lapack-0.5: Numerical Linear Algebra using LAPACK

Numeric.LAPACK.Matrix.Shape

Synopsis

# Documentation

For singular values

However, diagonal matrices produced by singular value decomposition may be non-square and Hermitian must be square.

type RealDiagonal size = BandedHermitian U0 size Source #

For Hermitian eigenvalues

type BandedHermitian offDiag size = Quadratic Packed HermitianUnknownDefiniteness (Bands offDiag) (Bands offDiag) size Source #

type BandedUnitUpper super size = BandedUnitTriangular U0 super size Source #

type BandedUnitTriangular sub super size = Quadratic Packed Unit (Bands sub) (Bands super) size Source #

type BandedUpper super size = BandedTriangular U0 super size Source #

type BandedLower sub size = BandedTriangular sub U0 size Source #

type BandedTriangular sub super size = Quadratic Packed Arbitrary (Bands sub) (Bands super) size Source #

type BandedGeneral sub super = Omni Packed Arbitrary (Bands sub) (Bands super) Size Big Big Source #

type Banded sub super meas vert horiz = Omni Packed Arbitrary (Bands sub) (Bands super) meas vert horiz Source #

newtype GenTriangularLoUp diag size a lo up Source #

Constructors

 GenTriangularLoUp FieldsrunGenTriangularLoUp :: Triangular lo diag up size

newtype GenTriangularDiag lo up size a diag Source #

Constructors

 GenTriangularDiag FieldsrunGenTriangularDiag :: Triangular lo diag up size

type Triangular lo diag up size = Quadratic Packed diag lo up size Source #

data UpLoSingleton lo up where Source #

Constructors

 Lower :: UpLoSingleton Filled Empty Upper :: UpLoSingleton Empty Filled

class (PowerStrip lo, PowerStrip up) => DiagUpLoC lo up where Source #

Methods

switchDiagUpLo :: f Empty Empty -> f Empty Filled -> f Filled Empty -> f lo up Source #

#### Instances

Instances details
 Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape MethodsswitchDiagUpLo :: f Empty Empty -> f Empty Filled -> f Filled Empty -> f Filled Empty Source # Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape MethodsswitchDiagUpLo :: f Empty Empty -> f Empty Filled -> f Filled Empty -> f Empty Filled Source # Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape MethodsswitchDiagUpLo :: f Empty Empty -> f Empty Filled -> f Filled Empty -> f Empty Empty Source #

type DiagUpLo lo up = (DiagUpLoC lo up, DiagUpLoC up lo) Source #

class DiagUpLoC lo up => UpLoC lo up where Source #

Methods

switchUpLo :: f Empty Filled -> f Filled Empty -> f lo up Source #

#### Instances

Instances details
 Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape Methods Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape Methods

type UpLo lo up = (UpLoC lo up, UpLoC up lo) Source #

type QuadraticMeas pack property lower upper meas height width = Omni pack property lower upper meas Small Small height width Source #

type Quadratic pack property lower upper size = QuadraticMeas pack property lower upper Shape size size Source #

type Square sh = Full Shape Small Small sh sh Source #

general :: Order -> height -> width -> General height width Source #

tall :: (C height, C width) => Order -> height -> width -> Tall height width Source #

wide :: (C height, C width) => Order -> height -> width -> Wide height width Source #

liberalSquare :: (C height, C width) => Order -> height -> width -> LiberalSquare height width Source #

square :: C sh => Order -> sh -> Square sh Source #

diagonal :: Order -> size -> Diagonal size Source #

identity :: Order -> size -> Identity size Source #

autoUplo :: UpLo lo up => UpLoSingleton lo up Source #

triangular :: (DiagUpLo lo up, TriDiag diag) => Order -> size -> Triangular lo diag up size Source #

unitTriangular :: DiagUpLo lo up => Order -> size -> Triangular lo Unit up size Source #

arbitraryTriangular :: DiagUpLo lo up => Order -> size -> Triangular lo Arbitrary up size Source #

symmetric :: Order -> size -> Symmetric size Source #

bandedOffDiagonals :: Omni Packed property (Bands sub) (Bands super) meas vert horiz height width -> (UnaryProxy sub, UnaryProxy super) Source #

bandedGeneral :: (Natural sub, Natural super, C height, C width) => (UnaryProxy sub, UnaryProxy super) -> Order -> height -> width -> BandedGeneral sub super height width Source #

bandedHermitian :: Natural offDiag => UnaryProxy offDiag -> Order -> size -> BandedHermitian offDiag size Source #

data Order Source #

Constructors

 RowMajor ColumnMajor

#### Instances

Instances details
 Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Layout.Private Methods(==) :: Order -> Order -> Bool #(/=) :: Order -> Order -> Bool # Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Layout.Private MethodsshowsPrec :: Int -> Order -> ShowS #show :: Order -> String #showList :: [Order] -> ShowS # Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Layout.Private Methodsrnf :: Order -> () #

