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Ingy döt Net 2023-07-01 11:58:00 -04:00
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commit f23f22d71c
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49
Task/Cumulative-standard-deviation/Fortran/cumulative-standard-deviation-1.f Normal file
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program standard_deviation
implicit none
integer(kind=4), parameter :: dp = kind(0.0d0)
real(kind=dp), dimension(:), allocatable :: vals
integer(kind=4) :: i
real(kind=dp), dimension(8) :: sample_data = (/ 2, 4, 4, 4, 5, 5, 7, 9 /)
do i = lbound(sample_data, 1), ubound(sample_data, 1)
call sample_add(vals, sample_data(i))
write(*, fmt='(''#'',I1,1X,''value = '',F3.1,1X,''stddev ='',1X,F10.8)') &
i, sample_data(i), stddev(vals)
end do
if (allocated(vals)) deallocate(vals)
contains
! Adds value :val: to array :population: dynamically resizing array
subroutine sample_add(population, val)
real(kind=dp), dimension(:), allocatable, intent (inout) :: population
real(kind=dp), intent (in) :: val
real(kind=dp), dimension(:), allocatable :: tmp
integer(kind=4) :: n
if (.not. allocated(population)) then
allocate(population(1))
population(1) = val
else
n = size(population)
call move_alloc(population, tmp)
allocate(population(n + 1))
population(1:n) = tmp
population(n + 1) = val
endif
end subroutine sample_add
! Calculates standard deviation for given set of values
real(kind=dp) function stddev(vals)
real(kind=dp), dimension(:), intent(in) :: vals
real(kind=dp) :: mean
integer(kind=4) :: n
n = size(vals)
mean = sum(vals)/n
stddev = sqrt(sum((vals - mean)**2)/n)
end function stddev
end program standard_deviation

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Task/Cumulative-standard-deviation/Fortran/cumulative-standard-deviation-2.f Normal file
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REAL FUNCTION STDDEV(X) !Standard deviation for successive values.
REAL X !The latest value.
REAL V !Scratchpad.
INTEGER N !Ongoing: count of the values.
REAL EX,EX2 !Ongoing: sum of X and X**2.
SAVE N,EX,EX2 !Retain values from one invocation to the next.
DATA N,EX,EX2/0,0.0,0.0/ !Initial values.
N = N + 1 !Another value arrives.
EX = X + EX !Augment the total.
EX2 = X**2 + EX2 !Augment the sum of squares.
V = EX2/N - (EX/N)**2 !The variance, but, it might come out negative!
STDDEV = SIGN(SQRT(ABS(V)),V) !Protect the SQRT, but produce a negative result if so.
END FUNCTION STDDEV !For the sequence of received X values.
REAL FUNCTION STDDEVP(X) !Standard deviation for successive values.
REAL X !The latest value.
INTEGER N !Ongoing: count of the values.
REAL A,V !Ongoing: average, and sum of squared deviations.
SAVE N,A,V !Retain values from one invocation to the next.
DATA N,A,V/0,0.0,0.0/ !Initial values.
N = N + 1 !Another value arrives.
V = (N - 1)*(X - A)**2 /N + V !First, as it requires the existing average.
A = (X - A)/N + A != [x + (n - 1).A)]/n: recover the total from the average.
STDDEVP = SQRT(V/N) !V can never be negative, even with limited precision.
END FUNCTION STDDEVP !For the sequence of received X values.
REAL FUNCTION STDDEVW(X) !Standard deviation for successive values.
REAL X !The latest value.
REAL V,D !Scratchpads.
INTEGER N !Ongoing: count of the values.
REAL EX,EX2 !Ongoing: sum of X and X**2.
REAL W !Ongoing: working mean.
SAVE N,EX,EX2,W !Retain values from one invocation to the next.
DATA N,EX,EX2/0,0.0,0.0/ !Initial values.
IF (N.LE.0) W = X !Take the first value as the working mean.
N = N + 1 !Another value arrives.
D = X - W !Its deviation from the working mean.
EX = D + EX !Augment the total.
EX2 = D**2 + EX2 !Augment the sum of squares.
V = EX2/N - (EX/N)**2 !The variance, but, it might come out negative!
STDDEVW = SIGN(SQRT(ABS(V)),V) !Protect the SQRT, but produce a negative result if so.
END FUNCTION STDDEVW !For the sequence of received X values.
REAL FUNCTION STDDEVPW(X) !Standard deviation for successive values.
REAL X !The latest value.
INTEGER N !Ongoing: count of the values.
REAL A,V !Ongoing: average, and sum of squared deviations.
REAL W !Ongoing: working mean.
SAVE N,A,V,W !Retain values from one invocation to the next.
DATA N,A,V/0,0.0,0.0/ !Initial values.
IF (N.LE.0) W = X !Oh for self-modifying code!
N = N + 1 !Another value arrives.
D = X - W !Its deviation from the working mean.
V = (N - 1)*(D - A)**2 /N + V !First, as it requires the existing average.
A = (D - A)/N + A != [x + (n - 1).A)]/n: recover the total from the average.
STDDEVPW = SQRT(V/N) !V can never be negative, even with limited precision.
END FUNCTION STDDEVPW !For the sequence of received X values.
PROGRAM TEST
INTEGER I !A stepper.
REAL A(8) !The example data.
DATA A/2.0,3*4.0,2*5.0,7.0,9.0/ !Alas, another opportunity to use @ passed over.
REAL B !An offsetting base.
WRITE (6,1)
1 FORMAT ("Progressive calculation of the standard deviation."/
1 " I",7X,"A(I) EX EX2 Av V*N Ed Ed2 wAv V*N")
B = 1000000 !Provoke truncation error.
DO I = 1,8 !Step along the data series,
WRITE (6,2) I,INT(A(I) + B), !No fractional part, so I don't want F11.0.
1 STDDEV(A(I) + B),STDDEVP(A(I) + B), !Showing progressive values.
2 STDDEVW(A(I) + B),STDDEVPW(A(I) + B) !These with a working mean.
2 FORMAT (I2,I11,1X,4F12.6) !Should do for the example.
END DO !On to the next value.
END