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jiri 2006-09-11 23:07:22 +00:00
parent e49b73e9e9
commit d55727cb83
5 changed files with 71 additions and 24 deletions
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45
matexp.h
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@ -248,28 +248,43 @@ return r;
//this simple implementation seems not to be numerically stable enough
//and probably not efficient either
//@@@ make more efficient - for nilpotent mat at known power and
template<class M, class V>
const V exptimesnaive(const M &mat, V vec) //uses just matrix vector multiplication
void exptimesdestructive(const M &mat, V &result, V &rhs, bool transpose=false, const double scale=1. ) //uses just matrix vector multiplication
{
if(mat.nrows()!=mat.ncols()||(unsigned int) mat.nrows() != (unsigned int)vec.size()) laerror("inappropriate sizes in exptimes");
if(mat.nrows()!=mat.ncols()||(unsigned int) mat.nrows() != (unsigned int)rhs.size()) laerror("inappropriate sizes in exptimes");
int power;
//prepare the polynom of and effectively scale the matrix
NRVec<typename LA_traits<V>::elementtype> taylor2=exp_aux<M,typename LA_traits<V>::elementtype>(mat,power);
cerr <<"test power "<<power<<endl;
V tmp;
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];
if(i>1) rhs=result; //apply again to the result of previous application
else result=rhs;
tmp=rhs; //now rhs can be used as scratch
result*=taylor2[0];
for(int j=1; j<taylor2.size(); ++j)
{
y=mat*y;
result.axpy(taylor2[j],y);
mat.gemv(0.,rhs,transpose?'t':'n',scale,tmp);
tmp=rhs;
result.axpy(taylor2[j],tmp);
}
}
return;
}
template<class M, class V>
const V exptimes(const M &mat, V rhs, bool transpose=false, const double scale=1.)
{
V result;
exptimesdestructive(mat,result,rhs,transpose,scale);
return result;
}
@ -279,8 +294,7 @@ return result;
#ifdef EXPOKIT
//this comes from dgexpv from expokit, it had to be translated to C to make a template
// dgexpv.f -- translated by f2c (version 20030320).
@ -323,13 +337,13 @@ extern "C" void FORNAME(dnchbv)(int *, double *, double *, int *, double *, doub
//partial template specialization leaving still free room for generic matrix type
template<class M>
extern void exptimes(const M &mat, NRVec<double> &result, const NRVec<double> &rhs, bool transpose=false, const double t=1., int mxkrylov=0, double tol=1e-14, int mxstep=1000, int mxreject=0, int ideg=6)
extern void dgexpv(const M &mat, NRVec<double> &result, const NRVec<double> &rhs, bool transpose=false, const double t=1., int mxkrylov=0, double tol=1e-14, int mxstep=1000, int mxreject=0, int ideg=6)
{
if(mat.nrows()!= mat.ncols()) laerror("non-square matrix in exptimes");
int n=mat.nrows();
int m;
if(mxkrylov) m=mxkrylov; else m= n>100? 100: n-1;
if (m >= n || m <= 0) laerror("illegal mxkrylov");
if(mxkrylov) m=mxkrylov; else m= n>100? 100: (n>1?n-1:1);
if (m > n || m <= 0) laerror("illegal mxkrylov");
if(result.size()!=n || rhs.size()!=n) laerror("inconsistent vector and matrix size in exptimes");
const double *v=rhs;
@ -766,6 +780,9 @@ return;
#undef FORNAME
#undef pow_dd
#endif
//EXPOKIT
//@@@ power series matrix logarithm?

4
noncblas.cc
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@ -186,9 +186,9 @@ void cblas_dgemv(const enum CBLAS_ORDER Order,
const double *X, const int incX, const double beta,
double *Y, const int incY)
{
if(Order!=CblasRowMajor) laerror("CblasRowMajor order asserted");
if(Order!=CblasRowMajor) FORNAME(dgemv) (TransA==CblasNoTrans?"N":"T", &N, &M, &alpha, A, &lda, X, &incX, &beta, Y, &incY );
//swap n-m and toggle transposition
FORNAME(dgemv) (TransA==CblasNoTrans?"T":"N", &N, &M, &alpha, A, &lda, X, &incX, &beta, Y, &incY );
else FORNAME(dgemv) (TransA==CblasNoTrans?"T":"N", &N, &M, &alpha, A, &lda, X, &incX, &beta, Y, &incY );
}

