sigma Namespace Reference

The primary namespace for the sigma library. More...

Namespaces
namespace	detail_
	The namespace that contains the implementation details of the library.

Classes
class	Uncertain
	Models an unceratin variable. More...

Typedefs
using	UFloat = Uncertain<float>
	Typedef for an uncertain float.
using	UDouble = Uncertain<double>
	Typedef for an uncertain double.

Functions
template<typename T>
Uncertain< T >	operator- (const Uncertain< T > &a)
	Negation Operation.
template<typename T>
Uncertain< T >	operator+ (const Uncertain< T > &lhs, const Uncertain< T > &rhs)
	Addition Operation.
template<typename T>
Uncertain< T >	operator+ (const Uncertain< T > &lhs, double rhs)
template<typename T>
Uncertain< T >	operator+ (double lhs, const Uncertain< T > &rhs)
template<typename T>
Uncertain< T > &	operator+= (Uncertain< T > &lhs, const Uncertain< T > &rhs)
	Inplace Addition Operation.
template<typename T>
Uncertain< T > &	operator+= (Uncertain< T > &lhs, double rhs)
template<typename T>
Uncertain< T >	operator- (const Uncertain< T > &lhs, const Uncertain< T > &rhs)
	Subtraction Operation.
template<typename T>
Uncertain< T >	operator- (const Uncertain< T > &lhs, double rhs)
template<typename T>
Uncertain< T >	operator- (double lhs, const Uncertain< T > &rhs)
template<typename T>
Uncertain< T > &	operator-= (Uncertain< T > &lhs, const Uncertain< T > &rhs)
	Inplace Subtraction Operation.
template<typename T>
Uncertain< T > &	operator-= (Uncertain< T > &lhs, double rhs)
template<typename T>
Uncertain< T >	operator* (const Uncertain< T > &lhs, const Uncertain< T > &rhs)
	Multiplication Operation.
template<typename T>
Uncertain< T >	operator* (const Uncertain< T > &lhs, double rhs)
template<typename T>
Uncertain< T >	operator* (double lhs, const Uncertain< T > &rhs)
template<typename T>
Uncertain< T > &	operator*= (Uncertain< T > &lhs, const Uncertain< T > &rhs)
	Inplace Multiplication Operation.
template<typename T>
Uncertain< T > &	operator*= (Uncertain< T > &lhs, double rhs)
template<typename T>
Uncertain< T >	operator/ (const Uncertain< T > &lhs, const Uncertain< T > &rhs)
	Division Operation.
template<typename T>
Uncertain< T >	operator/ (double lhs, const Uncertain< T > &rhs)
template<typename T>
Uncertain< T >	operator/ (const Uncertain< T > &lhs, double rhs)
template<typename T>
Uncertain< T > &	operator/= (Uncertain< T > &lhs, const Uncertain< T > &rhs)
	Inplace Division Operation.
template<typename T>
Uncertain< T > &	operator/= (Uncertain< T > &lhs, double rhs)
template<typename T>
Uncertain< T >	abs (const Uncertain< T > &a)
	Absolute Value.
template<typename T>
Uncertain< T >	fabs (const Uncertain< T > &a)
	Absolute Value.
template<typename T>
Uncertain< T >	abs2 (const Uncertain< T > &a)
	The Square of the Absolute Value.
template<typename T>
Uncertain< T >	ceil (const Uncertain< T > &a)
	Nearest integer not less than the given value.
template<typename T>
Uncertain< T >	floor (const Uncertain< T > &a)
	Nearest integer not greater than the given value.
template<typename T>
Uncertain< T >	fmod (const Uncertain< T > &a, const Uncertain< T > &b)
	Floating point module.
template<typename T>
Uncertain< T >	fmod (const Uncertain< T > &a, double b)
template<typename T>
Uncertain< T >	fmod (double a, const Uncertain< T > &b)
template<typename T>
Uncertain< T >	copysign (const Uncertain< T > &a, const Uncertain< T > &b)
	Copy the sign of one value to another.
template<typename T, typename U>
Uncertain< T >	copysign (const Uncertain< T > &a, const U &b)
	Copy the sign of one value to another.
template<typename T, typename U>
U	copysign (const U &a, const Uncertain< T > &b)
	Copy the sign of one value to another.
template<typename T>
Uncertain< T >	trunc (const Uncertain< T > &a)
	Remove the fractional part from a variable.
template<typename T>
Uncertain< T >	round (const Uncertain< T > &a)
	Round to the nearest integar, away from zero in halfway case.
template<typename T>
const Uncertain< T > &	conj (const Uncertain< T > &a)
	Complex Conjugate.
template<typename T>
const Uncertain< T > &	real (const Uncertain< T > &a)
	Get the real part of a value.
template<typename T>
Uncertain< T >	imag (const Uncertain< T > &a)
	Get the imaginary part of a value.
template<typename T>
Uncertain< T >	erf (const Uncertain< T > &a)
	Error function.
template<typename T>
Uncertain< T >	erfc (const Uncertain< T > &a)
	Complementary error function.
template<typename T>
Uncertain< T >	tgamma (const Uncertain< T > &a)
	Gamma function.
template<typename T>
Uncertain< T >	lgamma (const Uncertain< T > &a)
	Gamma function Natural Logarithm.
template<typename T, typename U>
Uncertain< T >	pow (const Uncertain< T > &a, const U &exp)
	Exponentiation of a variable.
template<typename T>
