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dcdflib.c
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dcdflib.c
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#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include "cdflib.h"
/*
-----------------------------------------------------------------------
COMPUTATION OF LN(GAMMA(B)/GAMMA(A+B)) WHEN B .GE. 8
--------
IN THIS ALGORITHM, DEL(X) IS THE FUNCTION DEFINED BY
LN(GAMMA(X)) = (X - 0.5)*LN(X) - X + 0.5*LN(2*PI) + DEL(X).
-----------------------------------------------------------------------
*/
double algdiv(double *a,double *b)
{
static double c0 = .833333333333333e-01;
static double c1 = -.277777777760991e-02;
static double c2 = .793650666825390e-03;
static double c3 = -.595202931351870e-03;
static double c4 = .837308034031215e-03;
static double c5 = -.165322962780713e-02;
static double algdiv,c,d,h,s11,s3,s5,s7,s9,t,u,v,w,x,x2,T1;
/*
..
.. Executable Statements ..
*/
if(*a <= *b) goto S10;
h = *b/ *a;
c = 1.0e0/(1.0e0+h);
x = h/(1.0e0+h);
d = *a+(*b-0.5e0);
goto S20;
S10:
h = *a/ *b;
c = h/(1.0e0+h);
x = 1.0e0/(1.0e0+h);
d = *b+(*a-0.5e0);
S20:
/*
SET SN = (1 - X**N)/(1 - X)
*/
x2 = x*x;
s3 = 1.0e0+(x+x2);
s5 = 1.0e0+(x+x2*s3);
s7 = 1.0e0+(x+x2*s5);
s9 = 1.0e0+(x+x2*s7);
s11 = 1.0e0+(x+x2*s9);
/*
SET W = DEL(B) - DEL(A + B)
*/
t = pow(1.0e0/ *b,2.0);
w = ((((c5*s11*t+c4*s9)*t+c3*s7)*t+c2*s5)*t+c1*s3)*t+c0;
w *= (c/ *b);
/*
COMBINE THE RESULTS
*/
T1 = *a/ *b;
u = d*alnrel(&T1);
v = *a*(log(*b)-1.0e0);
if(u <= v) goto S30;
algdiv = w-v-u;
return algdiv;
S30:
algdiv = w-u-v;
return algdiv;
}
double alngam(double *x)
/*
**********************************************************************
double alngam(double *x)
double precision LN of the GAMma function
Function
Returns the natural logarithm of GAMMA(X).
Arguments
X --> value at which scaled log gamma is to be returned
X is DOUBLE PRECISION
Method
If X .le. 6.0, then use recursion to get X below 3
then apply rational approximation number 5236 of
Hart et al, Computer Approximations, John Wiley and
Sons, NY, 1968.
If X .gt. 6.0, then use recursion to get X to at least 12 and
then use formula 5423 of the same source.
**********************************************************************
*/
{
#define hln2pi 0.91893853320467274178e0
static double coef[5] = {
0.83333333333333023564e-1,-0.27777777768818808e-2,0.79365006754279e-3,
-0.594997310889e-3,0.8065880899e-3
};
static double scoefd[4] = {
0.62003838007126989331e2,0.9822521104713994894e1,-0.8906016659497461257e1,
0.1000000000000000000e1
};
static double scoefn[9] = {
0.62003838007127258804e2,0.36036772530024836321e2,0.20782472531792126786e2,
0.6338067999387272343e1,0.215994312846059073e1,0.3980671310203570498e0,
0.1093115956710439502e0,0.92381945590275995e-2,0.29737866448101651e-2
};
static int K1 = 9;
static int K3 = 4;
static int K5 = 5;
static double alngam,offset,prod,xx;
static int i,n;
static double T2,T4,T6;
/*
..
.. Executable Statements ..
