Safe Haskell	None
Language	Haskell98

Numeric.LAPACK.Matrix.Shape.Omni

Synopsis

data Omni pack property lower upper meas vert horiz height width where
- Full :: (Property property, Strip lower, Strip upper) => Full meas vert horiz height width -> Omni Unpacked property lower upper meas vert horiz height width
- UpperTriangular :: TriDiag diag => UpperTriangular size -> Omni Packed diag Empty Filled Shape Small Small size size
- LowerTriangular :: TriDiag diag => LowerTriangular size -> Omni Packed diag Filled Empty Shape Small Small size size
- Symmetric :: Symmetric size -> Omni Packed Symmetric Filled Filled Shape Small Small size size
- Hermitian :: (C neg, C zero, C pos) => Hermitian size -> Omni Packed (Hermitian neg zero pos) Filled Filled Shape Small Small size size
- Banded :: (Natural sub, Natural super) => Banded sub super meas vert horiz height width -> Omni Packed Arbitrary (Bands sub) (Bands super) meas vert horiz height width
- UnitBandedTriangular :: (BandedTriangular sub super, BandedTriangular super sub) => BandedSquare sub super size -> Omni Packed Unit (Bands sub) (Bands super) Shape Small Small size size
- BandedHermitian :: (C neg, C zero, C pos, Natural offDiag) => BandedHermitian offDiag size -> Omni Packed (Hermitian neg zero pos) (Bands offDiag) (Bands offDiag) Shape Small Small size size
data Unit
data Arbitrary
data Symmetric
data Hermitian neg zero pos
type HermitianUnknownDefiniteness = Hermitian True True True
type HermitianPositiveDefinite = Hermitian False False True
type HermitianPositiveSemidefinite = Hermitian False True True
type HermitianNegativeDefinite = Hermitian True False False
type HermitianNegativeSemidefinite = Hermitian True True False
hermitianSet :: (C neg, C zero, C pos) => Omni pack (Hermitian neg zero pos) lower upper meas vert horiz height width -> (Singleton neg, Singleton zero, Singleton pos)
class Property diag => TriDiag diag where
- switchTriDiag :: f Unit -> f Arbitrary -> f diag
data DiagSingleton diag where
- Unit :: DiagSingleton Unit
- Arbitrary :: DiagSingleton Arbitrary
autoDiag :: TriDiag diag => DiagSingleton diag
charFromTriDiag :: TriDiag diag => DiagSingleton diag -> Char
packTag :: Packing pack => Omni pack propery lower upper meas vert horiz height width -> PackingSingleton pack
class Property property
property :: Property property => Omni pack property lower upper meas vert horiz height width -> PropertySingleton property
data PropertySingleton property where
- PropArbitrary :: PropertySingleton Arbitrary
- PropUnit :: PropertySingleton Unit
- PropSymmetric :: PropertySingleton Symmetric
- PropHermitian :: (C neg, C zero, C pos) => PropertySingleton (Hermitian neg zero pos)
propertySingleton :: Property property => PropertySingleton property
class (MultipliedBands c Filled ~ Filled, MultipliedBands c Empty ~ c) => Strip c where
- switchStrip :: (forall offDiag. Natural offDiag => f (Bands offDiag)) -> f Filled -> f c
strips :: (Strip lower, Strip upper) => Omni pack property lower upper meas vert horiz height width -> (StripSingleton lower, StripSingleton upper)
data StripSingleton c where
- StripBands :: Natural offDiag => HeadSingleton offDiag -> StripSingleton (Bands offDiag)
- StripFilled :: StripSingleton Filled
stripSingleton :: Strip c => StripSingleton c
class Strip c => PowerStrip c where
- switchPowerStrip :: f Empty -> f Filled -> f c
data PowerStripSingleton c where
- Empty :: PowerStripSingleton Empty
- Filled :: PowerStripSingleton Filled
powerStripSingleton :: PowerStrip c => PowerStripSingleton c
powerStrips :: (PowerStrip lower, PowerStrip upper) => Omni pack property lower upper meas vert horiz height width -> (PowerStripSingleton lower, PowerStripSingleton upper)
class (Natural sub, Natural super) => BandedTriangular sub super
data BandedTriangularSingleton sub super where
- BandedDiagonal :: BandedTriangularSingleton Zero Zero
- BandedUpper :: Natural offDiag => BandedTriangularSingleton Zero (Succ offDiag)
- BandedLower :: Natural offDiag => BandedTriangularSingleton (Succ offDiag) Zero
bandedTriangularSingleton :: BandedTriangular sub super => Banded sub super meas vert horiz height width -> BandedTriangularSingleton sub super
extent :: (Measure meas, C vert, C horiz) => Omni pack property lower upper meas vert horiz height width -> Extent meas vert horiz height width
height :: (Measure meas, C vert, C horiz) => Omni pack property lower upper meas vert horiz height width -> height
width :: (Measure meas, C vert, C horiz) => Omni pack property lower upper meas vert horiz height width -> width
squareSize :: Omni pack property lower upper Shape Small Small sh sh -> sh
mapHeight :: (C heightA, C heightB, C vert, C horiz) => (heightA -> heightB) -> Omni pack property lower upper Size vert horiz heightA width -> Omni pack property lower upper Size vert horiz heightB width
mapWidth :: (C widthA, C widthB, C vert, C horiz) => (widthA -> widthB) -> Omni pack property lower upper Size vert horiz height widthA -> Omni pack property lower upper Size vert horiz height widthB
mapSquareSize :: (C shA, C shB) => (shA -> shB) -> Omni pack property lower upper Shape Small Small shA shA -> Omni pack property lower upper Shape Small Small shB shB
order :: Omni pack property lower upper meas vert horiz height width -> Order
transpose :: (Measure meas, C vert, C horiz) => Omni pack property lower upper meas vert horiz height width -> Omni pack property upper lower meas horiz vert width height
class (Property property, Strip lower, Strip upper, Measured meas vert, Measured meas horiz) => Cons pack property lower upper meas vert horiz where
- cons :: (C height, C width) => MeasureTarget meas height ~ MeasureTarget meas width => Order -> Dimension meas height width -> Omni pack property lower upper meas vert horiz height width
type family Plain pack property lower upper meas vert horiz height width
class FromPlain pack property lower upper meas vert horiz height width => ToPlain pack property lower upper meas vert horiz height width
toPlain :: ToPlain pack property lower upper meas vert horiz height width => Omni pack property lower upper meas vert horiz height width -> Plain pack property lower upper meas vert horiz height width
class FromPlain pack property lower upper meas vert horiz height width
fromPlain :: FromPlain pack property lower upper meas vert horiz height width => Plain pack property lower upper meas vert horiz height width -> Omni pack property lower upper meas vert horiz height width
toFull :: (Property property, Strip lower, Strip upper) => Omni Unpacked property lower upper meas vert horiz height width -> Full meas vert horiz height width
fromFull :: (Property property, Strip lower, Strip upper) => Full meas vert horiz height width -> Omni Unpacked property lower upper meas vert horiz height width
toBanded :: (Natural sub, Natural super) => Omni Packed Arbitrary (Bands sub) (Bands super) meas vert horiz height width -> Banded sub super meas vert horiz height width
toBandedHermitian :: (C neg, C zero, C pos, Natural offDiag) => Omni Packed (Hermitian neg zero pos) (Bands offDiag) (Bands offDiag) Shape Small Small size size -> BandedHermitian offDiag size
type family MultipliedBands bandsA bandsB
type family MultipliedStrip contA contB
type family MultipliedProperty propA propB
type family UnitIfTriangular lower upper
type family MergeUnit unit0 unit1
class Quadratic pack property lower upper
quadratic :: (Quadratic pack property lower upper, C sh) => Order -> sh -> Omni pack property lower upper Shape Small Small sh sh
uncheckedDiagonal :: (Packing pack, TriDiag diag) => Order -> size -> Omni pack diag Empty Empty Shape Small Small size size
data Power pack property lower upper meas vert horiz height width where
- PowerIdentity :: Packing pack => PowerQuadratic pack Unit Empty Empty sh
- PowerDiagonal :: Packing pack => Power pack property Empty Empty meas vert horiz height width
- PowerUpperTriangular :: (Packing pack, TriDiag diag) => PowerQuadratic pack diag Empty Filled sh
- PowerLowerTriangular :: (Packing pack, TriDiag diag) => PowerQuadratic pack diag Filled Empty sh
- PowerSymmetric :: Packing pack => PowerQuadratic pack Symmetric Filled Filled sh
- PowerHermitian :: (Packing pack, C neg, C zero, C pos) => PowerQuadratic pack (Hermitian neg zero pos) Filled Filled sh
- PowerFull :: Power Unpacked property lower upper meas vert horiz height width
powerSingleton :: (Packing pack, Property property, PowerStrip lower, PowerStrip upper, Measure meas, C vert, C horiz) => Omni pack property lower upper meas vert horiz height width -> Power pack property lower upper meas vert horiz height width

