numeric-quest-0.1: Math and quantum mechanics 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] transposed :: [[a]] -> [[a]] adjoint :: Scalar 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])] 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]] add_to_diagonal :: Num 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

class Scalar a where

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

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

adjoint :: Scalar 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])]

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

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

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

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

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

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

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