Numeric.VariablePrecision.Complex

Newtype wrapper around Complex. When both of Complex and this module need to be imported, use qualified imports.

Documentation

data VComplex p

Newtype wrapper around Complex so that instances can be written for HasPrecision and VariablePrecision.

Instances

Typeable1 VComplex

VariablePrecision VComplex

HasPrecision VComplex

Normed VComplex

Eq (VComplex p)

NaturalNumber p => Floating (VComplex p)

NaturalNumber p => Fractional (VComplex p)

Data p => Data (VComplex p)

NaturalNumber p => Num (VComplex p)

NaturalNumber p => Read (VComplex p)

NaturalNumber p => Show (VComplex p)

(.+) :: NaturalNumber p => VFloat p -> VFloat p -> VComplex p

Alike to :+, constructs a complex number from a real part and an imaginary part.

(.*) :: NaturalNumber p => VFloat p -> VComplex p -> VComplex p

Real-complex multiplication.

(*.) :: NaturalNumber p => VComplex p -> VFloat p -> VComplex p

Complex-real multiplication.

toComplex :: VComplex p -> Complex (VFloat p)

Convert VComplex to Complex.

fromComplex :: Complex (VFloat p) -> VComplex p

Convert Complex to VComplex.

withComplex :: (Complex (VFloat p) -> Complex (VFloat q)) -> VComplex p -> VComplex q

Lift an operation on Complex to one on VComplex.

mapComplex :: (RealFloat a, RealFloat b) => (a -> b) -> Complex a -> Complex b

Apply a function to both components of a complex number.

recodeComplex :: (RealFloat a, RealFloat b) => Complex a -> Complex b

Much like mapComplex recodeFloat.

scaleComplex :: NaturalNumber p => Int -> VComplex p -> VComplex p

Much like withComplex scaleComplex'.

realPart :: NaturalNumber p => VComplex p -> VFloat p

Real part.

imagPart :: NaturalNumber p => VComplex p -> VFloat p

Imaginary part.

conjugate :: NaturalNumber p => VComplex p -> VComplex p

Conjugate.

magnitude :: NaturalNumber p => VComplex p -> VFloat p

Magnitude.

magnitude2 :: NaturalNumber p => VComplex p -> VFloat p

Magnitude squared.

sqr :: NaturalNumber p => VComplex p -> VComplex p

Complex square.

phase :: NaturalNumber p => VComplex p -> VFloat p

Phase.

polar :: NaturalNumber p => VComplex p -> (VFloat p, VFloat p)

Polar form.

cis :: NaturalNumber p => VFloat p -> VComplex p

Unit at phase.

mkPolar :: NaturalNumber p => VFloat p -> VFloat p -> VComplex p

From polar form.

scaleComplex' :: RealFloat r => Int -> Complex r -> Complex r

Much like mapComplex scaleFloat.

magnitude2' :: RealFloat r => Complex r -> r

Magnitude squared.

sqr' :: RealFloat r => Complex r -> Complex r

Complex square.

data DComplex

A concrete format suitable for storage or wire transmission.

Constructors

DComplex

Fields

dRealPart :: !DFloat

dImagPart :: !DFloat

Instances

Eq DComplex

Data DComplex

Ord DComplex

Read DComplex

Show DComplex

Typeable DComplex

toDComplex :: NaturalNumber p => VComplex p -> DComplex

Freeze a VComplex.

fromDComplex :: NaturalNumber p => DComplex -> Maybe (VComplex p)

Thaw a DComplex. Results in Nothing on precision mismatch.

withDComplex :: DComplex -> (forall p. NaturalNumber p => Maybe (VComplex p) -> r) -> r

Thaw a DComplex to its natural precision. Nothing is passed on precision mismatch between real and imaginary parts.