-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | International Geomagnetic Reference Field
--   
--   An implemetation of the International Geomagnetic Reference Field, a
--   model of the Earth's magnetic field.
--   
--   Includes model coefficients from the 11th Edition of the IGRF.
@package igrf
@version 0.4.0.0


-- | Provides definitions of associated Legendre functions used in
--   spherical harmonic models.
module Math.SphericalHarmonics.AssociatedLegendre

-- | Computes the associated Legendre function of degree <tt>n</tt> and
--   order <tt>m</tt>. Note that the resulting function may not be a
--   polynomial, as when <tt>m</tt> is odd it involves a fractional power
--   of <tt>x</tt>. As used in the geodesy and magnetics literature, these
--   functions do not include the Condon-Shortley phase.
associatedLegendreFunction :: (Floating a, Ord a) => Int -> Int -> a -> a

-- | Computes the Schmidt semi-normalized associated Legendre function of
--   degree <tt>n</tt> and order <tt>m</tt>. As used in the geodesy and
--   magnetics literature, these functions do not include the
--   Condon-Shortley phase.
schmidtSemiNormalizedAssociatedLegendreFunction :: (Floating a, Ord a) => Int -> Int -> a -> a


-- | Provides spherical harmonic models of scalar-valued functions.
module Math.SphericalHarmonics

-- | Represents a spherical harmonic model of a scalar-valued function.
data SphericalHarmonicModel a

-- | Creates a spherical harmonic model. Result in an error if the length
--   of the list is not a triangular number.
sphericalHarmonicModel :: Fractional a => [[(a, a)]] -> SphericalHarmonicModel a

-- | Creates a spherical harmonic model, scaling coefficients for the
--   supplied reference radius. Result in an error if the length of the
--   list is not a triangular number.
scaledSphericalHarmonicModel :: Fractional a => a -> [[(a, a)]] -> SphericalHarmonicModel a

-- | Computes the scalar value of the spherical harmonic model at a
--   specified spherical position.
evaluateModel :: (RealFloat a, Ord a) => SphericalHarmonicModel a -> a -> a -> a -> a

-- | Computes the scalar value of the spherical harmonic model at a
--   specified Cartesian position.
evaluateModelCartesian :: (RealFloat a, Ord a) => SphericalHarmonicModel a -> a -> a -> a -> a

-- | Computes the gradient of the scalar value of the spherical harmonic
--   model, in spherical coordinates, at a specified location.
evaluateModelGradient :: (RealFloat a, Ord a) => SphericalHarmonicModel a -> a -> a -> a -> (a, a, a)

-- | Computes the gradient of the scalar value of the spherical harmonic
--   model at a specified location, in Cartesian coordinates. The result is
--   expressed in right-handed coordinates centered at the origin of the
--   sphere, with the positive Z-axis piercing the north pole and the
--   positive x-axis piercing the reference meridian.
evaluateModelGradientCartesian :: (RealFloat a, Ord a) => SphericalHarmonicModel a -> a -> a -> a -> (a, a, a)

-- | Computes the gradient of the scalar value of the spherical harmonic
--   model at a specified location, in Cartesian coordinates. The result is
--   expressed in a reference frame locally tangent to the sphere at the
--   specified location.
evaluateModelGradientInLocalTangentPlane :: (RealFloat a, Ord a) => SphericalHarmonicModel a -> a -> a -> a -> (a, a, a)
instance GHC.Base.Functor Math.SphericalHarmonics.SphericalHarmonicModel
instance (GHC.Real.Fractional a, GHC.Classes.Eq a) => Data.AdditiveGroup.AdditiveGroup (Math.SphericalHarmonics.SphericalHarmonicModel a)
instance (GHC.Real.Fractional a, GHC.Classes.Eq a) => Data.VectorSpace.VectorSpace (Math.SphericalHarmonics.SphericalHarmonicModel a)


-- | Parse
--   <a>https://www.ngdc.noaa.gov/IAGA/vmod/coeffs/igrf13coeffs.txt</a>
module IGRF.Parser

-- | Parse
--   <a>https://www.ngdc.noaa.gov/IAGA/vmod/coeffs/igrf13coeffs.txt</a> and
--   return a list of models.
parseModels :: Text -> [(Text, Text, SphericalHarmonicModel Double)]


-- | An implementation of the International Geomagnetic Reference Field, as
--   defined at <a>http://www.ngdc.noaa.gov/IAGA/vmod/igrf.html</a>.
module IGRF

-- | Represents a spherical harmonic model of a magnetic field.
data MagneticModel a
MagneticModel :: SphericalHarmonicModel a -> SphericalHarmonicModel a -> MagneticModel a

-- | Field at model epoch in nT, reference radius in km
[fieldAtEpoch] :: MagneticModel a -> SphericalHarmonicModel a

-- | Secular variation in nT / yr, reference radius in km
[secularVariation] :: MagneticModel a -> SphericalHarmonicModel a

-- | The International Geomagnetic Reference Field model, 11th edition.
--   Model epoch is January 1st, 2010.
igrf11 :: Fractional a => MagneticModel a

-- | The International Geomagnetic Reference Field model, 12th edition.
--   Model epoch is January 1st, 2015.
igrf12 :: Fractional a => MagneticModel a

-- | The International Geomagnetic Reference Field model, 13th edition.
--   Model epoch is January 1st, 2020.
igrf13 :: Fractional a => MagneticModel a

-- | Gets a spherical harmonic model of a magnetic field at a specified
--   time offset from the model epoch.
fieldAtTime :: (Fractional a, Eq a) => MagneticModel a -> a -> SphericalHarmonicModel a

-- | Computes the gradient of the scalar value of the spherical harmonic
--   model at a specified location, in Cartesian coordinates. The result is
--   expressed in a reference frame locally tangent to the sphere at the
--   specified location.
evaluateModelGradientInLocalTangentPlane :: (RealFloat a, Ord a) => SphericalHarmonicModel a -> a -> a -> a -> (a, a, a)