Module s2_sky_mod

module s2_sky_mod

        ! Uses
    use s2_types_mod, only: s2_sp, s2_spc, s2_dp, pi
    use s2_error_mod
    use s2_vect_mod
    use s2_pl_mod

        ! Types
    public type s2_sky

        ! Variables
    integer, public, parameter :: S2_SKY_RING = 1
    integer, public, parameter :: S2_SKY_NEST = 2
    integer, public, parameter :: S2_SKY_FUN_TYPE_SPHERE = 1
    integer, public, parameter :: S2_SKY_FUN_TYPE_PLANE = 2
    integer, public, parameter :: S2_SKY_DEFAULT_FTYPE = S2_SKY_FUN_TYPE_SPHERE
    integer, public, parameter :: S2_SKY_FILE_TYPE_MAP = 1
    integer, public, parameter :: S2_SKY_FILE_TYPE_SKY = 2
    integer, public, parameter :: S2_SKY_FILE_TYPE_ALM = 3

        ! Interfaces
    public interface s2_sky_init

        ! Subroutines and functions
    private function s2_sky_init_empty (nside, pix_scheme, lmax, mmax) result (sky)
    private function s2_sky_init_map (map, nside, pix_scheme, lmax, mmax) result (sky)
    private function s2_sky_init_alm (alm, lmax, mmax, nside, pix_scheme) result (sky)
    private function s2_sky_init_ab (x_ab, interp, nside, pix_scheme, lmax, mmax, sdw) result (sky)
    private function s2_sky_init_fun (fun, nside, pix_scheme, lmax, mmax, param, fun_type_in) result (sky)
    private function s2_sky_init_file (filename, file_type, extension) result (sky)
    private function s2_sky_init_file_map (filename, extension_in) result (sky)
    private function s2_sky_init_file_alm (filename) result (sky)
    private function s2_sky_init_file_sky (filename) result (sky)
    private function s2_sky_init_copy (orig) result (copy)
    public subroutine s2_sky_free (sky)
    public subroutine s2_sky_remove_map (sky)
    public subroutine s2_sky_compute_alm (sky, lmax, mmax, message)
    public subroutine s2_sky_compute_alm_iter (sky, iter_order, lmax, mmax, message)
    public subroutine s2_sky_compute_map (sky, nside, message)
    public subroutine s2_sky_map_convert (sky, pix_scheme)
    public subroutine s2_sky_conv (sky, beam)
    public subroutine s2_sky_offset (sky, offset)
    public subroutine s2_sky_scale (sky, scale)
    public function s2_sky_add (a, b, subtract) result (c)
    public function s2_sky_product (a, b, divide) result (c)
    public subroutine s2_sky_thres (sky, thres_lower, thres_upper)
    public subroutine s2_sky_thres_abs (sky, thres)
    public function s2_sky_error_twonorm (a, b) result (er)
    public function s2_sky_rms (a) result (rms)
    public subroutine s2_sky_dilate (sky, a, b, norm_preserve)
    public subroutine s2_sky_rotate (sky, alpha, beta, gamma)
    public function s2_sky_power_map (sky) result (power)
    public function s2_sky_power_alm (sky) result (power)
    public function s2_sky_azimuthal_bl (sky, cutoff_prop_in) result (mmax_min)
    public function s2_sky_admiss (sky) result (admiss)
    public subroutine s2_sky_admiss_dil (sky, dilation1, dilation2, admiss, norm_preserve_in)
    public subroutine s2_sky_extract_ab_fsht (sky, xtp, L)
    public subroutine s2_sky_extract_ab (sky, x_ab)
    private function s2_sky_interp_ab (x_ab, alpha, beta, interp, sdw) result (interp_val)
    public subroutine s2_sky_downsample (sky, nside_down, mask)
    private subroutine s2_sky_down_nsideby2 (sky, mask_in)
    public subroutine s2_sky_upsample (sky, nside_up)
    private subroutine s2_sky_up_nsideby2 (sky)
    private subroutine s2_sky_valid_sizes (sky)
    public subroutine s2_sky_draw_dot (sky, alpha, beta, large)
    public subroutine s2_sky_write_map_file (sky, filename, comment)
    public subroutine s2_sky_write_alm_file (sky, filename, comment)
    public subroutine s2_sky_io_fits_write (filename, sky, comment)
    private subroutine s2_sky_io_fits_read (filename, sky)
    private subroutine s2_sky_io_fits_error_check (status, halt)
    private subroutine s2_sky_io_fits_exists (filename, status, exists)
    private subroutine s2_sky_io_fits_del (filename, status)
    public subroutine s2_sky_set_lmax (sky, lmax, mmax_in)
    public subroutine s2_sky_set_nside (sky, nside)
    public function s2_sky_get_init (sky) result (init)
    public function s2_sky_get_nside (sky) result (nside)
    public function s2_sky_get_npix (sky) result (npix)
    public function s2_sky_get_lmax (sky) result (lmax)
    public function s2_sky_get_mmax (sky) result (mmax)
    public function s2_sky_get_pix_scheme (sky) result (pix_scheme)
    public subroutine s2_sky_get_map (sky, map)
    public function s2_sky_get_map_pix (sky, ipix) result (map_pix)
    public subroutine s2_sky_get_alm (sky, alm)
    public function s2_sky_get_cl (sky) result (cl)
    public subroutine s2_sky_get_cm (sky, cm)
    public function s2_sky_get_map_status (sky) result (map_status)
    public function s2_sky_get_alm_status (sky) result (alm_status)
    public function s2_sky_get_n_param (sky) result (n_param)
    public subroutine s2_sky_get_param (sky, param)

end module s2_sky_mod

Provides functionality to support and manipulate a function defined on the sky(/sphere). Support is provided to representing the sky in both real (map) space and in harmonic (alm) space, and also to convert between the two representations. One may also scale, dilate, rotate, downsample and add functions defined on the sky. The sky pixelisation used is currently based on HEALPix.