*/
if(!(*x <= 6.0e0)) goto S70;
prod = 1.0e0;
xx = *x;
if(!(*x > 3.0e0)) goto S30;
S10:
if(!(xx > 3.0e0)) goto S20;
xx -= 1.0e0;
prod *= xx;
goto S10;
S30:
S20:
if(!(*x < 2.0e0)) goto S60;
S40:
if(!(xx < 2.0e0)) goto S50;
prod /= xx;
xx += 1.0e0;
goto S40;
S60:
S50:
T2 = xx-2.0e0;
T4 = xx-2.0e0;
alngam = devlpl(scoefn,&K1,&T2)/devlpl(scoefd,&K3,&T4);
/*
COMPUTE RATIONAL APPROXIMATION TO GAMMA(X)
*/
alngam *= prod;
alngam = log(alngam);
goto S110;
S70:
offset = hln2pi;
/*
IF NECESSARY MAKE X AT LEAST 12 AND CARRY CORRECTION IN OFFSET
*/
n = fifidint(12.0e0-*x);
if(!(n > 0)) goto S90;
prod = 1.0e0;
for(i=1; i<=n; i++) prod *= (*x+(double)(i-1));
offset -= log(prod);
xx = *x+(double)n;
goto S100;
S90:
xx = *x;
S100:
/*
COMPUTE POWER SERIES
*/
T6 = 1.0e0/pow(xx,2.0);
alngam = devlpl(coef,&K5,&T6)/xx;
alngam += (offset+(xx-0.5e0)*log(xx)-xx);
S110:
return alngam;
#undef hln2pi
}
double alnrel(double *a)
/*
-----------------------------------------------------------------------
EVALUATION OF THE FUNCTION LN(1 + A)
-----------------------------------------------------------------------
*/
{
static double p1 = -.129418923021993e+01;
static double p2 = .405303492862024e+00;
static double p3 = -.178874546012214e-01;
static double q1 = -.162752256355323e+01;
static double q2 = .747811014037616e+00;
static double q3 = -.845104217945565e-01;
static double alnrel,t,t2,w,x;
/*
..
.. Executable Statements ..
*/
if(fabs(*a) > 0.375e0) goto S10;
t = *a/(*a+2.0e0);
t2 = t*t;
w = (((p3*t2+p2)*t2+p1)*t2+1.0e0)/(((q3*t2+q2)*t2+q1)*t2+1.0e0);
alnrel = 2.0e0*t*w;
return alnrel;
S10:
x = 1.e0+*a;
alnrel = log(x);
return alnrel;
}
double apser(double *a,double *b,double *x,double *eps)
/*
-----------------------------------------------------------------------
APSER YIELDS THE INCOMPLETE BETA RATIO I(SUB(1-X))(B,A) FOR
A .LE. MIN(EPS,EPS*B), B*X .LE. 1, AND X .LE. 0.5. USED WHEN
A IS VERY SMALL. USE ONLY IF ABOVE INEQUALITIES ARE SATISFIED.
-----------------------------------------------------------------------
*/
{
static double g = .577215664901533e0;
static double apser,aj,bx,c,j,s,t,tol;
/*
..
.. Executable Statements ..
*/
bx = *b**x;
t = *x-bx;
if(*b**eps > 2.e-2) goto S10;
c = log(*x)+psi(b)+g+t;
goto S20;
S10:
c = log(bx)+g+t;
S20:
tol = 5.0e0**eps*fabs(c);
j = 1.0e0;
s = 0.0e0;
S30:
j += 1.0e0;
t *= (*x-bx/j);
aj = t/j;
s += aj;
if(fabs(aj) > tol) goto S30;
apser = -(*a*(c+s));
return apser;
}
double basym(double *a,double *b,double *lambda,double *eps)
/*
-----------------------------------------------------------------------
ASYMPTOTIC EXPANSION FOR IX(A,B) FOR LARGE A AND B.
LAMBDA = (A + B)*Y - B AND EPS IS THE TOLERANCE USED.
IT IS ASSUMED THAT LAMBDA IS NONNEGATIVE AND THAT
A AND B ARE GREATER THAN OR EQUAL TO 15.
-----------------------------------------------------------------------
*/
{
static double e0 = 1.12837916709551e0;
static double e1 = .353553390593274e0;
static int num = 20;
/*
------------------------
****** NUM IS THE MAXIMUM VALUE THAT N CAN TAKE IN THE DO LOOP
ENDING AT STATEMENT 50. IT IS REQUIRED THAT NUM BE EVEN.
