void main () { void impex(int, real_t, real_t, real_t [], void (*)(real_t, real_t [], real_t [], int), int (*)(real_t, real_t [], real_t **, int), real_t, real_t, int, real_t, real_t [], void (*)(real_t [], real_t [], int), int *fail, void (*)(real_t *, real_t, real_t, real_t, real_t **, real_t [], int, real_t)); void dupvec(int, int, int, real_t [], real_t []); real_t vecvec(int, int, int, real_t [], real_t []); void elmvec(int, int, int, real_t [], real_t [], real_t); int n,fail,i,it; real_t t,tend,eps,hmax,l,h2,y[4],sw[4],f1[4],f2[4],z[4],x[4], n1,n2; printf("The results with IMPEX are:\n\n"); n=3; nje=nfe=0; t=0.0; tend=400.0; eps=1.0e-5; hmax=400.0; y[1]=y[2]=y[3]=0.0; sw[1]=sw[2]=sw[3]=1.0; print[1]=0.1; print[2]=1.0; print[3]=10.0; print[4]=100.0; print[5]=400.0; dupvec(1,n,0,z,y); for (i=1; i<=n; i++) x[i] = (y[i] == 0.0) ? eps : (1.0+eps)*y[i]; n1=sqrt(vecvec(1,n,0,x,x))*eps; f(t,x,f1,n); for (it=1; it<=5; it++) { f(t,z,f2,n); elmvec(1,n,0,f2,f1,-1.0); n2=n1/sqrt(vecvec(1,n,0,f2,f2)); dupvec(1,n,0,z,x); elmvec(1,n,0,z,f2,n2); } f(t,z,f2,n); elmvec(1,n,0,f2,f1,-1.0); l=sqrt(vecvec(1,n,0,f2,f2))/n1; h2=pow(eps*320.0,1.0/5.0)/(4.0*l); printf("EPS = %e\nInterval of integration = (%1.0f,%3.0f)\n" "Maximally allowed stepsize = %e\n\nLipschconst = %e\n" "Starting stepsize = %e\nFunctional eval = %2d\n\n" " X ERROR Y[1] Y[2] NFE NJE\n", eps,t,tend,hmax,l,h2,nfe); impex(n,t,tend,y,f,available,h2,hmax,0,eps,sw,update,&fail, control); printf("\nNumber of functional evaluations =%4d\n" "Number of Jacobian evaluations = %3d\n",nfe,nje); }
int DoTest(int N, TYPE *alpha0, int incX, int incY) { int iret; const int npad=Mmax(4*Mabs(incY), 16); const TYPE padval=(-2271.0); TYPE *Yg, *Yt, *X, *x, *y; #ifdef TREAL TYPE alpha = *alpha0; #else TYPE *alpha = alpha0; #endif Yg = getvec(npad, padval, N, incY); Yt = dupvec(npad, N, Yg, incY); X = getvec(0, padval, N, incX); /* no padding for read-only X */ x = X; y = Yg + (npad SHIFT); if (incX < 1) x -= ((N-1)SHIFT) * incX; if (incY < 1) y -= ((N-1)SHIFT) * incY; good_axpy(N, alpha, x, incX, y, incY); y = Yt + (npad SHIFT); if (incY < 1) y -= ((N-1)SHIFT) * incY; TEST_AXPY(N, alpha, x, incX, y, incY); iret = CheckY(npad, padval, N, Yg, incY, Yt, incY); free(X); free(Yg); free(Yt); return(iret); }
int DoTest(int N, TYPE *alpha0, int incY) { int iret; const int npad=Mmax(4*Mabs(incY), 16); const TYPE padval=(-2271.0); TYPE *Yg, *Yt, *y; #ifdef TREAL TYPE alpha = *alpha0; #else TYPE *alpha = alpha0; #endif Yg = getvec(npad, padval, N, incY); Yt = dupvec(npad, N, Yg, incY); y = Yg + (npad SHIFT); if (incY < 1) y -= ((N-1)SHIFT) * incY; good_set(N, alpha, y, incY); y = Yt + (npad SHIFT); if (incY < 1) y -= ((N-1)SHIFT) * incY; TEST_SET(N, alpha, Yt+(npad SHIFT), incY); iret = CheckY(npad, padval, N, Yg, incY, Yt, incY); free(Yg); free(Yt); return(iret); }
void gssnewton(int m, int n, real_t par[], real_t rv[], real_t **jjinv, int (*funct)(int, int, real_t[], real_t[]), void (*jacobian)(int, int, real_t[], real_t[], real_t **), real_t in[], real_t out[]) { int *allocate_integer_vector(int, int); real_t *allocate_real_vector(int, int); real_t **allocate_real_matrix(int, int, int, int); void free_integer_vector(int *, int); void free_real_vector(real_t *, int); void free_real_matrix(real_t **, int, int, int); real_t vecvec(int, int, int, real_t [], real_t []); void dupvec(int, int, int, real_t [], real_t []); void elmvec(int, int, int, real_t [], real_t [], real_t); void lsqortdec(real_t **, int, int, real_t [], real_t [], int []); void lsqsol(real_t **, int, int, real_t [], int [], real_t []); void lsqinv(real_t **, int, real_t [], int []); int i,j,inr,mit,text,it,itmax,inrmax,tim,feval,fevalmax,conv, testthf,dampingon,*ci,fail; real_t rho,res1,res2,rn,reltolpar,abstolpar,abstolres,stap,normx, **jac,*pr,*aid,*sol,*fu2,aux[6]; ci=allocate_integer_vector(1,n); pr=allocate_real_vector(1,n); aid=allocate_real_vector(1,n); sol=allocate_real_vector(1,n); fu2=allocate_real_vector(1,m); jac=allocate_real_matrix(1,m+1,1,n); itmax=fevalmax=in[5]; aux[2]=n*in[0]; tim=in[7]; reltolpar=in[1]*in[1]; abstolpar=in[2]*in[2]; abstolres=in[4]*in[4]; inrmax=in[6]; dupvec(1,n,0,pr,par); if (m < n) for (i=1; i<=n; i++) jac[m+1][i]=0.0; text=4; mit=0; testthf=1; res2=stap=out[5]=out[6]=out[7]=0.0; (*funct)(m,n,par,fu2); rn=vecvec(1,m,0,fu2,fu2); out[3]=sqrt(rn); feval=1; dampingon=0; fail=0; it=1; do { out[5]=it; (*jacobian)(m,n,par,fu2,jac); if (!testthf) { text=7; fail=1; break; } lsqortdec(jac,m,n,aux,aid,ci); if (aux[3] != n) { text=5; fail=1; break; } lsqsol(jac,m,n,aid,ci,fu2); dupvec(1,n,0,sol,fu2); stap=vecvec(1,n,0,sol,sol); rho=2.0; normx=vecvec(1,n,0,par,par); if (stap > reltolpar*normx+abstolpar || it == 1 && stap > 0.0) { inr=0; do { rho /= 2.0; if (inr > 0) { res1=res2; dupvec(1,m,0,rv,fu2); dampingon = inr > 1; } for (i=1; i<=n; i++) pr[i]=par[i]-sol[i]*rho; feval++; if (!(*funct)(m,n,pr,fu2)) { text=6; fail=1; break; } res2=vecvec(1,m,0,fu2,fu2); conv = inr >= inrmax; inr++; } while ((inr == 1) ? (dampingon || res2 >= rn) : (!conv && (rn <= res1 || res2 < res1))); if (fail) break; if (conv) { mit++; if (mit < tim) conv=0; } else mit=0; if (inr > 1) { rho *= 2.0; elmvec(1,n,0,par,sol,-rho); rn=res1; if (inr > 2) out[7]=it; } else { dupvec(1,n,0,par,pr); rn=res2; dupvec(1,m,0,rv,fu2); } if (rn <= abstolres) { text=1; itmax=it; } else if (conv && inrmax > 0) { text=3; itmax=it; } else dupvec(1,m,0,fu2,rv); } else { text=2; rho=1.0; itmax=it; } it++; } while (it <= itmax && feval < fevalmax); if (!fail) { lsqinv(jac,n,aid,ci); for (i=1; i<=n; i++) { jjinv[i][i]=jac[i][i]; for (j=i+1; j<=n; j++) jjinv[i][j]=jjinv[j][i]=jac[i][j]; } } out[6]=sqrt(stap)*rho; out[2]=sqrt(rn); out[4]=feval; out[1]=text; out[8]=aux[3]; out[9]=aux[5]; free_integer_vector(ci,1); free_real_vector(pr,1); free_real_vector(aid,1); free_real_vector(sol,1); free_real_vector(fu2,1); free_real_matrix(jac,1,m+1,1); }