Documentation

data Omni pack property lower upper meas vert horiz height width where Source #

Constructors

Full :: (Property property, Strip lower, Strip upper) => Full meas vert horiz height width -> Omni Unpacked property lower upper meas vert horiz height width
UpperTriangular :: TriDiag diag => UpperTriangular size -> Omni Packed diag Empty Filled Shape Small Small size size
LowerTriangular :: TriDiag diag => LowerTriangular size -> Omni Packed diag Filled Empty Shape Small Small size size
Symmetric :: Symmetric size -> Omni Packed Symmetric Filled Filled Shape Small Small size size
Hermitian :: (C neg, C zero, C pos) => Hermitian size -> Omni Packed (Hermitian neg zero pos) Filled Filled Shape Small Small size size
Banded :: (Natural sub, Natural super) => Banded sub super meas vert horiz height width -> Omni Packed Arbitrary (Bands sub) (Bands super) meas vert horiz height width
UnitBandedTriangular :: (BandedTriangular sub super, BandedTriangular super sub) => BandedSquare sub super size -> Omni Packed Unit (Bands sub) (Bands super) Shape Small Small size size
BandedHermitian :: (C neg, C zero, C pos, Natural offDiag) => BandedHermitian offDiag size -> Omni Packed (Hermitian neg zero pos) (Bands offDiag) (Bands offDiag) Shape Small Small size size

Instances

(Measure meas, C vert, C horiz, Eq height, Eq width) => Eq (Omni pack property lower upper meas vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods (==) :: Omni pack property lower upper meas vert horiz height width -> Omni pack property lower upper meas vert horiz height width -> Bool # (/=) :: Omni pack property lower upper meas vert horiz height width -> Omni pack property lower upper meas vert horiz height width -> Bool #
(Measure meas, C vert, C horiz, Show height, Show width) => Show (Omni pack property lower upper meas vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods showsPrec :: Int -> Omni pack property lower upper meas vert horiz height width -> ShowS # show :: Omni pack property lower upper meas vert horiz height width -> String # showList :: [Omni pack property lower upper meas vert horiz height width] -> ShowS #
(Measure meas, C vert, C horiz, C height, C width) => C (Omni pack property lower upper meas vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods size :: Omni pack property lower upper meas vert horiz height width -> Int #
(Measure meas, C vert, C horiz, NFData height, NFData width) => NFData (Omni pack property lower upper meas vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods rnf :: Omni pack property lower upper meas vert horiz height width -> () #

data Unit Source #

Instances

Property Unit Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods switchProperty :: f Arbitrary -> f Unit -> f Symmetric -> (forall neg zero pos. (C neg, C zero, C pos) => f (Hermitian neg zero pos)) -> f Unit
TriDiag Unit Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods switchTriDiag :: f Unit -> f Arbitrary -> f Unit Source #
SqRt Unit Source #
Instance details Defined in Numeric.LAPACK.Matrix.Function Methods sqrt :: (Packing pack, PowerStrip lower, PowerStrip upper, C sh, Real a) => Quadratic pack Unit lower upper sh a -> Quadratic pack Unit lower upper sh a Source #
(BandedTriangular sub super, BandedTriangular super sub) => Quadratic Packed Unit (Bands sub) (Bands super) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods quadratic :: C sh => Order -> sh -> Omni Packed Unit (Bands sub) (Bands super) Shape Small Small sh sh Source #
(BandedTriangular sub super, BandedTriangular super sub, Shape ~ meas, Small ~ vert, Small ~ horiz) => Cons Packed Unit (Bands sub) (Bands super) meas vert horiz Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods cons :: (C height, C width, MeasureTarget meas height ~ MeasureTarget meas width) => Order -> Dimension meas height width -> Omni Packed Unit (Bands sub) (Bands super) meas vert horiz height width Source #
(BandedTriangular sub super, BandedTriangular super sub, height ~ width) => ToPlain Packed Unit (Bands sub) (Bands super) Shape Small Small height width Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods toPlain :: Omni Packed Unit (Bands sub) (Bands super) Shape Small Small height width -> Plain Packed Unit (Bands sub) (Bands super) Shape Small Small height width Source #
(BandedTriangular sub super, BandedTriangular super sub, height ~ width) => FromPlain Packed Unit (Bands sub) (Bands super) Shape Small Small height width Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Associated Types type Plain Packed Unit (Bands sub) (Bands super) Shape Small Small height width :: Type Source # Methods fromPlain :: Plain Packed Unit (Bands sub) (Bands super) Shape Small Small height width -> Omni Packed Unit (Bands sub) (Bands super) Shape Small Small height width Source #
type MergeUnit Unit unit1 Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type MergeUnit Unit unit1 = unit1
type MultipliedProperty Unit Symmetric Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type MultipliedProperty Unit Symmetric = Arbitrary
type MultipliedProperty Unit Arbitrary Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type MultipliedProperty Unit Arbitrary = Arbitrary
type MultipliedProperty Unit Unit Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type MultipliedProperty Unit Unit = Unit
type Plain Packed Unit (Bands sub) (Bands super) Shape Small Small height width Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type Plain Packed Unit (Bands sub) (Bands super) Shape Small Small height width = BandedSquare sub super height
type MultipliedProperty Unit (Hermitian neg zero pos) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type MultipliedProperty Unit (Hermitian neg zero pos) = Arbitrary

