15. Vectorized implementations (in Octave)

• 15.1. Vector A가 있을때, $sum(A.^2)$ ?
• 15.2. loop 제거방법
• 15.3. Built-in Function: vectorize (fun)
• 15.4. Vectorization built-in 함수 목록 in Octave

최대한 loop사용을 줄이고, array요소의 개별적 연산을 줄이는 행렬연산에 익숙해질(훈련할) 필요가 있다. The goal in vectorization is to write code that avoids loops and uses whole-array operations.

15.1. Vector A가 있을때, $sum(A.^2)$ ?

$A * A^T$

15.2. loop 제거방법

출처: https://octave.org/doc/v4.0.1/Basic-Vectorization.html#Basic-Vectorization

Loop 사용

for i = 1:n  
  for j = 1:m  
    c(i,j) = a(i,j) + b(i,j);  
  endfor  
endfor

Vectorization

c = a + b;

Loop 사용

for i = 1:n-1  
  a(i) = b(i+1) - b(i);  
endfor

Vectorization

a = b(2:n) - b(1:n-1);

Loop 사용

for i = 1:n  
  if (a(i) > 5)  
    a(i) -= 20  
  endif  
endfor

Vectorization

a(a>5) -= 20;

15.3. Built-in Function: vectorize (fun)

Create a vectorized version of the inline function fun by replacing all occurrences of , /, etc., with ., ./, etc. This may be useful, for example, when using inline functions with numerical integration or optimization where a vector-valued function is expected.

fcn = vectorize (inline ("x^2 - 1"))  
   ⇒ fcn = f(x) = x.^2 - 1  
quadv (fcn, 0, 3)  
   ⇒ 6

15.4. Vectorization built-in 함수 목록 in Octave

• Index manipulation
  • find
  • sub2ind
  • ind2sub
  • sort
  • unique
  • lookup
  • ifelse / merge
• Repetition
  • repmat
  • repelems
• Vectorized arithmetic
  • sum
  • prod
  • cumsum
  • cumprod
  • sumsq
  • diff
  • dot
  • cummax
  • cummin
• Shape of higher dimensional arrays
  • reshape
  • resize
  • permute
  • squeeze
  • deal