chebyshev_coefficients_oct_m Module Reference

Data Types
interface	chebyshev_exp_imagtime_t
interface	chebyshev_exp_t
type	chebyshev_function_t
interface	chebyshev_get_coefficients
interface	chebyshev_get_error
interface	chebyshev_numerical_t
interface	complex_function_i

Functions/Subroutines
subroutine	chebyshev_set_parameters (this, half_span, middle_point, deltat)
class(chebyshev_exp_t) function, pointer	chebyshev_exp_constructor (half_span, middle_point, deltat)
subroutine	chebyshev_exp_coefficients (this, order, coefficients)
real(real64) function	chebyshev_exp_error (this, order)
	Use the error estimate from Lubich, C. From Quantum to Classical Molecular Dynamics: Reduced Models and Numerical Analysis. (EMS Press, 2008), doi:10.4171/067, Theorems 2.1 to 2.4. More...
class(chebyshev_exp_imagtime_t) function, pointer	chebyshev_exp_imagtime_constructor (half_span, middle_point, deltat)
subroutine	chebyshev_exp_imagtime_coefficients (this, order, coefficients)
real(real64) function	chebyshev_exp_imagtime_error (this, order)
	Use the error estimate from Hochbruck, M. & Ostermann, A. Exponential integrators. Acta Numerica 19, 209–286 (2010), Theorem 4.1 (page 265) and L. Bergamaschi and M. Vianello: Efficient computation of the exponential operator for large, sparse, symmetric matrices, Numer. Linear Algebra Appl. 7, 27–45 (2000), eq. 2.7. More...
class(chebyshev_numerical_t) function, pointer	chebyshev_numerical_constructor (half_span, middle_point, deltat, complex_function)
subroutine	chebyshev_numerical_coefficients (this, order, coefficients)
	use a discrete cosine transform to compute the coefficients because no analytical formula is available for the phi_k functions More...
real(real64) function	chebyshev_numerical_error (this, order)
	use the error estimate from Lubich, C. From Quantum to Classical Molecular Dynamics: Reduced Models and Numerical Analysis. (EMS Press, 2008), doi:10.4171/067, Theorems 2.1 to 2.4 More...

Function/Subroutine Documentation

chebyshev_set_parameters()

subroutine chebyshev_coefficients_oct_m::chebyshev_set_parameters ( class(chebyshev_function_t), intent(inout)  this, real(real64), intent(in)  half_span, real(real64), intent(in)  middle_point, real(real64), intent(in)  deltat  )

private

Definition at line 210 of file chebyshev_coefficients.F90.

chebyshev_exp_constructor()

class(chebyshev_exp_t) function, pointer chebyshev_coefficients_oct_m::chebyshev_exp_constructor ( real(real64), intent(in)  half_span, real(real64), intent(in)  middle_point, real(real64), intent(in)  deltat  )

private

Definition at line 225 of file chebyshev_coefficients.F90.

chebyshev_exp_coefficients()

subroutine chebyshev_coefficients_oct_m::chebyshev_exp_coefficients ( class(chebyshev_exp_t), intent(in)  this, integer, intent(in)  order, complex(real64), dimension(:), intent(out), allocatable  coefficients  )

private

Definition at line 239 of file chebyshev_coefficients.F90.

chebyshev_exp_error()

real(real64) function chebyshev_coefficients_oct_m::chebyshev_exp_error ( class(chebyshev_exp_t), intent(in)  this, integer, intent(in)  order  )

private

Use the error estimate from Lubich, C. From Quantum to Classical Molecular Dynamics: Reduced Models and Numerical Analysis. (EMS Press, 2008), doi:10.4171/067, Theorems 2.1 to 2.4.

Definition at line 258 of file chebyshev_coefficients.F90.

chebyshev_exp_imagtime_constructor()

class(chebyshev_exp_imagtime_t) function, pointer chebyshev_coefficients_oct_m::chebyshev_exp_imagtime_constructor ( real(real64), intent(in)  half_span, real(real64), intent(in)  middle_point, real(real64), intent(in)  deltat  )

private

Definition at line 275 of file chebyshev_coefficients.F90.

chebyshev_exp_imagtime_coefficients()

subroutine chebyshev_coefficients_oct_m::chebyshev_exp_imagtime_coefficients ( class(chebyshev_exp_imagtime_t), intent(in)  this, integer, intent(in)  order, complex(real64), dimension(:), intent(out), allocatable  coefficients  )

private

Definition at line 289 of file chebyshev_coefficients.F90.

chebyshev_exp_imagtime_error()

real(real64) function chebyshev_coefficients_oct_m::chebyshev_exp_imagtime_error ( class(chebyshev_exp_imagtime_t), intent(in)  this, integer, intent(in)  order  )

private

Use the error estimate from Hochbruck, M. & Ostermann, A. Exponential integrators. Acta Numerica 19, 209–286 (2010), Theorem 4.1 (page 265) and L. Bergamaschi and M. Vianello: Efficient computation of the exponential operator for large, sparse, symmetric matrices, Numer. Linear Algebra Appl. 7, 27–45 (2000), eq. 2.7.

Definition at line 310 of file chebyshev_coefficients.F90.

chebyshev_numerical_constructor()

class(chebyshev_numerical_t) function, pointer chebyshev_coefficients_oct_m::chebyshev_numerical_constructor ( real(real64), intent(in)  half_span, real(real64), intent(in)  middle_point, real(real64), intent(in)  deltat, procedure(complex_function_i)  complex_function  )

private

Definition at line 329 of file chebyshev_coefficients.F90.

chebyshev_numerical_coefficients()

subroutine chebyshev_coefficients_oct_m::chebyshev_numerical_coefficients ( class(chebyshev_numerical_t), intent(in)  this, integer, intent(in)  order, complex(real64), dimension(:), intent(out), allocatable  coefficients  )

private

use a discrete cosine transform to compute the coefficients because no analytical formula is available for the phi_k functions

Definition at line 347 of file chebyshev_coefficients.F90.

chebyshev_numerical_error()

real(real64) function chebyshev_coefficients_oct_m::chebyshev_numerical_error ( class(chebyshev_numerical_t), intent(in)  this, integer, intent(in)  order  )

private

use the error estimate from Lubich, C. From Quantum to Classical Molecular Dynamics: Reduced Models and Numerical Analysis. (EMS Press, 2008), doi:10.4171/067, Theorems 2.1 to 2.4

Definition at line 385 of file chebyshev_coefficients.F90.