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jiri 2005-01-31 23:08:03 +00:00
parent 46d841aabf
commit 2af0920423
12 changed files with 150 additions and 31 deletions
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11
davidson.h
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@ -1,9 +1,14 @@
#include "vec.h"
#include "smat.h"
#include "mat.h"
#include "sparsemat.h"
#include "nonclass.h"
//Davidson diagonalization of real symmetric matrix
//matrix can be any class which provides nrows(), diagonalof() and operator*(const NRVec<T>) methods
//matrix can be any class which has nrows(), ncols(), diagonalof() and NRVec::gemv() available
//does not even have to be explicitly stored - direct CI
//n<0 highest eigenvalues, n>0 lowest eigenvalues
template <class T, class matrix>
extern void davidson(const matrix &a, NRVec<T> *vecs /*input-output*/, T *vals, const int n=1, const double eps=1e-10);
export template <typename T, typename Matrix>
extern void davidson(const Matrix &bigmat, NRVec<T> *eivecs /*input-output*/, NRVec<T> &eivals, int nroots=1, const double accur=1e-6, int nits=50, const int ndvdmx = 500, const bool incore=1);

23
mat.cc
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@ -34,6 +34,25 @@ NRMat<T> & NRMat<T>::operator=(const T &a)
//get diagonal; for compatibility with large matrices do not return newly created object
template <typename T>
void NRMat<T>::diagonalof(NRVec<T> &r) const
{
#ifdef DEBUG
if (nn != mm) laerror("diagonalof() non-square matrix");
if (r.size() != nn) laerror("diagonalof() incompatible vector");
#endif
#ifdef MATPTR
for (int i=0; i< nn; i++) r[i] = v[i][i];
#else
{int i,j; for (i=j=0; j< nn; ++j, i+=nn+1) r[j] = v[i];}
#endif
}
// M += a
template <typename T>
NRMat<T> & NRMat<T>::operator+=(const T &a)
@ -750,7 +769,7 @@ INSTANTIZE(int)
INSTANTIZE(char)
export template <class T>
export template <typename T>
ostream& operator<<(ostream &s, const NRMat<T> &x)
{
int i,j,n,m;
@ -764,7 +783,7 @@ ostream& operator<<(ostream &s, const NRMat<T> &x)
return s;
}
export template <class T>
export template <typename T>
istream& operator>>(istream &s, NRMat<T> &x)
{
int i,j,n,m;

6
mat.h
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@ -58,6 +58,7 @@ public:
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
void diagonalof(NRVec<T> &) const; //get diagonal
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
@ -348,8 +349,9 @@ NRMat<T>::~NRMat()
template <typename T>
NRMat<T> & NRMat<T>::operator=(const NRMat<T> &rhs)
{
if (this == &rhs) return *this;
if (count) {
if (this !=&rhs)
{
if (count)
if (--(*count) ==0 ) {
#ifdef MATPTR
delete[] (v[0]);