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 #

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

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

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

class Property diag => TriDiag diag Source #

Minimal complete definition

switchTriDiag

#### Instances

Instances details
 Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni MethodsswitchTriDiag :: f Unit -> f Arbitrary -> f Arbitrary Source # Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni MethodsswitchTriDiag :: f Unit -> f Arbitrary -> f Unit Source #

data DiagSingleton diag where Source #

Constructors

 Unit :: DiagSingleton Unit Arbitrary :: DiagSingleton Arbitrary

#### Instances

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

class Property property Source #

Minimal complete definition

switchProperty

#### Instances

Instances details
 Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni MethodsswitchProperty :: f Arbitrary -> f Unit -> f Symmetric -> (forall neg zero pos. (C neg, C zero, C pos) => f (Hermitian neg zero pos)) -> f Symmetric Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni MethodsswitchProperty :: f Arbitrary -> f Unit -> f Symmetric -> (forall neg zero pos. (C neg, C zero, C pos) => f (Hermitian neg zero pos)) -> f Arbitrary Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni MethodsswitchProperty :: 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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni MethodsswitchProperty :: 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)

class Strip c => PowerStrip c Source #

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

Pun intended.

Minimal complete definition

switchPowerStrip

#### Instances

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

data PowerStripSingleton c where Source #

Constructors

 Empty :: PowerStripSingleton Empty Filled :: PowerStripSingleton Filled

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

Minimal complete definition

switchStrip

#### Instances

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

data StripSingleton c where Source #

Constructors

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

data Arbitrary Source #

#### Instances

Instances details
 Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni MethodsswitchProperty :: f Arbitrary -> f Unit -> f Symmetric -> (forall neg zero pos. (C neg, C zero, C pos) => f (Hermitian neg zero pos)) -> f Arbitrary Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni MethodsswitchTriDiag :: f Unit -> f Arbitrary -> f Arbitrary Source # Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Array.Private Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Array.Private Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Array.Private Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Array.Private Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Quadratic MethodsdiagonalAux :: (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 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 detailsDefined in Numeric.LAPACK.Matrix.Function MethodsliftReal :: (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 # Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Function Methodslog :: (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 # Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Function Methodsexp :: (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 # Source # For Full matrices: Explicit solution for matrices up to size 2. Solution via sqrtDenmanBeavers for larger sizes. Instance detailsDefined in Numeric.LAPACK.Matrix.Function Methodssqrt :: (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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni Methodsquadratic :: 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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni Methodscons :: (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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni MethodstoPlain :: 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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni Associated Typestype Plain Unpacked Arbitrary Filled Filled meas vert horiz height width Source # MethodsfromPlain :: 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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni Methodsquadratic :: 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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni Methodscons :: (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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni MethodstoPlain :: 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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni Associated Typestype Plain Packed Arbitrary (Bands sub) (Bands super) meas vert horiz height width Source # MethodsfromPlain :: 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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni type MergeUnit Arbitrary unit1 = Arbitrary type MultipliedProperty Arbitrary propB Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni type MultipliedProperty Arbitrary propB = Arbitrary Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni type Plain Unpacked Arbitrary Filled Filled meas vert horiz height width Source # Instance detailsDefined 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 detailsDefined 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 Unit Source #

#### Instances

Instances details
 Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni MethodsswitchProperty :: f Arbitrary -> f Unit -> f Symmetric -> (forall neg zero pos. (C neg, C zero, C pos) => f (Hermitian neg zero pos)) -> f Unit Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni MethodsswitchTriDiag :: f Unit -> f Arbitrary -> f Unit Source # Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Function Methodssqrt :: (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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni Methodsquadratic :: 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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni Methodscons :: (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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni MethodstoPlain :: 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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni Associated Typestype Plain Packed Unit (Bands sub) (Bands super) Shape Small Small height width Source # MethodsfromPlain :: 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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni type MergeUnit Unit unit1 = unit1 Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni type Plain Packed Unit (Bands sub) (Bands super) Shape Small Small height width Source # Instance detailsDefined 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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni type MultipliedProperty Unit (Hermitian neg zero pos) = Arbitrary

