Negate a matrix in haskell?

Question

If I am using a vector package, how can I get a negative of a matrix? Just "Minusing" it doesn't work.

So from:

 1 2 3
 3 4 5
 6 7 8

I want to get:

 -1 -2 -3
 -3 -4 -5
 -6 -7 -8

No, multiplying by -1 doesn't work either:

let m = fromList [[10,20,30], [11,12, 13]]
Prelude Data.Vector> :t m
m :: Vector [Integer]
Prelude Data.Vector> (-1)*m


<interactive>:1:3:
    No instance for (Num (Vector [Integer]))
      arising from the literal `1'
    Possible fix:
      add an instance declaration for (Num (Vector [Integer]))
    In the expression: 1
    In the first argument of `(*)', namely `(- 1)'
    In the expression: (- 1) * m

Answer 1

I think you are confused about the purpose of the vector library. The description of it is:

An efficient implementation of Int-indexed arrays (both mutable and immutable), with a powerful loop optimisation framework .

So it is just an array class - if you want to perform matrix operations on it you will have to code the solutions yourself.

What you really want is to use a true matrix library. hmatrix is a library that does this. Firstly install it using the hmatrix installation instructions .

This is how you would write your program using hmatrix :

> import Data.Packed.Matrix
> let matrix = (3><3)[1,2,3,3,4,5,6,7,8]
> mapMatrix negate matrix
(3><3)
 [ -1.0, -2.0, -3.0
 , -3.0, -4.0, -5.0
 , -6.0, -7.0, -8.0 ]

There are heaps of matrix operations with the library, just read the Data.Packed.Matrix and the Numeric.Container docs

Answer 2

Have you tried Data.Vector.map (* (-1)) ?

---

For a matrix defined as m :: Vector [Integer] , that is a Data.Vector.Vector of lists of Integers, you can

Data.Vector.map (Prelude.map negate) m

The outer map maps function (Prelude.map negate) over the vector. The inner map negates all elements of a list.