readd inverse cdf for raw floats. rework examples.
This commit is contained in:
parent
e05baa6fee
commit
487de4a731
Binary file not shown.
|
|
@ -4,6 +4,7 @@
|
|||
#include <stdint.h>
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include <sys/types.h>
|
||||
#include <time.h>
|
||||
|
||||
#define EXIT_ON_ERROR 0
|
||||
|
|
@ -20,6 +21,7 @@
|
|||
return error; \
|
||||
} \
|
||||
} while (0)
|
||||
#define NUM_SAMPLES 10
|
||||
|
||||
struct box {
|
||||
int empty;
|
||||
|
|
@ -41,7 +43,6 @@ float cdf_uniform_0_1(float x)
|
|||
|
||||
float cdf_squared_0_1(float x)
|
||||
{
|
||||
float result;
|
||||
if (x < 0) {
|
||||
return 0;
|
||||
} else if (x > 1) {
|
||||
|
|
@ -174,7 +175,76 @@ struct box cdf_beta(float x)
|
|||
}
|
||||
|
||||
// Inverse cdf at point
|
||||
struct box inverse_cdf(struct box cdf_box(float), float p)
|
||||
// Two versions of this function:
|
||||
// - raw, dealing with cdfs that return floats
|
||||
// - box, dealing with cdfs that return a box.
|
||||
|
||||
// Inverse cdf
|
||||
struct box inverse_cdf_float(float cdf(float), float 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
|
||||
|
||||
float low = -1.0;
|
||||
float 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) {
|
||||
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))) {
|
||||
float mid = (high + low) / 2;
|
||||
int mid_not_new = (mid == low) || (mid == high);
|
||||
// float width = high - low;
|
||||
// if ((width < 1e-8) || mid_not_new){
|
||||
if (mid_not_new) {
|
||||
convergence_condition = 1;
|
||||
} else {
|
||||
float 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 {
|
||||
PROCESS_ERROR("Search process did not converge, in function inverse_cdf");
|
||||
}
|
||||
|
||||
}
|
||||
}
|
||||
|
||||
struct box inverse_cdf_box(struct box cdf_box(float), float p)
|
||||
{
|
||||
// given a cdf: [-Inf, Inf] => Box([0,1])
|
||||
// returns a box with either
|
||||
|
|
@ -277,10 +347,16 @@ float rand_0_to_1(uint32_t* seed)
|
|||
}
|
||||
|
||||
// Sampler based on inverse cdf and randomness function
|
||||
struct box sampler(struct box cdf(float), uint32_t* seed)
|
||||
struct box sampler_box_cdf(struct box cdf(float), uint32_t* seed)
|
||||
{
|
||||
float p = rand_0_to_1(seed);
|
||||
struct box result = inverse_cdf(cdf, p);
|
||||
struct box result = inverse_cdf_box(cdf, p);
|
||||
return result;
|
||||
}
|
||||
struct box sampler_float_cdf(float cdf(float), uint32_t* seed)
|
||||
{
|
||||
float p = rand_0_to_1(seed);
|
||||
struct box result = inverse_cdf_float(cdf, p);
|
||||
return result;
|
||||
}
|
||||
|
||||
|
|
@ -294,83 +370,97 @@ float sampler_normal_0_1(uint32_t* seed)
|
|||
return z;
|
||||
}
|
||||
|
||||
int main()
|
||||
{
|
||||
|
||||
// Get the inverse cdf of a [0,1] uniform distribution at 0.5
|
||||
struct box result_1 = inverse_cdf(cdf_uniform_0_1, 0.5);
|
||||
char* name_1 = "cdf_uniform_0_1";
|
||||
if (result_1.empty) {
|
||||
printf("Inverse for %s not calculated\n", name_1);
|
||||
// Some testers
|
||||
void test_inverse_cdf_float(char* cdf_name, float cdf_float(float)){
|
||||
struct box result = inverse_cdf_float(cdf_float, 0.5);
|
||||
if (result.empty) {
|
||||
printf("Inverse for %s not calculated\n", cdf_name);
|
||||
exit(1);
|
||||
} else {
|
||||
printf("Inverse of %s at %f is: %f\n", name_1, 0.5, result_1.content);
|
||||
printf("Inverse of %s at %f is: %f\n", cdf_name, 0.5, result.content);
|
||||
}
|
||||
|
||||
// Get the inverse cdf of a [0,1] squared distribution at 0.5
|
||||
struct box result_2 = inverse_cdf(cdf_squared_0_1, 0.5);
|
||||
char* name_2 = "cdf_squared_0_1";
|
||||
if (result_2.empty) {
|
||||
printf("Inverse for %s not calculated\n", name_2);
|
||||
}
|
||||
void test_inverse_cdf_box(char* cdf_name, struct box cdf_box(float)){
|
||||
struct box result = inverse_cdf_box(cdf_box, 0.5);
|
||||
if (result.empty) {
|
||||
printf("Inverse for %s not calculated\n", cdf_name);
|
||||
exit(1);
|
||||
} else {
|
||||
printf("Inverse of %s at %f is: %f\n", name_2, 0.5, result_2.content);
|
||||
printf("Inverse of %s at %f is: %f\n", cdf_name, 0.5, result.content);
|
||||
}
|
||||
|
||||
// Get the inverse of a normal(0,1) cdf distribution
|
||||
struct box result_3 = inverse_cdf(cdf_normal_0_1, 0.5);
|
||||
char* name_3 = "cdf_normal_0_1";
|
||||
if (result_3.empty) {
|
||||
printf("Inverse for %s not calculated\n", name_3);
|
||||
exit(1);
|
||||
} else {
|
||||
printf("Inverse of %s at %f is: %f\n", name_3, 0.5, result_3.content);
|
||||
}
|
||||
|
||||
// Use the sampler on a normal(0,1)
|
||||
// set randomness seed
|
||||
uint32_t* seed = malloc(sizeof(uint32_t));
|
||||
*seed = 1000; // xorshift can't start with 0
|
||||
int n = 100;
|
||||
|
||||
printf("\n\nGetting some samples from %s:\n", name_3);
|
||||
void test_and_time_sampler_float(char* cdf_name, float cdf_float(float), uint32_t* seed){
|
||||
printf("\nGetting some samples from %s:\n", cdf_name);
|
||||
clock_t begin = clock();
|
||||
for (int i = 0; i < n; i++) {
|
||||
struct box sample = sampler(cdf_normal_0_1, seed);
|
||||
for (int i = 0; i < NUM_SAMPLES; i++) {
|
||||
struct box sample = sampler_float_cdf(cdf_float, seed);
|
||||
if (sample.empty) {
|
||||
printf("Error in sampler function");
|
||||
printf("Error in sampler function for %s", cdf_name);
|
||||
} else {
|
||||
printf("%f\n", sample.content);
|
||||
}
|
||||
}
|
||||
clock_t end = clock();
|
||||
float time_spent = (float)(end - begin) / CLOCKS_PER_SEC;
|
||||
printf("Time spent: %f", time_spent);
|
||||
|
||||
// Get some normal samples using the previous method.
