/[gsl]/gsl/cdf/inverse_normal.c
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revision 1.1.2.2 by bjg, Sat Mar 1 20:29:21 2003 UTC revision 1.1.2.3 by bjg, Sat Mar 8 22:26:19 2003 UTC
# Line 1  Line 1 
1  /* cdf/inverse_normal.c  /* cdf/inverse_normal.c
2   *   *
3   * Copyright (C) 2002 Przemyslaw Sliwa and Jason H. Stover.   * Copyright (C) 2002 Przemyslaw Sliwa and Jason H. Stover.
4   *   *
5   * This program is free software; you can redistribute it and/or modify   * This program is free software; you can redistribute it and/or modify
6   * it under the terms of the GNU General Public License as published by   * it under the terms of the GNU General Public License as published by
7   * the Free Software Foundation; either version 2 of the License, or (at   * the Free Software Foundation; either version 2 of the License, or (at
8   * your option) any later version.   * your option) any later version.
9   *   *
10   * This program is distributed in the hope that it will be useful, but   * This program is distributed in the hope that it will be useful, but
11   * WITHOUT ANY WARRANTY; without even the implied warranty of   * WITHOUT ANY WARRANTY; without even the implied warranty of
12   * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU   * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
13   * General Public License for more details.   * General Public License for more details.
14   *   *
15   * You should have received a copy of the GNU General Public License   * You should have received a copy of the GNU General Public License
16   * along with this program; if not, write to the Free Software   * along with this program; if not, write to the Free Software
17   * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307, USA.   * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307, USA.
18   */   */
19    
20  /*  /*
21   * Computes the inverse normal cumulative distribution function   * Computes the inverse normal cumulative distribution function
22   * according to the algorithm shown in   * according to the algorithm shown in
23   *   *
24   *      Wichura, M.J. (1988).   *      Wichura, M.J. (1988).
25   *      Algorithm AS 241: The Percentage Points of the Normal Distribution.   *      Algorithm AS 241: The Percentage Points of the Normal Distribution.
26   *      Applied Statistics, 37, 477-484.   *      Applied Statistics, 37, 477-484.
27   */   */
28    
29  #include <config.h>  #include <config.h>
30  #include <gsl/gsl_errno.h>  #include <gsl/gsl_errno.h>
31  #include <gsl/gsl_math.h>  #include <gsl/gsl_math.h>
32  #include <gsl/gsl_cdf.h>  #include <gsl/gsl_cdf.h>
33  #include <gsl/gsl_cdf_result.h>  
34  #include "error.h"  #include "rat_eval.h"
35    
36  int gsl_cdf_inv_normal_e(double p, gsl_cdf_result * result)      double
37  {  gsl_cdf_ugaussian_P_inv (double p)
38    double q, r, ret_val;  {
39      double r, x;
40    q = p - .5;  
41    if (fabs (q) <= .425)    double q = p - 0.5;
42      {  
43        r = .180625 - q * q;    if (fabs (q) <= 0.425)
44        ret_val = q * (((((((r * 2509.0809287301226727 +      {
45                             33430.575583588128105) * r +        const double a[8] = { 3.387132872796366608, 133.14166789178437745,
46                            67265.770927008700853) * r +          1971.5909503065514427, 13731.693765509461125,
47                           45921.953931549871457) * r +          45921.953931549871457, 67265.770927008700853,
48                          13731.693765509461125) * r +          33430.575583588128105, 2509.0809287301226727
49                         1971.5909503065514427) * r +        };
50                        133.14166789178437745) * r +  
51                       3.387132872796366608) /        const double b[8] = { 1.0, 42.313330701600911252,
52          (((((((r          687.1870074920579083, 5394.1960214247511077,
53                 * 5226.495278852854561 + 28729.085735721942674) * r +          21213.794301586595867, 39307.89580009271061,
54                39307.89580009271061) * r + 21213.794301586595867) * r +          28729.085735721942674, 5226.495278852854561
55              5394.1960214247511077) * r + 687.1870074920579083) * r +        };
56            42.313330701600911252) * r + 1.);  
57        result->val = ret_val;        r = 0.180625 - q * q;
58        return GSL_SUCCESS;        
59      }        x = q * rat_eval (a, 8, b, 8, r);
