sum_kbn
sum_kbn(A)
Returns the sum of all array elements, using the Kahan-Babuska-Neumaier compensated summation algorithm for additional accuracy.
Examples
"""
sum_kbn(A)
Compute the sum of all elements in array `A` using the Kahan-Babuska-Neumaier compensated summation algorithm for additional accuracy.
# Arguments
- `A::AbstractArray`: The input array.
# Returns
- The sum of all elements in `A`.
# Examples
```julia
julia> sum_kbn([1, 2, 3, 4, 5])
15
julia> sum_kbn([0.1, 0.2, 0.3, 0.4, 0.5])
1.5Notes
The Kahan-Babuska-Neumaier compensated summation algorithm reduces the numerical errors that can occur when summing a large number of floating-point values.
""" function sum_kbn(A::AbstractArray) sum = zero(eltype(A)) compensation = zero(eltype(A)) for i in eachindex(A) y = A[i] - compensation t = sum + y compensation = (t - sum) - y sum = t end return sum end
**Example usage:**
1. **Compute the sum of an integer array:**
```julia
julia> sum_kbn([1, 2, 3, 4, 5])
15The function correctly computes the sum of all elements in the integer array.
- Compute the sum of a floating-point array:
julia> sum_kbn([0.1, 0.2, 0.3, 0.4, 0.5]) 1.5The Kahan-Babuska-Neumaier algorithm helps reduce numerical errors when summing floating-point values.
Please note that the sum_kbn function is not a built-in Julia function and would need to be defined separately in your code or imported from a package that provides it.
See Also
Array, broadcast, cat, combinations, conj!, digits!, fieldnames, fill, fill!, last, length, maximum, minimum, ones, parent, parentindexes, partitions, permutations, pointer, pointer_to_array, promote_shape, rand!, reshape, scale, similar, sum, sum_kbn, takebuf_array, transpose!, vec, zeros,User Contributed Notes
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