Uncertain< T >	pow (const Uncertain< T > &a, const Uncertain< T > &exp)
	Exponentiation of a variable by an uncertain variable.
template<typename T>
Uncertain< T >	sqrt (const Uncertain< T > &a)
	Calculate the square root of an uncertain variable.
template<typename T>
Uncertain< T >	cbrt (const Uncertain< T > &a)
	Calculate the cube root of an uncertain variable.
template<typename T>
Uncertain< T >	exp (const Uncertain< T > &a)
	Calculate the Euler's number raised to the power of an uncertain variable.
template<typename T>
Uncertain< T >	exp2 (const Uncertain< T > &a)
	Calculate 2 raised to the power of an uncertain variable.
template<typename T>
Uncertain< T >	expm1 (const Uncertain< T > &a)
	Calculate the Euler's number raised to the power of an uncertain variable, then subtract 1.
template<typename T>
Uncertain< T >	log (const Uncertain< T > &a)
	Calculate the natural logarithm of a variable.
template<typename T>
Uncertain< T >	log10 (const Uncertain< T > &a)
	Calculate the base 10 logarithm of a variable.
template<typename T>
Uncertain< T >	log2 (const Uncertain< T > &a)
	Calculate the base 2 logarithm of a variable.
template<typename T>
Uncertain< T >	log1p (const Uncertain< T > &a)
	Calculate the natural logarithm of one plus a variable.
template<typename T>
Uncertain< T >	hypot (const Uncertain< T > &a, const Uncertain< T > &b)
	Calculate the square root of the sum of squared arguments.
template<typename T, typename U>
Uncertain< T >	hypot (const Uncertain< T > &a, const U &b)
	Calculate the square root of the sum of squared arguments.
template<typename T, typename U>
Uncertain< T >	hypot (const U &a, const Uncertain< T > &b)
	Calculate the square root of the sum of squared arguments.
template<typename T>
Uncertain< T >	sinh (const Uncertain< T > &a)
	Hyperbolic sine of the variable.
template<typename T>
Uncertain< T >	cosh (const Uncertain< T > &a)
	Hyperbolic cosine of the variable.
template<typename T>
Uncertain< T >	tanh (const Uncertain< T > &a)
	Hyperbolic tangent of the variable.
template<typename T>
Uncertain< T >	asinh (const Uncertain< T > &a)
	Hyperbolic arcsine of the variable.
template<typename T>
Uncertain< T >	acosh (const Uncertain< T > &a)
	Hyperbolic arccosine of the variable.
template<typename T>
Uncertain< T >	atanh (const Uncertain< T > &a)
	Hyperbolic arctangent of the variable.
template<typename T>
Uncertain< T >	degrees (const Uncertain< T > &a)
	Convert from radians to degrees.
template<typename T>
Uncertain< T >	radians (const Uncertain< T > &a)
	Convert from degrees to radians.
template<typename T>
Uncertain< T >	sin (const Uncertain< T > &a)
	Sine of the variable.
template<typename T>
Uncertain< T >	cos (const Uncertain< T > &a)
	Cosine of the variable.
template<typename T>
Uncertain< T >	tan (const Uncertain< T > &a)
	Tangent of the variable.
template<typename T>
Uncertain< T >	asin (const Uncertain< T > &a)
	Arcsine of the variable.
template<typename T>
Uncertain< T >	acos (const Uncertain< T > &a)
	Arccosine of the variable.
template<typename T>
Uncertain< T >	atan (const Uncertain< T > &a)
	Arctangent of the variable.
template<typename T>
Uncertain< T >	atan2 (const Uncertain< T > &y, const Uncertain< T > &x)
	Two argument arctangent.
template<typename T, typename U>
Uncertain< T >	atan2 (const Uncertain< T > &y, const U &x)
	Two argument arctangent.
template<typename T, typename U>
Uncertain< T >	atan2 (const U &y, const Uncertain< T > &x)
	Two argument arctangent.
template<typename ValueType>
std::ostream &	operator<< (std::ostream &os, const Uncertain< ValueType > &u)
	Overload stream insertion to print uncertain variable.
template<typename ValueType1, typename ValueType2>
bool	operator== (const Uncertain< ValueType1 > &lhs, const Uncertain< ValueType2 > &rhs)
	Compare two variables for equality.
template<typename ValueType1, typename ValueType2>
bool	operator!= (const Uncertain< ValueType1 > &lhs, const Uncertain< ValueType2 > &rhs)
	Compare two variables for inequality.
template<typename ValueType1, typename ValueType2>
bool	operator< (const Uncertain< ValueType1 > &lhs, const Uncertain< ValueType2 > &rhs)
	Whether one variable is less than another.
template<typename ValueType1, typename ValueType2>
bool	operator> (const Uncertain< ValueType1 > &lhs, const Uncertain< ValueType2 > &rhs)
	Whether one variable is greater than another.
template<typename ValueType1, typename ValueType2>
bool	operator<= (const Uncertain< ValueType1 > &lhs, const Uncertain< ValueType2 > &rhs)
	Whether one variable is less than or equal to another.
template<typename ValueType1, typename ValueType2>
bool	operator>= (const Uncertain< ValueType1 > &lhs, const Uncertain< ValueType2 > &rhs)
	Whether one variable is greater than or equal to another.

