Past exam of the year 1 of the computer science course of the University of Oxford / 2016 / Functional programming, design and analysis of algorithms / 4 / d

Table of contents
- Solution d

Solution

Generate successive matrix powers and take cumulative sums using matrix addition:

seriesMat :: Num a => Matrix a -> [Matrix a]
seriesMat m = scanl1 addMat (iterate (multMat m) m)

For the stipulated square matrix, iterate (multMat m) m produces m, m*m, m*(m*m), and so on. Associativity of exact matrix multiplication identifies these as

M, M^{2}, M^{3}, \dots

. The left scan scanl1 addMat then returns

[M, M + M^{2}, M + M^{2} + M^{3}, \dots] .

All dimensions remain compatible. The infinite outer list is available a finite prefix at a time under lazy evaluation; no convergence of the matrix geometric series is needed. With floating-point entries, the expression specifies this particular multiplication and addition order, since machine arithmetic need not obey the exact algebraic laws.

 Ancestors (11)

 View article source

 Discussion (0) New discussion

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version