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]