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simulation.c
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simulation.c
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/**
* Algorithm for PPG signal reconstruction from compressively sampled input.
*/
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <stdbool.h>
#include <time.h>
#include "setup.h"
double max(double a, double b) {
return (a > b ? a : b) ;
}
// TODO: implement fast DCT so this isn't needed.
void dct_1D(double *X, size_t N, double *X_DCT) {
memset(X_DCT, 0, sizeof(double) * N);
const double factor_1 = 2.0 / sqrt(N);
const double factor_0 = factor_1 / sqrt(2);
for (size_t k = 0; k < N; ++k) {
for (size_t n = 0; n < N; ++n) {
X_DCT[k] += cos((M_PI / N) * (n + 0.5) * k) * X[n];
}
}
X_DCT[0] *= factor_0;
for (size_t k = 1; k < N; ++k) {
X_DCT[k] *= factor_1;
}
}
void idct_1D(double *X_DCT, size_t N, double *X) {
memset(X, 0, sizeof(double) * N);
const double factor_1 = 2.0 / sqrt(N);
const double factor_0 = factor_1 / sqrt(2);
for (size_t n = 0; n < N; ++n) {
X[n] += X_DCT[0] * factor_0;
}
for (size_t k = 1; k < N; ++k) {
for (size_t n = 0; n < N; ++n) {
X[n] += cos((M_PI / N) * (n + 0.5) * k) * X_DCT[k] * factor_1;
}
}
}
void random_sample_idct_1D(double *X_DCT, size_t N, bool *phi_flags, size_t M, double *Y) {
memset(Y, 0, sizeof(double) * M);
const double factor_1 = 2.0 / sqrt(N);
const double factor_0 = factor_1 / sqrt(2);
for (size_t m = 0; m < M; ++m) {
Y[m] = X_DCT[0] * factor_0;
}
size_t m = 0;
for (size_t n = 0; n < N; ++n) {
if (phi_flags[n]) {
for (size_t k = 1; k < N; ++k) {
Y[m] += cos((M_PI / N) * (n + 0.5) * k) * X_DCT[k] * factor_1;
}
m++;
}
}
}
void vec_sub_update(double *vec, double *b, size_t N) {
for (size_t i = 0; i < N; ++i) {
vec[i] -= b[i];
}
}
void calc_Anorm2_randsampleDCT(bool *phi_flags, size_t N, double *A_norm2) {
memset(A_norm2, 0, sizeof(double) * N);
const double factor_1 = 2.0 / sqrt(N);
const double factor_0 = factor_1 / sqrt(2);
for (size_t n = 0; n < N; ++n) {
if (phi_flags[n]) {
A_norm2[0] += factor_0 * factor_0;
for (size_t k = 1; k < N; ++k) {
A_norm2[k] += pow(cos((M_PI / N) * (n + 0.5) * k) * factor_1, 2);
}
}
}
}
void cd_lasso_randsampleDCT(double *y, bool *phi_flags,
size_t M, size_t N, double lambda,
double *s_hat, double tol) {
// Y is M-dim, phi_flags controls which DCT components to use, x_hat is Nx1
// We don't need an explicit (A) matrix, as we know it's going to randomly
// sample from the IDCT. We can call the functions which can calculate the
// products we want from phi_flags and the definition of the DCT.
double *A_norm2 = malloc(sizeof(double) * N);
calc_Anorm2_randsampleDCT(phi_flags, N, A_norm2);
// can initialize with anything I think...
for (size_t k = 0; k < N; ++k) {
s_hat[k] = 0.5;
}
double *y_hat = malloc(sizeof(double) * M);
random_sample_idct_1D(s_hat, N, phi_flags, M, y_hat);
double *r = malloc(sizeof(double) * M);
memcpy(r, y, sizeof(double) * M);
vec_sub_update(r, y_hat, M);
const double factor_1 = 2.0 / sqrt(N);
const double factor_0 = factor_1 / sqrt(2);
double max_sk = 0.5; // depends on initialization
while (true) {
double max_dsk = 0;
for (size_t k = 0; k < N; ++k) {
if (A_norm2[k] == 0.0)
continue;
double factor = (k == 0 ? factor_0 : factor_1);
double s_k0 = s_hat[k];
// r += A[:,k] .* s[k]
double rho_k = 0;
size_t m = 0;
for (size_t n = 0; n < N; ++n) {
if (phi_flags[n]) {
r[m] += s_hat[k] * cos((M_PI / N) * (n + 0.5) * k) * factor;
rho_k += r[m] * cos((M_PI / N) * (n + 0.5) * k) * factor;
m++;
}
}
double sign = (rho_k > 0 ? 1.0 : -1.0);
s_hat[k] = (sign * max(fabs(rho_k) - lambda, 0)) / A_norm2[k];
double dsk = fabs(s_hat[k] - s_k0);
max_dsk = max(dsk, max_dsk);
max_sk = max(fabs(s_hat[k]), max_sk);
// Adding back the residual contribution from s_hat[k]
m = 0;
for (size_t n = 0; n < N; ++n) {
if (phi_flags[n]) {
r[m++] -= s_hat[k] * cos((M_PI / N) * (n + 0.5) * k) * factor;
}
}
}
if ((max_dsk / max_sk) < tol) break;
}
free(r);
free(y_hat);
free(A_norm2);
}
void get_random_sample_flags_from_file(char *filepath, size_t N, bool *flags) {
FILE *fp = fopen(filepath, "r");
if (fp) {
int val;
for (int i = 0; i < N; ++i) {
// I'm afraid of int value clobbering many bools in one shot
// somehow.
