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dcdflib.c
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#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include "cdflib.h"
static void E0000(int, int *, double *, double *, unsigned long *,
unsigned long *, double *, double *, double *,
double *, double *, double *, double *);
static void E0001(int, int *, double *, double *, double *, double *,
unsigned long *, unsigned long *, double *, double *,
double *, double *);
/*
* A comment about ints and longs - whether ints or longs are used should
* make no difference, but where double r-values are assigned to ints the
* r-value is cast converted to a long, which is then assigned to the int
* to be compatible with the operation of fifidint.
*/
/*
-----------------------------------------------------------------------
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 = (long) (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 = (long) (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 = (long) (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 = (long) (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;