THE ARRAYS A0, B0, C, D HAVE DIMENSION NUM + 1.
------------------------
E0 = 2/SQRT(PI)
E1 = 2**(-3/2)
------------------------
*/
static int K3 = 1;
static double basym,bsum,dsum,f,h,h2,hn,j0,j1,r,r0,r1,s,sum,t,t0,t1,u,w,w0,z,z0,
z2,zn,znm1;
static int i,im1,imj,j,m,mm1,mmj,n,np1;
static double a0[21],b0[21],c[21],d[21],T1,T2;
/*
..
.. Executable Statements ..
*/
basym = 0.0e0;
if(*a >= *b) goto S10;
h = *a/ *b;
r0 = 1.0e0/(1.0e0+h);
r1 = (*b-*a)/ *b;
w0 = 1.0e0/sqrt(*a*(1.0e0+h));
goto S20;
S10:
h = *b/ *a;
r0 = 1.0e0/(1.0e0+h);
r1 = (*b-*a)/ *a;
w0 = 1.0e0/sqrt(*b*(1.0e0+h));
S20:
T1 = -(*lambda/ *a);
T2 = *lambda/ *b;
f = *a*rlog1(&T1)+*b*rlog1(&T2);
t = exp(-f);
if(t == 0.0e0) return basym;
z0 = sqrt(f);
z = 0.5e0*(z0/e1);
z2 = f+f;
a0[0] = 2.0e0/3.0e0*r1;
c[0] = -(0.5e0*a0[0]);
d[0] = -c[0];
j0 = 0.5e0/e0*erfc1(&K3,&z0);
j1 = e1;
sum = j0+d[0]*w0*j1;
s = 1.0e0;
h2 = h*h;
hn = 1.0e0;
w = w0;
znm1 = z;
zn = z2;
for(n=2; n<=num; n+=2) {
hn = h2*hn;
a0[n-1] = 2.0e0*r0*(1.0e0+h*hn)/((double)n+2.0e0);
np1 = n+1;
s += hn;
a0[np1-1] = 2.0e0*r1*s/((double)n+3.0e0);
for(i=n; i<=np1; i++) {
r = -(0.5e0*((double)i+1.0e0));
b0[0] = r*a0[0];
for(m=2; m<=i; m++) {
bsum = 0.0e0;
mm1 = m-1;
for(j=1; j<=mm1; j++) {
mmj = m-j;
bsum += (((double)j*r-(double)mmj)*a0[j-1]*b0[mmj-1]);
}
b0[m-1] = r*a0[m-1]+bsum/(double)m;
}
c[i-1] = b0[i-1]/((double)i+1.0e0);
dsum = 0.0e0;
im1 = i-1;
for(j=1; j<=im1; j++) {
imj = i-j;
dsum += (d[imj-1]*c[j-1]);
}
d[i-1] = -(dsum+c[i-1]);
}
j0 = e1*znm1+((double)n-1.0e0)*j0;
j1 = e1*zn+(double)n*j1;
znm1 = z2*znm1;
zn = z2*zn;
w = w0*w;
t0 = d[n-1]*w*j0;
w = w0*w;
t1 = d[np1-1]*w*j1;
sum += (t0+t1);
if(fabs(t0)+fabs(t1) <= *eps*sum) goto S80;
}
S80:
u = exp(-bcorr(a,b));
basym = e0*t*u*sum;
return basym;
}
double bcorr(double *a0,double *b0)
/*
-----------------------------------------------------------------------
EVALUATION OF DEL(A0) + DEL(B0) - DEL(A0 + B0) WHERE
LN(GAMMA(A)) = (A - 0.5)*LN(A) - A + 0.5*LN(2*PI) + DEL(A).
IT IS ASSUMED THAT A0 .GE. 8 AND B0 .GE. 8.
-----------------------------------------------------------------------
*/
{
static double c0 = .833333333333333e-01;
static double c1 = -.277777777760991e-02;
static double c2 = .793650666825390e-03;
static double c3 = -.595202931351870e-03;
static double c4 = .837308034031215e-03;
static double c5 = -.165322962780713e-02;
static double bcorr,a,b,c,h,s11,s3,s5,s7,s9,t,w,x,x2;
/*
..