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

Version: 0.1 August 2004

Description of Types

s2_sky

public type s2_sky
    private
    logical :: init = .false.
    integer :: nside = 0
    integer :: npix = 0
    integer :: lmax = 0
    integer :: mmax = 0
    integer :: pix_scheme = S2_SKY_RING
    real (kind=s2_sp), allocatable, dimension (:) :: map
    complex (kind=s2_spc), allocatable, dimension (:,:) :: alm
    logical :: map_status = .false.
    logical :: alm_status = .false.
    real (kind=s2_sp), allocatable, dimension (:) :: param
    integer :: n_param = 0
end type s2_sky

Description of Variables

S2_SKY_RING

integer, public, parameter :: S2_SKY_RING = 1

Healpix pixelisation ring type.

S2_SKY_NEST

integer, public, parameter :: S2_SKY_NEST = 2

Healpix pixelisation nest type.

S2_SKY_FUN_TYPE_SPHERE

integer, public, parameter :: S2_SKY_FUN_TYPE_SPHERE = 1

Specifier to indicate function passed to construct sky is defined on the sphere.

S2_SKY_FUN_TYPE_PLANE

integer, public, parameter :: S2_SKY_FUN_TYPE_PLANE = 2

Specifier to indicate function passed to construct sky is defined on the plane (and will be numerically projected onto the sphere).

S2_SKY_DEFAULT_FTYPE

integer, public, parameter :: S2_SKY_DEFAULT_FTYPE = S2_SKY_FUN_TYPE_SPHERE

Default function type if fun_type flag is not specified.

S2_SKY_FILE_TYPE_MAP

integer, public, parameter :: S2_SKY_FILE_TYPE_MAP = 1

Map fits file type.

S2_SKY_FILE_TYPE_SKY

integer, public, parameter :: S2_SKY_FILE_TYPE_SKY = 2

Full s2_sky file type.

S2_SKY_FILE_TYPE_ALM

integer, public, parameter :: S2_SKY_FILE_TYPE_ALM = 3

Alm fits file type.

Description of Interfaces

s2_sky_init

public interface s2_sky_init
    module procedure s2_sky_init_map
    module procedure s2_sky_init_alm
    module procedure s2_sky_init_ab
    module procedure s2_sky_init_fun
    module procedure s2_sky_init_file
    module procedure s2_sky_init_copy
end interface s2_sky_init

Description of Subroutines and Functions

s2_sky_init_empty

private function s2_sky_init_empty (nside, pix_scheme, lmax, mmax) result (sky)
    integer, optional, intent(in) :: nside
    integer, optional, intent(in) :: pix_scheme
    integer, optional, intent(in) :: lmax
    integer, optional, intent(in) :: mmax
    type (s2_sky) :: sky
    ! Calls: s2_error, s2_sky_valid_sizes
end function s2_sky_init_empty

Initialised an empty sky at a specified resolution. Neither the map or alm sky representations are allocated. They are allocated when required.

Variables:

[nside]: Healpix nside.
[pix_scheme]: Pixelisation scheme for map.
[lmax]: Alm lmax.
[mmax]: Alm lmin.
sky: The returned sky initialised with resolutions.

Author: J. D. McEwen

Version: 0.1 August 2004

s2_sky_init_map

private function s2_sky_init_map (map, nside, pix_scheme, lmax, mmax) result (sky)
    real (kind=s2_sp), intent(in), dimension (:) :: map
    integer, intent(in) :: nside
    integer, intent(in) :: pix_scheme
    integer, optional, intent(in) :: lmax
    integer, optional, intent(in) :: mmax
    type (s2_sky) :: sky
    ! Calls: s2_error
end function s2_sky_init_map

Initalise a sky from a specified map.

Variables:

map: The map array used to initialised the sky.
nside: Healpix nside.
pix_scheme: Pixelisation scheme for map. The passed map is assumed to be in this format.
[lmax]: Alm lmax.
[mmax]: Alm mmax.
sky: The returned sky initialised with the specified map.

Author: J. D. McEwen

Version: 0.1 August 2004

s2_sky_init_alm

private function s2_sky_init_alm (alm, lmax, mmax, nside, pix_scheme) result (sky)
    complex (kind=s2_spc), intent(in), dimension (:,:) :: alm
    integer, intent(in) :: lmax
    integer, intent(in) :: mmax
    integer, optional, intent(in) :: nside
    integer, optional, intent(in) :: pix_scheme
    type (s2_sky) :: sky
    ! Calls: s2_error
end function s2_sky_init_alm

Initalise a sky from a specified alm.

Variables:

alm: The alm array used to initialised the sky.
lmax: Alm lmax.
mmax: Alm mmax.
[nside]: Healpix nside.
[pix_scheme]: Pixelisation scheme for map. No map is initialised but if created this will be the default pixelisation scheme.
sky: The returned sky initialised with the specified alm.

Author: J. D. McEwen

Version: 0.1 August 2004

s2_sky_init_ab

private function s2_sky_init_ab (x_ab, interp, nside, pix_scheme, lmax, mmax, sdw) result (sky)
    real (kind=s2_sp), intent(in), dimension (:,:) :: x_ab
    logical, intent(in) :: interp
    integer, intent(in) :: nside
    integer, intent(in) :: pix_scheme
    integer, optional, intent(in) :: lmax
    integer, optional, intent(in) :: mmax
    logical, optional, intent(in) :: sdw
    type (s2_sky) :: sky
    ! Calls: pix2ang_nest, pix2ang_ring, s2_error
end function s2_sky_init_ab

Initialise a sky from the ecp (equi-sampled) alpha-beta array defined on the sphere.

Notes:

Linear interpolation performed if interp=.true.

Variables:

x_ab: Ecp (equi-sampled) alpha-beta array defining a function on the sphere to construct sky from.
interp: Logical specifying whether interpolation is to be performed.
nside: Healpix nside.
pix_scheme: Pixelisation scheme for map.
[lmax]: Alm lmax.
[mmax]: Alm mmax.
[sdw]: Logical to specify SDW pixelisation.
sky: The returned sky initialised from the ecp (equi-sampled) alpha-beta array defined over the sphere.