30
nonclass.cc
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@ -186,12 +186,14 @@ extern "C" void FORNAME(dsyev)(const char *JOBZ, const char *UPLO, const int *N,
// a will contain eigenvectors (columns if corder==1), w eigenvalues
void diagonalize(NRMat<double> &a, NRVec<double> &w, const bool eivec,
const bool corder)
const bool corder, int n)
{
int n = a.nrows();
if (n != a.ncols()) laerror("diagonalize() call with non-square matrix");
int m = a.nrows();
if (m != a.ncols()) laerror("diagonalize() call with non-square matrix");
if (a.nrows() != w.size())
laerror("inconsistent dimension of eigenvalue vector in diagonalize()");
if(n==0) n=m;
if(n<0||n>m) laerror("actual dimension out of range in diagonalize");
a.copyonwrite();
w.copyonwrite();
@ -204,10 +206,10 @@ void diagonalize(NRMat<double> &a, NRVec<double> &w, const bool eivec,
double WORKX;
// First call is to determine size of workspace
FORNAME(dsyev)(&vectors, &U, &n, a, &n, w, (double *)&WORKX, &LWORK, &r );
FORNAME(dsyev)(&vectors, &U, &n, a, &m, w, (double *)&WORKX, &LWORK, &r );
LWORK = (int)WORKX;
double *WORK = new double[LWORK];
FORNAME(dsyev)(&vectors, &U, &n, a, &n, w, WORK, &LWORK, &r );
FORNAME(dsyev)(&vectors, &U, &n, a, &m, w, WORK, &LWORK, &r );
delete[] WORK;
if (vectors == 'V' && corder) a.transposeme();
@ -216,6 +218,7 @@ void diagonalize(NRMat<double> &a, NRVec<double> &w, const bool eivec,
}
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);
@ -526,18 +529,23 @@ double trace2(const NRSMat<double> &a, const NRSMat<double> &b,
//generalized diagonalization, eivecs will be in columns of a
void gendiagonalize(NRMat<double> &a, NRVec<double> &w, NRMat<double> b)
//counts with actual dimension smaller than allocated dimension
void gendiagonalize(NRMat<double> &a, NRVec<double> &w, NRMat<double> b, int n)
{
if(a.nrows()!=a.ncols() || a.nrows()!=w.size() || a.nrows()!=b.nrows() || b.nrows()!=b.ncols() ) laerror("incompatible Mats in gendiagonalize");
a.copyonwrite();
w.copyonwrite();
b.copyonwrite();
int n=w.size();
NRVec<double> dl(n);
int m=w.size();
NRVec<double> dl(m);
int i,j;
double x;
if(n==0) n=m;
if(n<0 || n>m) laerror("actual dimension in gendiagonalize out of range");
//transform the problem to usual diagonalization
/*
c
@ -620,7 +628,7 @@ for(j=0; j<n ; ++j)
{
for(i=j;i<n;++i)
{
x = a(i,j) - cblas_ddot(i-j,&a(j,j),n,&b(i,j),1)
x = a(i,j) - cblas_ddot(i-j,&a(j,j),m,&b(i,j),1)
- cblas_ddot(j,&a(j,0),1,&b(i,0),1);
a(i,j) = x/dl[i];
}
@ -630,7 +638,7 @@ for(j=0; j<n ; ++j)
for(i=1;i<n;++i) for(j=0; j<i; ++j) a(j,i)=a(i,j);
//diagonalize by a standard procedure
diagonalize(a,w,1,1);
diagonalize(a,w,1,1,n);
//transform the eigenvectors back
/*
@ -669,7 +677,7 @@ for(j=0; j<n; ++j)//eigenvector loop
{
for(int i=n-1; i>=0; --i)//component loop
{
if(i<n-1) a(i,j) -= cblas_ddot(n-1-i,&b(i+1,i),n,&a(i+1,j),n);
if(i<n-1) a(i,j) -= cblas_ddot(n-1-i,&b(i+1,i),m,&a(i+1,j),m);
a(i,j) /= dl[i];
}
}

8
nonclass.h
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@ -1,3 +1,6 @@
#ifndef _LA_NONCLASS_H_
#define _LA_NONCLASS_H_
#include "vec.h"
#include "smat.h"
#include "mat.h"
@ -48,7 +51,7 @@ 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(NRMat<T> &a, NRVec<T> &w, const bool eivec=1, const bool corder=1, int n=0); \
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);
@ -72,7 +75,7 @@ extern NRMat<double> matrixfunction(NRMat<double> a, complex<double> (*f)(const
//generalized diagonalization of symmetric matrix with symmetric positive definite metric matrix b
extern void gendiagonalize(NRMat<double> &a, NRVec<double> &w, NRMat<double> b);
extern void gendiagonalize(NRMat<double> &a, NRVec<double> &w, NRMat<double> b, const int n=0);
//functions on matrices
inline NRMat<double> sqrt(const NRSMat<double> &a) { return matrixfunction(a,&sqrt); }
@ -98,3 +101,4 @@ const NRMat<T> inverse(NRMat<T> a, T *det=0)
return result;
}
#endif