void praxis( int n, double *x, int *data, double (*funct)(double *, void *data), double *in, double *out) { int illc,i,j,k,k2,nl,maxf,nf,kl,kt,ktm,emergency; double s,sl,dn,dmin,fx,f1,lds,ldt,sf,df,qf1,qd0,qd1,qa,qb,qc,m2,m4, small,vsmall,large,vlarge,scbd,ldfac,t2,macheps,reltol, abstol,h,**v,*d,*y,*z,*q0,*q1,**a,em[8],l; /* * Seed random number generator */ #ifdef MSWIN srand(34084320); #else srand48(34084320); #endif // for (i=0; i<8; ++i) x[i+1] = (double)data->x[i]; d=allocate_real_vector(1,n); y=allocate_real_vector(1,n); z=allocate_real_vector(1,n); q0=allocate_real_vector(1,n); q1=allocate_real_vector(1,n); v=allocate_real_matrix(1,n,1,n); a=allocate_real_matrix(1,n,1,n); // heuristic numbers: // // If the axes may be badly scaled (which is to be avoided if // possible), then set scbd = 10. otherwise set scbd=1. // // If the problem is known to be ill-conditioned, set ILLC = true. // // KTM is the number of iterations without improvement before the // algorithm terminates. KTM = 4 is very cautious; usually KTM = 1 // is satisfactory. // macheps=in[0]; reltol=in[1]; abstol=in[2]; maxf=in[5]; h=in[6]; scbd=in[7]; ktm=in[8]; illc = in[9] < 0.0; small=macheps*macheps; vsmall=small*small; large=1.0/small; vlarge=1.0/vsmall; m2=reltol; m4=sqrt(m2); srand(1); ldfac = (illc ? 0.1 : 0.01); kt=nl=0; nf=1; out[3]=qf1=fx=(*funct)(x, data); abstol=t2=small+fabs(abstol); dmin=small; if (h < abstol*100.0) h=abstol*100; ldt=h; inimat(1,n,1,n,v,0.0); for (i=1; i<=n; i++) v[i][i]=1.0; d[1]=qd0=qd1=0.0; dupvec(1,n,0,q1,x); inivec(1,n,q0,0.0); emergency=0; while (1) { sf=d[1]; d[1]=s=0.0; praxismin(1,2,&(d[1]),&s,&fx,0, n,x,v,&qa,&qb,&qc,qd0,qd1,q0,q1,&nf, &nl,&fx,m2,m4,dmin,ldt,reltol,abstol,small,h,funct, data); if (s <= 0.0) mulcol(1,n,1,1,v,v,-1.0); if (sf <= 0.9*d[1] || 0.9*sf >= d[1]) inivec(2,n,d,0.0); for (k=2; k<=n; k++) { dupvec(1,n,0,y,x); sf=fx; illc = (illc || kt > 0); while (1) { kl=k; df=0.0; if (illc) { /* random stop to get off resulting valley */ for (i=1; i<=n; i++) { s=z[i]=(0.1*ldt+t2*pow(10.0,kt))* #ifdef MSWIN ((double)(rand())/RAND_MAX-0.5); #else (drand48()-0.5); #endif elmveccol(1,n,i,x,v,s); } fx=(*funct)(x, data); nf++; } for (k2=k; k2<=n; k2++) { sl=fx; s=0.0; praxismin(k2,2,&(d[k2]),&s,&fx,0, n,x,v,&qa,&qb,&qc,qd0,qd1,q0,q1,&nf, &nl,&fx,m2,m4,dmin,ldt,reltol,abstol,small,h,funct, data); s = illc ? d[k2]*(s+z[k2])*(s+z[k2]) : sl-fx; if (df < s) { df=s; kl=k2; } } if (!illc && df < fabs(100.0*macheps*fx)) illc=1; else break; } for (k2=1; k2<=k-1; k2++) { s=0.0; praxismin(k2,2,&(d[k2]),&s,&fx,0, n,x,v,&qa,&qb,&qc,qd0,qd1,q0,q1,&nf, &nl,&fx,m2,m4,dmin,ldt,reltol,abstol,small,h,funct, data); } f1=fx; fx=sf; lds=0.0; for (i=1; i<=n; i++) { sl=x[i]; x[i]=y[i]; y[i] = sl -= y[i]; lds += sl*sl; } lds=sqrt(lds); if (lds > small) { for (i=kl-1; i>=k; i--) { for (j=1; j<=n; j++) v[j][i+1]=v[j][i]; d[i+1]=d[i]; } d[k]=0.0; dupcolvec(1,n,k,v,y); mulcol(1,n,k,k,v,v,1.0/lds); praxismin(k,4,&(d[k]),&lds,&f1,1, n,x,v,&qa,&qb,&qc,qd0,qd1,q0,q1,&nf, &nl,&fx,m2,m4,dmin,ldt,reltol,abstol,small,h,funct, data); if (lds <= 0.0) { lds = -lds; mulcol(1,n,k,k,v,v,-1.0); } } ldt *= ldfac; if (ldt < lds) ldt=lds; t2=m2*sqrt(vecvec(1,n,0,x,x))+abstol; kt = (ldt > 0.5*t2) ? 0 : kt+1; if (kt > ktm) { out[1]=0.0; emergency=1; } } if (emergency) break; /* quad */ s=fx; fx=qf1; qf1=s; qd1=0.0; for (i=1; i<=n; i++) { s=x[i]; x[i]=l=q1[i]; q1[i]=s; qd1 += (s-l)*(s-l); } l=qd1=sqrt(qd1); s=0.0; if ((qd0*qd1 > DBL_MIN) && (nl >=3*n*n)) { praxismin(0,2,&s,&l,&qf1,1, n,x,v,&qa,&qb,&qc,qd0,qd1,q0,q1,&nf, &nl,&fx,m2,m4,dmin,ldt,reltol,abstol,small,h,funct, data); qa=l*(l-qd1)/(qd0*(qd0+qd1)); qb=(l+qd0)*(qd1-l)/(qd0*qd1); qc=l*(l+qd0)/(qd1*(qd0+qd1)); } else { fx=qf1; qa=qb=0.0; qc=1.0; } qd0=qd1; for (i=1; i<=n; i++) { s=q0[i]; q0[i]=x[i]; x[i]=qa*s+qb*x[i]+qc*q1[i]; } /* end of quad */ dn=0.0; for (i=1; i<=n; i++) { d[i]=1.0/sqrt(d[i]); if (dn < d[i]) dn=d[i]; } for (j=1; j<=n; j++) { s=d[j]/dn; mulcol(1,n,j,j,v,v,s); } if (scbd > 1.0) { s=vlarge; for (i=1; i<=n; i++) { sl=z[i]=sqrt(mattam(1,n,i,i,v,v)); if (sl < m4) z[i]=m4; if (s > sl) s=sl; } for (i=1; i<=n; i++) { sl=s/z[i]; z[i]=1.0/sl; if (z[i] > scbd) { sl=1.0/scbd; z[i]=scbd; } mulrow(1,n,i,i,v,v,sl); } } for (i=1; i<=n; i++) ichrowcol(i+1,n,i,i,v); em[0]=em[2]=macheps; em[4]=10*n; em[6]=vsmall; dupmat(1,n,1,n,a,v); if (qrisngvaldec(a,n,n,d,v,em) != 0) { out[1]=2.0; emergency=1; } if (emergency) break; if (scbd > 1.0) { for (i=1; i<=n; i++) mulrow(1,n,i,i,v,v,z[i]); for (i=1; i<=n; i++) { s=sqrt(tammat(1,n,i,i,v,v)); d[i] *= s; s=1.0/s; mulcol(1,n,i,i,v,v,s); } } for (i=1; i<=n; i++) { s=dn*d[i]; d[i] = (s > large) ? vsmall : ((s < small) ? vlarge : 1.0/(s*s)); } /* sort */ for (i=1; i<=n-1; i++) { k=i; s=d[i]; for (j=i+1; j<=n; j++) if (d[j] > s) { k=j; s=d[j]; } if (k > i) { d[k]=d[i]; d[i]=s; for (j=1; j<=n; j++) { s=v[j][i]; v[j][i]=v[j][k]; v[j][k]=s; } } } /* end of sort */ dmin=d[n]; if (dmin < small) dmin=small; illc = (m2*d[1]) > dmin; if (nf >= maxf) { out[1]=1.0; break; } } out[2]=fx; out[4]=nf; out[5]=nl; out[6]=ldt; free_real_vector(d,1); free_real_vector(y,1); free_real_vector(z,1); free_real_vector(q0,1); free_real_vector(q1,1); free_real_matrix(v,1,n,1); free_real_matrix(a,1,n,1); // for (i=0; i<40; ++i) data->x[i] = (double)x[i+1]; }
