void free_ivector(int *v, long nl, long nh)
/* free an int vector allocated with ivector() */
{
	free((FREE_ARG) (v+nl-NR_END));
}

void free_cvector(unsigned char *v, long nl, long nh)
/* free an unsigned char vector allocated with cvector() */
{
	free((FREE_ARG) (v+nl-NR_END));
}

void free_lvector(unsigned long *v, long nl, long nh)
/* free an unsigned long vector allocated with lvector() */
{
	free((FREE_ARG) (v+nl-NR_END));
}

void free_dvector(double *v, long nl, long nh)
/* free a double vector allocated with dvector() */
{
	free((FREE_ARG) (v+nl-NR_END));
}

void free_matrix(float **m, long nrl, long nrh, long ncl, long nch)
/* free a float matrix allocated by matrix() */
{
	free((FREE_ARG) (m[nrl]+ncl-NR_END));
	free((FREE_ARG) (m+nrl-NR_END));
}

void free_dmatrix(double **m, long nrl, long nrh, long ncl, long nch)
/* free a double matrix allocated by dmatrix() */
{
	free((FREE_ARG) (m[nrl]+ncl-NR_END));
	free((FREE_ARG) (m+nrl-NR_END));
}

void free_imatrix(int **m, long nrl, long nrh, long ncl, long nch)
/* free an int matrix allocated by imatrix() */
{
	free((FREE_ARG) (m[nrl]+ncl-NR_END));
	free((FREE_ARG) (m+nrl-NR_END));
}

void free_submatrix(float **b, long nrl, long nrh, long ncl, long nch)
/* free a submatrix allocated by submatrix() */
{
	free((FREE_ARG) (b+nrl-NR_END));
}

void free_convert_matrix(float **b, long nrl, long nrh, long ncl, long nch)
/* free a matrix allocated by convert_matrix() */
{
	free((FREE_ARG) (b+nrl-NR_END));
}

void free_f3tensor(float ***t, long nrl, long nrh, long ncl, long nch,
	long ndl, long ndh)
/* free a float f3tensor allocated by f3tensor() */
{
	free((FREE_ARG) (t[nrl][ncl]+ndl-NR_END));
	free((FREE_ARG) (t[nrl]+ncl-NR_END));
	free((FREE_ARG) (t+nrl-NR_END));
}
#define NRANSI
#include "nrutil.h"
#define SWAP(a,b) temp=(a);(a)=(b);(b)=temp;
#define M 7
#define NSTACK 50

void sort2(unsigned long n, float arr[], float brr[])
{
	unsigned long i,ir=n,j,k,l=1;
	int *istack,jstack=0;
	float a,b,temp;

	istack=ivector(1,NSTACK);
	for (;;) {
		if (ir-l < M) {
			for (j=l+1;j<=ir;j++) {
				a=arr[j];
				b=brr[j];
				for (i=j-1;i>=l;i--) {
					if (arr[i] <= a) break;
					arr[i+1]=arr[i];
					brr[i+1]=brr[i];
				}
				arr[i+1]=a;
				brr[i+1]=b;
			}
			if (!jstack) {
				free_ivector(istack,1,NSTACK);
				return;
			}
			ir=istack[jstack];
			l=istack[jstack-1];
			jstack -= 2;
		} else {
			k=(l+ir) >> 1;
			SWAP(arr[k],arr[l+1])
			SWAP(brr[k],brr[l+1])
			if (arr[l] > arr[ir]) {
				SWAP(arr[l],arr[ir])
				SWAP(brr[l],brr[ir])
			}
			if (arr[l+1] > arr[ir]) {
				SWAP(arr[l+1],arr[ir])
				SWAP(brr[l+1],brr[ir])
			}
			if (arr[l] > arr[l+1]) {
				SWAP(arr[l],arr[l+1])
				SWAP(brr[l],brr[l+1])
			}
			i=l+1;
			j=ir;
			a=arr[l+1];
			b=brr[l+1];
			for (;;) {
				do i++; while (arr[i] < a);
				do j--; while (arr[j] > a);
				if (j < i) break;
				SWAP(arr[i],arr[j])
				SWAP(brr[i],brr[j])
			}
			arr[l+1]=arr[j];
			arr[j]=a;
			brr[l+1]=brr[j];
			brr[j]=b;
			jstack += 2;
			if (jstack > NSTACK) nrerror("NSTACK too small in sort2.");
			if (ir-i+1 >= j-l) {
				istack[jstack]=ir;
				istack[jstack-1]=i;
				ir=j-1;
			} else {
				istack[jstack]=j-1;
				istack[jstack-1]=l;
				l=i;
			}
		}
	}
}
#undef M
#undef NSTACK
#undef SWAP
#undef NRANSI

void crank(unsigned long n, float w[], float *s)
{
	unsigned long j=1,ji,jt;
	float t,rank;

