#include <math.h>
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <unistd.h>
#include <time.h>
#include "gdrs.h"

Functions
void	handle_sql3error (sqlite3 db, sqlite3_stmt stmt)
	Function that wraps repetitive code for SQLite3 errors. More...

int	loadgdrs (struct gdrs_struct gdrs, const char fname)
	Function to translate from SQLite3 database to internal data structures. More...

int	readtable (sqlite3 db, const char column, struct datablock *table, struct appdata ad)
	Helper function to read a column from the "core" table into a datablock. More...

void	cleargdrs (struct gdrs_struct gdrs)
	Clear out the GDRs data structure. More...

double	globaldist (double y, int year, struct gdrs_struct gdrs, int ppp_or_mer, double dist_deriv)
	Calculate the fraction of global population below a specified income level in the given year. More...

double	globalquintile (double q, int year, struct gdrs_struct *gdrs, int ppp_or_mer)
	Calculate the income at a given quintile for the world as a whole. More...

double	nationalquintile (double q, double ybar, double sigma)
	Calculate the income at a given quintile for a country. More...

void	combine_gap (struct fixedfactor *gap, int i, double newgap, int combine)
	Calculate and store luxury emissions. More...

void	calc_kab (struct fixedfactor gap, double totgap, int year, int period, int combine, struct gdrs_struct *gdrs)
	Calculate and store "Kyoto gap" for Kyoto-adjusted baselines. More...

void	calc_luxemiss (struct fixedfactor gap, double totgap, int year, int period, int combine, struct gdrs_struct *gdrs)
	Calculate and store luxury emissions. More...

void	calcallocs (struct gdrs_struct *gdrs)
	Calculate allocations for all years. More...

void	nextrci (int year, struct gdrs_struct *gdrs)
	Calculate the GDRs Responsibility-Capacity Indicator for a particular year. More...

double	M (double a, double zc, double ybar, double sigma)
	Calculate a function $M_a(y_c,\bar{y},\sigma)$ that is repeatedly used in calculations. More...

double	a_gamma (double gamma, double y, double a, double b)
	Calculate the $a_\gamma(y;a,b)$ function. More...

double	b_gamma (double gamma, double y, double b)
	Calculate the $b_\gamma(y;b)$ function. More...

double	A_gamma (double gamma, double za, double zb, double yl, double yu, double ybar, double sigma)
	Calculate the $A_\gamma(a,b;y_l,y_u/\pi_i,\bar{y}_i,\sigma_i)$ function. More...

double	B_gamma (double gamma, double za, double zb, double yu, double ybar, double sigma)
	Calculate the $B_\gamma(a,b;y_u/\pi_i,\bar{y}_i,\sigma_i)$ function. More...

double	capbetween (double za, double zb, double zl, double zu, double yl, double yu_ppp, double ybar, double sigma, double pi, double luxmult)
	Calculate capacity per capita between two income limits. More...

double	respbetween (double gamma, double za, double zb, double zl, double zu, double yl, double yu_ppp, double ybar, double sigma, double A)
	Calculate responsibility between two income limits. More...

double	rhat (double E, double gamma, double sigma, double ybar)
	Calculate the factor $\hat{r}_i$ for a country. More...

double	c_indiv (double y, double yl, double yu, int do_interp)
	Calculate individual per capita capacity $c_i(y)$ at a specified income level. More...

double	r_indiv (double gamma, double y, double yl, double yu, double A, int do_interp)
	Calculate individual per capita annual responsibility $r_i(y)$ at a specified income level. More...

double	luxcap (int year, struct gdrs_struct *gdrs)
	If calculating luxury-capped baselines adjust the luxury threshold if needed to stay above emergency pathway. More...

void	calcybar (struct gdrs_struct *gdrs)
	Calculate mean income from GDP and population. More...

struct datablock	z (double y, struct gdrs_struct *gdrs, int ppp_or_mer)
	Calculate the "z" transformed version of an income level for all countries and years. More...

int	dump2sql3 (const char *fname, struct gdrs_struct gdrs)
	After the calculation, write all results to the SQLite3 database. More...

Function Documentation

◆ a_gamma()

double a_gamma	(	double	gamma,
		double	y,
		double	a,
		double	b
	)

Calculate the $a_\gamma(y;a,b)$ function.