data Arbitrary Source #

Instances

Property Arbitrary Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods switchProperty :: f Arbitrary -> f Unit -> f Symmetric -> (forall neg zero pos. (C neg, C zero, C pos) => f (Hermitian neg zero pos)) -> f Arbitrary
TriDiag Arbitrary Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods switchTriDiag :: f Unit -> f Arbitrary -> f Arbitrary Source #
Subtractive Arbitrary Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array.Private
Additive Arbitrary Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array.Private
Scale Arbitrary Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array.Private
Homogeneous Arbitrary Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array.Private
Diagonal Arbitrary Source #
Instance details Defined in Numeric.LAPACK.Matrix.Quadratic Methods diagonalAux :: (Quadratic pack Arbitrary lower upper, C sh, Floating a) => Quadratic pack Arbitrary lower upper sh -> Vector sh a -> Quadratic pack Arbitrary lower upper sh a
LiftReal Arbitrary Source #	Generic algorithm that applies a scalar function to the elements of the diagonal factor of a full, triangular or diagonal matrix with distinct eigenvalues. It is not checked whether the matrix has distinct eigenvalues.
Instance details Defined in Numeric.LAPACK.Matrix.Function Methods liftReal :: (Packing pack, PowerStrip lower, PowerStrip upper, C sh, Real a) => (a -> a) -> Quadratic pack Arbitrary lower upper sh a -> Quadratic pack Arbitrary lower upper sh a Source #
Log Arbitrary Source #
Instance details Defined in Numeric.LAPACK.Matrix.Function Methods log :: (Packing pack, PowerStrip lower, PowerStrip upper, C sh, Real a) => Quadratic pack Arbitrary lower upper sh a -> Quadratic pack Arbitrary lower upper sh a Source #
Exp Arbitrary Source #
Instance details Defined in Numeric.LAPACK.Matrix.Function Methods exp :: (Packing pack, PowerStrip lower, PowerStrip upper, C sh, Floating a) => Quadratic pack Arbitrary lower upper sh a -> Quadratic pack Arbitrary lower upper sh a Source #
SqRt Arbitrary Source #	For Full matrices: Explicit solution for matrices up to size 2. Solution via `sqrtDenmanBeavers` for larger sizes.
Instance details Defined in Numeric.LAPACK.Matrix.Function Methods sqrt :: (Packing pack, PowerStrip lower, PowerStrip upper, C sh, Real a) => Quadratic pack Arbitrary lower upper sh a -> Quadratic pack Arbitrary lower upper sh a Source #
(Strip lower, Strip upper) => Quadratic Unpacked Arbitrary lower upper Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods quadratic :: C sh => Order -> sh -> Omni Unpacked Arbitrary lower upper Shape Small Small sh sh Source #
(Strip lower, Strip upper, Measured meas vert, Measured meas horiz) => Cons Unpacked Arbitrary lower upper meas vert horiz Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods cons :: (C height, C width, MeasureTarget meas height ~ MeasureTarget meas width) => Order -> Dimension meas height width -> Omni Unpacked Arbitrary lower upper meas vert horiz height width Source #
ToPlain Unpacked Arbitrary Filled Filled meas vert horiz height width Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods toPlain :: Omni Unpacked Arbitrary Filled Filled meas vert horiz height width -> Plain Unpacked Arbitrary Filled Filled meas vert horiz height width Source #
FromPlain Unpacked Arbitrary Filled Filled meas vert horiz height width Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Associated Types type Plain Unpacked Arbitrary Filled Filled meas vert horiz height width :: Type Source # Methods fromPlain :: Plain Unpacked Arbitrary Filled Filled meas vert horiz height width -> Omni Unpacked Arbitrary Filled Filled meas vert horiz height width Source #
(Natural sub, Natural super) => Quadratic Packed Arbitrary (Bands sub) (Bands super) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods quadratic :: C sh => Order -> sh -> Omni Packed Arbitrary (Bands sub) (Bands super) Shape Small Small sh sh Source #
(Measured meas vert, Measured meas horiz, Natural sub, Natural super) => Cons Packed Arbitrary (Bands sub) (Bands super) meas vert horiz Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods cons :: (C height, C width, MeasureTarget meas height ~ MeasureTarget meas width) => Order -> Dimension meas height width -> Omni Packed Arbitrary (Bands sub) (Bands super) meas vert horiz height width Source #
(Natural sub, Natural super) => ToPlain Packed Arbitrary (Bands sub) (Bands super) meas vert horiz height width Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods toPlain :: Omni Packed Arbitrary (Bands sub) (Bands super) meas vert horiz height width -> Plain Packed Arbitrary (Bands sub) (Bands super) meas vert horiz height width Source #
(Natural sub, Natural super) => FromPlain Packed Arbitrary (Bands sub) (Bands super) meas vert horiz height width Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Associated Types type Plain Packed Arbitrary (Bands sub) (Bands super) meas vert horiz height width :: Type Source # Methods fromPlain :: Plain Packed Arbitrary (Bands sub) (Bands super) meas vert horiz height width -> Omni Packed Arbitrary (Bands sub) (Bands super) meas vert horiz height width Source #
type MergeUnit Arbitrary unit1 Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type MergeUnit Arbitrary unit1 = Arbitrary
type MultipliedProperty Arbitrary propB Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type MultipliedProperty Arbitrary propB = Arbitrary
type MultipliedProperty Unit Arbitrary Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type MultipliedProperty Unit Arbitrary = Arbitrary
type Plain Unpacked Arbitrary Filled Filled meas vert horiz height width Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type Plain Unpacked Arbitrary Filled Filled meas vert horiz height width = Full meas vert horiz height width
type Plain Packed Arbitrary (Bands sub) (Bands super) meas vert horiz height width Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type Plain Packed Arbitrary (Bands sub) (Bands super) meas vert horiz height width = Banded sub super meas vert horiz height width

