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stdlib_stats.fypp
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#:include "common.fypp"
#:set RANKS = range(1, MAXRANK + 1)
#:set REDRANKS = range(2, MAXRANK + 1)
#:set RC_KINDS_TYPES = REAL_KINDS_TYPES + CMPLX_KINDS_TYPES
#:set IR_KINDS_TYPES_OUTPUT = list(zip(INT_KINDS,INT_TYPES, ['dp']*len(INT_KINDS))) + list(zip(REAL_KINDS, REAL_TYPES, REAL_KINDS))
module stdlib_stats
!! Provides support for various statistical methods. This includes currently
!! descriptive statistics
!! ([Specification](../page/specs/stdlib_stats.html))
use stdlib_kinds, only: sp, dp, xdp, qp, &
int8, int16, int32, int64
implicit none
private
! Public API
public :: corr, cov, mean, median, moment, var
interface corr
!! version: experimental
!!
!! Pearson correlation of array elements
!! ([Specification](../page/specs/stdlib_stats.html#corr-pearson-correlation-of-array-elements))
#:for k1, t1 in RC_KINDS_TYPES
#:set RName = rname("corr",1, t1, k1)
module function ${RName}$(x, dim, mask) result(res)
${t1}$, intent(in) :: x(:)
integer, intent(in) :: dim
logical, intent(in), optional :: mask
real(${k1}$) :: res
end function ${RName}$
#:endfor
#:for k1, t1 in INT_KINDS_TYPES
#:set RName = rname("corr",1, t1, k1, 'dp')
module function ${RName}$(x, dim, mask) result(res)
${t1}$, intent(in) :: x(:)
integer, intent(in) :: dim
logical, intent(in), optional :: mask
real(dp) :: res
end function ${RName}$
#:endfor
#:for k1, t1 in RC_KINDS_TYPES
#:set RName = rname("corr_mask",1, t1, k1)
module function ${RName}$(x, dim, mask) result(res)
${t1}$, intent(in) :: x(:)
integer, intent(in) :: dim
logical, intent(in) :: mask(:)
real(${k1}$) :: res
end function ${RName}$
#:endfor
#:for k1, t1 in INT_KINDS_TYPES
#:set RName = rname("corr_mask",1, t1, k1, 'dp')
module function ${RName}$(x, dim, mask) result(res)
${t1}$, intent(in) :: x(:)
integer, intent(in) :: dim
logical, intent(in) :: mask(:)
real(dp) :: res
end function ${RName}$
#:endfor
#:for k1, t1 in RC_KINDS_TYPES
#:set RName = rname("corr",2, t1, k1)
module function ${RName}$(x, dim, mask) result(res)
${t1}$, intent(in) :: x(:, :)
integer, intent(in) :: dim
logical, intent(in), optional :: mask
${t1}$ :: res(merge(size(x, 1), size(x, 2), mask = 1<dim)&
, merge(size(x, 1), size(x, 2), mask = 1<dim))
end function ${RName}$
#:endfor
#:for k1, t1 in INT_KINDS_TYPES
#:set RName = rname("corr",2, t1, k1, 'dp')
module function ${RName}$(x, dim, mask) result(res)
${t1}$, intent(in) :: x(:, :)
integer, intent(in) :: dim
logical, intent(in), optional :: mask
real(dp) :: res(merge(size(x, 1), size(x, 2), mask = 1<dim)&
, merge(size(x, 1), size(x, 2), mask = 1<dim))
end function ${RName}$
#:endfor
#:for k1, t1 in RC_KINDS_TYPES
#:set RName = rname("corr_mask",2, t1, k1)
module function ${RName}$(x, dim, mask) result(res)
${t1}$, intent(in) :: x(:, :)
integer, intent(in) :: dim
logical, intent(in) :: mask(:,:)
${t1}$ :: res(merge(size(x, 1), size(x, 2), mask = 1<dim)&
, merge(size(x, 1), size(x, 2), mask = 1<dim))
end function ${RName}$
#:endfor
#:for k1, t1 in INT_KINDS_TYPES
#:set RName = rname("corr_mask",2, t1, k1, 'dp')
module function ${RName}$(x, dim, mask) result(res)
${t1}$, intent(in) :: x(:, :)
integer, intent(in) :: dim
logical, intent(in) :: mask(:,:)
real(dp) :: res(merge(size(x, 1), size(x, 2), mask = 1<dim)&
, merge(size(x, 1), size(x, 2), mask = 1<dim))
end function ${RName}$
#:endfor
end interface corr
interface cov
!! version: experimental
!!
