fputc(' ',file);
|
||||
}
|
||||
fprintf(file, "\n");
|
||||
}
|
||||
n1 = n2+1;
|
||||
}
|
||||
} else {
|
||||
for (i=1; i<=r; i++) {
|
||||
for (j=1; j<=c; j++) {
|
||||
if (issym) {
|
||||
int ii,jj;
|
||||
if (i >= j) {
|
||||
ii=i;
|
||||
jj=j;
|
||||
} else {
|
||||
ii=j;
|
||||
jj=i;
|
||||
}
|
||||
fprintf(file, f, ((complex<double>)a[ii*(ii+1)/2+jj]).real(), ((complex<double>)a[ii*(ii+1)/2+jj]).imag());
|
||||
} else fprintf(file,f,((complex<double>)a[(i-1)*c+j-1]).real(), ((complex<double>)a[(i-1)*c+j-1]).imag());
|
||||
putc(j<c?' ':'\n',file);
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// LA errorr handler
|
||||
void laerror(const char *s1, const char *s2, const char *s3, const char *s4)
|
||||
{
|
||||
std::cerr << "LA:ERROR - ";
|
||||
if(!s1)
|
||||
std::cerr << "udefined.";
|
||||
else {
|
||||
if(s1) std::cerr << s1;
|
||||
if(s2) std::cerr << s2;
|
||||
if(s3) std::cerr << s3;
|
||||
if(s4) std::cerr << s4;
|
||||
}
|
||||
std::cerr << endl;
|
||||
exit(1);
|
||||
}
|
||||
|
||||
//////////////////////
|
||||
// LAPACK interface //
|
||||
//////////////////////
|
||||
|
||||
// A will be overwritten, B will contain the solutions, A is nxn, B is rhs x n
|
||||
void linear_solve(NRMat<double> &A, NRMat<double> *B, double *det)
|
||||
{
|
||||
int r, *ipiv;
|
||||
|
||||
if (A.nrows() != A.ncols()) laerror("linear_solve() call for non-square matrix");
|
||||
if (B && A.nrows() != B->ncols()) laerror("incompatible matrices in linear_solve()");
|
||||
A.copyonwrite();
|
||||
if (B) B->copyonwrite();
|
||||
ipiv = new int[A.nrows()];
|
||||
r = clapack_dgesv(CblasRowMajor, A.nrows(), B ? B->nrows() : 0, A[0], A.ncols(),
|
||||
ipiv, B ? B[0] : (double *)0, B ? B->ncols() : A.nrows());
|
||||
if (r < 0) {
|
||||
delete[] ipiv;
|
||||
laerror("illegal argument in lapack_gesv");
|
||||
}
|
||||
if (det && r>=0) {
|
||||
*det = A[0][0];
|
||||
for (int i=1; i<A.nrows(); ++i) *det *= A[i][i];
|
||||
//change sign of det by parity of ipiv permutation
|
||||
for (int i=0; i<A.nrows(); ++i) *det = -(*det);
|
||||
}
|
||||
delete [] ipiv;
|
||||
if (r>0 && B) laerror("singular matrix in lapack_gesv");
|
||||
}
|
||||
|
||||
|
||||
// Next routines are not available in clapack, fotran ones will b used with an
|
||||
// additional swap/transpose of outputs when needed
|
||||
|
||||
extern "C" void FORNAME(dspsv)(const char *UPLO, const int *N, const int *NRHS,
|
||||
double *AP, int *IPIV, double *B, const int *LDB, int *INFO);
|
||||
|
||||
void linear_solve(NRSMat<double> &a, NRMat<double> *b, double *det)
|
||||
{
|
||||
int r, *ipiv;
|
||||
if (det) cerr << "@@@ sign of the determinant not implemented correctly yet\n";
|
||||
if (b && a.nrows() != b->ncols())
|
||||
laerror("incompatible matrices in symmetric linear_solve()");
|
||||
a.copyonwrite();
|
||||
if (b) b->copyonwrite();
|
||||
ipiv = new int[a.nrows()];
|
||||
char U = 'U';
|
||||
int n = a.nrows();
|
||||
int nrhs = 0;
|
||||
if (b) nrhs = b->nrows();
|
||||
int ldb = b ? b->ncols() : a.nrows();
|
||||
FORNAME(dspsv)(&U, &n, &nrhs, a, ipiv, b?(*b)[0]:0, &ldb,&r);
|
||||
if (r < 0) {
|
||||
delete[] ipiv;
|
||||
laerror("illegal argument in spsv() call of linear_solve()");
|
||||
}
|
||||
if (det && r >= 0) {
|
||||
*det = a(0,0);
|
||||
for (int i=1; i<a.nrows(); i++) *det *= a(i,i);
|
||||
for (int i=0; i<a.nrows(); i++)
|
||||
if (ipiv[i] != i) *det = -(*det);
|
||||
}
|
||||
delete[] ipiv;
|
||||
if (r > 0 && b) laerror("singular matrix in linear_solve(SMat&, Mat*, double*");
|
||||
}
|
||||
|
||||
|
||||
extern "C" void FORNAME(dsyev)(const char *JOBZ, const char *UPLO, const int *N,
|
||||
double *A, const int *LDA, double *W, double *WORK, const int *LWORK, int *INFO);
|
||||
|
||||
// a will contain eigenvectors, w eigenvalues
|
||||
void diagonalize(NRMat<double> &a, NRVec<double> &w, const bool eivec,
|
||||
const bool corder)
|
||||
{
|
||||
int n = a.nrows();
|
||||
if (n != a.ncols()) laerror("diagonalize() call with non-square matrix");
|
||||
if (a.nrows() != w.size())
|
||||
laerror("inconsistent dimension of eigenvalue vector in diagonalize()");
|
||||
|
||||
a.copyonwrite();
|
||||
w.copyonwrite();
|
||||
|
||||
int r = 0;
|
||||
char U ='U';
|
||||
char vectors = 'V';
|
||||
if (!eivec) vectors = 'N';
|
||||
int LWORK = -1;
|
||||
double WORKX;
|
||||
|
||||
// First call is to determine size of workspace
|
||||
FORNAME(dsyev)(&vectors, &U, &n, a, &n, w, (double *)&WORKX, &LWORK, &r );
|
||||
LWORK = (int)WORKX;
|
||||
double *WORK = new double[LWORK];
|
||||
FORNAME(dsyev)(&vectors, &U, &n, a, &n, w, WORK, &LWORK, &r );
|
||||
delete[] WORK;
|
||||
if (vectors == 'V' && corder) a.transposeme();
|
||||
|
||||
if (r < 0) laerror("illegal argument in syev() of diagonalize()");
|
||||
if (r > 0) laerror("convergence problem in syev() of diagonalize()");
|
||||
}
|
||||
|
||||
|
||||
extern "C" void FORNAME(dspev)(const char *JOBZ, const char *UPLO, const int *N,
|
||||
double *AP, double *W, double *Z, const int *LDZ, double *WORK, int *INFO);
|
||||
|
||||
// v will contain eigenvectors, w eigenvalues
|
||||
void diagonalize(NRSMat<double> &a, NRVec<double> &w, NRMat<double> *v,
|
||||
const bool corder)
|
||||
{
|
||||
int n = a.nrows();
|
||||
if (v) if (v->nrows() != v ->ncols() || n != v->nrows())
|
||||
laerror("diagonalize() call with inconsistent dimensions");
|
||||
if (n != w.size()) laerror("inconsistent dimension of eigenvalue vector");
|
||||
|
||||
a.copyonwrite();
|
||||
w.copyonwrite();
|
||||
|
||||
int r = 0;
|
||||
char U = 'U';
|
||||
char job = v ? 'v' : 'n';
|
||||
|
||||
double *WORK = new double[3*n];
|
||||
FORNAME(dspev)(&job, &U, &n, a, w, v?(*v)[0]:(double *)0, &n, WORK, &r );
|
||||
delete[] WORK;
|
||||
if (v && corder) v->transposeme();
|
||||
|
||||
if (r < 0) laerror("illegal argument in spev() of diagonalize()");
|
||||
if (r > 0) laerror("convergence problem in spev() of diagonalize()");
|
||||
}
|
||||
|
||||
|
||||
extern "C" void FORNAME(dgesvd)(const char *JOBU, const char *JOBVT, const int *M,
|
||||
const int *N, double *A, const int *LDA, double *S, double *U, const int *LDU,
|
||||
double *VT, const int *LDVT, double *WORK, const int *LWORK, int *INFO );
|
||||
|
||||
void singular_decomposition(NRMat<double> &a, NRMat<double> *u, NRVec<double> &s,
|
||||
NRMat<double> *v, const bool corder)
|
||||
{
|
||||
int m = a.nrows();
|
||||
int n = a.ncols();
|
||||
if (u) if (m != u->nrows() || m!= u->ncols())
|
||||
laerror("inconsistent dimension of U Mat in singular_decomposition()");
|
||||
if (s.size() < m && s.size() < n)
|
||||
laerror("inconsistent dimension of S Vec in singular_decomposition()");
|
||||
if (v) if (n != v->nrows() || n != v->ncols())
|
||||
laerror("inconsistent dimension of V Mat in singular_decomposition()");
|
||||
|
||||
a.copyonwrite();
|
||||
s.copyonwrite();
|
||||
if (u) u->copyonwrite();
|
||||
if (v) v->copyonwrite();
|
||||
|
||||
// C-order (transposed) input and swap u,v matrices,
|
||||
// v should be transposed at the end
|
||||
char jobu = u ? 'A' : 'N';
|
||||
char jobv = v ? 'A' : 'N';
|
||||
double work0;
|
||||
int lwork = -1;
|
||||
int r;
|
||||
FORNAME(dgesvd)(&jobv, &jobu, &n, &m, a, &n, s, v?(*v)[0]:0, &n,
|
||||
u?(*u)[0]:0, &m, &work0, &lwork, &r);
|
||||
lwork = (int) work0;
|
||||
double *work = new double[lwork];
|
||||
FORNAME(dgesvd)(&jobv, &jobu, &n, &m, a, &n, s, v?(*v)[0]:0, &n,
|
||||
u?(*u)[0]:0, &m, &work0, &lwork, &r);
|
||||
delete[] work;
|
||||
if (v && corder) v->transposeme();
|
||||
|
||||
if (r < 0) laerror("illegal argument in gesvd() of singular_decomposition()");
|
||||
if (r > 0) laerror("convergence problem in gesvd() of ingular_decomposition()");
|
||||
}
|
||||
|
||||
|
||||
extern "C" void FORNAME(dgeev)(const char *JOBVL, const char *JOBVR, const int *N,
|
||||
double *A, const int *LDA, double *WR, double *WI, double *VL, const int *LDVL,
|
||||
double *VR, const int *LDVR, double *WORK, const int *LWORK, int *INFO );
|
||||
|
||||
void gdiagonalize(NRMat<double> &a, NRVec<double> &wr, NRVec<double> &wi,
|
||||
NRMat<double> *vl, NRMat<double> *vr, const bool corder)
|
||||
{
|
||||
int n = a.nrows();
|
||||
if (n != a.ncols()) laerror("gdiagonalize() call for a non-square matrix");
|
||||
if (n != wr.size())
|
||||
laerror("inconsistent dimension of eigen vector in gdiagonalize()");
|
||||
if (vl) if (n != vl->nrows() || n != vl->ncols())
|
||||
laerror("inconsistent dimension of vl in gdiagonalize()");
|
||||
if (vr) if (n != vr->nrows() || n != vr->ncols())
|
||||
laerror("inconsistent dimension of vr in gdiagonalize()");
|
||||
|
||||
a.copyonwrite();
|
||||
wr.copyonwrite();
|
||||
wi.copyonwrite();
|
||||
if (vl) vl->copyonwrite();
|
||||
if (vr) vr->copyonwrite();
|
||||
|
||||
char jobvl = vl ? 'V' : 'N';
|
||||
char jobvr = vr ? 'V' : 'N';
|
||||
double work0;
|
||||
int lwork = -1;
|
||||
int r;
|
||||
FORNAME(dgeev)(&jobvr, &jobvl, &n, a, &n, wr, wi, vr?vr[0]:(double *)0,
|
||||
&n, vl?vl[0]:(double *)0, &n, &work0, &lwork, &r);
|
||||
lwork = (int) work0;
|
||||
double *work = new double[lwork];
|
||||
FORNAME(dgeev)(&jobvr, &jobvl, &n, a, &n, wr, wi, vr?vr[0]:(double *)0,
|
||||
&n, vl?vl[0]:(double *)0, &n, &work0, &lwork, &r);
|
||||
delete[] work;
|
||||
|
||||
if (corder) {
|
||||
if (vl) vl->transposeme();
|
||||
if (vr) vr->transposeme();
|
||||
}
|
||||
|
||||
if (r < 0) laerror("illegal argument in geev() of gdiagonalize()");
|
||||
if (r > 0) laerror("convergence problem in geev() of gdiagonalize()");
|
||||
}
|
||||
|
||||
void gdiagonalize(NRMat<double> &a, NRVec< complex<double> > &w,
|
||||
NRMat< complex<double> >*vl, NRMat< complex<double> > *vr)
|
||||
{
|
||||
int n = a.nrows();
|
||||
if(n != a.ncols()) laerror("gdiagonalize() call for a non-square matrix");
|
||||
|
||||
NRVec<double> wr(n), wi(n);
|
||||
NRMat<double> *rvl = 0;
|
||||
NRMat<double> *rvr = 0;
|
||||
if (vl) rvl = new NRMat<double>(n, n);
|
||||
if (vr) rvr = new NRMat<double>(n, n);
|
||||
gdiagonalize(a, wr, wi, rvl, rvr, 0);
|
||||
|
||||
//process the results into complex matrices
|
||||
int i;
|
||||
for (i=0; i<n; i++) w[i] = complex<double>(wr[i], wi[i]);
|
||||
if (rvl || rvr) {
|
||||
i = 0;
|
||||
while (i < n) {
|
||||
if (wi[i] == 0) {
|
||||
if (vl) for (int j=0; j<n; j++) (*vl)[i][j] = (*rvl)[i][j];
|
||||
if (vr) for (int j=0; j<n; j++) (*vr)[i][j] = (*rvr)[i][j];
|
||||
i++;
|
||||
} else {
|
||||
if (vl)
|
||||
for (int j=0; j<n; j++) {
|
||||
(*vl)[i][j] = complex<double>((*rvl)[i][j], (*rvl)[i+1][j]);
|
||||
(*vl)[i+1][j] = complex<double>((*rvl)[i][j], -(*rvl)[i+1][j]);
|
||||
}
|
||||
if (vr)
|
||||
for (int j=0; j<n; j++) {
|
||||
(*vr)[i][j] = complex<double>((*rvr)[i][j], (*rvr)[i+1][j]);
|
||||
(*vr)[i+1][j] = complex<double>((*rvr)[i][j], -(*rvr)[i+1][j]);
|
||||
}
|
||||
i += 2;
|
||||
}
|
||||
}
|
||||
}
|
||||
if (rvl) delete rvl;
|
||||
if (rvr) delete rvr;
|
||||
}
|
||||
|
||||
|
||||
const NRMat<double> realpart(const NRMat< complex<double> > &a)
|
||||
{
|
||||
NRMat<double> result(a.nrows(), a.ncols());
|
||||
cblas_dcopy(a.nrows()*a.ncols(), (const double *)a[0], 2, result, 1);
|
||||
return result;
|
||||
}
|
||||
|
||||
const NRMat<double> imagpart(const NRMat< complex<double> > &a)
|
||||
{
|
||||
NRMat<double> result(a.nrows(), a.ncols());
|
||||
cblas_dcopy(a.nrows()*a.ncols(), (const double *)a[0]+1, 2, result, 1);
|
||||
return result;
|
||||
}
|
||||
|
||||
const NRMat< complex<double> > realmatrix (const NRMat<double> &a)
|
||||
{
|
||||
NRMat <complex<double> > result(a.nrows(), a.ncols());
|
||||
cblas_dcopy(a.nrows()*a.ncols(), a, 1, (double *)result[0], 2);
|
||||
return result;
|
||||
}
|
||||
|
||||
const NRMat< complex<double> > imagmatrix (const NRMat<double> &a)
|
||||
{
|
||||
NRMat< complex<double> > result(a.nrows(), a.ncols());