data Symmetric Source #

Instances

Property Symmetric Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods switchProperty :: f Arbitrary -> f Unit -> f Symmetric -> (forall neg zero pos. (C neg, C zero, C pos) => f (Hermitian neg zero pos)) -> f Symmetric
Subtractive Symmetric Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array.Private
Additive Symmetric Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array.Private
Scale Symmetric Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array.Private
Homogeneous Symmetric Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array.Private
Diagonal Symmetric Source #
Instance details Defined in Numeric.LAPACK.Matrix.Quadratic Methods diagonalAux :: (Quadratic pack Symmetric lower upper, C sh, Floating a) => Quadratic pack Symmetric lower upper sh -> Vector sh a -> Quadratic pack Symmetric lower upper sh a
LiftReal Symmetric Source #
Instance details Defined in Numeric.LAPACK.Matrix.Function Methods liftReal :: (Packing pack, PowerStrip lower, PowerStrip upper, C sh, Real a) => (a -> a) -> Quadratic pack Symmetric lower upper sh a -> Quadratic pack Symmetric lower upper sh a Source #
Log Symmetric Source #
Instance details Defined in Numeric.LAPACK.Matrix.Function Methods log :: (Packing pack, PowerStrip lower, PowerStrip upper, C sh, Real a) => Quadratic pack Symmetric lower upper sh a -> Quadratic pack Symmetric lower upper sh a Source #
Exp Symmetric Source #
Instance details Defined in Numeric.LAPACK.Matrix.Function Methods exp :: (Packing pack, PowerStrip lower, PowerStrip upper, C sh, Floating a) => Quadratic pack Symmetric lower upper sh a -> Quadratic pack Symmetric lower upper sh a Source #
SqRt Symmetric Source #
Instance details Defined in Numeric.LAPACK.Matrix.Function Methods sqrt :: (Packing pack, PowerStrip lower, PowerStrip upper, C sh, Real a) => Quadratic pack Symmetric lower upper sh a -> Quadratic pack Symmetric lower upper sh a Source #
Quadratic Packed Symmetric Filled Filled Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods quadratic :: C sh => Order -> sh -> Omni Packed Symmetric Filled Filled Shape Small Small sh sh Source #
(Shape ~ meas, Small ~ vert, Small ~ horiz) => Cons Packed Symmetric Filled Filled meas vert horiz Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods cons :: (C height, C width, MeasureTarget meas height ~ MeasureTarget meas width) => Order -> Dimension meas height width -> Omni Packed Symmetric Filled Filled meas vert horiz height width Source #
(Packing pack, height ~ width) => ToPlain pack Symmetric Filled Filled Shape Small Small height width Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods toPlain :: Omni pack Symmetric Filled Filled Shape Small Small height width -> Plain pack Symmetric Filled Filled Shape Small Small height width Source #
(Packing pack, height ~ width) => FromPlain pack Symmetric Filled Filled Shape Small Small height width Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Associated Types type Plain pack Symmetric Filled Filled Shape Small Small height width :: Type Source # Methods fromPlain :: Plain pack Symmetric Filled Filled Shape Small Small height width -> Omni pack Symmetric Filled Filled Shape Small Small height width Source #
type MultipliedProperty Symmetric propB Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type MultipliedProperty Symmetric propB = Arbitrary
type MultipliedProperty Unit Symmetric Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type MultipliedProperty Unit Symmetric = Arbitrary
type Plain pack Symmetric Filled Filled Shape Small Small height width Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type Plain pack Symmetric Filled Filled Shape Small Small height width = SymmetricP pack height

data Hermitian neg zero pos Source #

Instances

(C neg, C zero, C pos) => Quadratic Packed (Hermitian neg zero pos) Filled Filled Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods quadratic :: C sh => Order -> sh -> Omni Packed (Hermitian neg zero pos) Filled Filled Shape Small Small sh sh Source #
(C neg, C zero, C pos, Shape ~ meas, Small ~ vert, Small ~ horiz) => Cons Packed (Hermitian neg zero pos) Filled Filled meas vert horiz Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods cons :: (C height, C width, MeasureTarget meas height ~ MeasureTarget meas width) => Order -> Dimension meas height width -> Omni Packed (Hermitian neg zero pos) Filled Filled meas vert horiz height width Source #
(Packing pack, C neg, C zero, C pos, height ~ width) => ToPlain pack (Hermitian neg zero pos) Filled Filled Shape Small Small height width Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods toPlain :: Omni pack (Hermitian neg zero pos) Filled Filled Shape Small Small height width -> Plain pack (Hermitian neg zero pos) Filled Filled Shape Small Small height width Source #
(Packing pack, C neg, C zero, C pos, height ~ width) => FromPlain pack (Hermitian neg zero pos) Filled Filled Shape Small Small height width Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Associated Types type Plain pack (Hermitian neg zero pos) Filled Filled Shape Small Small height width :: Type Source # Methods fromPlain :: Plain pack (Hermitian neg zero pos) Filled Filled Shape Small Small height width -> Omni pack (Hermitian neg zero pos) Filled Filled Shape Small Small height width Source #
(C neg, C zero, C pos, sub ~ super, Natural super) => Quadratic Packed (Hermitian neg zero pos) (Bands sub) (Bands super) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods quadratic :: C sh => Order -> sh -> Omni Packed (Hermitian neg zero pos) (Bands sub) (Bands super) Shape Small Small sh sh Source #
(C neg, C zero, C pos, Natural sub, sub ~ super, Shape ~ meas, Small ~ vert, Small ~ horiz) => Cons Packed (Hermitian neg zero pos) (Bands sub) (Bands super) meas vert horiz Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods cons :: (C height, C width, MeasureTarget meas height ~ MeasureTarget meas width) => Order -> Dimension meas height width -> Omni Packed (Hermitian neg zero pos) (Bands sub) (Bands super) meas vert horiz height width Source #
(Natural sub, sub ~ super, height ~ width, C neg, C zero, C pos) => ToPlain Packed (Hermitian neg zero pos) (Bands sub) (Bands super) Shape Small Small height width Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods toPlain :: Omni Packed (Hermitian neg zero pos) (Bands sub) (Bands super) Shape Small Small height width -> Plain Packed (Hermitian neg zero pos) (Bands sub) (Bands super) Shape Small Small height width Source #
(Natural sub, sub ~ super, height ~ width, C neg, C zero, C pos) => FromPlain Packed (Hermitian neg zero pos) (Bands sub) (Bands super) Shape Small Small height width Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Associated Types type Plain Packed (Hermitian neg zero pos) (Bands sub) (Bands super) Shape Small Small height width :: Type Source # Methods fromPlain :: Plain Packed (Hermitian neg zero pos) (Bands sub) (Bands super) Shape Small Small height width -> Omni Packed (Hermitian neg zero pos) (Bands sub) (Bands super) Shape Small Small height width Source #
(C neg, C zero, C pos) => Property (Hermitian neg zero pos) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods switchProperty :: f Arbitrary -> f Unit -> f Symmetric -> (forall neg0 zero0 pos0. (C neg0, C zero0, C pos0) => f (Hermitian neg0 zero0 pos0)) -> f (Hermitian neg zero pos)
(C neg, C zero, neg ~ pos) => Subtractive (Hermitian neg zero pos) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array.Private
(C neg, C zero, C pos) => Additive (Hermitian neg zero pos) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array.Private
(zero ~ True, neg ~ pos, C pos) => Homogeneous (Hermitian neg zero pos) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array.Private
(neg ~ True, zero ~ True, pos ~ True) => LiftReal (Hermitian neg zero pos) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Function Methods liftReal :: (Packing pack, PowerStrip lower, PowerStrip upper, C sh, Real a) => (a -> a) -> Quadratic pack (Hermitian neg zero pos) lower upper sh a -> Quadratic pack (Hermitian neg zero pos) lower upper sh a Source #
(neg ~ True, zero ~ True, pos ~ True) => Log (Hermitian neg zero pos) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Function Methods log :: (Packing pack, PowerStrip lower, PowerStrip upper, C sh, Real a) => Quadratic pack (Hermitian neg zero pos) lower upper sh a -> Quadratic pack (Hermitian neg zero pos) lower upper sh a Source #
(neg ~ True, zero ~ True, pos ~ True) => Exp (Hermitian neg zero pos) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Function Methods exp :: (Packing pack, PowerStrip lower, PowerStrip upper, C sh, Floating a) => Quadratic pack (Hermitian neg zero pos) lower upper sh a -> Quadratic pack (Hermitian neg zero pos) lower upper sh a Source #
(neg ~ False, C zero, C pos) => SqRt (Hermitian neg zero pos) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Function Methods sqrt :: (Packing pack, PowerStrip lower, PowerStrip upper, C sh, Real a) => Quadratic pack (Hermitian neg zero pos) lower upper sh a -> Quadratic pack (Hermitian neg zero pos) lower upper sh a Source #
type MultipliedProperty Unit (Hermitian neg zero pos) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type MultipliedProperty Unit (Hermitian neg zero pos) = Arbitrary
type Plain pack (Hermitian neg zero pos) Filled Filled Shape Small Small height width Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type Plain pack (Hermitian neg zero pos) Filled Filled Shape Small Small height width = HermitianP pack height
type Plain Packed (Hermitian neg zero pos) (Bands sub) (Bands super) Shape Small Small height width Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type Plain Packed (Hermitian neg zero pos) (Bands sub) (Bands super) Shape Small Small height width = BandedHermitian sub height
type MultipliedProperty (Hermitian neg zero pos) propB Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type MultipliedProperty (Hermitian neg zero pos) propB = Arbitrary

