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jiri
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matexp.h
200
matexp.h
@ -6,6 +6,16 @@
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// is defined containing definition of an element type, norm and axpy operation
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#include "la_traits.h"
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#include "laerror.h"
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#ifndef NONCBLAS
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extern "C" {
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#include "cblas.h"
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#include "clapack.h"
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}
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#else
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#include "noncblas.h"
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#endif
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template<class T,class R>
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const T polynom0(const T &x, const NRVec<R> &c)
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@ -264,26 +274,69 @@ for(int i=1; i<=(1<<power); ++i) //unfortunatelly, here we have to repeat it man
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return result;
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}
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//this comes from dgexpv from expokit, it had to be translated to C to make a template
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// dgexpv.f -- translated by f2c (version 20030320).
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static double dipow(double x,int i)
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{
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double y=1.0;
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if(x==0.0)
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{
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if(i>0) return(0.0);
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if(i==0) laerror("dipow: 0^0");
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return(1./x);
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}
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if(i) {
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if(i<0) {i= -i; x= 1.0/x;}
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do
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{
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if(i&1) y *= x;
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x *= x;
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}
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while((i >>= 1)/*!=0*/);
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}
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return(y);
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}
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static int nint(double x)
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{
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int sgn= x>=0 ? 1 : -1;
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return sgn * (int)(abs(x)+.5);
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}
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#ifdef FORTRAN_
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#define FORNAME(x) x##_
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#else
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#define FORNAME(x) x
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#endif
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extern "C" void FORNAME(dgpadm)(const int *, int *, double *, double *, int *, double *, int *, int *, int *, int *, int *);
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extern "C" void FORNAME(dnchbv)(int *, double *, double *, int *, double *, double *);
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//partial template specialization leaving still free room for generic matrix type
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template<class M>
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extern void exptimes(const M &mat, NRVec<double> &result, bool transpose, const double t, const NRVec<double> &rhs)
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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)
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{
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if(mat.nrows()!= mat.ncols()) laerorr("non-square matrix in exptimes");
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n=mat.nrows();
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if(result.size()!=n || rhs.size()!=n) laerorr("inconsistent vector and matrix size in exptimes");
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if(mat.nrows()!= mat.ncols()) laerror("non-square matrix in exptimes");
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int n=mat.nrows();
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int m;
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if(mxkrylov) m=mxkrylov; else m= n>100? 100: n-1;
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if (m >= n || m <= 0) laerror("illegal mxkrylov");
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if(result.size()!=n || rhs.size()!=n) laerror("inconsistent vector and matrix size in exptimes");
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const double *v=rhs;
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double *w=result;
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double anorm=mat.norm();
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// dgexpv.f -- translated by f2c (version 20030320).
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int dgexpv(int n, int m, double t,
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double *v, double *w, double tol, double *anorm,
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double *wsp, int *lwsp, int *iwsp, int *liwsp,
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int *itrace, int mxstep=1000, int mxreject=0, int ideg=6)
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{
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static const double c_b4 = 1.;
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static const int c__1 = 1;
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static const double c_b8 = 10.;
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static const double c_b25 = 0.;
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int iflag;
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@ -291,10 +344,7 @@ int iflag;
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int i__1, i__2;
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double d__1;
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double d_sign(double *, double *), pow_di(double *, int *), pow_dd(double *, double *),
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d_lg10(double *);
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int i_dnnt(double *);
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double d_int(double *);
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#define pow_dd(x,y) (exp(y*log(x)))
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/* Local variables */
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int ibrkflag;
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@ -307,31 +357,17 @@ int iflag;
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double xm;
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int j1v;
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double hij, sgn, eps, hj1j, sqr1, beta;
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extern double ddot_(int *, double *, int *, double *,
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int *);
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double hump;
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extern double dnrm2_(int *, double *, int *);
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extern /* Subroutine */ int dscal_(int *, double *, double *,
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int *);
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int ifree, lfree;
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double t_old__;
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extern /* Subroutine */ int dgemv_(char *, int *, int *,
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double *, double *, int *, double *, int *,
