Numeric.LAPACK.Matrix.Superscript

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.

Documentation

class Superscript sup where

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

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

Instances

Superscript Adjoint

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

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

Superscript Conjugate

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

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

Superscript Inverse

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

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

Superscript None

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

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

Superscript Power

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

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

Superscript PseudoInverse

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

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

Superscript Transpose

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

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

data None

Instances

Superscript None

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

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

data Exponent None typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typB xlB xuB lowerB upperB measB vertB horizB heightB widthB a

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 typA xlA xuA lowerA upperA measA vertA horizA heightA widthA a. Exponent None typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typA xlA xuA lowerA upperA measA vertA horizA heightA widthA a

data Transpose

Instances

Superscript Transpose

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

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

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

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 typA xlA xuA lowerA upperA measA vertA horizA heightA widthA a. (Transpose typA, TransposeExtra typA xlA, TransposeExtra typA xuA) => Exponent Transpose typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typA xuA xlA upperA lowerA measA horizA vertA widthA heightA a

data Adjoint

Instances

Superscript Adjoint

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

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

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

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 typA xlA xuA lowerA upperA measA vertA horizA heightA widthA a. (Transpose typA, Complex typA, TransposeExtra typA xlA, TransposeExtra typA xuA) => Exponent Adjoint typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typA xuA xlA upperA lowerA measA horizA vertA widthA heightA a

data Conjugate

Instances

Superscript Conjugate

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

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

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

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 typA xlA xuA lowerA upperA measA vertA horizA heightA widthA a. Complex typA => Exponent Conjugate typA xlA xuA lowerA upperA measA vertA horizA heightA widthA typA xlA xuA lowerA upperA measA vertA horizA heightA widthA a

data Inverse

Instances

Superscript Inverse

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

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

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

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 typA xlA xuA lowerA upperA measA heightA widthA a. (Inverse typA, InverseExtra typA xlA, InverseExtra typA xuA, PowerStrip lowerA, PowerStrip upperA) => Exponent Inverse typA xlA xuA lowerA upperA measA Small Small heightA widthA typA xlA xuA lowerA upperA measA Small Small widthA heightA a

data PseudoInverse

Instances

Superscript PseudoInverse

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

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

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

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 typA a heightA. typA ~ Array Unpacked Arbitrary => RealOf a -> Exponent PseudoInverse typA () () Filled Filled Shape Small Small heightA heightA typA () () Filled Filled Shape Small Small heightA heightA a

data Power

Instances

Superscript Power

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

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

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

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 typA xlA xuA lowerA upperA heightA a. (Power typA, PowerExtra typA xlA, PowerExtra typA xuA, PowerStrip lowerA, PowerStrip upperA) => Integer -> Exponent Power typA xlA xuA lowerA upperA Shape Small Small heightA heightA typA xlA xuA lowerA upperA Shape Small Small heightA heightA a