sre_math.c

hmmer源程序

/*****************************************************************
 * HMMER - Biological sequence analysis with profile HMMs
 * Copyright (C) 1992-1999 Washington University School of Medicine
 * All Rights Reserved
 * 
 *     This source code is distributed under the terms of the
 *     GNU General Public License. See the files COPYING and LICENSE
 *     for details.
 *****************************************************************/

/* sre_math.c
 * 
 * Portability for and extensions to C math library.
 * RCS $Id: sre_math.c,v 1.6 1999/09/17 20:15:10 eddy Exp $
 */

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include "squid.h"

#ifdef MEMDEBUG
#include "dbmalloc.h"
#endif

static int sre_reseed = 0;	/* TRUE to reinit sre_random() */
static int sre_randseed = 666;	/* default seed for sre_random()   */

/* Function: ExponentialRandom()
 * Date:     SRE, Mon Sep  6 21:24:29 1999 [St. Louis]
 *
 * Purpose:  Pick an exponentially distributed random variable
 *           0 > x >= infinity
 *           
 * Args:     (void)
 *
 * Returns:  x
 */
float
ExponentialRandom(void)
{
  float x;

  do x = sre_random(); while (x == 0.0);
  return -log(x);
}    

/* Function: Gaussrandom()
 * 
 * Pick a Gaussian-distributed random variable
 * with some mean and standard deviation, and
 * return it.
 * 
 * Based on RANLIB.c public domain implementation.
 * Thanks to the authors, Barry W. Brown and James Lovato,
 * University of Texas, M.D. Anderson Cancer Center, Houston TX.
 * Their implementation is from Ahrens and Dieter, "Extensions 
 * of Forsythe's method for random sampling from the normal
 * distribution", Math. Comput. 27:927-937 (1973).
 *
 * Impenetrability of the code is to be blamed on its FORTRAN/f2c lineage.
 * 
 */
float
Gaussrandom(float mean, float stddev)
{
  static float a[32] = {
    0.0,3.917609E-2,7.841241E-2,0.11777,0.1573107,0.1970991,0.2372021,0.2776904,    0.3186394,0.36013,0.4022501,0.4450965,0.4887764,0.5334097,0.5791322,
    0.626099,0.6744898,0.7245144,0.7764218,0.8305109,0.8871466,0.9467818,
    1.00999,1.077516,1.150349,1.229859,1.318011,1.417797,1.534121,1.67594,
    1.862732,2.153875
  };
  static float d[31] = {
    0.0,0.0,0.0,0.0,0.0,0.2636843,0.2425085,0.2255674,0.2116342,0.1999243,
    0.1899108,0.1812252,0.1736014,0.1668419,0.1607967,0.1553497,0.1504094,
    0.1459026,0.14177,0.1379632,0.1344418,0.1311722,0.128126,0.1252791,
    0.1226109,0.1201036,0.1177417,0.1155119,0.1134023,0.1114027,0.1095039
  };
  static float t[31] = {
    7.673828E-4,2.30687E-3,3.860618E-3,5.438454E-3,7.0507E-3,8.708396E-3,
    1.042357E-2,1.220953E-2,1.408125E-2,1.605579E-2,1.81529E-2,2.039573E-2,
    2.281177E-2,2.543407E-2,2.830296E-2,3.146822E-2,3.499233E-2,3.895483E-2,
    4.345878E-2,4.864035E-2,5.468334E-2,6.184222E-2,7.047983E-2,8.113195E-2,
    9.462444E-2,0.1123001,0.136498,0.1716886,0.2276241,0.330498,0.5847031
  };
  static float h[31] = {
    3.920617E-2,3.932705E-2,3.951E-2,3.975703E-2,4.007093E-2,4.045533E-2,
    4.091481E-2,4.145507E-2,4.208311E-2,4.280748E-2,4.363863E-2,4.458932E-2,
    4.567523E-2,4.691571E-2,4.833487E-2,4.996298E-2,5.183859E-2,5.401138E-2,
    5.654656E-2,5.95313E-2,6.308489E-2,6.737503E-2,7.264544E-2,7.926471E-2,
    8.781922E-2,9.930398E-2,0.11556,0.1404344,0.1836142,0.2790016,0.7010474
  };
  static long i;
  static float snorm,u,s,ustar,aa,w,y,tt;

