void NR::gauleg(const DP x1, const DP x2, Vec_O_DP &x, Vec_O_DP &w)
{
const DP EPS=1.0e-14;
int m,j,i;
DP z1,z,xm,xl,pp,p3,p2,p1;
int n=x.size();
m=(n+1)/2;
xm=0.5*(x2+x1);
xl=0.5*(x2-x1);
for (i=0;i<m;i++) {
z=cos(3.141592654*(i+0.75)/(n+0.5));
do {
p1=1.0;
p2=0.0;
for (j=0;j<n;j++) {
p3=p2;
p2=p1;
p1=((2.0*j+1.0)*z*p2-j*p3)/(j+1);
}
pp=n*(z*p1-p2)/(z*z-1.0);
z1=z;
z=z1-p1/pp;
} while (fabs(z-z1) > EPS);
x[i]=xm-xl*z;
x[n-1-i]=xm+xl*z;
w[i]=2.0*xl/((1.0-z*z)*pp*pp);
w[n-1-i]=w[i];
}
}
void NR::svdfit(Vec_I_DP &x, Vec_I_DP &y, Vec_I_DP &sig, Vec_O_DP &a,
Mat_O_DP &u, Mat_O_DP &v, Vec_O_DP &w, DP &chisq,
void funcs(const DP, Vec_O_DP &))
{
int i,j;
const DP TOL=1.0e-13;
DP wmax,tmp,thresh,sum;
int ndata=x.size();
int ma=a.size();
Vec_DP b(ndata),afunc(ma);
for (i=0;i<ndata;i++) {
funcs(x[i],afunc);
tmp=1.0/sig[i];
for (j=0;j<ma;j++) u[i][j]=afunc[j]*tmp;
b[i]=y[i]*tmp;
}
svdcmp(u,w,v);
wmax=0.0;
for (j=0;j<ma;j++)
if (w[j] > wmax) wmax=w[j];
thresh=TOL*wmax;
for (j=0;j<ma;j++)
if (w[j] < thresh) w[j]=0.0;
svbksb(u,w,v,b,a);
chisq=0.0;
for (i=0;i<ndata;i++) {
funcs(x[i],afunc);
sum=0.0;
for (j=0;j<ma;j++) sum += a[j]*afunc[j];
chisq += (tmp=(y[i]-sum)/sig[i],tmp*tmp);
}
}
void NR::sprstm(Vec_I_DP &sa, Vec_I_INT &ija, Vec_I_DP &sb, Vec_I_INT &ijb,
const DP thresh, Vec_O_DP &sc, Vec_O_INT &ijc)
{
int i,ijma,ijmb,j,k,ma,mb,mbb;
DP sum;
if (ija[0] != ijb[0]) nrerror("sprstm: sizes do not match");
int nmax=sc.size();
ijc[0]=k=ija[0];
for (i=0;i<ija[0]-1;i++) {
for (j=0;j<ijb[0]-1;j++) {
if (i == j) sum=sa[i]*sb[j]; else sum=0.0e0;
mb=ijb[j];
for (ma=ija[i];ma<ija[i+1];ma++) {
ijma=ija[ma];
if (ijma == j) sum += sa[ma]*sb[j];
else {
while (mb < ijb[j+1]) {
ijmb=ijb[mb];
if (ijmb == i) {
sum += sa[i]*sb[mb++];
continue;
} else if (ijmb < ijma) {
mb++;
continue;
} else if (ijmb == ijma) {
sum += sa[ma]*sb[mb++];
continue;
}
break;
}
}
}
for (mbb=mb;mbb<ijb[j+1];mbb++) {
if (ijb[mbb] == i) sum += sa[i]*sb[mbb];
}
if (i == j) sc[i]=sum;
else if (fabs(sum) > thresh) {
if (k > nmax-1) nrerror("sprstm: sc and ijc too small");
sc[k]=sum;
ijc[k++]=j;
}
}
ijc[i+1]=k;
}
}
void NR::predic(Vec_I_DP &data, Vec_I_DP &d, Vec_O_DP &future)