int peidefunct(int nrow, int ncol, real_t par[], real_t res[], int n, int m, int nobs, int *nbp, int first, int *sec, int *max, int *nis, real_t eps1, int weight, int bp[], real_t save[], real_t ymax[], real_t y[], real_t **yp, real_t **fy, real_t **fp, int cobs[], real_t tobs[], real_t obs[], real_t in[], real_t aux[], int clean, int (*deriv)(int,int,real_t [],real_t [],real_t,real_t []), int (*jacdfdy)(int,int,real_t [],real_t [],real_t,real_t **), int (*jacdfdp)(int,int,real_t [],real_t [],real_t,real_t **), void (*callystart)(int,int,real_t [],real_t [],real_t[]), void (*monitor)(int,int,int,real_t [],real_t [],int,int)) { /* this function is internally used by PEIDE */ void peidereset(int, int, real_t, real_t, real_t, real_t, real_t [], real_t [], real_t *, real_t *, real_t *, int *); void peideorder(int, int, real_t, real_t [], real_t [], real_t *, real_t *, real_t *, real_t *, real_t *, int *); void peidestep(int, int, int, real_t, real_t, real_t, real_t, real_t [], real_t [], real_t [], real_t [], int *, real_t *); real_t peideinterpol(int, int, int, real_t, real_t []); int l,k,knew,fails,same,kpold,n6,nnpar,j5n,cobsii,*p,evaluate, evaluated,decompose,conv,extra,npar,i,j,jj,ii; real_t xold,hold,a0,tolup,tol,toldwn,tolconv,h,ch,chnew,error, dfi,tobsdif,a[6],*delta,*lastdelta,*df,*y0,**jacob,xend, hmax,hmin,eps,s,aa,x,t,c; p=allocate_integer_vector(1,n); delta=allocate_real_vector(1,n); lastdelta=allocate_real_vector(1,n); df=allocate_real_vector(1,n); y0=allocate_real_vector(1,n); jacob=allocate_real_matrix(1,n,1,n); if (*sec) { *sec=0; goto Finish; } xend=tobs[nobs]; eps=in[2]; npar=m; extra=(*nis)=0; ii=1; jj = (*nbp == 0) ? 0 : 1; n6=n*6; inivec(-3,-1,save,0.0); inivec(n6+1,(6+m)*n,y,0.0); inimat(1,nobs+(*nbp),1,m+(*nbp),yp,0.0); t=tobs[1]; x=tobs[0]; (*callystart)(n,m,par,y,ymax); hmax=tobs[1]-tobs[0]; hmin=hmax*in[1]; /* evaluate jacobian */ evaluate=0; decompose=evaluated=1; if (!(*jacdfdy)(n,m,par,y,x,fy)) { save[-3]=4.0; goto Finish; } nnpar=n*npar; Newstart: k=1; kpold=0; same=2; peideorder(n,k,eps,a,save,&tol,&tolup,&toldwn,&tolconv, &a0,&decompose); if (!(*deriv)(n,m,par,y,x,df)) { save[-3]=3.0; goto Finish; } s=FLT_MIN; for (i=1; i<=n; i++) { aa=matvec(1,n,i,fy,df)/ymax[i]; s += aa*aa; } h=sqrt(2.0*eps/sqrt(s)); if (h > hmax) h=hmax; else if (h < hmin) h=hmin; xold=x; hold=h; ch=1.0; for (i=1; i<=n; i++) { save[i]=y[i]; save[n+i]=y[n+i]=df[i]*h; } fails=0; while (x < xend) { if (x+h <= xend) x += h; else { h=xend-x; x=xend; ch=h/hold; c=1.0; for (j=n; j<=k*n; j += n) { c *= ch; for (i=j+1; i<=j+n; i++) y[i] *= c; } same = (same < 3) ? 3 : same+1; } /* prediction */ for (l=1; l<=n; l++) { for (i=l; i<=(k-1)*n+l; i += n) for (j=(k-1)*n+l; j>=i; j -= n) y[j] += y[j+n]; delta[l]=0.0; } evaluated=0; /* correction and estimation local error */ for (l=1; l<=3; l++) { if (!(*deriv)(n,m,par,y,x,df)) { save[-3]=3; goto Finish; } for (i=1; i<=n; i++) df[i]=df[i]*h-y[n+i]; if (evaluate) { /* evaluate jacobian */ evaluate=0; decompose=evaluated=1; if (!(*jacdfdy)(n,m,par,y,x,fy)) { save[-3]=4.0; goto Finish; } } if (decompose) { /* decompose jacobian */ decompose=0; c = -a0*h; for (j=1; j<=n; j++) { for (i=1; i<=n; i++) jacob[i][j]=fy[i][j]*c; jacob[j][j] += 1.0; } dec(jacob,n,aux,p); } sol(jacob,n,p,df); conv=1; for (i=1; i<=n; i++) { dfi=df[i]; y[i] += a0*dfi; y[n+i] += dfi; delta[i] += dfi; conv=(conv && (fabs(dfi) < tolconv*ymax[i])); } if (conv) { s=FLT_MIN; for (i=1; i<=n; i++) { aa=delta[i]/ymax[i]; s += aa*aa; } error=s; break; } } /* acceptance or rejection */ if (!conv) { if (!evaluated) evaluate=1; else { ch /= 4.0; if (h < 4.0*hmin) { save[-1] += 10.0; hmin /= 10.0; if (save[-1] > 40.0) goto Finish; } } peidereset(n,k,hmin,hmax,hold,xold,y,save,&ch,&x, &h,&decompose); } else if (error > tol) { fails++; if (h > 1.1*hmin) { if (fails > 2) { peidereset(n,k,hmin,hmax,hold,xold,y,save,&ch,&x, &h,&decompose); goto Newstart; } else { /* calculate step and order */ peidestep(n,k,fails,tolup,toldwn,tol,error,delta, lastdelta,y,ymax,&knew,&chnew); if (knew != k) { k=knew; peideorder(n,k,eps,a,save,&tol,&tolup, &toldwn,&tolconv,&a0,&decompose); } ch *= chnew; peidereset(n,k,hmin,hmax,hold,xold,y,save,&ch,&x, &h,&decompose); } } else { if (k == 1) { /* violate eps criterion */ save[-2] += 1.0; same=4; goto Errortestok; } k=1; peidereset(n,k,hmin,hmax,hold,xold,y,save,&ch,&x, &h,&decompose); peideorder(n,k,eps,a,save,&tol,&tolup, &toldwn,&tolconv,&a0,&decompose); same=2; } } else { Errortestok: fails=0; for (i=1; i<=n; i++) { c=delta[i]; for (l=2; l<=k; l++) y[l*n+i] += a[l]*c; if (fabs(y[i]) > ymax[i]) ymax[i]=fabs(y[i]); } same--; if (same == 1) dupvec(1,n,0,lastdelta,delta); else if (same == 0) { /* calculate step and order */ peidestep(n,k,fails,tolup,toldwn,tol,error,delta, lastdelta,y,ymax,&knew,&chnew); if (chnew > 1.1) { if (k != knew) { if (knew > k) mulvec(knew*n+1,knew*n+n,-knew*n,y,delta, a[k]/knew); k=knew; peideorder(n,k,eps,a,save,&tol,&tolup, &toldwn,&tolconv,&a0,&decompose); } same=k+1; if (chnew*h > hmax) chnew=hmax/h; h *= chnew; c=1.0; for (j=n; j<=k*n; j += n) { c *= chnew; mulvec(j+1,j+n,0,y,y,c); } decompose=1; } else same=10; } (*nis)++; /* start of an integration step of yp */ if (clean) { hold=h; xold=x; kpold=k; ch=1.0; dupvec(1,k*n+n,0,save,y); } else { if (h != hold) { ch=h/hold; c=1.0; for (j=n6+nnpar; j<=kpold*nnpar+n6; j += nnpar) { c *= ch; for (i=j+1; i<=j+nnpar; i++) y[i] *= c; } hold=h; } if (k > kpold) inivec(n6+k*nnpar+1,n6+k*nnpar+nnpar,y,0.0); xold=x; kpold=k; ch=1.0; dupvec(1,k*n+n,0,save,y); /* evaluate jacobian */ evaluate=0; decompose=evaluated=1; if (!(*jacdfdy)(n,m,par,y,x,fy)) { save[-3]=4.0; goto Finish; } /* decompose jacobian */ decompose=0; c = -a0*h; for (j=1; j<=n; j++) { for (i=1; i<=n; i++) jacob[i][j]=fy[i][j]*c; jacob[j][j] += 1.0; } dec(jacob,n,aux,p); if (!(*jacdfdp)(n,m,par,y,x,fp)) { save[-3]=5.0; goto Finish; } if (npar > m) inimat(1,n,m+1,npar,fp,0.0); /* prediction */ for (l=0; l<=k-1; l++) for (j=k-1; j>=l; j--) elmvec(j*nnpar+n6+1,j*nnpar+n6+nnpar,nnpar, y,y,1.0); /* correction */ for (j=1; j<=npar; j++) { j5n=(j+5)*n; dupvec(1,n,j5n,y0,y); for (i=1; i<=n; i++) df[i]=h*(fp[i][j]+matvec(1,n,i,fy,y0))- y[nnpar+j5n+i]; sol(jacob,n,p,df); for (l=0; l<=k; l++) { i=l*nnpar+j5n; elmvec(i+1,i+n,-i,y,df,a[l]); } } } while (x >= t) { /* calculate a row of the jacobian matrix and an element of the residual vector */ tobsdif=(tobs[ii]-x)/h; cobsii=cobs[ii]; res[ii]=peideinterpol(cobsii,n,k,tobsdif,y)-obs[ii]; if (!clean) { for (i=1; i<=npar; i++) yp[ii][i]=peideinterpol(cobsii+(i+5)*n,nnpar,k, tobsdif,y); /* introducing break-points */ if (bp[jj] != ii) { } else if (first && fabs(res[ii]) < eps1) { (*nbp)--; for (i=jj; i<=(*nbp); i++) bp[i]=bp[i+1]; bp[*nbp+1]=0; } else { extra++; if (first) par[m+jj]=obs[ii]; /* introducing a jacobian row and a residual vector element for continuity requirements */ yp[nobs+jj][m+jj] = -weight; mulrow(1,npar,nobs+jj,ii,yp,yp,weight); res[nobs+jj]=weight*(res[ii]+obs[ii]-par[m+jj]); } } if (ii == nobs) goto Finish; else { t=tobs[ii+1]; if (bp[jj] == ii && jj < *nbp) jj++; hmax=t-tobs[ii]; hmin=hmax*in[1]; ii++; } } /* break-points introduce new initial values for y & yp */ if (extra > 0) { for (i=1; i<=n; i++) { y[i]=peideinterpol(i,n,k,tobsdif,y); for (j=1; j<=npar; j++) y[i+(j+5)*n]=peideinterpol(i+(j+5)*n,nnpar, k,tobsdif,y); } for (l=1; l<=extra; l++) { cobsii=cobs[bp[npar-m+l]]; y[cobsii]=par[npar+l]; for (i=1; i<=npar+extra; i++) y[cobsii+(5+i)*n]=0.0; inivec(1+nnpar+(l+5)*n,nnpar+(l+6)*n,y,0.0); y[cobsii+(5+npar+l)*n]=1.0; } npar += extra; extra=0; x=tobs[ii-1]; /* evaluate jacobian */ evaluate=0; decompose=evaluated=1; if (!(*jacdfdy)(n,m,par,y,x,fy)) { save[-3]=4.0; goto Finish; } nnpar=n*npar; goto Newstart; } } } Finish: if (save[-2] > *max) *max=save[-2]; if (!first) (*monitor)(1,ncol,nrow,par,res,weight,*nis); free_integer_vector(p,1); free_real_vector(delta,1); free_real_vector(lastdelta,1); free_real_vector(df,1); free_real_vector(y0,1); free_real_matrix(jacob,1,n,1); return (save[-1] <= 40.0 && save[-3] == 0.0); }
void peide(int n, int m, int nobs, int *nbp, real_t par[], real_t res[], int bp[], real_t **jtjinv, real_t in[], real_t out[], int (*deriv)(int,int,real_t [],real_t [],real_t,real_t []), int (*jacdfdy)(int,int,real_t [],real_t [],real_t,real_t **), int (*jacdfdp)(int,int,real_t [],real_t [],real_t,real_t **), void (*callystart)(int,int,real_t [],real_t [],real_t[]), void (*data)(int,real_t [],real_t [],int[]), void (*monitor)(int,int,int,real_t [],real_t [],int,int)) { int i,j,weight,ncol,nrow,away,max,nfe,nis,*cobs, first,sec,clean,nbpold,maxfe,fe,it,err,emergency; real_t eps1,res1,in3,in4,fac3,fac4,aux[4],*obs,*save,*tobs, **yp,*ymax,*y,**fy,**fp,w,**aid,temp, vv,ww,w2,mu,res2,fpar,fparpres,lambda,lambdamin,p,pw, reltolres,abstolres,em[8],*val,*b,*bb,*parpres,**jaco; static real_t save1[35]={1.0, 1.0, 9.0, 4.0, 0.0, 2.0/3.0, 1.0, 1.0/3.0, 36.0, 20.25, 1.0, 6.0/11.0, 1.0, 6.0/11.0, 1.0/11.0, 84.028, 53.778, 0.25, 0.48, 1.0, 0.7, 0.2, 0.02, 156.25, 108.51, 0.027778, 120.0/274.0, 1.0, 225.0/274.0, 85.0/274.0, 15.0/274.0, 1.0/274.0, 0.0, 187.69, 0.0047361}; nbpold=(*nbp); cobs=allocate_integer_vector(1,nobs); obs=allocate_real_vector(1,nobs); save=allocate_real_vector(-38,6*n); tobs=allocate_real_vector(0,nobs); ymax=allocate_real_vector(1,n); y=allocate_real_vector(1,6*n*(nbpold+m+1)); yp=allocate_real_matrix(1,nbpold+nobs,1,nbpold+m); fy=allocate_real_matrix(1,n,1,n); fp=allocate_real_matrix(1,n,1,m+nbpold); aid=allocate_real_matrix(1,m+nbpold,1,m+nbpold); for (i=0; i<=34; i++) save[-38+i]=save1[i]; (*data)(nobs,tobs,obs,cobs); weight=1; first=sec=0; clean=(*nbp > 0); aux[2]=FLT_EPSILON; eps1=1.0e10; out[1]=0.0; bp[0]=max=0; /* smooth integration without break-points */ if (!peidefunct(nobs,m,par,res, n,m,nobs,nbp,first,&sec,&max,&nis,eps1,weight,bp, save,ymax,y,yp,fy,fp,cobs,tobs,obs,in,aux,clean,deriv, jacdfdy,jacdfdp,callystart,monitor)) goto Escape; res1=sqrt(vecvec(1,nobs,0,res,res)); nfe=1; if (in[5] == 1.0) { out[1]=1.0; goto Escape; } if (clean) { first=1; clean=0; fac3=sqrt(sqrt(in[3]/res1)); fac4=sqrt(sqrt(in[4]/res1)); eps1=res1*fac4; if (!peidefunct(nobs,m,par,res, n,m,nobs,nbp,first,&sec,&max,&nis,eps1,weight,bp, save,ymax,y,yp,fy,fp,cobs,tobs,obs,in,aux,clean,deriv, jacdfdy,jacdfdp,callystart,monitor)) goto Escape; first=0; } else nfe=0; ncol=m+(*nbp); nrow=nobs+(*nbp); sec=1; in3=in[3]; in4=in[4]; in[3]=res1; weight=away=0; out[4]=out[5]=w=0.0; temp=sqrt(weight)+1.0; weight=temp*temp; while (weight != 16 && *nbp > 0) { if (away == 0 && w != 0.0) { /* if no break-points were omitted then one function function evaluation is saved */ w=weight/w; for (i=nobs+1; i<=nrow; i++) { for (j=1; j<=ncol; j++) yp[i][j] *= w; res[i] *= w; } sec=1; nfe--; } in[3] *= fac3*weight; in[4]=eps1; (*monitor)(2,ncol,nrow,par,res,weight,nis); /* marquardt's method */ val=allocate_real_vector(1,ncol); b=allocate_real_vector(1,ncol); bb=allocate_real_vector(1,ncol); parpres=allocate_real_vector(1,ncol); jaco=allocate_real_matrix(1,nrow,1,ncol); vv=10.0; w2=0.5; mu=0.01; ww = (in[6] < 1.0e-7) ? 1.0e-8 : 1.0e-1*in[6]; em[0]=em[2]=em[6]=in[0]; em[4]=10*ncol; reltolres=in[3]; abstolres=in[4]*in[4]; maxfe=in[5]; err=0; fe=it=1; p=fpar=res2=0.0; pw = -log(ww*in[0])/2.30; if (!peidefunct(nrow,ncol,par,res, n,m,nobs,nbp,first,&sec,&max,&nis,eps1, weight,bp,save,ymax,y,yp,fy,fp,cobs,tobs,obs, in,aux,clean,deriv,jacdfdy,jacdfdp, callystart,monitor)) err=3; else { fpar=vecvec(1,nrow,0,res,res); out[3]=sqrt(fpar); emergency=0; it=1; do { dupmat(1,nrow,1,ncol,jaco,yp); i=qrisngvaldec(jaco,nrow,ncol,val,aid,em); if (it == 1) lambda=in[6]*vecvec(1,ncol,0,val,val); else if (p == 0.0) lambda *= w2; for (i=1; i<=ncol; i++) b[i]=val[i]*tamvec(1,nrow,i,jaco,res); while (1) { for (i=1; i<=ncol; i++) bb[i]=b[i]/(val[i]*val[i]+lambda); for (i=1; i<=ncol; i++) parpres[i]=par[i]-matvec(1,ncol,i,aid,bb); fe++; if (fe >= maxfe) err=1; else if (!peidefunct(nrow,ncol,parpres,res, n,m,nobs,nbp,first,&sec,&max,&nis, eps1,weight,bp,save,ymax,y,yp,fy,fp, cobs,tobs,obs,in,aux,clean,deriv, jacdfdy,jacdfdp,callystart,monitor)) err=2; if (err != 0) { emergency=1; break; } fparpres=vecvec(1,nrow,0,res,res); res2=fpar-fparpres; if (res2 < mu*vecvec(1,ncol,0,b,bb)) { p += 1.0; lambda *= vv; if (p == 1.0) { lambdamin=ww*vecvec(1,ncol,0,val,val); if (lambda < lambdamin) lambda=lambdamin; } if (p >= pw) { err=4; emergency=1; break; } } else { dupvec(1,ncol,0,par,parpres); fpar=fparpres; break; } } if (emergency) break; it++; } while (fpar>abstolres && res2>reltolres*fpar+abstolres); for (i=1; i<=ncol; i++) mulcol(1,ncol,i,i,jaco,aid,1.0/(val[i]+in[0])); for (i=1; i<=ncol; i++) for (j=1; j<=i; j++) aid[i][j]=aid[j][i]=mattam(1,ncol,i,j,jaco,jaco); lambda=lambdamin=val[1]; for (i=2; i<=ncol; i++) if (val[i] > lambda) lambda=val[i]; else if (val[i] < lambdamin) lambdamin=val[i]; temp=lambda/(lambdamin+in[0]); out[7]=temp*temp; out[2]=sqrt(fpar); out[6]=sqrt(res2+fpar)-out[2]; } out[4]=fe; out[5]=it-1; out[1]=err; free_real_vector(val,1); free_real_vector(b,1); free_real_vector(bb,1); free_real_vector(parpres,1); free_real_matrix(jaco,1,nrow,1); if (out[1] > 0.0) goto Escape; /* the relative starting value of lambda is adjusted to the last value of lambda used */ away=out[4]-out[5]-1.0; in[6] *= pow(5.0,away)*pow(2.0,away-out[5]); nfe += out[4]; w=weight; temp=sqrt(weight)+1.0; eps1=temp*temp*in[4]*fac4; away=0; /* omit useless break-points */ for (j=1; j<=(*nbp); j++) if (fabs(obs[bp[j]]+res[bp[j]]-par[j+m]) < eps1) { (*nbp)--; for (i=j; i<=(*nbp); i++) bp[i]=bp[i+1]; dupvec(j+m,(*nbp)+m,1,par,par); j--; away++; bp[*nbp+1]=0; } ncol -= away; nrow -= away; temp=sqrt(weight)+1.0; weight=temp*temp; } in[3]=in3; in[4]=in4; *nbp=0; weight=1; (*monitor)(2,m,nobs,par,res,weight,nis); /* marquardt's method */ val=allocate_real_vector(1,m); b=allocate_real_vector(1,m); bb=allocate_real_vector(1,m); parpres=allocate_real_vector(1,m); jaco=allocate_real_matrix(1,nobs,1,m); vv=10.0; w2=0.5; mu=0.01; ww = (in[6] < 1.0e-7) ? 1.0e-8 : 1.0e-1*in[6]; em[0]=em[2]=em[6]=in[0]; em[4]=10*m; reltolres=in[3]; abstolres=in[4]*in[4]; maxfe=in[5]; err=0; fe=it=1; p=fpar=res2=0.0; pw = -log(ww*in[0])/2.30; if (!peidefunct(nobs,m,par,res, n,m,nobs,nbp,first,&sec,&max,&nis,eps1,weight,bp, save,ymax,y,yp,fy,fp,cobs,tobs,obs,in,aux,clean, deriv,jacdfdy,jacdfdp,callystart,monitor)) err=3; else { fpar=vecvec(1,nobs,0,res,res); out[3]=sqrt(fpar); emergency=0; it=1; do { dupmat(1,nobs,1,m,jaco,yp); i=qrisngvaldec(jaco,nobs,m,val,jtjinv,em); if (it == 1) lambda=in[6]*vecvec(1,m,0,val,val); else if (p == 0.0) lambda *= w2; for (i=1; i<=m; i++) b[i]=val[i]*tamvec(1,nobs,i,jaco,res); while (1) { for (i=1; i<=m; i++) bb[i]=b[i]/(val[i]*val[i]+lambda); for (i=1; i<=m; i++) parpres[i]=par[i]-matvec(1,m,i,jtjinv,bb); fe++; if (fe >= maxfe) err=1; else if (!peidefunct(nobs,m,parpres,res, n,m,nobs,nbp,first,&sec,&max,&nis,eps1, weight,bp,save,ymax,y,yp,fy,fp,cobs,tobs, obs,in,aux,clean,deriv,jacdfdy,jacdfdp, callystart,monitor)) err=2; if (err != 0) { emergency=1; break; } fparpres=vecvec(1,nobs,0,res,res); res2=fpar-fparpres; if (res2 < mu*vecvec(1,m,0,b,bb)) { p += 1.0; lambda *= vv; if (p == 1.0) { lambdamin=ww*vecvec(1,m,0,val,val); if (lambda < lambdamin) lambda=lambdamin; } if (p >= pw) { err=4; emergency=1; break; } } else { dupvec(1,m,0,par,parpres); fpar=fparpres; break; } } if (emergency) break; it++; } while (fpar>abstolres && res2>reltolres*fpar+abstolres); for (i=1; i<=m; i++) mulcol(1,m,i,i,jaco,jtjinv,1.0/(val[i]+in[0])); for (i=1; i<=m; i++) for (j=1; j<=i; j++) jtjinv[i][j]=jtjinv[j][i]=mattam(1,m,i,j,jaco,jaco); lambda=lambdamin=val[1]; for (i=2; i<=m; i++) if (val[i] > lambda) lambda=val[i]; else if (val[i] < lambdamin) lambdamin=val[i]; temp=lambda/(lambdamin+in[0]); out[7]=temp*temp; out[2]=sqrt(fpar); out[6]=sqrt(res2+fpar)-out[2]; } out[4]=fe; out[5]=it-1; out[1]=err; free_real_vector(val,1); free_real_vector(b,1); free_real_vector(bb,1); free_real_vector(parpres,1); free_real_matrix(jaco,1,nobs,1); nfe += out[4]; Escape: if (out[1] == 3.0) out[1]=2.0; else if (out[1] == 4.0) out[1]=6.0; if (save[-3] != 0.0) out[1]=save[-3]; out[3]=res1; out[4]=nfe; out[5]=max; free_integer_vector(cobs,1); free_real_vector(obs,1); free_real_vector(save,-38); free_real_vector(tobs,0); free_real_vector(ymax,1); free_real_vector(y,1); free_real_matrix(yp,1,nbpold+nobs,1); free_real_matrix(fy,1,n,1); free_real_matrix(fp,1,n,1); free_real_matrix(aid,1,m+nbpold,1); }
real_t flemin(int n, real_t x[], real_t g[], real_t h[], real_t (*funct)(int, real_t[], real_t[]), real_t in[], real_t out[]) { real_t *allocate_real_vector(int, int); void free_real_vector(real_t *, int); real_t vecvec(int, int, int, real_t [], real_t []); void elmvec(int, int, int, real_t [], real_t [], real_t); real_t symmatvec(int, int, int, real_t [], real_t []); void inivec(int, int, real_t [], real_t); void inisymd(int, int, int, real_t [], real_t); void mulvec(int, int, int, real_t [], real_t [], real_t); void dupvec(int, int, int, real_t [], real_t []); void linemin(int, real_t [], real_t [], real_t, real_t *, real_t [], real_t (*)(int, real_t[], real_t[]), real_t, real_t *, real_t, real_t *, int *, int, real_t []); void davupd(real_t [], int, real_t [], real_t [], real_t, real_t); void fleupd(real_t [], int, real_t [], real_t [], real_t, real_t); int i,it,cntl,evl,evlmax; real_t f,f0,fmin,mu,dg,dg0,nrmdelta,alfa,reltol,abstol,eps,tolg, aid,*v,*delta,*s; v=allocate_real_vector(1,n); delta=allocate_real_vector(1,n); s=allocate_real_vector(1,n); reltol=in[1]; abstol=in[2]; mu=in[3]; tolg=in[4]; fmin=in[5]; alfa=in[6]; evlmax=in[7]; out[4]=0.0; it=0; f=(*funct)(n,x,g); evl=1; cntl=0; if (alfa > 0.0) { inivec(1,(n*(n+1))/2,h,0.0); inisymd(1,n,0,h,alfa); } for (i=1; i<=n; i++) delta[i] = -symmatvec(1,n,i,h,g); dg=sqrt(vecvec(1,n,0,g,g)); nrmdelta=sqrt(vecvec(1,n,0,delta,delta)); eps=sqrt(vecvec(1,n,0,x,x))*reltol+abstol; dg0=vecvec(1,n,0,delta,g); it++; while ((nrmdelta > eps || dg > tolg) && (evl < evlmax)) { dupvec(1,n,0,s,x); dupvec(1,n,0,v,g); if (it >= n) alfa=1.0; else { if (it != 1) alfa /= nrmdelta; else { alfa=2.0*(fmin-f)/dg0; if (alfa > 1.0) alfa=1.0; } } elmvec(1,n,0,x,delta,alfa); f0=f; f=(*funct)(n,x,g); evl++; dg=vecvec(1,n,0,delta,g); if (it == 1 || f0-f < -mu*dg0*alfa) { /* line minimization */ i=evlmax-evl; cntl++; linemin(n,s,delta,nrmdelta,&alfa,g,funct,f0,&f, dg0,&dg,&i,0,in); evl += i; dupvec(1,n,0,x,s); } if (alfa != 1.0) mulvec(1,n,0,delta,delta,alfa); mulvec(1,n,0,v,v,-1.0); elmvec(1,n,0,v,g,1.0); for (i=1; i<=n; i++) s[i]=symmatvec(1,n,i,h,v); aid=vecvec(1,n,0,v,s); dg=(dg-dg0)*alfa; if (dg > 0.0) if (dg >= aid) fleupd(h,n,delta,s,1.0/dg,(1.0+aid/dg)/dg); else davupd(h,n,delta,s,1.0/dg,1.0/aid); for (i=1; i<=n; i++) delta[i] = -symmatvec(1,n,i,h,g); alfa *= nrmdelta; nrmdelta=sqrt(vecvec(1,n,0,delta,delta)); eps=sqrt(vecvec(1,n,0,x,x))*reltol+abstol; dg=sqrt(vecvec(1,n,0,g,g)); dg0=vecvec(1,n,0,delta,g); if (dg0 > 0.0) { out[4] = -1.0; break; } it++; } out[0]=nrmdelta; out[1]=dg; out[2]=evl; out[3]=cntl; free_real_vector(v,1); free_real_vector(delta,1); free_real_vector(s,1); return f; }
void ark(real_t *t, real_t *te, int *m0, int *m, real_t u[], void (*derivative)(int *, int *, real_t *, real_t[]), real_t data[], void (*out)(int *, int *, real_t *, real_t *, real_t [], real_t [])) { real_t *allocate_real_vector(int, int); real_t **allocate_real_matrix(int, int, int, int); void free_real_vector(real_t *, int); void free_real_matrix(real_t **, int, int, int); void inivec(int, int, real_t [], real_t); void mulvec(int, int, int, real_t [], real_t [], real_t); void dupvec(int, int, int, real_t [], real_t []); real_t vecvec(int, int, int, real_t [], real_t []); void elmvec(int, int, int, real_t [], real_t [], real_t); void decsol(real_t **, int, real_t [], real_t []); real_t arkmui(int, int, int, real_t []); real_t arklabda(int, int, int, int, real_t []); static real_t th1[8] = {1.0, 0.5, 1.0/6.0, 1.0/3.0, 1.0/24.0, 1.0/12.0, 0.125, 0.25}; static real_t ec0,ec1,ec2,tau0,tau1,tau2,taus,t2; int p,n,q,start,step1,last,i,j,k,l,n1,m00; real_t thetanm1,tau,betan,qinv,eta,*mu,*lambda,*thetha,*ro,*r, **alfa,th[9],aux[4],s,ss,theta0,tauacc,taustab, aa,bb,cc,ec,mt,lt; n=data[1]; m00=(*m0); mu=allocate_real_vector(1,n); lambda=allocate_real_vector(1,n); thetha=allocate_real_vector(0,n); ro=allocate_real_vector(m00,*m); r=allocate_real_vector(m00,*m); alfa=allocate_real_matrix(1,8,1,n+1); p=data[2]; ec1=ec2=0.0; betan=data[3]; thetanm1 = (p == 3) ? 