type HermitianUnknownDefiniteness = Hermitian True True True Source #

type HermitianPositiveDefinite = Hermitian False False True Source #

type HermitianPositiveSemidefinite = Hermitian False True True Source #

type HermitianNegativeDefinite = Hermitian True False False Source #

type HermitianNegativeSemidefinite = Hermitian True True False Source #

hermitianSet :: (C neg, C zero, C pos) => Omni pack (Hermitian neg zero pos) lower upper meas vert horiz height width -> (Singleton neg, Singleton zero, Singleton pos) Source #

class Property diag => TriDiag diag where Source #

Methods

switchTriDiag :: f Unit -> f Arbitrary -> f diag Source #

Instances

TriDiag Arbitrary Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods switchTriDiag :: f Unit -> f Arbitrary -> f Arbitrary Source #
TriDiag Unit Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods switchTriDiag :: f Unit -> f Arbitrary -> f Unit Source #

data DiagSingleton diag where Source #

Constructors

Unit :: DiagSingleton Unit
Arbitrary :: DiagSingleton Arbitrary

Instances

Eq (DiagSingleton diag) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods (==) :: DiagSingleton diag -> DiagSingleton diag -> Bool # (/=) :: DiagSingleton diag -> DiagSingleton diag -> Bool #
Show (DiagSingleton diag) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods showsPrec :: Int -> DiagSingleton diag -> ShowS # show :: DiagSingleton diag -> String # showList :: [DiagSingleton diag] -> ShowS #
NFData (DiagSingleton diag) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods rnf :: DiagSingleton diag -> () #

autoDiag :: TriDiag diag => DiagSingleton diag Source #

charFromTriDiag :: TriDiag diag => DiagSingleton diag -> Char Source #

packTag :: Packing pack => Omni pack propery lower upper meas vert horiz height width -> PackingSingleton pack Source #

class Property property Source #

Minimal complete definition

switchProperty

Instances

Property Symmetric Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods switchProperty :: f Arbitrary -> f Unit -> f Symmetric -> (forall neg zero pos. (C neg, C zero, C pos) => f (Hermitian neg zero pos)) -> f Symmetric
Property Arbitrary Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods switchProperty :: f Arbitrary -> f Unit -> f Symmetric -> (forall neg zero pos. (C neg, C zero, C pos) => f (Hermitian neg zero pos)) -> f Arbitrary
Property Unit Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods switchProperty :: f Arbitrary -> f Unit -> f Symmetric -> (forall neg zero pos. (C neg, C zero, C pos) => f (Hermitian neg zero pos)) -> f Unit
(C neg, C zero, C pos) => Property (Hermitian neg zero pos) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods switchProperty :: f Arbitrary -> f Unit -> f Symmetric -> (forall neg0 zero0 pos0. (C neg0, C zero0, C pos0) => f (Hermitian neg0 zero0 pos0)) -> f (Hermitian neg zero pos)

property :: Property property => Omni pack property lower upper meas vert horiz height width -> PropertySingleton property Source #

data PropertySingleton property where Source #

Constructors

PropArbitrary :: PropertySingleton Arbitrary
PropUnit :: PropertySingleton Unit
PropSymmetric :: PropertySingleton Symmetric
PropHermitian :: (C neg, C zero, C pos) => PropertySingleton (Hermitian neg zero pos)

propertySingleton :: Property property => PropertySingleton property Source #

class (MultipliedBands c Filled ~ Filled, MultipliedBands c Empty ~ c) => Strip c where Source #

Methods

switchStrip :: (forall offDiag. Natural offDiag => f (Bands offDiag)) -> f Filled -> f c Source #

Instances

Strip Filled Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods switchStrip :: (forall offDiag. Natural offDiag => f (Bands offDiag)) -> f Filled -> f Filled Source #
Natural offDiag => Strip (Bands offDiag) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods switchStrip :: (forall offDiag0. Natural offDiag0 => f (Bands offDiag0)) -> f Filled -> f (Bands offDiag) Source #

strips :: (Strip lower, Strip upper) => Omni pack property lower upper meas vert horiz height width -> (StripSingleton lower, StripSingleton upper) Source #

data StripSingleton c where Source #

Constructors

StripBands :: Natural offDiag => HeadSingleton offDiag -> StripSingleton (Bands offDiag)
StripFilled :: StripSingleton Filled

stripSingleton :: Strip c => StripSingleton c Source #

class Strip c => PowerStrip c where Source #

PowerStrip is either PowerStripSingleton or PowerStripSingleton. These are the Strips that are preserved in matrix powers.

Pun intended.