{
int k,j;
DP sum,discrp;
int ndata=data.size();
int m=d.size();
int nfut=future.size();
Vec_DP reg(m);
for (j=0;j<m;j++) reg[j]=data[ndata-1-j];
for (j=0;j<nfut;j++) {
discrp=0.0;
sum=discrp;
for (k=0;k<m;k++) sum += d[k]*reg[k];
for (k=m-1;k>=1;k--) reg[k]=reg[k-1];
future[j]=reg[0]=sum;
}
}
void NR::fred2(const DP a, const DP b, Vec_O_DP &t, Vec_O_DP &f, Vec_O_DP &w,
DP g(const DP), DP ak(const DP, const DP))
{
int i,j;
DP d;
int n=t.size();
Mat_DP omk(n,n);
Vec_INT indx(n);
gauleg(a,b,t,w);
for (i=0;i<n;i++) {
for (j=0;j<n;j++)
omk[i][j]=DP(i == j)-ak(t[i],t[j])*w[j];
f[i]=g(t[i]);
}
ludcmp(omk,indx,d);
lubksb(omk,indx,f);
}
void NR::sprsin(Mat_I_DP &a, const DP thresh, Vec_O_DP &sa, Vec_O_INT &ija)
{
int i,j,k;
int n=a.nrows();
int nmax=sa.size();
for (j=0;j<n;j++) sa[j]=a[j][j];
ija[0]=n+1;
k=n;
for (i=0;i<n;i++) {
for (j=0;j<n;j++) {
if (fabs(a[i][j]) >= thresh && i != j) {
if (++k > nmax) nrerror("sprsin: sa and ija too small");
sa[k]=a[i][j];
ija[k]=j;
}
}
ija[i+1]=k+1;
}
}
void NR::zbrak(DP fx(const DP), const DP x1, const DP x2, const int n,
Vec_O_DP &xb1, Vec_O_DP &xb2, int &nroot)
{
int i;
DP x,fp,fc,dx;
int nb=xb1.size();
nroot=0;
dx=(x2-x1)/n;
fp=fx(x=x1);
for (i=0;i<n;i++) {
fc=fx(x += dx);
if (fc*fp <= 0.0) {
xb1[nroot]=x-dx;
xb2[nroot++]=x;
if(nroot == nb) return;
}
fp=fc;
}
}
void NR::gauher(Vec_O_DP &x, Vec_O_DP &w)
{
const DP EPS=1.0e-14,PIM4=0.7511255444649425;
const int MAXIT=10;
int i,its,j,m;
DP p1,p2,p3,pp,z,z1;
int n=x.size();
m=(n+1)/2;
for (i=0;i<m;i++) {
if (i == 0) {
z=sqrt(DP(2*n+1))-1.85575*pow(DP(2*n+1),-0.16667);
} else if (i == 1) {
z -= 1.14*pow(DP(n),0.426)/z;
} else if (i == 2) {
z=1.86*z-0.86*x[0];
} else if (i == 3) {
z=1.91*z-0.91*x[1];
} else {
z=2.0*z-x[i-2];
}
for (its=0;its<MAXIT;its++) {
p1=PIM4;
p2=0.0;
for (j=0;j<n;j++) {
p3=p2;
p2=p1;
p1=z*sqrt(2.0/(j+1))*p2-sqrt(DP(j)/(j+1))*p3;
}
pp=sqrt(DP(2*n))*p2;
z1=z;
z=z1-p1/pp;
if (fabs(z-z1) <= EPS) break;
}
if (its >= MAXIT) nrerror("too many iterations in gauher");
x[i]=z;
x[n-1-i] = -z;
w[i]=2.0/(pp*pp);
w[n-1-i]=w[i];
}
}
void NR::memcof(Vec_I_DP &data, DP &xms, Vec_O_DP &d)
{
