Mathematical functions and numerical integration

The escape.core.math module provides methods for common mathematical functions and numerical integration techniques.

escape.core.math.abs(obj)

Returns a functor or parameter which computes an absolute value.

Parameters:

obj: float, int, parameter_obj, functor_obj, cplx_functor_obj or variable

Input argument.

Returns:

object of type functor_obj or parameter_obj depending on the type of obj

escape.core.math.arg(obj)

Returns a functor which computes the arg value.

Parameters:

obj: functor_obj, cplx_functor_obj or variable

Input argument.

Returns:

object of type functor_obj

escape.core.math.conj(obj)

Returns a functor which computes conjugate of obj.

Parameters:

obj: functor_obj, cplx_functor_obj or variable

Input argument.

Returns:

object of type cplx_functor_obj

escape.core.math.cos(obj)

Returns a functor or parameter which computes a cosine value.

Parameters:

obj: float, int, parameter_obj, functor_obj, cplx_functor_obj or variable

Input argument.

Returns:

object of type functor_obj, cplx_functor_obj or parameter_obj depending on the type of obj

escape.core.math.cosh(obj)

Returns a functor or parameter which computes a hyperbolic cosine value.

Parameters:

obj: float, int, parameter_obj, functor_obj, cplx_functor_obj or variable

Input argument.

Returns:

object of type functor_obj, cplx_functor_obj or parameter_obj depending on the type of obj

escape.core.math.cyl_bessel_j(a, z)

Method to create the cylindrical Bessel functor of the first kind or functional parameter.

Parameters:

a: parameter_obj or float value

the order of the function

z: object - functor, variable or parameter

z - the argument of the function

Returns:

instance of functor_obj or parameter_obj depending on ‘z’ type

escape.core.math.erf(obj)

Returns a functor or parameter which computes an error function value.

Parameters:

obj: float, int, parameter_obj, functor_obj or variable

Input argument.

Returns:

object of type functor_obj or parameter_obj depending on the type of obj

escape.core.math.exp(obj)

Returns a functor or parameter which computes an exponential function value.

Parameters:

obj: float, int, parameter_obj, functor_obj, cplx_functor_obj or variable

Input argument.

Returns:

object of type functor_obj, cplx_functor_obj or parameter_obj depending on the type of obj

escape.core.math.gamma_p(a, z, bool normalized=True)

Method to create lower limit gamma functor or functional parameter.

Parameters:

a: parameter_obj or float value

parameter a

z: object - functor, variable or parameter

z - value, can be functor or parameter

normalized - boolean

if True the values returned by the generated instance will always lay between [0, 1]

Returns:

instance of functor_obj or parameter_obj depending on ‘z’ type

escape.core.math.gamma_q(a, z, bool normalized=True)

Method to create upper limit gamma functor or functional parameter.

Parameters:

a: parameter_obj or float value

parameter a

z: object - functor, variable or parameter

z - value, can be functor or parameter

normalized - boolean

if True the values returned by the generated instance will always lay between [0, 1]

Returns:

instance of functor_obj or parameter_obj depending on ‘z’ type

escape.core.math.imag(obj)

Returns a functor which computes imaginary part of obj.

Parameters:

obj: functor_obj, cplx_functor_obj or variable

Input argument.

Returns:

object of type functor_obj

escape.core.math.integral(fun, x, a, b, int numpoints=7, epsabs=None, epsrel=None, maxiter=None)

Returns functor which computes a result of definite integral of type

\(I=\int_a^b f(x)dx\),

where \(x\) - is a variable or parameter,

The integration limits ‘a’ and ‘b’ can be parameters, functors or numeric values.

Parameters:

fun: functor_obj or parameter_obj with variable or parameter ‘x’

integrated functor or parameter

x: variable or independent parameter

integration variable

a: parameter_obj, functor_obj, variable_obj or double value

• lower integration limit

b: parameter_obj, functor_obj, variable_obj or double value

• upper integration limit

numpoints - integer

number of points of Gauss-Kronrod quadratures method. Supported values are [7, 15, 21, 31, 51, 61]

epsabs: float value or None

absolute tolerance of integration result, used only for adaptive integration. If set to None, Default value of 1e-5 is used

epsrel: float value or None

relative tolerance of integration result, used only for adaptive integration. If set to None, Default value of 0 is used’

maxiter: positive integer value or None

maximum number of iterations of adaptive integration. If set to None or zero adaptive integration is not used.

