{- Copyright (c) 2008, Scott E. Dillard All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. -} {- | Vec : a library for fixed-length lists and low-dimensional linear algebra Scott E. Dillard <sedillard@gmail.com> The darcs repository is at <http://graphics.cs.ucdavis.edu/~sdillard/Vec> Some examples can be found at <http://graphics.cs.ucdavis.edu/~sdillard/Vec/examples> /Synopsis/ Vectors are represented by lists with type-encoded lengths. The constructor is @:.@, which acts like a cons both at the value and type levels, with @()@ taking the place of nil. So @x:.y:.z:.()@ is a 3d vector. The library provides a set of common list-like functions (map, fold, etc) for working with vectors. Built up from these functions are a small but useful set of linear algebra operations: matrix multiplication, determinants, solving linear systems, inverting matrices. /Design/ * Simplicity : Beyond the initial complexities of type-level lists and numbers, I've tried to keep the API simple. There is no vector-space class, nor a complicated hierarchy of linear\/affine\/projective transformations. These can be added on top of the library easily. * Purity : The library is written in the functional style. For most functions this does not hinder performance at all, but some I am still working on (Gaussian elimination) so if this library is a bottleneck you can easily drop down to C. * Low Dimension : Although the dimensionality is limited only by what GHC will handle, the library is meant for 2,3 and 4 dimensions. For general linear algebra, check out the excellent hmatrix library and blas bindings. To the point of simplicity, vectors and matrices are instances of Num and Fractional. All arithmetic is done component-wise and literals construct uniform vectors and matrices. There are many interesting projects aiming to overhaul Haskell's number classes, but for now the type of @(*)@ is @a -> a -> a@ so that's what we're working with. It is easy to incorporate this library into a more mathematically consistent class hierarchy (provided you can design one.) The rule is simple : If the method is unary, it's a map. If it's binary, it's a zipWith. /Performance/ @(:.)@ is strict in both arguments, but it is also polymorphic, so at runtime vectors will be realized as linked lists, albeit with less pattern matching. However the library provides packed representations for 2,3 and 4d vectors of Ints, Floats and Doubles. @'Vec3F' x y z@ constructs a packed vector of unboxed Floats. Functions @'pack'@ and @'unpack'@ convert between packed and unpacked types. When vector operations are bracketed by 'pack' and 'unpack', GHC can unfold them into very efficient code. The 'Storable' and 'UArray' instances for vectors also store them efficiently and generate fast code. Without optimizations, the code falls back into linked-list mode. The optimizations depend on inlining, so you may need to increase your unfolding threshold in certain situations. /GHC Extensions/ This library makes heavy use of functional dependencies. I have tried to tweak things so that they \"just work.\" However, every now and then you will get incomprehensible error messages, usually about how this isn't an instance of that. These are how type errors typically manifest, so first double check to make sure you aren't trying to mix vectors of different dimension or component types. If you still get these errors, manual type annotations usually make them go away. /Related Work/ See previous work by David Menendez, <http://haskell.org/pipermail/haskell/2005-May/015815.html> and of course Oleg Kiselyov, <http://okmij.org/ftp/papers/number-parameterized-types.pdf> Other vector and linear algebra packages : vector-space, by Conal Elliott : <http://hackage.haskell.org/cgi-bin/hackage-scripts/package/vector-space> hmatrix, by Alberto Ruiz : <http://hackage.haskell.org/cgi-bin/hackage-scripts/package/hmatrix> blas bindings, by Patrick Perry : <http://hackage.haskell.org/cgi-bin/hackage-scripts/package/blas> templatized geometry library (C++), by Oliver Kreylos : <http://graphics.cs.ucdavis.edu/~okreylos/ResDev/Geometry/index.html> -} module Data.Vec (module X) where import Data.Vec.Base as X import Data.Vec.LinAlg as X import Data.Vec.Packed as X import Data.Vec.Nat as X