Methods

switchPowerStrip :: f Empty -> f Filled -> f c Source #

Instances

PowerStrip Filled Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods switchPowerStrip :: f Empty -> f Filled -> f Filled Source #
offDiag ~ U0 => PowerStrip (Bands offDiag) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods switchPowerStrip :: f Empty -> f Filled -> f (Bands offDiag) Source #

data PowerStripSingleton c where Source #

Constructors

Empty :: PowerStripSingleton Empty
Filled :: PowerStripSingleton Filled

powerStripSingleton :: PowerStrip c => PowerStripSingleton c Source #

powerStrips :: (PowerStrip lower, PowerStrip upper) => Omni pack property lower upper meas vert horiz height width -> (PowerStripSingleton lower, PowerStripSingleton upper) Source #

class (Natural sub, Natural super) => BandedTriangular sub super Source #

Minimal complete definition

switchBandedTriangular

Instances

BandedTriangular Zero Zero Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods switchBandedTriangular :: f Zero Zero -> (forall offDiag. Natural offDiag => f Zero (Succ offDiag)) -> (forall offDiag. Natural offDiag => f (Succ offDiag) Zero) -> f Zero Zero
Natural super => BandedTriangular Zero (Succ super) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods switchBandedTriangular :: f Zero Zero -> (forall offDiag. Natural offDiag => f Zero (Succ offDiag)) -> (forall offDiag. Natural offDiag => f (Succ offDiag) Zero) -> f Zero (Succ super)
Natural sub => BandedTriangular (Succ sub) Zero Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods switchBandedTriangular :: f Zero Zero -> (forall offDiag. Natural offDiag => f Zero (Succ offDiag)) -> (forall offDiag. Natural offDiag => f (Succ offDiag) Zero) -> f (Succ sub) Zero

data BandedTriangularSingleton sub super where Source #

Constructors

BandedDiagonal :: BandedTriangularSingleton Zero Zero
BandedUpper :: Natural offDiag => BandedTriangularSingleton Zero (Succ offDiag)
BandedLower :: Natural offDiag => BandedTriangularSingleton (Succ offDiag) Zero

bandedTriangularSingleton :: BandedTriangular sub super => Banded sub super meas vert horiz height width -> BandedTriangularSingleton sub super Source #

extent :: (Measure meas, C vert, C horiz) => Omni pack property lower upper meas vert horiz height width -> Extent meas vert horiz height width Source #

height :: (Measure meas, C vert, C horiz) => Omni pack property lower upper meas vert horiz height width -> height Source #

width :: (Measure meas, C vert, C horiz) => Omni pack property lower upper meas vert horiz height width -> width Source #

squareSize :: Omni pack property lower upper Shape Small Small sh sh -> sh Source #

mapHeight :: (C heightA, C heightB, C vert, C horiz) => (heightA -> heightB) -> Omni pack property lower upper Size vert horiz heightA width -> Omni pack property lower upper Size vert horiz heightB width Source #

mapWidth :: (C widthA, C widthB, C vert, C horiz) => (widthA -> widthB) -> Omni pack property lower upper Size vert horiz height widthA -> Omni pack property lower upper Size vert horiz height widthB Source #

mapSquareSize :: (C shA, C shB) => (shA -> shB) -> Omni pack property lower upper Shape Small Small shA shA -> Omni pack property lower upper Shape Small Small shB shB Source #

order :: Omni pack property lower upper meas vert horiz height width -> Order Source #

transpose :: (Measure meas, C vert, C horiz) => Omni pack property lower upper meas vert horiz height width -> Omni pack property upper lower meas horiz vert width height Source #

class (Property property, Strip lower, Strip upper, Measured meas vert, Measured meas horiz) => Cons pack property lower upper meas vert horiz where Source #

Construct a shape from order, dimensions and type information.

Methods

cons :: (C height, C width) => MeasureTarget meas height ~ MeasureTarget meas width => Order -> Dimension meas height width -> Omni pack property lower upper meas vert horiz height width Source #

Instances

(Strip lower, Strip upper, Measured meas vert, Measured meas horiz) => Cons Unpacked Arbitrary lower upper meas vert horiz Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods cons :: (C height, C width, MeasureTarget meas height ~ MeasureTarget meas width) => Order -> Dimension meas height width -> Omni Unpacked Arbitrary lower upper meas vert horiz height width Source #
(TriDiag diag, Shape ~ meas, Small ~ vert, Small ~ horiz) => Cons Packed diag Filled Empty meas vert horiz Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods cons :: (C height, C width, MeasureTarget meas height ~ MeasureTarget meas width) => Order -> Dimension meas height width -> Omni Packed diag Filled Empty meas vert horiz height width Source #
(TriDiag diag, Shape ~ meas, Small ~ vert, Small ~ horiz) => Cons Packed diag Empty Filled meas vert horiz Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods cons :: (C height, C width, MeasureTarget meas height ~ MeasureTarget meas width) => Order -> Dimension meas height width -> Omni Packed diag Empty Filled meas vert horiz height width Source #
(Shape ~ meas, Small ~ vert, Small ~ horiz) => Cons Packed Symmetric Filled Filled meas vert horiz Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods cons :: (C height, C width, MeasureTarget meas height ~ MeasureTarget meas width) => Order -> Dimension meas height width -> Omni Packed Symmetric Filled Filled meas vert horiz height width Source #
(Measured meas vert, Measured meas horiz, Natural sub, Natural super) => Cons Packed Arbitrary (Bands sub) (Bands super) meas vert horiz Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods cons :: (C height, C width, MeasureTarget meas height ~ MeasureTarget meas width) => Order -> Dimension meas height width -> Omni Packed Arbitrary (Bands sub) (Bands super) meas vert horiz height width Source #
(BandedTriangular sub super, BandedTriangular super sub, Shape ~ meas, Small ~ vert, Small ~ horiz) => Cons Packed Unit (Bands sub) (Bands super) meas vert horiz Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods cons :: (C height, C width, MeasureTarget meas height ~ MeasureTarget meas width) => Order -> Dimension meas height width -> Omni Packed Unit (Bands sub) (Bands super) meas vert horiz height width Source #
(C neg, C zero, C pos, Shape ~ meas, Small ~ vert, Small ~ horiz) => Cons Packed (Hermitian neg zero pos) Filled Filled meas vert horiz Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods cons :: (C height, C width, MeasureTarget meas height ~ MeasureTarget meas width) => Order -> Dimension meas height width -> Omni Packed (Hermitian neg zero pos) Filled Filled meas vert horiz height width Source #
(C neg, C zero, C pos, Natural sub, sub ~ super, Shape ~ meas, Small ~ vert, Small ~ horiz) => Cons Packed (Hermitian neg zero pos) (Bands sub) (Bands super) meas vert horiz Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods cons :: (C height, C width, MeasureTarget meas height ~ MeasureTarget meas width) => Order -> Dimension meas height width -> Omni Packed (Hermitian neg zero pos) (Bands sub) (Bands super) meas vert horiz height width Source #

type family Plain pack property lower upper meas vert horiz height width Source #