Parameters

gamma	Elasticity
y	Income (PPP) at which to evaluate the function
a	Lower income limit
b	Upper income limit

Returns

\[0 \mbox{ if } |a - b| < \epsilon\]

or

\[a_\gamma(y;a,b) = \frac{1}{b - a}\left[\frac{\gamma}{\gamma +1}\left(y^{\gamma+1}-a^{\gamma+1}\right)-a\left(y^\gamma - a^\gamma\right)\right],\]

Note: See Technical report.; All incomes are assumed to be in PPP terms.

Todo:: Check input values

Definition at line 1299 of file gdrs.c.

◆ A_gamma()

double A_gamma	(	double	gamma,
		double	za,
		double	zb,
		double	yl,
		double	yu,
		double	ybar,
		double	sigma
	)

Calculate the $A_\gamma(a,b;y_l,y_u/\pi_i,\bar{y}_i,\sigma_i)$ function.

Parameters

gamma	Elasticity
za	Lower income limit (transformed variable)
zb	Upper income limit (transformed variable)
yl	Development threshold
yu	Luxury threshold
ybar	Mean income for the country
sigma	Standard deviation of log income for the country

Returns

\[0 \mbox{ if } |y_u - y_l| < \epsilon\]

or

\[A_\gamma(a,b) = \frac{1}{y/\pi_i-y_l}\left[ \frac{\gamma}{\gamma+1}\left(M_{\gamma+1}(a) - M_{\gamma+1}(b)\right) - y_l\left(M_\gamma(a) - M_\gamma(b)\right) + \frac{y_l^{\gamma+1}}{\gamma+1} \left(M_0(b) - M_0(a)\right)\right],\]

Note: See Technical report.; All incomes are assumed to be in PPP terms; this means that the luxury threshold has already been converted to PPP terms.; Values for z's and y's can be positive infinity, and z's can be negative infinity.

Todo:: Check input values

Definition at line 1347 of file gdrs.c.

◆ b_gamma()

double b_gamma	(	double	gamma,
		double	y,
		double	b
	)

Calculate the $b_\gamma(y;b)$ function.

Parameters

gamma	Elasticity
y	Income (PPP) at which to evaluate the function
b	Upper income limit

Returns: \[b_\gamma(y;b) = y^\gamma - b^\gamma.\]

Note: See Technical report.; All incomes are assumed to be in PPP terms.

Todo:: Check input values

Definition at line 1325 of file gdrs.c.

◆ B_gamma()

double B_gamma	(	double	gamma,
		double	za,
		double	zb,
		double	yu,
		double	ybar,
		double	sigma
	)

Calculate the $B_\gamma(a,b;y_u/\pi_i,\bar{y}_i,\sigma_i)$ function.

Parameters

gamma	Elasticity
za	Lower income limit (transformed variable)
zb	Upper income limit (transformed variable)
yu	Luxury threshold
ybar	Mean income for the country
sigma	Standard deviation of log income for the country

Returns: \[B_\gamma(a,b) = \left(M_\gamma(a)-M_\gamma(b)\right) - \left(\frac{y_u}{\pi_i}\right)^\gamma\left(M_0(a) - M_0(b)\right),\]

Note: See Technical report.; All incomes are assumed to be in PPP terms; this means that the luxury threshold has already been converted to PPP terms.; Values for z's and y's can be positive infinity, and z's can be negative infinity.

Todo:: Check input values

Definition at line 1379 of file gdrs.c.

◆ c_indiv()

double c_indiv	(	double	y,
		double	yl,
		double	yu,
		int	do_interp
	)

Calculate individual per capita capacity $c_i(y)$ at a specified income level.

Parameters

y	Income at which to calculate c_indiv
yl	Development threshold
yu	Luxury threshold
do_interp	Boolean: are we interpolating between thresholds?

Returns: Individual capacity per capita at income $y$

Note: All incomes are in MER terms.

Definition at line 1519 of file gdrs.c.

◆ calc_kab()

void calc_kab	(	struct fixedfactor *	gap,
		double *	totgap,
		int	year,
		int	period,
		int	combine,
		struct gdrs_struct *	gdrs
	)

Calculate and store "Kyoto gap" for Kyoto-adjusted baselines.

