blockmath.h File Reference

Go to the source code of this file.

Macros
#define	MAXITER   100
#define	EPSILON   1.0e-15
#define	INV_SQRT_2PI   0.3989422804014326779399461

Functions
struct datablock	transform (struct datablock dbin, double(*f)(double), struct appdata ad)
	Apply a function to a datablock. More...
struct datablock	binop (struct datablock a, struct datablock b, char op, struct appdata ad)
	Carry out a binary operation (+, -, *, /) on two datablock structures. More...
struct datablock	scalmult (double scalar, struct datablock dbin, struct appdata ad)
	Multiply a datablock by a scaling factor. More...
struct timeseries	filter (struct datablock data, struct fixedfactor filter, struct appdata ad)
	Aggregate data in a datablock using a fixedfactor "filter" to produce a timeseries. More...
double	filteryr (int year, struct datablock data, struct fixedfactor filter, struct appdata ad)
	Aggregate data in a datablock using a fixedfactor "filter" for a particular year. More...
double	gini2sdlog (double gini)
	The standard deviation of the log of income corresponding to a given Gini, assuming lognormal. More...
double	pnorm (double x)
	The cumulative standardized normal distribution. More...
double	quick_qnorm (double p)
	Abramowitz & Stegun approximation to qnorm to get a good first guess. More...
double	qnorm (double p)
	The inverse cumulative standardized normal distribution. More...
double	dnorm (double x)
	The standard normal probability density. More...
double	ztransf (double y, double ybar, double sigma)
	The transformed value \( z = \frac{1}{\sigma} \ln\left(y/\bar y\right) + \frac{1}{2}\sigma\). More...

Macro Definition Documentation

EPSILON

#define EPSILON   1.0e-15

Definition at line 22 of file blockmath.h.

INV_SQRT_2PI

#define INV_SQRT_2PI   0.3989422804014326779399461

Definition at line 24 of file blockmath.h.

MAXITER

#define MAXITER   100

Definition at line 20 of file blockmath.h.

Function Documentation

binop()

struct datablock binop	(	struct datablock	a,
		struct datablock	b,
		char	op,
		struct appdata	ad
	)

Carry out a binary operation (+, -, *, /) on two datablock structures.

Parameters

a	First input datablock
b	Second input datablock
op	Binary operation to carry out
ad	appdata structure with dimensions

Returns

The result as a datablock

Definition at line 69 of file blockmath.c.

dnorm()

double dnorm

(

double

x

)

The standard normal probability density.

Parameters

x	The value at which the density function is computed

Returns

The standard normal probability density at the specified value

Definition at line 201 of file blockmath.c.

filter()

struct timeseries filter	(	struct datablock	data,
		struct fixedfactor	filter,
		struct appdata	ad
	)

Aggregate data in a datablock using a fixedfactor "filter" to produce a timeseries.

Parameters

data	Datablock with data
filter	Fixed factor with coefficients (typically 1 and 0) to multiply data by before summing
ad	appdata with dimensions

Returns

A time series, calculated as sum(filter * data)

Definition at line 250 of file blockmath.c.

filteryr()

double filteryr	(	int	year,
		struct datablock	data,
		struct fixedfactor	filter,
		struct appdata	ad
	)

Aggregate data in a datablock using a fixedfactor "filter" for a particular year.

Parameters

year	Year for which to evaluate result
data	Datablock with data
filter	Fixed factor with coefficients (typically 1 and 0) to multiply data by before summing
ad	appdata with dimensions

Returns

A single value, calculated as sum(filter * data) for year "year"

Definition at line 279 of file blockmath.c.

gini2sdlog()

double gini2sdlog

(

double

gini

)

The standard deviation of the log of income corresponding to a given Gini, assuming lognormal.

Parameters

gini	The Gini coefficient value at which to evaluate the function (in percentage points, 0..100)

Returns

The standard deviation of the log of income, or NaN if out of bounds

Definition at line 235 of file blockmath.c.

pnorm()

double pnorm

(

double

x

)

The cumulative standardized normal distribution.

Parameters

x	Value at which to evaluate the function

Returns

Cumulative standardized normal distribution \(N(x)\)

Definition at line 128 of file blockmath.c.

qnorm()

double qnorm

(

double

p

)

The inverse cumulative standardized normal distribution.

Parameters

p	The probability at which to evaluate the function

Returns

Inverse cumulative standardized normal distribution, \(N^{-1}(p)\), or NaN if exceed max iterations

Note

Carries out a standard Newton method, using quick_qnorm to get a first guess

Definition at line 167 of file blockmath.c.

quick_qnorm()

double quick_qnorm

(

double

p

)

Abramowitz & Stegun approximation to qnorm to get a good first guess.

Parameters

p	Probability level at which to evaluate the function

Returns

Approximation to qnorm

Note

Uses A&S formula 26.2.22, good to 3e-3

Definition at line 140 of file blockmath.c.

scalmult()

struct datablock scalmult	(	double	scalar,
		struct datablock	dbin,
		struct appdata	ad
	)

Multiply a datablock by a scaling factor.

Parameters

scalar	The factor to multiply dbin by
dbin	The input datablock
ad	appdata structure with dimensions

Returns

The result as a datablock

Definition at line 103 of file blockmath.c.

transform()

struct datablock transform	(	struct datablock	dbin,
		double(*)(double)	f,
		struct appdata	ad
	)

Apply a function to a datablock.

This file implements special mathematical functions, and math operations on data structures

Parameters

dbin	The datablock to transform
f	A function to apply to each element of the datablock
ad	appdata structure with dimensions

Returns

The datablock after applying function f

Definition at line 38 of file blockmath.c.

ztransf()

double ztransf	(	double	y,
		double	ybar,
		double	sigma
	)

The transformed value \( z = \frac{1}{\sigma} \ln\left(y/\bar y\right) + \frac{1}{2}\sigma\).

Parameters

y	The income at which the function is evaluated
ybar	Mean income for the country
sigma	Standard deviation of the log of income for the country

Returns

The transformed value z

Definition at line 213 of file blockmath.c.