numeric-quest-0.1.1: Math and quantum mechanics Source code Contents Index

Orthogonals

Synopsis

bra_ket :: (Scalar a, Num a) => [a] -> [a] -> a class Scalar a where coupled :: a -> a norm :: [a] -> a almostZero :: a -> Bool scaled :: [a] -> [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 :: (Fractional a, Scalar 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 :: (Fractional a, Scalar a) => [[a]] -> ([[a]], [[a]]) determinant :: (Fractional a, Scalar 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 removeEach :: [a] -> [[a]] alternate :: Num a => [a] -> [a] parityFlip :: Num a => Int -> a -> a scaleVec :: Num a => a -> [a] -> [a] addVec :: Num a => [a] -> [a] -> [a] sumVec :: Num a => [[a]] -> [a] similar_to :: (Fractional a, Scalar a) => [[a]] -> [[a]] iterated_eigenvalues :: (Scalar a1, Fractional a1, Num a) => [[a1]] -> a -> [[a1]] eigenvalues :: (Scalar a1, Fractional a1, 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]

Documentation

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

class Scalar a where Source

Methods coupled :: a -> a Source norm :: [a] -> a Source almostZero :: a -> Bool Source scaled :: [a] -> [a] Source Instances Scalar Double Scalar Float Integral a => Scalar (Ratio a) RealFloat a => Scalar (Complex a)

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

determinant :: (Fractional a, Scalar 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

Add some lists.

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

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

eigenvalues :: (Scalar a1, Fractional a1, 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

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