*** empty log message ***

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jiri 2006-09-11 21:33:24 +00:00
parent 6103d7527a
commit e2251f66f1

202
matexp.h
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@ -6,6 +6,16 @@
// is defined containing definition of an element type, norm and axpy operation // is defined containing definition of an element type, norm and axpy operation
#include "la_traits.h" #include "la_traits.h"
#include "laerror.h"
#ifndef NONCBLAS
extern "C" {
#include "cblas.h"
#include "clapack.h"
}
#else
#include "noncblas.h"
#endif
template<class T,class R> template<class T,class R>
const T polynom0(const T &x, const NRVec<R> &c) const T polynom0(const T &x, const NRVec<R> &c)
@ -264,26 +274,69 @@ for(int i=1; i<=(1<<power); ++i) //unfortunatelly, here we have to repeat it man
return result; return result;
} }
//this comes from dgexpv from expokit, it had to be translated to C to make a template //this comes from dgexpv from expokit, it had to be translated to C to make a template
// dgexpv.f -- translated by f2c (version 20030320).
static double dipow(double x,int i)
{
double y=1.0;
if(x==0.0)
{
if(i>0) return(0.0);
if(i==0) laerror("dipow: 0^0");
return(1./x);
}
if(i) {
if(i<0) {i= -i; x= 1.0/x;}
do
{
if(i&1) y *= x;
x *= x;
}
while((i >>= 1)/*!=0*/);
}
return(y);
}
static int nint(double x)
{
int sgn= x>=0 ? 1 : -1;
return sgn * (int)(abs(x)+.5);
}
#ifdef FORTRAN_
#define FORNAME(x) x##_
#else
#define FORNAME(x) x
#endif
extern "C" void FORNAME(dgpadm)(const int *, int *, double *, double *, int *, double *, int *, int *, int *, int *, int *);
extern "C" void FORNAME(dnchbv)(int *, double *, double *, int *, double *, double *);
//partial template specialization leaving still free room for generic matrix type //partial template specialization leaving still free room for generic matrix type
template<class M> template<class M>
extern void exptimes(const M &mat, NRVec<double> &result, bool transpose, const double t, const NRVec<double> &rhs) 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)
{ {
if(mat.nrows()!= mat.ncols()) laerorr("non-square matrix in exptimes"); if(mat.nrows()!= mat.ncols()) laerror("non-square matrix in exptimes");
n=mat.nrows(); int n=mat.nrows();
if(result.size()!=n || rhs.size()!=n) laerorr("inconsistent vector and matrix size in exptimes"); int m;
if(mxkrylov) m=mxkrylov; else m= n>100? 100: n-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;
double *w=result;
double anorm=mat.norm();
// dgexpv.f -- translated by f2c (version 20030320).
int dgexpv(int n, int m, double t,
double *v, double *w, double tol, double *anorm,
double *wsp, int *lwsp, int *iwsp, int *liwsp,
int *itrace, int mxstep=1000, int mxreject=0, int ideg=6)
{
static const double c_b4 = 1.;
static const int c__1 = 1;
static const double c_b8 = 10.;
static const double c_b25 = 0.;
int iflag; int iflag;
@ -291,10 +344,7 @@ int iflag;
int i__1, i__2; int i__1, i__2;
double d__1; double d__1;
double d_sign(double *, double *), pow_di(double *, int *), pow_dd(double *, double *), #define pow_dd(x,y) (exp(y*log(x)))
