update the documentation

`The streams might be finite.`
Borgvall committed Jan 14, 2012
1 parent 51bdf34 commit 69842aba819db7cbf56a5481643c72cb51e07bae
Showing with 16 additions and 6 deletions.
 @@ -40,7 +40,8 @@ import Numeric.AD.Internal.Composition -- | The 'findZero' function finds a zero of a scalar function using -- Halley's method; its output is a stream of increasingly accurate --- results. (Modulo the usual caveats.) +-- results. (Modulo the usual caveats.) If the stream becomes constant +-- ("it converges"), no further elements are returned. -- -- Examples: -- @@ -60,7 +61,8 @@ findZero f = go -- | The 'inverse' function inverts a scalar function using -- Halley's method; its output is a stream of increasingly accurate --- results. (Modulo the usual caveats.) +-- results. (Modulo the usual caveats.) If the stream becomes constant +-- ("it converges"), no further elements are returned. -- -- Note: the @take 10 \$ inverse sqrt 1 (sqrt 10)@ example that works for Newton's method -- fails with Halley's method because the preconditions do not hold. @@ -72,6 +74,8 @@ inverse f x0 y = findZero (\x -> f x - lift y) x0 -- | The 'fixedPoint' function find a fixedpoint of a scalar -- function using Halley's method; its output is a stream of -- increasingly accurate results. (Modulo the usual caveats.) +-- If the stream becomes constant ("it converges"), no further +-- elements are returned. -- -- > take 10 \$ fixedPoint cos 1 -- converges to 0.7390851332151607 fixedPoint :: (Fractional a, Eq a) => UU a -> a -> [a] @@ -80,7 +84,8 @@ fixedPoint f = findZero (\x -> f x - x) -- | The 'extremum' function finds an extremum of a scalar -- function using Halley's method; produces a stream of increasingly --- accurate results. (Modulo the usual caveats.) +-- accurate results. (Modulo the usual caveats.) If the stream becomes +-- constant ("it converges"), no further elements are returned. -- -- > take 10 \$ extremum cos 1 -- convert to 0 extremum :: (Fractional a, Eq a) => UU a -> a -> [a]
 @@ -37,7 +37,8 @@ import Numeric.AD.Internal.Composition -- | The 'findZero' function finds a zero of a scalar function using -- Newton's method; its output is a stream of increasingly accurate --- results. (Modulo the usual caveats.) +-- results. (Modulo the usual caveats.) If the stream becomes constant +-- ("it converges"), no further elements are returned. -- -- Examples: -- @@ -57,7 +58,8 @@ findZero f = go -- | The 'inverseNewton' function inverts a scalar function using -- Newton's method; its output is a stream of increasingly accurate --- results. (Modulo the usual caveats.) +-- results. (Modulo the usual caveats.) If the stream becomes +-- constant ("it converges"), no further elements are returned. -- -- Example: -- @@ -70,6 +72,8 @@ inverse f x0 y = findZero (\x -> f x - lift y) x0 -- | The 'fixedPoint' function find a fixedpoint of a scalar -- function using Newton's method; its output is a stream of -- increasingly accurate results. (Modulo the usual caveats.) +-- If the stream becomes constant ("it converges"), no further +-- elements are returned. -- -- > take 10 \$ fixedPoint cos 1 -- converges to 0.7390851332151607 fixedPoint :: (Fractional a, Eq a) => UU a -> a -> [a] @@ -78,7 +82,8 @@ fixedPoint f = findZero (\x -> f x - x) -- | The 'extremum' function finds an extremum of a scalar -- function using Newton's method; produces a stream of increasingly --- accurate results. (Modulo the usual caveats.) +-- accurate results. (Modulo the usual caveats.) If the stream +-- becomes constant ("it converges"), no further elements are returned. -- -- > take 10 \$ extremum cos 1 -- convert to 0 extremum :: (Fractional a, Eq a) => UU a -> a -> [a]