#:include "common.fypp"
#:set RANKS = range(1, MAXRANK + 1)
#:set RC_KINDS_TYPES = REAL_KINDS_TYPES + CMPLX_KINDS_TYPES
submodule (stdlib_stats) stdlib_stats_var
use, intrinsic:: ieee_arithmetic, only: ieee_value, ieee_quiet_nan
use stdlib_error, only: error_stop
use stdlib_optval, only: optval
implicit none
contains
#: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
real(${k1}$) :: n
${t1}$ :: mean
if (.not.optval(mask, .true.)) then
res = ieee_value(1._${k1}$, ieee_quiet_nan)
return
end if
n = real(size(x, kind = int64), ${k1}$)
mean = sum(x) / n
#:if t1[0] == 'r'
res = sum((x - mean)**2) / (n - merge(1, 0 , optval(corrected, .true.)))
#:else
res = sum(abs(x - mean)**2) / (n - merge(1, 0, optval(corrected, .true.)))
#:endif
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
real(dp) :: n, mean
if (.not.optval(mask, .true.)) then
res = ieee_value(1._dp, ieee_quiet_nan)
return
end if
n = real(size(x, kind = int64), dp)
mean = sum(real(x, dp)) / n
res = sum((real(x, dp) - mean)**2) / (n - merge(1, 0, optval(corrected, .true.)))
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${reduced_shape('x', rank, 'dim')}$
integer :: i
real(${k1}$) :: n
${t1}$ :: mean${reduced_shape('x', rank, 'dim')}$
if (.not.optval(mask, .true.)) then
res = ieee_value(1._${k1}$, ieee_quiet_nan)
return
end if
res = 0._${k1}$
select case(dim)
#:for fi in range(1, rank+1)
case(${fi}$)
n = size(x, dim)
mean = sum(x, dim) / n
do i = 1, size(x, dim)
#:if t1[0] == 'r'
res = res + (x${select_subarray(rank, [(fi, 'i')])}$ - mean)**2
#:else
res = res + abs(x${select_subarray(rank, [(fi, 'i')])}$ - mean)**2
#:endif
end do
#:endfor
case default
call error_stop("ERROR (var): wrong dimension")
end select
res = res / (n - merge(1, 0, optval(corrected, .true.)))
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${reduced_shape('x', rank, 'dim')}$
integer :: i
real(dp) :: n
real(dp) :: mean${reduced_shape('x', rank, 'dim')}$
if (.not.optval(mask, .true.)) then
res = ieee_value(1._dp, ieee_quiet_nan)
return
end if
res = 0._dp
select case(dim)
#:for fi in range(1, rank+1)
case(${fi}$)
n = size(x, dim)
mean = sum(real(x, dp), dim) / n
do i = 1, size(x, dim)
res = res + (real(x${select_subarray(rank, [(fi, 'i')])}$, dp) - mean)**2
end do
#:endfor
case default
call error_stop("ERROR (var): wrong dimension")
end select
res = res / (n - merge(1, 0, optval(corrected, .true.)))
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
real(${k1}$) :: n
${t1}$ :: mean
n = real(count(mask, kind = int64), ${k1}$)
mean = sum(x, mask) / n
#:if t1[0] == 'r'
res = sum((x - mean)**2, mask) / (n -&
#:else
res = sum(abs(x - mean)**2, mask) / (n -&
#:endif
merge(1, 0, (optval(corrected, .true.) .and. n > 0)))
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
real(dp) :: n, mean
n = real(count(mask, kind = int64), dp)
mean = sum(real(x, dp), mask) / n
res = sum((real(x, dp) - mean)**2, mask) / (n -&
merge(1, 0, (optval(corrected, .true.) .and. n > 0)))
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${reduced_shape('x', rank, 'dim')}$
integer :: i
real(${k1}$) :: n${reduced_shape('x', rank, 'dim')}$
${t1}$ :: mean${reduced_shape('x', rank, 'dim')}$
res = 0._${k1}$
select case(dim)
#:for fi in range(1, rank+1)
case(${fi}$)
n = count(mask, dim)
mean = sum(x, dim, mask) / n
do i = 1, size(x, dim)
#:if t1[0] == 'r'
res = res + merge( (x${select_subarray(rank, [(fi, 'i')])}$ - mean)**2,&
#:else
res = res + merge( abs(x${select_subarray(rank, [(fi, 'i')])}$ - mean)**2,&
#:endif
0._${k1}$,&
mask${select_subarray(rank, [(fi, 'i')])}$)
end do
#:endfor
case default
call error_stop("ERROR (var): wrong dimension")
end select
res = res / (n - merge(1, 0, (optval(corrected, .true.) .and. n > 0)))
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${reduced_shape('x', rank, 'dim')}$
integer :: i
real(dp) :: n${reduced_shape('x', rank, 'dim')}$
real(dp) :: mean${reduced_shape('x', rank, 'dim')}$
res = 0._dp
select case(dim)
#:for fi in range(1, rank+1)
case(${fi}$)
n = count(mask, dim)
mean = sum(real(x, dp), dim, mask) / n
do i = 1, size(x, dim)
res = res + merge((real(x${select_subarray(rank, [(fi, 'i')])}$, dp) - mean)**2,&
0._dp, mask${select_subarray(rank, [(fi, 'i')])}$)
end do
#:endfor
case default
call error_stop("ERROR (var): wrong dimension")
end select
res = res / (n - merge(1, 0, (optval(corrected, .true.) .and. n > 0)))
end function ${RName}$
#:endfor
#:endfor
end submodule