Returns:

object of type functor_obj (or parameter_obj if initial functor has only one variable)

escape.core.math.linterp(x, xp, yp)

One-dimensional linear interpolation functor.

New in version 0.9.1.

Returns the functor which is the one-dimensional piecewise linear interpolant to a function with given discrete data points (xp, yp), evaluated at values returned by x.

Parameters:

x: functor_obj or variable_obj

interpolated functor

xp: numpy array

sorted array of abscissas

yp: numpy array

• array of interpolated function values

Returns:

object of type functor_obj

escape.core.math.log(obj)

Returns a functor or parameter which computes a natural logarithm value.

Parameters:

obj: float, int, parameter_obj, functor_obj or variable

Input argument.

Returns:

object of type functor_obj or parameter_obj depending on the type of obj

escape.core.math.log10(obj)

Returns a functor or parameter which computes a decimal logarithm value.

Parameters:

obj: float, int, parameter_obj, functor_obj or variable

Input argument.

Returns:

object of type functor_obj or parameter_obj depending on the type of obj

escape.core.math.max(obj1, obj2)

Returns a functor or parameter which computes the largest value for two arguments.

Parameters:

obj1: float, int, parameter_obj, functor_obj or variable

Input argument 1.

obj2: float, int, parameter_obj, functor_obj or variable

Input argument 2.

Returns:

object of type functor_obj or parameter_obj depending on types of obj1 and obj2

escape.core.math.min(obj1, obj2)

Returns a functor or parameter which computes the smallest value for two arguments.

Parameters:

obj1: float, int, parameter_obj, functor_obj or variable

Input argument 1.

obj2: float, int, parameter_obj, functor_obj or variable

Input argument 2.

Returns:

object of type functor_obj or parameter_obj depending on types of obj1 and obj2

escape.core.math.norm(obj)

Returns a functor which computes the norm value.

Parameters:

obj: functor_obj, cplx_functor_obj or variable

Input argument.

Returns:

object of type functor_obj

escape.core.math.pow(obj1, obj2)

Returns a functor or parameter which computes the value of base obj1 raised to the power obj2.

Parameters:

obj1: float, int, parameter_obj, functor_obj or variable

Input argument 1.

obj2: float, int, parameter_obj, functor_obj or variable

Input argument 2.

Returns:

object of type functor_obj or parameter_obj depending on types of obj1 and obj2

escape.core.math.real(obj)

Returns a functor which computes real part of obj.

Parameters:

obj: functor_obj, cplx_functor_obj or variable

Input argument.

Returns:

object of type functor_obj

escape.core.math.sin(obj)

Returns a functor or parameter which computes a sine value.

Parameters:

obj: float, int, parameter_obj, functor_obj, cplx_functor_obj or variable

Input argument.

Returns:

object of type functor_obj, cplx_functor_obj or parameter_obj depending on the type of obj

escape.core.math.sinh(obj)

Returns a functor or parameter which computes a hyperbolic sine value.

Parameters:

obj: float, int, parameter_obj, functor_obj, cplx_functor_obj or variable

Input argument.

Returns:

object of type functor_obj, cplx_functor_obj or parameter_obj depending on the type of obj

escape.core.math.sqrt(obj)

Returns a functor or parameter which computes a square root value.

Parameters:

obj: float, int, parameter_obj, functor_obj, cplx_functor_obj or variable

Input argument.

Returns:

object of type functor_obj, cplx_functor_obj or parameter_obj depending on the type of obj

escape.core.math.tan(obj)

Returns a functor or parameter which computes a tangent value.

Parameters:

obj: float, int, parameter_obj, functor_obj, cplx_functor_obj or variable

Input argument.

Returns:

object of type functor_obj, cplx_functor_obj or parameter_obj depending on the type of obj

escape.core.math.tanh(obj)

Returns a functor or parameter which computes a hyperbolic tangent value.

Parameters:

obj: float, int, parameter_obj, functor_obj, cplx_functor_obj or variable

Input argument.

Returns:

object of type functor_obj, cplx_functor_obj or parameter_obj depending on the type of obj

escape.core.math.tgamma(z)

Method to create a true gamma functor or functional parameter.

Parameters:

z: object - functor, variable or parameter

Returns:

instance of functor_obj or parameter_obj depending on ‘obj’ type