Action: BF_CUSTOM

Module	ves
Description	Usage
Basis functions given by arbitrary mathematical expressions.

Details and examples

Basis functions given by arbitrary mathematical expressions.

This allows you to define basis functions using arbitrary mathematical expressions that are parsed using the lepton library. The basis functions $f_{i}(x)$ are given in mathematical expressions with x as a variable using the numbered FUNC keywords that start from FUNC1. Consistent with other basis functions is $f_{0}(x)=1$ defined as the constant. The interval on which the basis functions are defined is given using the MINIMUM and MAXIMUM keywords.

Using the TRANSFORM keyword it is possible to define a function $x(t)$ that is used to transform the argument before calculating the basis functions values. The variables min and max can be used to indicate the minimum and the maximum of the interval. By default the arguments are not transformed, i.e. $x(t)=t$.

For periodic basis functions you should use the PERIODIC flag to indicate that they are periodic.

The basis functions $f_{i}(x)$ and the transform function $x(t)$ need to be well behaved in the interval on which the basis functions are defined, e.g. not result in a not a number (nan) or infinity (inf). The code will not perform checks to make sure that this is the case unless the flag CHECK_NAN_INF is enabled.

Examples

Defining Legendre polynomial basis functions of order 6 using BF_CUSTOM where the appropriate transform function is given by the TRANSFORM keyword. This is just an example of what can be done, in practice you should use BF_LEGENDRE for Legendre polynomial basis functions.

Click on the labels of the actions for more information on what each action computes

BF_CUSTOMBasis functions given by arbitrary mathematical expressions. More details ...
 TRANSFORMAn optional function that can be used to transform the argument before calculating the basis function values=(t-(min+max)/2)/((max-min)/2)
 FUNC1The basis functions f_i(x) given in mathematical expressions using _x_ as a variable=x
 FUNC2The basis functions f_i(x) given in mathematical expressions using _x_ as a variable=(1/2)*(3*x^2-1)
 FUNC3The basis functions f_i(x) given in mathematical expressions using _x_ as a variable=(1/2)*(5*x^3-3*x)
 FUNC4The basis functions f_i(x) given in mathematical expressions using _x_ as a variable=(1/8)*(35*x^4-30*x^2+3)
 FUNC5The basis functions f_i(x) given in mathematical expressions using _x_ as a variable=(1/8)*(63*x^5-70*x^3+15*x)
 FUNC6The basis functions f_i(x) given in mathematical expressions using _x_ as a variable=(1/16)*(231*x^6-315*x^4+105*x^2-5)
 MINIMUMThe minimum of the interval on which the basis functions are defined=-4.0
 MAXIMUMThe maximum of the interval on which the basis functions are defined=4.0
 LABELa label for the action so that its output can be referenced in the input to other actions=bf1
... BF_CUSTOM
The BF_CUSTOM action with label bf1 calculates something

Defining Fourier basis functions of order 3 using BF_CUSTOM where the periodicity is indicated using the PERIODIC flag. This is just an example of what can be done, in practice you should use BF_FOURIER for Fourier basis functions.

Click on the labels of the actions for more information on what each action computes

BF_CUSTOMBasis functions given by arbitrary mathematical expressions. More details ...
 FUNC1The basis functions f_i(x) given in mathematical expressions using _x_ as a variable=cos(x)
 FUNC2The basis functions f_i(x) given in mathematical expressions using _x_ as a variable=sin(x)
 FUNC3The basis functions f_i(x) given in mathematical expressions using _x_ as a variable=cos(2*x)
 FUNC4The basis functions f_i(x) given in mathematical expressions using _x_ as a variable=sin(2*x)
 FUNC5The basis functions f_i(x) given in mathematical expressions using _x_ as a variable=cos(3*x)
 FUNC6The basis functions f_i(x) given in mathematical expressions using _x_ as a variable=sin(3*x)
 MINIMUMThe minimum of the interval on which the basis functions are defined=-pi
 MAXIMUMThe maximum of the interval on which the basis functions are defined=+pi
 LABELa label for the action so that its output can be referenced in the input to other actions=bf1
 PERIODIC Indicate that the basis functions are periodic
... BF_CUSTOM
The BF_CUSTOM action with label bf1 calculates something

Full list of keywords

The following table describes the keywords and options that can be used with this action

Keyword	Type	Default	Description
MINIMUM	compulsory	none	The minimum of the interval on which the basis functions are defined
MAXIMUM	compulsory	none	The maximum of the interval on which the basis functions are defined
DEBUG_INFOThis keyword do not have examples	optional	false	Print out more detailed information about the basis set
FUNC	optional	not used	The basis functions f_i(x) given in mathematical expressions using x as a variable
TRANSFORM	optional	not used	An optional function that can be used to transform the argument before calculating the basis function values
PERIODIC	optional	false	Indicate that the basis functions are periodic
CHECK_NAN_INFThis keyword do not have examples	optional	false	Check that the basis functions do not result in a not a number (nan) or infinity (inf)