Instances

type Plain pack Symmetric Filled Filled Shape Small Small height width Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type Plain pack Symmetric Filled Filled Shape Small Small height width = SymmetricP pack height
type Plain pack diag Filled Empty Shape Small Small height width Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type Plain pack diag Filled Empty Shape Small Small height width = LowerTriangularP pack height
type Plain pack diag Empty Filled Shape Small Small height width Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type Plain pack diag Empty Filled Shape Small Small height width = UpperTriangularP pack height
type Plain Unpacked Arbitrary Filled Filled meas vert horiz height width Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type Plain Unpacked Arbitrary Filled Filled meas vert horiz height width = Full meas vert horiz height width
type Plain Packed Arbitrary (Bands sub) (Bands super) meas vert horiz height width Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type Plain Packed Arbitrary (Bands sub) (Bands super) meas vert horiz height width = Banded sub super meas vert horiz height width
type Plain Packed Unit (Bands sub) (Bands super) Shape Small Small height width Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type Plain Packed Unit (Bands sub) (Bands super) Shape Small Small height width = BandedSquare sub super height
type Plain pack (Hermitian neg zero pos) Filled Filled Shape Small Small height width Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type Plain pack (Hermitian neg zero pos) Filled Filled Shape Small Small height width = HermitianP pack height
type Plain Packed (Hermitian neg zero pos) (Bands sub) (Bands super) Shape Small Small height width Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type Plain Packed (Hermitian neg zero pos) (Bands sub) (Bands super) Shape Small Small height width = BandedHermitian sub height

class FromPlain pack property lower upper meas vert horiz height width => ToPlain pack property lower upper meas vert horiz height width Source #

Minimal complete definition

toPlain

Instances

(Packing pack, height ~ width) => ToPlain pack Symmetric Filled Filled Shape Small Small height width Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods toPlain :: Omni pack Symmetric Filled Filled Shape Small Small height width -> Plain pack Symmetric Filled Filled Shape Small Small height width Source #
(Packing pack, TriDiag diag, height ~ width) => ToPlain pack diag Filled Empty Shape Small Small height width Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods toPlain :: Omni pack diag Filled Empty Shape Small Small height width -> Plain pack diag Filled Empty Shape Small Small height width Source #
(Packing pack, TriDiag diag, height ~ width) => ToPlain pack diag Empty Filled Shape Small Small height width Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods toPlain :: Omni pack diag Empty Filled Shape Small Small height width -> Plain pack diag Empty Filled Shape Small Small height width Source #
ToPlain Unpacked Arbitrary Filled Filled meas vert horiz height width Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods toPlain :: Omni Unpacked Arbitrary Filled Filled meas vert horiz height width -> Plain Unpacked Arbitrary Filled Filled meas vert horiz height width Source #
(Natural sub, Natural super) => ToPlain Packed Arbitrary (Bands sub) (Bands super) meas vert horiz height width Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods toPlain :: Omni Packed Arbitrary (Bands sub) (Bands super) meas vert horiz height width -> Plain Packed Arbitrary (Bands sub) (Bands super) meas vert horiz height width Source #
(BandedTriangular sub super, BandedTriangular super sub, height ~ width) => ToPlain Packed Unit (Bands sub) (Bands super) Shape Small Small height width Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods toPlain :: Omni Packed Unit (Bands sub) (Bands super) Shape Small Small height width -> Plain Packed Unit (Bands sub) (Bands super) Shape Small Small height width Source #
(Packing pack, C neg, C zero, C pos, height ~ width) => ToPlain pack (Hermitian neg zero pos) Filled Filled Shape Small Small height width Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods toPlain :: Omni pack (Hermitian neg zero pos) Filled Filled Shape Small Small height width -> Plain pack (Hermitian neg zero pos) Filled Filled Shape Small Small height width Source #
(Natural sub, sub ~ super, height ~ width, C neg, C zero, C pos) => ToPlain Packed (Hermitian neg zero pos) (Bands sub) (Bands super) Shape Small Small height width Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods toPlain :: Omni Packed (Hermitian neg zero pos) (Bands sub) (Bands super) Shape Small Small height width -> Plain Packed (Hermitian neg zero pos) (Bands sub) (Bands super) Shape Small Small height width Source #

toPlain :: ToPlain pack property lower upper meas vert horiz height width => Omni pack property lower upper meas vert horiz height width -> Plain pack property lower upper meas vert horiz height width Source #

class FromPlain pack property lower upper meas vert horiz height width Source #

Minimal complete definition

fromPlain

Instances

(Packing pack, height ~ width) => FromPlain pack Symmetric Filled Filled Shape Small Small height width Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Associated Types type Plain pack Symmetric Filled Filled Shape Small Small height width :: Type Source # Methods fromPlain :: Plain pack Symmetric Filled Filled Shape Small Small height width -> Omni pack Symmetric Filled Filled Shape Small Small height width Source #
(Packing pack, TriDiag diag, height ~ width) => FromPlain pack diag Filled Empty Shape Small Small height width Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Associated Types type Plain pack diag Filled Empty Shape Small Small height width :: Type Source # Methods fromPlain :: Plain pack diag Filled Empty Shape Small Small height width -> Omni pack diag Filled Empty Shape Small Small height width Source #
(Packing pack, TriDiag diag, height ~ width) => FromPlain pack diag Empty Filled Shape Small Small height width Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Associated Types type Plain pack diag Empty Filled Shape Small Small height width :: Type Source # Methods fromPlain :: Plain pack diag Empty Filled Shape Small Small height width -> Omni pack diag Empty Filled Shape Small Small height width Source #
FromPlain Unpacked Arbitrary Filled Filled meas vert horiz height width Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Associated Types type Plain Unpacked Arbitrary Filled Filled meas vert horiz height width :: Type Source # Methods fromPlain :: Plain Unpacked Arbitrary Filled Filled meas vert horiz height width -> Omni Unpacked Arbitrary Filled Filled meas vert horiz height width Source #
(Natural sub, Natural super) => FromPlain Packed Arbitrary (Bands sub) (Bands super) meas vert horiz height width Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Associated Types type Plain Packed Arbitrary (Bands sub) (Bands super) meas vert horiz height width :: Type Source # Methods fromPlain :: Plain Packed Arbitrary (Bands sub) (Bands super) meas vert horiz height width -> Omni Packed Arbitrary (Bands sub) (Bands super) meas vert horiz height width Source #
(BandedTriangular sub super, BandedTriangular super sub, height ~ width) => FromPlain Packed Unit (Bands sub) (Bands super) Shape Small Small height width Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Associated Types type Plain Packed Unit (Bands sub) (Bands super) Shape Small Small height width :: Type Source # Methods fromPlain :: Plain Packed Unit (Bands sub) (Bands super) Shape Small Small height width -> Omni Packed Unit (Bands sub) (Bands super) Shape Small Small height width Source #
(Packing pack, C neg, C zero, C pos, height ~ width) => FromPlain pack (Hermitian neg zero pos) Filled Filled Shape Small Small height width Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Associated Types type Plain pack (Hermitian neg zero pos) Filled Filled Shape Small Small height width :: Type Source # Methods fromPlain :: Plain pack (Hermitian neg zero pos) Filled Filled Shape Small Small height width -> Omni pack (Hermitian neg zero pos) Filled Filled Shape Small Small height width Source #
(Natural sub, sub ~ super, height ~ width, C neg, C zero, C pos) => FromPlain Packed (Hermitian neg zero pos) (Bands sub) (Bands super) Shape Small Small height width Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Associated Types type Plain Packed (Hermitian neg zero pos) (Bands sub) (Bands super) Shape Small Small height width :: Type Source # Methods fromPlain :: Plain Packed (Hermitian neg zero pos) (Bands sub) (Bands super) Shape Small Small height width -> Omni Packed (Hermitian neg zero pos) (Bands sub) (Bands super) Shape Small Small height width Source #