  u = sre_random();
  s = 0.0;
  if(u > 0.5) s = 1.0;
  u += (u-s);
  u = 32.0*u;
  i = (long) (u);
  if(i == 32) i = 31;
  if(i == 0) goto S100;
  /*
   * START CENTER
   */
  ustar = u-(float)i;
  aa = *(a+i-1);
S40:
  if(ustar <= *(t+i-1)) goto S60;
  w = (ustar-*(t+i-1))**(h+i-1);
S50:
  /*
   * EXIT   (BOTH CASES)
   */
  y = aa+w;
  snorm = y;
  if(s == 1.0) snorm = -y;
  return (stddev*snorm + mean);
S60:
  /*
   * CENTER CONTINUED
   */
  u = sre_random();
  w = u*(*(a+i)-aa);
  tt = (0.5*w+aa)*w;
  goto S80;
S70:
  tt = u;
  ustar = sre_random();
S80:
  if(ustar > tt) goto S50;
  u = sre_random();
  if(ustar >= u) goto S70;
  ustar = sre_random();
  goto S40;
S100:
  /*
   * START TAIL
   */
  i = 6;
  aa = *(a+31);
  goto S120;
S110:
  aa += *(d+i-1);
  i += 1;
S120:
  u += u;
  if(u < 1.0) goto S110;
  u -= 1.0;
S140:
  w = u**(d+i-1);
  tt = (0.5*w+aa)*w;
  goto S160;
S150:
  tt = u;
S160:
  ustar = sre_random();
  if(ustar > tt) goto S50;
  u = sre_random();
  if(ustar >= u) goto S150;
  u = sre_random();
  goto S140;
}

  
/* Function: Linefit()
 * 
 * Purpose:  Given points x[0..N-1] and y[0..N-1], fit to
 *           a straight line y = a + bx.
 *           a, b, and the linear correlation coefficient r
 *           are filled in for return.
 *           
 * Args:     x     - x values of data
 *           y     - y values of data               
 *           N     - number of data points
 *           ret_a - RETURN: intercept
 *           ret_b - RETURN: slope
 *           ret_r - RETURN: correlation coefficient  
 *           
 * Return:   1 on success, 0 on failure.
 */
int          
Linefit(float *x, float *y, int N, float *ret_a, float *ret_b, float *ret_r) 
{				
  float xavg, yavg;
  float sxx, syy, sxy;
  int   i;
  
  /* Calculate averages, xavg and yavg
   */
  xavg = yavg = 0.0;
  for (i = 0; i < N; i++)
    {
      xavg += x[i];
      yavg += y[i];
    }
  xavg /= (float) N;
  yavg /= (float) N;

  sxx = syy = sxy = 0.0;
  for (i = 0; i < N; i++)
    {
      sxx    += (x[i] - xavg) * (x[i] - xavg);
      syy    += (y[i] - yavg) * (y[i] - xavg);
      sxy    += (x[i] - xavg) * (y[i] - yavg);
    }
  *ret_b = sxy / sxx;
  *ret_a = yavg - xavg*(*ret_b);
  *ret_r = sxy / (sqrt(sxx) * sqrt(syy));
  return 1;
}


/* Function: WeightedLinefit()
 * 
 * Purpose:  Given points x[0..N-1] and y[0..N-1] with
 *           variances (measurement errors) var[0..N-1],  
 *           fit to a straight line y = mx + b.
 *           
 * Method:   Algorithm from Numerical Recipes in C, [Press88].
 *           
 * Return:   (void)
 *           ret_m contains slope; ret_b contains intercept 
 */                
void
WeightedLinefit(float *x, float *y, float *var, int N, float *ret_m, float *ret_b) 
{
  int    i;
  double s;
  double sx, sy;
  double sxx, sxy;
  double delta;
  double m, b;
  
  s = sx = sy = sxx = sxy = 0.;
  for (i = 0; i < N; i++)
    {
      s   += 1./var[i];
      sx  += x[i] / var[i];
      sy  += y[i] / var[i];
      sxx += x[i] * x[i] / var[i];
      sxy += x[i] * y[i] / var[i];
    }

  delta = s * sxx - (sx * sx);
  b = (sxx * sy - sx * sxy) / delta;
  m = (s * sxy - sx * sy) / delta;

