UnitFractionsDecomposition2

Documentation

threeDigitsK :: Double -> Double

Rounding to thousandth.

type ErrorImpact = Int

Characterizes the impact of the absolute error sign on the approximation.

absErr2Frac :: Double -> Double -> Double

Absolute error with sign for the two unit fractions approximations and the first argument (a in the related paper) being taken as the second parameter for the function. The second argument here is expected to be fromIntegral a0 where elem a0 [2..] == True.

absErrUDecomp3 :: [Double] -> Double -> Double

elemSolution2 :: Integral a => Int -> a -> Double -> Bool

setOfSolutionsGmin :: ErrorImpact -> Double -> (Double, Double)

Searches for the minimum absolute error solution to two unit fractions decomposition (approximation) for the fraction in the isRangeN True values with taking into account the sign of the absolute error.

If the ErrorImpact parameter is equal to 0 , then absolute error can be of any sign, otherwise the sign of it is the same as the sign of the ErrorImpact argument.

suitable2 :: Double -> (Double, Double)

Searches for the minimum absolute error solution to two unit fractions decomposition (approximation) for the fraction in k the isRangeN k = True.

suitable21G :: ErrorImpact -> Double -> Maybe ([Double], Double)

Allows to take into account the sign of the absolute error of the aproximation. If the ErrorImpact parameter is equal to 0 , then absolute error can be of any sign, otherwise the sign of it is the same as the sign of the ErrorImpact argument.

suitable21 :: Double -> Maybe ([Double], Double)

isRangeN :: Double -> Bool

isRangeNPref :: Double -> Bool

The preferable range of the argument for suitable2 and suitable21 functions. For arguments in this range the functions always have informative results.

check1FracDecompG :: ErrorImpact -> Double -> Maybe ([Double], Double)

Allows to take into account the sign of the absolute error of the aproximation. If the ErrorImpact parameter is equal to 0 , then absolute error can be of any sign, otherwise the sign of it is the same as the sign of the ErrorImpact argument.

check3FracDecompPartialG :: ErrorImpact -> Bool -> Double -> Maybe ([Double], Double)

Allows to take into account the sign of the absolute error of the aproximation. If the ErrorImpact parameter is equal to 0 , then absolute error can be of any sign, otherwise the sign of it is the same as the sign of the ErrorImpact argument.

check3FracDecompPartialPG :: ErrorImpact -> Bool -> [Int] -> Double -> Maybe ([Double], Double)

Allows to take into account the sign of the absolute error of the aproximation. If the ErrorImpact parameter is equal to 0 , then absolute error can be of any sign, otherwise the sign of it is the same as the sign of the ErrorImpact argument.

lessErrSimpleDecompPG :: ErrorImpact -> [Int] -> Double -> (Int, Maybe ([Double], Double), Double)

Allows to take into account the sign of the absolute error of the aproximation. If the ErrorImpact parameter is equal to 0 , then absolute error can be of any sign, otherwise the sign of it is the same as the sign of the ErrorImpact argument.

lessErrDenomsPG :: ErrorImpact -> [Int] -> Double -> [Integer]

Allows to take into account the sign of the absolute error of the aproximation. If the ErrorImpact parameter is equal to 0 , then absolute error can be of any sign, otherwise the sign of it is the same as the sign of the ErrorImpact argument.

check1FracDecomp :: Double -> Maybe ([Double], Double)

Tries to approximate the fraction by just one unit fraction. Can be used for the numbers between 0.005 and 0.501.

check3FracDecompPartial :: Bool -> Double -> Maybe ([Double], Double)

Function to find the less by absolute value error approximation. One of the denominators is taken from the range [2..10]. The two others are taken from the appropriate suitable21 applicattion.

check3FracDecompPartialP :: Bool -> [Int] -> Double -> Maybe ([Double], Double)

Extended version of the check3FracDecompPartial with the first denominator being taken not - only from the [2..10], but also from the custom user provided list. -

lessErrSimpleDecompP :: [Int] -> Double -> (Int, Maybe ([Double], Double), Double)

lessErrDenomsP :: [Int] -> Double -> [Integer]

Returns a list of denominators for fraction decomposition using also those ones from the the list provided as the first argument. Searches for the least error from the checked ones.