fromPlain :: FromPlain pack property lower upper meas vert horiz height width => Plain pack property lower upper meas vert horiz height width -> Omni pack property lower upper meas vert horiz height width Source #

toFull :: (Property property, Strip lower, Strip upper) => Omni Unpacked property lower upper meas vert horiz height width -> Full meas vert horiz height width Source #

fromFull :: (Property property, Strip lower, Strip upper) => Full meas vert horiz height width -> Omni Unpacked property lower upper meas vert horiz height width Source #

toBanded :: (Natural sub, Natural super) => Omni Packed Arbitrary (Bands sub) (Bands super) meas vert horiz height width -> Banded sub super meas vert horiz height width Source #

toBandedHermitian :: (C neg, C zero, C pos, Natural offDiag) => Omni Packed (Hermitian neg zero pos) (Bands offDiag) (Bands offDiag) Shape Small Small size size -> BandedHermitian offDiag size Source #

type family MultipliedBands bandsA bandsB Source #

Instances

type MultipliedBands Filled bandsB Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type MultipliedBands Filled bandsB = Filled
type MultipliedBands (Bands k) Filled Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type MultipliedBands (Bands k) Filled = Filled
type MultipliedBands (Bands k) (Bands l) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type MultipliedBands (Bands k) (Bands l) = Bands (k :+: l)

type family MultipliedStrip contA contB Source #

Instances

type MultipliedStrip Filled contB Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type MultipliedStrip Filled contB = Filled
type MultipliedStrip Empty contB Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type MultipliedStrip Empty contB = contB

type family MultipliedProperty propA propB Source #

Instances

type MultipliedProperty Symmetric propB Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type MultipliedProperty Symmetric propB = Arbitrary
type MultipliedProperty Arbitrary propB Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type MultipliedProperty Arbitrary propB = Arbitrary
type MultipliedProperty Unit Symmetric Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type MultipliedProperty Unit Symmetric = Arbitrary
type MultipliedProperty Unit Arbitrary Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type MultipliedProperty Unit Arbitrary = Arbitrary
type MultipliedProperty Unit Unit Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type MultipliedProperty Unit Unit = Unit
type MultipliedProperty Unit (Hermitian neg zero pos) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type MultipliedProperty Unit (Hermitian neg zero pos) = Arbitrary
type MultipliedProperty (Hermitian neg zero pos) propB Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type MultipliedProperty (Hermitian neg zero pos) propB = Arbitrary

type family UnitIfTriangular lower upper Source #

Instances

type UnitIfTriangular Filled Filled Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type UnitIfTriangular Filled Filled = Arbitrary
type UnitIfTriangular Filled Empty Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type UnitIfTriangular Filled Empty = Unit
type UnitIfTriangular Empty upper Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type UnitIfTriangular Empty upper = Unit
type UnitIfTriangular Filled (Bands (Succ k)) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type UnitIfTriangular Filled (Bands (Succ k)) = Arbitrary
type UnitIfTriangular (Bands (Succ k)) Filled Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type UnitIfTriangular (Bands (Succ k)) Filled = Arbitrary
type UnitIfTriangular (Bands (Succ k)) Empty Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type UnitIfTriangular (Bands (Succ k)) Empty = Unit
type UnitIfTriangular (Bands (Succ k)) (Bands (Succ l)) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type UnitIfTriangular (Bands (Succ k)) (Bands (Succ l)) = Arbitrary

type family MergeUnit unit0 unit1 Source #

Instances

type MergeUnit Arbitrary unit1 Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type MergeUnit Arbitrary unit1 = Arbitrary
type MergeUnit Unit unit1 Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni type MergeUnit Unit unit1 = unit1

class Quadratic pack property lower upper Source #

Minimal complete definition

quadratic

Instances

(Strip lower, Strip upper) => Quadratic Unpacked Arbitrary lower upper Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods quadratic :: C sh => Order -> sh -> Omni Unpacked Arbitrary lower upper Shape Small Small sh sh Source #
TriDiag diag => Quadratic Packed diag Filled Empty Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods quadratic :: C sh => Order -> sh -> Omni Packed diag Filled Empty Shape Small Small sh sh Source #
TriDiag diag => Quadratic Packed diag Empty Filled Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods quadratic :: C sh => Order -> sh -> Omni Packed diag Empty Filled Shape Small Small sh sh Source #
Quadratic Packed Symmetric Filled Filled Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods quadratic :: C sh => Order -> sh -> Omni Packed Symmetric Filled Filled Shape Small Small sh sh Source #
(Natural sub, Natural super) => Quadratic Packed Arbitrary (Bands sub) (Bands super) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods quadratic :: C sh => Order -> sh -> Omni Packed Arbitrary (Bands sub) (Bands super) Shape Small Small sh sh Source #
(BandedTriangular sub super, BandedTriangular super sub) => Quadratic Packed Unit (Bands sub) (Bands super) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods quadratic :: C sh => Order -> sh -> Omni Packed Unit (Bands sub) (Bands super) Shape Small Small sh sh Source #
(C neg, C zero, C pos) => Quadratic Packed (Hermitian neg zero pos) Filled Filled Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods quadratic :: C sh => Order -> sh -> Omni Packed (Hermitian neg zero pos) Filled Filled Shape Small Small sh sh Source #
(C neg, C zero, C pos, sub ~ super, Natural super) => Quadratic Packed (Hermitian neg zero pos) (Bands sub) (Bands super) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Omni Methods quadratic :: C sh => Order -> sh -> Omni Packed (Hermitian neg zero pos) (Bands sub) (Bands super) Shape Small Small sh sh Source #

quadratic :: (Quadratic pack property lower upper, C sh) => Order -> sh -> Omni pack property lower upper Shape Small Small sh sh Source #

uncheckedDiagonal :: (Packing pack, TriDiag diag) => Order -> size -> Omni pack diag Empty Empty Shape Small Small size size Source #

data Power pack property lower upper meas vert horiz height width where Source #

Constructors

PowerIdentity :: Packing pack => PowerQuadratic pack Unit Empty Empty sh
PowerDiagonal :: Packing pack => Power pack property Empty Empty meas vert horiz height width
PowerUpperTriangular :: (Packing pack, TriDiag diag) => PowerQuadratic pack diag Empty Filled sh
PowerLowerTriangular :: (Packing pack, TriDiag diag) => PowerQuadratic pack diag Filled Empty sh
PowerSymmetric :: Packing pack => PowerQuadratic pack Symmetric Filled Filled sh
PowerHermitian :: (Packing pack, C neg, C zero, C pos) => PowerQuadratic pack (Hermitian neg zero pos) Filled Filled sh
PowerFull :: Power Unpacked property lower upper meas vert horiz height width

powerSingleton :: (Packing pack, Property property, PowerStrip lower, PowerStrip upper, Measure meas, C vert, C horiz) => Omni pack property lower upper meas vert horiz height width -> Power pack property lower upper meas vert horiz height width Source #