|
||||
cblas_dcopy(a.nrows()*a.ncols(), a, 1, (double *)result[0]+1, 2);
|
||||
return result;
|
||||
}
|
||||
|
||||
|
||||
NRMat<double> matrixfunction(NRMat<double> a, complex<double>
|
||||
(*f)(const complex<double> &), const bool adjust)
|
||||
{
|
||||
int n = a.nrows();
|
||||
NRMat< complex<double> > u(n, n), v(n, n);
|
||||
NRVec< complex<double> > w(n);
|
||||
gdiagonalize(a, w, &u, &v);
|
||||
NRVec< complex<double> > z = diagofproduct(u, v, 1, 1);
|
||||
|
||||
for (int i=0; i<a.nrows(); i++) w[i] = (*f)(w[i]/z[i]);
|
||||
u.diagmultl(w);
|
||||
|
||||
NRMat< complex<double> > r(n, n);
|
||||
r.gemm(0.0, v, 'c', u, 'n', 1.0);
|
||||
double inorm = cblas_dnrm2(n*n, (double *)r[0]+1, 2);
|
||||
if (inorm > 1e-10) {
|
||||
cout << "norm = " << inorm << endl;
|
||||
laerror("nonzero norm of imaginary part of real matrixfunction");
|
||||
}
|
||||
return realpart(r);
|
||||
}
|
||||
|
||||
NRMat<double> matrixfunction(NRSMat<double> a, double (*f) (double))
|
||||
{
|
||||
int n = a.nrows();
|
||||
NRVec<double> w(n);
|
||||
NRMat<double> v(n, n);
|
||||
diagonalize(a, w, &v, 0);
|
||||
|
||||
for (int i=0; i<a.nrows(); i++) w[i] = (*f)(w[i]);
|
||||
NRMat<double> u = v;
|
||||
v.diagmultl(w);
|
||||
NRMat<double> r(n, n);
|
||||
r.gemm(0.0, u, 't', v, 'n', 1.0);
|
||||
return r;
|
||||
}
|
||||
|
||||
// instantize template to an addresable function
|
||||
complex<double> myclog (const complex<double> &x)
|
||||
{
|
||||
return log(x);
|
||||
}
|
||||
|
||||
NRMat<double> log(const NRMat<double> &a)
|
||||
{
|
||||
return matrixfunction(a, &myclog, 1);
|
||||
}
|
||||
|
||||
|
||||
const NRVec<double> diagofproduct(const NRMat<double> &a, const NRMat<double> &b,
|
||||
bool trb, bool conjb)
|
||||
{
|
||||
if (trb && (a.nrows() != b.nrows() || a.ncols() != b.ncols()) ||
|
||||
!trb && (a.nrows() != b.ncols() || a.ncols() != b.nrows()))
|
||||
laerror("incompatible Mats in diagofproduct<double>()");
|
||||
NRVec<double> result(a.nrows());
|
||||
if (trb)
|
||||
for(int i=0; i<a.nrows(); i++)
|
||||
result[i] = cblas_ddot(a.ncols(), a[i], 1, b[i], 1);
|
||||
else
|
||||
for(int i=0; i<a.nrows(); i++)
|
||||
result[i] = cblas_ddot(a.ncols(), a[i], 1, b[0]+i, b.ncols());
|
||||
|
||||
return result;
|
||||
}
|
||||
|
||||
|
||||
const NRVec< complex<double> > diagofproduct(const NRMat< complex<double> > &a,
|
||||
const NRMat< complex<double> > &b, bool trb, bool conjb)
|
||||
{
|
||||
if (trb && (a.nrows() != b.nrows() || a.ncols() != b.ncols()) ||
|
||||
!trb && (a.nrows() != b.ncols() || a.ncols() != b.nrows()))
|
||||
laerror("incompatible Mats in diagofproduct<complex>()");
|
||||
NRVec< complex<double> > result(a.nrows());
|
||||
if (trb) {
|
||||
if (conjb) {
|
||||
for(int i=0; i<a.nrows(); i++)
|
||||
cblas_zdotc_sub(a.ncols(), b[i], 1, a[i], 1, &result[i]);
|
||||
} else {
|
||||
for(int i=0; i<a.nrows(); i++)
|
||||
cblas_zdotu_sub(a.ncols(), b[i], 1, a[i], 1, &result[i]);
|
||||
}
|
||||
} else {
|
||||
if (conjb) {
|
||||
for(int i=0; i<a.nrows(); i++)
|
||||
cblas_zdotc_sub(a.ncols(), b[0]+i, b.ncols(), a[i], 1, &result[i]);
|
||||
} else {
|
||||
for(int i=0; i<a.nrows(); i++)
|
||||
cblas_zdotu_sub(a.ncols(), b[0]+i, b.ncols(), a[i], 1, &result[i]);
|
||||
}
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
|
||||
double trace2(const NRMat<double> &a, const NRMat<double> &b, bool trb)
|
||||
{
|
||||
if (trb && (a.nrows() != b.nrows() || a.ncols() != b.ncols()) ||
|
||||
!trb && (a.nrows() != b.ncols() || a.ncols() != b.nrows()))
|
||||
laerror("incompatible Mats in diagofproduct<complex>()");
|
||||
if (trb) return cblas_ddot(a.nrows()*a.ncols(), a, 1, b, 1);
|
||||
|
||||
double sum = 0.0;
|
||||
for (int i=0; i<a.nrows(); i++)
|
||||
sum += cblas_ddot(a.ncols(), a[i], 1, b[0]+i, b.ncols());
|
||||
|
||||
return sum;
|
||||
}
|
||||
|
||||
|
||||
double trace2(const NRSMat<double> &a, const NRSMat<double> &b,
|
||||
const bool diagscaled)
|
||||
{
|
||||
if (a.nrows() != b.nrows()) laerror("incompatible SMats in trace2()");
|
||||
|
||||
double r = 2.0*cblas_ddot(a.nrows()*(a.nrows()+1)/2, a, 1, b, 1);
|
||||
if (diagscaled) return r;
|
||||
for (int i=0; i<a.nrows(); i++) r -= a(i,i)*b(i,i);
|
||||
return r;
|
||||
}
|
||||
|
||||
|
|
@ -0,0 +1,85 @@
|
|||
#include "vec.h"
|
||||
#include "smat.h"
|
||||
#include "mat.h"
|
||||
|
||||
//MISC
|
||||
template <class T> extern const NRMat<T> diagonalmatrix(const NRVec<T> &x);
|
||||
template <class T> extern const NRVec<T> lineof(const NRMat<T> &x, const int i);
|
||||
template <class T> extern const NRVec<T> columnof(const NRMat<T> &x, const int i);
|
||||
template <class T> extern const NRVec<T> diagonalof(const NRMat<T> &x);
|
||||
|
||||
//more efficient commutator for a special case of full matrices
|
||||
template<class T>
|
||||
inline const NRMat<T> commutator ( const NRMat<T> &x, const NRMat<T> &y, const bool trx=0, const bool tryy=0)
|
||||
{
|
||||
NRMat<T> r(trx?x.ncols():x.nrows(), tryy?y.nrows():y.ncols());
|
||||
r.gemm((T)0,x,trx?'t':'n',y,tryy?'t':'n',(T)1);
|
||||
r.gemm((T)1,y,tryy?'t':'n',x,trx?'t':'n',(T)-1);
|
||||
return r;
|
||||
}
|
||||
|
||||
//more efficient commutator for a special case of full matrices
|
||||
template<class T>
|
||||
inline const NRMat<T> anticommutator ( const NRMat<T> &x, const NRMat<T> &y, const bool trx=0, const bool tryy=0)
|
||||
{
|
||||
NRMat<T> r(trx?x.ncols():x.nrows(), tryy?y.nrows():y.ncols());
|
||||
r.gemm((T)0,x,trx?'t':'n',y,tryy?'t':'n',(T)1);
|
||||
r.gemm((T)1,y,tryy?'t':'n',x,trx?'t':'n',(T)1);
|
||||
return r;
|
||||
}
|
||||
|
||||
|
||||
|
||||
|
||||
//////////////////////
|
||||
// LAPACK interface //
|
||||
//////////////////////
|
||||
|
||||
#define declare_la(T) \
|
||||
extern const NRVec<T> diagofproduct(const NRMat<T> &a, const NRMat<T> &b,\
|
||||
bool trb=0, bool conjb=0); \
|
||||
extern T trace2(const NRMat<T> &a, const NRMat<T> &b, bool trb=0); \
|
||||
extern T trace2(const NRSMat<T> &a, const NRSMat<T> &b, const bool diagscaled=0);\
|
||||
extern void linear_solve(NRMat<T> &a, NRMat<T> *b, double *det=0); \
|
||||
extern void linear_solve(NRSMat<T> &a, NRMat<T> *b, double *det=0); \
|
||||
extern void diagonalize(NRMat<T> &a, NRVec<T> &w, const bool eivec=1,\
|
||||
const bool corder=1); \
|
||||
extern void diagonalize(NRSMat<T> &a, NRVec<T> &w, NRMat<T> *v, const bool corder=1);\
|
||||
extern void singular_decomposition(NRMat<T> &a, NRMat<T> *u, NRVec<T> &s,\
|
||||
NRMat<T> *v, const bool corder=1);
|
||||
|
||||
declare_la(double)
|
||||
declare_la(complex<double>)
|
||||
|
||||
// Separate declarations
|
||||
extern void gdiagonalize(NRMat<double> &a, NRVec<double> &wr, NRVec<double> &wi,
|
||||
NRMat<double> *vl, NRMat<double> *vr, const bool corder=1);
|
||||
extern void gdiagonalize(NRMat<double> &a, NRVec< complex<double> > &w,
|
||||
NRMat< complex<double> >*vl, NRMat< complex<double> > *vr);
|
||||
extern NRMat<double> matrixfunction(NRSMat<double> a, double (*f) (double));
|
||||
extern NRMat<double> matrixfunction(NRMat<double> a, complex<double> (*f)(const complex<double> &),const bool adjust=0);
|
||||
|
||||
//functions on matrices
|
||||
inline NRMat<double> sqrt(const NRSMat<double> &a) { return matrixfunction(a,&sqrt); }
|
||||
inline NRMat<double> log(const NRSMat<double> &a) { return matrixfunction(a,&log); }
|
||||
extern NRMat<double> log(const NRMat<double> &a);
|
||||
|
||||
|
||||
extern const NRMat<double> realpart(const NRMat< complex<double> >&);
|
||||
extern const NRMat<double> imagpart(const NRMat< complex<double> >&);
|
||||
extern const NRMat< complex<double> > realmatrix (const NRMat<double>&);
|
||||
extern const NRMat< complex<double> > imagmatrix (const NRMat<double>&);
|
||||
|
||||
//inverse by means of linear solve, preserving rhs intact
|
||||
template<typename T>
|
||||
const NRMat<T> inverse(NRMat<T> a, T *det=0)
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if(a.nrows()!=a.ncols()) laerror("inverse() for non-square matrix");
|
||||
#endif
|
||||
NRMat<T> result(a.nrows(),a.nrows());
|
||||
result = (T)1.;
|
||||
linear_solve(a, &result, det);
|
||||
return result;
|
||||
}
|
||||
|
||||
|
|
@ -0,0 +1,399 @@
|
|||
#include "smat.h"
|
||||
// TODO
|
||||
// specialize unary minus
|
||||
|
||||
|
||||
//////////////////////////////////////////////////////////////////////////////
|
||||
////// forced instantization in the corresponding object file
|
||||
template NRSMat<double>;
|
||||
template NRSMat< complex<double> >;
|
||||
|
||||
|
||||
|
||||
/*
|
||||
* * Templates first, specializations for BLAS next
|
||||
*
|
||||
*/
|
||||
|
||||
// conversion ctor, symmetrize general Mat into SMat
|
||||
template <typename T>
|
||||
NRSMat<T>::NRSMat(const NRMat<T> &rhs)
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (nn != rhs.ncols()) laerror("attempt to convert non-square Mat to SMat");
|
||||
#endif
|
||||
count = new int;
|
||||
*count = 1;
|
||||
v = new T[NN2];
|
||||
int i, j, k=0;
|
||||
for (i=0; i<nn; i++)
|
||||
for (j=0; j<=i;j++) v[k++] = 0.5 * (rhs[i][j] + rhs[j][i]);
|
||||
}
|
||||
|
||||
|
||||
// dtor
|
||||
template <typename T>
|
||||
NRSMat<T>::~NRSMat()
|
||||
{
|
||||
if (!count) return;
|
||||
if (--(*count) <= 0) {
|
||||
if (v) delete[] (v);
|
||||
delete count;
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
// assignment with a physical copy
|
||||
template <typename T>
|
||||
NRSMat<T> & NRSMat<T>::operator|=(const NRSMat<T> &rhs)
|
||||
{
|
||||
if (this != &rhs) {
|
||||
if(!rhs.v) laerror("unallocated rhs in NRSMat operator |=");
|
||||
if(count)
|
||||
if(*count > 1) { // detach from the other
|
||||
--(*count);
|
||||
nn = 0;
|
||||
count = 0;
|
||||
v = 0;
|
||||
}
|
||||
if (nn != rhs.nn) {
|
||||
if(v) delete [] (v);
|
||||
nn = rhs.nn;
|
||||
}
|
||||
if (!v) v = new T[NN2];
|
||||
if (!count) count = new int;
|
||||
*count = 1;
|
||||
memcpy(v, rhs.v, NN2*sizeof(T));
|
||||
}
|
||||
return *this;
|
||||
}
|
||||
|
||||
// assignment
|
||||
template <typename T>
|
||||
NRSMat<T> & NRSMat<T>::operator=(const NRSMat<T> & rhs)
|
||||
{
|
||||
if (this == & rhs) return *this;
|
||||
if (count)
|
||||
if(--(*count) == 0) {
|
||||
delete [] v;
|
||||
delete count;
|
||||
}
|
||||
v = rhs.v;
|
||||
nn = rhs.nn;
|
||||
count = rhs.count;
|
||||
if (count) (*count)++;
|
||||
return *this;
|
||||
}
|
||||
|
||||
// assing to diagonal
|
||||
template <typename T>
|
||||
NRSMat<T> & NRSMat<T>::operator=(const T &a)
|
||||
{
|
||||
copyonwrite();
|
||||
for (int i=0; i<nn; i++) v[i*(i+1)/2+i] = a;
|
||||
return *this;
|
||||
}
|
||||
|
||||
// unary minus
|
||||
template <typename T>
|
||||
const NRSMat<T> NRSMat<T>::operator-() const
|
||||
{
|
||||
NRSMat<T> result(nn);
|
||||
for(int i=0; i<NN2; i++) result.v[i]= -v[i];
|
||||
return result;
|
||||
}
|
||||
|
||||
// trace of Smat
|
||||
template <typename T>
|
||||
const T NRSMat<T>::trace() const
|
||||
{
|
||||
T tmp = 0;
|
||||
for (int i=0; i<nn; i++) tmp += v[i*(i+1)/2+i];
|
||||
return tmp;
|
||||
}
|
||||
|
||||
// make new instation of the Smat, deep copy
|
||||
template <typename T>
|
||||
void NRSMat<T>::copyonwrite()
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (!count) laerror("probably an assignment to undefined Smat");
|
||||
#endif
|
||||
if (*count > 1) {
|
||||
(*count)--;
|
||||
count = new int;
|
||||
*count = 1;
|
||||
T *newv = new T[NN2];
|
||||
memcpy(newv, v, NN2*sizeof(T));
|
||||
v = newv;
|
||||
}
|
||||
}
|
||||
|
||||
// resize Smat
|
||||
template <typename T>
|
||||
void NRSMat<T>::resize(const int n)
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (n <= 0) laerror("illegal matrix dimension in resize of Smat");
|
||||
#endif
|
||||
if (count)
|
||||
if(*count > 1) { //detach from previous
|
||||
(*count)--;
|
||||
count = 0;
|
||||
v = 0;
|
||||
nn = 0;