Author: J. D. McEwen

Version: 0.1 - November 2004

s2_sky_init_fun

private function s2_sky_init_fun (fun, nside, pix_scheme, lmax, mmax, param, fun_type_in) result (sky)
    interface fun
        function fun (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 fun
    end interface fun
    integer, intent(in) :: nside
    integer, intent(in) :: pix_scheme
    integer, optional, intent(in) :: lmax
    integer, optional, intent(in) :: mmax
    real (kind=s2_sp), optional, intent(in), dimension (:) :: param
    integer, optional, intent(in) :: fun_type_in
    type (s2_sky) :: sky
    ! Calls: pix2ang_nest, pix2ang_ring, s2_error
end function s2_sky_init_fun

Initialise a sky from a template function.

Variables:

nside: Healpix nside.
pix_scheme: Pixelisation scheme for map.
[lmax]: Alm lmax.
[mmax]: Alm mmax.
[param]: Parameter array specifying analytic parameters for the function to be evaluated.
[fun_type_in]: Integer specifing the function type (whether function defined directly on sphere or whether defined on plane and to be numericall projected onto the sphere).
sky: The initialised sky with the template function evaluated over the map.

Author: J. D. McEwen

Version: 0.1 August 2004

s2_sky_init_file

private function s2_sky_init_file (filename, file_type, extension) result (sky)
    character (len=*), intent(in) :: filename
    integer, intent(in) :: file_type
    integer, optional, intent(in) :: extension
    type (s2_sky) :: sky
    ! Calls: s2_error
end function s2_sky_init_file

Wrapper to initialise a sky from either a map fits file or a full s2_sky fits file.

Variables:

filename: The fits filename to read the sky from.
file_type: Fit type specifier to specify whether to read from a fits map file or from a fits full s2_sky file.
[extension]: The fits extension the map to be read is stored in, If not specified the default is 1. (If file_type == S2_SKY_FILE_TYPE_MAP.)
sky: The initialised sky with the map, nside, etc. defined from the fits file.

Author: J. D. McEwen

Version: 0.1 April 2005

s2_sky_init_file_map

private function s2_sky_init_file_map (filename, extension_in) result (sky)
    character (len=*), intent(in) :: filename
    integer, optional, intent(in) :: extension_in
    type (s2_sky) :: sky
    ! Calls: input_map, s2_error
end function s2_sky_init_file_map

Initialise a sky from a map file.

Variables:

filename: The fits filename to read the map from.
[extension_in]: The fits extension the map to be read is stored in, If not specified the default is 1.
sky: The initialised sky with the map, nside, etc. defined from the map contained in the fits file.

Author: J. D. McEwen

Version: 0.1 August 2004

s2_sky_init_file_alm

private function s2_sky_init_file_alm (filename) result (sky)
    character (len=*), intent(in) :: filename
    type (s2_sky) :: sky
    ! Calls: fits2alms, s2_error
end function s2_sky_init_file_alm

Initialise a sky from a fits alm file.

Variables:

filename: The fits filename to read the alms from.
sky: The initialised sky with the alms, lmax and mmax defined from the alms contained in the fits file.

Author: J. D. McEwen

Version: 0.1 November 2005

s2_sky_init_file_sky

private function s2_sky_init_file_sky (filename) result (sky)
    character (len=*), intent(in) :: filename
    type (s2_sky) :: sky
    ! Calls: s2_error, s2_sky_io_fits_read
end function s2_sky_init_file_sky

Wrapper to initialise a sky data structure from a full s2_sky file. The sky structure is read and initialised by the routine s2_sky_io_fits_read.

Notes:

Cannot be part of s2_sky_init interface since has same signature as s2_sky_init_map_file.

Variables:

filename: Name of s2_sky fits file containing the sky data to be read.
sky: Returned sky structure initialised with the data contained in the input s2_sky fits file.

Author: J. D. McEwen

Version: 0.1 - April 2005

s2_sky_init_copy

private function s2_sky_init_copy (orig) result (copy)
    type (s2_sky), intent(in) :: orig
    type (s2_sky) :: copy
    ! Calls: s2_error
end function s2_sky_init_copy

Initialise a sky as a copy of another sky.

Variables:

orig: The original sky to copy.
copy: The initialised map copied from the original.

Author: J. D. McEwen

Version: 0.1 August 2004

s2_sky_free

public subroutine s2_sky_free (sky)
    type (s2_sky), intent(inout) :: sky
    ! Calls: s2_error
end subroutine s2_sky_free

Free all data associated with an initialised sky and reset all other attributes.

Variables:

sky: The sky to be freed.

Author: J. D. McEwen

Version: 0.1 August 2004

s2_sky_remove_map

public subroutine s2_sky_remove_map (sky)
    type (s2_sky), intent(inout) :: sky
    ! Calls: s2_error
end subroutine s2_sky_remove_map

Free all data associated with a map and reset all map related attributes.

Variables:

sky: The sky containing the map to be removed.

Author: J. D. McEwen

Version: 0.1 November 2007

s2_sky_compute_alm

public subroutine s2_sky_compute_alm (sky, lmax, mmax, message)
    type (s2_sky), intent(inout) :: sky
    integer, optional, intent(in) :: lmax
    integer, optional, intent(in) :: mmax
    logical, optional, intent(in) :: message
    ! Calls: map2alm, s2_error, s2_sky_map_convert, s2_sky_set_lmax, s2_sky_valid_sizes
end subroutine s2_sky_compute_alm

Compute the alms for a sky from the map representation. Errors occur if the initialised sky does not have a map defined.

Variables:

sky: The sky to compute the alms for.
[lmax]: If specified overwrites the lmax of the sky.
[mmax]: If specified overwrites the mmax of the sky.

Author: J. D. McEwen

Version: 0.1 August 2004

s2_sky_compute_alm_iter

public subroutine s2_sky_compute_alm_iter (sky, iter_order, lmax, mmax, message)
    type (s2_sky), intent(inout) :: sky
    integer, intent(in) :: iter_order
    integer, optional, intent(in) :: lmax
    integer, optional, intent(in) :: mmax
    logical, optional, intent(in) :: message
    ! Calls: alm2map, map2alm, s2_error, s2_sky_map_convert, s2_sky_set_lmax, s2_sky_valid_sizes
end subroutine s2_sky_compute_alm_iter

Compute the alms for a sky from the map representation using iteration. Errors occur if the initialised sky does not have a map defined.