	*s=0.0;
	while (j < n) {
		if (w[j+1] != w[j]) {
			w[j]=j;
			++j;
		} else {
			for (jt=j+1;jt<=n && w[jt]==w[j];jt++);
			rank=0.5*(j+jt-1);
			for (ji=j;ji<=(jt-1);ji++) w[ji]=rank;
			t=jt-j;
			*s += t*t*t-t;
			j=jt;
		}
	}
	if (j == n) w[n]=n;
}

float erfcc(float x)
{
	float t,z,ans;

	z=fabs(x);
	t=1.0/(1.0+0.5*z);
	ans=t*exp(-z*z-1.26551223+t*(1.00002368+t*(0.37409196+t*(0.09678418+
		t*(-0.18628806+t*(0.27886807+t*(-1.13520398+t*(1.48851587+
		t*(-0.82215223+t*0.17087277)))))))));
	return x >= 0.0 ? ans : 2.0-ans;
}

float betai(float a, float b, float x)
{
	float betacf(float a, float b, float x);
	float gammln(float xx);
	void nrerror(char error_text[]);
	float bt;

	if (x < 0.0 || x > 1.0) nrerror("Bad x in routine betai");
	if (x == 0.0 || x == 1.0) bt=0.0;
	else
		bt=exp(gammln(a+b)-gammln(a)-gammln(b)+a*log(x)+b*log(1.0-x));
	if (x < (a+1.0)/(a+b+2.0))
		return bt*betacf(a,b,x)/a;
	else
		return 1.0-bt*betacf(b,a,1.0-x)/b;
}


#define MAXIT 100
#define EPS 3.0e-7
#define FPMIN 1.0e-30

float betacf(float a, float b, float x)
{
	void nrerror(char error_text[]);
	int m,m2;
	float aa,c,d,del,h,qab,qam,qap;

	qab=a+b;
	qap=a+1.0;
	qam=a-1.0;
	c=1.0;
	d=1.0-qab*x/qap;
	if (fabs(d) < FPMIN) d=FPMIN;
	d=1.0/d;
	h=d;
	for (m=1;m<=MAXIT;m++) {
		m2=2*m;
		aa=m*(b-m)*x/((qam+m2)*(a+m2));
		d=1.0+aa*d;
		if (fabs(d) < FPMIN) d=FPMIN;
		c=1.0+aa/c;
		if (fabs(c) < FPMIN) c=FPMIN;
		d=1.0/d;
		h *= d*c;
		aa = -(a+m)*(qab+m)*x/((a+m2)*(qap+m2));
		d=1.0+aa*d;
		if (fabs(d) < FPMIN) d=FPMIN;
		c=1.0+aa/c;
		if (fabs(c) < FPMIN) c=FPMIN;
		d=1.0/d;
		del=d*c;
		h *= del;
		if (fabs(del-1.0) < EPS) break;
	}
	if (m > MAXIT) nrerror("a or b too big, or MAXIT too small in betacf");
	return h;
}
#undef MAXIT
#undef EPS
#undef FPMIN

//---------------------------------------------------------------------------

#define NRANSI
#include "nrutil.h"
#define SWAP(a,b) temp=(a);(a)=(b);(b)=temp;
#define M 7
#define NSTACK 50

void sort2i(unsigned long n, int arr[], int brr[])
{
	unsigned long i,ir=n,j,k,l=1;
	int *istack,jstack=0;
	int a,b,temp;