|
||||
}
|
||||
if (!count) { //new uninitialized vector or just detached
|
||||
count = new int;
|
||||
*count = 1;
|
||||
nn = n;
|
||||
v = new T[NN2];
|
||||
return;
|
||||
}
|
||||
if (n != nn) {
|
||||
nn = n;
|
||||
delete[] v;
|
||||
v = new T[NN2];
|
||||
}
|
||||
}
|
||||
|
||||
// write matrix to the file with specific format
|
||||
template <typename T>
|
||||
void NRSMat<T>::fprintf(FILE *file, const char *format, const int modulo) const
|
||||
{
|
||||
lawritemat(file, (const T *)(*this) ,nn, nn, format, 2, modulo, 1);
|
||||
}
|
||||
|
||||
// read matrix from the file with specific format
|
||||
template <class T>
|
||||
void NRSMat<T>::fscanf(FILE *f, const char *format)
|
||||
{
|
||||
int n, m;
|
||||
if (std::fscanf(f,"%d %d",&n,&m) != 2)
|
||||
laerror("cannot read matrix dimensions in SMat::fscanf");
|
||||
if (n != m) laerror("different dimensions of SMat");
|
||||
resize(n);
|
||||
for (int i=0; i<n; i++)
|
||||
for (int j=0; j<n; j++)
|
||||
if (std::fscanf(f,format,&((*this)(i,j))) != 1)
|
||||
laerror("Smat - cannot read matrix element");
|
||||
}
|
||||
|
||||
|
||||
/*
|
||||
* BLAS specializations for double and complex<double>
|
||||
*/
|
||||
|
||||
// SMat * Mat
|
||||
const NRMat<double> NRSMat<double>::operator*(const NRMat<double> &rhs) const
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (nn != rhs.nrows()) laerror("incompatible dimensions in SMat*Mat");
|
||||
#endif
|
||||
NRMat<double> result(nn, rhs.ncols());
|
||||
for (int k=0; k<rhs.ncols(); k++)
|
||||
cblas_dspmv(CblasRowMajor, CblasLower, nn, 1.0, v, rhs[0]+k, rhs.ncols(),
|
||||
0.0, result[0]+k, rhs.ncols());
|
||||
return result;
|
||||
}
|
||||
const NRMat< complex<double> >
|
||||
NRSMat< complex<double> >::operator*(const NRMat< complex<double> > &rhs) const
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (nn != rhs.nrows()) laerror("incompatible dimensions in SMat*Mat");
|
||||
#endif
|
||||
NRMat< complex<double> > result(nn, rhs.ncols());
|
||||
for (int k=0; k<rhs.ncols(); k++)
|
||||
cblas_zhpmv(CblasRowMajor, CblasLower, nn, &CONE, v, rhs[0]+k, rhs.ncols(),
|
||||
&CZERO, result[0]+k, rhs.ncols());
|
||||
return result;
|
||||
}
|
||||
|
||||
// SMat * SMat
|
||||
const NRMat<double> NRSMat<double>::operator*(const NRSMat<double> &rhs) const
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (nn != rhs.nn) laerror("incompatible dimensions in SMat*SMat");
|
||||
#endif
|
||||
NRMat<double> result(0.0, nn, nn);
|
||||
double *p, *q;
|
||||
|
||||
p = v;
|
||||
for (int i=0; i<nn;i++) {
|
||||
q = rhs.v;
|
||||
for (int k=0; k<=i; k++) {
|
||||
cblas_daxpy(k+1, *p++, q, 1, result[i], 1);
|
||||
q += k+1;
|
||||
}
|
||||
}
|
||||
|
||||
p = v;
|
||||
for (int i=0; i<nn;i++) {
|
||||
q = rhs.v+1;
|
||||
for (int j=1; j<nn; j++) {
|
||||
result[i][j] += cblas_ddot(i+1<j ? i+1 : j, p, 1, q, 1);
|
||||
q += j+1;
|
||||
}
|
||||
p += i+1;
|
||||
}
|
||||
|
||||
p = v;
|
||||
q = rhs.v;
|
||||
for (int i=0; i<nn; i++) {
|
||||
cblas_dger(CblasRowMajor, i, i+1, 1., p, 1, q, 1, result, nn);
|
||||
p += i+1;
|
||||
q += i+1;
|
||||
}
|
||||
|
||||
q = rhs.v+3;
|
||||
for (int j=2; j<nn; j++) {
|
||||
p = v+1;
|
||||
for (int i=1; i<j; i++) {
|
||||
cblas_daxpy(i, *++q, p, 1, result[0]+j, nn);
|
||||
p += i+1;
|
||||
}
|
||||
q += 2;
|
||||
}
|
||||
|
||||
return result;
|
||||
}
|
||||
const NRMat< complex<double> >
|
||||
NRSMat< complex<double> >::operator*(const NRSMat< complex<double> > &rhs) const
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (nn != rhs.nn) laerror("incompatible dimensions in SMat*SMat");
|
||||
#endif
|
||||
NRMat< complex<double> > result(0.0, nn, nn);
|
||||
NRMat< complex<double> > rhsmat(rhs);
|
||||
result = *this * rhsmat;
|
||||
return result;
|
||||
// laerror("complex SMat*Smat not implemented");
|
||||
}
|
||||
// S dot S
|
||||
const double NRSMat<double>::dot(const NRSMat<double> &rhs) const
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (nn != rhs.nn) laerror("dot of incompatible SMat's");
|
||||
#endif
|
||||
return cblas_ddot(NN2, v, 1, rhs.v, 1);
|
||||
}
|
||||
const complex<double>
|
||||
NRSMat< complex<double> >::dot(const NRSMat< complex<double> > &rhs) const
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (nn != rhs.nn) laerror("dot of incompatible SMat's");
|
||||
#endif
|
||||
complex<double> dot;
|
||||
cblas_zdotc_sub(nn, (void *)v, 1, (void *)rhs.v, 1, (void *)(&dot));
|
||||
return dot;
|
||||
}
|
||||
|
||||
// x = S * x
|
||||
const NRVec<double> NRSMat<double>::operator*(const NRVec<double> &rhs) const
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (nn!=rhs.size()) laerror("incompatible dimension in Smat*Vec");
|
||||
#endif
|
||||
NRVec<double> result(nn);
|
||||
cblas_dspmv(CblasRowMajor, CblasLower, nn, 1.0, v, rhs, 1, 0.0, result, 1);
|
||||
return result;
|
||||
}
|
||||
const NRVec< complex<double> >
|
||||
NRSMat< complex<double> >::operator*(const NRVec< complex<double> > &rhs) const
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (nn!=rhs.size()) laerror("incompatible dimension in Smat*Vec");
|
||||
#endif
|
||||
NRVec< complex<double> > result(nn);
|
||||
cblas_zhpmv(CblasRowMajor, CblasLower, nn, (void *)(&CONE), (void *)v,
|
||||
(const void *)rhs, 1, (void *)(&CZERO), (void *)result, 1);
|
||||
return result;
|
||||
}
|
||||
|
||||
// norm of the matrix
|
||||
const double NRSMat<double>::norm(const double scalar) const
|
||||
{
|
||||
if (!scalar) return cblas_dnrm2(NN2, v, 1);
|
||||
double sum = 0;
|
||||
int k = 0;
|
||||
for (int i=0; i<nn; ++i)
|
||||
for (int j=0; j<=i; ++j) {
|
||||
register double tmp;
|
||||
tmp = v[k++];
|
||||
if (i == j) tmp -= scalar;
|
||||
sum += tmp*tmp;
|
||||
}
|
||||
return sqrt(sum);
|
||||
}
|
||||
const double
|
||||
NRSMat< complex<double> >::norm(const complex<double> scalar) const
|
||||
{
|
||||
if (!(scalar.real()) && !(scalar.imag()))
|
||||
return cblas_dznrm2(NN2, (void *)v, 1);
|
||||
double sum = 0;
|
||||
complex<double> tmp;
|
||||
int k = 0;
|
||||
for (int i=0; i<nn; ++i)
|
||||
for (int j=0; j<=i; ++j) {
|
||||
tmp = v[k++];
|
||||
if (i == j) tmp -= scalar;
|
||||
sum += tmp.real()*tmp.real() + tmp.imag()*tmp.imag();
|
||||
}
|
||||
return sqrt(sum);
|
||||
}
|
||||
|
||||
// axpy: S = S * a
|
||||
void NRSMat<double>::axpy(const double alpha, const NRSMat<double> & x)
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (nn != x.nn) laerror("axpy of incompatible SMats");
|
||||
#endif
|
||||
copyonwrite();
|
||||
cblas_daxpy(NN2, alpha, x.v, 1, v, 1);
|
||||
}
|
||||
void NRSMat< complex<double> >::axpy(const complex<double> alpha,
|
||||
const NRSMat< complex<double> > & x)
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (nn != x.nn) laerror("axpy of incompatible SMats");
|
||||
#endif
|
||||
copyonwrite();
|
||||
cblas_zaxpy(nn, (void *)(&alpha), (void *)x.v, 1, (void *)v, 1);
|
||||
}
|
||||
|
||||
|
||||
export template <class T>
|
||||
ostream& operator<<(ostream &s, const NRSMat<T> &x)
|
||||
{
|
||||
int i,j,n;
|
||||
n=x.nrows();
|
||||
s << n << ' ' << n << '\n';
|
||||
for(i=0;i<n;i++)
|
||||
{
|
||||
for(j=0; j<n;j++) s << x(i,j) << (j==n-1 ? '\n' : ' ');
|
||||
}
|
||||
return s;
|
||||
}
|
||||
|
||||
|
||||
export template <class T>
|
||||
istream& operator>>(istream &s, NRSMat<T> &x)
|
||||
{
|
||||
int i,j,n,m;
|
||||
s >> n >> m;
|
||||
if(n!=m) laerror("input symmetric matrix not square");
|
||||
x.resize(n);
|
||||
for(i=0;i<n;i++) for(j=0; j<m;j++) s>>x(i,j);
|
||||
return s;
|
||||
}
|
||||
|
||||
|
||||
//////////////////////////////////////////////////////////////////////////////
|
||||
//// forced instantization in the corespoding object file
|
||||
#define INSTANTIZE(T) \
|
||||
template ostream & operator<<(ostream &s, const NRSMat< T > &x); \
|
||||
template istream & operator>>(istream &s, NRSMat< T > &x); \
|
||||
|
||||
INSTANTIZE(double)
|
||||
INSTANTIZE(complex<double>)
|
||||
|
||||
|
|
@ -0,0 +1,303 @@
|
|||
#ifndef _LA_SMAT_H_
|
||||
#define _LA_SMAT_H_
|
||||
|
||||
#include "vec.h"
|
||||
#include "mat.h"
|
||||
|
||||
#define NN2 (nn*(nn+1)/2)
|
||||
template <class T>
|
||||
class NRSMat { // symmetric or complex hermitean matrix in packed form
|
||||
protected:
|
||||
int nn;
|
||||
T *v;
|
||||
int *count;
|
||||
public:
|
||||
friend class NRVec<T>;
|
||||
friend class NRMat<T>;
|
||||
|
||||
inline NRSMat<T>::NRSMat() : nn(0),v(0),count(0) {};
|
||||
inline explicit NRSMat(const int n); // Zero-based array
|
||||
inline NRSMat(const T &a, const int n); //Initialize to constant
|
||||
inline NRSMat(const T *a, const int n); // Initialize to array
|
||||
inline NRSMat(const NRSMat &rhs); // Copy constructor
|
||||
explicit NRSMat(const NRMat<T> &rhs); // symmetric part of general matrix
|
||||
explicit NRSMat(const NRVec<T> &rhs, const int n); //construct matrix from vector
|
||||
NRSMat & operator|=(const NRSMat &rhs); //assignment to a new copy
|
||||
NRSMat & operator=(const NRSMat &rhs); //assignment
|
||||
NRSMat & operator=(const T &a); //assign a to diagonal
|
||||
inline NRSMat & operator*=(const T &a);
|
||||
inline NRSMat & operator+=(const T &a);
|
||||
inline NRSMat & operator-=(const T &a);
|
||||
inline NRSMat & operator+=(const NRSMat &rhs);
|
||||
inline NRSMat & operator-=(const NRSMat &rhs);
|
||||
const NRSMat operator-() const; //unary minus
|
||||
inline int getcount() const {return count?*count:0;}
|
||||
inline const NRSMat operator*(const T &a) const;
|
||||
inline const NRSMat operator+(const T &a) const;
|
||||
inline const NRSMat operator-(const T &a) const;
|
||||
inline const NRSMat operator+(const NRSMat &rhs) const;
|
||||
inline const NRSMat operator-(const NRSMat &rhs) const;
|
||||
inline const NRMat<T> operator+(const NRMat<T> &rhs) const;
|
||||
inline const NRMat<T> operator-(const NRMat<T> &rhs) const;
|
||||
const NRMat<T> operator*(const NRSMat &rhs) const; // SMat*SMat
|
||||
const NRMat<T> operator*(const NRMat<T> &rhs) const; // SMat*Mat
|
||||
const T dot(const NRSMat &rhs) const; // Smat.Smat
|
||||
const NRVec<T> operator*(const NRVec<T> &rhs) const;
|
||||
inline const T& operator[](const int ij) const;
|
||||
inline T& operator[](const int ij);
|
||||
inline const T& operator()(const int i, const int j) const;
|
||||
inline T& operator()(const int i, const int j);
|
||||
inline int nrows() const;
|
||||
inline int ncols() const;
|
||||
const double norm(const T scalar=(T)0) const;
|
||||
void axpy(const T alpha, const NRSMat &x); // this+= a*x
|
||||
inline const T amax() const;
|
||||
const T trace() const;
|
||||
void copyonwrite();
|
||||
void resize(const int n);
|
||||
inline operator T*(); //get a pointer to the data
|
||||
inline operator const T*() const; //get a pointer to the data
|
||||
~NRSMat();
|
||||
void fprintf(FILE *f, const char *format, const int modulo) const;
|
||||
void fscanf(FILE *f, const char *format);
|
||||
//members concerning sparse matrix
|
||||
explicit NRSMat(const SparseMat<T> &rhs); // dense from sparse
|
||||
inline void simplify() {}; //just for compatibility with sparse ones
|
||||
};
|
||||
|
||||
// INLINES
|
||||
// ctors
|
||||
template <typename T>
|
||||
inline NRSMat<T>::NRSMat(const int n) : nn(n), v(new T[NN2]),
|
||||
count(new int) {*count = 1;}
|
||||
|
||||
template <typename T>
|
||||
inline NRSMat<T>::NRSMat(const T& a, const int n) : nn(n),
|
||||
v(new T[NN2]), count(new int)
|
||||
{
|
||||
*count =1;
|
||||
if(a != (T)0) for(int i=0; i<NN2; i++) v[i] = a;
|
||||
}
|
||||
|
||||
template <typename T>
|
||||
inline NRSMat<T>::NRSMat(const T *a, const int n) : nn(n),
|
||||
v(new T[NN2]), count(new int)
|
||||
{
|
||||
*count = 1;
|
||||
memcpy(v, a, NN2*sizeof(T));
|
||||
}
|
||||
|
||||
template <typename T>
|
||||
inline NRSMat<T>::NRSMat(const NRSMat<T> &rhs) //copy constructor
|
