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LSpace v => [DualVector v] -> Seminorm v","name":"spanNorm","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:spanNorm"},{"display_html":"euclideanNorm :: HilbertSpace v => Norm v","name":"euclideanNorm","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:euclideanNorm"},{"display_html":"(|$|) :: (LSpace v, Floating (Scalar v)) => Seminorm v -> v -> Scalar v","name":"|$|","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:-124--36--124-"},{"display_html":"normSq :: LSpace v => Seminorm v -> v -> Scalar v","name":"normSq","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:normSq"},{"display_html":"(<$|) :: LSpace v => Norm v -> v -> DualVector v","name":"<$|","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:-60--36--124-"},{"display_html":"scaleNorm :: forall v. LSpace v => Scalar v -> Norm v -> Norm v","name":"scaleNorm","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:scaleNorm"},{"display_html":"normSpanningSystem :: SimpleSpace v => Seminorm v -> [DualVector v]","name":"normSpanningSystem","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:normSpanningSystem"},{"display_html":"normSpanningSystem' :: (FiniteDimensional v, IEEE (Scalar v)) => Seminorm v -> [v]","name":"normSpanningSystem'","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:normSpanningSystem-39-"},{"display_html":"type Variance v = Norm (DualVector v)","name":"Variance","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#t:Variance"},{"display_html":"spanVariance :: forall v. LSpace v => [v] -> Variance v","name":"spanVariance","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:spanVariance"},{"display_html":"(|&>) :: LSpace v => DualVector v -> Variance v -> v","name":"|&>","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:-124--38--62-"},{"display_html":"varianceSpanningSystem :: forall v. SimpleSpace v => Variance v -> [v]","name":"varianceSpanningSystem","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:varianceSpanningSystem"},{"display_html":"dualNorm :: SimpleSpace v => Norm v -> Variance v","name":"dualNorm","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:dualNorm"},{"display_html":"dualNorm' :: forall v. SimpleSpace v => Variance v -> Norm v","name":"dualNorm'","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:dualNorm-39-"},{"display_html":"dependence :: forall u v. 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(SimpleSpace u, SimpleSpace v, Scalar u ~ Scalar v) => (u +> v) -> v +> u","name":"pseudoInverse","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:pseudoInverse"},{"display_html":"roughDet :: (FiniteDimensional v, IEEE (Scalar v)) => (v +> v) -> Scalar v","name":"roughDet","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:roughDet"},{"display_html":"linearRegressionW :: forall s x m y. (LinearSpace x, SimpleSpace y, SimpleSpace m, Scalar x ~ s, Scalar y ~ s, Scalar m ~ s, RealFrac' s) => Norm y -> (x -> m +> y) -> [(x, y)] -> m","name":"linearRegressionW","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:linearRegressionW"},{"display_html":"linearRegression :: forall s x m y. (LinearSpace x, SimpleSpace y, SimpleSpace m, Scalar x ~ s, Scalar y ~ s, Scalar m ~ s, RealFrac' s) => (x -> m +> y) -> [(x, (y, Norm y))] -> LinearRegressionResult x y m","name":"linearRegression","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:linearRegression"},{"display_html":"data LinearRegressionResult x y m","name":"LinearRegressionResult","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#t:LinearRegressionResult"},{"display_html":"linearFit_χν² :: LinearRegressionResult x y m -> Scalar m","name":"linearFit_χν²","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:linearFit_-967--957--178-"},{"display_html":"linearFit_bestModel :: LinearRegressionResult x y m -> m","name":"linearFit_bestModel","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:linearFit_bestModel"},{"display_html":"linearFit_modelUncertainty :: LinearRegressionResult x y m -> Norm m","name":"linearFit_modelUncertainty","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:linearFit_modelUncertainty"},{"display_html":"eigen :: (FiniteDimensional v, HilbertSpace v, IEEE (Scalar v)) => (v +> v) -> [(Scalar v, v)]","name":"eigen","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:eigen"},{"display_html":"constructEigenSystem :: (LSpace v, RealFloat (Scalar v)) => Norm v -> Scalar v -> (v -+> v) -> [v] -> [[Eigenvector v]]","name":"constructEigenSystem","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:constructEigenSystem"},{"display_html":"roughEigenSystem :: (FiniteDimensional v, IEEE (Scalar v)) => Norm v -> (v +> v) -> [Eigenvector v]","name":"roughEigenSystem","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:roughEigenSystem"},{"display_html":"finishEigenSystem :: forall v. (LSpace v, RealFloat (Scalar v)) => Norm v -> [Eigenvector v] -> [Eigenvector v]","name":"finishEigenSystem","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:finishEigenSystem"},{"display_html":"data Eigenvector v = Eigenvector {}","name":"Eigenvector Eigenvector ev_Eigenvalue ev_Eigenvector ev_FunctionApplied ev_Deviation ev_Badness","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#t:Eigenvector"},{"display_html":"module Math.LinearMap.Category.Instances.Deriving","name":"","module":"Math.LinearMap.Category","link":""},{"display_html":"module Data.VectorSpace","name":"","module":"Math.LinearMap.Category","link":""},{"display_html":"type LSpace v = (LinearSpace v, LinearSpace (Scalar v), LinearSpace (DualVector v), Num' (Scalar v))","name":"LSpace","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#t:LSpace"},{"display_html":"class (VectorSpace v, PseudoAffine v) => TensorSpace v where","name":"TensorSpace TensorProduct scalarSpaceWitness linearManifoldWitness zeroTensor toFlatTensor fromFlatTensor addTensors subtractTensors scaleTensor negateTensor tensorProduct tensorProducts transposeTensor fmapTensor fzipTensorWith coerceFmapTensorProduct wellDefinedVector wellDefinedTensor","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#t:TensorSpace"},{"display_html":"class (TensorSpace v, Num (Scalar v)) => LinearSpace v where","name":"LinearSpace DualVector trace dualSpaceWitness linearId idTensor sampleLinearFunction toLinearForm fromLinearForm coerceDoubleDual contractLinearMapAgainst contractTensorMap contractMapTensor contractTensorFn applyDualVector applyLinear composeLinear tensorId applyTensorFunctional applyTensorLinMap useTupleLinearSpaceComponents","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#t:LinearSpace"},{"display_html":"class LinearSpace v => SemiInner v where","name":"SemiInner dualBasisCandidates tensorDualBasisCandidates symTensorDualBasisCandidates symTensorTensorDualBasisCandidates","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#t:SemiInner"},{"display_html":"cartesianDualBasisCandidates :: [DualVector v] -> (v -> [ℝ]) -> [(Int, v)] -> Forest (Int, DualVector v)","name":"cartesianDualBasisCandidates","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:cartesianDualBasisCandidates"},{"display_html":"embedFreeSubspace :: forall v t r. (HasCallStack, SemiInner v, RealFrac' (Scalar v), Traversable t) => t v -> Maybe (ReifiedLens' v (t (Scalar v)))","name":"embedFreeSubspace","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:embedFreeSubspace"},{"display_html":"class (LSpace v, Eq v) => FiniteDimensional v where","name":"FiniteDimensional SubBasis entireBasis enumerateSubBasis subbasisDimension decomposeLinMap decomposeLinMapWithin recomposeSB recomposeSBTensor recomposeLinMap recomposeContraLinMap recomposeContraLinMapTensor uncanonicallyFromDual uncanonicallyToDual tensorEquality dualFinitenessWitness","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#t:FiniteDimensional"},{"display_html":"addV :: AdditiveGroup w => LinearFunction s (w, w) w","name":"addV","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:addV"},{"display_html":"scale :: VectorSpace v => Bilinear (Scalar v) v v","name":"scale","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:scale"},{"display_html":"inner :: InnerSpace v => Bilinear v v (Scalar v)","name":"inner","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:inner"},{"display_html":"flipBilin :: Bilinear v w y -> Bilinear w v y","name":"flipBilin","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:flipBilin"},{"display_html":"bilinearFunction :: (v -> w -> y) -> Bilinear v w y","name":"bilinearFunction","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:bilinearFunction"},{"display_html":"(.⊗) :: (TensorSpace v, HasBasis v, TensorSpace w, Num' (Scalar v), Scalar v ~ Scalar w) => Basis v -> w -> v ⊗ w","name":".⊗","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:.