40 |
return 0.0; |
return 0.0; |
41 |
} |
} |
42 |
|
|
43 |
|
/* Consider, small, large and intermediate cases separately. The |
44 |
|
boundaries at 0.05 and 0.95 have not been optimised, but seem ok |
45 |
|
for an initial approximation. */ |
46 |
|
|
47 |
if (p < 0.05) |
if (p < 0.05) |
48 |
{ |
{ |
49 |
double x0 = exp((lgamma(b) + log(p))/b); |
double x0 = exp ((lgamma (b) + log (p)) / b); |
50 |
x = x0; |
x = x0; |
51 |
} |
} |
52 |
else if (p > 0.95) |
else if (p > 0.95) |
53 |
{ |
{ |
54 |
double x0 = -log(1-p) + lgamma(b); |
double x0 = -log (1 - p) + lgamma (b); |
55 |
x = x0; |
x = x0; |
56 |
} |
} |
57 |
else |
else |
58 |
{ |
{ |
59 |
double xg = gsl_cdf_ugaussian_Pinv (p); |
double xg = gsl_cdf_ugaussian_Pinv (p); |
60 |
double x0 = (xg < -sqrt(b)) ? b : sqrt (b) * xg + b; |
double x0 = (xg < -sqrt (b)) ? b : sqrt (b) * xg + b; |
61 |
x = x0; |
x = x0; |
62 |
} |
} |
63 |
|
|
65 |
to an improved value of x (Abramowitz & Stegun, 3.6.6) |
to an improved value of x (Abramowitz & Stegun, 3.6.6) |
66 |
|
|
67 |
where E(x)=P-integ(phi(u),u,x0,x) and phi(u) is the pdf. |
where E(x)=P-integ(phi(u),u,x0,x) and phi(u) is the pdf. |
68 |
*/ |
*/ |
69 |
|
|
70 |
{ |
{ |
71 |
double lambda, dp, phi; |
double lambda, dp, phi; |
72 |
|
|
73 |
start: |
start: |
74 |
dp = p - gsl_cdf_gamma_P (x, 1.0, b) ; |
dp = p - gsl_cdf_gamma_P (x, 1.0, b); |
75 |
phi = gsl_ran_gamma_pdf (x, 1.0, b); |
phi = gsl_ran_gamma_pdf (x, b, 1.0); |
76 |
|
|
77 |
if (dp == 0.0) |
if (dp == 0.0) |
78 |
goto end; |
goto end; |
79 |
|
|
80 |
lambda = dp / GSL_MAX(2*fabs(dp/x), phi); |
lambda = dp / GSL_MAX (2 * fabs (dp / x), phi); |
81 |
|
|
82 |
{ |
{ |
83 |
double step0 = lambda; |
double step0 = lambda; |
84 |
double step1 = -((b-1)/x - 1)*lambda*lambda/4.0; |
double step1 = -((b - 1) / x - 1) * lambda * lambda / 4.0; |
85 |
|
|
86 |
double step = step0; |
double step = step0; |
87 |
if (fabs(step1) < fabs(step0)) |
if (fabs (step1) < fabs (step0)) |
88 |
step += step1; |
step += step1; |
89 |
|
|
90 |
if (x + step > 0) |
if (x + step > 0) |
91 |
x += step; |
x += step; |
92 |
else |
else |
93 |
{ |
{ |
94 |
x /= 2.0; |
x /= 2.0; |
95 |
} |
} |
96 |
|
|
97 |
if (fabs(step0) > 1e-10*x) |
if (fabs (step0) > 1e-10 * x) |
98 |
goto start; |
goto start; |
99 |
} |
} |
100 |
|
|
101 |
} |
} |
102 |
|
|
103 |
end: |
end: |
104 |
return a * x; |
return a * x; |
105 |
} |
} |
106 |
|
|
118 |
return GSL_POSINF; |
return GSL_POSINF; |
119 |
} |
} |
120 |
|
|
121 |
|
/* Consider, small, large and intermediate cases separately. The |
122 |
|
boundaries at 0.05 and 0.95 have not been optimised, but seem ok |
123 |
|
for an initial approximation. */ |
124 |
|
|
125 |
if (p < 0.05) |
if (p < 0.05) |
126 |
{ |
{ |
127 |
double x0 = -log(p) + lgamma(b); |
double x0 = -log (p) + lgamma (b); |
128 |
x = x0; |
x = x0; |
129 |
} |
} |
130 |
else if (p > 0.95) |
else if (p > 0.95) |
131 |
{ |
{ |
132 |
double x0 = exp((lgamma(b) + log1p(-p))/b); |
double x0 = exp ((lgamma (b) + log1p (-p)) / b); |
133 |
x = x0; |
x = x0; |
134 |
} |
} |
135 |
else |
else |
136 |
{ |
{ |
137 |
double xg = gsl_cdf_ugaussian_Qinv (p); |
double xg = gsl_cdf_ugaussian_Qinv (p); |
138 |
double x0 = (xg < -sqrt(b)) ? b : sqrt (b) * xg + b; |
double x0 = (xg < -sqrt (b)) ? b : sqrt (b) * xg + b; |
139 |
x = x0; |
x = x0; |
140 |
} |
} |
141 |
|
|
143 |
to an improved value of x (Abramowitz & Stegun, 3.6.6) |
to an improved value of x (Abramowitz & Stegun, 3.6.6) |
144 |
|
|
145 |
where E(x)=P-integ(phi(u),u,x0,x) and phi(u) is the pdf. |
where E(x)=P-integ(phi(u),u,x0,x) and phi(u) is the pdf. |
146 |
*/ |
*/ |
147 |
|
|
148 |
{ |
{ |
149 |
double lambda, dp, phi; |
double lambda, dp, phi; |
150 |
|
|
151 |
start: |
start: |
152 |
dp = -(p - gsl_cdf_gamma_Q (x, 1.0, b)) ; |
dp = -(p - gsl_cdf_gamma_Q (x, 1.0, b)); |
153 |
phi = gsl_ran_gamma_pdf (x, 1.0, b); |
phi = gsl_ran_gamma_pdf (x, 1.0, b); |
154 |
|
|
155 |
if (dp == 0.0) |
if (dp == 0.0) |
156 |
goto end; |
goto end; |
157 |
|
|
158 |
lambda = dp / GSL_MAX(2*fabs(dp/x), phi); |
lambda = dp / GSL_MAX (2 * fabs (dp / x), phi); |
159 |
|
|
160 |
{ |
{ |
161 |
double step0 = lambda; |
double step0 = lambda; |
162 |
double step1 = -((b-1)/x - 1)*lambda*lambda/4.0; |
double step1 = -((b - 1) / x - 1) * lambda * lambda / 4.0; |
163 |
|
|
164 |
double step = step0; |
double step = step0; |
165 |
if (fabs(step1) < fabs(step0)) |
if (fabs (step1) < fabs (step0)) |
166 |
step += step1; |
step += step1; |
167 |
|
|
168 |
if (x + step > 0) |
if (x + step > 0) |
169 |
x += step; |
x += step; |
170 |
else |
else |
171 |
{ |
{ |
172 |
x /= 2.0; |
x /= 2.0; |
173 |
} |
} |
174 |
|
|
175 |
if (fabs(step0) > 1e-10*x) |
if (fabs (step0) > 1e-10 * x) |
176 |
goto start; |
goto start; |
177 |
} |
} |
178 |
|
|
179 |
} |
} |
180 |
|
|
181 |
end: |
end: |
182 |
return a * x; |
return a * x; |
183 |
} |
} |