||||
{
|
||||
v = rhs.v;
|
||||
nn = rhs.nn;
|
||||
count = rhs.count;
|
||||
if (count) (*count)++;
|
||||
}
|
||||
|
||||
template <typename T>
|
||||
NRSMat<T>::NRSMat(const NRVec<T> &rhs, const int n) // type conversion
|
||||
{
|
||||
nn = n;
|
||||
#ifdef DEBUG
|
||||
if (NN2 != rhs.size())
|
||||
laerror("matrix dimensions incompatible with vector length");
|
||||
#endif
|
||||
count = rhs.count;
|
||||
v = rhs.v;
|
||||
(*count)++;
|
||||
}
|
||||
|
||||
// S *= a
|
||||
inline NRSMat<double> & NRSMat<double>::operator*=(const double & a)
|
||||
{
|
||||
copyonwrite();
|
||||
cblas_dscal(NN2, a, v, 1);
|
||||
return *this;
|
||||
}
|
||||
inline NRSMat< complex<double> > &
|
||||
NRSMat< complex<double> >::operator*=(const complex<double> & a)
|
||||
{
|
||||
copyonwrite();
|
||||
cblas_zscal(nn, (void *)(&a), (void *)v, 1);
|
||||
return *this;
|
||||
}
|
||||
|
||||
|
||||
// S += D
|
||||
template <typename T>
|
||||
inline NRSMat<T> & NRSMat<T>::operator+=(const T &a)
|
||||
{
|
||||
copyonwrite();
|
||||
for (int i=0; i<nn; i++) v[i*(i+1)/2+i] += a;
|
||||
return *this;
|
||||
}
|
||||
|
||||
// S -= D
|
||||
template <typename T>
|
||||
inline NRSMat<T> & NRSMat<T>::operator-=(const T &a)
|
||||
{
|
||||
copyonwrite();
|
||||
for (int i=0; i<nn; i++) v[i*(i+1)/2+i] -= a;
|
||||
return *this;
|
||||
}
|
||||
|
||||
// S += S
|
||||
inline NRSMat<double> &
|
||||
NRSMat<double>::operator+=(const NRSMat<double> & rhs)
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (nn != rhs.nn) laerror("incompatible SMats in SMat::operator+=");
|
||||
#endif
|
||||
copyonwrite();
|
||||
cblas_daxpy(NN2, 1.0, rhs.v, 1, v, 1);
|
||||
return *this;
|
||||
}
|
||||
NRSMat< complex<double> > &
|
||||
NRSMat< complex<double> >::operator+=(const NRSMat< complex<double> > & rhs)
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (nn != rhs.nn) laerror("incompatible SMats in SMat::operator+=");
|
||||
#endif
|
||||
copyonwrite();
|
||||
cblas_zaxpy(NN2, (void *)(&CONE), (void *)(&rhs.v), 1, (void *)(&v), 1);
|
||||
return *this;
|
||||
}
|
||||
|
||||
// S -= S
|
||||
inline NRSMat<double> &
|
||||
NRSMat<double>::operator-=(const NRSMat<double> & rhs)
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (nn != rhs.nn) laerror("incompatible SMats in SMat::operator-=");
|
||||
#endif
|
||||
copyonwrite();
|
||||
cblas_daxpy(NN2, -1.0, rhs.v, 1, v, 1);
|
||||
return *this;
|
||||
}
|
||||
inline NRSMat< complex<double> > &
|
||||
NRSMat< complex<double> >::operator-=(const NRSMat< complex<double> > & rhs)
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (nn != rhs.nn) laerror("incompatible SMats in SMat::operator-=");
|
||||
#endif
|
||||
copyonwrite();
|
||||
cblas_zaxpy(NN2, (void *)(&CMONE), (void *)(&rhs.v), 1, (void *)(&v), 1);
|
||||
return *this;
|
||||
}
|
||||
|
||||
// SMat + Mat
|
||||
template <typename T>
|
||||
inline const NRMat<T> NRSMat<T>::operator+(const NRMat<T> &rhs) const
|
||||
{
|
||||
return NRMat<T>(rhs) += *this;
|
||||
}
|
||||
|
||||
// SMat - Mat
|
||||
template <typename T>
|
||||
inline const NRMat<T> NRSMat<T>::operator-(const NRMat<T> &rhs) const
|
||||
{
|
||||
return NRMat<T>(-rhs) += *this;
|
||||
}
|
||||
|
||||
// access the element, linear array case
|
||||
template <typename T>
|
||||
inline T & NRSMat<T>::operator[](const int ij)
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (*count != 1) laerror("lval [] with count > 1 in Smat");
|
||||
if (ij<0 || ij>=NN2) laerror("SMat [] out of range");
|
||||
if (!v) laerror("[] for unallocated Smat");
|
||||
#endif
|
||||
return v[ij];
|
||||
}
|
||||
template <typename T>
|
||||
inline const T & NRSMat<T>::operator[](const int ij) const
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (ij<0 || ij>=NN2) laerror("SMat [] out of range");
|
||||
if (!v) laerror("[] for unallocated Smat");
|
||||
#endif
|
||||
return v[ij];
|
||||
}
|
||||
|
||||
// access the element, 2-dim array case
|
||||
template <typename T>
|
||||
inline T & NRSMat<T>::operator()(const int i, const int j)
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (*count != 1) laerror("lval (i,j) with count > 1 in Smat");
|
||||
if (i<0 || i>=nn || j<0 || j>=nn) laerror("SMat (i,j) out of range");
|
||||
if (!v) laerror("(i,j) for unallocated Smat");
|
||||
#endif
|
||||
return i>=j ? v[i*(i+1)/2+j] : v[j*(j+1)/2+i];
|
||||
}
|
||||
template <typename T>
|
||||
inline const T & NRSMat<T>::operator()(const int i, const int j) const
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (i<0 || i>=nn || j<0 || j>=nn) laerror("SMat (i,j) out of range");
|
||||
if (!v) laerror("(i,j) for unallocated Smat");
|
||||
#endif
|
||||
return i>=j ? v[i*(i+1)/2+j] : v[j*(j+1)/2+i];
|
||||
}
|
||||
|
||||
// return the number of rows and columns
|
||||
template <typename T>
|
||||
inline int NRSMat<T>::nrows() const
|
||||
{
|
||||
return nn;
|
||||
}
|
||||
template <typename T>
|
||||
inline int NRSMat<T>::ncols() const
|
||||
{
|
||||
return nn;
|
||||
}
|
||||
|
||||
// max value
|
||||
inline const double NRSMat<double>::amax() const
|
||||
{
|
||||
return v[cblas_idamax(NN2, v, 1)];
|
||||
}
|
||||
inline const complex<double> NRSMat< complex<double> >::amax() const
|
||||
{
|
||||
return v[cblas_izamax(NN2, (void *)v, 1)];
|
||||
}
|
||||
|
||||
// reference pointer to Smat
|
||||
template <typename T>
|
||||
inline NRSMat<T>:: operator T*()
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (!v) laerror("unallocated SMat in operator T*");
|
||||
#endif
|
||||
return v;
|
||||
}
|
||||
template <typename T>
|
||||
inline NRSMat<T>:: operator const T*() const
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (!v) laerror("unallocated SMat in operator T*");
|
||||
#endif
|
||||
return v;
|
||||
}
|
||||
|
||||
|
||||
|
||||
// I/O
|
||||
template <typename T> extern ostream& operator<<(ostream &s, const NRSMat<T> &x);
|
||||
template <typename T> extern istream& operator>>(istream &s, NRSMat<T> &x);
|
||||
|
||||
|
||||
|
||||
|
||||
// generate operators: SMat + a, a + SMat, SMat * a
|
||||
NRVECMAT_OPER(SMat,+)
|
||||
NRVECMAT_OPER(SMat,-)
|
||||
NRVECMAT_OPER(SMat,*)
|
||||
// generate SMat + SMat, SMat - SMat
|
||||
NRVECMAT_OPER2(SMat,+)
|
||||
NRVECMAT_OPER2(SMat,-)
|
||||
|
||||
#endif /* _LA_SMAT_H_ */
|
||||
File diff suppressed because it is too large
Load Diff
|
|
@ -0,0 +1,220 @@
|
|||
//for vectors and dense matrices we shall need
|
||||
#include "la.h"
|
||||
|
||||
template<class T>
|
||||
inline const T MAX(const T &a, const T &b)
|
||||
{return b > a ? (b) : (a);}
|
||||
|
||||
template<class T>
|
||||
inline void SWAP(T &a, T &b)
|
||||
{T dum=a; a=b; b=dum;}
|
||||
|
||||
|
||||
//threshold for neglecting elements, if not defined, no tests are done except exact zero test in simplify - might be even faster
|
||||
//seems to perform better with a threshold, in spite of abs() tests
|
||||
#define SPARSEEPSILON 1e-13
|
||||
|
||||
typedef unsigned int SPMatindex;
|
||||
typedef int SPMatindexdiff; //more clear would be to use traits
|
||||
|
||||
//element of a linked list
|
||||
template<class T>
|
||||
struct matel
|
||||
{
|
||||
T elem;
|
||||
SPMatindex row;
|
||||
SPMatindex col;
|
||||
matel *next;
|
||||
};
|
||||
|
||||
|
||||
template <class T>
|
||||
class SparseMat {
|
||||
protected:
|
||||
SPMatindex nn;
|
||||
SPMatindex mm;
|
||||
bool symmetric;
|
||||
unsigned int nonzero;
|
||||
int *count;
|
||||
matel<T> *list;
|
||||
private:
|
||||
matel<T> **rowsorted; //NULL terminated
|
||||
matel<T> **colsorted; //NULL terminated
|
||||
void unsort();
|
||||
void deletelist();
|
||||
void copylist(const matel<T> *l);
|
||||
public:
|
||||
//iterator
|
||||
typedef class iterator {
|
||||
private:
|
||||
matel<T> *p;
|
||||
public:
|
||||
iterator() {};
|
||||
~iterator() {};
|
||||
iterator(matel<T> *list): p(list) {};
|
||||
bool operator==(const iterator rhs) const {return p==rhs.p;}
|
||||
bool operator!=(const iterator rhs) const {return p!=rhs.p;}
|
||||
iterator operator++() {return p=p->next;}
|
||||
iterator operator++(int) {matel<T> *q=p; p=p->next; return q;}
|
||||
matel<T> & operator*() const {return *p;}
|
||||
matel<T> * operator->() const {return p;}
|
||||
};
|
||||
iterator begin() const {return list;}
|
||||
iterator end() const {return NULL;}
|
||||
|
||||
//constructors etc.
|
||||
inline SparseMat() :nn(0),mm(0),symmetric(0),nonzero(0),count(NULL),list(NULL),rowsorted(NULL),colsorted(NULL) {};
|
||||
inline SparseMat(const SPMatindex n, const SPMatindex m) :nn(n),mm(m),symmetric(0),nonzero(0),count(new int(1)),list(NULL),rowsorted(NULL),colsorted(NULL) {};
|
||||
SparseMat(const SparseMat &rhs); //copy constructor
|
||||
inline int getcount() const {return count?*count:0;}
|
||||
explicit SparseMat(const NRMat<T> &rhs); //construct from a dense one
|
||||
explicit SparseMat(const NRSMat<T> &rhs); //construct from a dense symmetric one
|
||||
SparseMat & operator=(const SparseMat &rhs);
|
||||
SparseMat & operator=(const T a); //assign a to diagonal
|
||||
SparseMat & operator+=(const T a); //assign a to diagonal
|
||||
SparseMat & operator-=(const T a); //assign a to diagonal
|
||||
SparseMat & operator*=(const T a); //multiply by a scalar
|
||||
SparseMat & operator+=(const SparseMat &rhs);
|
||||
SparseMat & addtriangle(const SparseMat &rhs, const bool lower, const char sign);
|
||||
SparseMat & join(SparseMat &rhs); //more efficient +=, rhs will be emptied
|
||||
SparseMat & operator-=(const SparseMat &rhs);
|
||||
inline const SparseMat operator+(const T &rhs) const {return SparseMat(*this) += rhs;}
|
||||
inline const SparseMat operator-(const T &rhs) const {return SparseMat(*this) -= rhs;}
|
||||
inline const SparseMat operator*(const T &rhs) const {return SparseMat(*this) *= rhs;}
|
||||
inline const SparseMat operator+(const SparseMat &rhs) const {return SparseMat(*this) += rhs;} //must not be symmetric+general
|
||||
inline const SparseMat operator-(const SparseMat &rhs) const {return SparseMat(*this) -= rhs;} //must not be symmetric+general
|
||||
const NRVec<T> multiplyvector(const NRVec<T> &rhs, const bool transp=0) const; //sparse matrix * dense vector optionally transposed
|
||||
inline const NRVec<T> operator*(const NRVec<T> &rhs) const {return multiplyvector(rhs);} //sparse matrix * dense vector
|
||||
const SparseMat operator*(const SparseMat &rhs) const;
|
||||
void gemm(const T beta, const SparseMat &a, const char transa, const SparseMat &b, const char transb, const T alpha);//this := alpha*op( A )*op( B ) + beta*this, if this is symemtric, only half will be added onto it
|
||||
const T dot(const SparseMat &rhs) const; //supervector dot product
|
||||
const T dot(const NRMat<T> &rhs) const; //supervector dot product
|
||||
inline ~SparseMat();
|
||||
void axpy(const T alpha, const SparseMat &x, const bool transp=0); // this+= a*x(transposed)
|
||||
inline matel<T> *getlist() const {return list;}
|
||||
void setlist(matel<T> *l) {list=l;}
|
||||
inline SPMatindex nrows() const {return nn;}
|
||||
inline SPMatindex ncols() const {return mm;}
|
||||
void resize(const SPMatindex n, const SPMatindex m);
|
||||
void transposeme();
|
||||
const SparseMat transpose() const;
|
||||
inline void setsymmetric() {if(nn!=mm) laerror("non-square cannot be symmetric"); symmetric=1;}
|
||||
inline void defineunsymmetric() {symmetric=0;} //just define and do nothing with it
|
||||
void setunsymmetric();//unwind the matrix assuming it was indeed symmetric
|
||||
inline bool issymmetric() const {return symmetric;}
|
||||
unsigned int length() const;
|
||||
void copyonwrite();
|
||||
void simplify();
|
||||
const T trace() const;
|
||||
const T norm(const T scalar=(T)0) const; //is const only mathematically, not in internal implementation - we have to simplify first
|
||||
unsigned int sort(int type) const;