Detailed Description

The primary namespace for the sigma library.

This is the primary namespace that contains the class used to represent uncertain variables and the functions that act on them.

Function Documentation

abs()

template<typename T>

Uncertain< T > sigma::abs

(

const Uncertain< T > &

a

)

Absolute Value.

Template Parameters

T	The value type of the variable

Parameters

a	The variable

Returns

The absolute value of a

Exceptions

none	No throw guarantee

abs2()

template<typename T>

Uncertain< T > sigma::abs2

(

const Uncertain< T > &

a

)

The Square of the Absolute Value.

Template Parameters

T	The value type of the variable

Parameters

a	The variable

Returns

The square of the absolute value of a

Exceptions

none	No throw guarantee

acos()

template<typename T>

Uncertain< T > sigma::acos

(

const Uncertain< T > &

a

)

Arccosine of the variable.

Template Parameters

T	The value type of the variable

Parameters

a	The variable

Returns

A variable that is the arccosine value of a

Exceptions

none	No throw guarantee

acosh()

template<typename T>

Uncertain< T > sigma::acosh

(

const Uncertain< T > &

a

)

Hyperbolic arccosine of the variable.

Template Parameters

T	The value type of the variable

Parameters

a	The variable

Returns

A variable that is the hyperbolic arccosine value of a

Exceptions

none	No throw guarantee

asin()

template<typename T>

Uncertain< T > sigma::asin

(

const Uncertain< T > &

a

)

Arcsine of the variable.

Template Parameters

T	The value type of the variable

Parameters

a	The variable

Returns

A variable that is the arcsine value of a

Exceptions

none	No throw guarantee

asinh()

template<typename T>

Uncertain< T > sigma::asinh

(

const Uncertain< T > &

a

)

Hyperbolic arcsine of the variable.