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double *, double *, int *, ftnlen);
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int iexph;
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double t_new__;
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extern /* Subroutine */ int dcopy_(int *, double *, int *,
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double *, int *);
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int nexph;
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extern /* Subroutine */ int daxpy_(int *, double *, double *,
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int *, double *, int *);
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double t_now__;
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int nstep;
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double t_out__;
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int nmult;
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double vnorm;
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extern "C" void FORNAME(dgpadm)(const int *, int *, double *, double *, int *, double *, int *, int *, int *, int *, int *)
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extern "C" void FORNAME(dnchbv)(int *, double *, double *, int *, double *, double *);
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int nscale;
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double rndoff, t_step__, avnorm;
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int ireject;
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@ -385,7 +421,6 @@ int iflag;
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/* computes: y(1:n) <- A*x(1:n) */
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/* where A is the principal matrix. */
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/* itrace : (input) running mode. 0=silent, 1=print step-by-step info */
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/* iflag : (output) exit flag. */
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/* <0 - bad input arguments */
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@ -449,30 +484,20 @@ int iflag;
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/* EXPOKIT: Software Package for Computing Matrix Exponentials. */
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/* ACM - Transactions On Mathematical Software, 24(1):130-156, 1998 */
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/* ----------------------------------------------------------------------| */
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iflag = 0;
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i__1 = m + 2;
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int lwsp= n * (m + 2) + i__1 * i__1 * 5 + ideg + 1;
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double *wsp = new double[lwsp];
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int *iwsp = new int[m+2];
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/* --- check restrictions on input parameters ... */
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/* Parameter adjustments */
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--w;
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--v;
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--wsp;
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--iwsp;
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/* Function Body */
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iflag = 0;
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/* Computing 2nd power */
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i__1 = m + 2;
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if (*lwsp < n * (m + 2) + i__1 * i__1 * 5 + ideg + 1) {
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iflag = -1;
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}
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if (*liwsp < m + 2) {
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iflag = -2;
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}
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if (m >= n || m <= 0) {
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iflag = -3;
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}
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if (iflag != 0) {
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la_error("bad sizes (in input of DGEXPV)");
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}
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/* --- initialisations ... */
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@ -481,7 +506,7 @@ int iflag;
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iv = 1;
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ih = iv + n * (m + 1) + n;
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ifree = ih + mh * mh;
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lfree = *lwsp - ifree + 1;
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lfree = lwsp - ifree + 1;
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ibrkflag = 0;
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mbrkdwn = m;
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nmult = 0;
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@ -508,13 +533,13 @@ L1:
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if (tol <= eps) {
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tol = sqrt(eps);
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}
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rndoff = eps * *anorm;
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rndoff = eps * anorm;
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break_tol__ = 1e-7;
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/* >>> break_tol = tol */
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/* >>> break_tol = anorm*tol */
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sgn = d_sign(&c_b4, t);
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dcopy_(n, &v[1], &c__1, &w[1], &c__1);
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beta = dnrm2_(n, &w[1], &c__1);
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sgn = t>=0?1. : -1.;
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cblas_dcopy(n, &v[1], 1, &w[1], 1);
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beta = cblas_dnrm2(n, &w[1], 1);
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vnorm = beta;
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hump = beta;
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@ -524,14 +549,14 @@ L1:
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xm = 1. / (double) (m);
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d__1 = (m + 1) / 2.72;
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i__1 = m + 1;
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p1 = tol * pow_di(&d__1, &i__1) * sqrt((m + 1) * 6.2800000000000002);
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d__1 = p1 / (beta * 4. * *anorm);
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t_new__ = 1. / *anorm * pow_dd(&d__1, &xm);
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d__1 = d_lg10(&t_new__) - sqr1;
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i__1 = i_dnnt(&d__1) - 1;
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p1 = pow_di(&c_b8, &i__1);
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p1 = tol * dipow(d__1, i__1) * sqrt((m + 1) * 6.28);
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d__1 = p1 / (beta * 4. * anorm);
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t_new__ = 1. / anorm * pow_dd(d__1, xm);
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d__1 = log10(t_new__) - sqr1;
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i__1 = nint(d__1) - 1;
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p1 = dipow(10., i__1);
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d__1 = t_new__ / p1 + .55;
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t_new__ = d_int(&d__1) * p1;
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t_new__ = floor(d__1) * p1;
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/* --- step-by-step integration ... */
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@ -562,14 +587,12 @@ L100:
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(matvec)(&wsp[j1v - n], &wsp[j1v]);
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i__2 = j;
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for (i__ = 1; i__ <= i__2; ++i__) {
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hij = ddot_(n, &wsp[iv + (i__ - 1) * n], &c__1, &wsp[j1v], &c__1)