|
||||
inline void add(const SPMatindex n, const SPMatindex m, const T elem) {matel<T> *ltmp= new matel<T>; ltmp->next=list; list=ltmp; list->row=n; list->col=m; list->elem=elem;}
|
||||
void addsafe(const SPMatindex n, const SPMatindex m, const T elem);
|
||||
};
|
||||
|
||||
template <class T>
|
||||
extern istream& operator>>(istream &s, SparseMat<T> &x);
|
||||
|
||||
template <class T>
|
||||
extern ostream& operator<<(ostream &s, const SparseMat<T> &x);
|
||||
|
||||
//destructor
|
||||
template <class T>
|
||||
SparseMat<T>::~SparseMat()
|
||||
{
|
||||
unsort();
|
||||
if(!count) return;
|
||||
if(--(*count)<=0)
|
||||
{
|
||||
deletelist();
|
||||
delete count;
|
||||
}
|
||||
}
|
||||
|
||||
//copy constructor (sort arrays are not going to be copied)
|
||||
template <class T>
|
||||
SparseMat<T>::SparseMat(const SparseMat<T> &rhs)
|
||||
{
|
||||
#ifdef debug
|
||||
if(! &rhs) laerror("SparseMat copy constructor with NULL argument");
|
||||
#endif
|
||||
nn=rhs.nn;
|
||||
mm=rhs.mm;
|
||||
symmetric=rhs.symmetric;
|
||||
if(rhs.list&&!rhs.count) laerror("some inconsistency in SparseMat contructors or assignments");
|
||||
list=rhs.list;
|
||||
if(list) {count=rhs.count; (*count)++;} else count=new int(1); //make the matrix defined, but empty and not shared
|
||||
colsorted=rowsorted=NULL;
|
||||
nonzero=0;
|
||||
}
|
||||
|
||||
template <class T>
|
||||
const SparseMat<T> SparseMat<T>::transpose() const
|
||||
{
|
||||
if(list&&!count) laerror("some inconsistency in SparseMat transpose");
|
||||
SparseMat<T> result;
|
||||
result.nn=mm;
|
||||
result.mm=nn;
|
||||
result.symmetric=symmetric;
|
||||
if(result.symmetric)
|
||||
{
|
||||
result.list=list;
|
||||
if(list) {result.count=count; (*result.count)++;} else result.count=new int(1); //make the matrix defined, but empty and not shared
|
||||
}
|
||||
else //really transpose it
|
||||
{
|
||||
result.count=new int(1);
|
||||
result.list=NULL;
|
||||
matel<T> *l =list;
|
||||
while(l)
|
||||
{
|
||||
result.add(l->col,l->row,l->elem);
|
||||
l=l->next;
|
||||
}
|
||||
}
|
||||
result.colsorted=result.rowsorted=NULL;
|
||||
result.nonzero=0;
|
||||
return result;
|
||||
}
|
||||
|
||||
|
||||
|
||||
template<class T>
|
||||
inline const SparseMat<T> commutator ( const SparseMat<T> &x, const SparseMat<T> &y, const bool trx=0, const bool tryy=0)
|
||||
{
|
||||
SparseMat<T> r;
|
||||
r.gemm((T)0,x,trx?'t':'n',y,tryy?'t':'n',(T)1);
|
||||
r.gemm((T)1,y,tryy?'t':'n',x,trx?'t':'n',(T)-1); //saves a temporary and simplifies the whole sum
|
||||
return r;
|
||||
}
|
||||
|
||||
template<class T>
|
||||
inline const SparseMat<T> anticommutator ( const SparseMat<T> &x, const SparseMat<T> &y, const bool trx=0, const bool tryy=0)
|
||||
{
|
||||
SparseMat<T> r;
|
||||
r.gemm((T)0,x,trx?'t':'n',y,tryy?'t':'n',(T)1);
|
||||
r.gemm((T)1,y,tryy?'t':'n',x,trx?'t':'n',(T)1); //saves a temporary and simplifies the whole sum
|
||||
return r;
|
||||
}
|
||||
|
||||
//add sparse to dense
|
||||
template<class T>
|
||||
NRMat<T> & NRMat<T>::operator+=(const SparseMat<T> &rhs)
|
||||
{
|
||||
if(nn!=rhs.nrows()||mm!=rhs.ncols()) laerror("incompatible matrices in +=");
|
||||
matel<T> *l=rhs.getlist();
|
||||
bool sym=rhs.issymmetric();
|
||||
while(l)
|
||||
{
|
||||
#ifdef MATPTR
|
||||
v[l->row][l->col] +=l->elem;
|
||||
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;
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
|
|
@ -0,0 +1,15 @@
|
|||
////////////////////////////////////////////////////////////////////////////
|
||||
//traits classes
|
||||
|
||||
#ifndef _SPARSEMAT_TRAITS_INCL
|
||||
#define _SPARSEMAT_TRAITS_INCL
|
||||
|
||||
|
||||
template<> struct NRMat_traits<SparseMat<double> > {
|
||||
typedef double elementtype;
|
||||
typedef SparseMat<double> producttype;
|
||||
static double norm (const SparseMat<double> &x) {return x.norm();}
|
||||
static void axpy (SparseMat<double>&s, const SparseMat<double> &x, const double c) {s.axpy(c,x);}
|
||||
};
|
||||
|
||||
#endif
|
||||
|
|
@ -0,0 +1,31 @@
|
|||
#include "la.h"
|
||||
/*Strassen algorithm*/
|
||||
// called routine is fortran-compatible
|
||||
extern "C" void fmm(const char c_transa,const char c_transb,const int m,const int n,const int k,const double alpha,
|
||||
const double *a,const int lda,const double *b,const int ldb,const double beta,double *c,const int ldc,
|
||||
double *d_aux,int i_naux);
|
||||
extern "C" void strassen_cutoff(int c, int c1, int c2, int c3);
|
||||
|
||||
void NRMat<double>::s_cutoff(const int c, const int c1, const int c2, const int c3) const
|
||||
{ strassen_cutoff(c,c1,c2,c3);}
|
||||
void NRMat<double>::strassen(const double beta, const NRMat<double> &a, const char transa, const NRMat<double> &b, const char transb, const double alpha)
|
||||
{
|
||||
int l(transa=='n'?a.nn:a.mm);
|
||||
int k(transa=='n'?a.mm:a.nn);
|
||||
int kk(transb=='n'?b.nn:b.mm);
|
||||
int ll(transb=='n'?b.mm:b.nn);
|
||||
|
||||
if(l!=nn|| ll!=mm||k!=kk) laerror("incompatible (or undefined size) matrices in strassen");
|
||||
|
||||
copyonwrite();
|
||||
//swap transpositions and order of matrices
|
||||
fmm(transb,transa,mm,nn,k,alpha,b,b.mm, a, a.mm, beta,*this, mm,NULL,0);
|
||||
}
|
||||
|
||||
//stub for f77 blas called from strassen routine
|
||||
extern "C" void xerbla_(const char *msg)
|
||||
{
|
||||
laerror(msg);
|
||||
}
|
||||
|
||||
|
||||
|
|
@ -0,0 +1,775 @@
|
|||
// g++ -D _GLIBCPP_NO_TEMPLATE_EXPORT -g testblas.cc testblas2.cc nrutil_modif.cc -L/usr/local/lib/atlas -lstrassen -lf77blas -lcblas -latlas -ltraceback -lbfd -liberty
|
||||
|
||||
#include <time.h>
|
||||
#include "la.h"
|
||||
#include "traceback.h"
|
||||
#include "sparsemat.h"
|
||||
#include "matexp.h"
|
||||
#include "fourindex.h"
|
||||
|
||||
|
||||
extern void test(const NRVec<double> &);
|
||||
|
||||
double ad;
|
||||
void f1(const double *c)
|
||||
{
|
||||
ad=*c;
|
||||
}
|
||||
|
||||
void f2(double *c)
|
||||
{
|
||||
*c=ad;
|
||||
}
|
||||
|
||||
|
||||
inline int randind(const int n)
|
||||
{
|
||||
return int(random()/(1.+RAND_MAX)*n);
|
||||
}
|
||||
|
||||
complex<double> mycident (const complex<double>&x) {return x;}
|
||||
|
||||
|
||||
int main()
|
||||
{
|
||||
sigtraceback(SIGSEGV,1);
|
||||
sigtraceback(SIGABRT,1);
|
||||
sigtraceback(SIGBUS,1);
|
||||
sigtraceback(SIGFPE,1);
|
||||
NRVec<double> x(1.,10);
|
||||
NRVec<double> y(2.,10);
|
||||
NRVec<double> z(-2.,10);
|
||||
|
||||
y.axpy(3,x);
|
||||
|
||||
y+=z;
|
||||
/*
|
||||
cout <<y;
|
||||
NRVec<double> a(x);
|
||||
|
||||
NRVec<double> b;
|
||||
b|=x;
|
||||
|
||||
NRVec<double> c;
|
||||
c=a;
|
||||
|
||||
y =10. *y ;
|
||||
|
||||
int i;
|
||||
for(i=0;i<y.size();i++) cout <<y[i] <<" ";
|
||||
cout <<"\n";
|
||||
|
||||
cout << y*z <<"\n";
|
||||
|
||||
z|=x;
|
||||
z[1]=5;
|
||||
|
||||
cout <<"zunit= "<<z.unitvector()<<"\n";
|
||||
cout <<"z= "<<z<<"\n";
|
||||
test(x);
|
||||
|
||||
x = x*5;
|
||||
|
||||
|
||||
cout <<"x= "<<x<<"\n";
|
||||
cout <<"y= "<<y<<"\n";
|
||||
|
||||
NRVec<double> u;
|
||||
u=x+y;
|
||||
cout <<"u= "<<u<<"\n";
|
||||
|
||||
NRMat<double> aa(0.,3,3);
|
||||
aa[0][0]=aa[1][1]=aa(2,2)=2.;
|
||||
|
||||
NRMat<double> bb(aa);
|
||||
|
||||
double *p;
|
||||
aa.copyonwrite(); p= &aa[2][2];
|
||||
*p=3.;
|
||||
bb.copyonwrite(); bb(0,2)=1.;
|
||||
|
||||
cout << "aa= " <<aa <<"\n";
|
||||
cout << "bb= " <<bb <<"\n";
|
||||
cout <<"aa trace "<<aa.trace() <<"\n";
|
||||
cout << "bbt= " <<bb.transpose() <<"\n";
|
||||
NRMat<double> cc=aa & bb;
|
||||
cout << "aa o+ bb= " << cc <<"\n";
|
||||
cout << cc.rsum() <<"\n";
|
||||
cout << cc.csum() <<"\n";
|
||||
|
||||
NRVec<double>w(3);
|
||||
w[0]=1; w[1]=2;w[2]=3;
|
||||
NRVec<double> v(0.,3);
|
||||
v.gemv(0.,bb,'n',1.,w);
|
||||
cout << " v= " <<v <<"\n";
|
||||
v.gemv(0.,bb,'t',1.,w);
|
||||
cout << " v= " <<v <<"\n";
|
||||
|
||||
*/
|
||||
/*
|
||||
const int n=6000;
|
||||
NRMat<double> bb(1.,n,n);
|
||||
for(int i=0;i<n;i++) for(int j=0;j<n;j++) bb[i][j]=2.;
|
||||
for(int i=0;i<n;i++) for(int j=0;j<i;j++) {double t; t=bb[i][j] +bb[j][j]; bb[i][j]=t;bb[j][i]=t;}
|
||||
*/
|
||||
|
||||
/*
|
||||
NRMat<double> amat,bmat,cmat;
|
||||
cin >>amat;
|
||||
cin >>bmat;
|
||||
cmat=amat*bmat;
|
||||
cout<<cmat;
|
||||
cmat.copyonwrite(); cmat[0][0]=0;
|
||||
NRMat<double> amat(1.,2,2);
|
||||
NRMat<double> bmat(amat);
|
||||
NRMat<double> dmat(amat);
|
||||
//NRMat<double> cmat; cmat=bmat*2.;
|
||||
NRMat<double> cmat(bmat*2); //more efficient
|
||||
dmat.copyonwrite(); dmat[0][0]=0;
|
||||
|
||||
cout<<amat;
|
||||
cout<<bmat;
|
||||
cout<<cmat;
|
||||
cout<<dmat;
|
||||
|
||||
|
||||
NRMat<double> amat;
|
||||
NRVec<double> avec;
|
||||
|
||||
cin >>amat;
|
||||
cin >>avec;
|
||||
|
||||
cout << amat*avec;
|
||||
cout << avec*amat;
|
||||
|
||||
NRVec<double> avec(0.,10);
|
||||
|
||||
f1(avec);
|
||||
f2(avec);
|
||||
|
||||
NRVec<double> uu(3);
|
||||
uu[0]=1; uu[1]=2; uu[2]=3;
|
||||
cout << uu << (uu|uu) <<"\n";
|
||||
|
||||
NRSMat<double> sa(0.,3);
|
||||
sa(0,0)=1; sa(0,2)=5; sa(2,2)=10;sa(1,0)=2;sa(1,1)=3; sa(2,1)=-1;
|
||||
|
||||
NRSMat<double> sb(0.,3);
|
||||
sb(0,0)=-2; sb(0,2)=1; sb(2,2)=2;sb(1,0)=-1;sb(1,1)=7; sb(2,1)=3;
|
||||
|
||||
cout << "symetr\n" <<sa << -sa <<"\n";
|
||||
cout << "symetr\n" <<sb <<"\n";
|
||||
|
||||
cout << "sa*sb\n" << sa*sb <<"\n";
|
||||
cout << "sb*sa\n" << sb*sa <<"\n";
|
||||
|
||||
NRMat<double> m10(10.,3,3);
|
||||
cout << "10 + sa" << m10 + sa <<"\n";
|
||||
*/
|
||||
|
||||
/*
|
||||
|
||||
const int dim=256;
|
||||
NRMat<double> big1(dim,dim),big2(dim,dim),big3;
|
||||
for(int i=0;i<dim;i++)
|
||||
for(int j=0;j<dim;j++)
|
||||
{
|
||||
big1[i][j]=i*i+j*j*j-3*j;
|
||||
big2[i][j]=i*i/(j+1)+j*j-3*j;
|
||||
}
|
||||
double t=clock()/((double) (CLOCKS_PER_SEC));
|
||||
big3= big1*big2;
|
||||
cout <<" big1*big2 "<<big3[0][0]<<" time "<<clock()/((double) (CLOCKS_PER_SEC))-t <<"\n";
|
||||
|
||||
*/
|
||||
|
||||
/*
|
||||
NRMat<double> atest, btest,ctest;
|
||||
{
|
||||
int cc,c1,c2,c3;
|
||||
cin >>cc>>c1>>c2>>c3;
|
||||
atest.s_cutoff(cc,c1,c2,c3);
|
||||
}
|
||||
cin>>atest;
|
||||
cin>>btest;
|
||||
|
||||
NRMat<double> dtest(atest.nrows(),btest.ncols());
|
||||
dtest.gemm(0., atest, 't', btest, 'n', 1.);
|
||||
cout << dtest;
|
||||
|
||||
NRMat<double> etest(atest.nrows(),btest.ncols());
|
||||
etest.strassen(0., atest, 't', btest, 'n', 1.);
|
||||
cout << etest;
|
||||
*/
|
||||
|
||||
if(0)
|
||||
{
|
||||
int dim;
|
||||
cin >>dim;
|
||||
NRMat<double> big1(dim,dim),big2(dim,dim),big3,big4(dim,dim);
|
||||
for(int i=0;i<dim;i++)
|
||||
for(int j=0;j<dim;j++)
|
||||
{
|
||||
big1[i][j]=i*i+j*j*j-3*j;
|
||||
big2[i][j]=i*i/(j+1)+j*j-3*j;
|
||||
}
|
||||
double t=clock()/((double) (CLOCKS_PER_SEC));
|
||||
big3= big1*big2;
|
||||
cout <<" classical big1*big2 "<<big3[0][0]<<" time "<<clock()/((double) (CLOCKS_PER_SEC))-t <<"\n";
|
||||
|
||||
for (int c=64; c<=512;c+=64)
|
||||
{
|
||||
big4.s_cutoff(c,c,c,c);
|
||||
t=clock()/((double) (CLOCKS_PER_SEC));
|
||||
big4.strassen(0., big1, 'n', big2, 'n', 1.);
|
||||
cout <<"cutoff "<<c<<" big1*big2 "<<big4[0][0]<<" time "<<clock()/((double) (CLOCKS_PER_SEC))-t <<"\n";
|
||||
}
|
||||
}
|
||||
|
||||
if(0)
|
||||
{
|
||||
NRMat<double> a(3,3),b;
|
||||
NRVec<double> v(3);
|
||||
for(int i=0;i<3;i++) for(int j=0;j<3;j++) { a[i][j]= i*i+j; v[i]=10-i;}
|
||||
b=a;
|
||||
b*= sin(1.)+1;
|
||||
cout << a <<v;
|
||||
a.diagmultl(v);
|
||||
cout << a;
|
||||
b.diagmultr(v);
|
||||
cout << b;
|
||||
}
|
||||
|
||||
if(0)
|
||||
{
|
||||
NRMat<double> a(3,3),b;
|
||||
NRVec<double> v(10);
|
||||
v[0]=2;v[1]=3;v[2]=1;v[3]=-3;v[4]=2;v[5]=-1;v[6]=3;v[7]=-2;v[8]=1;v[9]=1;
|
||||
for(int i=0;i<3;i++) for(int j=0;j<3;j++) { a[i][j]= (i+j)/10.; }
|
||||
cout <<a;
|
||||
cout << a.norm() <<"\n";
|
||||
b=a*a;
|
||||
cout << b.norm() <<"\n";
|
