Convolution Functions

Functions for convolving time series. More...

Collaboration diagram for Convolution Functions:

Functions
array[] int	calc_conv_indices_len (int s, int xlen, int ylen)
array[] int	calc_conv_indices_xlen (int s, int xlen, int ylen)
vector	convolve_to_report (vector infections, vector delay_rev_pmf, int seeding_time)
vector	convolve_with_rev_pmf (vector x, vector y, int len)

Description

Functions for convolving time series.

Functions from convolve.stan for implementing convolutions between infections and delay distributions.

Function Documentation

calc_conv_indices_len()

array[] int calc_conv_indices_len	(	int	s,
		int	xlen,
		int	ylen )

#include </github/workspace/inst/stan/functions/convolve.stan>

Calculate convolution indices for the case where s > xlen

Parameters

s	Current position in the output vector
xlen	Length of the x vector
ylen	Length of the y vector

Returns

An array of integers: {start_x, end_x, start_y, end_y}

Definition at line 39 of file convolve.stan.

                                                             {
  int s_minus_ylen = s - ylen;
  int start_x = max(1, s_minus_ylen + 1);
  int end_x = xlen;
  int start_y = max(1, 1 - s_minus_ylen);;
  int end_y = ylen + xlen - s;
  return {start_x, end_x, start_y, end_y};
}

Referenced by convolve_with_rev_pmf().

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calc_conv_indices_xlen()

array[] int calc_conv_indices_xlen	(	int	s,
		int	xlen,
		int	ylen )

#include </github/workspace/inst/stan/functions/convolve.stan>

convolution_functions Functions

This file contains functions for performing discrete convolutions, which are used throughout the model to combine time series with delay distributions. Calculate convolution indices for the case where s <= xlen

Parameters

s	Current position in the output vector
xlen	Length of the x vector
ylen	Length of the y vector

Returns

An array of integers: {start_x, end_x, start_y, end_y}

Definition at line 20 of file convolve.stan.

                                                              {
  int s_minus_ylen = s - ylen;
  int start_x = max(1, s_minus_ylen + 1);
  int end_x = s;
  int start_y = max(1, 1 - s_minus_ylen);
  int end_y = ylen;
  return {start_x, end_x, start_y, end_y};
}

Referenced by convolve_with_rev_pmf().

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convolve_to_report()

vector convolve_to_report	(	vector	infections,
		vector	delay_rev_pmf,
		int	seeding_time )

#include </github/workspace/inst/stan/functions/convolve.stan>

Convolve infections to reported cases.

This function convolves a vector of infections with a reversed delay distribution to produce a vector of reported cases.

Parameters

infections	A vector of infection counts.
delay_rev_pmf	A vector representing the reversed probability mass function of the delay distribution.
seeding_time	The number of initial time steps to exclude from the output.

Returns

A vector of reported cases, starting from seeding_time + 1.

Definition at line 105 of file convolve.stan.

                                            {
  int t = num_elements(infections);
  int delays = num_elements(delay_rev_pmf);
 
  if (delays == 0) {
    return infections[(seeding_time + 1):t];
  }
 
  vector[t] unobs_reports = convolve_with_rev_pmf(infections, delay_rev_pmf, t);
  return unobs_reports[(seeding_time + 1):t];
}

References convolve_with_rev_pmf().

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convolve_with_rev_pmf()

vector convolve_with_rev_pmf	(	vector	x,
		vector	y,
		int	len )

#include </github/workspace/inst/stan/functions/convolve.stan>

Convolve a vector with a reversed probability mass function.

This function performs a discrete convolution of two vectors, where the second vector is assumed to be an already reversed probability mass function.

Parameters

x	The input vector to be convolved.
y	The already reversed probability mass function vector.
len	The desired length of the output vector.

Returns

A vector of length len containing the convolution result.

Exceptions

If	len is not of equal length to the sum of the lengths of x and y.

Definition at line 62 of file convolve.stan.

                                                          {
  int xlen = num_elements(x);
  int ylen = num_elements(y);
  vector[len] z;
 
  if (xlen + ylen - 1 < len) {
    reject("convolve_with_rev_pmf: len is longer than x and y convolved");
  }
 
  if (xlen > len) {
    reject("convolve_with_rev_pmf: len is shorter than x");
  }
 
  for (s in 1:xlen) {
    array[4] int indices = calc_conv_indices_xlen(s, xlen, ylen);
    z[s] = dot_product(x[indices[1]:indices[2]], y[indices[3]:indices[4]]);
  }
 
  if (len > xlen) {
    for (s in (xlen + 1):len) {
      array[4] int indices = calc_conv_indices_len(s, xlen, ylen);
      z[s] = dot_product(x[indices[1]:indices[2]], y[indices[3]:indices[4]]);
    }
  }
 
  return z;
}

References calc_conv_indices_len(), and calc_conv_indices_xlen().

Referenced by convolve_to_report(), and get_delay_rev_pmf().

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