data Filled Source #

#### Instances

Instances details
 Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Layout.Private Methods(==) :: Filled -> Filled -> Bool #(/=) :: Filled -> Filled -> Bool # Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Layout.Private MethodsshowsPrec :: Int -> Filled -> ShowS #showList :: [Filled] -> ShowS # Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni MethodsswitchPowerStrip :: f Empty -> f Filled -> f Filled Source # Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni MethodsswitchStrip :: (forall offDiag. Natural offDiag => f (Bands offDiag)) -> f Filled -> f Filled Source # Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape MethodsswitchDiagUpLo :: f Empty Empty -> f Empty Filled -> f Filled Empty -> f Filled Empty Source # Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape MethodsswitchDiagUpLo :: f Empty Empty -> f Empty Filled -> f Filled Empty -> f Empty Filled Source # Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape Methods Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape Methods TriDiag diag => Quadratic Packed diag Filled Empty Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni Methodsquadratic :: C sh => Order -> sh -> Omni Packed diag Filled Empty Shape Small Small sh sh Source # TriDiag diag => Quadratic Packed diag Empty Filled Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni Methodsquadratic :: C sh => Order -> sh -> Omni Packed diag Empty Filled Shape Small Small sh sh Source # Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni Methodsquadratic :: C sh => Order -> sh -> Omni Packed Symmetric Filled Filled Shape Small Small sh sh Source # (TriDiag diag, Shape ~ meas, Small ~ vert, Small ~ horiz) => Cons Packed diag Filled Empty meas vert horiz Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni Methodscons :: (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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni Methodscons :: (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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni Methodscons :: (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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni MethodstoPlain :: 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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni MethodstoPlain :: 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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni MethodstoPlain :: 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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni MethodstoPlain :: Omni Unpacked Arbitrary Filled Filled meas vert horiz height width -> Plain Unpacked Arbitrary Filled Filled meas vert horiz height width Source # (Packing pack, height ~ width) => FromPlain pack Symmetric Filled Filled Shape Small Small height width Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni Associated Typestype Plain pack Symmetric Filled Filled Shape Small Small height width Source # MethodsfromPlain :: 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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni Associated Typestype Plain pack diag Filled Empty Shape Small Small height width Source # MethodsfromPlain :: 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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni Associated Typestype Plain pack diag Empty Filled Shape Small Small height width Source # MethodsfromPlain :: 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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni Associated Typestype Plain Unpacked Arbitrary Filled Filled meas vert horiz height width Source # MethodsfromPlain :: Plain Unpacked Arbitrary Filled Filled meas vert horiz height width -> Omni Unpacked Arbitrary Filled Filled meas vert horiz height width Source # (C neg, C zero, C pos) => Quadratic Packed (Hermitian neg zero pos) Filled Filled Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni Methodsquadratic :: 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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni Methodscons :: (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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni MethodstoPlain :: 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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni Associated Typestype Plain pack (Hermitian neg zero pos) Filled Filled Shape Small Small height width Source # MethodsfromPlain :: 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 # Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni type MultipliedStrip Filled contB Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni type MultipliedStrip Filled contB = Filled type MultipliedBands Filled bandsB Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni type MultipliedBands Filled bandsB = Filled type Plain pack Symmetric Filled Filled Shape Small Small height width Source # Instance detailsDefined 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 detailsDefined 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 detailsDefined 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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni type Plain Unpacked Arbitrary Filled Filled meas vert horiz height width = Full meas vert horiz height width type UnitIfTriangular Filled (Bands (Succ k)) Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni type UnitIfTriangular Filled (Bands (Succ k)) = Arbitrary type Plain pack (Hermitian neg zero pos) Filled Filled Shape Small Small height width Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni type Plain pack (Hermitian neg zero pos) Filled Filled Shape Small Small height width = HermitianP pack height type UnitIfTriangular (Bands (Succ k)) Filled Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni type UnitIfTriangular (Bands (Succ k)) Filled = Arbitrary type MultipliedBands (Bands k) Filled Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni type MultipliedBands (Bands k) Filled = Filled