||||
cout << exp(a);
|
||||
cout << exp(a.norm()) <<"\n";
|
||||
cout << ipow(a,3);
|
||||
cout<<ipow(a,11);
|
||||
cout <<commutator(a,b);
|
||||
|
||||
}
|
||||
|
||||
if(0)
|
||||
{
|
||||
NRMat<double> a(3,3);
|
||||
for(int i=0;i<3;i++) for(int j=0;j<3;j++) { a[i][j]= (i+j)/10.; }
|
||||
NRSMat<double> b(a);
|
||||
NRMat<double> c(b);
|
||||
cout <<a;
|
||||
cout <<b;
|
||||
cout <<c;
|
||||
}
|
||||
|
||||
if(0)
|
||||
{
|
||||
NRMat<double> a(3,3);
|
||||
a[0][0]=1; a[0][1]=2;a[0][2]=3;
|
||||
a[1][0]=4; a[1][1]=-5;a[1][2]=7;
|
||||
a[2][0]=-3;a[2][1]=10;a[2][2]=2;
|
||||
NRMat<double> b(2,3);
|
||||
b[0][0]=1;b[0][1]=2;b[0][2]=3;
|
||||
b[1][0]=2;b[1][1]=4;b[1][2]=6;
|
||||
cout <<a;
|
||||
cout <<b;
|
||||
linear_solve(a,&b);
|
||||
cout <<a;
|
||||
cout <<b;
|
||||
}
|
||||
|
||||
if(0)
|
||||
{
|
||||
NRMat<double> a(3,3);
|
||||
for(int i=0;i<3;i++) for(int j=0;j<3;j++) { a[i][j]= (i+j)/10.; }
|
||||
NRVec<double> b(3);
|
||||
cout <<a;
|
||||
diagonalize(a,b);
|
||||
cout <<a;
|
||||
cout <<b;
|
||||
}
|
||||
|
||||
if(0)
|
||||
{
|
||||
NRSMat<double> a(3);
|
||||
NRMat<double>v(3,3);
|
||||
for(int i=0;i<3;i++) for(int j=0;j<3;j++) { a(i,j)= (i+j)/10.; }
|
||||
NRVec<double> b(3);
|
||||
cout <<a;
|
||||
NRMat<double>c=(NRMat<double>)a; //nebo NRMat<double>c(a);
|
||||
NRMat<double>d=exp(c);
|
||||
diagonalize(a,b,&v);
|
||||
cout <<b;
|
||||
cout <<v;
|
||||
cout <<d;
|
||||
diagonalize(d,b);
|
||||
cout <<b;
|
||||
cout <<d;
|
||||
}
|
||||
|
||||
if(0)
|
||||
{
|
||||
NRMat<double> a;
|
||||
cin >>a ;
|
||||
NRMat<double> b=a.transpose();
|
||||
NRMat<double> u(a.nrows(),a.nrows()),v(a.ncols(),a.ncols());
|
||||
NRVec<double>s(a.ncols());
|
||||
singular_decomposition(a,&u,s,&v);
|
||||
//singular_decomposition(a,NULL,s,NULL); //this does not work when linked with static version of lapack, works with .so.3 version (from suse distrib)
|
||||
cout <<u;
|
||||
cout <<s;
|
||||
cout <<v;
|
||||
//singular_decomposition(b,&v,s,&u);
|
||||
//cout <<v;
|
||||
//cout <<s;
|
||||
//cout <<u;
|
||||
}
|
||||
|
||||
if(0)
|
||||
{
|
||||
//diagonalize a general matrix and reconstruct it back; assume real eigenvalues
|
||||
//double aa[]={1,2,3,4,-5,7,-3,10,2};
|
||||
//NRMat<double> a(aa,3,3);
|
||||
NRMat<double> a;
|
||||
cin >>a;
|
||||
cout <<a ;
|
||||
int n=a.nrows();
|
||||
NRMat<double> u(n,n),v(n,n);
|
||||
NRVec<double>wr(n),wi(n);
|
||||
gdiagonalize(a,wr,wi,&u,&v,0);
|
||||
cout <<u;
|
||||
cout <<wr;
|
||||
cout <<wi;
|
||||
cout <<v;
|
||||
|
||||
NRVec<double>z=diagofproduct(u,v,1);
|
||||
for(int i=0;i<a.nrows();++i) wr[i]/=z[i];//account for normalization of eigenvectors
|
||||
u.diagmultl(wr);
|
||||
v.transposeme();
|
||||
cout <<v*u;
|
||||
|
||||
}
|
||||
|
||||
if(0)
|
||||
{
|
||||
//diagonalize a general matrix and reconstruct it back; allow complex eigenvalues
|
||||
NRMat<double> a;
|
||||
cin >>a;
|
||||
cout <<a ;
|
||||
int n=a.nrows();
|
||||
NRMat<complex<double> > u(n,n),v(n,n);
|
||||
NRVec<complex<double> >w(n);
|
||||
gdiagonalize(a,w,&u,&v);
|
||||
cout <<u;
|
||||
cout <<w;
|
||||
cout <<v;
|
||||
|
||||
NRVec<complex<double> >z=diagofproduct(u,v,1,1);
|
||||
//NRMat<complex<double> > zz=u*v.transpose(1);
|
||||
cout <<z;
|
||||
//cout <<zz;
|
||||
for(int i=0;i<a.nrows();++i) w[i]/=z[i];//account for normalization of eigenvectors
|
||||
u.diagmultl(w);
|
||||
cout <<v.transpose(1)*u;
|
||||
|
||||
}
|
||||
|
||||
|
||||
|
||||
if(0)
|
||||
{
|
||||
SparseMat<double> a(4,4);
|
||||
NRVec<double> v(4);
|
||||
v[0]=1;v[1]=2;v[2]=3;v[3]=4;
|
||||
a=1.;
|
||||
a.copyonwrite();
|
||||
a.add(3,0,.5);
|
||||
a.add(0,2,.2);
|
||||
a.add(2,1,.1);
|
||||
a.add(3,3,1.);
|
||||
a.add(1,1,-1.);
|
||||
SparseMat<double> c(a);
|
||||
c*=10.;
|
||||
cout <<a;
|
||||
a.simplify();
|
||||
cout <<a;
|
||||
cout <<c;
|
||||
NRMat<double>b(c);
|
||||
cout <<b;
|
||||
cout << b*v;
|
||||
cout <<c*v;
|
||||
cout <<v*b;
|
||||
cout <<v*c;
|
||||
}
|
||||
|
||||
if(0)
|
||||
{
|
||||
SparseMat<double> a(4,4),b(4,4);
|
||||
a=1.;
|
||||
a.copyonwrite();
|
||||
a.add(3,0,.5);
|
||||
b.add(0,2,.2);
|
||||
b.add(2,1,.1);
|
||||
b.add(3,3,1.);
|
||||
b.add(1,1,-1.);
|
||||
SparseMat<double>c=a+b;
|
||||
cout <<c;
|
||||
a.join(b);
|
||||
cout<<a;
|
||||
cout<<b;
|
||||
}
|
||||
|
||||
if(0)
|
||||
{
|
||||
SparseMat<double> a(4,4),b(4,4);
|
||||
a=0.; b=2;
|
||||
a.add(3,0,.5);
|
||||
a.add(0,2,.2);
|
||||
a.add(1,1,1);
|
||||
a.add(1,0,.2);
|
||||
b.add(2,1,.1);
|
||||
b.add(3,3,1.);
|
||||
b.add(1,1,-1.);
|
||||
NRMat<double> aa(a),bb(b);
|
||||
SparseMat<double>c;
|
||||
NRMat<double>cc;
|
||||
//cout << NRMat<double>(c);
|
||||
//cout <<cc;
|
||||
//cout <<"norms "<<c.norm()<<" " <<cc.norm()<<endl;
|
||||
cout <<"original matrix \n"<<aa;
|
||||
cout <<(cc=exp(aa));
|
||||
c=exp(a);
|
||||
cout <<NRMat<double>(c);
|
||||
cout <<"norms2 "<<c.norm()<<" " <<cc.norm()<<endl;
|
||||
}
|
||||
|
||||
#define sparsity (n/4)
|
||||
if(0)
|
||||
{
|
||||
for(int n=8; n<=1024*1024;n+=n)
|
||||
{
|
||||
SparseMat<double> aa(n,n);
|
||||
cout << "\n\n\ntiming for size "<<n<<endl;
|
||||
if(n<=512) {
|
||||
NRMat<double> a(0.,n,n);
|
||||
for(int i=0; i<sparsity;i++) a(randind(n),randind(n))=random()/(1.+RAND_MAX);
|
||||
double t0=clock()/((double) (CLOCKS_PER_SEC));
|
||||
//cout <<a;
|
||||
NRMat<double> b(exp(a));
|
||||
//cout <<b;
|
||||
cout <<"dense norm "<<b.norm() <<"\n";
|
||||
cout << "test commutator " <<commutator(a,b).norm() <<endl;
|
||||
double t1=clock()/((double) (CLOCKS_PER_SEC));
|
||||
cout << "dense time " <<n<<' '<< t1-t0 <<endl;
|
||||
aa=SparseMat<double>(a);
|
||||
}
|
||||
else
|
||||
{
|
||||
for(int i=0; i<sparsity;i++) aa.add(randind(n),randind(n),random()/(1.+RAND_MAX));
|
||||
}
|
||||
//cout <<aa;
|
||||
double t2=clock()/((double) (CLOCKS_PER_SEC));
|
||||
SparseMat<double> bb(exp(aa));
|
||||
//cout <<bb;
|
||||
cout <<"sparse norm "<<bb.norm() <<"\n";
|
||||
cout << "test commutator " <<commutator(aa,bb).norm() <<endl;
|
||||
double t3=clock()/((double) (CLOCKS_PER_SEC));
|
||||
cout <<"sparse length "<<bb.length()<<"\n";
|
||||
cout << "sparse time "<<n<<' ' << t3-t2 <<endl;
|
||||
}
|
||||
}
|
||||
|
||||
if(1)
|
||||
{
|
||||
int n;
|
||||
cin>>n;
|
||||
SparseMat<double> aa(n,n);
|
||||
for(int i=0; i<sparsity;i++) aa.add(randind(n),randind(n),random()/(1.+RAND_MAX));
|
||||
SparseMat<double> bb=exp(aa);
|
||||
NRVec<double> v(n);
|
||||
for(int i=0; i<n;++i) v[i]=random()/(1.+RAND_MAX);
|
||||
NRVec<double> res1=bb*v;
|
||||
NRVec<double> res2=exptimes(aa,v);
|
||||
cout <<"difference = "<<(res1-res2).norm()<<endl;
|
||||
}
|
||||
|
||||
|
||||
if(0)
|
||||
{
|
||||
SparseMat<double> a(4,4),b(4,4),d;
|
||||
a=0.; b=2;
|
||||
a.add(3,0,.5);
|
||||
a.add(0,2,.2);
|
||||
a.add(1,1,1);
|
||||
a.add(1,0,.2);
|
||||
b.add(2,1,.1);
|
||||
b.add(3,3,1.);
|
||||
b.add(1,1,-1.);
|
||||
NRMat<double> aa(a),bb(b),dd;
|
||||
SparseMat<double>c;
|
||||
NRMat<double>cc;
|
||||
|
||||
c=commutator(a,b);
|
||||
cc=commutator(aa,bb);
|
||||
|
||||
cout <<cc;
|
||||
cout <<NRMat<double>(c);
|
||||
cout <<"norms2 "<<c.norm()<<" " <<cc.norm()<<endl;
|
||||
}
|
||||
|
||||
/*
|
||||
NRVec<double> v(10.,10);
|
||||
v+= 5.;
|
||||
cout <<v;
|
||||
*/
|
||||
if(0)
|
||||
{
|
||||
const int n=3;
|
||||
NRMat<double> a(n,n);
|
||||
for(int i=0;i<n;++i) for(int j=0;j<i;++j)
|
||||
{
|
||||
a(i,j)= random()/(1.+RAND_MAX);
|
||||
a(j,i)= -a(i,j);
|
||||
}
|
||||
NRMat<double> b; b|=a;
|
||||
NRVec<double> er(n),ei(n);
|
||||
NRMat<double> vr(n,n),vl(n,n);
|
||||
gdiagonalize(b,er,ei,&vl,&vr);
|
||||
cout <<er<<ei;
|
||||
cout <<"left eivec\n"<<vl <<"right eivec\n"<<vr;
|
||||
NRMat<double> u=exp(a*.125);
|
||||
cout <<"norms "<<u.norm() << ' '<<(u-1.).norm()<<endl;
|
||||
gdiagonalize(u,er,ei,&vl,&vr);
|
||||
cout <<er<<ei;
|
||||
cout <<"left eivec\n"<<vl <<"right eivec\n"<<vr;
|
||||
}
|
||||
|
||||
if(0)
|
||||
{
|
||||
/*
|
||||
int n;
|
||||
cin>>n;
|
||||
NRMat<double> a(n,n);
|
||||
for(int i=0;i<n;++i) for(int j=0;j<i;++j)
|
||||
{
|
||||
a(i,j)= random()/(1.+RAND_MAX);
|
||||
a(j,i)= -a(i,j);
|
||||
}
|
||||
NRMat<double> b=exp(a);
|
||||
cout <<a;
|
||||
*/
|
||||
NRMat<double> a,b;
|
||||
cin >>b;
|
||||
int n=b.nrows();
|
||||
cout <<"difference from identity = "<<b.norm(1.)<<endl;
|
||||
|
||||
NRMat<double> x(0.,n,n),x0;
|
||||
double r;
|
||||
int i=0;
|
||||
do
|
||||
{
|
||||
x0=x;
|
||||
NRMat<double> y=exp(x*-.5);
|
||||
x+= y*b*y;
|
||||
x-= 1.;
|
||||
x=(x-x.transpose())*.5;
|
||||
cout <<"matrix x\n"<<x;
|
||||
cout <<"iter "<<i <<" residue "<< (r=(exp(x)-b).norm())<<endl;
|
||||
cout <<"iter "<<i <<" conv "<<(r=(x-x0).norm())<<endl;
|
||||
++i;
|
||||
} while(abs(r)>1e-10);
|
||||
cout <<"result\n"<<x<<endl;
|
||||
cout <<"exp(result)"<<exp(x)<<endl;
|
||||
NRMat<double> c=log(b); //matrixfunction(a,&mycident,1);
|
||||
cout <<c;
|
||||
NRMat<double> d=exp(c);
|
||||
cout <<"exp(log(x))\n"<<d;
|
||||
cout<<(d-b).norm()<<endl;
|
||||
|
||||
}
|
||||
|
||||
if(0)
|
||||
{
|
||||
int n;
|
||||
cin>>n;
|
||||
NRMat<double> a(n,n);
|
||||
for(int i=0;i<n;++i) for(int j=0;j<=i;++j)
|
||||
{
|
||||
a(i,j)= .1*random()/(1.+RAND_MAX);
|
||||
a(j,i)= a(i,j);
|
||||
}
|
||||
NRMat<double> b=exp(a);
|
||||
NRMat<double> s=exp(a*.5);
|
||||
NRMat<double> y(0.,n,n);
|
||||
NRMat<double> z(0.,n,n);
|
||||
double r;
|
||||
int i=0;
|
||||
y=b;z=1.;
|
||||
cout << "norm = "<<b.norm(1.)<<endl;
|
||||
do
|
||||
{
|
||||
NRMat<double> tmp=z*y*-1.+3.;
|
||||
NRMat<double> ynew=y*tmp*.5;
|
||||
z=tmp*z*.5;
|
||||
y=ynew;
|
||||
cout <<"iter "<<i <<" residue "<< (r=(y-s).norm())<<endl;
|
||||
++i;
|
||||
} while(abs(r)>1e-10);
|
||||
}
|
||||
|
||||
|
||||
if(0)
|
||||
{
|
||||
int n=3;
|
||||
NRMat<double> a(n,n);
|
||||
a(0,0)=1.;
|
||||
a(0,1)=2.;
|
||||
a(1,0)=2.;
|
||||
a(1,1)=6.;
|
||||
a(2,2)=-4;
|
||||
a(0,2)=1;
|
||||
cout <<a;
|
||||
double d;
|
||||
NRMat<double> c=inverse(a,&d);
|
||||
cout <<a<<c;
|
||||
}
|
||||
|
||||
if(0)
|
||||
{
|
||||
NRMat<double> a(3,3);
|
||||
NRMat<double> b=a;
|
||||
for(int i=1; i<4;i++) b=b*b;
|
||||
}
|
||||
|
||||
if(0)
|
||||
{
|
||||
NRMat<double> a;
|
||||
cin >>a;
|
||||
NRMat<double> b=exp(a);
|
||||
NRMat<double> c=log(b);
|
||||
cout <<a;
|
||||
cout <<b;
|
||||
cout <<c;
|
||||
cout << (b-exp(c)).norm() <<endl;
|
||||
}
|
||||
|
||||
if(00)
|
||||
{
|
||||
NRMat<double> a;
|
||||
cin >>a;
|
||||
NRMat<double> c=log(a); //matrixfunction(a,&mycident,1);
|
||||
cout <<c;
|
||||
NRMat<double> b=exp(c);
|
||||
cout <<"exp(log(x))\n"<<b;
|
||||
cout<<(b-a).norm()<<endl;
|
||||
}
|
||||
|
||||
if(0)
|
||||
{
|
||||
//check my exponential with respect to spectral decomposition one
|
||||
NRSMat<double> a;
|
||||
cin >>a;
|
||||
NRMat<double> aa(a);
|
||||
NRMat<double> b=exp(aa);
|
||||
NRMat<double> c=matrixfunction(a,&exp);
|
||||
cout <<a;
|
||||
cout <<b;
|
||||
cout <<c;
|
||||
cout << (b-c).norm()/b.norm() <<endl;
|
||||
}
|
||||
|
||||
if(0)
|
||||
{
|
||||
//verify BCH expansion
|
||||
NRMat<double> h;
|
||||
NRMat<double> t;
|
||||
cin >>h;
|
||||
cin >>t;
|
||||
NRMat<double> r1= exp(-t) * h * exp(t);
|
||||
NRMat<double> r2=BCHexpansion(h,t,30);
|
||||
cout <<r1;
|
||||
cout <<r2;
|
||||
cout <<"error = "<<(r1-r2).norm()<<endl;
|
||||
}
|
||||
|
||||
if(0)
|
||||
{
|
||||
int n;
|
||||
cin >>n;
|
||||
SparseMat<double> a(n,n);
|
||||
for(int i=0;i<n;++i) for(int j=0;j<=i;++j)
|
||||
{
|
||||
a.add(i,j,random()/(1.+RAND_MAX));
|
||||
}
|
||||
a.setsymmetric();
|
||||
NRSMat<double> aa(a);
|
||||
NRMat<double> aaa(a);
|
||||
NRVec<double> w(n);
|
||||
NRMat<double> v(n,n);
|
||||
//cout <<aa;
|
||||
diagonalize(aa, w, &v,0);
|
||||
//cout <<w;
|
||||
//cout <<v;
|
||||
//cout << v*aaa*v.transpose();
|
||||
cout << (v*aaa*v.transpose() - diagonalmatrix(w)).norm()<<endl;
|
||||
}
|
||||
|
||||
if(0)
|
||||
{
|
||||