	istack=ivector(1,NSTACK);
	for (;;) {
		if (ir-l < M) {
			for (j=l+1;j<=ir;j++) {
				a=arr[j];
				b=brr[j];
				for (i=j-1;i>=l;i--) {
					if (arr[i] <= a) break;
					arr[i+1]=arr[i];
					brr[i+1]=brr[i];
				}
				arr[i+1]=a;
				brr[i+1]=b;
			}
			if (!jstack) {
				free_ivector(istack,1,NSTACK);
				return;
			}
			ir=istack[jstack];
			l=istack[jstack-1];
			jstack -= 2;
		} else {
			k=(l+ir) >> 1;
			SWAP(arr[k],arr[l+1])
			SWAP(brr[k],brr[l+1])
			if (arr[l] > arr[ir]) {
				SWAP(arr[l],arr[ir])
				SWAP(brr[l],brr[ir])
			}
			if (arr[l+1] > arr[ir]) {
				SWAP(arr[l+1],arr[ir])
				SWAP(brr[l+1],brr[ir])
			}
			if (arr[l] > arr[l+1]) {
				SWAP(arr[l],arr[l+1])
				SWAP(brr[l],brr[l+1])
			}
			i=l+1;
			j=ir;
			a=arr[l+1];
			b=brr[l+1];
			for (;;) {
				do i++; while (arr[i] < a);
				do j--; while (arr[j] > a);
				if (j < i) break;
				SWAP(arr[i],arr[j])
				SWAP(brr[i],brr[j])
			}
			arr[l+1]=arr[j];
			arr[j]=a;
			brr[l+1]=brr[j];
			brr[j]=b;
			jstack += 2;
			if (jstack > NSTACK) nrerror("NSTACK too small in sort2.");
			if (ir-i+1 >= j-l) {
				istack[jstack]=ir;
				istack[jstack-1]=i;
				ir=j-1;
			} else {
				istack[jstack]=j-1;
				istack[jstack-1]=l;
				l=i;
			}
		}
	}
}
#undef M
#undef NSTACK
#undef SWAP
#undef NRANSI

//---------------------------------------------------------------------------
void svdcmp(float **a, int m, int n, float w[], float **v)
{
	float pythag(float a, float b);
	int flag,i,its,j,jj,k,l,nm;
	float anorm,c,f,g,h,s,scale,x,y,z,*rv1;