data Bands offDiag Source #

#### Instances

Instances details
 Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape MethodsswitchDiagUpLo :: f Empty Empty -> f Empty Filled -> f Filled Empty -> f Filled Empty Source # Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape MethodsswitchDiagUpLo :: f Empty Empty -> f Empty Filled -> f Filled Empty -> f Empty Filled Source # Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape MethodsswitchDiagUpLo :: f Empty Empty -> f Empty Filled -> f Filled Empty -> f Empty Empty Source # Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape Methods Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape Methods TriDiag diag => Quadratic Packed diag Filled Empty Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni Methodsquadratic :: C sh => Order -> sh -> Omni Packed diag Filled Empty Shape Small Small sh sh Source # TriDiag diag => Quadratic Packed diag Empty Filled Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni Methodsquadratic :: C sh => Order -> sh -> Omni Packed diag Empty Filled Shape Small Small sh sh Source # (TriDiag diag, Shape ~ meas, Small ~ vert, Small ~ horiz) => Cons Packed diag Filled Empty meas vert horiz Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni Methodscons :: (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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni Methodscons :: (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 # (Packing pack, TriDiag diag, height ~ width) => ToPlain pack diag Filled Empty Shape Small Small height width Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni MethodstoPlain :: 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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni MethodstoPlain :: Omni pack diag Empty Filled Shape Small Small height width -> Plain pack diag Empty 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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni Associated Typestype Plain pack diag Filled Empty Shape Small Small height width Source # MethodsfromPlain :: 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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni Associated Typestype Plain pack diag Empty Filled Shape Small Small height width Source # MethodsfromPlain :: Plain pack diag Empty Filled Shape Small Small height width -> Omni pack diag Empty Filled Shape Small Small height width Source # (Natural sub, Natural super) => Quadratic Packed Arbitrary (Bands sub) (Bands super) Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni Methodsquadratic :: 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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni Methodsquadratic :: C sh => Order -> sh -> Omni Packed Unit (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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni Methodscons :: (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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni Methodscons :: (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 # (Natural sub, Natural super) => ToPlain Packed Arbitrary (Bands sub) (Bands super) meas vert horiz height width Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni MethodstoPlain :: 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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni MethodstoPlain :: 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 # (Natural sub, Natural super) => FromPlain Packed Arbitrary (Bands sub) (Bands super) meas vert horiz height width Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni Associated Typestype Plain Packed Arbitrary (Bands sub) (Bands super) meas vert horiz height width Source # MethodsfromPlain :: 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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni Associated Typestype Plain Packed Unit (Bands sub) (Bands super) Shape Small Small height width Source # MethodsfromPlain :: 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 # (C neg, C zero, C pos, sub ~ super, Natural super) => Quadratic Packed (Hermitian neg zero pos) (Bands sub) (Bands super) Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni Methodsquadratic :: 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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni Methodscons :: (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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni MethodstoPlain :: 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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni Associated Typestype Plain Packed (Hermitian neg zero pos) (Bands sub) (Bands super) Shape Small Small height width Source # MethodsfromPlain :: 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 # Eq (Bands offDiag) Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Layout.Private Methods(==) :: Bands offDiag -> Bands offDiag -> Bool #(/=) :: Bands offDiag -> Bands offDiag -> Bool # Natural offDiag => Show (Bands offDiag) Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Layout.Private MethodsshowsPrec :: Int -> Bands offDiag -> ShowS #show :: Bands offDiag -> String #showList :: [Bands offDiag] -> ShowS # offDiag ~ U0 => PowerStrip (Bands offDiag) Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni MethodsswitchPowerStrip :: f Empty -> f Filled -> f (Bands offDiag) Source # Natural offDiag => Strip (Bands offDiag) Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni MethodsswitchStrip :: (forall offDiag0. Natural offDiag0 => f (Bands offDiag0)) -> f Filled -> f (Bands offDiag) Source # Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni type UnitIfTriangular Empty upper Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni type UnitIfTriangular Empty upper = Unit type MultipliedStrip Empty contB Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni type MultipliedStrip Empty contB = contB type Plain pack diag Filled Empty Shape Small Small height width Source # Instance detailsDefined 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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni type Plain pack diag Empty Filled Shape Small Small height width = UpperTriangularP pack height type Plain Packed Arbitrary (Bands sub) (Bands super) meas vert horiz height width Source # Instance detailsDefined 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 detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni type Plain Packed Unit (Bands sub) (Bands super) Shape Small Small height width = BandedSquare sub super height type UnitIfTriangular Filled (Bands (Succ k)) Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni type UnitIfTriangular Filled (Bands (Succ k)) = Arbitrary type Plain Packed (Hermitian neg zero pos) (Bands sub) (Bands super) Shape Small Small height width Source # Instance detailsDefined 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 UnitIfTriangular (Bands (Succ k)) Filled Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni type UnitIfTriangular (Bands (Succ k)) Filled = Arbitrary type UnitIfTriangular (Bands (Succ k)) Empty Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni type UnitIfTriangular (Bands (Succ k)) Empty = Unit type MultipliedBands (Bands k) Filled Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni type MultipliedBands (Bands k) Filled = Filled type UnitIfTriangular (Bands (Succ k)) (Bands (Succ l)) Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni type UnitIfTriangular (Bands (Succ k)) (Bands (Succ l)) = Arbitrary type MultipliedBands (Bands k) (Bands l) Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Shape.Omni type MultipliedBands (Bands k) (Bands l) = Bands (k :+: l)

addOffDiagonals :: (Natural subA, Natural superA, Natural subB, Natural superB, (subA :+: subB) ~ subC, (superA :+: superB) ~ superC) => (UnaryProxy subA, UnaryProxy superA) -> (UnaryProxy subB, UnaryProxy superB) -> ((Nat subC, Nat superC), (UnaryProxy subC, UnaryProxy superC)) Source #

class Packing pack Source #

Minimal complete definition

autoPacking

#### Instances

Instances details
 Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Layout.Private Methods Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Layout.Private Methods

data Packed Source #

#### Instances

Instances details