|
||||
clock_t begin_2 = clock();
|
||||
printf("\n\nGetting some samples from sampler_normal_0_1\n");
|
||||
for (int i = 0; i < n; i++) {
|
||||
float normal_sample = sampler_normal_0_1(seed);
|
||||
printf("%f\n", normal_sample);
|
||||
printf("Time spent: %f\n", time_spent);
|
||||
}
|
||||
clock_t end_2 = clock();
|
||||
float time_spent_2 = (float)(end_2 - begin_2) / CLOCKS_PER_SEC;
|
||||
printf("Time spent: %f", time_spent_2);
|
||||
|
||||
// Get some beta samples
|
||||
clock_t begin_3 = clock();
|
||||
printf("\n\nGetting some samples from box sampler_dangerous_beta\n");
|
||||
for (int i = 0; i < n; i++) {
|
||||
struct box sample = sampler(cdf_dangerous_beta, seed);
|
||||
void test_and_time_sampler_box(char* cdf_name, struct box cdf_box(float), uint32_t* seed){
|
||||
printf("\nGetting some samples from %s:\n", cdf_name);
|
||||
clock_t begin = clock();
|
||||
for (int i = 0; i < NUM_SAMPLES; i++) {
|
||||
struct box sample = sampler_box_cdf(cdf_box, seed);
|
||||
if (sample.empty) {
|
||||
printf("Error in sampler function");
|
||||
printf("Error in sampler function for %s", cdf_name);
|
||||
} else {
|
||||
printf("%f\n", sample.content);
|
||||
}
|
||||
}
|
||||
clock_t end_3 = clock();
|
||||
float time_spent_3 = (float)(end_3 - begin_3) / CLOCKS_PER_SEC;
|
||||
printf("Time spent: %f\n", time_spent_3);
|
||||
clock_t end = clock();
|
||||
float time_spent = (float)(end - begin) / CLOCKS_PER_SEC;
|
||||
printf("Time spent: %f\n", time_spent);
|
||||
}
|
||||
|
||||
int main()
|
||||
{
|
||||
// Test inverse cdf float
|
||||
test_inverse_cdf_float("cdf_uniform_0_1", cdf_uniform_0_1);
|
||||
test_inverse_cdf_float("cdf_squared_0_1", cdf_squared_0_1);
|
||||
test_inverse_cdf_float("cdf_normal_0_1", cdf_normal_0_1);
|
||||
|
||||
// Test inverse cdf box
|
||||
test_inverse_cdf_box("cdf_beta", cdf_beta);
|
||||
|
||||
// Testing samplers
|
||||
// set randomness seed
|
||||
uint32_t* seed = malloc(sizeof(uint32_t));
|
||||
*seed = 1000; // xorshift can't start with 0
|
||||
|
||||
// Test float sampler
|
||||
test_and_time_sampler_float("cdf_uniform_0_1", cdf_uniform_0_1, seed);
|
||||
test_and_time_sampler_float("cdf_squared_0_1", cdf_squared_0_1, seed);
|
||||
test_and_time_sampler_float("cdf_normal_0_1", cdf_normal_0_1, seed);
|
||||
|
||||
// Get some normal samples using a previous approach
|
||||
printf("\nGetting some samples from sampler_normal_0_1\n");
|
||||
|
||||
clock_t begin_2 = clock();
|
||||
|
||||
for (int i = 0; i < NUM_SAMPLES; i++) {
|
||||
float normal_sample = sampler_normal_0_1(seed);
|
||||
printf("%f\n", normal_sample);
|
||||
}
|
||||
|
||||
clock_t end_2 = clock();
|
||||
float time_spent_2 = (float)(end_2 - begin_2) / CLOCKS_PER_SEC;
|
||||
printf("Time spent: %f\n", time_spent_2);
|
||||
|
||||
// Test box sampler
|
||||
test_and_time_sampler_box("cdf_beta", cdf_beta, seed);
|
||||
|
||||
free(seed);
|
||||
return 0;
|
||||
}
|
||||
|
|
|
|||
Loading…
Reference in New Issue
Block a user