Chebyshev

These functions provide methods for discrete derivative and integral calculations. More...

Functions
def	SUAVE.Methods.Utilities.Chebyshev.chebyshev_data.chebyshev_data (N=16, integration=True, **options)
def	SUAVE.Methods.Utilities.Chebyshev.linear_data.linear_data (N=16, integration=True, **options)

Detailed Description

These functions provide methods for discrete derivative and integral calculations.

Function Documentation

chebyshev_data()

def SUAVE.Methods.Utilities.Chebyshev.chebyshev_data.chebyshev_data	(		N = 16,
			integration = True,
		**	options
	)

Calculates the differentiation and integration matricies
using chebyshev's pseudospectral algorithm, based on cosine
spaced samples in x.

D and I are not symmetric
get derivatives with df_dy = np.dot(D,f)
get integral with    int_f = np.dot(I,f)
    where f is either a 1-d vector or 2-d column array
    
A full example is available in the function code.

Assumptions:
None

Source:
N/A

Inputs:
N                      [-]        Number of points
integration (optional) <boolean>  Determines if the integration operator is calculated

Outputs:
x                      [-]        N-number of cosine spaced control points, in range [0,1]
D                      [-]        Differentiation operation matrix
I                      [-]        Integration operation matrix, or None if integration = False

Properties Used:
N/A

linear_data()

def SUAVE.Methods.Utilities.Chebyshev.linear_data.linear_data	(		N = 16,
			integration = True,
		**	options
	)

Calculates the differentiation and integration matricies
using chebyshev's pseudospectral algorithm, based on linearly
spaced samples in x.

D and I are not symmetric
get derivatives with df_dy = np.dot(D,f)
get integral with    int_f = np.dot(I,f)
    where f is either a 1-d vector or 2-d column array
    
A full example of how these operators are used is available in 
the chebyshev_data.py (same folder)

Assumptions:
None

Source:
N/A

Inputs:
N                      [-]        Number of points
integration (optional) <boolean>  Determines if the integration operator is calculated

Outputs:
x                      [-]        N-number of cosine spaced control points, in range [0,1]
D                      [-]        Differentiation operation matrix
I                      [-]        Integration operation matrix, or None if integration = False

Properties Used:
N/A