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;
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hij = cblas_ddot(n, &wsp[iv + (i__ - 1) * n], 1, &wsp[j1v], 1);
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d__1 = -hij;
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daxpy_(n, &d__1, &wsp[iv + (i__ - 1) * n], &c__1, &wsp[j1v], &
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c__1);
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cblas_daxpy(n, d__1, &wsp[iv + (i__ - 1) * n], 1, &wsp[j1v], 1);
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wsp[ih + (j - 1) * mh + i__ - 1] = hij;
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}
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hj1j = dnrm2_(n, &wsp[j1v], &c__1);
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hj1j = cblas_dnrm2(n, &wsp[j1v], 1);
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/* --- if `happy breakdown' go straightforward at the end ... */
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if (hj1j <= break_tol__) {
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/* print*,'happy breakdown: mbrkdwn =',j,' h =',hj1j */
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@ -582,13 +605,13 @@ L100:
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}
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wsp[ih + (j - 1) * mh + j] = hj1j;
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d__1 = 1. / hj1j;
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dscal_(n, &d__1, &wsp[j1v], &c__1);
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cblas_dscal(n, d__1, &wsp[j1v], 1);
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j1v += n;
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/* L200: */
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}
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++nmult;
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(matvec)(&wsp[j1v - n], &wsp[j1v]);
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avnorm = dnrm2_(n, &wsp[j1v], &c__1);
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avnorm = cblas_dnrm2(n, &wsp[j1v], 1);
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/* --- set 1 for the 2-corrected scheme ... */
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@ -649,18 +672,18 @@ L401:
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ireject < mxreject)) {
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t_old__ = t_step__;
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d__1 = t_step__ * tol / err_loc__;
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t_step__ = t_step__ * .9 * pow_dd(&d__1, &xm);
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d__1 = d_lg10(&t_step__) - sqr1;
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i__1 = i_dnnt(&d__1) - 1;
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p1 = pow_di(&c_b8, &i__1);
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t_step__ = t_step__ * .9 * pow_dd(d__1, xm);
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d__1 = log10(t_step__) - sqr1;
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i__1 = nint(d__1) - 1;
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p1 = dipow(10., i__1);
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d__1 = t_step__ / p1 + .55;
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t_step__ = d_int(&d__1) * p1;
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if (*itrace != 0) {
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t_step__ = floor(d__1) * p1;
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#ifdef DEBUG
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/* print*,'t_step =',t_old */
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/* print*,'err_loc =',err_loc */
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/* print*,'err_required =',delta*t_old*tol */
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/* print*,'stepsize rejected, stepping down to:',t_step */
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}
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#endif
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++ireject;
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++nreject;
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if (mxreject != 0 && ireject > mxreject) {
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@ -675,20 +698,19 @@ L401:
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/* Computing MAX */
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i__1 = 0, i__2 = k1 - 1;
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mx = mbrkdwn + max(i__1,i__2);
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dgemv_("n", n, &mx, &beta, &wsp[iv], n, &wsp[iexph], &c__1, &c_b25, &w[1],
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&c__1, (ftnlen)1);
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beta = dnrm2_(n, &w[1], &c__1);
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cblas_dgemv(CblasRowMajor, CblasTrans, n, mx, beta, &wsp[iv], n, &wsp[iexph], 1, 0., &w[1],1);
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beta = cblas_dnrm2(n, &w[1], 1);
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hump = max(hump,beta);
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/* --- suggested value for the next stepsize ... */
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d__1 = t_step__ * tol / err_loc__;
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t_new__ = t_step__ * .9 * pow_dd(&d__1, &xm);
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d__1 = d_lg10(&t_new__) - sqr1;
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i__1 = i_dnnt(&d__1) - 1;
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p1 = pow_di(&c_b8, &i__1);
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t_new__ = t_step__ * .9 * pow_dd(d__1, xm);
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d__1 = log10(t_new__) - sqr1;
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i__1 = nint(d__1) - 1;
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p1 = dipow(10., i__1);
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d__1 = t_new__ / p1 + .55;
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t_new__ = d_int(&d__1) * p1;
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t_new__ = floor(d__1) * p1;
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err_loc__ = max(err_loc__,rndoff);
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/* --- update the time covered ... */
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@ -697,13 +719,13 @@ L401:
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/* --- display and keep some information ... */
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if (*itrace != 0) {
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#ifdef DEBUG
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/* print*,'integration',nstep,'---------------------------------' */
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/* print*,'scale-square =',ns */
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/* print*,'step_size =',t_step */
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/* print*,'err_loc =',err_loc */
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/* print*,'next_step =',t_new */
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}
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#endif
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step_min__ = min(step_min__,t_step__);
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step_max__ = max(step_max__,t_step__);
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s_error__ += err_loc__;
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@ -731,11 +753,11 @@ L500:
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/* wsp(9) = hump/vnorm */
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/* wsp(10) = beta/vnorm */
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if(iflag) laerror("dgexpv error");
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return;
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}
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delete[] ++wsp; delete[] ++iwsp;
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return;
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}
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#undef FORNAME
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#undef pow_dd
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//@@@ power series matrix logarithm?
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