Safe Haskell	None
Language	Haskell98

Numeric.LAPACK.Matrix.Superscript

Description

This module provides an infix operator and some data constructors that shall resemble mathematical notation. E.g. you can write a#^T for Matrix.transpose a. It is clearly abuse of the type system because I suspect you will never write algorithms that are generic in the superscript type.

Synopsis

class Superscript sup where
- data Exponent sup typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a
- (#^) :: (Measure measA, C vertA, C horizA) => (C widthA, C heightA) => (Measure measB, C vertB, C horizB) => (C widthB, C heightB) => Floating a => Matrix typA xlA xuA lowerA upperA measA vertA horizA heightA widthA a -> Exponent sup typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a -> Matrix typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a
data None
data Transpose
data Adjoint
data Conjugate
data Inverse
data PseudoInverse
data Power

Documentation

class Superscript sup where Source #

left associative in contrast to ^, ^^ etc. because there is no law analogous to power law (x^a)^b = x^(a*b).

Associated Types

data Exponent sup typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a Source #

Methods

(#^) :: (Measure measA, C vertA, C horizA) => (C widthA, C heightA) => (Measure measB, C vertB, C horizB) => (C widthB, C heightB) => Floating a => Matrix typA xlA xuA lowerA upperA measA vertA horizA heightA widthA a -> Exponent sup typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a -> Matrix typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a infixl 8 Source #

Instances

Superscript Power Source #
Instance details Defined in Numeric.LAPACK.Matrix.Superscript Associated Types data Exponent Power typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a :: Type Source # Methods (#^) :: (Measure measA, C vertA, C horizA, C widthA, C heightA, Measure measB, C vertB, C horizB, C widthB, C heightB, Floating a) => Matrix typA xlA xuA lowerA upperA measA vertA horizA heightA widthA a -> Exponent Power typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a -> Matrix typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a Source #
Superscript PseudoInverse Source #
Instance details Defined in Numeric.LAPACK.Matrix.Superscript Associated Types data Exponent PseudoInverse typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a :: Type Source # Methods (#^) :: (Measure measA, C vertA, C horizA, C widthA, C heightA, Measure measB, C vertB, C horizB, C widthB, C heightB, Floating a) => Matrix typA xlA xuA lowerA upperA measA vertA horizA heightA widthA a -> Exponent PseudoInverse typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a -> Matrix typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a Source #
Superscript Inverse Source #
Instance details Defined in Numeric.LAPACK.Matrix.Superscript Associated Types data Exponent Inverse typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a :: Type Source # Methods (#^) :: (Measure measA, C vertA, C horizA, C widthA, C heightA, Measure measB, C vertB, C horizB, C widthB, C heightB, Floating a) => Matrix typA xlA xuA lowerA upperA measA vertA horizA heightA widthA a -> Exponent Inverse typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a -> Matrix typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a Source #
Superscript Conjugate Source #
Instance details Defined in Numeric.LAPACK.Matrix.Superscript Associated Types data Exponent Conjugate typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a :: Type Source # Methods (#^) :: (Measure measA, C vertA, C horizA, C widthA, C heightA, Measure measB, C vertB, C horizB, C widthB, C heightB, Floating a) => Matrix typA xlA xuA lowerA upperA measA vertA horizA heightA widthA a -> Exponent Conjugate typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a -> Matrix typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a Source #
Superscript Adjoint Source #
Instance details Defined in Numeric.LAPACK.Matrix.Superscript Associated Types data Exponent Adjoint typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a :: Type Source # Methods (#^) :: (Measure measA, C vertA, C horizA, C widthA, C heightA, Measure measB, C vertB, C horizB, C widthB, C heightB, Floating a) => Matrix typA xlA xuA lowerA upperA measA vertA horizA heightA widthA a -> Exponent Adjoint typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a -> Matrix typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a Source #
Superscript Transpose Source #
Instance details Defined in Numeric.LAPACK.Matrix.Superscript Associated Types data Exponent Transpose typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a :: Type Source # Methods (#^) :: (Measure measA, C vertA, C horizA, C widthA, C heightA, Measure measB, C vertB, C horizB, C widthB, C heightB, Floating a) => Matrix typA xlA xuA lowerA upperA measA vertA horizA heightA widthA a -> Exponent Transpose typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a -> Matrix typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a Source #
Superscript None Source #
Instance details Defined in Numeric.LAPACK.Matrix.Superscript Associated Types data Exponent None typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a :: Type Source # Methods (#^) :: (Measure measA, C vertA, C horizA, C widthA, C heightA, Measure measB, C vertB, C horizB, C widthB, C heightB, Floating a) => Matrix typA xlA xuA lowerA upperA measA vertA horizA heightA widthA a -> Exponent None typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a -> Matrix typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a Source #

data None Source #

Instances

Superscript None Source #
Instance details Defined in Numeric.LAPACK.Matrix.Superscript Associated Types data Exponent None typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a :: Type Source # Methods (#^) :: (Measure measA, C vertA, C horizA, C widthA, C heightA, Measure measB, C vertB, C horizB, C widthB, C heightB, Floating a) => Matrix typA xlA xuA lowerA upperA measA vertA horizA heightA widthA a -> Exponent None typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a -> Matrix typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a Source #
data Exponent None typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a Source #
Instance details Defined in Numeric.LAPACK.Matrix.Superscript data Exponent None typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a where N :: forall typ xl xu lower upper meas vert horiz height width typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a. Exponent None typ xl xu lower upper meas vert horiz height width typ xl xu lower upper meas vert horiz height width a