Variables:

sky: The sky to compute the alms for.
iter_order: Number of iterations to perform (iter_order=0 gives same results as s2_sky_compute_alm
[lmax]: If specified overwrites the lmax of the sky.
[mmax]: If specified overwrites the mmax of the sky.

Author: J. D. McEwen

Version: 0.1 November 2007

s2_sky_compute_map

public subroutine s2_sky_compute_map (sky, nside, message)
    type (s2_sky), intent(inout) :: sky
    integer, optional, intent(in) :: nside
    logical, optional, intent(in) :: message
    ! Calls: alm2map, s2_error, s2_sky_set_nside, s2_sky_valid_sizes
end subroutine s2_sky_compute_map

Compute the map for a sky from the alm representation. Errors occur if the initialised sky does not have an alm defined.

Variables:

sky: The sky to compute the map for.
[nside]: If specified overwrites the nside of the sky.

Author: J. D. McEwen

Version: 0.1 August 2004

s2_sky_map_convert

public subroutine s2_sky_map_convert (sky, pix_scheme)
    type (s2_sky), intent(inout) :: sky
    integer, intent(in) :: pix_scheme
    ! Calls: convert_nest2ring, convert_ring2nest, s2_error
end subroutine s2_sky_map_convert

Convert the map pixelisation scheme to that specified. If the map is already in the required pixelisation scheme then do nothing.

Variables:

sky: Sky to convert pixelisation scheme.
pix_scheme: Required pixelisation scheme.

Author: J. D. McEwen

Version: 0.1 August 2004

s2_sky_conv

public subroutine s2_sky_conv (sky, beam)
    type (s2_sky), intent(inout) :: sky
    type (s2_pl), intent(in) :: beam
    ! Calls: s2_error, s2_pl_conv, s2_sky_compute_map
end subroutine s2_sky_conv

Convolve a sky with a beam.

Notes:

Sky alms must already be defined since if not lmax and mmax may not be defined.

Variables:

sky: Sky to convolve with beam. Convolved sky on ouput.
beam: Beam to convolve with sky.

Author: J. D. McEwen

Version: 0.1 May 2005

s2_sky_offset

public subroutine s2_sky_offset (sky, offset)
    type (s2_sky), intent(inout) :: sky
    real (kind=s2_sp), intent(in) :: offset
    ! Calls: s2_error, s2_sky_compute_alm, s2_sky_compute_map
end subroutine s2_sky_offset

Add an offset to the sky.

Variables:

sky: Sky to add offset to.
offset: Offset to add.

Author: J. D. McEwen

Version: 0.1 June 2006

s2_sky_scale

public subroutine s2_sky_scale (sky, scale)
    type (s2_sky), intent(inout) :: sky
    real (kind=s2_sp), intent(in) :: scale
    ! Calls: s2_error
end subroutine s2_sky_scale

Scale both the sky map and alm.

Variables:

sky: Sky to scale.
scale: Scale to apply

Author: J. D. McEwen

Version: 0.1 August 2004

s2_sky_add

public function s2_sky_add (a, b, subtract) result (c)
    type (s2_sky), intent(inout) :: a
    type (s2_sky), intent(inout) :: b
    logical, optional, intent(in) :: subtract
    type (s2_sky) :: c
    ! Calls: s2_error, s2_sky_compute_map, s2_sky_map_convert
end function s2_sky_add

Add the maps of two skys.

Variables:

a: First sky to be added.
b: Second sky to be added
[subtract]: Logcal specifying whether to subtract, rather than add maps.
c: The output initialised sky whos map is the sum of the maps of the other two passed skies.

Author: J. D. McEwen

Version: 0.1 August 2004

s2_sky_product

public function s2_sky_product (a, b, divide) result (c)
    type (s2_sky), intent(inout) :: a
    type (s2_sky), intent(inout) :: b
    logical, optional, intent(in) :: divide
    type (s2_sky) :: c
    ! Calls: s2_error, s2_sky_compute_map, s2_sky_map_convert
end function s2_sky_product

Multiply two sky maps together.

Variables:

a: First sky.
b: Second sky.
[divide]: Logcal specifying whether to dive, rather than multiply maps (if so result is a/b).
c: The output initialised sky whos map is the product of the maps of the other two passed skies.

Author: J. D. McEwen

Version: 0.1 August 2005

s2_sky_thres

public subroutine s2_sky_thres (sky, thres_lower, thres_upper)
    type (s2_sky), intent(inout) :: sky
    real (kind=s2_sp), intent(in) :: thres_lower
    real (kind=s2_sp), intent(in) :: thres_upper
    ! Calls: s2_error, s2_sky_compute_alm, s2_sky_compute_map
end subroutine s2_sky_thres

Threshold all values outside range to specified limits.

Variables:

sky: Sky to threshold.
thres_lower: Lower threshold value.
thres_upper: Upper threshold value.

Author: J. D. McEwen

Version: 0.1 April 2007

s2_sky_thres_abs

public subroutine s2_sky_thres_abs (sky, thres)
    type (s2_sky), intent(inout) :: sky
    real (kind=s2_sp), intent(in) :: thres
    ! Calls: s2_error, s2_sky_compute_alm, s2_sky_compute_map
end subroutine s2_sky_thres_abs

Threshold all values below (in absolute value) specified threshold.

Variables:

sky: Sky to threshold.
thres: Threshold value.

Author: J. D. McEwen

Version: 0.1 April 2007

s2_sky_error_twonorm

public function s2_sky_error_twonorm (a, b) result (er)
    type (s2_sky), intent(inout) :: a
    type (s2_sky), intent(inout) :: b
    real (kind=s2_sp) :: er
    ! Calls: s2_error, s2_sky_compute_map, s2_sky_map_convert
end function s2_sky_error_twonorm

Compute two-norm error (i.e. mean square error) or two sky maps.

Variables:

a: First sky.
b: Second sky.
error: Two-norm error computed by er = sqrt( int( (a(w)-b(w))^2 )dw ).

Author: J. D. McEwen

Version: 0.1 April 2007

s2_sky_rms

public function s2_sky_rms (a) result (rms)
    type (s2_sky), intent(inout) :: a
    real (kind=s2_sp) :: rms
    ! Calls: s2_error, s2_sky_compute_map
end function s2_sky_rms

Compute root-mean squared value of sky (same as error_twonorm with second sky set to zero).

