squiggle.c/extra.c

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C
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2023-11-18 20:25:12 +00:00
#include <float.h>
#include <limits.h>
#include <math.h>
#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>
#include <sys/types.h>
#include <time.h>
// Some error niceties; these won't be used until later
#define MAX_ERROR_LENGTH 500
#define EXIT_ON_ERROR 0
#define PROCESS_ERROR(error_msg) process_error(error_msg, EXIT_ON_ERROR, __FILE__, __LINE__)
// # More cool stuff
// This is no longer necessary to do basic estimation,
// but is still cool
// ## Sample from an arbitrary cdf
struct box {
int empty;
double content;
char* error_msg;
};
struct box process_error(const char* error_msg, int should_exit, char* file, int line)
{
if (should_exit) {
printf("@, in %s (%d)", file, line);
exit(1);
} else {
char error_msg[MAX_ERROR_LENGTH];
snprintf(error_msg, MAX_ERROR_LENGTH, "@, in %s (%d)", file, line); // NOLINT: We are being carefull here by considering MAX_ERROR_LENGTH explicitly.
struct box error = { .empty = 1, .error_msg = error_msg };
return error;
}
}
// Inverse cdf at point
// Two versions of this function:
// - raw, dealing with cdfs that return doubles
// - input: cdf: double => double, p
// - output: Box(number|error)
// - box, dealing with cdfs that return a box.
// - input: cdf: double => Box(number|error), p
// - output: Box(number|error)
struct box inverse_cdf_double(double cdf(double), double p)
{
// given a cdf: [-Inf, Inf] => [0,1]
// returns a box with either
// x such that cdf(x) = p
// or an error
// if EXIT_ON_ERROR is set to 1, it exits instead of providing an error
double low = -1.0;
double high = 1.0;
// 1. Make sure that cdf(low) < p < cdf(high)
int interval_found = 0;
while ((!interval_found) && (low > -FLT_MAX / 4) && (high < FLT_MAX / 4)) {
// ^ Using FLT_MIN and FLT_MAX is overkill
// but it's also the *correct* thing to do.
int low_condition = (cdf(low) < p);
int high_condition = (p < cdf(high));
if (low_condition && high_condition) {
interval_found = 1;
} else if (!low_condition) {
low = low * 2;
} else if (!high_condition) {
high = high * 2;
}
}
if (!interval_found) {
return PROCESS_ERROR("Interval containing the target value not found, in function inverse_cdf");
} else {
int convergence_condition = 0;
int count = 0;
while (!convergence_condition && (count < (INT_MAX / 2))) {
double mid = (high + low) / 2;
int mid_not_new = (mid == low) || (mid == high);
// double width = high - low;
// if ((width < 1e-8) || mid_not_new){
if (mid_not_new) {
convergence_condition = 1;
} else {
double mid_sign = cdf(mid) - p;
if (mid_sign < 0) {
low = mid;
} else if (mid_sign > 0) {
high = mid;
} else if (mid_sign == 0) {
low = mid;
high = mid;
}
}
}
if (convergence_condition) {
struct box result = { .empty = 0, .content = low };
return result;
} else {
return PROCESS_ERROR("Search process did not converge, in function inverse_cdf");
}
}
}
struct box inverse_cdf_box(struct box cdf_box(double), double p)
{
// given a cdf: [-Inf, Inf] => Box([0,1])
// returns a box with either
// x such that cdf(x) = p
// or an error
// if EXIT_ON_ERROR is set to 1, it exits instead of providing an error
double low = -1.0;
double high = 1.0;
// 1. Make sure that cdf(low) < p < cdf(high)
int interval_found = 0;
while ((!interval_found) && (low > -FLT_MAX / 4) && (high < FLT_MAX / 4)) {
// ^ Using FLT_MIN and FLT_MAX is overkill
// but it's also the *correct* thing to do.