d_lg10(double *);
int i_dnnt(double *);
double d_int(double *);
/* Local variables */ /* Local variables */
int ibrkflag; int ibrkflag;
@ -307,31 +357,17 @@ int iflag;
double xm; double xm;
int j1v; int j1v;
double hij, sgn, eps, hj1j, sqr1, beta; double hij, sgn, eps, hj1j, sqr1, beta;
extern double ddot_(int *, double *, int *, double *,
int *);
double hump; double hump;
extern double dnrm2_(int *, double *, int *);
extern /* Subroutine */ int dscal_(int *, double *, double *,
int *);
int ifree, lfree; int ifree, lfree;
double t_old__; double t_old__;
extern /* Subroutine */ int dgemv_(char *, int *, int *,
double *, double *, int *, double *, int *,
double *, double *, int *, ftnlen);
int iexph; int iexph;
double t_new__; double t_new__;
extern /* Subroutine */ int dcopy_(int *, double *, int *,
double *, int *);
int nexph; int nexph;
extern /* Subroutine */ int daxpy_(int *, double *, double *,
int *, double *, int *);
double t_now__; double t_now__;
int nstep; int nstep;
double t_out__; double t_out__;
int nmult; int nmult;
double vnorm; double vnorm;
extern "C" void FORNAME(dgpadm)(const int *, int *, double *, double *, int *, double *, int *, int *, int *, int *, int *)
extern "C" void FORNAME(dnchbv)(int *, double *, double *, int *, double *, double *);
int nscale; int nscale;
double rndoff, t_step__, avnorm; double rndoff, t_step__, avnorm;
int ireject; int ireject;
@ -385,7 +421,6 @@ int iflag;
/* computes: y(1:n) <- A*x(1:n) */ /* computes: y(1:n) <- A*x(1:n) */
/* where A is the principal matrix. */ /* where A is the principal matrix. */
/* itrace : (input) running mode. 0=silent, 1=print step-by-step info */
/* iflag : (output) exit flag. */ /* iflag : (output) exit flag. */
/* <0 - bad input arguments */ /* <0 - bad input arguments */
@ -449,30 +484,20 @@ int iflag;
/* EXPOKIT: Software Package for Computing Matrix Exponentials. */ /* EXPOKIT: Software Package for Computing Matrix Exponentials. */
/* ACM - Transactions On Mathematical Software, 24(1):130-156, 1998 */ /* ACM - Transactions On Mathematical Software, 24(1):130-156, 1998 */
/* ----------------------------------------------------------------------| */ /* ----------------------------------------------------------------------| */
iflag = 0;
i__1 = m + 2;
int lwsp= n * (m + 2) + i__1 * i__1 * 5 + ideg + 1;
double *wsp = new double[lwsp];
int *iwsp = new int[m+2];
/* --- check restrictions on input parameters ... */
/* Parameter adjustments */ /* Parameter adjustments */
--w; --w;
--v; --v;
--wsp; --wsp;
--iwsp; --iwsp;
/* Function Body */
iflag = 0;
/* Computing 2nd power */
i__1 = m + 2;
if (*lwsp < n * (m + 2) + i__1 * i__1 * 5 + ideg + 1) {
iflag = -1;
}
if (*liwsp < m + 2) {
iflag = -2;
}
if (m >= n || m <= 0) {
iflag = -3;
}
if (iflag != 0) {
la_error("bad sizes (in input of DGEXPV)");
}
/* --- initialisations ... */ /* --- initialisations ... */
@ -481,7 +506,7 @@ int iflag;
iv = 1; iv = 1;
ih = iv + n * (m + 1) + n; ih = iv + n * (m + 1) + n;
ifree = ih + mh * mh; ifree = ih + mh * mh;
lfree = *lwsp - ifree + 1; lfree = lwsp - ifree + 1;
ibrkflag = 0; ibrkflag = 0;
