void NR::kendl2(Mat_I_DP &tab, DP &tau, DP &z, DP &prob)
{
int k,l,nn,mm,m2,m1,lj,li,kj,ki;
DP svar,s=0.0,points,pairs,en2=0.0,en1=0.0;
int i=tab.nrows();
int j=tab.ncols();
nn=i*j;
points=tab[i-1][j-1];
for (k=0;k<=nn-2;k++) {
ki=(k/j);
kj=k-j*ki;
points += tab[ki][kj];
for (l=k+1;l<=nn-1;l++) {
li=l/j;
lj=l-j*li;
mm=(m1=li-ki)*(m2=lj-kj);
pairs=tab[ki][kj]*tab[li][lj];
if (mm != 0) {
en1 += pairs;
en2 += pairs;
s += (mm > 0 ? pairs : -pairs);
} else {
if (m1 != 0) en1 += pairs;
if (m2 != 0) en2 += pairs;
}
}
}
tau=s/sqrt(en1*en2);
svar=(4.0*points+10.0)/(9.0*points*(points-1.0));
z=tau/sqrt(svar);
prob=erfcc(fabs(z)/1.4142136);
}
void NR::copy(Mat_O_DP &aout, Mat_I_DP &ain)
{
int i,j;
int n=ain.nrows();
for (i=0;i<n;i++)
for (j=0;j<n;j++)
aout[j][i]=ain[j][i];
}
DP NR::anorm2(Mat_I_DP &a)
{
int i,j;
DP sum=0.0;
int n=a.nrows();
for (j=0;j<n;j++)
for (i=0;i<n;i++)
sum += a[i][j]*a[i][j];
return sqrt(sum)/n;
}
void NR::banmul(Mat_I_DP &a, const int m1, const int m2, Vec_I_DP &x,
Vec_O_DP &b)
{
int i,j,k,tmploop;
int n=a.nrows();
for (i=0;i<n;i++) {
k=i-m1;
tmploop=MIN(m1+m2+1,int(n-k));
b[i]=0.0;
for (j=MAX(0,-k);j<tmploop;j++) b[i] += a[i][j]*x[j+k];
}
}
void NR::cholsl(Mat_I_DP &a, Vec_I_DP &p, Vec_I_DP &b, Vec_O_DP &x)
{
int i,k;
DP sum;
int n=a.nrows();
for (i=0;i<n;i++) {
for (sum=b[i],k=i-1;k>=0;k--) sum -= a[i][k]*x[k];
x[i]=sum/p[i];
}
for (i=n-1;i>=0;i--) {
for (sum=x[i],k=i+1;k<n;k++) sum -= a[k][i]*x[k];
x[i]=sum/p[i];
}
}
void NR::resid(Mat_O_DP &res, Mat_I_DP &u, Mat_I_DP &rhs)
{
int i,j;
DP h,h2i;
int n=u.nrows();
h=1.0/(n-1);
h2i=1.0/(h*h);
for (j=1;j<n-1;j++)
for (i=1;i<n-1;i++)
res[i][j] = -h2i*(u[i+1][j]+u[i-1][j]+u[i][j+1]
+u[i][j-1]-4.0*u[i][j])+rhs[i][j];
for (i=0;i<n;i++)
res[i][0]=res[i][n-1]=res[0][i]=res[n-1][i]=0.0;
}
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::banbks(Mat_I_DP &a, const int m1, const int m2, Mat_I_DP &al,
Vec_I_INT &indx, Vec_IO_DP &b)
{
int i,j,k,l,mm;
DP dum;
int n=a.nrows();
mm=m1+m2+1;
l=m1;
for (k=0;k<n;k++) {
j=indx[k]-1;
if (j!=k) SWAP(b[k],b[j]);
if (l<n) l++;
for (j=k+1;j<l;j++) b[j] -= al[k][j-k-1]*b[k];
}
l=1;
for (i=n-1;i>=0;i--) {
dum=b[i];
for (k=1;k<l;k++) dum -= a[i][k]*b[k+i];
b[i]=dum/a[i][0];
if (l<mm) l++;
}
}