Safe Haskell	Safe
Language	Haskell98

Orthogonals

Synopsis

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] #