Re: [Haskell] ANNOUNCE: An index-aware linear algebra library in Haskell
On Friday 14 April 2006 17:02, Frederik Eaton wrote:
An index-aware linear algebra library in Haskell
Excellent work! Is it possible to create a vector or matrix whose size is not known at compile time?
- Due to the need to specify index types at some point, input of vectors is difficult. I have provided two functions in Fu.Vector.Base which should cover most of the cases:
listVec :: Vector v e => [e] -> (forall n . (ReflectNum n) => v (L n) -> w) -> w listMat :: Vector v e => [[e]] -> (forall n m . (ReflectNum n, ReflectNum m) => v (L m, L n) -> w) -> w
However, these aren't useful in interactive situations. So I have also provided some template-haskell routines
http://ofb.net/~frederik/futility/src/Vector/Template.hs
which can be used to instantiate vectors directly. For example:
(In examples.hs):
-- matrix with elements of type Double v6 = trans $(dAM [[1,2,3,4]])
v7 = $(dAM [[1,0,0],[0,1,0],[0,0,1],[1,1,1]])
-- Alberto
Yes, certainly... Otherwise the library would not be much use! If it seems counterintuitive, as it did to me at first, you should check out the "Implicit Configurations" paper, which uses modular arithmetic as an example. My version of their code is in http://ofb.net/~frederik/futility/src/Prepose.hs The function I mainly use is: reifyIntegral :: Integral a => a -> (forall s. ReflectNum s => s -> w) -> w which turns an integral value into a type of the ReflectNum class which represents that value, and calls the provided polymorphic function with a dummy value (actually 'undefined') of that type; then returning the function's result. Frederik On Sat, Apr 15, 2006 at 06:14:44PM +0200, Alberto Ruiz wrote:
On Friday 14 April 2006 17:02, Frederik Eaton wrote:
An index-aware linear algebra library in Haskell
Excellent work!
Is it possible to create a vector or matrix whose size is not known at compile time?
- Due to the need to specify index types at some point, input of vectors is difficult. I have provided two functions in Fu.Vector.Base which should cover most of the cases:
listVec :: Vector v e => [e] -> (forall n . (ReflectNum n) => v (L n) -> w) -> w listMat :: Vector v e => [[e]] -> (forall n m . (ReflectNum n, ReflectNum m) => v (L m, L n) -> w) -> w
However, these aren't useful in interactive situations. So I have also provided some template-haskell routines
http://ofb.net/~frederik/futility/src/Vector/Template.hs
which can be used to instantiate vectors directly. For example:
(In examples.hs):
-- matrix with elements of type Double v6 = trans $(dAM [[1,2,3,4]])
v7 = $(dAM [[1,0,0],[0,1,0],[0,0,1],[1,1,1]])
-- Alberto
It is really counterintuitive! I will study carefully your library and the "Implicit Configurations" paper. Using static dimension checking we can write very solid code for matrix computations... However, I don't know how to write some definitions. For instance, this is ok: m = $(dAM [[1,2,3]]) but with: x = [[1,2,3]] :: [[Double]] m1 = $(dAM x) m2 = listMat x main = do print m1 print m2 I get: Vector/examples.hs:35:11: GHC stage restriction: `x' is used in a top-level splice, and must be imported, not defined locally In the first argument of `dAM', namely `x' In the definition of `m1': m1 = $[splice](dAM x) Vector/examples.hs:40:10: Inferred type is less polymorphic than expected Quantified type variable `m' escapes Quantified type variable `n' escapes Expected type: (v (L m, L n) -> w) -> t Inferred type: (forall n1 m1. (ReflectNum n1, ReflectNum m1) => v (L m1, L n1) -> w) -> w In the first argument of `print', namely `m2' In the result of a 'do' expression: print m2 I would also like to create a matrix from a data file: main = do let m1 = $(dAM [[1,2],[3,4::Double]]) s <- readFile "data.txt" let list = read s :: [[Double]] --let m2 = $(dAM list) let m2 = listMat list print $ m2 *> trans m1 But I get a similar error. Perhaps I must provide information about the expected dimensions, but I don't know how to do it. -- Alberto On Saturday 15 April 2006 22:09, Frederik Eaton wrote:
Yes, certainly... Otherwise the library would not be much use! If it seems counterintuitive, as it did to me at first, you should check out the "Implicit Configurations" paper, which uses modular arithmetic as an example. My version of their code is in
http://ofb.net/~frederik/futility/src/Prepose.hs
The function I mainly use is:
reifyIntegral :: Integral a => a -> (forall s. ReflectNum s => s -> w) -> w
which turns an integral value into a type of the ReflectNum class which represents that value, and calls the provided polymorphic function with a dummy value (actually 'undefined') of that type; then returning the function's result.