  *ret_m = m;
  *ret_b = b;
}
  

/* Function: Gammln()
 *
 * Returns the natural log of the gamma function of x.
 * x is > 0.0.  
 *
 * Adapted from a public domain implementation in the
 * NCBI core math library. Thanks to John Spouge and
 * the NCBI. (According to the NCBI, that's Dr. John
 * "Gammas Galore" Spouge to you, pal.)
 */
double
Gammln(double x)
{
  int i;
  double xx, tx;
  double tmp, value;
  static double cof[11] = {
    4.694580336184385e+04,
    -1.560605207784446e+05,
    2.065049568014106e+05,
    -1.388934775095388e+05,
    5.031796415085709e+04,
    -9.601592329182778e+03,
    8.785855930895250e+02,
    -3.155153906098611e+01,
    2.908143421162229e-01,
    -2.319827630494973e-04,
    1.251639670050933e-10
  };
  
  /* Protect against x=0. We see this in Dirichlet code,
   * for terms alpha = 0. This is a severe hack but it is effective
   * and (we think?) safe. (due to GJM)
   */ 
  if (x <= 0.0) return 999999.; 

  xx       = x - 1.0;
  tx = tmp = xx + 11.0;
  value    = 1.0;
  for (i = 10; i >= 0; i--)	/* sum least significant terms first */
    {
      value += cof[i] / tmp;
      tmp   -= 1.0;
    }
  value  = log(value);
  tx    += 0.5;
  value += 0.918938533 + (xx+0.5)*log(tx) - tx;
  return value;
}


/* Vector operations for doubles and floats.
 * DNorm(), FNorm()   -- normalize a probability vector of length n.
 *                       return 0 if all values were zero.
 * DScale(), FScale() -- multiply all items in vector by scale
 * DSet(), FSet()     -- set all items in vector to value.
 * DAdd(), FAdd()     -- add vec2 to vec1.
 * DDot(), FDot()     -- calculate dot product of two vectors.
 * DCopy(), FCopy()   -- set vec1 to be same as vec2. 
 * DMax(), FMax()     -- return index of maximum element in vec 
 */                      
int
DNorm(double *vec, int n)
{
  int    x;
  double sum;

  sum = 0.0;
  for (x = 0; x < n; x++) sum += vec[x];
  if (sum != 0.0)
    for (x = 0; x < n; x++) vec[x] /= sum;
  else
    { squid_errno = SQERR_DIVZERO; return 0; }
  return 1;
}
int
FNorm(float *vec, int n)
{
  int    x;
  float  sum;

  sum = 0.0;
  for (x = 0; x < n; x++) sum += vec[x];
  if (sum != 0.0)
    for (x = 0; x < n; x++) vec[x] /= sum;
  else
    { squid_errno = SQERR_DIVZERO; return 0; }
  return 1;
}
  
void
DScale(double *vec, int n, double scale)
{
  int x;
  for (x = 0; x < n; x++)
    vec[x] *= scale;
}
void
FScale(float *vec, int n, float scale)
{
  int x;
  for (x = 0; x < n; x++)
    vec[x] *= scale;
}

void
DSet(double *vec, int n, double value)
{
  int x; 
  for (x = 0; x < n; x++)
    vec[x] = value;
}
void
FSet(float *vec, int n, float value)
{
  int x; 
  for (x = 0; x < n; x++)
    vec[x] = value;
}

double 
DSum(double *vec, int n)
{
  double sum = 0.;
  int    x;
  for (x = 0; x < n; x++)
    sum += vec[x];
  return sum;
}
float 
FSum(float *vec, int n)
{
  float sum = 0.;
  int   x;
  for (x = 0; x < n; x++)
    sum += vec[x];
  return sum;
}

void