Variables:

a: Sky to compute RMS value of.
rms: RMS value of sky computed by er = sqrt( int( (a(w))^2 )dw ).

Author: J. D. McEwen

Version: 0.1 April 2007

s2_sky_dilate

public subroutine s2_sky_dilate (sky, a, b, norm_preserve)
    type (s2_sky), intent(inout) :: sky
    real (kind=s2_sp), intent(in) :: a
    real (kind=s2_sp), intent(in) :: b
    logical, intent(in) :: norm_preserve
    ! Calls: ang2pix_nest, ang2pix_ring, pix2ang_nest, pix2ang_ring, s2_error
end subroutine s2_sky_dilate

Dilate the map of a sky. The dilation may be performed in two orthogonal directions. To perform the usual isotropic dilation set a=b.

Variables:

sky: Sky to dilate.
a: First dilation scale.
b: Second dilation scale.
norm_preserve: Logical specifying whether a norm preserving `cocycle' factor is to be applied.

Author: J. D. McEwen

Version: 0.1 August 2004

s2_sky_rotate

public subroutine s2_sky_rotate (sky, alpha, beta, gamma)
    type (s2_sky), intent(inout) :: sky
    real (kind=s2_sp) :: alpha
    real (kind=s2_sp) :: beta
    real (kind=s2_sp) :: gamma
    ! Calls: ang2pix_nest, ang2pix_ring, pix2ang_nest, pix2ang_ring, s2_error, s2_vect_free, s2_vect_rotate
end subroutine s2_sky_rotate

Rotate the map of a sky. The rotation is perform in real space. The rotation is defined by the rotation routine in the s2_vect_mod class.

Variables

sky: The sky rotated.
alpha: Alpha Euler angle of the rotation.
beta: Beta Euler angle of the rotation.
gamma: Gamma Euler angle of the rotation.

Author: J. D. McEwen

Version: 0.1 August 2004

s2_sky_power_map

public function s2_sky_power_map (sky) result (power)
    type (s2_sky), intent(in) :: sky
    real (kind=s2_sp) :: power
    ! Calls: s2_error
end function s2_sky_power_map

Compute power of function on sphere in map space.

Variables:

sky: Sky to compute power of.
power: Full power computed.

Author: J. D. McEwen

Version: 0.1 May 2006

s2_sky_power_alm

public function s2_sky_power_alm (sky) result (power)
    type (s2_sky), intent(in) :: sky
    real (kind=s2_sp) :: power
    ! Calls: s2_error, s2_pl_free
end function s2_sky_power_alm

Compute power of function on sphere in alm space.

Variables:

sky: Sky to compute power of.
power: Full power computed.

Author: J. D. McEwen

Version: 0.1 May 2006

s2_sky_azimuthal_bl

public function s2_sky_azimuthal_bl (sky, cutoff_prop_in) result (mmax_min)
    type (s2_sky), intent(in) :: sky
    real (kind=s2_sp), optional, intent(in) :: cutoff_prop_in
    integer :: mmax_min
    ! Calls: s2_error, s2_pl_free, s2_pl_get_spec, s2_sky_get_cm
end function s2_sky_azimuthal_bl

Find azimuthal band limit of sky. Finds lowest m' value such that cutoff_prop*100 percent of the cm power is contained in the alms with m index below m'.

Notes:

Only successful if alms for the sky are already computed. Cannot mmax may not be defined.

Variables

sky: Sky to find azimuthal band limit for.
[cutoff_prop_in]: Cutoff proportion to use when finding azimuthal band limit. If not specified default value is used.
mmax_min: The azimuthal band limit found.

Author: J. D. McEwen

Version: 0.1 May 2005

s2_sky_admiss

public function s2_sky_admiss (sky) result (admiss)
    type (s2_sky), intent(in) :: sky
    real (kind=s2_sp) :: admiss
    ! Calls: pix2ang_nest, pix2ang_ring, s2_error
end function s2_sky_admiss

Calculte the normalised numerical admissibility of a wavelet defined on the sphere.

Notes:

To developers: Have a consistent area element in every term of discretised integral thus it cancels and may be removed.

Variables:

sky: Sky to calculate wavelet admissibility of.
admiss: Normalised numerical admissibility value calculated.

Author: J. D. McEwen

Version: 0.1 August 2004

s2_sky_admiss_dil

public subroutine s2_sky_admiss_dil (sky, dilation1, dilation2, admiss, norm_preserve_in)
    type (s2_sky), intent(in) :: sky
    real (kind=s2_sp), intent(in), dimension (:) :: dilation1
    real (kind=s2_sp), intent(in), dimension (:) :: dilation2
    real (kind=s2_sp), intent(out), dimension (:) :: admiss
    logical, optional, intent(in) :: norm_preserve_in
    ! Calls: s2_error, s2_sky_dilate, s2_sky_free
end subroutine s2_sky_admiss_dil

Compute admissibility for function defined on sphere for a range of dilations.

Variables:

sky: Original (undilated) sky to calculated dilations of.
dilation1: Array of first dilation components.
dilation2: Array of second dilation components.
admiss: Array of admissibility values calculated corresponding to the dilated version of the passed function defined on the sphere.
[norm_preserve_in]: Logical to specify whether dilations are to preserve the 2-norm.

Author: J. D. McEwen

Version: 0.1 - November 2004

s2_sky_extract_ab_fsht

public subroutine s2_sky_extract_ab_fsht (sky, xtp, L)
    type (s2_sky), intent(in) :: sky
    real (kind=s2_sp), intent(out), dimension (0:L,0:2*L) :: xtp
    integer, intent(in) :: L
    ! Calls: ang2pix_nest, ang2pix_ring, s2_error
end subroutine s2_sky_extract_ab_fsht

Extra an ecp (equispaced) sampled theta-phi array over the sphere for the grid used for the Fast Spherical Harmonic Transform.

Notes:

No interpolation performed.
The size of xtp must already be specified and allocated.

Variables:

sky: Sky to extract theta-phi array representation of.
xtp: The extracted discrete theta-phi data array corresponding to the given sky.