.. Executable Statements ..
*/
a = fifdmin1(*a0,*b0);
b = fifdmax1(*a0,*b0);
h = a/b;
c = h/(1.0e0+h);
x = 1.0e0/(1.0e0+h);
x2 = x*x;
/*
SET SN = (1 - X**N)/(1 - X)
*/
s3 = 1.0e0+(x+x2);
s5 = 1.0e0+(x+x2*s3);
s7 = 1.0e0+(x+x2*s5);
s9 = 1.0e0+(x+x2*s7);
s11 = 1.0e0+(x+x2*s9);
/*
SET W = DEL(B) - DEL(A + B)
*/
t = pow(1.0e0/b,2.0);
w = ((((c5*s11*t+c4*s9)*t+c3*s7)*t+c2*s5)*t+c1*s3)*t+c0;
w *= (c/b);
/*
COMPUTE DEL(A) + W
*/
t = pow(1.0e0/a,2.0);
bcorr = (((((c5*t+c4)*t+c3)*t+c2)*t+c1)*t+c0)/a+w;
return bcorr;
}
double betaln(double *a0,double *b0)
/*
-----------------------------------------------------------------------
EVALUATION OF THE LOGARITHM OF THE BETA FUNCTION
-----------------------------------------------------------------------
E = 0.5*LN(2*PI)
--------------------------
*/
{
static double e = .918938533204673e0;
static double betaln,a,b,c,h,u,v,w,z;
static int i,n;
static double T1;
/*
..
.. Executable Statements ..
*/
a = fifdmin1(*a0,*b0);
b = fifdmax1(*a0,*b0);
if(a >= 8.0e0) goto S100;
if(a >= 1.0e0) goto S20;
/*
-----------------------------------------------------------------------
PROCEDURE WHEN A .LT. 1
-----------------------------------------------------------------------
*/
if(b >= 8.0e0) goto S10;
T1 = a+b;
betaln = gamln(&a)+(gamln(&b)-gamln(&T1));
return betaln;
S10:
betaln = gamln(&a)+algdiv(&a,&b);
return betaln;
S20:
/*
-----------------------------------------------------------------------
PROCEDURE WHEN 1 .LE. A .LT. 8
-----------------------------------------------------------------------
*/
if(a > 2.0e0) goto S40;
if(b > 2.0e0) goto S30;
betaln = gamln(&a)+gamln(&b)-gsumln(&a,&b);
return betaln;
S30:
w = 0.0e0;
if(b < 8.0e0) goto S60;
betaln = gamln(&a)+algdiv(&a,&b);
return betaln;
S40:
/*
REDUCTION OF A WHEN B .LE. 1000
*/
if(b > 1000.0e0) goto S80;
n = a-1.0e0;
w = 1.0e0;
for(i=1; i<=n; i++) {
a -= 1.0e0;
h = a/b;
w *= (h/(1.0e0+h));
}
w = log(w);
if(b < 8.0e0) goto S60;
betaln = w+gamln(&a)+algdiv(&a,&b);
return betaln;
S60:
/*
REDUCTION OF B WHEN B .LT. 8
*/
n = b-1.0e0;
z = 1.0e0;
for(i=1; i<=n; i++) {
b -= 1.0e0;
z *= (b/(a+b));
}
betaln = w+log(z)+(gamln(&a)+(gamln(&b)-gsumln(&a,&b)));
return betaln;
S80:
/*
REDUCTION OF A WHEN B .GT. 1000
*/
n = a-1.0e0;
w = 1.0e0;
for(i=1; i<=n; i++) {
a -= 1.0e0;
w *= (a/(1.0e0+a/b));
}
betaln = log(w)-(double)n*log(b)+(gamln(&a)+algdiv(&a,&b));
return betaln;
S100:
/*
-----------------------------------------------------------------------
PROCEDURE WHEN A .GE. 8
-----------------------------------------------------------------------
*/
w = bcorr(&a,&b);
h = a/b;
c = h/(1.0e0+h);
u = -((a-0.5e0)*log(c));
v = b*alnrel(&h);
if(u <= v) goto S110;
betaln = -(0.5e0*log(b))+e+w-v-u;
return betaln;
S110:
betaln = -(0.5e0*log(b))+e+w-u-v;
return betaln;
}
double bfrac(double *a,double *b,double *x,double *y,double *lambda,
double *eps)
/*
-----------------------------------------------------------------------
CONTINUED FRACTION EXPANSION FOR IX(A,B) WHEN A,B .GT. 1.