Template Parameters

T	The value type of the variable

Parameters

a	The variable

Returns

A variable that is the hyperbolic arcsine value of a

Exceptions

none	No throw guarantee

atan()

template<typename T>

Uncertain< T > sigma::atan

(

const Uncertain< T > &

a

)

Arctangent of the variable.

Template Parameters

T	The value type of the variable

Parameters

a	The variable

Returns

A variable that is the arctangent value of a

Exceptions

none	No throw guarantee

atan2() [1/3]

template<typename T, typename U>

Uncertain< T > sigma::atan2	(	const U &	y,
		const Uncertain< T > &	x )

Two argument arctangent.

Template Parameters

T	The value type of the variable
U	The numeric type of y

Parameters

y	The first variable
x	The first variable

Returns

The two argument arctangent value of y and x

Exceptions

none	No throw guarantee

atan2() [2/3]

template<typename T, typename U>

Uncertain< T > sigma::atan2	(	const Uncertain< T > &	y,
		const U &	x )

Two argument arctangent.

Template Parameters

T	The value type of the variable
U	The numeric type of x

Parameters

y	The first variable
x	The first variable

Returns

The two argument arctangent value of y and x

Exceptions

none	No throw guarantee

atan2() [3/3]

template<typename T>

Uncertain< T > sigma::atan2	(	const Uncertain< T > &	y,
		const Uncertain< T > &	x )

Two argument arctangent.

Template Parameters

T	The value type of the variable

Parameters

y	The first variable
x	The first variable

Returns

The two argument arctangent value of y and x

Exceptions

none	No throw guarantee

atanh()

template<typename T>

Uncertain< T > sigma::atanh

(

const Uncertain< T > &

a

)

Hyperbolic arctangent of the variable.

Template Parameters

T	The value type of the variable

Parameters

a	The variable

Returns

A variable that is the hyperbolic arctangent value of a

Exceptions

none	No throw guarantee

cbrt()

template<typename T>

Uncertain< T > sigma::cbrt

(

const Uncertain< T > &

a

)

Calculate the cube root of an uncertain variable.

Template Parameters

T	The value type of the variable

Parameters

a	The variable whose root is computed

Returns

A variable whose value is the cube root of a

Exceptions

none	No throw guarantee

ceil()

template<typename T>

Uncertain< T > sigma::ceil

(

const Uncertain< T > &

a

)

Nearest integer not less than the given value.

Note that this returns an Uncertain<T> value with no dependencies

Template Parameters

T	The value type of the variable

Parameters

a	The variable

Returns

The nearest integer not greater than a

Exceptions

none	No throw guarantee

conj()

template<typename T>

const Uncertain< T > & sigma::conj

(

const Uncertain< T > &

a

)

Complex Conjugate.

This is a stub to satisfy Eigen

Template Parameters

T	The value type of the variable

Parameters

a	The variable

Returns

The complex conjugate of a

Exceptions

none	No throw guarantee

copysign() [1/3]

template<typename T, typename U>

U sigma::copysign	(	const U &	a,
		const Uncertain< T > &	b )

Copy the sign of one value to another.

Template Parameters

T	The value type of b
U	The numeric type of a

Parameters

a	The variable whose magnitude is copied
b	The variable whose sign is copied

Returns

The copy of a with the sign of b

Exceptions

none	No throw guarantee

copysign() [2/3]

template<typename T, typename U>

Uncertain< T > sigma::copysign	(	const Uncertain< T > &	a,
		const U &	b )

Copy the sign of one value to another.

Template Parameters

T	The value type of a
U	The numeric type of b

Parameters

a	The variable whose magnitude is copied
b	The variable whose sign is copied

Returns

The copy of a with the sign of b

Exceptions

none	No throw guarantee

copysign() [3/3]

template<typename T>

Uncertain< T > sigma::copysign	(	const Uncertain< T > &	a,
		const Uncertain< T > &	b )

Copy the sign of one value to another.