mbrkdwn = m; mbrkdwn = m;
nmult = 0; nmult = 0;
@ -508,13 +533,13 @@ L1:
if (tol <= eps) { if (tol <= eps) {
tol = sqrt(eps); tol = sqrt(eps);
} }
rndoff = eps * *anorm; rndoff = eps * anorm;
break_tol__ = 1e-7; break_tol__ = 1e-7;
/* >>> break_tol = tol */ /* >>> break_tol = tol */
/* >>> break_tol = anorm*tol */ /* >>> break_tol = anorm*tol */
sgn = d_sign(&c_b4, t); sgn = t>=0?1. : -1.;
dcopy_(n, &v[1], &c__1, &w[1], &c__1); cblas_dcopy(n, &v[1], 1, &w[1], 1);
beta = dnrm2_(n, &w[1], &c__1); beta = cblas_dnrm2(n, &w[1], 1);
vnorm = beta; vnorm = beta;
hump = beta; hump = beta;
@ -524,14 +549,14 @@ L1:
xm = 1. / (double) (m); xm = 1. / (double) (m);
d__1 = (m + 1) / 2.72; d__1 = (m + 1) / 2.72;
i__1 = m + 1; i__1 = m + 1;
p1 = tol * pow_di(&d__1, &i__1) * sqrt((m + 1) * 6.2800000000000002); p1 = tol * dipow(d__1, i__1) * sqrt((m + 1) * 6.28);
d__1 = p1 / (beta * 4. * *anorm); d__1 = p1 / (beta * 4. * anorm);
t_new__ = 1. / *anorm * pow_dd(&d__1, &xm); t_new__ = 1. / anorm * pow_dd(d__1, xm);
d__1 = d_lg10(&t_new__) - sqr1; d__1 = log10(t_new__) - sqr1;
i__1 = i_dnnt(&d__1) - 1; i__1 = nint(d__1) - 1;
p1 = pow_di(&c_b8, &i__1); p1 = dipow(10., i__1);
d__1 = t_new__ / p1 + .55; d__1 = t_new__ / p1 + .55;
t_new__ = d_int(&d__1) * p1; t_new__ = floor(d__1) * p1;
/* --- step-by-step integration ... */ /* --- step-by-step integration ... */
@ -562,14 +587,12 @@ L100:
(matvec)(&wsp[j1v - n], &wsp[j1v]); (matvec)(&wsp[j1v - n], &wsp[j1v]);
i__2 = j; i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) { for (i__ = 1; i__ <= i__2; ++i__) {
hij = ddot_(n, &wsp[iv + (i__ - 1) * n], &c__1, &wsp[j1v], &c__1) hij = cblas_ddot(n, &wsp[iv + (i__ - 1) * n], 1, &wsp[j1v], 1);
;
d__1 = -hij; d__1 = -hij;
daxpy_(n, &d__1, &wsp[iv + (i__ - 1) * n], &c__1, &wsp[j1v], & cblas_daxpy(n, d__1, &wsp[iv + (i__ - 1) * n], 1, &wsp[j1v], 1);
c__1);
wsp[ih + (j - 1) * mh + i__ - 1] = hij; wsp[ih + (j - 1) * mh + i__ - 1] = hij;
} }
hj1j = dnrm2_(n, &wsp[j1v], &c__1); hj1j = cblas_dnrm2(n, &wsp[j1v], 1);
/* --- if `happy breakdown' go straightforward at the end ... */ /* --- if `happy breakdown' go straightforward at the end ... */
if (hj1j <= break_tol__) { if (hj1j <= break_tol__) {
/* print*,'happy breakdown: mbrkdwn =',j,' h =',hj1j */ /* print*,'happy breakdown: mbrkdwn =',j,' h =',hj1j */
@ -582,13 +605,13 @@ L100:
} }
wsp[ih + (j - 1) * mh + j] = hj1j; wsp[ih + (j - 1) * mh + j] = hj1j;
d__1 = 1. / hj1j; d__1 = 1. / hj1j;
dscal_(n, &d__1, &wsp[j1v], &c__1); cblas_dscal(n, d__1, &wsp[j1v], 1);
j1v += n; j1v += n;
/* L200: */ /* L200: */
} }
++nmult; ++nmult;
(matvec)(&wsp[j1v - n], &wsp[j1v]); (matvec)(&wsp[j1v - n], &wsp[j1v]);
avnorm = dnrm2_(n, &wsp[j1v], &c__1); avnorm = cblas_dnrm2(n, &wsp[j1v], 1);
/* --- set 1 for the 2-corrected scheme ... */ /* --- set 1 for the 2-corrected scheme ... */
@ -649,18 +672,18 @@ L401:
ireject < mxreject)) { ireject < mxreject)) {
t_old__ = t_step__; t_old__ = t_step__;
d__1 = t_step__ * tol / err_loc__; d__1 = t_step__ * tol / err_loc__;
t_step__ = t_step__ * .9 * pow_dd(&d__1, &xm); t_step__ = t_step__ * .9 * pow_dd(d__1, xm);