NRMat<complex<double> > a;
|
||||
cin >>a;
|
||||
NRMat<complex<double> > b=exp(a);
|
||||
cout <<b;
|
||||
}
|
||||
|
||||
if(0)
|
||||
{
|
||||
int n;
|
||||
cin >>n;
|
||||
//NRMat<double> a(n,n);
|
||||
NRSMat<double> a(n);
|
||||
for(int i=0;i<n;++i) for(int j=0;j<=i;++j)
|
||||
{
|
||||
a(j,i)=a(i,j)=random()/(1.+RAND_MAX);
|
||||
}
|
||||
cout <<a;
|
||||
NRMat<double> y(1,n);
|
||||
for(int i=0;i<n;++i) y(0,i)=random()/(1.+RAND_MAX);
|
||||
cout <<y;
|
||||
linear_solve(a,&y);
|
||||
cout << y;
|
||||
}
|
||||
|
||||
if(0)
|
||||
{
|
||||
int n;
|
||||
cin >>n;
|
||||
SparseMat<double> a(n,n);
|
||||
int spars=n*n/3;
|
||||
for(int i=0; i<spars;i++) a.add(randind(n),randind(n),random()/(1.+RAND_MAX));
|
||||
|
||||
NRMat<double> aa(a);
|
||||
NRVec<double> v(aa[0],n*n);
|
||||
|
||||
cout <<a;
|
||||
cout <<aa;
|
||||
cout <<v;
|
||||
|
||||
cout <<"test "<<aa.dot(aa)<<endl;
|
||||
cout <<"test "<<v*v<<endl;
|
||||
cout <<"test "<<a.dot(aa)<<endl;
|
||||
cout <<"test "<<a.dot(a)<<endl;
|
||||
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
|
||||
|
||||
|
|
@ -0,0 +1,348 @@
|
|||
#include <iostream>
|
||||
#include "vec.h"
|
||||
|
||||
//////////////////////////////////////////////////////////////////////////////
|
||||
//// forced instantization in the corespoding object file
|
||||
#define INSTANTIZE(T) \
|
||||
template ostream & operator<<(ostream &s, const NRVec< T > &x); \
|
||||
template istream & operator>>(istream &s, NRVec< T > &x); \
|
||||
|
||||
INSTANTIZE(double)
|
||||
INSTANTIZE(complex<double>)
|
||||
template NRVec<double>;
|
||||
template NRVec< complex<double> >;
|
||||
|
||||
|
||||
/*
|
||||
* Templates first, specializations for BLAS next
|
||||
*/
|
||||
|
||||
// conversion ctor
|
||||
#ifndef MATPTR
|
||||
template <typename T>
|
||||
NRVec<T>::NRVec(const NRMat<T> &rhs)
|
||||
{
|
||||
nn = rhs.nn*rhs.mm;
|
||||
v = rhs.v;
|
||||
count = rhs.count;
|
||||
(*count)++;
|
||||
}
|
||||
#endif
|
||||
|
||||
// dtor
|
||||
template <typename T>
|
||||
NRVec<T>::~NRVec()
|
||||
{
|
||||
if(!count) return;
|
||||
if(--(*count) <= 0) {
|
||||
if(v) delete[] (v);
|
||||
delete count;
|
||||
}
|
||||
}
|
||||
|
||||
// detach from a physical vector and make own copy
|
||||
template <typename T>
|
||||
void NRVec<T>::copyonwrite()
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if(!count) laerror("probably an assignment to undefined vector");
|
||||
#endif
|
||||
if(*count > 1)
|
||||
{
|
||||
(*count)--;
|
||||
count = new int;
|
||||
*count = 1;
|
||||
T *newv = new T[nn];
|
||||
memcpy(newv, v, nn*sizeof(T));
|
||||
v = newv;
|
||||
}
|
||||
}
|
||||
|
||||
// Asignment
|
||||
template <typename T>
|
||||
NRVec<T> & NRVec<T>::operator=(const NRVec<T> &rhs)
|
||||
{
|
||||
if (this != &rhs)
|
||||
{
|
||||
if(count)
|
||||
if(--(*count) == 0)
|
||||
{
|
||||
delete[] v;
|
||||
delete count;
|
||||
}
|
||||
v = rhs.v;
|
||||
nn = rhs.nn;
|
||||
count = rhs.count;
|
||||
if(count) (*count)++;
|
||||
}
|
||||
return *this;
|
||||
}
|
||||
|
||||
// Resize
|
||||
template <typename T>
|
||||
void NRVec<T>::resize(const int n)
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if(n<=0) laerror("illegal vector dimension");
|
||||
#endif
|
||||
if(count)
|
||||
if(*count > 1) {
|
||||
(*count)--;
|
||||
count = 0;
|
||||
v = 0;
|
||||
nn = 0;
|
||||
}
|
||||
if(!count) {
|
||||
count = new int;
|
||||
*count = 1;
|
||||
nn = n;
|
||||
v = new T[nn];
|
||||
return;
|
||||
}
|
||||
// *count = 1 in this branch
|
||||
if (n != nn) {
|
||||
nn = n;
|
||||
delete[] v;
|
||||
v = new T[nn];
|
||||
}
|
||||
}
|
||||
|
||||
// ostream << NRVec
|
||||
template <typename T>
|
||||
ostream & operator<<(ostream &s, const NRVec<T> &x)
|
||||
{
|
||||
int i, n;
|
||||
|
||||
n = x.size();
|
||||
s << n << endl;
|
||||
for(i=0; i<n; i++) s << x[i] << (i == n-1 ? '\n' : ' ');
|
||||
return s;
|
||||
}
|
||||
|
||||
// istream >> NRVec
|
||||
template <typename T>
|
||||
istream & operator>>(istream &s, NRVec<T> &x)
|
||||
{
|
||||
int i,n;
|
||||
|
||||
s >> n;
|
||||
x.resize(n);
|
||||
for(i=0; i<n; i++) s >> x[i];
|
||||
return s;
|
||||
}
|
||||
|
||||
// formatted print for NRVec
|
||||
template<typename T>
|
||||
void NRVec<T>::fprintf(FILE *file, const char *format, const int modulo) const
|
||||
{
|
||||
lawritemat(file, v, 1, nn, format, 1, modulo, 0);
|
||||
}
|
||||
|
||||
// formatted scan for NRVec
|
||||
template <class T>
|
||||
void NRVec<T>::fscanf(FILE *f, const char *format)
|
||||
{
|
||||
int n;
|
||||
|
||||
if(std::fscanf(f, "%d", &n) != 1) laerror("cannot read vector dimension");
|
||||
resize(n);
|
||||
for (int i=0; i<n; i++)
|
||||
if (std::fscanf(f, format, v+i) != 1)
|
||||
laerror("cannot read the vector eleemnt");
|
||||
}
|
||||
|
||||
// assignmet with a physical copy
|
||||
template <typename T>
|
||||
NRVec<T> & NRVec<T>::operator|=(const NRVec<T> &rhs)
|
||||
{
|
||||
if (this != &rhs) {
|
||||
#ifdef DEBUG
|
||||
if (!rhs.v) laerror("unallocated rhs in NRVec operator |=");
|
||||
#endif
|
||||
if (count)
|
||||
if (*count > 1) {
|
||||
--(*count);
|
||||
nn = 0;
|
||||
count = 0;
|
||||
v = 0;
|
||||
}
|
||||
if (nn != rhs.nn) {
|
||||
if (v) delete[] (v);
|
||||
nn = rhs.nn;
|
||||
}
|
||||
if(!v) v = new T[nn];
|
||||
if(!count) count = new int;
|
||||
*count = 1;
|
||||
memcpy(v, rhs.v, nn*sizeof(T));
|
||||
}
|
||||
return *this;
|
||||
}
|
||||
|
||||
// unary minus
|
||||
template <typename T>
|
||||
const NRVec<T> NRVec<T>::operator-() const
|
||||
{
|
||||
NRVec<T> result(nn);
|
||||
for (int i=0; i<nn; i++) result.v[i]= -v[i];
|
||||
return result;
|
||||
}
|
||||
|
||||
// axpy call for T = double (not strided)
|
||||
void NRVec<double>::axpy(const double alpha, const NRVec<double> &x)
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (nn != x.nn) laerror("axpy of incompatible vectors");
|
||||
#endif
|
||||
copyonwrite();
|
||||
cblas_daxpy(nn, alpha, x.v, 1, v, 1);
|
||||
}
|
||||
|
||||
// axpy call for T = complex<double> (not strided)
|
||||
void NRVec< complex<double> >::axpy(const complex<double> alpha,
|
||||
const NRVec< complex<double> > &x)
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (nn != x.nn) laerror("axpy of incompatible vectors");
|
||||
#endif
|
||||
copyonwrite();
|
||||
cblas_zaxpy(nn, (void *)(&alpha), (void *)(x.v), 1, (void *)v, 1);
|
||||
}
|
||||
|
||||
// axpy call for T = double (strided)
|
||||
void NRVec<double>::axpy(const double alpha, const double *x, const int stride)
|
||||
{
|
||||
copyonwrite();
|
||||
cblas_daxpy(nn, alpha, x, stride, v, 1);
|
||||
}
|
||||
|
||||
// axpy call for T = complex<double> (strided)
|
||||
void NRVec< complex<double> >::axpy(const complex<double> alpha,
|
||||
const complex<double> *x, const int stride)
|
||||
{
|
||||
copyonwrite();
|
||||
cblas_zaxpy(nn, (void *)(&alpha), (void *)x, stride, v, 1);
|
||||
}
|
||||
|
||||
// unary minus
|
||||
const NRVec<double> NRVec<double>::operator-() const
|
||||
{
|
||||
NRVec<double> result(*this);
|
||||
result.copyonwrite();
|
||||
cblas_dscal(nn, -1.0, result.v, 1);
|
||||
return result;
|
||||
}
|
||||
const NRVec< complex<double> >
|
||||
NRVec< complex<double> >::operator-() const
|
||||
{
|
||||
NRVec< complex<double> > result(*this);
|
||||
result.copyonwrite();
|
||||
cblas_zdscal(nn, -1.0, (void *)(result.v), 1);
|
||||
return result;
|
||||
}
|
||||
|
||||
// assignment of scalar to every element
|
||||
template <typename T>
|
||||
NRVec<T> & NRVec<T>::operator=(const T &a)
|
||||
{
|
||||
copyonwrite();
|
||||
if(a != (T)0)
|
||||
for (int i=0; i<nn; i++) v[i] = a;
|
||||
else
|
||||
memset(v, 0, nn*sizeof(T));
|
||||
return *this;
|
||||
}
|
||||
|
||||
// Normalization of NRVec<double>
|
||||
NRVec<double> & NRVec<double>::normalize()
|
||||
{
|
||||
double tmp;
|
||||
|
||||
tmp = cblas_dnrm2(nn, v, 1);
|
||||
#ifdef DEBUG
|
||||
if(!tmp) laerror("normalization of zero vector");
|
||||
#endif
|
||||
copyonwrite();
|
||||
tmp = 1.0/tmp;
|
||||
cblas_dscal(nn, tmp, v, 1);
|
||||
return *this;
|
||||
}
|
||||
|
||||
// Normalization of NRVec< complex<double> >
|
||||
NRVec< complex<double> > & NRVec< complex<double> >::normalize()
|
||||
{
|
||||
complex<double> tmp;
|
||||
tmp = cblas_dznrm2(nn, (void *)v, 1);
|
||||
#ifdef DEBUG
|
||||
if(!(tmp.real()) && !(tmp.imag())) laerror("normalization of zero vector");
|
||||
#endif
|
||||
copyonwrite();
|
||||
tmp = 1.0/tmp;
|
||||
cblas_zscal(nn, (void *)(&tmp), (void *)v, 1);
|
||||
return *this;
|
||||
}
|
||||
|
||||
// gemv call
|
||||
void NRVec<double>::gemv(const double beta, const NRMat<double> &A,
|
||||
const char trans, const double alpha, const NRVec &x)
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if ((trans == 'n'?A.ncols():A.nrows()) != x.size())
|
||||
laerror("incompatible sizes in gemv A*x");
|
||||
#endif
|
||||
cblas_dgemv(CblasRowMajor, (trans=='n' ? CblasNoTrans:CblasTrans),
|
||||
A.nrows(), A.ncols(), alpha, A[0], A.ncols(), x.v, 1, beta, v, 1);
|
||||
}
|
||||
void NRVec< complex<double> >::gemv(const complex<double> beta,
|
||||
const NRMat< complex<double> > &A, const char trans,
|
||||
const complex<double> alpha, const NRVec &x)
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if ((trans == 'n'?A.ncols():A.nrows()) != x.size())
|
||||
laerror("incompatible sizes in gemv A*x");
|
||||
#endif
|
||||
cblas_zgemv(CblasRowMajor, (trans=='n' ? CblasNoTrans:CblasTrans),
|
||||
A.nrows(), A.ncols(), (void *)(&alpha), (void *)A[0], A.ncols(),
|
||||
(void *)x.v, 1, (void *)(&beta), (void *)v, 1);
|
||||
}
|
||||
|
||||
// Vec * Mat
|
||||
const NRVec<double> NRVec<double>::operator*(const NRMat<double> &mat) const
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if(mat.nrows() != nn) laerror("incompatible sizes in Vec*Mat");
|
||||
#endif
|
||||
int n = mat.ncols();
|
||||
NRVec<double> result(n);
|
||||
cblas_dgemv(CblasRowMajor, CblasTrans, nn, n, 1.0, mat[0], n, v, 1,
|
||||
0.0, result.v, 1);
|
||||
return result;
|
||||
}
|
||||
const NRVec< complex<double> >
|
||||
NRVec< complex<double> >::operator*(const NRMat< complex<double> > &mat) const
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if(mat.nrows() != nn) laerror("incompatible sizes in Vec*Mat");
|
||||
#endif
|
||||
int n = mat.ncols();
|
||||
NRVec< complex<double> > result(n);
|
||||
cblas_zgemv(CblasRowMajor, CblasTrans, nn, n, &CONE, mat[0], n, v, 1,
|
||||
&CZERO, result.v, 1);
|
||||
return result;
|
||||
}
|
||||
|
||||
// Direc product Mat = Vec | Vec
|
||||
const NRMat<double> NRVec<double>::operator|(const NRVec<double> &b) const
|
||||
{
|
||||
NRMat<double> result(0.,nn,b.nn);
|
||||
cblas_dger(CblasRowMajor, nn, b.nn, 1., v, 1, b.v, 1, result, b.nn);
|
||||
return result;
|
||||
}
|
||||
const NRMat< complex<double> >
|
||||
NRVec< complex<double> >::operator|(const NRVec< complex<double> > &b) const
|
||||
{
|
||||
NRMat< complex<double> > result(0.,nn,b.nn);
|
||||
cblas_zgerc(CblasRowMajor, nn, b.nn, &CONE, v, 1, b.v, 1, result, b.nn);
|
||||
return result;
|
||||
}
|
||||
|
||||
|
||||
|
|
@ -0,0 +1,380 @@
|
|||
#ifndef _LA_VEC_H_
|
||||
#define _LA_VEC_H_
|
||||
|
||||
extern "C" {
|
||||
#include "cblas.h"
|
||||
}
|
||||
#include <stdio.h>
|
||||
#include <complex>
|
||||
#include <string.h>
|
||||
#include <iostream>
|
||||
|
||||
using namespace std;
|
||||
|
||||
template <typename T> class NRVec;
|
||||
template <typename T> class NRSMat;
|
||||
template <typename T> class NRMat;
|
||||
template <typename T> class SparseMat;
|
||||
|
||||
//////////////////////////////////////////////////////////////////////////////
|
||||
// Forward declarations
|
||||
void laerror(const char *s1=0, const char *s2=0, const char *s3=0, const char *s4=0);
|
||||
template <typename T> void lawritemat(FILE *file,const T *a,int r,int c,
|
||||
