Module cswt_tmpl_mod

module cswt_tmpl_mod

        ! Uses
    use s2_types_mod
    use cswt_error_mod

        ! Subroutines and functions
    public function cswt_tmpl_s2_costhetaon2 (theta, phi, param) result (val)
    public function cswt_tmpl_s2_gaussian (theta, phi, param) result (val)
    public function cswt_tmpl_s2_butterfly (theta, phi, param) result (val)
    public function cswt_tmpl_s2_mexhat (theta, phi, param) result (val)
    public function cswt_tmpl_s2_morlet (theta, phi, param) result (val)
    public function cswt_tmpl_pln_gaussian (r, phi, param) result (val)
    public function cswt_tmpl_pln_butterfly (r, phi, param) result (val)
    public function cswt_tmpl_pln_mexhat (r, phi, param) result (val)
    public function cswt_tmpl_pln_morlet (r, phi, param) result (val)

end module cswt_tmpl_mod

Contains definitions of template functions defined on both the sky and the plane used to initialise spherical wavelets. The functions defined on the plane are projected onto the sphere numerically, whereas those functions defined on the sphere have already been analytically projected from the plane.

Author: J. D. McEwen (mcewen@mrao.cam.ac.uk)

Version: 0.2 - November 2004

Description of Subroutines and Functions

cswt_tmpl_s2_costhetaon2

public function cswt_tmpl_s2_costhetaon2 (theta, phi, param) result (val)
    real (kind=s2_sp), intent(in) :: theta
    real (kind=s2_sp), intent(in) :: phi
    real (kind=s2_sp), optional, intent(in), dimension (:) :: param
    real (kind=s2_sp) :: val
end function cswt_tmpl_s2_costhetaon2

Template function defined on the sphere. f(theta,phi) = cos(theta/2.0e0)

Notes:

Param array not used.

Variables:

theta: Theta spherical coordiante in range [0,pi].
phi: Phi spherical coordinate in range [0,2pi).
[param]: Optional parameter array.

Author: J. D. McEwen

Version: 0.2 - November 2004

cswt_tmpl_s2_gaussian

public function cswt_tmpl_s2_gaussian (theta, phi, param) result (val)
    real (kind=s2_sp), intent(in) :: theta
    real (kind=s2_sp), intent(in) :: phi
    real (kind=s2_sp), optional, intent(in), dimension (:) :: param
    real (kind=s2_sp) :: val
end function cswt_tmpl_s2_gaussian

Template function defined on the sphere. 2d Gaussian.

Notes:

One parameter in param array: taken as eccentricity.
Two parameters in param array: taken as standard deviations.
Error occurs if param array has length greater than 2.
If no parameter array is given then sigma_x=1 and sigma_y=1.

Variables:

theta: Theta spherical coordiante in range [0,pi].
phi: Phi spherical coordinate in range [0,2pi).
[param]: Optional parameter array.

Author: J. D. McEwen

Version: 0.2 - November 2004

cswt_tmpl_s2_butterfly

public function cswt_tmpl_s2_butterfly (theta, phi, param) result (val)
    real (kind=s2_sp), intent(in) :: theta
    real (kind=s2_sp), intent(in) :: phi
    real (kind=s2_sp), optional, intent(in), dimension (:) :: param
    real (kind=s2_sp) :: val
end function cswt_tmpl_s2_butterfly

Template function defined on the sphere. Butterfly is a Gaussian in y direction and first derrivative of Gaussian in x direction.

Notes:

One parameter in param array: taken as eccentricity.
Two parameters in param array: taken as standard deviations.
Error occurs if param array has length greater than 2.
If no parameter array is given then sigma_x=1 and sigma_y=1.

Variables:

theta: Theta spherical coordiante in range [0,pi].
phi: Phi spherical coordinate in range [0,2pi).
[param]: Optional parameter array.

Author: J. D. McEwen

Version: 0.2 - November 2004

cswt_tmpl_s2_mexhat

public function cswt_tmpl_s2_mexhat (theta, phi, param) result (val)
    real (kind=s2_sp), intent(in) :: theta
    real (kind=s2_sp), intent(in) :: phi
    real (kind=s2_sp), optional, intent(in), dimension (:) :: param
    real (kind=s2_sp) :: val
end function cswt_tmpl_s2_mexhat

Template function defined on the sphere. Mexican hat is negative of Laplacian of 2D Gaussian.

Notes:

One parameter in param array: taken as eccentricity.
Two parameters in param array: taken as standard deviations.
Error occurs if param array has length greater than 2.
If no parameter array is given then sigma_x=1 and sigma_y=1.

Variables:

theta: Theta spherical coordiante in range [0,pi].
phi: Phi spherical coordinate in range [0,2pi).
[param]: Optional parameter array.