!! Covariance of array elements
!! ([Specification](../page/specs/stdlib_stats.html#cov-covariance-of-array-elements))
#:for k1, t1 in RC_KINDS_TYPES
#:set RName = rname("cov",1, t1, k1)
module function ${RName}$(x, dim, mask, corrected) result(res)
${t1}$, intent(in) :: x(:)
integer, intent(in) :: dim
logical, intent(in), optional :: mask
logical, intent(in), optional :: corrected
real(${k1}$) :: res
end function ${RName}$
#:endfor
#:for k1, t1 in INT_KINDS_TYPES
#:set RName = rname("cov",1, t1, k1, 'dp')
module function ${RName}$(x, dim, mask, corrected) result(res)
${t1}$, intent(in) :: x(:)
integer, intent(in) :: dim
logical, intent(in), optional :: mask
logical, intent(in), optional :: corrected
real(dp) :: res
end function ${RName}$
#:endfor
#:for k1, t1 in RC_KINDS_TYPES
#:set RName = rname("cov_mask",1, t1, k1)
module function ${RName}$(x, dim, mask, corrected) result(res)
${t1}$, intent(in) :: x(:)
integer, intent(in) :: dim
logical, intent(in) :: mask(:)
logical, intent(in), optional :: corrected
real(${k1}$) :: res
end function ${RName}$
#:endfor
#:for k1, t1 in INT_KINDS_TYPES
#:set RName = rname("cov_mask",1, t1, k1, 'dp')
module function ${RName}$(x, dim, mask, corrected) result(res)
${t1}$, intent(in) :: x(:)
integer, intent(in) :: dim
logical, intent(in) :: mask(:)
logical, intent(in), optional :: corrected
real(dp) :: res
end function ${RName}$
#:endfor
#:for k1, t1 in RC_KINDS_TYPES
#:set RName = rname("cov",2, t1, k1)
module function ${RName}$(x, dim, mask, corrected) result(res)
${t1}$, intent(in) :: x(:, :)
integer, intent(in) :: dim
logical, intent(in), optional :: mask
logical, intent(in), optional :: corrected
${t1}$ :: res(merge(size(x, 1), size(x, 2), mask = 1<dim)&
, merge(size(x, 1), size(x, 2), mask = 1<dim))
end function ${RName}$
#:endfor
#:for k1, t1 in INT_KINDS_TYPES
#:set RName = rname("cov",2, t1, k1, 'dp')
module function ${RName}$(x, dim, mask, corrected) result(res)
${t1}$, intent(in) :: x(:, :)
integer, intent(in) :: dim
logical, intent(in), optional :: mask
logical, intent(in), optional :: corrected
real(dp) :: res(merge(size(x, 1), size(x, 2), mask = 1<dim)&
, merge(size(x, 1), size(x, 2), mask = 1<dim))
end function ${RName}$
#:endfor
#:for k1, t1 in RC_KINDS_TYPES
#:set RName = rname("cov_mask",2, t1, k1)
module function ${RName}$(x, dim, mask, corrected) result(res)
${t1}$, intent(in) :: x(:, :)
integer, intent(in) :: dim
logical, intent(in) :: mask(:,:)
logical, intent(in), optional :: corrected
${t1}$ :: res(merge(size(x, 1), size(x, 2), mask = 1<dim)&
, merge(size(x, 1), size(x, 2), mask = 1<dim))
end function ${RName}$
#:endfor
#:for k1, t1 in INT_KINDS_TYPES
#:set RName = rname("cov_mask",2, t1, k1, 'dp')
module function ${RName}$(x, dim, mask, corrected) result(res)
${t1}$, intent(in) :: x(:, :)
integer, intent(in) :: dim
logical, intent(in) :: mask(:,:)
logical, intent(in), optional :: corrected
real(dp) :: res(merge(size(x, 1), size(x, 2), mask = 1<dim)&
, merge(size(x, 1), size(x, 2), mask = 1<dim))
end function ${RName}$
#:endfor
end interface cov
interface mean
!! version: experimental
!!
