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kalman_filter.c
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#include <stdbool.h>
#include <Python.h>
#include "numpy/arrayobject.h"
#include <cblas.h>
#include <utils.h>
void ckalman_filter(
// n: the total number of observations
int n,
// m: the dimension of the state vector
int m,
// d: the dimension of observations
int d,
// Filter State Estimate:
double *x,
// Covariance Matrix:
double *P,
double *dt, int incdt,
double *ct, int incct,
double *Tt, int incTt,
double *Zt, int incZt,
// Measurement Uncertainty / Noise:
double *HHt, int incHHt,
// Measurement Function:
double *GGt, int incGGt,
double *yt,
// Outputs:
double *loglik)
{
// Instantiate:
*loglik = 0;
// Coerce dtypes:
blasint blas_n = (blasint)n;
blasint blas_m = (blasint)m;
blasint blas_d = (blasint)d;
// Utilised array dimensions:
blasint m_x_m = m * m;
blasint m_x_d = m * d;
// integers and double precisions used in dcopy and dgemm
blasint intone = 1;
blasint intminusone = -1;
double dblone = 1.0, dblminusone = -1.0, dblzero = 0.0;
// Sequential Processing variables:
int N_obs = 0;
int na_sum;
// Time-series iterator:
int t = 0;
/* NA detection */
int *NAindices = malloc(sizeof(int) * d);
int *positions = malloc(sizeof(int) * d);
/* Reduced arrays when NA's at time t */
double *yt_temp = malloc(sizeof(double) * (d - 1));
double *ct_temp = malloc(sizeof(double) * (d - 1));
double *Zt_temp = malloc(sizeof(double) * (d - 1) * m);
double *GGt_temp = malloc(sizeof(double) * (d - 1));
double *Zt_t = malloc(sizeof(double) * (d * m));
double *Zt_tSP = malloc(sizeof(double) * m);
double *at = malloc(sizeof(double) * m);
double *Pt = malloc(sizeof(double) * m * m);
double *tmpmxSP = (double *)calloc(m, sizeof(double));
double *tmpmxm = (double *)calloc(m_x_m, sizeof(double));
// kalman_filter specific definitions:
double V;
double Ft;
double tmpFtinv;
double *Kt = malloc(sizeof(double) * m);
/* at = x */
cblas_dcopy(blas_m, x, intone, at, intone);
/* Pt = P */
cblas_dcopy(m_x_m, P, intone, Pt, intone);
/*********************************************************************************/
/* ---------- ----------------- Begin Kalman Filter ----------------- ---------- */
/*********************************************************************************/
// Iterate over all time steps:
while (t < n)
{
// How many NA's at time t?
na_sum = numberofNA(&yt[d * t], NAindices, positions, d);
#ifdef DEBUGMODE
printf("\nNumber of NAs in iter %i: %i\n", t, na_sum);
#endif
/*********************************************************************************/
/* ---------- ---------- ---------- filter step ---------- ---------- ---------- */
/*********************************************************************************/
/*****************************************/
/* ---------- case 1: no NA's:---------- */
/*****************************************/
if (na_sum == 0)
{
// Create Zt for time t
cblas_dcopy(m_x_d, &Zt[m_x_d * t * incZt], intone, Zt_t, intone);
// Increment number of observations:
N_obs += d;
// Sequential Processing - Univariate Treatment of the Multivariate Series:
for (int SP = 0; SP < d; SP++)
{
#ifdef DEBUGMODE
printf("SP = %i", SP);
#endif
// Get the specific values of Z for SP:
for (int j = 0; j < m; j++)
{
Zt_tSP[j] = Zt_t[SP + j * d];
}
// Step 1 - Measurement Error:
// Compute Vt[SP,t] = yt[SP,t] - ct[SP,t * incct] + Zt[SP,,t * incZt] %*% at[SP,t]
V = yt[SP + d * t] - ct[SP + d * t * incct];
#ifdef DEBUGMODE
print_array(Zt_tSP, 1, m, "Zt_tSP");
#endif
// vt[SP,t] = vt[SP,t] - Zt[SP,, t * incZt] %*% at[,t]
cblas_dgemm(CblasColMajor, CblasNoTrans, CblasNoTrans,
intone, intone, blas_m,
dblminusone, Zt_tSP, intone,
at, blas_m,
dblone, &V, intone);
// Step 2 - Function of Covariance Matrix:
// Compute Ft = Zt[SP,,t * incZt] %*% Pt %*% t(Zt[SP,,t * incZt]) + diag(GGt)[SP]
// First, Let us calculate:
// Pt %*% t(Zt[SP,,t * incZt])
// because we use this result twice
