minimax_exp_k15 Module Reference

Routines to calculate the minimax coefficients in order to approximate 1/x as a sum over exponential functions 1/x ~ SUM_{i}^{K} w_i EXP(-a_i * x) for x belonging to [1:Rc]. This module contains coefficients for minimax approximations with 1 <= k <= 15. More...

Functions/Subroutines
subroutine, public	check_range_k15 (k, Rc, ierr)
	Check that the range for the minimax approximation is not too small for the chosen number of integration point, or that the number of integration point is not exceeding the maximum allowed by the actual implementation. More...
real(kind=dp) function, public	get_minimax_numerical_error (Rc, aw)
	Sample numerical error and return its maximum. More...
subroutine, public	get_minimax_coeff_k15 (k, Rc, aw, mm_error)
	Get minimax coefficients: k15 implementation (coefficients up to k=15 terms). All a_i and w_i have been fitted with a 12th order polynomial as a function of Rc for each value of K. More...

Detailed Description

Routines to calculate the minimax coefficients in order to approximate 1/x as a sum over exponential functions 1/x ~ SUM_{i}^{K} w_i EXP(-a_i * x) for x belonging to [1:Rc]. This module contains coefficients for minimax approximations with 1 <= k <= 15.

History

11.2012 created [Mauro Del Ben] 02.2015 changed module name minimax to minimax_k15 to replace this module with new minimax module, added function to get minimax error [Patrick Seewald]

Function/Subroutine Documentation

check_range_k15()

subroutine, public minimax_exp_k15::check_range_k15	(	integer, intent(in)	k,
		real(kind=dp), intent(in)	Rc,
		integer	ierr
	)

Check that the range for the minimax approximation is not too small for the chosen number of integration point, or that the number of integration point is not exceeding the maximum allowed by the actual implementation.

Parameters

k	...
Rc	...
ierr	...

Author

Mauro Del Ben

Definition at line 43 of file minimax_exp_k15.F.

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get_minimax_numerical_error()

real(kind=dp) function, public minimax_exp_k15::get_minimax_numerical_error	(	real(kind=dp), intent(in)	Rc,
		real(kind=dp), dimension(:), intent(in)	aw
	)

Sample numerical error and return its maximum.

Parameters

Rc	...
aw	...

Returns

...

Author

Patrick Seewald

Definition at line 99 of file minimax_exp_k15.F.

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get_minimax_coeff_k15()

subroutine, public minimax_exp_k15::get_minimax_coeff_k15	(	integer, intent(in)	k,
		real(kind=dp), intent(in)	Rc,
		real(kind=dp), dimension(2*k), intent(out)	aw,
		real(kind=dp), intent(out), optional	mm_error
	)

Get minimax coefficients: k15 implementation (coefficients up to k=15 terms). All a_i and w_i have been fitted with a 12th order polynomial as a function of Rc for each value of K.

Parameters

k	...
Rc	...
aw	...
mm_error	...

Author

Mauro Del Ben

Definition at line 132 of file minimax_exp_k15.F.

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