// I don't want to bother checking that though, so val it is.
fscanf(fp, "%d\n", &val);
flags[i] = (bool) val;
}
}
fclose(fp);
}
/*
void get_random_sample_flags(size_t N, size_t m, bool *flags) {
for (int i = 0; i < N; ++i) {
flags[i] = false;
}
if (m > N) m = N;
int n_flags = 0;
while (n_flags < m) {
size_t idx = rand() % N;
if (!flags[idx]) {
flags[idx] = true;
n_flags++;
}
}
}
*/
void get_selected_elements(double *seq, bool *flags, int N, int m, double *out) {
size_t idx = 0;
for (int i = 0; i < N; ++i) {
if (flags[i]) {
out[idx++] = seq[i];
}
if (idx == m) break;
}
}
void ppg(double *t0, double *X0, size_t N0,
bool *phi_flags, const PPG_Params params,
double *Xr) {
/*
* t0 : sample instants (in s)
* X0 : original samples (which we are trying to reconstruct)
* N0 : number of samples we have
* phi_flags: boolean flags to denote which observations we are selecting,
* this should have been randomly generated previously
* params : simulation/experiment parameters
* Xr : where we should store the reconstructed signal (output)
*/
size_t N_window = params.N_window;
size_t M = params.M;
double *y = malloc(sizeof(double) * M);
double *s = malloc(sizeof(double) * N_window);
double *xr = malloc(sizeof(double) * N_window);
for (size_t t = 0; t < N0 - N_window + 1; t += N_window / 2) {
get_selected_elements(X0 + t, phi_flags, N_window, M, y);
cd_lasso_randsampleDCT(y, phi_flags, M, N_window, 0.01, s, 1.0e-2);
idct_1D(s, N_window, xr);
memcpy(Xr + t + N_window / 4,
xr + N_window / 4,
sizeof(double) * N_window / 2);
}
free(xr);
free(s);
free(y);
}
/*
* argv[0]
* argv[1]: samples.csv
* argv[2]: reconstructed.csv
* argv[3]: phi_flags.csv
*/
int main(int argc, char **argv) {
if (argc < 4) {
fprintf(stderr, "Not enough arguments!\n");
fprintf(stderr, "argv[1]: samples.csv\n");
fprintf(stderr, "argv[2]: reconstructed.csv\n");
fprintf(stderr, "argv[3]: phi_flags.csv\n");
}
srand(time(NULL));
PPG_Params params = get_ppg_params();
printf("f0: %.1lf\nT0: %.3lf\n", params.f0, params.T0);
printf("N_window: %ld\nM: %ld\n", params.N_window, params.M);
const size_t MAX_N = params.MAX_SAMPLES;
size_t N0 = 0;
double t0[MAX_N], X0[MAX_N];
double Xr[MAX_N];
FILE* fp_samples = fopen(argv[1], "r");
if (!fp_samples) {
fprintf(stderr, "Couldn't open file %s!\n", argv[1]);
exit(EXIT_FAILURE);
} else {
while (fscanf(fp_samples, "%lf,%lf\n", &t0[N0], &X0[N0]) == 2) {
N0++;
if (N0 == MAX_N) break;
}
fclose(fp_samples);
}
printf("Read %ld samples.\n", N0);
size_t N_window = params.N_window;
bool *phi_flags = malloc(sizeof(bool) * N_window);
get_random_sample_flags_from_file(argv[3], N_window, phi_flags);
// get_random_sample_flags(N_window, M, phi_flags);
// Just making things simpler and removing the chance of incomplete windows.
N0 = NEAREST_MULTIPLE(N0, N_window / 2);
printf("N0: %ld\n", N0);
// call ppg algorithm
ppg(t0, X0, N0, phi_flags, params, Xr);
printf("Writing to file %s...\n", argv[2]);
FILE *fp_write = fopen(argv[2], "w");
if (!fp_write) {
fprintf(stderr, "Couldn't open file %s for writing!\n", argv[2]);
} else {
for (size_t i = 0; i < N0; ++i) {
fprintf(fp_write, "%f,%f\n", t0[i], Xr[i]);
}
}
fclose(fp_write);
free(phi_flags);
return 0;
}