	rv1=vector(1,n);
	g=scale=anorm=0.0;
	for (i=1;i<=n;i++) {
		l=i+1;
		rv1[i]=scale*g;
		g=s=scale=0.0;
		if (i <= m) {
			for (k=i;k<=m;k++) scale += fabs(a[k][i]);
			if (scale) {
				for (k=i;k<=m;k++) {
					a[k][i] /= scale;
					s += a[k][i]*a[k][i];
				}
				f=a[i][i];
				g = -SIGN(sqrt(s),f);
				h=f*g-s;
				a[i][i]=f-g;
				for (j=l;j<=n;j++) {
					for (s=0.0,k=i;k<=m;k++) s += a[k][i]*a[k][j];
					f=s/h;
					for (k=i;k<=m;k++) a[k][j] += f*a[k][i];
				}
				for (k=i;k<=m;k++) a[k][i] *= scale;
			}
		}
		w[i]=scale *g;
		g=s=scale=0.0;
		if (i <= m && i != n) {
			for (k=l;k<=n;k++) scale += fabs(a[i][k]);
			if (scale) {
				for (k=l;k<=n;k++) {
					a[i][k] /= scale;
					s += a[i][k]*a[i][k];
				}
				f=a[i][l];
				g = -SIGN(sqrt(s),f);
				h=f*g-s;
				a[i][l]=f-g;
				for (k=l;k<=n;k++) rv1[k]=a[i][k]/h;
				for (j=l;j<=m;j++) {
					for (s=0.0,k=l;k<=n;k++) s += a[j][k]*a[i][k];
					for (k=l;k<=n;k++) a[j][k] += s*rv1[k];
				}
				for (k=l;k<=n;k++) a[i][k] *= scale;
			}
		}
		anorm=FMAX(anorm,(fabs(w[i])+fabs(rv1[i])));
	}
	for (i=n;i>=1;i--) {
		if (i < n) {
			if (g) {
				for (j=l;j<=n;j++)
					v[j][i]=(a[i][j]/a[i][l])/g;
				for (j=l;j<=n;j++) {
					for (s=0.0,k=l;k<=n;k++) s += a[i][k]*v[k][j];
					for (k=l;k<=n;k++) v[k][j] += s*v[k][i];
				}
			}
			for (j=l;j<=n;j++) v[i][j]=v[j][i]=0.0;
		}
		v[i][i]=1.0;
		g=rv1[i];
		l=i;
	}
	for (i=IMIN(m,n);i>=1;i--) {
		l=i+1;
		g=w[i];
		for (j=l;j<=n;j++) a[i][j]=0.0;
		if (g) {
			g=1.0/g;
			for (j=l;j<=n;j++) {
				for (s=0.0,k=l;k<=m;k++) s += a[k][i]*a[k][j];
				f=(s/a[i][i])*g;
				for (k=i;k<=m;k++) a[k][j] += f*a[k][i];
			}
			for (j=i;j<=m;j++) a[j][i] *= g;
		} else for (j=i;j<=m;j++) a[j][i]=0.0;
		++a[i][i];
	}
	for (k=n;k>=1;k--) {
		for (its=1;its<=30;its++) {
			flag=1;
			for (l=k;l>=1;l--) {
				nm=l-1;
				if ((float)(fabs(rv1[l])+anorm) == anorm) {
					flag=0;
					break;
				}
				if ((float)(fabs(w[nm])+anorm) == anorm) break;
			}
			if (flag) {
				c=0.0;
				s=1.0;
				for (i=l;i<=k;i++) {
					f=s*rv1[i];
					rv1[i]=c*rv1[i];
					if ((float)(fabs(f)+anorm) == anorm) break;
					g=w[i];
					h=pythag(f,g);
					w[i]=h;
					h=1.0/h;
					c=g*h;
					s = -f*h;
					for (j=1;j<=m;j++) {
						y=a[j][nm];
						z=a[j][i];
						a[j][nm]=y*c+z*s;
						a[j][i]=z*c-y*s;
					}
				}
			}
			z=w[k];
			if (l == k) {
				if (z < 0.0) {
					w[k] = -z;
					for (j=1;j<=n;j++) v[j][k] = -v[j][k];
				}
				break;
			}
			if (its == 30) nrerror("no convergence in 30 svdcmp iterations");
			x=w[l];
			nm=k-1;
			y=w[nm];
			g=rv1[nm];
			h=rv1[k];
			f=((y-z)*(y+z)+(g-h)*(g+h))/(2.0*h*y);
			g=pythag(f,1.0);
			f=((x-z)*(x+z)+h*((y/(f+SIGN(g,f)))-h))/x;
			c=s=1.0;
			for (j=l;j<=nm;j++) {
				i=j+1;
				g=rv1[i];
				y=w[i];
				h=s*g;
				g=c*g;
				z=pythag(f,h);
				rv1[j]=z;
				c=f/z;
				s=h/z;
				f=x*c+g*s;
				g = g*c-x*s;
				h=y*s;
				y *= c;
				for (jj=1;jj<=n;jj++) {
					x=v[jj][j];
					z=v[jj][i];
					v[jj][j]=x*c+z*s;
					v[jj][i]=z*c-x*s;
				}
				z=pythag(f,h);
				w[j]=z;
				if (z) {
					z=1.0/z;
					c=f*z;
					s=h*z;
				}
				f=c*g+s*y;
				x=c*y-s*g;
				for (jj=1;jj<=m;jj++) {
					y=a[jj][j];
					z=a[jj][i];
					a[jj][j]=y*c+z*s;
					a[jj][i]=z*c-y*s;
				}
			}
			rv1[l]=0.0;
			rv1[k]=f;
			w[k]=x;
		}
	}
	free_vector(rv1,1,n);
}

float pythag(float a, float b)
{
	float absa,absb;
	absa=fabs(a);
	absb=fabs(b);
	if (absa > absb) return absa*sqrt(1.0+SQR(absb/absa));
	else return (absb == 0.0 ? 0.0 : absb*sqrt(1.0+SQR(absa/absb)));
}


void kendl1(float data1[], float data2[], unsigned long n, float *tau,
	float *z, float *prob)
{
	float erfcc(float x);
	unsigned long n2=0,n1=0,k,j;
	long is=0;
	float svar,aa,a2,a1;

	for (j=1;j<n;j++) {
		for (k=(j+1);k<=n;k++) {
			a1=data1[j]-data1[k];
			a2=data2[j]-data2[k];
			aa=a1*a2;
			if (aa) {
				++n1;
				++n2;
				aa > 0.0 ? ++is : --is;
			} else {
				if (a1) ++n1;
				if (a2) ++n2;
			}
		}
	}
	*tau=is/(sqrt((double) n1)*sqrt((double) n2));
	svar=(4.0*n+10.0)/(9.0*n*(n-1.0));
	*z=(*tau)/sqrt(svar);
	*prob=erfcc(fabs(*z)/1.4142136);
}