!! Mean of array elements
!! ([Specification](../page/specs/stdlib_stats.html#mean-mean-of-array-elements))
#:for k1, t1 in RC_KINDS_TYPES
#:for rank in RANKS
#:set RName = rname("mean_all",rank, t1, k1)
module function ${RName}$ (x, mask) result(res)
${t1}$, intent(in) :: x${ranksuffix(rank)}$
logical, intent(in), optional :: mask
${t1}$ :: res
end function ${RName}$
#:endfor
#:endfor
#:for k1, t1 in INT_KINDS_TYPES
#:for rank in RANKS
#:set RName = rname('mean_all', rank, t1, k1,'dp')
module function ${RName}$(x, mask) result(res)
${t1}$, intent(in) :: x${ranksuffix(rank)}$
logical, intent(in), optional :: mask
real(dp) :: res
end function ${RName}$
#:endfor
#:endfor
#:for k1, t1 in RC_KINDS_TYPES
#:for rank in RANKS
#:set RName = rname("mean",rank, t1, k1)
module function ${RName}$(x, dim, mask) result(res)
${t1}$, intent(in) :: x${ranksuffix(rank)}$
integer, intent(in) :: dim
logical, intent(in), optional :: mask
${t1}$ :: res${reduced_shape('x', rank, 'dim')}$
end function ${RName}$
#:endfor
#:endfor
#:for k1, t1 in INT_KINDS_TYPES
#:for rank in RANKS
#:set RName = rname("mean",rank, t1, k1,'dp')
module function ${RName}$(x, dim, mask) result(res)
${t1}$, intent(in) :: x${ranksuffix(rank)}$
integer, intent(in) :: dim
logical, intent(in), optional :: mask
real(dp) :: res${reduced_shape('x', rank, 'dim')}$
end function ${RName}$
#:endfor
#:endfor
#:for k1, t1 in RC_KINDS_TYPES
#:for rank in RANKS
#:set RName = rname('mean_mask_all',rank, t1, k1)
module function ${RName}$(x, mask) result(res)
${t1}$, intent(in) :: x${ranksuffix(rank)}$
logical, intent(in) :: mask${ranksuffix(rank)}$
${t1}$ :: res
end function ${RName}$
#:endfor
#:endfor
#:for k1, t1 in INT_KINDS_TYPES
#:for rank in RANKS
#:set RName = rname('mean_mask_all',rank, t1, k1, 'dp')
module function ${RName}$(x, mask) result(res)
${t1}$, intent(in) :: x${ranksuffix(rank)}$
logical, intent(in) :: mask${ranksuffix(rank)}$
real(dp) :: res
end function ${RName}$
#:endfor
#:endfor
#:for k1, t1 in RC_KINDS_TYPES
#:for rank in RANKS
#:set RName = rname('mean_mask',rank, t1, k1)
module function ${RName}$(x, dim, mask) result(res)
${t1}$, intent(in) :: x${ranksuffix(rank)}$
integer, intent(in) :: dim
logical, intent(in) :: mask${ranksuffix(rank)}$
${t1}$ :: res${reduced_shape('x', rank, 'dim')}$
end function ${RName}$
#:endfor
#:endfor
#:for k1, t1 in INT_KINDS_TYPES
#:for rank in RANKS
#:set RName = rname('mean_mask',rank, t1, k1, 'dp')
module function ${RName}$(x, dim, mask) result(res)
${t1}$, intent(in) :: x${ranksuffix(rank)}$
integer, intent(in) :: dim
logical, intent(in) :: mask${ranksuffix(rank)}$
real(dp) :: res${reduced_shape('x', rank, 'dim')}$
end function ${RName}$
#:endfor
#:endfor
end interface mean
interface median
!! version: experimental
!!