IT IS ASSUMED THAT LAMBDA = (A + B)*Y - B.
-----------------------------------------------------------------------
*/
{
static double bfrac,alpha,an,anp1,beta,bn,bnp1,c,c0,c1,e,n,p,r,r0,s,t,w,yp1;
/*
..
.. Executable Statements ..
*/
bfrac = brcomp(a,b,x,y);
if(bfrac == 0.0e0) return bfrac;
c = 1.0e0+*lambda;
c0 = *b/ *a;
c1 = 1.0e0+1.0e0/ *a;
yp1 = *y+1.0e0;
n = 0.0e0;
p = 1.0e0;
s = *a+1.0e0;
an = 0.0e0;
bn = anp1 = 1.0e0;
bnp1 = c/c1;
r = c1/c;
S10:
/*
CONTINUED FRACTION CALCULATION
*/
n += 1.0e0;
t = n/ *a;
w = n*(*b-n)**x;
e = *a/s;
alpha = p*(p+c0)*e*e*(w**x);
e = (1.0e0+t)/(c1+t+t);
beta = n+w/s+e*(c+n*yp1);
p = 1.0e0+t;
s += 2.0e0;
/*
UPDATE AN, BN, ANP1, AND BNP1
*/
t = alpha*an+beta*anp1;
an = anp1;
anp1 = t;
t = alpha*bn+beta*bnp1;
bn = bnp1;
bnp1 = t;
r0 = r;
r = anp1/bnp1;
if(fabs(r-r0) <= *eps*r) goto S20;
/*
RESCALE AN, BN, ANP1, AND BNP1
*/
an /= bnp1;
bn /= bnp1;
anp1 = r;
bnp1 = 1.0e0;
goto S10;
S20:
/*
TERMINATION
*/
bfrac *= r;
return bfrac;
}
void bgrat(double *a,double *b,double *x,double *y,double *w,
double *eps,int *ierr)
/*
-----------------------------------------------------------------------
ASYMPTOTIC EXPANSION FOR IX(A,B) WHEN A IS LARGER THAN B.
THE RESULT OF THE EXPANSION IS ADDED TO W. IT IS ASSUMED
THAT A .GE. 15 AND B .LE. 1. EPS IS THE TOLERANCE USED.
IERR IS A VARIABLE THAT REPORTS THE STATUS OF THE RESULTS.
-----------------------------------------------------------------------
*/
{
static double bm1,bp2n,cn,coef,dj,j,l,lnx,n2,nu,p,q,r,s,sum,t,t2,u,v,z;
static int i,n,nm1;
static double c[30],d[30],T1;
/*
..
.. Executable Statements ..
