numeric-quest-0.2.0.2: Math and quantum mechanics

Orthogonals

Synopsis

# Documentation

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

class Eq a => Scalar a where Source #

Minimal complete definition

Methods

coupled :: a -> a Source #

norm :: [a] -> a Source #

almostZero :: a -> Bool Source #

scaled :: [a] -> [a] Source #

Instances

 Source # Methodsnorm :: [Double] -> Double Source #scaled :: [Double] -> [Double] Source # Source # Methodsnorm :: [Float] -> Float Source #scaled :: [Float] -> [Float] Source # Integral a => Scalar (Ratio a) Source # Methodscoupled :: Ratio a -> Ratio a Source #norm :: [Ratio a] -> Ratio a Source #scaled :: [Ratio a] -> [Ratio a] Source # RealFloat a => Scalar (Complex a) Source # Methodscoupled :: Complex a -> Complex a Source #norm :: [Complex a] -> Complex a Source #scaled :: [Complex a] -> [Complex a] Source #

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

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

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

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

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

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

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

transposed :: [[a]] -> [[a]] Source #

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

removeEach :: [a] -> [[a]] Source #

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

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

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

Weight a list of numbers by a scalar.

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

Add corresponding numbers of two lists.

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

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

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

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

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

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

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

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

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

diagonals :: [[a]] -> [a] Source #