!! Median of array elements
!! ([Specification](../page/specs/stdlib_stats.html#median-median-of-array-elements))
#:for k1, t1, o1 in IR_KINDS_TYPES_OUTPUT
#:for rank in RANKS
#:set name = rname("median_all",rank, t1, k1, o1)
module function ${name}$ (x, mask) result(res)
${t1}$, intent(in) :: x${ranksuffix(rank)}$
logical, intent(in), optional :: mask
real(${o1}$) :: res
end function ${name}$
#:endfor
#:endfor
#:for k1, t1, o1 in IR_KINDS_TYPES_OUTPUT
#:for rank in RANKS
#:set name = rname("median",rank, t1, k1, o1)
module function ${name}$(x, dim, mask) result(res)
${t1}$, intent(in) :: x${ranksuffix(rank)}$
integer, intent(in) :: dim
logical, intent(in), optional :: mask
real(${o1}$) :: res${reduced_shape('x', rank, 'dim')}$
end function ${name}$
#:endfor
#:endfor
#:for k1, t1, o1 in IR_KINDS_TYPES_OUTPUT
#:for rank in RANKS
#:set name = rname('median_all_mask',rank, t1, k1, o1)
module function ${name}$(x, mask) result(res)
${t1}$, intent(in) :: x${ranksuffix(rank)}$
logical, intent(in) :: mask${ranksuffix(rank)}$
real(${o1}$) :: res
end function ${name}$
#:endfor
#:endfor
#:for k1, t1, o1 in IR_KINDS_TYPES_OUTPUT
#:for rank in RANKS
#:set name = rname('median_mask',rank, t1, k1, o1)
module function ${name}$(x, dim, mask) result(res)
${t1}$, intent(in) :: x${ranksuffix(rank)}$
integer, intent(in) :: dim
logical, intent(in) :: mask${ranksuffix(rank)}$
real(${o1}$) :: res${reduced_shape('x', rank, 'dim')}$
end function ${name}$
#:endfor
#:endfor
end interface
interface var
!! version: experimental
!!
!! Variance of array elements
!! ([Specification](../page/specs/stdlib_stats.html#var-variance-of-array-elements))
#:for k1, t1 in RC_KINDS_TYPES
#:for rank in RANKS
#:set RName = rname("var_all",rank, t1, k1)
module function ${RName}$(x, mask, corrected) result(res)
${t1}$, intent(in) :: x${ranksuffix(rank)}$
logical, intent(in), optional :: mask
logical, intent(in), optional :: corrected
real(${k1}$) :: res
end function ${RName}$
#:endfor
#:endfor
#:for k1, t1 in INT_KINDS_TYPES
#:for rank in RANKS
#:set RName = rname("var_all",rank, t1, k1, 'dp')
module function ${RName}$(x, mask, corrected) result(res)
${t1}$, intent(in) :: x${ranksuffix(rank)}$
logical, intent(in), optional :: mask
logical, intent(in), optional :: corrected
real(dp) :: res
end function ${RName}$
#:endfor
#:endfor
#:for k1, t1 in RC_KINDS_TYPES
#:for rank in RANKS
#:set RName = rname("var",rank, t1, k1)
module function ${RName}$(x, dim, mask, corrected) result(res)
${t1}$, intent(in) :: x${ranksuffix(rank)}$
integer, intent(in) :: dim
logical, intent(in), optional :: mask
logical, intent(in), optional :: corrected
real(${k1}$) :: res${reduced_shape('x', rank, 'dim')}$
end function ${RName}$
#:endfor
#:endfor
#:for k1, t1 in INT_KINDS_TYPES
#:for rank in RANKS
#:set RName = rname("var",rank, t1, k1, 'dp')
module function ${RName}$(x, dim, mask, corrected) result(res)
${t1}$, intent(in) :: x${ranksuffix(rank)}$
integer, intent(in) :: dim
logical, intent(in), optional :: mask
logical, intent(in), optional :: corrected
real(dp) :: res${reduced_shape('x', rank, 'dim')}$
end function ${RName}$
#:endfor
#:endfor
#:for k1, t1 in RC_KINDS_TYPES
#:for rank in RANKS
#:set RName = rname("var_mask_all",rank, t1, k1)
module function ${RName}$(x, mask, corrected) result(res)
${t1}$, intent(in) :: x${ranksuffix(rank)}$
logical, intent(in) :: mask${ranksuffix(rank)}$