0.75 : 1.0; theta0=1.0-thetanm1; s=1.0; for (j=n-1; j>=1; j--) { s = -s*theta0+data[n+10-j]; mu[j]=data[n+11-j]/s; lambda[j]=mu[j]-theta0; } for (i=1; i<=8; i++) for (j=0; j<=n; j++) if (i == 1) alfa[i][j+1]=1.0; else if (j == 0) alfa[i][j+1]=0.0; else if (i == 2 || i == 4 || i == 8) alfa[i][j+1]=pow(arkmui(j,n,p,lambda),(i+2)/3); else if ((i == 3 || i == 6) && j > 1) { s=0.0; for (l=1; l<=j-1; l++) s += arklabda(j,l,n,p,lambda)* pow(arkmui(l,n,p,lambda),i/3); alfa[i][j+1]=s; } else if (i == 5 && j > 2) { s=0.0; for (l=2; l<=j-1; l++) { ss=0.0; for (k=1; k<=l-1; k++) ss += arklabda(l,k,n,p,lambda)* arkmui(k,n,p,lambda); s += arklabda(j,l,n,p,lambda)*ss; } alfa[i][j+1]=s; } else if (i == 7 && j > 1) { s=0.0; for (l=1; l<=j-1; l++) s += arklabda(j,l,n,p,lambda)*arkmui(l,n,p,lambda); alfa[i][j+1]=s*arkmui(j,n,p,lambda); } else alfa[i][j+1]=0.0; n1 = ((n < 4) ? n+1 : ((n < 7) ? 4 : 8)); for (i=1; i<=8; i++) th[i]=th1[i-1]; if (p == 3 && n < 7) th[1]=th[2]=0.0; aux[2]=FLT_EPSILON; decsol(alfa,n1,aux,th); inivec(0,n,thetha,0.0); dupvec(0,n1-1,1,thetha,th); if (!(p == 3 && n < 7)) { thetha[0] -= theta0; thetha[n-1] -= thetanm1; q=p+1; } else q=3; qinv=1.0/q; start=(data[8] == 0.0); data[10]=0.0; last=0; dupvec(*m0,*m,0,r,u); (*derivative)(m0,m,t,r); do { /* stepsize */ eta=sqrt(vecvec(*m0,*m,0,u,u))*data[7]+data[6]; if (eta > 0.0) { if (start) { if (data[8] == 0) { tauacc=data[5]; step1=1; } else if (step1) { tauacc=pow(eta/ec2,qinv); if (tauacc > 10.0*tau2) tauacc=10.0*tau2; else step1=0; } else { bb=(ec2-ec1)/tau1; cc = -bb*t2+ec2; ec=bb*(*t)+cc; tauacc = (ec < 0.0) ? tau2 : pow(eta/ec,qinv); start=0; } } else { aa=((ec0-ec1)/tau0+(ec2-ec1)/tau1)/(tau1+tau0); bb=(ec2-ec1)/tau1-(2.0*t2-tau1)*aa; cc = -(aa*t2+bb)*t2+ec2; ec=(aa*(*t)+bb)*(*t)+cc; tauacc = ((ec < 0.0) ? taus : pow(eta/ec,qinv)); if (tauacc > 2.0*taus) tauacc=2.0*taus; if (tauacc < taus/2.0) tauacc=taus/2.0; } } else tauacc=data[5]; if (tauacc < data[5]) tauacc=data[5]; taustab=betan/data[4]; if (taustab < data[5]) { data[10]=1.0; break; } tau = ((tauacc > taustab) ? taustab : tauacc); taus=tau; if (tau >= (*te)-(*t)) { tau=(*te)-(*t); last=1; } tau0=tau1; tau1=tau2; tau2=tau; /* difference scheme */ mulvec(*m0,*m,0,ro,r,thetha[0]); if (p == 3) elmvec(*m0,*m,0,u,r,0.25*tau); for (i=1; i<=n-1; i++) { mt=mu[i]*tau; lt=lambda[i]*tau; for (j=(*m0); j<=(*m); j++) r[j]=lt*r[j]+u[j]; s=(*t)+mt; (*derivative)(m0,m,&s,r); if (thetha[i] != 0.0) elmvec(*m0,*m,0,ro,r,thetha[i]); if (i == n) { data[9]=sqrt(vecvec(*m0,*m,0,ro,ro))*tau; ec0=ec1; ec1=ec2; ec2=data[9]/pow(tau,q); } } elmvec(*m0,*m,0,u,r,thetanm1*tau); dupvec(*m0,*m,0,r,u); s=(*t)+tau; (*derivative)(m0,m,&s,r); if (thetha[n] != 0.0) elmvec(*m0,*m,0,ro,r,thetha[n]); data[9]=sqrt(vecvec(*m0,*m,0,ro,ro))*tau; ec0=ec1; ec1=ec2; ec2=data[9]/pow(tau,q); t2=(*t); if (last) { last=0; (*t)=(*te); } else (*t) += tau; data[8] += 1.0; (*out)(m0,m,t,te,u,data); } while ((*t) != (*te)); free_real_vector(mu,1); free_real_vector(lambda,1); free_real_vector(thetha,0); free_real_vector(ro,m00); free_real_vector(r,m00); free_real_matrix(alfa,1,8,1); }
void lupzerortpol(int n, int m, real_t b[], real_t c[], real_t zer[], real_t em[]) { real_t infnrmvec(int, int, int *, real_t []); void dupvec(int, int, int, real_t [], real_t []); int i,posdef,j,k,t,converge; real_t nrm,dlam,eps,delta,e,ep,err,p,q,qp,r,s,tot; nrm=fabs(b[0]); for (i=1; i<=n-2; i++) if (c[i]+fabs(b[i]) > nrm) nrm=c[i]+fabs(b[i]); if (n > 1) nrm = (nrm+1 >= c[n-1]+fabs(b[n-1])) ? nrm+1.0 : (c[n-1]+fabs(b[n-1])); em[1]=nrm; for (i=n; i>=1; i--) b[i]=b[i-1]; for (i=n; i>=2; i--) c[i]=c[i-1]; posdef = (em[6] == 1.0); dlam=em[2]; eps=em[0]; c[1]=err=q=s=0.0; tot=b[1]; for (i=n; i>=1; i--) { p=q; q=sqrt(c[i]); e=b[i]-p-q; if (e < tot) tot=e; } if (posdef && (tot < 0.0)) tot=0.0; else for(i=1; i<=n; i++) b[i] -= tot; t=0; for (k=1; k<=m; k++) { converge=0; /* next qr transformation */ do { t++; tot += s; delta=b[n]-s; i=n; e=fabs(eps*tot); if (dlam < e) dlam=e; if (delta <= dlam) { converge=1; break; } e=c[n]/delta; qp=delta+e; p=1.0; for (i=n-1; i>=k; i--) { q=b[i]-s-e; r=q/qp; p=p*r+1.0; ep=e*r; b[i+1]=qp+ep; delta=q-ep; if (delta <= dlam) { converge=1; break; } e=c[i]/q; qp=delta+e; c[i+1]=qp*ep; } if (converge) break; b[k]=qp; s=qp/p; } while (tot+s > tot); /* end of qr transformation */ if (!converge) { /* irregular end of iteration, deflate minimum diagonal element */ s=0.0; i=k; delta=qp; for (j=k+1; j<=n; j++) if (b[j] < delta) { i=j; delta=b[j]; } } /* convergence */ if (i < n) c[i+1]=c[i]*e/qp; for (j=i-1; j>=k; j--) { b[j+1]=b[j]-s; c[j+1]=c[j]; } b[k]=tot; c[k] = err += fabs(delta); } em[5]=t; em[3]=infnrmvec(1,m,&t,c); dupvec(1,m,0,zer,b); }