cblas_dgemm(CblasColMajor, CblasNoTrans, CblasTrans,
blas_m, intone, blas_m,
dblone, Pt, blas_m,
Zt_tSP, intone,
dblzero, tmpmxSP, blas_m);
// Ft = GGt[SP]
Ft = GGt[SP + (d * t * incGGt)];
// Ft = Zt[SP,,t*incZt] %*% tmpmxSP + Ft
cblas_dgemm(CblasColMajor, CblasNoTrans, CblasNoTrans,
intone, intone, blas_m,
dblone, Zt_tSP, intone,
tmpmxSP, blas_m,
dblone, &Ft, intone);
// Step 3 - Calculate the Kalman Gain:
// Compute Kt = Pt %*% t(Zt[SP,,i * incZt]) %*% (1/Ft)
// Inv Ft:
tmpFtinv = 1 / Ft;
// Kt is an m x 1 matrix
// We already have tmpSPxm:
// Kt = tmpmxSP %*% tmpFtinv
cblas_dgemm(CblasColMajor, CblasNoTrans, CblasNoTrans,
blas_m, intone, intone,
dblone, tmpmxSP, blas_m,
&tmpFtinv, intone,
dblzero, Kt, blas_m);
// Step 4 - Correct State Vector mean and Covariance:
// Correction to att based upon prediction error:
// att = Kt %*% V + att
cblas_dgemm(CblasColMajor, CblasNoTrans, CblasNoTrans,
blas_m, intone, intone,
dblone, Kt, blas_m,
&V, intone,
dblone, at, blas_m);
// Correction to covariance based upon Kalman Gain:
// ptt = ptt - ptt %*% t(Z[SP,,i * incZt]) %*% t(Ktt)
// ptt = ptt - tempmxSP %*% t(Ktt)
cblas_dgemm(CblasColMajor, CblasNoTrans, CblasTrans,
blas_m, blas_m, intone,
dblminusone, tmpmxSP, blas_m,
Kt, blas_m,
dblone, Pt, blas_m);
// Step 5 - Update Log-Likelihood Score:
*loglik -= 0.5 * (log(Ft) + (V * V * tmpFtinv));
#ifdef DEBUGMODE
printf("\n Log-Likelihood: %f \n", *loglik);
#endif
}
}
/*********************************************************************************/
/* ---------- ---------- ------- prediction step -------- ---------- ---------- */
/*********************************************************************************/
/* ---------------------------------------------------------------------- */
/* at[,t + 1] = dt[,t * incdt] + Tt[,,t * incTt] %*% att[,t] */
/* ---------------------------------------------------------------------- */
#ifdef DEBUGMODE
print_array(at, 1, m, "at:");
#endif
// tmpmxSP = Tt[,,i * incTt] %*% att[,i]
cblas_dgemm(CblasColMajor, CblasNoTrans, CblasNoTrans,
blas_m, intone, blas_m,
dblone, &Tt[m_x_m * t * incTt], blas_m,
at, blas_m,
dblzero, tmpmxSP, blas_m);
/* at[,t + 1] = dt[,t] + at[,t] */
cblas_dcopy(blas_m, &dt[m * t * incdt], intone, at, intone);
cblas_daxpy(blas_m, dblone, tmpmxSP, intone, at, intone);
#ifdef DEBUGMODE
print_array(at, 1, m, "atp1:");
print_array(Pt, m, m, "Pt:");
#endif
/* ------------------------------------------------------------------------------------- */
/* Pt[,,t + 1] = Tt[,,t * incTt] %*% Ptt[,,t] %*% t(Tt[,,t * incTt]) + HHt[,,t * incHHt] */
/* ------------------------------------------------------------------------------------- */
/* tmpmxm = Ptt[,,i] %*% t(Tt[,,i * incTt]) */
cblas_dgemm(CblasColMajor, CblasNoTrans, CblasTrans,
blas_m, blas_m, blas_m,
dblone, Pt, blas_m,
&Tt[m_x_m * t * incTt], blas_m,
dblzero, tmpmxm, blas_m);
/* Pt[,,i + 1] = HHt[,,i * incHHt] */
cblas_dcopy(m_x_m, &HHt[m_x_m * t * incHHt], intone, Pt, intone);
#ifdef DEBUGMODE
print_array(&HHt[m_x_m * t * incHHt], m, m, "HHt:");
#endif
/* Pt[,,i + 1] = Tt[,,i * incTt] %*% tmpmxm + Pt[,,i + 1] */
cblas_dgemm(CblasColMajor, CblasNoTrans, CblasNoTrans,
blas_m, blas_m, blas_m,
dblone, &Tt[m_x_m * t * incTt], blas_m,
tmpmxm, blas_m,
dblone, Pt, blas_m);
#ifdef DEBUGMODE
print_array(at, 1, m, "at:");
print_array(Pt, m, m, "Pt:");
printf("\n---------- iteration %i ----------\n", t + 1);
#endif
// Iterate:
t++;
}
/**************************************************************/
/* ---------- ---------- end recursions ---------- ---------- */
/**************************************************************/
// Update the final Log-Likelihood Score:
*loglik -= 0.5 * N_obs * log(2 * M_PI);
// Memory clean - vectors / matrices:
free(tmpmxSP);
free(tmpmxm);
free(positions);
free(yt_temp);
free(ct_temp);
free(Zt_temp);
free(GGt_temp);
free(Zt_t);
free(Zt_tSP);
free(NAindices);
free(Kt);
free(at);
free(Pt);
}