data Transpose Source #

Instances

Superscript Transpose Source #
Instance details Defined in Numeric.LAPACK.Matrix.Superscript Associated Types data Exponent Transpose typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a :: Type Source # Methods (#^) :: (Measure measA, C vertA, C horizA, C widthA, C heightA, Measure measB, C vertB, C horizB, C widthB, C heightB, Floating a) => Matrix typA xlA xuA lowerA upperA measA vertA horizA heightA widthA a -> Exponent Transpose typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a -> Matrix typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a Source #
data Exponent Transpose typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a Source #
Instance details Defined in Numeric.LAPACK.Matrix.Superscript data Exponent Transpose typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a where T :: forall typ xl xu lower upper meas vert horiz height width typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a. (Transpose typ, TransposeExtra typ xl, TransposeExtra typ xu) => Exponent Transpose typ xl xu lower upper meas vert horiz height width typ xu xl upper lower meas horiz vert width height a

data Adjoint Source #

Instances

Superscript Adjoint Source #
Instance details Defined in Numeric.LAPACK.Matrix.Superscript Associated Types data Exponent Adjoint typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a :: Type Source # Methods (#^) :: (Measure measA, C vertA, C horizA, C widthA, C heightA, Measure measB, C vertB, C horizB, C widthB, C heightB, Floating a) => Matrix typA xlA xuA lowerA upperA measA vertA horizA heightA widthA a -> Exponent Adjoint typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a -> Matrix typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a Source #
data Exponent Adjoint typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a Source #
Instance details Defined in Numeric.LAPACK.Matrix.Superscript data Exponent Adjoint typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a where A :: forall typ xl xu lower upper meas vert horiz height width typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a. (Transpose typ, Complex typ, TransposeExtra typ xl, TransposeExtra typ xu) => Exponent Adjoint typ xl xu lower upper meas vert horiz height width typ xu xl upper lower meas horiz vert width height a

data Conjugate Source #

Instances

Superscript Conjugate Source #
Instance details Defined in Numeric.LAPACK.Matrix.Superscript Associated Types data Exponent Conjugate typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a :: Type Source # Methods (#^) :: (Measure measA, C vertA, C horizA, C widthA, C heightA, Measure measB, C vertB, C horizB, C widthB, C heightB, Floating a) => Matrix typA xlA xuA lowerA upperA measA vertA horizA heightA widthA a -> Exponent Conjugate typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a -> Matrix typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a Source #
data Exponent Conjugate typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a Source #
Instance details Defined in Numeric.LAPACK.Matrix.Superscript data Exponent Conjugate typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a where C :: forall typ xl xu lower upper meas vert horiz height width typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a. Complex typ => Exponent Conjugate typ xl xu lower upper meas vert horiz height width typ xl xu lower upper meas vert horiz height width a

data Inverse Source #

Instances

Superscript Inverse Source #
Instance details Defined in Numeric.LAPACK.Matrix.Superscript Associated Types data Exponent Inverse typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a :: Type Source # Methods (#^) :: (Measure measA, C vertA, C horizA, C widthA, C heightA, Measure measB, C vertB, C horizB, C widthB, C heightB, Floating a) => Matrix typA xlA xuA lowerA upperA measA vertA horizA heightA widthA a -> Exponent Inverse typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a -> Matrix typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a Source #
data Exponent Inverse typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a Source #
Instance details Defined in Numeric.LAPACK.Matrix.Superscript data Exponent Inverse typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a where Inv :: forall typ xl xu lower upper meas vertA horizA height width typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a. (Inverse typ, InverseExtra typ xl, InverseExtra typ xu, PowerStrip lower, PowerStrip upper) => Exponent Inverse typ xl xu lower upper meas Small Small height width typ xl xu lower upper meas Small Small width height a

data PseudoInverse Source #

Instances

Superscript PseudoInverse Source #
Instance details Defined in Numeric.LAPACK.Matrix.Superscript Associated Types data Exponent PseudoInverse typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a :: Type Source # Methods (#^) :: (Measure measA, C vertA, C horizA, C widthA, C heightA, Measure measB, C vertB, C horizB, C widthB, C heightB, Floating a) => Matrix typA xlA xuA lowerA upperA measA vertA horizA heightA widthA a -> Exponent PseudoInverse typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a -> Matrix typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a Source #
data Exponent PseudoInverse typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a Source #
Instance details Defined in Numeric.LAPACK.Matrix.Superscript data Exponent PseudoInverse typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a where Pseudo :: forall typ xlA xuA lowerA upperA measA vertA horizA sh widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a. typ ~ Array Unpacked Arbitrary => RealOf a -> Exponent PseudoInverse typ () () Filled Filled Shape Small Small sh sh typ () () Filled Filled Shape Small Small sh sh a

data Power Source #

Instances

Superscript Power Source #
Instance details Defined in Numeric.LAPACK.Matrix.Superscript Associated Types data Exponent Power typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a :: Type Source # Methods (#^) :: (Measure measA, C vertA, C horizA, C widthA, C heightA, Measure measB, C vertB, C horizB, C widthB, C heightB, Floating a) => Matrix typA xlA xuA lowerA upperA measA vertA horizA heightA widthA a -> Exponent Power typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a -> Matrix typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a Source #
data Exponent Power typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a Source #
Instance details Defined in Numeric.LAPACK.Matrix.Superscript data Exponent Power typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a where Exp :: forall typ xl xu lower upper measA vertA horizA sh widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a. (Power typ, PowerExtra typ xl, PowerExtra typ xu, PowerStrip lower, PowerStrip upper) => Integer -> Exponent Power typ xl xu lower upper Shape Small Small sh sh typ xl xu lower upper Shape Small Small sh sh a