void quanewbnd(int n, int lw, int rw, real_t x[], real_t f[], real_t jac[], int (*funct)(int, int, int, real_t[], real_t[]), real_t in[], real_t out[]) { real_t *allocate_real_vector(int, int); void free_real_vector(real_t *, int); real_t vecvec(int, int, int, real_t [], real_t []); void elmvec(int, int, int, real_t [], real_t [], real_t); void mulvec(int, int, int, real_t [], real_t [], real_t); void dupvec(int, int, int, real_t [], real_t []); void decsolbnd(real_t [], int, int, int, real_t [], real_t []); int l,it,fcnt,fmax,err,b,i,j,k,r,m; real_t macheps,reltol,abstol,tolres,nd,mz,res,*delta,mul,crit, *pp,*s,aux[6],*lu; delta=allocate_real_vector(1,n); nd=0.0; macheps=in[0]; reltol=in[1]; abstol=in[2]; tolres=in[3]; fmax=in[4]; mz=macheps*macheps; it=fcnt=0; b=lw+rw; l=(n-1)*b+n; b++; res=sqrt(vecvec(1,n,0,f,f)); err=0; while (1) { if (err != 0 || (res < tolres && sqrt(nd) < sqrt(vecvec(1,n,0,x,x))*reltol+abstol)) break; it++; if (it != 1) { /* update jac */ pp=allocate_real_vector(1,n); s=allocate_real_vector(1,n); crit=nd*mz; for (i=1; i<=n; i++) pp[i]=delta[i]*delta[i]; r=k=1; m=rw+1; for (i=1; i<=n; i++) { mul=0.0; for (j=r; j<=m; j++) mul += pp[j]; j=r-k; if (fabs(mul) > crit) elmvec(k,m-j,j,jac,delta,f[i]/mul); k += b; if (i > lw) r++; else k--; if (m < n) m++; } free_real_vector(pp,1); free_real_vector(s,1); } /* direction */ lu=allocate_real_vector(1,l); aux[2]=macheps; mulvec(1,n,0,delta,f,-1.0); dupvec(1,l,0,lu,jac); decsolbnd(lu,n,lw,rw,aux,delta); free_real_vector(lu,1); if (aux[3] != n) { err=3; break; } else { elmvec(1,n,0,x,delta,1.0); nd=vecvec(1,n,0,delta,delta); /* evaluate */ fcnt += n; if (!((*funct)(n,1,n,x,f))) { err=2; break; } if (fcnt > fmax) err=1; res=sqrt(vecvec(1,n,0,f,f)); } } out[1]=sqrt(nd); out[2]=res; out[3]=fcnt; out[4]=it; out[5]=err; free_real_vector(delta,1); }
/*------------------------------------------------------------------------------- calculate the least squares solution of an overdetermined system of nonlinear equations with Marquardt's method -------------------------------------------------------------------------------*/ void Ti_Optimization::MarquardtforCylinderFitting( int m, int n, double**g_pnt, double* const par, double*& g, double**v, int (*funct)(int m, int n, double* const par, double* g,double**g_pnt), void (*jacobian)(int m, int n, double* const par, double*& g, double **jac,double**g_pnt), double in[], double out[] ) { int maxfe,fe,it,i,j,err,emergency; double vv,ww,w,mu,res,fpar,fparpres,lambda,lambdamin,p,pw,reltolres, abstolres,em[8],*val,*b,*bb,*parpres,**jac,temp; val = allocate_real_vector(1,n); b = allocate_real_vector(1,n); bb = allocate_real_vector(1,n); parpres = allocate_real_vector(1,n); jac = allocate_real_matrix(1,m,1,n); assert( (val != NULL) && (b != NULL) && (bb != NULL) && (parpres!= NULL)&& (jac != NULL) ); vv = 10.0; w = 0.5; mu = 0.01; ww = (in[6] < 1.0e-7) ? 1.0e-8 : 1.0e-1*in[6]; em[0] = em[2] = em[6] = in[0]; em[4] = 10*n; reltolres =in[3]; abstolres=in[4]*in[4]; maxfe=(int)in[5]; err=0; fe=it=1; p=fpar=res=0.0; pw = -log(ww*in[0])/2.30; if (!(*funct)(m,n,par,g,g_pnt)) { err=3; out[4]=fe; out[5]=it-1; out[1]=err; free_real_vector(val,1); free_real_vector(b,1); free_real_vector(bb,1); free_real_vector(parpres,1); free_real_matrix(jac,1,m,1); return; } fpar=vecvec(1,m,0,g,g);// norm of residual vector out[3]=sqrt(fpar); emergency=0; it=1; do { (*jacobian)(m,n,par,g,jac,g_pnt); i = qrisngvaldec(jac,m,n,val,v,em); if (it == 1) lambda = in[6]*vecvec(1,n,0,val,val); else if (p == 0.0) lambda *= w; for (i=1; i<=n; i++) b[i] = val[i]*tamvec(1,m,i,jac,g); while (1) { for (i=1; i<=n; i++) bb[i]=b[i]/(val[i]*val[i]+lambda); for (i=1; i<=n; i++) parpres[i]=par[i]-matvec(1,n,i,v,bb); //normalization ,this section only used for cylinder fitting, //when it is used in other situations,it should be removed temp = sqrt(parpres[4]*parpres[4]+parpres[5]*parpres[5]+parpres[6]*parpres[6]); parpres[4] /= temp; parpres[5] /= temp; parpres[6] /= temp; //end normalization fe++; if (fe >= maxfe) err=1; else if (!(*funct)(m,n,parpres,g,g_pnt)) err=2; if (err != 0) { emergency = 1; break; } fparpres=vecvec(1,m,0,g,g); res=fpar-fparpres; if (res < mu*vecvec(1,n,0,b,bb)) { p += 1.0; lambda *= vv; if (p == 1.0) { lambdamin=ww*vecvec(1,n,0,val,val); if (lambda < lambdamin) lambda=lambdamin; } if (p >= pw) { err=4; emergency=1; break; } } // end if else { dupvec(1,n,0,par,parpres); fpar=fparpres; break; } // end else } // end while if (emergency) break; it++; } while ( (fpar > abstolres) && (res > reltolres*fpar+abstolres) ); for (i=1; i<=n; i++) mulcol(1,n,i,i,jac,v,1.0/(val[i]+in[0])); for (i=1; i<=n; i++) { for (j=1; j<=i; j++) v[i][j]=v[j][i]=mattam(1,n,i,j,jac,jac); lambda=lambdamin=val[1]; } for (i=2; i<=n; i++) { if (val[i] > lambda) lambda=val[i]; else { if (val[i] < lambdamin) lambdamin=val[i]; } } temp=lambda/(lambdamin+in[0]); out[7]=temp*temp; out[2]=sqrt(fpar); out[6]=sqrt(res+fpar)-out[2]; out[4]=fe; out[5]=it-1; out[1]=err; if(val != NULL) { free_real_vector(val,1); val = NULL; } if (b != NULL) { free_real_vector(b,1); b = NULL; } if(bb!=NULL) { free_real_vector(bb,1); bb = NULL; } if(parpres != NULL) { free_real_vector(parpres,1); parpres = NULL; } if (jac != NULL) { free_real_matrix(jac,1,m,1); jac = NULL; } }