logical, intent(in), optional :: corrected
real(${k1}$) :: res
end function ${RName}$
#:endfor
#:endfor
#:for k1, t1 in INT_KINDS_TYPES
#:for rank in RANKS
#:set RName = rname("var_mask_all",rank, t1, k1, 'dp')
module function ${RName}$(x, mask, corrected) result(res)
${t1}$, intent(in) :: x${ranksuffix(rank)}$
logical, intent(in) :: mask${ranksuffix(rank)}$
logical, intent(in), optional :: corrected
real(dp) :: res
end function ${RName}$
#:endfor
#:endfor
#:for k1, t1 in RC_KINDS_TYPES
#:for rank in RANKS
#:set RName = rname("var_mask",rank, t1, k1)
module function ${RName}$(x, dim, mask, corrected) result(res)
${t1}$, intent(in) :: x${ranksuffix(rank)}$
integer, intent(in) :: dim
logical, intent(in) :: mask${ranksuffix(rank)}$
logical, intent(in), optional :: corrected
real(${k1}$) :: res${reduced_shape('x', rank, 'dim')}$
end function ${RName}$
#:endfor
#:endfor
#:for k1, t1 in INT_KINDS_TYPES
#:for rank in RANKS
#:set RName = rname("var_mask",rank, t1, k1, 'dp')
module function ${RName}$(x, dim, mask, corrected) result(res)
${t1}$, intent(in) :: x${ranksuffix(rank)}$
integer, intent(in) :: dim
logical, intent(in) :: mask${ranksuffix(rank)}$
logical, intent(in), optional :: corrected
real(dp) :: res${reduced_shape('x', rank, 'dim')}$
end function ${RName}$
#:endfor
#:endfor
end interface var
interface moment
!! version: experimental
!!
!! Central moment of array elements
!! ([Specification](../page/specs/stdlib_stats.html#moment-central-moments-of-array-elements))
#:for k1, t1 in RC_KINDS_TYPES
#:for rank in RANKS
#:set RName = rname("moment_all",rank, t1, k1)
module function ${RName}$(x, order, center, mask) result(res)
${t1}$, intent(in) :: x${ranksuffix(rank)}$
integer, intent(in) :: order
${t1}$, intent(in), optional :: center
logical, intent(in), optional :: mask
${t1}$ :: res
end function ${RName}$
#:endfor
#:endfor
#:for k1, t1 in INT_KINDS_TYPES
#:for rank in RANKS
#:set RName = rname("moment_all",rank, t1, k1, 'dp')
module function ${RName}$(x, order, center, mask) result(res)
${t1}$, intent(in) :: x${ranksuffix(rank)}$
integer, intent(in) :: order
real(dp), intent(in), optional :: center
logical, intent(in), optional :: mask
real(dp) :: res
end function ${RName}$
#:endfor
#:endfor
#:for k1, t1 in RC_KINDS_TYPES
#:for rank in REDRANKS
#:set RName = rname("moment_scalar",rank, t1, k1)
module function ${RName}$(x, order, dim, center, mask) result(res)
${t1}$, intent(in) :: x${ranksuffix(rank)}$
integer, intent(in) :: order
integer, intent(in) :: dim
${t1}$, intent(in) :: center
logical, intent(in), optional :: mask
${t1}$ :: res${reduced_shape('x', rank, 'dim')}$
end function ${RName}$
#:endfor
#:endfor
#:for k1, t1 in RC_KINDS_TYPES
#:for rank in RANKS
#:set RName = rname("moment",rank, t1, k1)
module function ${RName}$(x, order, dim, center, mask) result(res)
${t1}$, intent(in) :: x${ranksuffix(rank)}$
integer, intent(in) :: order
integer, intent(in) :: dim
${t1}$, intent(in), optional :: center${reduced_shape('x', rank, 'dim')}$
logical, intent(in), optional :: mask
${t1}$ :: res${reduced_shape('x', rank, 'dim')}$
end function ${RName}$
#:endfor
#:endfor
#:for k1, t1 in INT_KINDS_TYPES
#:for rank in REDRANKS
#:set RName = rname("moment_scalar",rank, t1, k1, 'dp')
module function ${RName}$(x, order, dim, center, mask) result(res)
${t1}$, intent(in) :: x${ranksuffix(rank)}$