*/
bm1 = *b-0.5e0-0.5e0;
nu = *a+0.5e0*bm1;
if(*y > 0.375e0) goto S10;
T1 = -*y;
lnx = alnrel(&T1);
goto S20;
S10:
lnx = log(*x);
S20:
z = -(nu*lnx);
if(*b*z == 0.0e0) goto S70;
/*
COMPUTATION OF THE EXPANSION
SET R = EXP(-Z)*Z**B/GAMMA(B)
*/
r = *b*(1.0e0+gam1(b))*exp(*b*log(z));
r *= (exp(*a*lnx)*exp(0.5e0*bm1*lnx));
u = algdiv(b,a)+*b*log(nu);
u = r*exp(-u);
if(u == 0.0e0) goto S70;
grat1(b,&z,&r,&p,&q,eps);
v = 0.25e0*pow(1.0e0/nu,2.0);
t2 = 0.25e0*lnx*lnx;
l = *w/u;
j = q/r;
sum = j;
t = cn = 1.0e0;
n2 = 0.0e0;
for(n=1; n<=30; n++) {
bp2n = *b+n2;
j = (bp2n*(bp2n+1.0e0)*j+(z+bp2n+1.0e0)*t)*v;
n2 += 2.0e0;
t *= t2;
cn /= (n2*(n2+1.0e0));
c[n-1] = cn;
s = 0.0e0;
if(n == 1) goto S40;
nm1 = n-1;
coef = *b-(double)n;
for(i=1; i<=nm1; i++) {
s += (coef*c[i-1]*d[n-i-1]);
coef += *b;
}
S40:
d[n-1] = bm1*cn+s/(double)n;
dj = d[n-1]*j;
sum += dj;
if(sum <= 0.0e0) goto S70;
if(fabs(dj) <= *eps*(sum+l)) goto S60;
}
S60:
/*
ADD THE RESULTS TO W
*/
*ierr = 0;
*w += (u*sum);
return;
S70:
/*
THE EXPANSION CANNOT BE COMPUTED
*/
*ierr = 1;
return;
}
double bpser(double *a,double *b,double *x,double *eps)
/*
-----------------------------------------------------------------------
POWER SERIES EXPANSION FOR EVALUATING IX(A,B) WHEN B .LE. 1
OR B*X .LE. 0.7. EPS IS THE TOLERANCE USED.
-----------------------------------------------------------------------
*/
{
static double bpser,a0,apb,b0,c,n,sum,t,tol,u,w,z;
static int i,m;
/*
..
.. Executable Statements ..
*/
bpser = 0.0e0;
if(*x == 0.0e0) return bpser;
/*
-----------------------------------------------------------------------
COMPUTE THE FACTOR X**A/(A*BETA(A,B))
-----------------------------------------------------------------------
*/
a0 = fifdmin1(*a,*b);
if(a0 < 1.0e0) goto S10;
z = *a*log(*x)-betaln(a,b);
bpser = exp(z)/ *a;
goto S100;
S10:
b0 = fifdmax1(*a,*b);
if(b0 >= 8.0e0) goto S90;
if(b0 > 1.0e0) goto S40;
/*
PROCEDURE FOR A0 .LT. 1 AND B0 .LE. 1
*/
bpser = pow(*x,*a);
if(bpser == 0.0e0) return bpser;
apb = *a+*b;
if(apb > 1.0e0) goto S20;
z = 1.0e0+gam1(&apb);
goto S30;
S20:
u = *a+*b-1.e0;
z = (1.0e0+gam1(&u))/apb;
S30:
c = (1.0e0+gam1(a))*(1.0e0+gam1(b))/z;
bpser *= (c*(*b/apb));
goto S100;
S40:
/*
PROCEDURE FOR A0 .LT. 1 AND 1 .LT. B0 .LT. 8
*/
u = gamln1(&a0);
m = b0-1.0e0;
if(m < 1) goto S60;
c = 1.0e0;
for(i=1; i<=m; i++) {
b0 -= 1.0e0;
c *= (b0/(a0+b0));
}
u = log(c)+u;
S60:
z = *a*log(*x)-u;
b0 -= 1.0e0;
apb = a0+b0;
if(apb > 1.0e0) goto S70;
t = 1.0e0+gam1(&apb);
goto S80;
S70:
u = a0+b0-1.e0;
t = (1.0e0+gam1(&u))/apb;
S80:
bpser = exp(z)*(a0/ *a)*(1.0e0+gam1(&b0))/t;
goto S100;
S90:
/*
PROCEDURE FOR A0 .LT. 1 AND B0 .GE. 8
*/
u = gamln1(&a0)+algdiv(&a0,&b0);
z = *a*log(*x)-u;
bpser = a0/ *a*exp(z);
S100:
if(bpser == 0.0e0 || *a <= 0.1e0**eps) return bpser;
/*
-----------------------------------------------------------------------
COMPUTE THE SERIES
-----------------------------------------------------------------------
*/
sum = n = 0.0e0;
c = 1.0e0;
tol = *eps/ *a;
S110:
n += 1.0e0;
c *= ((0.5e0+(0.5e0-*b/n))**x);
w = c/(*a+n);
sum += w;
if(fabs(w) > tol) goto S110;
bpser *= (1.0e0+*a*sum);
return bpser;
}
void bratio(double *a,double *b,double *x,double *y,double *w,
double *w1,int *ierr)
/*
-----------------------------------------------------------------------
EVALUATION OF THE INCOMPLETE BETA FUNCTION IX(A,B)
--------------------
IT IS ASSUMED THAT A AND B ARE NONNEGATIVE, AND THAT X .LE. 1
AND Y = 1 - X. BRATIO ASSIGNS W AND W1 THE VALUES
W = IX(A,B)
W1 = 1 - IX(A,B)
IERR IS A VARIABLE THAT REPORTS THE STATUS OF THE RESULTS.