14
t.cc
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@ -675,9 +675,12 @@ int n;
double f;
cin>>n >>f ;
NRMat<double> a(n,n);
for(int i=0;i<n;++i) for(int j=0;j<n;++j)
NRVec<double>u(n),v,w;
for(int i=0;i<n;++i)
{
a(i,j)= f*random()/(1.+RAND_MAX);
u[i]=f*random()/(1.+RAND_MAX);
for(int j=0;j<n;++j)
a(i,j)= f*random()/(1.+RAND_MAX);
}
//cout <<"a matrix \n"<<a;
//cout<<"EXP\n";
@ -695,6 +698,13 @@ c=exp(a,false);
cout <<" tricky exp took "<<clock()/((double) (CLOCKS_PER_SEC))-t<<endl;
cout<<"error2 = "<<(c-b).norm()/b.norm()<<endl;
v=b*u;
t=clock()/((double) (CLOCKS_PER_SEC));
w=exptimes(a,u);
cout <<"exptimes took "<<clock()/((double) (CLOCKS_PER_SEC))-t<<endl;
cout <<"error of exptimes = "<<(v-w).norm()/v.norm()<<endl;
}

6
vec.cc
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@ -450,6 +450,7 @@ void NRVec<double>::gemv(const double beta, const NRMat<double> &A,
if ((trans == 'n'?A.ncols():A.nrows()) != x.size())
laerror("incompatible sizes in gemv A*x");
#endif
copyonwrite();
cblas_dgemv(CblasRowMajor, (trans=='n' ? CblasNoTrans:CblasTrans),
A.nrows(), A.ncols(), alpha, A, A.ncols(), x.v, 1, beta, v, 1);
}
@ -463,6 +464,7 @@ void NRVec< complex<double> >::gemv(const complex<double> beta,
if ((trans == 'n'?A.ncols():A.nrows()) != x.size())
laerror("incompatible sizes in gemv A*x");
#endif
copyonwrite();
cblas_zgemv(CblasRowMajor, (trans=='n' ? CblasNoTrans:CblasTrans),
A.nrows(), A.ncols(), &alpha, A, A.ncols(),
x.v, 1, &beta, v, 1);
@ -476,7 +478,7 @@ void NRVec<double>::gemv(const double beta, const NRSMat<double> &A,
#ifdef DEBUG
if (A.ncols()!=x.size()) laerror("incompatible dimension in gemv A*x");
#endif
NRVec<double> result(nn);
copyonwrite();
cblas_dspmv(CblasRowMajor, CblasLower, A.ncols(), alpha, A, x.v, 1, beta, v, 1);
}
@ -489,7 +491,7 @@ void NRVec< complex<double> >::gemv(const complex<double> beta,
#ifdef DEBUG
if (A.ncols()!=x.size()) laerror("incompatible dimension in gemv");
#endif
NRVec< complex<double> > result(nn);
copyonwrite();
cblas_zhpmv(CblasRowMajor, CblasLower, A.ncols(), &alpha, A,
x.v, 1, &beta, v, 1);
}

26
vec.h
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@ -42,7 +42,8 @@ public:
inline NRVec(): nn(0),v(0),count(0){};
explicit inline 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 T *a, const int n);
inline NRVec(T *a, const int n, bool skeleton);
inline NRVec(const NRVec &rhs);
inline explicit NRVec(const NRSMat<T> & S);
#ifdef MATPTR
@ -136,10 +137,27 @@ inline NRVec<T>::NRVec(const T& a, const int n) : nn(n), v(new T[n]), count(new
}
template <typename T>
inline NRVec<T>::NRVec(const T *a, const int n) : nn(n), v(new T[n]), count(new int)
inline NRVec<T>::NRVec(const T *a, const int n) : nn(n), count(new int)
{
*count = 1;
memcpy(v, a, n*sizeof(T));
v=new T[n];
*count = 1;
memcpy(v, a, n*sizeof(T));
}
template <typename T>
inline NRVec<T>::NRVec(T *a, const int n, bool skeleton) : nn(n), count(new int)
{
if(!skeleton)
{
v=new T[n];
*count = 1;
memcpy(v, a, n*sizeof(T));
}
else
{
*count = 2;
v=a;
}
}
template <typename T>