Parameters

gap	Difference between nominal baseline and luxury-adjusted baseline (if doing luxury-capping)
totgap	Sum of gaps across all countries
year	Current year for the calculation
period	For sequencing: PER_BEFORE_EP, PER_SEQUENCE, or PER_GDRS
combine	If more than one gap, how are they being combined? GAP_COMBINE_NONE, GAP_COMBINE_ADD, GAP_COMBINE_MAX, GAP_COMBINE_MIN
gdrs	The global data structure for the GDRs calculation

Definition at line 812 of file gdrs.c.

◆ calc_luxemiss()

void calc_luxemiss	(	struct fixedfactor *	gap,
		double *	totgap,
		int	year,
		int	period,
		int	combine,
		struct gdrs_struct *	gdrs
	)

Calculate and store luxury emissions.

Parameters

gap	Difference between nominal baseline and luxury-adjusted baseline (if doing luxury-capping)
totgap	Sum of gaps across all countries
year	Current year for the calculation
period	For sequencing: PER_BEFORE_EP, PER_SEQUENCE, or PER_GDRS
combine	If more than one gap, how are they being combined? GAP_COMBINE_NONE, GAP_COMBINE_ADD, GAP_COMBINE_MAX, GAP_COMBINE_MIN
gdrs	The global data structure for the GDRs calculation

Set gdrs.lux_emiss, gdrs.lux_emiss_applied

Definition at line 892 of file gdrs.c.

◆ calcallocs()

void calcallocs ( struct gdrs_struct * gdrs )

Calculate allocations for all years.

Parameters

gdrs	The global data structure for the GDRs calculation Set gdrs.a1domrdxn, gdrs.alloc_gdrs

Definition at line 947 of file gdrs.c.

◆ calcybar()

void calcybar ( struct gdrs_struct * gdrs )

Calculate mean income from GDP and population.

Parameters

gdrs	Global data structure with data, parameters, etc. Set gdrs.ybar_ppp

Definition at line 1714 of file gdrs.c.

◆ capbetween()

double capbetween	(	double	za,
		double	zb,
		double	zl,
		double	zu,
		double	yl,
		double	yu_ppp,
		double	ybar,
		double	sigma,
		double	pi,
		double	luxmult
	)

Calculate capacity per capita between two income limits.

Parameters

za	Lower income limit (transformed variable)
zb	Upper income limit (transformed variable)
zl	Development threshold (transformed variable)
zu	Luxury threshold (transformed variable)
yl	Development threshold
yu_ppp	Luxury threshold in PPP terms
ybar	Mean income for the country
sigma	Standard deviation of log income for the country
pi	Inverse of ppp2mer ratio
luxmult	Tax multiplier on high incomes

Returns: Average per capita contribution to national capacity from those with incomes between the income limits

Note: All incomes are assumed to be in PPP terms.; The return value must be multiplied by national population.; There is a lot of redundancy in the passed parameters, but for speed these are calculated once in function next_rci.; Values for z's and y's can be positive infinity, and z's can be negative infinity.

Definition at line 1408 of file gdrs.c.

◆ cleargdrs()

void cleargdrs ( struct gdrs_struct gdrs )

Clear out the GDRs data structure.

Parameters

gdrs	The main data structure, containing data, information, and calculated outputs

Definition at line 621 of file gdrs.c.

◆ combine_gap()

void combine_gap	(	struct fixedfactor *	gap,
		int	i,
		double	newgap,
		int	combine
	)

Calculate and store luxury emissions.

Parameters

gap	Difference between nominal baseline and luxury-adjusted baseline (if doing luxury-capping)
i	Value in gap to set
newgap	New value for entry i
combine	If more than one gap, how are they being combined? GAP_COMBINE_NONE, GAP_COMBINE_ADD, GAP_COMBINE_MAX, GAP_COMBINE_MIN

Definition at line 782 of file gdrs.c.

◆ dump2sql3()

int dump2sql3	(	const char *	fname,
		struct gdrs_struct	gdrs
	)

After the calculation, write all results to the SQLite3 database.

Parameters

fname	Filename for the SQLite3 database
gdrs	Global structure with data and parameters

Returns: Success code Add the table "gdrs" to the SQLite3 database

Definition at line 1800 of file gdrs.c.