Author: J. D. McEwen

Version: 0.1 - April 2008

s2_sky_extract_ab

public subroutine s2_sky_extract_ab (sky, x_ab)
    type (s2_sky), intent(in) :: sky
    real (kind=s2_sp), intent(out), dimension (:,:) :: x_ab
    ! Calls: ang2pix_nest, ang2pix_ring, s2_error
end subroutine s2_sky_extract_ab

Extra an ecp (equispaced) sampled alpha-beta array over the sphere corresponding to the given sky.

Notes:

No interpolation performed.
The size of x_ab must already be specified and allocated.

Variables:

sky: Sky to extract alpha-beta array representation of.
x_ab: The extracted discrete alpha-beta data array corresponding to the given sky.

Author: J. D. McEwen

Version: 0.1 - November 2004

s2_sky_interp_ab

private function s2_sky_interp_ab (x_ab, alpha, beta, interp, sdw) result (interp_val)
    real (kind=s2_sp), intent(in), dimension (:,:) :: x_ab
    real (kind=s2_dp), intent(inout) :: alpha
    real (kind=s2_dp), intent(inout) :: beta
    logical, intent(in) :: interp
    logical, optional, intent(in) :: sdw
    real (kind=s2_sp) :: interp_val
end function s2_sky_interp_ab

Interpolate a pixelised ab array for any continuous value in the appropriate angle ranges.

Notes:

Linear interpolation used.
Angles outside the valid range for alpha [0,2*pi] and beta [0,pi] are mapped onto the mod of the angle for the relevant range.

Variables:

x_ab: The discrete ab data array to be interpolated.
alpha: The alpha continuous angle to interpolate at.
beta: The beta continuous angle to interpolate at.
interp: Logical to specify whether interpolation is to be performed. If not, then the nearest (lower) sample is simply taken.
[sdw]: Logical to specify SDW pixelisation.

Author: J. D. McEwen

Version: 0.1 - November 2004

s2_sky_downsample

public subroutine s2_sky_downsample (sky, nside_down, mask)
    type (s2_sky), intent(inout) :: sky
    integer, intent(in) :: nside_down
    logical, optional, intent(in) :: mask
    ! Calls: s2_error, s2_sky_down_nsideby2
end subroutine s2_sky_downsample

Downsample a sky map nside to the specified (lower!) nside.

Variables:

sky: Sky to be downsampled.
nside_down: The new nside of the downsampled sky.
mask: Logical specifying whether sky to downsample is a mask (in which case pixels are multiplied to downsample rather than averaged).

Author: J. D. McEwen

Version: 0.1 August 2004

s2_sky_down_nsideby2

private subroutine s2_sky_down_nsideby2 (sky, mask_in)
    type (s2_sky), intent(inout) :: sky
    logical, optional, intent(in) :: mask_in
    ! Calls: s2_error, s2_sky_map_convert
end subroutine s2_sky_down_nsideby2

Downsample a sky map nside by a factor of two.

Variables:

sky: Sky to be downsampled.
mask_in: Logical specifying whether sky to downsample is a mask (in which case pixels are multiplied to downsample rather than averaged).

Author: J. D. McEwen

Version: 0.1 August 2004

s2_sky_upsample

public subroutine s2_sky_upsample (sky, nside_up)
    type (s2_sky), intent(inout) :: sky
    integer, intent(in) :: nside_up
    ! Calls: s2_error, s2_sky_up_nsideby2
end subroutine s2_sky_upsample

Up-sample a sky map nside to the specified (greater!) nside. Map is up-sampled by simply setting all sub pixels in a nested region to the value of the parent pixel).

Variables:

sky: Sky to be upsampled.
nside_down: The new nside of the downsampled sky.

Author: J. D. McEwen

Version: 0.1 August 2005

s2_sky_up_nsideby2

private subroutine s2_sky_up_nsideby2 (sky)
    type (s2_sky), intent(inout) :: sky
    ! Calls: s2_error, s2_sky_map_convert
end subroutine s2_sky_up_nsideby2

Up-sample a sky map nside by a factor of two (simply set all sub pixels in a nested region to the value of the parent pixel).

Variables:

sky: Sky to be up-sampled.

Author: J. D. McEwen

Version: 0.1 August 2005

s2_sky_valid_sizes

private subroutine s2_sky_valid_sizes (sky)
    type (s2_sky), intent(in) :: sky
    ! Calls: s2_error
end subroutine s2_sky_valid_sizes

Check the nside, lmax and mmax resolutions are valid. Invalid if any are negative. Also warning given if lmax > 3*nside of mmax < lmax

Variables:

sky: Sky to check sizes of.

Author: J. D. McEwen

Version: 0.1 August 2004

s2_sky_draw_dot

public subroutine s2_sky_draw_dot (sky, alpha, beta, large)
    type (s2_sky), intent(inout) :: sky
    real (kind=s2_sp), intent(in), dimension (:) :: alpha
    real (kind=s2_sp), intent(in), dimension (:) :: beta
    logical, optional, intent(in) :: large
    ! Calls: ang2pix_nest, neighbours_nest, s2_error, s2_sky_map_convert
end subroutine s2_sky_draw_dot

Draw dots on sky map at specified positions.

Variables:

sky: Sky to draw dots on map of.
alpha: Alpha array of dot positions.
beta: Beta array of dot positions. (Must have same size as alpha array.)
[large]: Logical to indicate whether to draw large dots.

Author: J. D. McEwen

Version: 0.1 August 2004

s2_sky_write_map_file

public subroutine s2_sky_write_map_file (sky, filename, comment)
    type (s2_sky), intent(in) :: sky
    character (len=*), intent(in) :: filename
    character (len=*), optional, intent(in) :: comment
    ! Calls: add_card, s2_error, write_bintab
end subroutine s2_sky_write_map_file

Write a sky map to a fits file.

Variables:

sky: Sky containing the map to write to a fits file.
filename: Name of the output fits file.
[comment]: Optional additional comment to be added to the fits file header.