Author: J. D. McEwen

Version: 0.2 - November 2004

cswt_tmpl_s2_morlet

public function cswt_tmpl_s2_morlet (theta, phi, param) result (val)
    real (kind=s2_sp), intent(in) :: theta
    real (kind=s2_sp), intent(in) :: phi
    real (kind=s2_sp), optional, intent(in), dimension (:) :: param
    real (kind=s2_sp) :: val
end function cswt_tmpl_s2_morlet

Template function defined on the sphere. Real Morlet wavelet.

Notes:

One parameter in param array: taken as k0 of wave vector, where k=(k0,0).
Error occurs if param array has length greater than 1.
If no parameter array is given then k0=10

Variables:

theta: Theta spherical coordiante in range [0,pi].
phi: Phi spherical coordinate in range [0,2pi).
[param]: Optional parameter array.

Author: J. D. McEwen

Version: 0.2 - November 2004

cswt_tmpl_pln_gaussian

public function cswt_tmpl_pln_gaussian (r, phi, param) result (val)
    real (kind=s2_sp), intent(in) :: r
    real (kind=s2_sp), intent(in) :: phi
    real (kind=s2_sp), optional, intent(in), dimension (:) :: param
    real (kind=s2_sp) :: val
    ! Calls: cswt_error
end function cswt_tmpl_pln_gaussian

Template function defined on the plane. Later projected onto sphere by numerical stereographic projection. 2d Gaussian.

Notes:

One parameter in param array: taken as eccentricity.
Two parameters in param array: taken as standard deviations.
Error occurs if param array has length greater than 2.
If no parameter array is given then sigma_x=1 and sigma_y=1.

Variables:

r: R polar coordinate in 2d.
phi: Phi polar coordinate in range [0,2pi).
[param]: Optional parameter array.

Author: J. D. McEwen

Version: 0.2 - November 2004

cswt_tmpl_pln_butterfly

public function cswt_tmpl_pln_butterfly (r, phi, param) result (val)
    real (kind=s2_sp), intent(in) :: r
    real (kind=s2_sp), intent(in) :: phi
    real (kind=s2_sp), optional, intent(in), dimension (:) :: param
    real (kind=s2_sp) :: val
    ! Calls: cswt_error
end function cswt_tmpl_pln_butterfly

Template function defined on the plane. Later projected onto sphere by numerical stereographic projection. Butterfly is a Gaussian in y direction and first derrivative of Gaussian in x direction.

Notes:

One parameter in param array: taken as eccentricity.
Two parameters in param array: taken as standard deviations.
Error occurs if param array has length greater than 2.
If no parameter array is given then sigma_x=1 and sigma_y=1.

Variables:

r: R polar coordinate in 2d.
phi: Phi polar coordinate in range [0,2pi).
[param]: Optional parameter array.

Author: J. D. McEwen

Version: 0.2 - November 2004

cswt_tmpl_pln_mexhat

public function cswt_tmpl_pln_mexhat (r, phi, param) result (val)
    real (kind=s2_sp), intent(in) :: r
    real (kind=s2_sp), intent(in) :: phi
    real (kind=s2_sp), optional, intent(in), dimension (:) :: param
    real (kind=s2_sp) :: val
    ! Calls: cswt_error
end function cswt_tmpl_pln_mexhat

Template function defined on the plane. Later projected onto sphere by numerical stereographic projection. Mexican hat is negative of Laplacian of 2D Gaussian.

Notes:

One parameter in param array: taken as eccentricity.
Two parameters in param array: taken as standard deviations.
Error occurs if param array has length greater than 2.
If no parameter array is given then sigma_x=1 and sigma_y=1.

Variables:

r: R polar coordinate in 2d.
phi: Phi polar coordinate in range [0,2pi).
[param]: Optional parameter array.

Author: J. D. McEwen

Version: 0.2 - November 2004

cswt_tmpl_pln_morlet

public function cswt_tmpl_pln_morlet (r, phi, param) result (val)
    real (kind=s2_sp), intent(in) :: r
    real (kind=s2_sp), intent(in) :: phi
    real (kind=s2_sp), optional, intent(in), dimension (:) :: param
    real (kind=s2_sp) :: val
    ! Calls: cswt_error
end function cswt_tmpl_pln_morlet

Template function defined on the plane. Later projected onto sphere by numerical stereographic projection. Real Morlet wavelet.

Notes:

One parameter in param array: taken as k0 of wave vector, where k=(k0,0).
Error occurs if param array has length greater than 1.
If no parameter array is given then k0=10

Variables:

r: R polar coordinate in 2d.
phi: Phi polar coordinate in range [0,2pi).
[param]: Optional parameter array.

Author: J. D. McEwen

Version: 0.2 - November 2004