Template Parameters

T	The value type of the variable

Parameters

a	The variable whose magnitude is copied
b	The variable whose sign is copied

Returns

The copy of a with the sign of b

Exceptions

none	No throw guarantee

cos()

template<typename T>

Uncertain< T > sigma::cos

(

const Uncertain< T > &

a

)

Cosine of the variable.

Template Parameters

T	The value type of the variable

Parameters

a	The variable

Returns

A variable that is the cosine value of a

Exceptions

none	No throw guarantee

cosh()

template<typename T>

Uncertain< T > sigma::cosh

(

const Uncertain< T > &

a

)

Hyperbolic cosine of the variable.

Template Parameters

T	The value type of the variable

Parameters

a	The variable

Returns

A variable that is the hyperbolic cosine value of a

Exceptions

none	No throw guarantee

degrees()

template<typename T>

Uncertain< T > sigma::degrees

(

const Uncertain< T > &

a

)

Convert from radians to degrees.

Template Parameters

T	The value type of the variable

Parameters

a	The variable

Returns

The variable a in degrees

Exceptions

none	No throw guarantee

erf()

template<typename T>

Uncertain< T > sigma::erf

(

const Uncertain< T > &

a

)

Error function.

Template Parameters

T	The value type of the variable

Parameters

a	The variable

Returns

The error function value of a

Exceptions

none	No throw guarantee

erfc()

template<typename T>

Uncertain< T > sigma::erfc

(

const Uncertain< T > &

a

)

Complementary error function.

Template Parameters

T	The value type of the variable

Parameters

a	The variable

Returns

The complementary error function value of a

Exceptions

none	No throw guarantee

exp()

template<typename T>

Uncertain< T > sigma::exp

(

const Uncertain< T > &

a

)

Calculate the Euler's number raised to the power of an uncertain variable.

Template Parameters

T	The value type of the variable

Parameters

a	The variable that is the exponent

Returns

A variable whose value is Euler's number raised by the mean of a

Exceptions

none	No throw guarantee

exp2()

template<typename T>

Uncertain< T > sigma::exp2

(

const Uncertain< T > &

a

)

Calculate 2 raised to the power of an uncertain variable.

Template Parameters

T	The value type of the variable

Parameters

a	The variable that is the exponent

Returns

A variable whose value is 2 raised by the mean of a

Exceptions

none	No throw guarantee

expm1()

template<typename T>

Uncertain< T > sigma::expm1

(

const Uncertain< T > &

a

)

Calculate the Euler's number raised to the power of an uncertain variable, then subtract 1.

Template Parameters

T	The value type of the variable

Parameters

a	The variable that is the exponent

Returns

A variable whose value is Euler's number raised by the mean of a, then subtract 1.

Exceptions

none	No throw guarantee

fabs()

template<typename T>

Uncertain< T > sigma::fabs

(

const Uncertain< T > &

a

)

Absolute Value.

Template Parameters

T	The value type of the variable

Parameters

a	The variable

Returns

The absolute value of a

Exceptions

none	No throw guarantee

floor()

template<typename T>

Uncertain< T > sigma::floor

(

const Uncertain< T > &

a

)

Nearest integer not greater than the given value.

Note that this returns an Uncertain<T> value with no dependencies

Template Parameters

T	The value type of the variable

Parameters

a	The variable

Returns

The nearest integer not greater than u

Exceptions

none	No throw guarantee

fmod() [1/3]

template<typename T>

Uncertain< T > sigma::fmod	(	const Uncertain< T > &	a,
		const Uncertain< T > &	b )

Floating point module.

Template Parameters

T	The value type of the variable

Parameters

a	The first variable
b	The first variable

Returns

A variable that is the floating point remainder of a / b

Exceptions

none	No throw guarantee

fmod() [2/3]

template<typename T>

Uncertain< T > sigma::fmod	(	const Uncertain< T > &	a,
		double	b )

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

fmod() [3/3]

template<typename T>

Uncertain< T > sigma::fmod	(	double	a,
		const Uncertain< T > &	b )

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

hypot() [1/3]

template<typename T, typename U>

Uncertain< T > sigma::hypot	(	const U &	a,
		const Uncertain< T > &	b )

Calculate the square root of the sum of squared arguments.

