Safe Haskell  None 

Language  Haskell98 
Synopsis
 class C shape => Permutable shape
 newtype IntIndexed sh = IntIndexed {
 deconsIntIndexed :: sh
 shapeInt :: C sh => sh > ZeroBased Int
Documentation
class C shape => Permutable shape Source #
Class of shapes where indices still make sense if we permute elements.
We use this for all matrix factorisations
involving permutations or more generally orthogonal transformations,
e.g. eigenvalue and singular value, LU and QR decompositions.
E.g. say, we have a square matrix with dimension 'Shape.Enumeration Ordering'.
Its vector of eigenvalues has the same dimension,
but it does not make sense to access the eigenvalues
with indices like LT
or EQ
.
Thus Enumeration
is no instance of Permutable
(and you should not add an orphan instance).
If you want to factor a matrix with a nonpermutable shape,
you should convert it temporarily to a permutable one,
like ZeroBased
(i.e. ShapeInt
) or IntIndexed
.
The Permutable
class has no method, so you could add any shape to it.
However, you should use good taste when adding an instance.
There is no strict criterion which shape type to add.
We tried to use ShapeInt
for eigenvalue vectors
and LiberalSquare
s as transformation matrices of eigenvalue decompositions.
However, this way, the type checker cannot infer
that the product of the factorisation is a strict square.
We also tried to use IntIndexed
for eigenvalue vectors
with according LiberalSquare
s transformations.
This has also the problem of inferring squares.
Additionally,
more such transformations lead to nested IntIndexed
wrappers
and for ShapeInt
even the first wrapper is unnecessary.
Instances
Permutable () Source #  
Defined in Numeric.LAPACK.Shape  
Permutable Zero Source #  
Defined in Numeric.LAPACK.Shape  
Integral n => Permutable (ZeroBased n) Source #  
Defined in Numeric.LAPACK.Shape  
Integral n => Permutable (OneBased n) Source #  
Defined in Numeric.LAPACK.Shape  
Ix n => Permutable (Range n) Source #  
Defined in Numeric.LAPACK.Shape  
Integral n => Permutable (Shifted n) Source #  
Defined in Numeric.LAPACK.Shape  
Permutable sh => Permutable (Deferred sh) Source #  
Defined in Numeric.LAPACK.Shape  
Integral n => Permutable (Cyclic n) Source #  
Defined in Numeric.LAPACK.Shape  
C sh => Permutable (IntIndexed sh) Source #  
Defined in Numeric.LAPACK.Shape  
Permutable sh => Permutable (Tagged s sh) Source #  
Defined in Numeric.LAPACK.Shape 
newtype IntIndexed sh Source #
This shape type wraps any other array shape type.
However, its Indexed
instance just uses zerobased Int
indices.
Thus it can turn any shape type into a Indexed
one.
The main usage is to make an arbitrary shape Permutable
.
IntIndexed  