◆ globaldist()

double globaldist	(	double	y,
		int	year,
		struct gdrs_struct *	gdrs,
		int	ppp_or_mer,
		double *	dist_deriv
	)

Calculate the fraction of global population below a specified income level in the given year.

Parameters

y	Income level below which to calculate the share of the global population
year	Year to report population share
gdrs	The global data structure for the GDRs calculation
ppp_or_mer	Whether using PPP or MER conversion rates
dist_deriv	Pointer to a variable to store the derivative of the function (for finding quintiles) or NULL

Returns: Fraction of the population below the specified income level

Note: Before this is run, ybar, sigma, and scalpop should be calculated.

Definition at line 687 of file gdrs.c.

◆ globalquintile()

double globalquintile	(	double	q,
		int	year,
		struct gdrs_struct *	gdrs,
		int	ppp_or_mer
	)

Calculate the income at a given quintile for the world as a whole.

Parameters

q	The quintile (e.g., 0.5 for the median)
year	The year in which to calculate the quintile
gdrs	The global data structure for the GDRs calculation
ppp_or_mer	Whether using PPP or MER conversion rates

Returns: The PPP income level for the corresponding global quintile

Note: Use Newton's method.

Definition at line 739 of file gdrs.c.

◆ handle_sql3error()

void handle_sql3error	(	sqlite3 *	db,
		sqlite3_stmt *	stmt
	)

Function that wraps repetitive code for SQLite3 errors.

This file handles the implementation of the GDRs algorithms

Parameters

db	An sqlite3 database handle
stmt	The return value from an SQL3 call

Definition at line 38 of file gdrs.c.

◆ loadgdrs()

int loadgdrs	(	struct gdrs_struct *	gdrs,
		const char *	fname
	)

Function to translate from SQLite3 database to internal data structures.

Parameters

gdrs	The data structure to fill
fname	File name of the SQLite3 database

Returns: Success code Set most values in the gdrs structure

Todo:: Implement percentiles

Definition at line 54 of file gdrs.c.

◆ luxcap()

double luxcap	(	int	year,
		struct gdrs_struct *	gdrs
	)

If calculating luxury-capped baselines adjust the luxury threshold if needed to stay above emergency pathway.

Parameters

year	Year for calculating the adjusted luxury cutoff
gdrs	Global data structure containing parameters and data for all calculations

Returns: Value of the luxury-capped baseline, or NaN Set gdrs.yu_adj and gdrs.zu_adj

Definition at line 1572 of file gdrs.c.

◆ M()

double M	(	double	a,
		double	zc,
		double	ybar,
		double	sigma
	)

Calculate a function $M_a(y_c,\bar{y},\sigma)$ that is repeatedly used in calculations.

Parameters

a	Elasticity
zc	Income cutoff, transformed into "z" variable $ z = \frac{1}{\sigma} \ln\left(y/\bar y\right) + \frac{1}{2}\sigma$
ybar	Mean income
sigma	Standard deviation of log income

Returns: \[M_a(y_c,\sigma,\bar y) = \bar{y}^a e^{\frac{\sigma^2}{2} a (a - 1)} \left[1 - N(z_c - a \sigma)\right],\]
where $N(\cdot)$ is the cumulative standardized normal distribution.

Note: See Equation (7) in the technical report; \[M_a(k y_c,\sigma, k\bar y) = k^aM_a(y_c, \sigma, \bar y)\]

Definition at line 1270 of file gdrs.c.

◆ nationalquintile()

double nationalquintile	(	double	q,
		double	ybar,
		double	sigma
	)

Calculate the income at a given quintile for a country.

Parameters

q	The quintile (e.g., 0.5 for the median, 0.2 for the bottom 20%, 0.8 for the top 20%)
ybar	Mean income
sigma	Standard deviation of log income

Returns: Income level for that quintile, assuming a lognormal distribution; value is
\[y = \bar{y} e^{\sigma N^{-1}(q) - \sigma^2/2}\]

Definition at line 769 of file gdrs.c.

◆ nextrci()

void nextrci	(	int	year,
		struct gdrs_struct *	gdrs
	)

Calculate the GDRs Responsibility-Capacity Indicator for a particular year.