19
smat.cc
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@ -34,7 +34,7 @@ NRSMat<T>::NRSMat(const NRMat<T> &rhs)
// assing to diagonal
// assign to diagonal
template <typename T>
NRSMat<T> & NRSMat<T>::operator=(const T &a)
{
@ -43,6 +43,17 @@ NRSMat<T> & NRSMat<T>::operator=(const T &a)
return *this;
}
//get diagonal
template <typename T>
void NRSMat<T>::diagonalof(NRVec<T> &r) const
{
#ifdef DEBUG
if(r.size()!=nn) laerror("incompatible vector in diagonalof()");
#endif
for (int i=0; i<nn; i++) r[i] = v[i*(i+1)/2+i];
}
// unary minus
template <typename T>
const NRSMat<T> NRSMat<T>::operator-() const
@ -71,7 +82,7 @@ void NRSMat<T>::fprintf(FILE *file, const char *format, const int modulo) const
}
// read matrix from the file with specific format
template <class T>
template <typename T>
void NRSMat<T>::fscanf(FILE *f, const char *format)
{
int n, m;
@ -268,7 +279,7 @@ void NRSMat< complex<double> >::axpy(const complex<double> alpha,
}
export template <class T>
export template <typename T>
ostream& operator<<(ostream &s, const NRSMat<T> &x)
{
int i,j,n;
@ -282,7 +293,7 @@ ostream& operator<<(ostream &s, const NRSMat<T> &x)
}
export template <class T>
export template <typename T>
istream& operator>>(istream &s, NRSMat<T> &x)
{
int i,j,n,m;

1
smat.h
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@ -43,6 +43,7 @@ public:
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;
void diagonalof(NRVec<T> &) const; //get diagonal
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;

18
sparsemat.cc
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@ -484,6 +484,24 @@ for(i=0;i<nn;++i)
}
}
//get diagonal, do not construct a new object, but store in existing one, important for huge CI matrices
template <class T>
void SparseMat<T>::diagonalof(NRVec<T> &r) const
{
#ifdef DEBUG
if(nn!=mm) laerror("diagonalof() non-square sparse matrix");
#endif
matel<T> *l=list;
r=(T)0;
while(l)
{
if(l->row == l->col) r[l->row]+= l->elem;
l= l->next;
}
}
//constructor dense matrix from sparse
export template <class T>
NRMat<T>::NRMat(const SparseMat<T> &rhs)

6
sparsemat.h
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@ -1,3 +1,6 @@
#ifndef _SPARSEMAT_H_
#define _SPARSEMAT_H_
//for vectors and dense matrices we shall need
#include "la.h"
@ -85,6 +88,7 @@ public:
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
void diagonalof(NRVec<T> &) const; //get diagonal
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
@ -219,4 +223,4 @@ while(l)
return *this;
}
#endif

43
t.cc
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@ -6,6 +6,7 @@
#include "sparsemat.h"
#include "matexp.h"
#include "fourindex.h"
#include "davidson.h"
extern void test(const NRVec<double> &x);
@ -489,7 +490,7 @@ for(int n=8; n<=1024*1024;n+=n)
}
}
if(1)
if(0)
{
int n;
cin>>n;
@ -536,7 +537,7 @@ 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)
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);
@ -772,7 +773,45 @@ cout <<"test "<<a.dot(a)<<endl;
}
if(0)
{
NRMat<double> amat,bmat;
cin >>amat;
cin >>bmat;
NRVec<double> v(amat.nrows());
gendiagonalize(amat,v,bmat,2);
cout <<amat;
cout <<v;
}
if(1)
{
int n,m;
cin>>n >>m;
NRMat<double> a(n,n);
NRVec<double> rr(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);
if(i==j) a(i,i)+= .5*(i-n);
}
NRMat<double> aa=a;
cout <<aa;
diagonalize(aa,rr);
cout <<aa;
cout <<rr;
NRVec<double> r(m);
NRVec<double> *eivecs = new NRVec<double>[m];
davidson(a,eivecs,r,m);
cout <<r;
}
}

8
test.cc Normal file
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@ -0,0 +1,8 @@
#include "vec.h"
int main(void)
{
NRVec<double> *p = new NRVec<double>[1000];
NRVec<double> q(10); q=1.;
p[500]|=q;
}

2
vec.h
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@ -521,7 +521,7 @@ void NRVec<T>::resize(const int n)
}
// assignmet with a physical copy
// assignmet with a physical (deep) copy
template <typename T>
NRVec<T> & NRVec<T>::operator|=(const NRVec<T> &rhs)
{