Safe Haskell | None |
---|---|

Language | Haskell98 |

## Synopsis

- type Vector = Array
- type family RealOf x
- type ComplexOf x = Complex (RealOf x)
- toList :: (C sh, Storable a) => Vector sh a -> [a]
- fromList :: (C sh, Storable a) => sh -> [a] -> Vector sh a
- autoFromList :: Storable a => [a] -> Vector (ZeroBased Int) a
- append :: (C shx, C shy, Storable a) => Array shx a -> Array shy a -> Array (shx ::+ shy) a
- (+++) :: (C shx, C shy, Storable a) => Vector shx a -> Vector shy a -> Vector (shx ::+ shy) a
- take :: (Integral n, Storable a) => n -> Array (ZeroBased n) a -> Array (ZeroBased n) a
- drop :: (Integral n, Storable a) => n -> Array (ZeroBased n) a -> Array (ZeroBased n) a
- takeLeft :: (C sh0, C sh1, Storable a) => Array (sh0 ::+ sh1) a -> Array sh0 a
- takeRight :: (C sh0, C sh1, Storable a) => Array (sh0 ::+ sh1) a -> Array sh1 a
- swap :: (Indexed sh, Storable a) => Index sh -> Index sh -> Vector sh a -> Vector sh a
- singleton :: Storable a => a -> Array () a
- constant :: (C sh, Floating a) => sh -> a -> Vector sh a
- zero :: (C sh, Floating a) => sh -> Vector sh a
- one :: (C sh, Floating a) => sh -> Vector sh a
- unit :: (Indexed sh, Floating a) => sh -> Index sh -> Vector sh a
- dot :: (C sh, Eq sh, Floating a) => Vector sh a -> Vector sh a -> a
- inner :: (C sh, Eq sh, Floating a) => Vector sh a -> Vector sh a -> a
- (-*|) :: (C sh, Eq sh, Floating a) => Vector sh a -> Vector sh a -> a
- sum :: (C sh, Floating a) => Vector sh a -> a
- absSum :: (C sh, Floating a) => Vector sh a -> RealOf a
- norm1 :: (C sh, Floating a) => Vector sh a -> RealOf a
- norm2 :: (C sh, Floating a) => Vector sh a -> RealOf a
- norm2Squared :: (C sh, Floating a) => Vector sh a -> RealOf a
- normInf :: (C sh, Floating a) => Vector sh a -> RealOf a
- normInf1 :: (C sh, Floating a) => Vector sh a -> RealOf a
- argAbsMaximum :: (InvIndexed sh, Floating a) => Vector sh a -> (Index sh, a)
- argAbs1Maximum :: (InvIndexed sh, Floating a) => Vector sh a -> (Index sh, a)
- product :: (C sh, Floating a) => Vector sh a -> a
- scale :: (C sh, Floating a) => a -> Vector sh a -> Vector sh a
- scaleReal :: (C sh, Floating a) => RealOf a -> Vector sh a -> Vector sh a
- (.*|) :: (C sh, Floating a) => a -> Vector sh a -> Vector sh a
- add :: (C sh, Eq sh, Floating a) => Vector sh a -> Vector sh a -> Vector sh a
- sub :: (C sh, Eq sh, Floating a) => Vector sh a -> Vector sh a -> Vector sh a
- (|+|) :: (C sh, Eq sh, Floating a) => Vector sh a -> Vector sh a -> Vector sh a
- (|-|) :: (C sh, Eq sh, Floating a) => Vector sh a -> Vector sh a -> Vector sh a
- negate :: (C sh, Floating a) => Vector sh a -> Vector sh a
- raise :: (C sh, Floating a) => a -> Array sh a -> Array sh a
- mac :: (C sh, Eq sh, Floating a) => a -> Vector sh a -> Vector sh a -> Vector sh a
- mul :: (C sh, Eq sh, Floating a) => Vector sh a -> Vector sh a -> Vector sh a
- mulConj :: (C sh, Eq sh, Floating a) => Vector sh a -> Vector sh a -> Vector sh a
- divide :: (C sh, Eq sh, Floating a) => Vector sh a -> Vector sh a -> Vector sh a
- recip :: (C sh, Floating a) => Vector sh a -> Vector sh a
- minimum :: (C sh, Real a) => Vector sh a -> a
- argMinimum :: (InvIndexed sh, Index sh ~ ix, Real a) => Vector sh a -> (ix, a)
- maximum :: (C sh, Real a) => Vector sh a -> a
- argMaximum :: (InvIndexed sh, Index sh ~ ix, Real a) => Vector sh a -> (ix, a)
- limits :: (C sh, Real a) => Vector sh a -> (a, a)
- argLimits :: (InvIndexed sh, Index sh ~ ix, Real a) => Vector sh a -> ((ix, a), (ix, a))
- foldl :: (C sh, Storable a) => (b -> a -> b) -> b -> Array sh a -> b
- foldl1 :: (C sh, Storable a) => (a -> a -> a) -> Array sh a -> a
- foldMap :: (C sh, Storable a, Ord a, Semigroup m) => (a -> m) -> Array sh a -> m
- conjugate :: (C sh, Floating a) => Vector sh a -> Vector sh a
- fromReal :: (C sh, Floating a) => Vector sh (RealOf a) -> Vector sh a
- toComplex :: (C sh, Floating a) => Vector sh a -> Vector sh (ComplexOf a)
- realPart :: (C sh, Floating a) => Vector sh a -> Vector sh (RealOf a)
- imaginaryPart :: (C sh, Real a) => Vector sh (Complex a) -> Vector sh a
- zipComplex :: (C sh, Eq sh, Real a) => Vector sh a -> Vector sh a -> Vector sh (Complex a)
- unzipComplex :: (C sh, Real a) => Vector sh (Complex a) -> (Vector sh a, Vector sh a)
- random :: (C sh, Floating a) => RandomDistribution -> sh -> Word64 -> Vector sh a
- data RandomDistribution