Author: J. D. McEwen

Version: 0.1 August 2004

s2_sky_write_alm_file

public subroutine s2_sky_write_alm_file (sky, filename, comment)
    type (s2_sky), intent(in) :: sky
    character (len=*), intent(in) :: filename
    character (len=*), optional, intent(in) :: comment
    ! Calls: add_card, alms2fits, s2_error
end subroutine s2_sky_write_alm_file

Write sky alms to a fits file.

Variables:

sky: Sky containing the alm to write to a fits file.
filename: Name of the output fits file.
[comment]: Optional additional comment to be added to the fits file header.

Author: J. D. McEwen

Version: 0.1 November 2005

s2_sky_io_fits_write

public subroutine s2_sky_io_fits_write (filename, sky, comment)
    character (len=*), intent(in) :: filename
    type (s2_sky), intent(in) :: sky
    character (len=*), optional, intent(in) :: comment
    ! Calls: ftclos, ftfiou, ftgiou, ftibin, ftiimg, ftinit, ftp2de, ftpcle, ftpcom, ftpdat, ftphpr, ftpkyj, ftpkyl, ftpkys, s2_error, s2_sky_io_fits_error_check, s2_sky_io_fits_exists
end subroutine s2_sky_io_fits_write

Write a s2_sky object to a fits file. All s2_sky data is writtend to the file (i.e. both the map and alms are written if present, as well as any sky function parameters and all other s2_sky variables.

Variables:

filename: Name of the output fits file to write the sky structure data to.
sky: The sky structure containing the data to be written to the output fits file.
[comment]: Optional comment string to be added to the output fits file header if present.

Author: J. D. McEwen

Version: 0.1 - April 2005

s2_sky_io_fits_read

private subroutine s2_sky_io_fits_read (filename, sky)
    character (len=*), intent(in) :: filename
    type (s2_sky), intent(out) :: sky
    ! Calls: ftclos, ftfiou, ftg2de, ftgcve, ftgiou, ftgkyj, ftgkyl, ftmahd, ftopen, ftthdu, s2_error, s2_sky_io_fits_error_check, s2_sky_io_fits_exists
end subroutine s2_sky_io_fits_read

Reads a full s2_sky fits file and allocates a new sky structure with the data read.

Variables:

filename: Name of s2_sky fits file containing the sky data to be read.
sky: Returned sky structure initialised with the data contained in the input s2_sky fits file.

Author: J. D. McEwen

Version: 0.1 - April 2005

s2_sky_io_fits_error_check

private subroutine s2_sky_io_fits_error_check (status, halt)
    integer, intent(inout) :: status
    logical, intent(in) :: halt
    ! Calls: ftgerr, ftgmsg
end subroutine s2_sky_io_fits_error_check

Check if a fits error has occured and print error message. Halt program execution if halt flag is set.

Notes:

Copied form cswt_tr_mod module.

Variables:

status: Fits integer status code.
halt: Logical to indicate whether to halt program execution if an error is detected.

Author: J. D. McEwen

Version: 0.1 - November 2004

s2_sky_io_fits_exists

private subroutine s2_sky_io_fits_exists (filename, status, exists)
    character (len=*), intent(in) :: filename
    integer, intent(inout) :: status
    logical, intent(out) :: exists
    ! Calls: ftclos, ftfiou, ftgiou, ftopen, s2_sky_io_fits_error_check
end subroutine s2_sky_io_fits_exists

Check if a fits file exists.

Notes:

Copied form cswt_tr_mod module.

Variables:

filename: Name of fits file to check existence of.
status: Fits integer status code.
exists: Logical indicating whether the fits file already exists.

Author: J. D. McEwen

Version: 0.1 - November 2004

s2_sky_io_fits_del

private subroutine s2_sky_io_fits_del (filename, status)
    character (len=*), intent(in) :: filename
    integer, intent(inout) :: status
    ! Calls: ftcmsg, ftdelt, ftfiou, ftgiou, ftopen
end subroutine s2_sky_io_fits_del

Delete a fits file.

Notes:

Copied form cswt_tr_mod module.

Variables:

filename: Name of fits file to detele.
status: Fits integer status code.

Author: J. D. McEwen

Version: 0.1 - November 2004

s2_sky_set_lmax

public subroutine s2_sky_set_lmax (sky, lmax, mmax_in)
    type (s2_sky), intent(inout) :: sky
    integer, intent(in) :: lmax
    integer, optional, intent(in) :: mmax_in
    ! Calls: s2_sky_valid_sizes
end subroutine s2_sky_set_lmax

Set a sky lmax. If alm is calculated it is removed.

Variables:

sky: Sky to set lmax of.
lmax: New lmax to set.
[mmax_in]: New mmax to set. If not specified defaults to new lmax.

Author: J. D. McEwen

Version: 0.1 August 2004

s2_sky_set_nside

public subroutine s2_sky_set_nside (sky, nside)
    type (s2_sky), intent(inout) :: sky
    integer, intent(in) :: nside
    ! Calls: s2_sky_valid_sizes
end subroutine s2_sky_set_nside

Set a sky nside. If map is calculated it is removed.

Variables:

sky: Sky to set nside of.
nside: New nside to set.

Author: J. D. McEwen

Version: 0.1 August 2004

s2_sky_get_init

public function s2_sky_get_init (sky) result (init)
    type (s2_sky), intent(in) :: sky
    logical :: init
end function s2_sky_get_init

Get init variable from the passed sky.

Variables:

sky: Sky object to get the variable of.
init: Object init variable returned.

Author: J. D. McEwen

Version: 0.1 August 2004

s2_sky_get_nside

public function s2_sky_get_nside (sky) result (nside)
    type (s2_sky), intent(in) :: sky
    integer :: nside
    ! Calls: s2_error
end function s2_sky_get_nside

Get nside variable from the passed sky.

Variables:

sky: Sky object to get the variable of.
nside: Object nside variable returned.

Author: J. D. McEwen

Version: 0.1 August 2004

s2_sky_get_npix

public function s2_sky_get_npix (sky) result (npix)
    type (s2_sky), intent(in) :: sky
    integer :: npix
    ! Calls: s2_error
end function s2_sky_get_npix

Get nside variable from the passed sky.

Variables:

sky: Sky object to get the variable of.
npix: Object npix variable returned.

