Orthogonals

Documentation

bra_ket :: (Scalar a, Num a) => [a] -> [a] -> a

class Eq a => Scalar a where

Minimal complete definition

coupled, norm, almostZero, scaled

Methods

coupled :: a -> a

norm :: [a] -> a

almostZero :: a -> Bool

scaled :: [a] -> [a]

Instances

Scalar Double

Methods

coupled :: Double -> Double

norm :: [Double] -> Double

almostZero :: Double -> Bool

scaled :: [Double] -> [Double]

Scalar Float

Methods

coupled :: Float -> Float

norm :: [Float] -> Float

almostZero :: Float -> Bool

scaled :: [Float] -> [Float]

Integral a => Scalar (Ratio a)

Methods

coupled :: Ratio a -> Ratio a

norm :: [Ratio a] -> Ratio a

almostZero :: Ratio a -> Bool

scaled :: [Ratio a] -> [Ratio a]

RealFloat a => Scalar (Complex a)

Methods

coupled :: Complex a -> Complex a

norm :: [Complex a] -> Complex a

almostZero :: Complex a -> Bool

scaled :: [Complex a] -> [Complex a]

norm1 :: Num a => [a] -> a

norminf :: (Num a, Ord a) => [a] -> a

matnorm1 :: (Num a, Ord a) => [[a]] -> a

matnorminf :: (Num a, Ord a) => [[a]] -> a

sum_product :: Num a => [a] -> [a] -> a

normalized :: (Scalar a, Fractional a) => [a] -> [a]

scaled' :: (Fractional t, Ord t) => [t] -> [t]

transposed :: [[a]] -> [[a]]

adjoint :: Scalar a => [[a]] -> [[a]]

matrix_zipWith :: (a -> b -> c) -> [[a]] -> [[b]] -> [[c]]

add_matrices :: Num a => t -> t1 -> [[a]] -> [[a]] -> [[a]]

matrix_matrix :: Num a => [[a]] -> [[a]] -> [[a]]

matrix_matrix' :: Num a => [[a]] -> [[a]] -> [[a]]

triangle_matrix' :: Num a => [[a]] -> [[a]] -> [[a]]

matrix_ket :: Num a => [[a]] -> [a] -> [a]

bra_matrix :: (Scalar a, Num a) => [a] -> [[a]] -> [a]

bra_matrix_ket :: (Scalar a, Num a) => [a] -> [[a]] -> [a] -> a

scalar_matrix :: Num a => a -> [[a]] -> [[a]]

orthogonals :: (Scalar a, Fractional a) => [a] -> [[a]]

gram_schmidt :: (Scalar a, Fractional a) => [[a]] -> [a] -> [a]

one_ket_triangle :: (Scalar a, Fractional a) => [[a]] -> [a] -> [([a], a)]

one_ket_solution :: (Scalar a, Fractional a) => [[a]] -> [a] -> [a]

many_kets_triangle :: (Scalar a, Fractional a) => [[a]] -> [[a]] -> [([a], [a])]

many_kets_solution :: (Scalar a, Fractional a) => [[a]] -> [[a]] -> [[a]]

inverse :: (Scalar a, Fractional a) => [[a]] -> [[a]]

factors_QR :: (Scalar a, Fractional a) => [[a]] -> ([[a]], [[a]])

determinant :: (Scalar a, Fractional a) => [[a]] -> a

determinantNaive :: Num a => [[a]] -> a

determinantClow :: Num a => [[a]] -> a

newClow :: Num a => [[a]] -> [[a]] -> [a]

extendClow :: Num a => [[a]] -> [[a]] -> [[a]]

longerClow :: Num a => [[a]] -> [[a]] -> [[a]]

nest :: Int -> (a -> a) -> a -> a

Compositional power of a function, i.e. apply the function n times to a value.

removeEach :: [a] -> [[a]]

alternate :: Num a => [a] -> [a]

parityFlip :: Num a => Int -> a -> a

scaleVec :: Num a => a -> [a] -> [a]

Weight a list of numbers by a scalar.

addVec :: Num a => [a] -> [a] -> [a]

Add corresponding numbers of two lists.

sumVec :: Num a => [[a]] -> [a]

Add some lists.

similar_to :: (Scalar a, Fractional a) => [[a]] -> [[a]]

iterated_eigenvalues :: (Scalar a1, Fractional a1, Eq a, Num a) => [[a1]] -> a -> [[a1]]

eigenvalues :: (Scalar a1, Fractional a1, Eq a, Num a) => [[a1]] -> a -> [a1]

add_to_diagonal :: Num a => a -> [[a]] -> [[a]]

eigenkets :: (Scalar a, Fractional a) => [[a]] -> [a] -> [[a]]

eigenket' :: (Scalar a, Fractional a) => [[a]] -> a -> a -> [a] -> [a]

unit_matrix :: Num a => Int -> [[a]]

unit_vector :: Num a => Int -> Int -> [a]

diagonals :: [[a]] -> [a]