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#include "misc.h"
#include <math.h>
#include <stdlib.h> /* for size_t */
double kahan_sum(double *x, size_t n)
{
/* Returns the sum of the elements of `x` using the Kahan summation algorithm.
*
* See https://en.wikipedia.org/wiki/Kahan_summation_algorithm. */
size_t i;
double sum, c, y, t;
sum = 0.0;
c = 0.0;
for (i = 0; i < n; i++) {
y = x[i] - c;
t = sum + y;
c = (t - sum) - y;
sum = t;
}
return sum;
}
double interp1d(double x, double *xp, double *yp, size_t n)
{
/* A fast interpolation routine which assumes that the values in `xp` are
* evenly spaced.
*
* If x < xp[0] returns yp[0] and if x > xp[n-1] returns yp[n-1]. */
size_t i;
if (x < xp[0]) return yp[0];
if (x > xp[n-1]) return yp[n-1];
i = (x-xp[0])/(xp[1]-xp[0]);
return yp[i] + (yp[i+1]-yp[i])*(x-xp[i])/(xp[i+1]-xp[i]);
}
int isclose(double a, double b, double rel_tol, double abs_tol)
{
/* Returns 1 if a and b are "close". This algorithm is taken from Python's
* math.isclose() function.
*
* See https://www.python.org/dev/peps/pep-0485/. */
return fabs(a-b) <= fmax(rel_tol*fmax(fabs(a),fabs(b)),abs_tol);
}
int allclose(double *a, double *b, size_t n, double rel_tol, double abs_tol)
{
/* Returns 1 if all the elements of a and b are "close". This algorithm is
* taken from Python's math.isclose() function.
*
* See https://www.python.org/dev/peps/pep-0485/. */
size_t i;
for (i = 0; i < n; i++) {
if (!isclose(a[i],b[i],rel_tol,abs_tol)) return 0;
}
return 1;
}
double logsumexp(double *a, size_t n)
{
/* Returns the log of the sum of the exponentials of the array `a`.
*
* This function is designed to reduce underflow when the exponentials of
* `a` are very small, for example when computing probabilities. */
size_t i;
double amax, sum;
amax = a[0];
for (i = 0; i < n; i++) {
if (a[i] > amax) amax = a[i];
}
sum = 0.0;
for (i = 0; i < n; i++) {
sum += exp(a[i]-amax);
}
sum = log(sum);
return amax + sum;
}
double norm(double x, double mu, double sigma)
{
/* Returns the PDF for a gaussian random variable with mean `mu` and
* standard deviation `sigma`. */
return exp(-pow(x-mu,2)/(2*pow(sigma,2)))/(sqrt(2*M_PI)*sigma);
}
double norm_cdf(double x, double mu, double sigma)
{
/* Returns the CDF for a gaussian random variable with mean `mu` and
* standard deviation `sigma`. */
return erfc(-(x-mu)/(sqrt(2)*sigma))/2.0;
}
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