IF NO INPUT ERRORS ARE DETECTED THEN IERR IS SET TO 0 AND
W AND W1 ARE COMPUTED. OTHERWISE, IF AN ERROR IS DETECTED,
THEN W AND W1 ARE ASSIGNED THE VALUE 0 AND IERR IS SET TO
ONE OF THE FOLLOWING VALUES ...
IERR = 1 IF A OR B IS NEGATIVE
IERR = 2 IF A = B = 0
IERR = 3 IF X .LT. 0 OR X .GT. 1
IERR = 4 IF Y .LT. 0 OR Y .GT. 1
IERR = 5 IF X + Y .NE. 1
IERR = 6 IF X = A = 0
IERR = 7 IF Y = B = 0
--------------------
WRITTEN BY ALFRED H. MORRIS, JR.
NAVAL SURFACE WARFARE CENTER
DAHLGREN, VIRGINIA
REVISED ... NOV 1991
-----------------------------------------------------------------------
*/
{
static int K1 = 1;
static double a0,b0,eps,lambda,t,x0,y0,z;
static int ierr1,ind,n;
static double T2,T3,T4,T5;
/*
..
.. Executable Statements ..
*/
/*
****** EPS IS A MACHINE DEPENDENT CONSTANT. EPS IS THE SMALLEST
FLOATING POINT NUMBER FOR WHICH 1.0 + EPS .GT. 1.0
*/
eps = spmpar(&K1);
*w = *w1 = 0.0e0;
if(*a < 0.0e0 || *b < 0.0e0) goto S270;
if(*a == 0.0e0 && *b == 0.0e0) goto S280;
if(*x < 0.0e0 || *x > 1.0e0) goto S290;
if(*y < 0.0e0 || *y > 1.0e0) goto S300;
z = *x+*y-0.5e0-0.5e0;
if(fabs(z) > 3.0e0*eps) goto S310;
*ierr = 0;
if(*x == 0.0e0) goto S210;
if(*y == 0.0e0) goto S230;
if(*a == 0.0e0) goto S240;
if(*b == 0.0e0) goto S220;
eps = fifdmax1(eps,1.e-15);
if(fifdmax1(*a,*b) < 1.e-3*eps) goto S260;
ind = 0;
a0 = *a;
b0 = *b;
x0 = *x;
y0 = *y;
if(fifdmin1(a0,b0) > 1.0e0) goto S40;
/*
PROCEDURE FOR A0 .LE. 1 OR B0 .LE. 1
*/
if(*x <= 0.5e0) goto S10;
ind = 1;
a0 = *b;
b0 = *a;
x0 = *y;
y0 = *x;
S10:
if(b0 < fifdmin1(eps,eps*a0)) goto S90;
if(a0 < fifdmin1(eps,eps*b0) && b0*x0 <= 1.0e0) goto S100;
if(fifdmax1(a0,b0) > 1.0e0) goto S20;
if(a0 >= fifdmin1(0.2e0,b0)) goto S110;
if(pow(x0,a0) <= 0.9e0) goto S110;
if(x0 >= 0.3e0) goto S120;
n = 20;
goto S140;
S20:
if(b0 <= 1.0e0) goto S110;
if(x0 >= 0.3e0) goto S120;
if(x0 >= 0.1e0) goto S30;
if(pow(x0*b0,a0) <= 0.7e0) goto S110;
S30:
if(b0 > 15.0e0) goto S150;
n = 20;
goto S140;
S40:
/*
PROCEDURE FOR A0 .GT. 1 AND B0 .GT. 1
*/
if(*a > *b) goto S50;
lambda = *a-(*a+*b)**x;
goto S60;
S50:
lambda = (*a+*b)**y-*b;
S60:
if(lambda >= 0.0e0) goto S70;
ind = 1;
a0 = *b;
b0 = *a;
x0 = *y;
y0 = *x;