Parameters

year	Year for which to calculate RCI
gdrs	Global data structure containing parameters and data Set gdrs.c, gdrs.r, gdrs.pop_above_dl, gdrs.pop_above_lux, gdrs.rci, gdrs.tax_revenue_mer_dens, tax_revenue_ppp_dens, gdrs.tax_pop_dens, gdrs.tax_income_mer_dens, tax_income_ppp_dens, gdrs.tax_pop_below

Note: IMPORTANT: alloc_gdrs for prev year is expected to be set by the calling function unless it is the first year

Definition at line 1107 of file gdrs.c.

◆ r_indiv()

double r_indiv	(	double	gamma,
		double	y,
		double	yl,
		double	yu,
		double	A,
		int	do_interp
	)

Calculate individual per capita annual responsibility $r_i(y)$ at a specified income level.

Parameters

gamma	Emissions elasticity
y	Income at which to calculate r_indiv
yl	Development threshold
yu	Luxury threshold
A	Overall coefficient (factor $\hat{r}_i$)

Returns: Individual annual responsibility per capita at income $y$

Note: All incomes are in PPP terms

Definition at line 1546 of file gdrs.c.

◆ readtable()

int readtable	(	sqlite3 *	db,
		const char *	column,
		struct datablock *	table,
		struct appdata	ad
	)

Helper function to read a column from the "core" table into a datablock.

Parameters

db	Handle for the SQLite3 database
column	Name of the column in the core table of the database
table	Internal data representation
ad	appdata structure with dimensions

Returns: Success code

Definition at line 576 of file gdrs.c.

◆ respbetween()

double respbetween	(	double	gamma,
		double	za,
		double	zb,
		double	zl,
		double	zu,
		double	yl,
		double	yu_ppp,
		double	ybar,
		double	sigma,
		double	A
	)

Calculate responsibility between two income limits.

Parameters

gamma	Emissions elasticity
za	Lower income limit (transformed variable)
zb	Upper income limit (transformed variable)
zl	Development threshold (transformed variable)
zu	Luxury threshold (transformed variable)
yl	Development threshold
yu_ppp	Luxury threshold in PPP terms
ybar	Mean income for the country
sigma	Standard deviation of log income for the country
A	Overall multiplicative constant to convert to emissions

Returns: Contribution to national responsibility from those with incomes between the income limits

Note: All incomes are assumed to be in PPP terms.; There is a lot of redundancy in the passed parameters, but for speed these are calculated once in function next_rci.; Values for z's and y's can be positive infinity, and z's can be negative infinity.

Definition at line 1459 of file gdrs.c.

◆ rhat()

double rhat	(	double	E,
		double	gamma,
		double	sigma,
		double	ybar
	)

Calculate the factor $\hat{r}_i$ for a country.

Parameters

E	Annual emissions
gamma	Emissions elasticity
sigma	Standard deviation of the log of income
ybar	Mean income

Returns: The factor
\[\hat{r}_i=\frac{E_{i}}{{\bar{y}_{i}}^{\gamma }}e^{-{\frac{\sigma _{i}^{2}}{\;2}}\gamma (\gamma -1)}\]

Note: Mean income ybar is assumed to be in PPP terms where this factor appears in formulas.

Definition at line 1503 of file gdrs.c.

◆ z()

struct datablock z	(	double	y,
		struct gdrs_struct *	gdrs,
		int	ppp_or_mer
	)

Calculate the "z" transformed version of an income level for all countries and years.

Parameters

y	The income at which to calculate z
gdrs	Global data structure with variables and parameters
ppp_or_mer	Whether using PPP or MER conversion rates

Returns: Value of z

Note: $ z = \frac{1}{\sigma} \ln\left(y/\bar y\right) + \frac{1}{2}\sigma$

Definition at line 1754 of file gdrs.c.

Functions

Function Documentation

◆ a_gamma()

◆ A_gamma()

◆ b_gamma()

◆ B_gamma()

◆ c_indiv()

◆ calc_kab()

◆ calc_luxemiss()

◆ calcallocs()

◆ calcybar()

◆ capbetween()

◆ cleargdrs()

◆ combine_gap()

◆ dump2sql3()

◆ globaldist()

◆ globalquintile()

◆ handle_sql3error()

◆ loadgdrs()

◆ luxcap()

◆ M()

◆ nationalquintile()

◆ nextrci()

◆ r_indiv()

◆ readtable()

◆ respbetween()

◆ rhat()

◆ z()