Template Parameters

T	The value type of the variable
U	The numeric type of a

Parameters

a	The first variable
b	The second variable

Returns

A variable whose value is the base 10 logarithm of a

Exceptions

none	No throw guarantee

hypot() [2/3]

template<typename T, typename U>

Uncertain< T > sigma::hypot	(	const Uncertain< T > &	a,
		const U &	b )

Calculate the square root of the sum of squared arguments.

Template Parameters

T	The value type of the variable
U	The numeric type of b

Parameters

a	The first variable
b	The second variable

Returns

A variable whose value is the base 10 logarithm of a

Exceptions

none	No throw guarantee

hypot() [3/3]

template<typename T>

Uncertain< T > sigma::hypot	(	const Uncertain< T > &	a,
		const Uncertain< T > &	b )

Calculate the square root of the sum of squared arguments.

Template Parameters

T	The value type of the variable

Parameters

a	The first variable
b	The second variable

Returns

A variable whose value is the base 10 logarithm of a

Exceptions

none	No throw guarantee

imag()

template<typename T>

Uncertain< T > sigma::imag

(

const Uncertain< T > &

a

)

Get the imaginary part of a value.

This is a stub to satisfy Eigen

Template Parameters

T	The value type of the variable

Parameters

a	The variable

Returns

The imaginary part of a

Exceptions

none	No throw guarantee

lgamma()

template<typename T>

Uncertain< T > sigma::lgamma

(

const Uncertain< T > &

a

)

Gamma function Natural Logarithm.

Template Parameters

T	The value type of the variable

Parameters

a	The variable

Returns

The natural logarithm of the gamma function value of a

Exceptions

none	No throw guarantee

log()

template<typename T>

Uncertain< T > sigma::log

(

const Uncertain< T > &

a

)

Calculate the natural logarithm of a variable.

Template Parameters

T	The value type of the variable

Parameters

a	The variable whose logarithm is determined

Returns

A variable whose value is the natural logarithm of a

Exceptions

none	No throw guarantee

log10()

template<typename T>

Uncertain< T > sigma::log10

(

const Uncertain< T > &

a

)

Calculate the base 10 logarithm of a variable.

Template Parameters

T	The value type of the variable

Parameters

a	The variable whose logarithm is determined

Returns

A variable whose value is the base 10 logarithm of a

Exceptions

none	No throw guarantee

log1p()

template<typename T>

Uncertain< T > sigma::log1p

(

const Uncertain< T > &

a

)

Calculate the natural logarithm of one plus a variable.

Template Parameters

T	The value type of the variable

Parameters

a	The variable whose logarithm is determined

Returns

A variable whose value is the natural logarithm of a + 1

Exceptions

none	No throw guarantee

log2()

template<typename T>

Uncertain< T > sigma::log2

(

const Uncertain< T > &

a

)

Calculate the base 2 logarithm of a variable.

Template Parameters

T	The value type of the variable

Parameters

a	The variable whose logarithm is determined

Returns

A variable whose value is the base 2 logarithm of a

Exceptions

none	No throw guarantee

operator*() [1/3]

template<typename T>

Uncertain< T > sigma::operator*	(	const Uncertain< T > &	lhs,
		const Uncertain< T > &	rhs )

Multiplication Operation.

Template Parameters

T	The value type of the variables

Parameters

lhs	The left-hand variable
rhs	The right-hand variable

Returns

A variable that is the product of lhs and rhs

Exceptions

none	No throw guarantee

operator*() [2/3]

template<typename T>

Uncertain< T > sigma::operator*	(	const Uncertain< T > &	lhs,
		double	rhs )

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

operator*() [3/3]

template<typename T>

Uncertain< T > sigma::operator*	(	double	lhs,
		const Uncertain< T > &	rhs )

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

operator*=() [1/2]

template<typename T>

Uncertain< T > & sigma::operator*=	(	Uncertain< T > &	lhs,
		const Uncertain< T > &	rhs )

Inplace Multiplication Operation.

Template Parameters

T	The value type of the variables

Parameters

lhs	The left-hand variable being modified
rhs	The right-hand variable

Returns

lhs as the product of itself and rhs

Exceptions

none	No throw guarantee

operator*=() [2/2]

template<typename T>

Uncertain< T > & sigma::operator*=	(	Uncertain< T > &	lhs,
		double	rhs )

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

operator+() [1/3]

template<typename T>

Uncertain< T > sigma::operator+	(	const Uncertain< T > &	lhs,
		const Uncertain< T > &	rhs )

Addition Operation.

Template Parameters

T	The value type of the variables

Parameters

lhs	The left-hand variable
rhs	The right-hand variable

Returns

A variable that is the sum of lhs and rhs

Exceptions

none	No throw guarantee

operator+() [2/3]

template<typename T>

Uncertain< T > sigma::operator+	(	const Uncertain< T > &	lhs,
		double	rhs )

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

operator+() [3/3]

template<typename T>

Uncertain< T > sigma::operator+	(	double	lhs,
		const Uncertain< T > &	rhs )

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

operator+=() [1/2]

template<typename T>

Uncertain< T > & sigma::operator+=	(	Uncertain< T > &	lhs,
		const Uncertain< T > &	rhs )

Inplace Addition Operation.

Template Parameters

T	The value type of the variables

Parameters

lhs	The left-hand variable being modified
rhs	The right-hand variable

Returns

lhs as the sum of itself and rhs

Exceptions

none	No throw guarantee

operator+=() [2/2]

template<typename T>

Uncertain< T > & sigma::operator+=	(	Uncertain< T > &	lhs,
		double	rhs )

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

operator-() [1/4]

template<typename T>

Uncertain< T > sigma::operator-

(

const Uncertain< T > &

a

)

Negation Operation.

Template Parameters

T	The value type of the variable

Parameters

a	The variable being negated

Returns

A copy of a, but with the sign of the mean reversed

Exceptions

none	No throw guarantee

operator-() [2/4]

template<typename T>

Uncertain< T > sigma::operator-	(	const Uncertain< T > &	lhs,
		const Uncertain< T > &	rhs )

Subtraction Operation.

Template Parameters

T	The value type of the variables

Parameters

lhs	The left-hand variable
rhs	The right-hand variable

Returns

A variable that is the difference of lhs and rhs

Exceptions

none	No throw guarantee

operator-() [3/4]

template<typename T>

Uncertain< T > sigma::operator-	(	const Uncertain< T > &	lhs,
		double	rhs )

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

operator-() [4/4]

template<typename T>

Uncertain< T > sigma::operator-	(	double	lhs,
		const Uncertain< T > &	rhs )

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

operator-=() [1/2]

template<typename T>

Uncertain< T > & sigma::operator-=	(	Uncertain< T > &	lhs,
		const Uncertain< T > &	rhs )

Inplace Subtraction Operation.

Template Parameters

T	The value type of the variables

Parameters

lhs	The left-hand variable being modified
rhs	The right-hand variable

Returns

lhs as the difference of itself and rhs

Exceptions

none	No throw guarantee

operator-=() [2/2]

template<typename T>

Uncertain< T > & sigma::operator-=	(	Uncertain< T > &	lhs,
		double	rhs )

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

operator/() [1/3]

template<typename T>

Uncertain< T > sigma::operator/	(	const Uncertain< T > &	lhs,
		const Uncertain< T > &	rhs )

Division Operation.

Template Parameters

T	The value type of the variables

Parameters

lhs	The left-hand variable
rhs	The right-hand variable

Returns

A variable that is the quotient of lhs and rhs

Exceptions

none	No throw guarantee

operator/() [2/3]

template<typename T>

Uncertain< T > sigma::operator/	(	const Uncertain< T > &	lhs,
		double	rhs )

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

operator/() [3/3]

template<typename T>

Uncertain< T > sigma::operator/	(	double	lhs,
		const Uncertain< T > &	rhs )

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

operator/=() [1/2]

template<typename T>

Uncertain< T > & sigma::operator/=	(	Uncertain< T > &	lhs,
		const Uncertain< T > &	rhs )

Inplace Division Operation.