integer, intent(in) :: order
integer, intent(in) :: dim
real(dp),intent(in) :: center
logical, intent(in), optional :: mask
real(dp) :: res${reduced_shape('x', rank, 'dim')}$
end function ${RName}$
#:endfor
#:endfor
#:for k1, t1 in INT_KINDS_TYPES
#:for rank in RANKS
#:set RName = rname("moment",rank, t1, k1, 'dp')
module function ${RName}$(x, order, dim, center, mask) result(res)
${t1}$, intent(in) :: x${ranksuffix(rank)}$
integer, intent(in) :: order
integer, intent(in) :: dim
real(dp),intent(in), optional :: center${reduced_shape('x', rank, 'dim')}$
logical, intent(in), optional :: mask
real(dp) :: res${reduced_shape('x', rank, 'dim')}$
end function ${RName}$
#:endfor
#:endfor
#:for k1, t1 in RC_KINDS_TYPES
#:for rank in RANKS
#:set RName = rname("moment_mask_all",rank, t1, k1)
module function ${RName}$(x, order, center, mask) result(res)
${t1}$, intent(in) :: x${ranksuffix(rank)}$
integer, intent(in) :: order
${t1}$, intent(in), optional :: center
logical, intent(in) :: mask${ranksuffix(rank)}$
${t1}$ :: res
end function ${RName}$
#:endfor
#:endfor
#:for k1, t1 in INT_KINDS_TYPES
#:for rank in RANKS
#:set RName = rname("moment_mask_all",rank, t1, k1, 'dp')
module function ${RName}$(x, order, center, mask) result(res)
${t1}$, intent(in) :: x${ranksuffix(rank)}$
integer, intent(in) :: order
real(dp),intent(in), optional :: center
logical, intent(in) :: mask${ranksuffix(rank)}$
real(dp) :: res
end function ${RName}$
#:endfor
#:endfor
#:for k1, t1 in RC_KINDS_TYPES
#:for rank in REDRANKS
#:set RName = rname("moment_mask_scalar",rank, t1, k1)
module function ${RName}$(x, order, dim, center, mask) result(res)
${t1}$, intent(in) :: x${ranksuffix(rank)}$
integer, intent(in) :: order
integer, intent(in) :: dim
${t1}$, intent(in) :: center
logical, intent(in) :: mask${ranksuffix(rank)}$
${t1}$ :: res${reduced_shape('x', rank, 'dim')}$
end function ${RName}$
#:endfor
#:endfor
#:for k1, t1 in RC_KINDS_TYPES
#:for rank in RANKS
#:set RName = rname("moment_mask",rank, t1, k1)
module function ${RName}$(x, order, dim, center, mask) result(res)
${t1}$, intent(in) :: x${ranksuffix(rank)}$
integer, intent(in) :: order
integer, intent(in) :: dim
${t1}$, intent(in), optional :: center${reduced_shape('x', rank, 'dim')}$
logical, intent(in) :: mask${ranksuffix(rank)}$
${t1}$ :: res${reduced_shape('x', rank, 'dim')}$
end function ${RName}$
#:endfor
#:endfor
#:for k1, t1 in INT_KINDS_TYPES
#:for rank in REDRANKS
#:set RName = rname("moment_mask_scalar",rank, t1, k1, 'dp')
module function ${RName}$(x, order, dim, center, mask) result(res)
${t1}$, intent(in) :: x${ranksuffix(rank)}$
integer, intent(in) :: order
integer, intent(in) :: dim
real(dp), intent(in) :: center
logical, intent(in) :: mask${ranksuffix(rank)}$
real(dp) :: res${reduced_shape('x', rank, 'dim')}$
end function ${RName}$
#:endfor
#:endfor
#:for k1, t1 in INT_KINDS_TYPES
#:for rank in RANKS
#:set RName = rname("moment_mask",rank, t1, k1, 'dp')
module function ${RName}$(x, order, dim, center, mask) result(res)
${t1}$, intent(in) :: x${ranksuffix(rank)}$
integer, intent(in) :: order
integer, intent(in) :: dim
real(dp), intent(in), optional :: center${reduced_shape('x', rank, 'dim')}$
logical, intent(in) :: mask${ranksuffix(rank)}$
real(dp) :: res${reduced_shape('x', rank, 'dim')}$
end function ${RName}$
#:endfor
#:endfor
end interface moment
end module stdlib_stats