Frederik
On Sat, Apr 15, 2006 at 06:14:44PM +0200, Alberto Ruiz wrote:
On Friday 14 April 2006 17:02, Frederik Eaton wrote:
An index-aware linear algebra library in Haskell
Excellent work!
Is it possible to create a vector or matrix whose size is not known at compile time?
Hi Alberto, Those are good questions, I've added some examples which hopefully clarify the situation. Input and output of vectors is not a strong point of the library, but I don't think there is a good alternative to the way I do it. http://ofb.net/~frederik/futility/src/Vector/read-example.hs (also, your example exposed some missing functionality. I've added three new functions; in addition to listMat, now there are listMatCol, listMatRow, and listMatSquare. Hopefully these should cover almost all use cases. http://ofb.net/~frederik/futility/src/Vector/Base.hs ) By the way, here is how I would download and run the thing, although you seem to have figured it out: $ wget http://ofb.net/~frederik/futility/futility-devel.tar.gz $ tar -xvzf futility-devel.tar.gz $ cd futility-devel/ $ ghc -fth --make Vector/read-example.hs -o read-example $ ./read-example <# 11.0, 23.0; 14.0, 30.0; 15.0, 33.0; 18.0, 40.0 #> <1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0> <1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0> <# 1.0, 5.0; 2.0, 6.0; 3.0, 6.0; 4.0, 7.0 #> <# 11.0, 23.0; 14.0, 30.0; 15.0, 33.0; 18.0, 40.0 #> <# -3.0, -5.0; -5.0, -7.0 #> <# 7.0, 10.0; 15.0, 22.0 #> As for your questions:
Vector/examples.hs:35:11: GHC stage restriction: `x' is used in a top-level splice, and must be imported, not defined locally In the first argument of `dAM', namely `x' In the definition of `m1': m1 = $[splice](dAM x)
This is a shortcoming of Template Haskell - it will not let you call a function from a splice if that function is defined in the same file as the splice. It should be possible to remove this shortcoming, but I don't know what is planned.
m2 = listMat x
This is not how listMat is used, see the example file above. listMat takes a list of lists and a function, and passes the matrix version of the list of lists to the function.
I would also like to create a matrix from a data file:
See 'v3' in the example. Cheers, Frederik On Sun, Apr 16, 2006 at 05:06:55PM +0200, Alberto Ruiz wrote:
It is really counterintuitive! I will study carefully your library and the "Implicit Configurations" paper. Using static dimension checking we can write very solid code for matrix computations...
However, I don't know how to write some definitions. For instance, this is ok:
m = $(dAM [[1,2,3]])
but with:
x = [[1,2,3]] :: [[Double]] m1 = $(dAM x) m2 = listMat x
main = do print m1 print m2
I get:
Vector/examples.hs:35:11: GHC stage restriction: `x' is used in a top-level splice, and must be imported, not defined locally In the first argument of `dAM', namely `x' In the definition of `m1': m1 = $[splice](dAM x)
Vector/examples.hs:40:10: Inferred type is less polymorphic than expected Quantified type variable `m' escapes Quantified type variable `n' escapes Expected type: (v (L m, L n) -> w) -> t Inferred type: (forall n1 m1. (ReflectNum n1, ReflectNum m1) => v (L m1, L n1) -> w) -> w In the first argument of `print', namely `m2' In the result of a 'do' expression: print m2
I would also like to create a matrix from a data file:
main = do let m1 = $(dAM [[1,2],[3,4::Double]]) s <- readFile "data.txt" let list = read s :: [[Double]] --let m2 = $(dAM list) let m2 = listMat list print $ m2 *> trans m1
But I get a similar error. Perhaps I must provide information about the expected dimensions, but I don't know how to do it.
-- Alberto
On Saturday 15 April 2006 22:09, Frederik Eaton wrote:
Yes, certainly... Otherwise the library would not be much use! If it seems counterintuitive, as it did to me at first, you should check out the "Implicit Configurations" paper, which uses modular arithmetic as an example. My version of their code is in
http://ofb.net/~frederik/futility/src/Prepose.hs
The function I mainly use is:
reifyIntegral :: Integral a => a -> (forall s. ReflectNum s => s -> w) -> w
which turns an integral value into a type of the ReflectNum class which represents that value, and calls the provided polymorphic function with a dummy value (actually 'undefined') of that type; then returning the function's result.
Frederik
On Sat, Apr 15, 2006 at 06:14:44PM +0200, Alberto Ruiz wrote:
On Friday 14 April 2006 17:02, Frederik Eaton wrote:
An index-aware linear algebra library in Haskell
Excellent work!
Is it possible to create a vector or matrix whose size is not known at compile time?
participants (2)
-
Alberto Ruiz -
Frederik Eaton