Template Parameters

T	The value type of the variables

Parameters

lhs	The left-hand variable being modified
rhs	The right-hand variable

Returns

lhs as the quotient of itself and rhs

Exceptions

none	No throw guarantee

operator/=() [2/2]

template<typename T>

Uncertain< T > & sigma::operator/=	(	Uncertain< T > &	lhs,
		double	rhs )

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

pow() [1/2]

template<typename T, typename U>

Uncertain< T > sigma::pow	(	const Uncertain< T > &	a,
		const U &	exp )

Exponentiation of a variable.

Template Parameters

T	The value type of the variable
U	The numeric type of the exponent

Parameters

a	The base variable
exp	The exponent to raise the base by

Returns

A variable that is a raise to the power exp

Exceptions

none	No throw guarantee

pow() [2/2]

template<typename T>

Uncertain< T > sigma::pow	(	const Uncertain< T > &	a,
		const Uncertain< T > &	exp )

Exponentiation of a variable by an uncertain variable.

Template Parameters

T	The value type of the variables

Parameters

a	The base variable
exp	The uncertain exponent to raise the base by

Returns

A variable that is a raise to the power exp

Exceptions

none	No throw guarantee

radians()

template<typename T>

Uncertain< T > sigma::radians

(

const Uncertain< T > &

a

)

Convert from degrees to radians.

Template Parameters

T	The value type of the variable

Parameters

a	The variable

Returns

The variable a in radians

Exceptions

none	No throw guarantee

real()

template<typename T>

const Uncertain< T > & sigma::real

(

const Uncertain< T > &

a

)

Get the real part of a value.

This is a stub to satisfy Eigen

Template Parameters

T	The value type of the variable

Parameters

a	The variable

Returns

The real part of a

Exceptions

none	No throw guarantee

round()

template<typename T>

Uncertain< T > sigma::round

(

const Uncertain< T > &

a

)

Round to the nearest integar, away from zero in halfway case.

Template Parameters

T	The value type of the variable

Parameters

a	The variable whose value is truncated

Returns

A variable whose value is the rounded value of a

Exceptions

none	No throw guarantee

sin()

template<typename T>

Uncertain< T > sigma::sin

(

const Uncertain< T > &

a

)

Sine of the variable.

Template Parameters

T	The value type of the variable

Parameters

a	The variable

Returns

A variable that is the sine value of a

Exceptions

none	No throw guarantee

sinh()

template<typename T>

Uncertain< T > sigma::sinh

(

const Uncertain< T > &

a

)

Hyperbolic sine of the variable.

Template Parameters

T	The value type of the variable

Parameters

a	The variable

Returns

A variable that is the hyperbolic sine value of a

Exceptions

none	No throw guarantee

sqrt()

template<typename T>

Uncertain< T > sigma::sqrt

(

const Uncertain< T > &

a

)

Calculate the square root of an uncertain variable.

Template Parameters

T	The value type of the variable

Parameters

a	The variable whose root is computed

Returns

A variable whose value is the square root of a

Exceptions

none	No throw guarantee

tan()

template<typename T>

Uncertain< T > sigma::tan

(

const Uncertain< T > &

a

)

Tangent of the variable.

Template Parameters

T	The value type of the variable

Parameters

a	The variable

Returns

A variable that is the tangent value of a

Exceptions

none	No throw guarantee

tanh()

template<typename T>

Uncertain< T > sigma::tanh

(

const Uncertain< T > &

a

)

Hyperbolic tangent of the variable.

Template Parameters

T	The value type of the variable

Parameters

a	The variable

Returns

A variable that is the hyperbolic tangent value of a

Exceptions

none	No throw guarantee

tgamma()

template<typename T>

Uncertain< T > sigma::tgamma

(

const Uncertain< T > &

a

)

Gamma function.

Template Parameters

T	The value type of the variable

Parameters

a	The variable

Returns

The gamma function value of a

Exceptions

none	No throw guarantee

trunc()

template<typename T>

Uncertain< T > sigma::trunc

(

const Uncertain< T > &

a

)

Remove the fractional part from a variable.

Template Parameters

T	The value type of the variable

Parameters

a	The variable whose value is truncated

Returns

A variable whose value is the truncated value of a

Exceptions

none	No throw guarantee