Module s2dw_stat_mod

module s2dw_stat_mod

        ! Uses
    use s2dw_types_mod
    use s2dw_error_mod
    use s2dw_core_mod
    use omp_lib

        ! Subroutines and functions
    public subroutine s2dw_stat_moments (wavdyn, J, B, N, alpha, mean, var, skew, kur, wavdyn_mask, five, six)
    public subroutine s2dw_stat_moments_write (filename, nsim, description, J, mu, var, skew, kur, five, six)
    public subroutine s2dw_stat_histogram (wavdyn, J, B, N, alpha, hist_nbins, hist_bins, hist_vals)
    public subroutine s2dw_stat_histogram_write (filename, J, hist_nbins, hist_bins, hist_vals)

end module s2dw_stat_mod

Functionality to compute statistics of wavelet coefficients.

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

Version: 0.1 February 2012

Description of Subroutines and Functions

s2dw_stat_moments

public subroutine s2dw_stat_moments (wavdyn, J, B, N, alpha, mean, var, skew, kur, wavdyn_mask, five, six)
    type (s2dw_wav_abg), intent(inout), dimension (0:J) :: wavdyn
    integer, intent(in) :: J
    integer, intent(in) :: B
    integer, intent(in) :: N
    real (kind=dp), intent(in) :: alpha
    real (kind=dp), intent(out), dimension (0:J) :: mean
    real (kind=dp), intent(out), dimension (0:J) :: var
    real (kind=dp), intent(out), dimension (0:J) :: skew
    real (kind=dp), intent(out), dimension (0:J) :: kur
    type (s2dw_wav_abg), optional, intent(in), dimension (0:J) :: wavdyn_mask
    real (kind=dp), optional, intent(out), dimension (0:J) :: five
    real (kind=dp), optional, intent(out), dimension (0:J) :: six
    ! Calls: s2dw_error
end subroutine s2dw_stat_moments

Compute moments of wavelets coefficients for each scale, including the mean, variance, skewness and kurtosis. The fifth- and sixth-order standardized moments can also be optionally returned.

Notes:

Memory for the computed moments must already be allocated by the calling routine.

Variables:

wavdyn(0:J)%coeff: Wavelet coefficients for each scale [input/ouput]. On ouput the wavelet coefficients will be masked if a mask was passed when calling this function.
J: Maximum analysis scale depth [input].
B: Harmonic band limit [input].
N: Azimuthal band limit [input].
bl_scoeff: Upper band limit for scaling coefficients [input].
alpha: Basis dilation factor [input].
mean(0:J): Mean of wavelet coefficients for each scale [output].
var(0:J): Variance of wavelet coefficients for each scale [output].
skew(0:J): Skewness of wavelet coefficients for each scale [output].
kur(0:J): Excess kurtosis of wavelet coefficients for each scale [output].
wavdyn_mask(0:J)%coeff: Binary mask defined in the wavelet domain (values of zero and one indicate wavelet coefficient are ignored and included, respectively, in the calculation of moments) [input].
five(0:J): Fifth-order moment of wavelet coefficients for each scale [output].
six(0:J): Excess sixth-order moment of wavelet coefficients for each scale [output].

Author: J. D. McEwen

Version: 0.1 February 2012

s2dw_stat_moments_write

public subroutine s2dw_stat_moments_write (filename, nsim, description, J, mu, var, skew, kur, five, six)
    character (len=*), intent(in) :: filename
    integer, intent(in) :: nsim
    character (len=STRING_LEN), intent(in), dimension (0:nsim-1) :: description
    integer, intent(in) :: J
    real (kind=dp), intent(in), dimension (0:nsim-1,0:J) :: mu
    real (kind=dp), intent(in), dimension (0:nsim-1,0:J) :: var
    real (kind=dp), intent(in), dimension (0:nsim-1,0:J) :: skew
    real (kind=dp), intent(in), dimension (0:nsim-1,0:J) :: kur
    real (kind=dp), optional, dimension (0:nsim-1,0:J) :: five
    real (kind=dp), optional, dimension (0:nsim-1,0:J) :: six
end subroutine s2dw_stat_moments_write

Write moments of wavelets coefficients for each scale, including the mean, variance, skewness and kurtosis. Moments are written to a single line (ordered mean, variance, skewness and kurtosis) for each set of wavelet coefficients. Fifth and sixth order standardized moments can also be optionally included.