# Documentation

append :: (C shx, C shy, Storable a) => Array shx a -> Array shy a -> Array (shx ::+ shy) a infixr 5 #

(+++) :: (C shx, C shy, Storable a) => Vector shx a -> Vector shy a -> Vector (shx ::+ shy) a infixr 5 Source #

Precedence and associativity (right) of (List.++).
This also matches `(::+)`

.

take :: (Integral n, Storable a) => n -> Array (ZeroBased n) a -> Array (ZeroBased n) a #

\(QC.NonNegative n) (Array16 x) -> x == Array.mapShape (Shape.ZeroBased . Shape.size) (Array.append (Array.take n x) (Array.drop n x))

drop :: (Integral n, Storable a) => n -> Array (ZeroBased n) a -> Array (ZeroBased n) a #

\(QC.NonNegative n) (Array16 x) -> x == Array.mapShape (Shape.ZeroBased . Shape.size) (Array.append (Array.take n x) (Array.drop n x))

takeLeft :: (C sh0, C sh1, Storable a) => Array (sh0 ::+ sh1) a -> Array sh0 a #

\(Array16 x) (Array16 y) -> let xy = Array.append x y in x == Array.takeLeft xy && y == Array.takeRight xy

constant :: (C sh, Floating a) => sh -> a -> Vector sh a Source #

constant () = singleton

However, singleton does not need `Floating`

constraint.

dot :: (C sh, Eq sh, Floating a) => Vector sh a -> Vector sh a -> a Source #

dot x y = Matrix.toScalar (singleRow x <#> singleColumn y)

inner :: (C sh, Eq sh, Floating a) => Vector sh a -> Vector sh a -> a Source #

inner x y = dot (conjugate x) y

(-*|) :: (C sh, Eq sh, Floating a) => Vector sh a -> Vector sh a -> a infixl 7 Source #

dot x y = Matrix.toScalar (singleRow x <#> singleColumn y)

absSum :: (C sh, Floating a) => Vector sh a -> RealOf a Source #

Sum of the absolute values of real numbers or components of complex numbers.
For real numbers it is equivalent to `norm1`

.

norm2 :: (C sh, Floating a) => Vector sh a -> RealOf a Source #

Euclidean norm of a vector or Frobenius norm of a matrix.

normInf1 :: (C sh, Floating a) => Vector sh a -> RealOf a Source #

Computes (almost) the infinity norm of the vector. For complex numbers every element is replaced by the sum of the absolute component values first.

argAbsMaximum :: (InvIndexed sh, Floating a) => Vector sh a -> (Index sh, a) Source #

Returns the index and value of the element with the maximal absolute value. Caution: It actually returns the value of the element, not its absolute value!

argAbs1Maximum :: (InvIndexed sh, Floating a) => Vector sh a -> (Index sh, a) Source #

Returns the index and value of the element with the maximal absolute value. The function does not strictly compare the absolute value of a complex number but the sum of the absolute complex components. Caution: It actually returns the value of the element, not its absolute value!

mulConj :: (C sh, Eq sh, Floating a) => Vector sh a -> Vector sh a -> Vector sh a Source #

\xs ys -> mulConj xs ys == mul (conjugate xs) ys

argMinimum :: (InvIndexed sh, Index sh ~ ix, Real a) => Vector sh a -> (ix, a) Source #

For restrictions see `limits`

.

argMaximum :: (InvIndexed sh, Index sh ~ ix, Real a) => Vector sh a -> (ix, a) Source #

For restrictions see `limits`

.

limits :: (C sh, Real a) => Vector sh a -> (a, a) Source #

It should hold `limits x = Array.limits x`

.
The function is based on fast BLAS functions.
It should be faster than `Array.minimum`

and `Array.maximum`

although it is certainly not as fast as possible.
It is less precise if minimum and maximum differ considerably in magnitude
and there are several minimum or maximum candidates of similar value.
E.g. you cannot rely on the property
that `raise (- minimum x) x`

has only non-negative elements.

data RandomDistribution Source #