lambda = fabs(lambda);
S70:
if(b0 < 40.0e0 && b0*x0 <= 0.7e0) goto S110;
if(b0 < 40.0e0) goto S160;
if(a0 > b0) goto S80;
if(a0 <= 100.0e0) goto S130;
if(lambda > 0.03e0*a0) goto S130;
goto S200;
S80:
if(b0 <= 100.0e0) goto S130;
if(lambda > 0.03e0*b0) goto S130;
goto S200;
S90:
/*
EVALUATION OF THE APPROPRIATE ALGORITHM
*/
*w = fpser(&a0,&b0,&x0,&eps);
*w1 = 0.5e0+(0.5e0-*w);
goto S250;
S100:
*w1 = apser(&a0,&b0,&x0,&eps);
*w = 0.5e0+(0.5e0-*w1);
goto S250;
S110:
*w = bpser(&a0,&b0,&x0,&eps);
*w1 = 0.5e0+(0.5e0-*w);
goto S250;
S120:
*w1 = bpser(&b0,&a0,&y0,&eps);
*w = 0.5e0+(0.5e0-*w1);
goto S250;
S130:
T2 = 15.0e0*eps;
*w = bfrac(&a0,&b0,&x0,&y0,&lambda,&T2);
*w1 = 0.5e0+(0.5e0-*w);
goto S250;
S140:
*w1 = bup(&b0,&a0,&y0,&x0,&n,&eps);
b0 += (double)n;
S150:
T3 = 15.0e0*eps;
bgrat(&b0,&a0,&y0,&x0,w1,&T3,&ierr1);
*w = 0.5e0+(0.5e0-*w1);
goto S250;
S160:
n = b0;
b0 -= (double)n;
if(b0 != 0.0e0) goto S170;
n -= 1;
b0 = 1.0e0;
S170:
*w = bup(&b0,&a0,&y0,&x0,&n,&eps);
if(x0 > 0.7e0) goto S180;
*w += bpser(&a0,&b0,&x0,&eps);
*w1 = 0.5e0+(0.5e0-*w);
goto S250;
S180:
if(a0 > 15.0e0) goto S190;
n = 20;
*w += bup(&a0,&b0,&x0,&y0,&n,&eps);
a0 += (double)n;
S190:
T4 = 15.0e0*eps;
bgrat(&a0,&b0,&x0,&y0,w,&T4,&ierr1);
*w1 = 0.5e0+(0.5e0-*w);
goto S250;
S200:
T5 = 100.0e0*eps;
*w = basym(&a0,&b0,&lambda,&T5);
*w1 = 0.5e0+(0.5e0-*w);
goto S250;
S210:
/*
TERMINATION OF THE PROCEDURE
*/
if(*a == 0.0e0) goto S320;
S220:
*w = 0.0e0;
*w1 = 1.0e0;
return;
S230:
if(*b == 0.0e0) goto S330;
S240:
*w = 1.0e0;
*w1 = 0.0e0;
return;
S250:
if(ind == 0) return;
t = *w;
*w = *w1;
*w1 = t;
return;
S260:
/*
PROCEDURE FOR A AND B .LT. 1.E-3*EPS
*/
*w = *b/(*a+*b);
*w1 = *a/(*a+*b);
return;
S270:
/*
ERROR RETURN
*/
*ierr = 1;
return;
S280:
*ierr = 2;
return;
S290:
*ierr = 3;
return;
S300:
*ierr = 4;
return;
S310:
*ierr = 5;
return;
S320:
*ierr = 6;
return;
S330:
*ierr = 7;
return;
}
double brcmp1(int *mu,double *a,double *b,double *x,double *y)
/*
-----------------------------------------------------------------------
EVALUATION OF EXP(MU) * (X**A*Y**B/BETA(A,B))
-----------------------------------------------------------------------
*/
{
static double Const = .398942280401433e0;