int k,j,i;
DP p=0.0;
int n=data.size();
int m=d.size();
Vec_DP wk1(n),wk2(n),wkm(m);
for (j=0;j<n;j++) p += SQR(data[j]);
xms=p/n;
wk1[0]=data[0];
wk2[n-2]=data[n-1];
for (j=1;j<n-1;j++) {
wk1[j]=data[j];
wk2[j-1]=data[j];
}
for (k=0;k<m;k++) {
DP num=0.0,denom=0.0;
for (j=0;j<(n-k-1);j++) {
num += (wk1[j]*wk2[j]);
denom += (SQR(wk1[j])+SQR(wk2[j]));
}
d[k]=2.0*num/denom;
xms *= (1.0-SQR(d[k]));
for (i=0;i<k;i++)
d[i]=wkm[i]-d[k]*wkm[k-1-i];
if (k == m-1)
return;
for (i=0;i<=k;i++) wkm[i]=d[i];
for (j=0;j<(n-k-2);j++) {
wk1[j] -= (wkm[k]*wk2[j]);
wk2[j]=wk2[j+1]-wkm[k]*wk1[j+1];
}
}
nrerror("never get here in memcof.");
}
void NR::period(Vec_I_DP &x, Vec_I_DP &y, const DP ofac, const DP hifac,
Vec_O_DP &px, Vec_O_DP &py, int &nout, int &jmax, DP &prob)
{
const DP TWOPI=6.283185307179586476;
int i,j;
DP ave,c,cc,cwtau,effm,expy,pnow,pymax,s,ss,sumc,sumcy,sums,sumsh,
sumsy,swtau,var,wtau,xave,xdif,xmax,xmin,yy,arg,wtemp;
int n=x.size();
int np=px.size();
Vec_DP wi(n),wpi(n),wpr(n),wr(n);
nout=0.5*ofac*hifac*n;
if (nout > np) nrerror("output arrays too short in period");
avevar(y,ave,var);
if (var == 0.0) nrerror("zero variance in period");
xmax=xmin=x[0];
for (j=0;j<n;j++) {
if (x[j] > xmax) xmax=x[j];
if (x[j] < xmin) xmin=x[j];
}
xdif=xmax-xmin;
xave=0.5*(xmax+xmin);
pymax=0.0;
pnow=1.0/(xdif*ofac);
for (j=0;j<n;j++) {
arg=TWOPI*((x[j]-xave)*pnow);
wpr[j]= -2.0*SQR(sin(0.5*arg));
wpi[j]=sin(arg);
wr[j]=cos(arg);
wi[j]=wpi[j];
}
for (i=0;i<nout;i++) {
px[i]=pnow;
sumsh=sumc=0.0;
for (j=0;j<n;j++) {
c=wr[j];
s=wi[j];
sumsh += s*c;
sumc += (c-s)*(c+s);
}
wtau=0.5*atan2(2.0*sumsh,sumc);
swtau=sin(wtau);
cwtau=cos(wtau);
sums=sumc=sumsy=sumcy=0.0;
for (j=0;j<n;j++) {
s=wi[j];
c=wr[j];
ss=s*cwtau-c*swtau;
cc=c*cwtau+s*swtau;
sums += ss*ss;
sumc += cc*cc;
yy=y[j]-ave;
sumsy += yy*ss;
sumcy += yy*cc;
wr[j]=((wtemp=wr[j])*wpr[j]-wi[j]*wpi[j])+wr[j];
wi[j]=(wi[j]*wpr[j]+wtemp*wpi[j])+wi[j];
}
py[i]=0.5*(sumcy*sumcy/sumc+sumsy*sumsy/sums)/var;
if (py[i] >= pymax) pymax=py[jmax=i];
pnow += 1.0/(ofac*xdif);
}
expy=exp(-pymax);
effm=2.0*nout/ofac;
prob=effm*expy;
if (prob > 0.01) prob=1.0-pow(1.0-expy,effm);
}