Matrix Multiplication In Haskell
ReshapeA23reshape 1d array to 2rows3columns. SwapRows i i a a assoc j.
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Haskell matrix multiplication DataMatrix If we improve the access pattern by multiplying a row-major matrix with a column-major matrix all become faster the gcc-compiled C finishes it 118s java takes 123s and the ghc-compiled Haskell takes around 58s which can be.
Matrix multiplication in haskell. Num a a. Matrix multiplication So we will use Haskells capability to define our own types either our own names for is correct by multiplying the two matrices and comparing to the identity. Otherwise known as the pairwise multiplication and summation of the first row of the first matrix and first column of the second matrix.
For instance with four matrices one can compute A B CD A BCD AB CD A BCD ABCD. This is the best choice when you know for sure that your matrices are small. TLN x TLN y TLN t Num a Matrix x t a - Matrix t y a - Matrix x y a You can extract the arrays dimension by generating an undefined of appropriate type together with the ScopedTypeVariables extension.
Three methods are provided for matrix multiplication. An depends on the order of matrix multiplications hence on where parens are put. - -- Element wise multiplication of each corresponding Matrix element -- returning dimensions row size and column size is equal to the.
I wrote a quick recursive solution using eight multiplication and its not very efficient because the real problem is Haskells List laziness. Monoid m a - m - Matrix a - m. Matrix multiplication following the Strassens algorithm.
Matrix multiplication following directly the definition. A - b - b - b - Matrix a - b. This code is completely untested and GHC may barf on compilation.
Recursive Matrix Mulitplication in Haskell First step to Strassens Algorithm Strassens algorithm states that we can multiply two 2 X 2 matrices in seven multiplication rather than eight. Three methods are provided for matrix multiplication. Let A 13 45 and B 11 02 Then A B 1 1 3 1 4 0 5 2 2 4 4 7 One thing to note is that this only makes sense if we enforce the constraint that matrix A and matrix B must be of the same dimension.
Variable B 16index range1to 6same as above in A. Then a multiplication of the vector with the matrix is performed where the necessary addition and multiplication of matrix elements are interpreted in the required fashion. Compose has a worst- case O n k m complexity due to the matrix-matrix multiplication.
Matrix multiplication following directly the definition. MatrixMult x y matrixMultT x transpose y. Complexity grows slower but also some work is added partitioning the matrix.
Never fear we can perform the equivalent of a loop fusion optimization in Haskell. Remember that the matrix product is associative but not commutative hence only the parens can be moved. Haskell does have linear algebra packages but I wanted to keep this solution as dependency-free as possible.
Instance Num a Num Matrix a where fromInteger x let b 0000 in Matrix array b ijif i j then fromInteger x else 0ij. B - a - b - b - Matrix a - b. A - b - b - b - Matrix a - b.
Num a a - a - a calcRow _ calcRow a bbs calcCell a b. Num a a - a - a matrixMultT _ matrixMultT aas b calcRow a b. Monoid m Matrix m - m.
To compute the successors we interpret and as the logical disjunction and conjunction resp 0 as false and 1. If possible you never actually want to use matrix-matrix multiplication only matrix-vector ones since the asymptotic time complexity is a lot better. S-langedit Matrix multiplication is a built-in with the S-Lang octothorpe operator.
B - a - b - b - Matrix a - b. Then well define matrix multiplication for this type using Haskells Semigroup class which you can think of as a generic interface for any operator that is associative. It is just a sketch about how it could be done.
Matrix let a matrix 3 2 102-131 Matrix let b matrix 2 3 312110 Matrix ab Matrix matrixN 3 matrixM 3 matrixElems 5142 Since my Num instance is generic it even works for complex matrices out of the box.
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