Author: J. D. McEwen

Version: 0.1 August 2004

s2_sky_get_lmax

public function s2_sky_get_lmax (sky) result (lmax)
    type (s2_sky), intent(in) :: sky
    integer :: lmax
    ! Calls: s2_error
end function s2_sky_get_lmax

Get lmax variable from the passed sky.

Variables:

sky: Sky object to get the variable of.
lmax: Object lmax variable returned.

Author: J. D. McEwen

Version: 0.1 August 2004

s2_sky_get_mmax

public function s2_sky_get_mmax (sky) result (mmax)
    type (s2_sky), intent(in) :: sky
    integer :: mmax
    ! Calls: s2_error
end function s2_sky_get_mmax

Get mmax variable from the passed sky.

Variables:

sky: Sky object to get the variable of.
mmax: Object mmax variable returned.

Author: J. D. McEwen

Version: 0.1 August 2004

s2_sky_get_pix_scheme

public function s2_sky_get_pix_scheme (sky) result (pix_scheme)
    type (s2_sky), intent(in) :: sky
    integer :: pix_scheme
    ! Calls: s2_error
end function s2_sky_get_pix_scheme

Get pix_scheme variable from the passed sky.

Variables:

sky: Sky object to get the variable of.
pix_scheme: Object pix_scheme variable returned.

Author: J. D. McEwen

Version: 0.1 August 2004

s2_sky_get_map

public subroutine s2_sky_get_map (sky, map)
    type (s2_sky), intent(in) :: sky
    real (kind=s2_sp), intent(out), dimension (:) :: map
    ! Calls: s2_error
end subroutine s2_sky_get_map

Get map variable from the passed sky.

Variables:

sky: Sky object to get the variable of.
map(:): Object map variable returned.

Author: J. D. McEwen

Version: 0.1 August 2004

s2_sky_get_map_pix

public function s2_sky_get_map_pix (sky, ipix) result (map_pix)
    type (s2_sky), intent(in) :: sky
    integer, intent(in) :: ipix
    real (kind=s2_sp) :: map_pix
    ! Calls: s2_error
end function s2_sky_get_map_pix

Get map pixel from the passed sky.

Variables:

sky: Sky object to get the variable of.
map_pix: Object map pixel variable returned.
ipix: The index of the pixel to get (in range [0:sky%npix-1]).

Author: J. D. McEwen

Version: 0.1 August 2004

s2_sky_get_alm

public subroutine s2_sky_get_alm (sky, alm)
    type (s2_sky), intent(in) :: sky
    complex (kind=s2_spc), intent(out), dimension (:,:) :: alm
    ! Calls: s2_error
end subroutine s2_sky_get_alm

Get alm variable from the passed sky.

Variables:

sky: Sky object to get the variable of.
alm(:,:): Object alm variable returned.

Author: J. D. McEwen

Version: 0.1 August 2004

s2_sky_get_cl

public function s2_sky_get_cl (sky) result (cl)
    type (s2_sky), intent(in) :: sky
    type (s2_pl) :: cl
    ! Calls: s2_error
end function s2_sky_get_cl

Compute cl for the given sky.

Notes:

Only successful if alms for the sky are already computed. Cannot mmax may not be defined.
Initialses a new pl object which must be freed by calling routine.
Map assumed real (thus alms only stored from m>=0) hence cl computed by: cl = 1/(2*l+1) * ( |a_{l,0}|^2 + 2 * \sum_{m=1}^l |a_{l,m}|^2 )

Variables:

sky: Sky object to get the variable of.
cl: Cls computed for the sky.

Author: J. D. McEwen

Version: 0.1 January 2005

s2_sky_get_cm

public subroutine s2_sky_get_cm (sky, cm)
    type (s2_sky), intent(in) :: sky
    real (kind=s2_sp), intent(out), dimension (0:) :: cm
    ! Calls: s2_error
end subroutine s2_sky_get_cm

Compute cm for the given sky.

Notes:

Only successful if alms for the sky are already computed. Cannot mmax may not be defined.
Map assumed real (thus alms only stored from m>=0) hence cm computed by: cm = 1/(2*(lmax-m)+2-dm0) * \sum_{l=m}^lmax [ 2*(1-dm0)*|a_{l,m}|^2 + dm0*|a_{l,0}|^2 ] where dm0 is the Kronecker delta.
Predominately used for determined azimuthal band limit of a sky.

Variables:

sky: Sky object to get the variable of.
cm: Cms computed for the sky.

Author: J. D. McEwen

Version: 0.1 April 2005

s2_sky_get_map_status

public function s2_sky_get_map_status (sky) result (map_status)
    type (s2_sky), intent(in) :: sky
    logical :: map_status
    ! Calls: s2_error
end function s2_sky_get_map_status

Get map_status variable from the passed sky.

Variables:

sky: Sky object to get the variable of.
map_status: Object map_status variable returned.

Author: J. D. McEwen

Version: 0.1 August 2004

s2_sky_get_alm_status

public function s2_sky_get_alm_status (sky) result (alm_status)
    type (s2_sky), intent(in) :: sky
    logical :: alm_status
    ! Calls: s2_error
end function s2_sky_get_alm_status

Get map_status variable from the passed sky.

Variables:

sky: Sky object to get variable of.
alm_status: Object alm_status variable returned.

Author: J. D. McEwen

Version: 0.1 August 2004

s2_sky_get_n_param

public function s2_sky_get_n_param (sky) result (n_param)
    type (s2_sky), intent(in) :: sky
    integer :: n_param
    ! Calls: s2_error
end function s2_sky_get_n_param

Get n_param variable from the passed sky.

Variables:

sky: Sky object to get variable of.
n_param: Object n_param variable returned.

Author: J. D. McEwen

Version: 0.1 November 2004

s2_sky_get_param

public subroutine s2_sky_get_param (sky, param)
    type (s2_sky), intent(in) :: sky
    real (kind=s2_sp), intent(out), dimension (:) :: param
    ! Calls: s2_error
end subroutine s2_sky_get_param

Get param variable from the passed sky.

Variables:

sky: Sky object to get the variable of.
param(:): Object param variable returned.

Author: J. D. McEwen

Version: 0.1 November 2004