struct box cdf_low = cdf_box(low);
if (cdf_low.empty) {
return PROCESS_ERROR(cdf_low.error_msg);
}
struct box cdf_high = cdf_box(high);
if (cdf_high.empty) {
return PROCESS_ERROR(cdf_low.error_msg);
}
int low_condition = (cdf_low.content < p);
int high_condition = (p < cdf_high.content);
if (low_condition && high_condition) {
interval_found = 1;
} else if (!low_condition) {
low = low * 2;
} else if (!high_condition) {
high = high * 2;
}
}
if (!interval_found) {
return PROCESS_ERROR("Interval containing the target value not found, in function inverse_cdf");
} else {
int convergence_condition = 0;
int count = 0;
while (!convergence_condition && (count < (INT_MAX / 2))) {
double mid = (high + low) / 2;
int mid_not_new = (mid == low) || (mid == high);
// double width = high - low;
if (mid_not_new) {
// if ((width < 1e-8) || mid_not_new){
convergence_condition = 1;
} else {
struct box cdf_mid = cdf_box(mid);
if (cdf_mid.empty) {
return PROCESS_ERROR(cdf_mid.error_msg);
}
double mid_sign = cdf_mid.content - p;
if (mid_sign < 0) {
low = mid;
} else if (mid_sign > 0) {
high = mid;
} else if (mid_sign == 0) {
low = mid;
high = mid;
}
}
}
if (convergence_condition) {
struct box result = { .empty = 0, .content = low };
return result;
} else {
return PROCESS_ERROR("Search process did not converge, in function inverse_cdf");
}
}
}
// Sampler based on inverse cdf and randomness function
struct box sampler_cdf_box(struct box cdf(double), uint64_t* seed)
{
double p = sample_unit_uniform(seed);
struct box result = inverse_cdf_box(cdf, p);
return result;
}
struct box sampler_cdf_double(double cdf(double), uint64_t* seed)
{
double p = sample_unit_uniform(seed);
struct box result = inverse_cdf_double(cdf, p);
return result;
}
/* Could also define other variations, e.g.,
double sampler_danger(struct box cdf(double), uint64_t* seed)
{
double p = sample_unit_uniform(seed);
struct box result = inverse_cdf_box(cdf, p);
if(result.empty){
exit(1);
}else{
return result.content;
}
}
*/
// Get confidence intervals, given a sampler
typedef struct ci_t {
float low;
float high;
} ci;
int compare_doubles(const void* p, const void* q)
{
// https://wikiless.esmailelbob.xyz/wiki/Qsort?lang=en
double x = *(const double*)p;
double y = *(const double*)q;
/* Avoid return x - y, which can cause undefined behaviour
because of signed integer overflow. */
if (x < y)
return -1; // Return -1 if you want ascending, 1 if you want descending order.
else if (x > y)
return 1; // Return 1 if you want ascending, -1 if you want descending order.
return 0;
}
ci get_90_confidence_interval(double (*sampler)(uint64_t*), uint64_t* seed)
{
int n = 100 * 1000;
double* samples_array = malloc(n * sizeof(double));
for (int i = 0; i < n; i++) {
samples_array[i] = sampler(seed);
}
qsort(samples_array, n, sizeof(double), compare_doubles);
ci result = {
.low = samples_array[5000],
.high = samples_array[94999],
};
free(samples_array);
return result;
}
// # Small algebra manipulations
// here I discover named structs,
// which mean that I don't have to be typing
// struct blah all the time.
typedef struct normal_params_t {
double mean;
double std;
} normal_params;
normal_params algebra_sum_normals(normal_params a, normal_params b)
{
normal_params result = {
.mean = a.mean + b.mean,
.std = sqrt((a.std * a.std) + (b.std * b.std)),
};
return result;
}
typedef struct lognormal_params_t {
double logmean;
double logstd;
} lognormal_params;
lognormal_params algebra_product_lognormals(lognormal_params a, lognormal_params b)
{
lognormal_params result = {
.logmean = a.logmean + b.logmean,
.logstd = sqrt((a.logstd * a.logstd) + (b.logstd * b.logstd)),
};
return result;
}
lognormal_params convert_ci_to_lognormal_params(ci x)
{
double loghigh = logf(x.high);
double loglow = logf(x.low);
double logmean = (loghigh + loglow) / 2.0;
double logstd = (loghigh - loglow) / (2.0 * NORMAL90CONFIDENCE);
lognormal_params result = { .logmean = logmean, .logstd = logstd };
return result;
}
ci convert_lognormal_params_to_ci(lognormal_params y)
{
double h = y.logstd * NORMAL90CONFIDENCE;
double loghigh = y.logmean + h;
double loglow = y.logmean - h;
ci result = { .low = exp(loglow), .high = exp(loghigh) };
return result;
}