-8855-"},{"display_html":"(·) :: TensorQuot v w => (v ⨸ w) -> v -> w","name":"·","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:-183-"},{"display_html":"type DualSpace v = v +> Scalar v","name":"DualSpace","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#t:DualSpace"},{"display_html":"riesz :: forall v. (FiniteDimensional v, InnerSpace v, SimpleSpace v) => DualVector v -+> v","name":"riesz","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:riesz"},{"display_html":"coRiesz :: forall v. (LSpace v, InnerSpace v) => v -+> DualVector v","name":"coRiesz","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:coRiesz"},{"display_html":"showsPrecAsRiesz :: forall v. (FiniteDimensional v, InnerSpace v, Show v, HasBasis (Scalar v), Basis (Scalar v) ~ ()) => Int -> DualSpace v -> ShowS","name":"showsPrecAsRiesz","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:showsPrecAsRiesz"},{"display_html":"(.<) :: (FiniteDimensional v, Num' (Scalar v), InnerSpace v, LSpace w, HasBasis w, Scalar v ~ Scalar w) => Basis w -> v -> v +> w","name":".<","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:.-60-"},{"display_html":"class (FiniteDimensional v, HasBasis v) => TensorDecomposable v where","name":"TensorDecomposable showsPrecBasis tensorDecomposition","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#t:TensorDecomposable"},{"display_html":"class TensorDecomposable u => RieszDecomposable u where","name":"RieszDecomposable rieszDecomposition","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#t:RieszDecomposable"},{"display_html":"tensorDecomposeShowsPrec :: forall u v s. (TensorDecomposable u, FiniteDimensional v, Show v, Scalar u ~ s, Scalar v ~ s) => Int -> Tensor s u v -> ShowS","name":"tensorDecomposeShowsPrec","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:tensorDecomposeShowsPrec"},{"display_html":"rieszDecomposeShowsPrec :: forall u v s. 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SimpleSpace v => Norm v -> [v] -> Norm v","name":"relaxNorm","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:relaxNorm"},{"display_html":"transformNorm :: forall v w. (LSpace v, LSpace w, Scalar v ~ Scalar w) => (v +> w) -> Norm w -> Norm v","name":"transformNorm","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:transformNorm"},{"display_html":"transformVariance :: forall v w. (LSpace v, LSpace w, Scalar v ~ Scalar w) => (v +> w) -> Variance v -> Variance w","name":"transformVariance","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:transformVariance"},{"display_html":"findNormalLength :: forall s. RealFrac' s => Norm s -> Maybe s","name":"findNormalLength","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:findNormalLength"},{"display_html":"normalLength :: forall s. RealFrac' s => Norm s -> s","name":"normalLength","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:normalLength"},{"display_html":"summandSpaceNorms :: forall u v. (SimpleSpace u, SimpleSpace v, Scalar u ~ Scalar v) => Norm (u, v) -> (Norm u, Norm v)","name":"summandSpaceNorms","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:summandSpaceNorms"},{"display_html":"sumSubspaceNorms :: forall u v. (LSpace u, LSpace v, Scalar u ~ Scalar v) => Norm u -> Norm v -> Norm (u, v)","name":"sumSubspaceNorms","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:sumSubspaceNorms"},{"display_html":"sharedNormSpanningSystem :: SimpleSpace v => Norm v -> Seminorm v -> [(DualVector v, Scalar v)]","name":"sharedNormSpanningSystem","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:sharedNormSpanningSystem"},{"display_html":"sharedSeminormSpanningSystem :: forall v. SimpleSpace v => Seminorm v -> Seminorm v -> [(DualVector v, Maybe (Scalar v))]","name":"sharedSeminormSpanningSystem","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:sharedSeminormSpanningSystem"},{"display_html":"sharedSeminormSpanningSystem' :: forall v. SimpleSpace v => Seminorm v -> Seminorm v -> [v]","name":"sharedSeminormSpanningSystem'","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:sharedSeminormSpanningSystem-39-"},{"display_html":"convexPolytopeHull :: forall v. SimpleSpace v => [v] -> [DualVector v]","name":"convexPolytopeHull","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:convexPolytopeHull"},{"display_html":"symmetricPolytopeOuterVertices :: forall v. SimpleSpace v => [DualVector v] -> [v]","name":"symmetricPolytopeOuterVertices","module":"Math.LinearMap.Category","link":"Math-LinearMap-Category.html#v:symmetricPolytopeOuterVertices"}]