Variables:

filename: Name of file to write wavelet coefficient moments to [input].
nsim: Number of sets of wavelet coefficient moments, i.e. number of skies/maps analysed [input].
description(0:nsim-1): Description of each set of wavelet coefficients stats, typically a filename [input].
J: Maximum analysis scale depth [input].
mean(0:nsim-1,0:J): Mean of wavelet coefficients for each map and scale [input].
var(0:nsim-1,0:J): Variance of wavelet coefficients for each map and scale [input].
skew(0:nsim-1,0:J): Skewness of wavelet coefficients for each map and scale [input].
kur(0:nsim-1,0:J): Excess kurtosis of wavelet coefficients for each map and scale [input].
five(0:J): Fifth-order moment of wavelet coefficients for each scale [input].
six(0:J): Excess sixth-order moment of wavelet coefficients for each scale [input].

Author: J. D. McEwen

Version: 0.1 February 2012

s2dw_stat_histogram

public subroutine s2dw_stat_histogram (wavdyn, J, B, N, alpha, hist_nbins, hist_bins, hist_vals)
    type (s2dw_wav_abg), intent(in), dimension (0:J) :: wavdyn
    integer, intent(in) :: J
    integer, intent(in) :: B
    integer, intent(in) :: N
    real (kind=dp), intent(in) :: alpha
    integer, intent(in) :: hist_nbins
    real (kind=dp), intent(out), dimension (0:J,0:hist_nbins-1) :: hist_bins
    integer, intent(out), dimension (0:J,0:hist_nbins-1) :: hist_vals
    ! Calls: s2dw_error
end subroutine s2dw_stat_histogram

Compute histogram of wavelets coefficients for each scale.

Notes:

Memory for the computed histograms must already be allocated by the calling routine.

Variables:

wavdyn(0:J)%coeff: Wavelet coefficients for each scale [input].
J: Maximum analysis scale depth [input].
B: Harmonic band limit [input].
N: Azimuthal band limit [input].
alpha: Basis dilation factor [input].
hist_nbins: Number of histogram bins [input].
hist_bins(0:J,0:hist_nbins-1): Central position of each bin [input].
hist_vals(0:J,0:hist_nbins-1): Count in each bin [output].

Author: S. M. Feeney

Version: 0.1 February 2012

s2dw_stat_histogram_write

public subroutine s2dw_stat_histogram_write (filename, J, hist_nbins, hist_bins, hist_vals)
    character (len=*), intent(in) :: filename
    integer, intent(in) :: J
    integer, intent(in) :: hist_nbins
    real (kind=dp), intent(in), dimension (0:J,0:hist_nbins-1) :: hist_bins
    integer, intent(in), dimension (0:J,0:hist_nbins-1) :: hist_vals
end subroutine s2dw_stat_histogram_write

Write histograms of wavelets coefficients for each scale. The first line of output contains the j = 0 bins, the second line contains the j = 0 bin counts and so on.

Variables:

filename: Name of file to write wavelet coefficient moments to [input].
nsim: Number of sets of wavelet coefficient moments, i.e. number of skies/maps analysed [input].
J: Maximum analysis scale depth [input].
hist_nbins: Number of histogram bins [input].
hist_bins(0:J,0:hist_nbins-1): Central position of each bin [input].
hist_vals(0:J,0:hist_nbins-1): Count in each bin [input].

Author: S. M. Feeney

Version: 0.1 February 2012