qlinear alternatives and similar packages
Based on the "Math" category.
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vector
An efficient implementation of Intindexed arrays (both mutable and immutable), with a powerful loop optimisation framework . 
statistics
A fast, high quality library for computing with statistics in Haskell. 
HerbiePlugin
GHC plugin that improves Haskell code's numerical stability 
hgeometry
HGeometry is a library for computing with geometric objects in Haskell. It defines basic geometric types and primitives, and it implements some geometric data structures and algorithms. The main two focusses are: (1) Strong type safety, and (2) implementations of geometric algorithms and data structures that have good asymptotic running time guarantees. 
computationalalgebra
GeneralPurpose Computer Algebra System as an EDSL in Haskell 
dimensional
Dimensional library variant built on Data Kinds, Closed Type Families, TypeNats (GHC 7.8+). 
mwcrandom
A very fast Haskell library for generating high quality pseudorandom numbers. 
numhask
A haskell numeric prelude, providing a clean structure for numbers and operations that combine them. 
cf
"Exact" real arithmetic for Haskell using continued fractions (Not formally proven correct) 
optimization
Some numerical optimization methods implemented in Haskell 
poly
Fast polynomial arithmetic in Haskell (dense and sparse, univariate and multivariate, usual and Laurent) 
safedecimal
Safe and very efficient arithmetic operations on fixed decimal point numbers 
equationalreasoning
Agdastyle equational reasoning in Haskell 
eigen
Haskel binding for Eigen library. Eigen is a C++ template library for linear algebra: matrices, vectors, numerical solvers, and related algorithms. 
polynomial
Haskell library for manipulating and evaluating polynomials 
vectorthunbox
Deriver for unboxed vectors using Template Haskell 
diagramssolve
Miscellaneous solver code for diagrams (lowdegree polynomials, tridiagonal matrices)
Less time debugging, more time building
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They vary from L1 to L5 with "L5" being the highest.
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README
QLinear
QLinear is type safe library for linear algebra based on "macroconstructors"
Constructors:
matrix
[matrix a b ; c d ]
builds matrix 2x2[ [a, b], [c, d] ]
Example:
[matrix 1 2; 3 4 ] ~+~ [matrix 2 3; 4 5 ] == [matrix 3 5; 7 9 ]
Also you can't, for example, add two matrix with different size.
[matrix 1 2; 3 4 ] ~+~ [matrix 1 2 3; 4 5 6; 7 8 9 ]  will not be compiled
 vector
>
[vector a b c d ]
builds matrix 4x1[ [a], [b], [c], [d] ]
 vector
>
operator
[operator (x, y) => (y, x) ]
builds matrix 2x2 of operator[ [0, 1], [1, 0] ]
that swaps coodrinates
[operator (x, y) => (2 * x, y) ]
builds matrix 2x2 of operator[ [2, 0], [0, 1] ]
that doublesx
coordinate
Example:
haskell
[operator (x, y) => (3 * y, x / 2) ] ~*~ [vector 2 8 ] == [vector 24 1 ]
Syntax:
 matrix:
val11 val12 .. val1n; val21 val22 .. val2n; ..; valm1 valm2 .. valmn
 vector:
val1 val2 .. valn
 operator:
(var1, var2, .., varn) => (exp1, exp2, .., expn)
whereval
isnumber literal
,variable
orany Haskell expression
between(
and)
var
is Haskell variable
*
exp
is any Haskell expressionAlso there are basic operations as determinant, transposition, etc.