60      
61    else        return x;
62      {      }
63        if (q < 0.)  
64          {    if (q < 0.0)
65            r = p;      {
66          }        r = p;
67        else      }
68          {    else
69            r = 1.0 - p;      {
70          }        r = 1.0 - p;
71        if (r <= 0.0)      }
72          {  
73            DOMAIN_ERROR(result);    r = sqrt (-log (r));
74          }  
75        r = sqrt (-log(r));    if (r <= 5.0)
76        if (r <= 5.0)      {
77          {        const double a[] = { 1.42343711074968357734, 4.6303378461565452959,
78            r += -1.6;          5.7694972214606914055, 3.64784832476320460504,
79            ret_val = (((((((r * 7.7454501427834140764e-4 +          1.27045825245236838258, 0.24178072517745061177,
80                             .0227238449892691845833) * r +          0.0227238449892691845833, 7.7454501427834140764e-4
81                            .24178072517745061177) * r +        };
82                           1.27045825245236838258) * r +  
83                          3.64784832476320460504) * r +        const double b[] = { 1.0, 2.05319162663775882187,
84                         5.7694972214606914055) * r +          1.6763848301838038494, 0.68976733498510000455,
85                        4.6303378461565452959) * r +          0.14810397642748007459, 0.0151986665636164571966,
86                       1.42343711074968357734) /          5.475938084995344946e-4, 1.05075007164441684324e-9
87              (((((((r        };
88                     * 1.05075007164441684324e-9 +  
89                     5.475938084995344946e-4) * r +        x = rat_eval (a, 8, b, 8, (r - 1.6));
90                    .0151986665636164571966) * r +      }
91                   .14810397642748007459) * r + .68976733498510000455) * r +    else
92                 1.6763848301838038494) * r + 2.05319162663775882187) * r +      {
93               1.0);        const double a[] = { 6.6579046435011037772, 5.4637849111641143699,
94          }          1.7848265399172913358, 0.29656057182850489123,
95        else          0.026532189526576123093, 0.0012426609473880784386,
96          {          2.71155556874348757815e-5, 2.01033439929228813265e-7
97            r += -5.0;        };
98            ret_val = (((((((r * 2.01033439929228813265e-7 +  
99                             2.71155556874348757815e-5) * r +        const double b[] = { 1.0, 0.59983220655588793769,
100                            .0012426609473880784386) * r +          0.13692988092273580531, 0.0148753612908506148525,
101                           .026532189526576123093) * r +          7.868691311456132591e-4, 1.8463183175100546818e-5,
102                          .29656057182850489123) * r +          1.4215117583164458887e-7, 2.04426310338993978564e-15
103                         1.7848265399172913358) * r +        };
104                        5.4637849111641143699) * r +  
105                       6.6579046435011037772) /        x = rat_eval (a, 8, b, 8, (r - 5.0));
106              (((((((r      }
107                     * 2.04426310338993978564e-15 +  
108                     1.4215117583164458887e-7) * r +    if (q < 0.0)
109                    1.8463183175100546818e-5) * r +      {
110                   7.868691311456132591e-4) * r +        return -x;
111                  .0148753612908506148525) * r +      }
112                 .13692988092273580531) * r + .59983220655588793769) * r +    else
113               1.0);      {
114          }        return x;
115        if (q < 0.0)      }
116          {  
117            ret_val = -ret_val;  }
118          }  
119        result->val = ret_val;  double
120        return GSL_SUCCESS;  gsl_cdf_ugaussian_Q_inv (double p)
121      }  {
122    result->val = ret_val;    return gsl_cdf_ugaussian_P_inv (1.0 - p);
123    return GSL_SUCCESS;  }
     
 }  
 /*  
  * No error code.  
  */  
 #include "eval.h"  
   
 double gsl_cdf_inv_normal ( double p )  
 {  
   EVAL_RESULT ( gsl_cdf_inv_normal_e ( p, &result));  
 }  
   
 /* int main(void) */  
   
 /*   { */  
   
 /*   double quantile, p; */  
 /*   int ifail; */  
   
 /*   for(p=1.0E-15; p<1.0; p+=1.0E-5) */  
 /*      { */  
 /*     quantile = gsl_normal_quantile(p, &ifail); */  
 /*     printf("VALUE: %.19f\tIFAIL %d\n", quantile, ifail); */  
 /*     } */  
   
 /*   return 0; */  
   
 /*   } */  

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