const char *form0,int nodim,int modulo, int issym);
|
||||
|
||||
// Memory allocated constants for cblas routines
|
||||
const static complex<double> CONE = 1.0, CMONE = -1.0, CZERO = 0.0;
|
||||
|
||||
// Macros to construct binary operators +,-,*, from +=, -=, *=
|
||||
// for 3 cases: X + a, a + X, X + Y
|
||||
#define NRVECMAT_OPER(E,X) \
|
||||
template<class T> \
|
||||
inline const NR##E<T> NR##E<T>::operator X(const T &a) const \
|
||||
{ return NR##E(*this) X##= a; } \
|
||||
\
|
||||
template<class T> \
|
||||
inline const NR##E<T> operator X(const T &a, const NR##E<T> &rhs) \
|
||||
{ return NR##E<T>(rhs) X##= a; }
|
||||
|
||||
#define NRVECMAT_OPER2(E,X) \
|
||||
template<class T> \
|
||||
inline const NR##E<T> NR##E<T>::operator X(const NR##E<T> &a) const \
|
||||
{ return NR##E(*this) X##= a; }
|
||||
|
||||
#include "smat.h"
|
||||
#include "mat.h"
|
||||
|
||||
// NRVec class
|
||||
template <typename T>
|
||||
class NRVec {
|
||||
protected:
|
||||
int nn;
|
||||
T *v;
|
||||
int *count;
|
||||
public:
|
||||
friend class NRSMat<T>;
|
||||
friend class NRMat<T>;
|
||||
|
||||
inline NRVec(): nn(0),v(0),count(0){};
|
||||
inline explicit NRVec(const int n) : nn(n), v(new T[n]), count(new int(1)) {};
|
||||
inline NRVec(const T &a, const int n);
|
||||
inline NRVec(const T *a, const int n);
|
||||
inline NRVec(const NRVec &rhs);
|
||||
inline explicit NRVec(const NRSMat<T> & S);
|
||||
#ifndef MATPTR
|
||||
explicit NRVec(const NRMat<T> &rhs);
|
||||
#endif
|
||||
NRVec & operator=(const NRVec &rhs);
|
||||
NRVec & operator=(const T &a); //assign a to every element
|
||||
NRVec & operator|=(const NRVec &rhs);
|
||||
const NRVec operator-() const;
|
||||
inline NRVec & operator+=(const NRVec &rhs);
|
||||
inline NRVec & operator-=(const NRVec &rhs);
|
||||
inline NRVec & operator+=(const T &a);
|
||||
inline NRVec & operator-=(const T &a);
|
||||
inline NRVec & operator*=(const T &a);
|
||||
inline int getcount() const {return count?*count:0;}
|
||||
inline const NRVec operator+(const NRVec &rhs) const;
|
||||
inline const NRVec operator-(const NRVec &rhs) const;
|
||||
inline const NRVec operator+(const T &a) const;
|
||||
inline const NRVec operator-(const T &a) const;
|
||||
inline const NRVec operator*(const T &a) const;
|
||||
inline const T operator*(const NRVec &rhs) const; //scalar product -> ddot
|
||||
inline const NRVec operator*(const NRSMat<T> & S) const;
|
||||
const NRVec operator*(const NRMat<T> &mat) const;
|
||||
const NRMat<T> operator|(const NRVec<T> &rhs) const;
|
||||
inline const T sum() const; //sum of its elements
|
||||
inline const T dot(const T *a, const int stride=1) const; // ddot with a stride-vector
|
||||
inline T & operator[](const int i);
|
||||
inline const T & operator[](const int i) const;
|
||||
inline int size() const;
|
||||
inline operator T*(); //get a pointer to the data
|
||||
inline operator const T*() const; //get a pointer to the data
|
||||
~NRVec();
|
||||
void axpy(const T alpha, const NRVec &x); // this+= a*x
|
||||
void axpy(const T alpha, const T *x, const int stride=1); // this+= a*x
|
||||
void gemv(const T beta, const NRMat<T> &a, const char trans,
|
||||
const T alpha, const NRVec &x);
|
||||
void copyonwrite();
|
||||
void resize(const int n);
|
||||
NRVec & normalize();
|
||||
inline const double norm() const;
|
||||
inline const T amax() const;
|
||||
inline const NRVec unitvector() const;
|
||||
void fprintf(FILE *f, const char *format, const int modulo) const;
|
||||
void fscanf(FILE *f, const char *format);
|
||||
//sparse matrix concerning members
|
||||
explicit NRVec(const SparseMat<T> &rhs); // dense from sparse matrix with one of dimensions =1
|
||||
const NRVec operator*(const SparseMat<T> &mat) const; //vector*matrix
|
||||
inline void simplify() {}; //just for compatibility with sparse ones
|
||||
void gemv(const T beta, const SparseMat<T> &a, const char trans, const T alpha, const NRVec &x);
|
||||
};
|
||||
|
||||
template <typename T> ostream & operator<<(ostream &s, const NRVec<T> &x);
|
||||
template <typename T> istream & operator>>(istream &s, NRVec<T> &x);
|
||||
|
||||
// INLINES
|
||||
|
||||
// ctors
|
||||
template <typename T>
|
||||
inline NRVec<T>::NRVec(const T& a, const int n) : nn(n), v(new T[n]), count(new int)
|
||||
{
|
||||
*count = 1;
|
||||
if(a != (T)0)
|
||||
for(int i=0; i<n; i++)
|
||||
v[i] = a;
|
||||
else
|
||||
memset(v, 0, nn*sizeof(T));
|
||||
}
|
||||
|
||||
template <typename T>
|
||||
inline NRVec<T>::NRVec(const T *a, const int n) : nn(n), v(new T[n]), count(new int)
|
||||
{
|
||||
*count = 1;
|
||||
memcpy(v, a, n*sizeof(T));
|
||||
}
|
||||
|
||||
template <typename T>
|
||||
inline NRVec<T>::NRVec(const NRVec<T> &rhs)
|
||||
{
|
||||
v = rhs.v;
|
||||
nn = rhs.nn;
|
||||
count = rhs.count;
|
||||
if(count) (*count)++;
|
||||
}
|
||||
|
||||
template <typename T>
|
||||
inline NRVec<T>::NRVec(const NRSMat<T> &rhs)
|
||||
{
|
||||
nn = rhs.nn;
|
||||
nn = NN2;
|
||||
v = rhs.v;
|
||||
count = rhs.count;
|
||||
(*count)++;
|
||||
}
|
||||
|
||||
// x += a
|
||||
inline NRVec<double> & NRVec<double>::operator+=(const double &a)
|
||||
{
|
||||
copyonwrite();
|
||||
cblas_daxpy(nn, 1.0, &a, 0, v, 1);
|
||||
return *this;
|
||||
}
|
||||
inline NRVec< complex<double> > &
|
||||
NRVec< complex<double> >::operator+=(const complex<double> &a)
|
||||
{
|
||||
copyonwrite();
|
||||
cblas_zaxpy(nn, (void *)(&CONE), (void *)(&a), 0, (void *)v, 1);
|
||||
return *this;
|
||||
}
|
||||
|
||||
// x -= a
|
||||
inline NRVec<double> & NRVec<double>::operator-=(const double &a)
|
||||
{
|
||||
copyonwrite();
|
||||
cblas_daxpy(nn, 1.0, &a, 0, v, 1);
|
||||
return *this;
|
||||
}
|
||||
inline NRVec< complex<double> > &
|
||||
NRVec< complex<double> >::operator-=(const complex<double> &a)
|
||||
{
|
||||
copyonwrite();
|
||||
cblas_zaxpy(nn, (void *)(&CMONE), (void *)(&a), 0, (void *)v, 1);
|
||||
return *this;
|
||||
}
|
||||
|
||||
// x += x
|
||||
inline NRVec<double> & NRVec<double>::operator+=(const NRVec<double> &rhs)
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (nn != rhs.nn) laerror("daxpy of incompatible vectors");
|
||||
#endif
|
||||
copyonwrite();
|
||||
cblas_daxpy(nn, 1.0, rhs.v, 1, v, 1);
|
||||
return *this;
|
||||
}
|
||||
inline NRVec< complex<double> > &
|
||||
NRVec< complex<double> >::operator+=(const NRVec< complex<double> > &rhs)
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (nn != rhs.nn) laerror("daxpy of incompatible vectors");
|
||||
#endif
|
||||
copyonwrite();
|
||||
cblas_zaxpy(nn, (void *)(&CONE), rhs.v, 1, v, 1);
|
||||
return *this;
|
||||
}
|
||||
|
||||
// x -= x
|
||||
inline NRVec<double> & NRVec<double>::operator-=(const NRVec<double> &rhs)
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (nn != rhs.nn) laerror("daxpy of incompatible vectors");
|
||||
#endif
|
||||
copyonwrite();
|
||||
cblas_daxpy(nn, -1.0, rhs.v, 1, v, 1);
|
||||
return *this;
|
||||
}
|
||||
inline NRVec< complex<double> > &
|
||||
NRVec< complex<double> >::operator-=(const NRVec< complex<double> > &rhs)
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (nn != rhs.nn) laerror("daxpy of incompatible vectors");
|
||||
#endif
|
||||
copyonwrite();
|
||||
cblas_zaxpy(nn, (void *)(&CMONE), (void *)rhs.v, 1, (void *)v, 1);
|
||||
return *this;
|
||||
}
|
||||
|
||||
// x *= a
|
||||
inline NRVec<double> & NRVec<double>::operator*=(const double &a)
|
||||
{
|
||||
copyonwrite();
|
||||
cblas_dscal(nn, a, v, 1);
|
||||
return *this;
|
||||
}
|
||||
inline NRVec< complex<double> > &
|
||||
NRVec< complex<double> >::operator*=(const complex<double> &a)
|
||||
{
|
||||
copyonwrite();
|
||||
cblas_zscal(nn, (void *)(&a), (void *)v, 1);
|
||||
return *this;
|
||||
}
|
||||
|
||||
// scalar product x.y
|
||||
inline const double NRVec<double>::operator*(const NRVec<double> &rhs) const
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (nn != rhs.nn) laerror("ddot of incompatible vectors");
|
||||
#endif
|
||||
return cblas_ddot(nn, v, 1, rhs.v, 1);
|
||||
}
|
||||
inline const complex<double>
|
||||
NRVec< complex<double> >::operator*(const NRVec< complex<double> > &rhs) const
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if (nn != rhs.nn) laerror("ddot of incompatible vectors");
|
||||
#endif
|
||||
complex<double> dot;
|
||||
cblas_zdotc_sub(nn, (void *)v, 1, (void *)rhs.v, 1, (void *)(&dot));
|
||||
return dot;
|
||||
}
|
||||
|
||||
// Vec * SMat = SMat * Vec
|
||||
template <typename T>
|
||||
inline const NRVec<T> NRVec<T>::operator*(const NRSMat<T> & S) const
|
||||
{
|
||||
return S * (*this);
|
||||
}
|
||||
|
||||
// Sum of elements
|
||||
inline const double NRVec<double>::sum() const
|
||||
{
|
||||
return cblas_dasum(nn, v, 1);
|
||||
}
|
||||
inline const complex<double>
|
||||
NRVec< complex<double> >::sum() const
|
||||
{
|
||||
complex<double> sum = CZERO;
|
||||
for (int i=0; i<nn; i++) sum += v[i];
|
||||
return sum;
|
||||
}
|
||||
|
||||
// Dot product: x * y
|
||||
inline const double NRVec<double>::dot(const double *y, const int stride) const
|
||||
{
|
||||
return cblas_ddot(nn, y, stride, v, 1);
|
||||
}
|
||||
inline const complex<double>
|
||||
NRVec< complex<double> >::dot(const complex<double> *y, const int stride) const
|
||||
{
|
||||
complex<double> dot;
|
||||
cblas_zdotc_sub(nn, y, stride, v, 1, (void *)(&dot));
|
||||
return dot;
|
||||
}
|
||||
|
||||
// x[i] returns i-th element
|
||||
template <typename T>
|
||||
inline T & NRVec<T>::operator[](const int i)
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if(*count != 1) laerror("possible lval [] with count > 1");
|
||||
if(i < 0 || i >= nn) laerror("NRVec out of range");
|
||||
if(!v) laerror("[] on unallocated NRVec");
|
||||
#endif
|
||||
return v[i];
|
||||
}
|
||||
template <typename T>
|
||||
inline const T & NRVec<T>::operator[](const int i) const
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if(i < 0 || i >= nn) laerror("NRVec out of range");
|
||||
if(!v) laerror("[] on unallocated NRVec");
|
||||
#endif
|
||||
return v[i];
|
||||
}
|
||||
|
||||
// length of the vector
|
||||
template <typename T>
|
||||
inline int NRVec<T>::size() const
|
||||
{
|
||||
return nn;
|
||||
}
|
||||
|
||||
// reference Vec to the first element
|
||||
template <typename T>
|
||||
inline NRVec<T>::operator T*()
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if(!v) laerror("unallocated NRVec in operator T*");
|
||||
#endif
|
||||
return v;
|
||||
}
|
||||
template <typename T>
|
||||
inline NRVec<T>::operator const T*() const
|
||||
{
|
||||
#ifdef DEBUG
|
||||
if(!v) laerror("unallocated NRVec in operator T*");
|
||||
#endif
|
||||
return v;
|
||||
}
|
||||
|
||||
// return norm of the Vec
|
||||
inline const double NRVec<double>::norm() const
|
||||
{
|
||||
return cblas_dnrm2(nn, v, 1);
|
||||
}
|
||||
inline const double NRVec< complex<double> >::norm() const
|
||||
{
|
||||
return cblas_dznrm2(nn, (void *)v, 1);
|
||||
}
|
||||
|
||||
// Max element of the array
|
||||
inline const double NRVec<double>::amax() const
|
||||
{
|
||||
return v[cblas_idamax(nn, v, 1)];
|
||||
}
|
||||
inline const complex<double> NRVec< complex<double> >::amax() const
|
||||
{
|
||||
return v[cblas_izamax(nn, (void *)v, 1)];
|
||||
}
|
||||
|
||||
|
||||
// Make Vec unitvector
|
||||
template <typename T>
|
||||
inline const NRVec<T> NRVec<T>::unitvector() const
|
||||
{
|
||||
return NRVec<T>(*this).normalize();
|
||||
}
|
||||
|
||||
// generate operators: Vec + a, a + Vec, Vec * a
|
||||
NRVECMAT_OPER(Vec,+)
|
||||
NRVECMAT_OPER(Vec,-)
|
||||
NRVECMAT_OPER(Vec,*)
|
||||
// generate operators: Vec + Vec, Vec - Vec
|
||||
NRVECMAT_OPER2(Vec,+)
|
||||
NRVECMAT_OPER2(Vec,-)
|
||||
|
||||
// Few forward declarations
|
||||
|
||||
|
||||
#endif /* _LA_VEC_H_ */
|
||||
Loading…
Reference in New Issue