d__1 = d_lg10(&t_step__) - sqr1; d__1 = log10(t_step__) - sqr1;
i__1 = i_dnnt(&d__1) - 1; i__1 = nint(d__1) - 1;
p1 = pow_di(&c_b8, &i__1); p1 = dipow(10., i__1);
d__1 = t_step__ / p1 + .55; d__1 = t_step__ / p1 + .55;
t_step__ = d_int(&d__1) * p1; t_step__ = floor(d__1) * p1;
if (*itrace != 0) { #ifdef DEBUG
/* print*,'t_step =',t_old */ /* print*,'t_step =',t_old */
/* print*,'err_loc =',err_loc */ /* print*,'err_loc =',err_loc */
/* print*,'err_required =',delta*t_old*tol */ /* print*,'err_required =',delta*t_old*tol */
/* print*,'stepsize rejected, stepping down to:',t_step */ /* print*,'stepsize rejected, stepping down to:',t_step */
} #endif
++ireject; ++ireject;
++nreject; ++nreject;
if (mxreject != 0 && ireject > mxreject) { if (mxreject != 0 && ireject > mxreject) {
@ -675,20 +698,19 @@ L401:
/* Computing MAX */ /* Computing MAX */
i__1 = 0, i__2 = k1 - 1; i__1 = 0, i__2 = k1 - 1;
mx = mbrkdwn + max(i__1,i__2); mx = mbrkdwn + max(i__1,i__2);
dgemv_("n", n, &mx, &beta, &wsp[iv], n, &wsp[iexph], &c__1, &c_b25, &w[1], cblas_dgemv(CblasRowMajor, CblasTrans, n, mx, beta, &wsp[iv], n, &wsp[iexph], 1, 0., &w[1],1);
&c__1, (ftnlen)1); beta = cblas_dnrm2(n, &w[1], 1);
beta = dnrm2_(n, &w[1], &c__1);
hump = max(hump,beta); hump = max(hump,beta);
/* --- suggested value for the next stepsize ... */ /* --- suggested value for the next stepsize ... */
d__1 = t_step__ * tol / err_loc__; d__1 = t_step__ * tol / err_loc__;
t_new__ = t_step__ * .9 * pow_dd(&d__1, &xm); t_new__ = t_step__ * .9 * pow_dd(d__1, xm);
d__1 = d_lg10(&t_new__) - sqr1; d__1 = log10(t_new__) - sqr1;
i__1 = i_dnnt(&d__1) - 1; i__1 = nint(d__1) - 1;
p1 = pow_di(&c_b8, &i__1); p1 = dipow(10., i__1);
d__1 = t_new__ / p1 + .55; d__1 = t_new__ / p1 + .55;
t_new__ = d_int(&d__1) * p1; t_new__ = floor(d__1) * p1;
err_loc__ = max(err_loc__,rndoff); err_loc__ = max(err_loc__,rndoff);
/* --- update the time covered ... */ /* --- update the time covered ... */
@ -697,13 +719,13 @@ L401:
/* --- display and keep some information ... */ /* --- display and keep some information ... */
if (*itrace != 0) { #ifdef DEBUG
/* print*,'integration',nstep,'---------------------------------' */ /* print*,'integration',nstep,'---------------------------------' */
/* print*,'scale-square =',ns */ /* print*,'scale-square =',ns */
/* print*,'step_size =',t_step */ /* print*,'step_size =',t_step */
/* print*,'err_loc =',err_loc */ /* print*,'err_loc =',err_loc */
/* print*,'next_step =',t_new */ /* print*,'next_step =',t_new */
} #endif
step_min__ = min(step_min__,t_step__); step_min__ = min(step_min__,t_step__);
step_max__ = max(step_max__,t_step__); step_max__ = max(step_max__,t_step__);
s_error__ += err_loc__; s_error__ += err_loc__;
@ -731,11 +753,11 @@ L500:
/* wsp(9) = hump/vnorm */ /* wsp(9) = hump/vnorm */
/* wsp(10) = beta/vnorm */ /* wsp(10) = beta/vnorm */
if(iflag) laerror("dgexpv error"); if(iflag) laerror("dgexpv error");
return; delete[] ++wsp; delete[] ++iwsp;
}
return; return;
} }
#undef FORNAME
#undef pow_dd
//@@@ power series matrix logarithm? //@@@ power series matrix logarithm?