## Matrix Operations

### June 22, 2010

Our Standard Prelude provides a matrix datatype with create, lookup and setting operations. In today’s exercise we extend the matrix datatype with some mathematical operations: sum two matrices, multiply a matrix by a scalar, multiply two matrices, and transpose a matrix.

- Addition of two matrices is done by adding elements in corresponding positions, assuming identical dimensions. For example:
- Multiplying a scalar times a matrix is done by multiplying the scalar times each element in turn. For example:
- The product of an
*m*×*n*matrix*A*and an*n*×*p*matrix*B*is the*m*×*p*matrix*C*whose entries are defined by . For example: - The transpose of a matrix interchanges the rows and columns of a matrix. For example:

Your task is to write functions that perform the four matrix operations described above. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

[…] Praxis – Matrix Operations By Remco Niemeijer In today’s Programming Praxis exercise our task is to implement four common matrix operations. The provided […]

My Haskell solution (see http://bonsaicode.wordpress.com/2010/06/22/programming-praxis-matrix-operations/ for a version with comments):

Here’s my Java solution.

@Remco,

Your Haskell solution is gorgeous (its simplicity astounds me). I’ll hopefully be able to churn out solutions like that in Haskell soon! =)

@Elvis Montero:

Thanks. Best of luck with learning Haskell. I can highly recommend it :)

@Remco,

Your post has inspired me to learn Haskell!

;;; A scheme solution. Nothing like the beauty of the haskell one though ;-)

;; Q1

(define (add-matrix m1 m2)

(cond ((or (null? m1) (null? m2)) ‘())

(else (cons (sum-list (car m1) (car m2))

(add-matrix (cdr m1) (cdr m2))))))

;; Q1 helper

(define (sum-list l1 l2)

(cond ((or (null? l1) (null? l2)) ‘())

(else (cons (+ (car l1) (car l2))

(sum-list (cdr l1) (cdr l2))))))

;; Q2

(define (scale s m)

(letrec ((scale* (lambda (m)

(cond ((null? m) ‘())

(else (cons (mul-list s (car m))

(scale* (cdr m))))))))

(scale* m)))

;; Q2 helper

(define (mul-list s l)

(letrec ((mul-list* (lambda (l)

(cond ((null? l) ‘())

(else (cons (* s (car l))

(mul-list* (cdr l))))))))

(mul-list* l)))

;; Q3

(define (X A B)

(cond ((null? A) ‘())

(else (cons (psum (car A) B)

(X (cdr A) B)))))

;; Q3 helper – genereate list of cross-sums

(define (psum l m)

(letrec ((psum* (lambda ™

(cond ((null? tm) ‘())

(else (cons (xs l (car tm))

(psum* (cdr tm))))))))

(psum* (transpose m))))

;; Q3 helper – multiply each element and sum result

(define (xs l1 l2)

(cond ((or (null? l1) (null? l2)) 0)

(else (+ (* (car l1) (car l2)) (xs (cdr l1) (cdr l2))))))

;; Q4

(define (transpose m)

(cond ((null? (car m)) ‘())

(else (cons (list-of-heads m)

(transpose (list-of-tails m))))))

;; Q4 helper

(define (list-of-heads m)

(cond ((null? m) ‘())

(else (cons (car (car m))

(list-of-heads (cdr m))))))

;; Q4 helper

(define (list-of-tails m)

(cond ((null? m) ‘())

(else (cons (cdr (car m))

(list-of-tails (cdr m))))))

bah.. indents lost :-(

one with proper indents on pocoo….

http://paste.pocoo.org/show/nZhGWlzvWmDhV9pRV5im/

Geir S: list-of-heads is just (map car m)

Interestingly I realized after writing it that I duplicated the Haskell version above in Scheme, though I put scalar multiplication into matrix multiplication. I have such a hard time reading Haskell that I couldn’t notice it before! No error checking. A matrix is a list of lists.

My Haskell solution:

Not nearly as sexy as @Remco’s, partly because I used a Matrix data type that complicated things somewhat unnecessarily. I wrote zipList from scratch before remembering there was a ‘transpose’ function in Data.List, but overall this was a good learning experience. I remember back when I was into C++, and I wrote some matrix classes–the header declarations alone were longer than this :-)

My Python solution with convenient operators overloading, though not very effective:

Scheme solution: