初階 Matlab 2

作者:蔡承佑

Skill

確認是否為整數
num == floor(num)

Binary Arithmetic Operations

不同的type做運算，最後結果會是容量最小的type

x/n得到0 因為 int16 沒辦法有小數點的數字

Linear Equation

有解

不能用 / 只能用 \
*mldivide

check error

A = rand(20, 20);
b = rand(20, 1);
x = A\b;
e = A*x-b;
max(abs(e))

ans = 8.8818e-16

無解 (2 equation 2 variables)

visualize

無解 (3 equation 2 variables)

MATLAB會找尋最接近三個解的點，而不是任一個正確的解

Underdetermined Equations

*cond

預估值error

bigger worse

Live Script

Scripts VS Functions

• Scripts have no workspace of their own

  • command window
  • modify existing variables of that workspace

• Scripts have no input or output arguments

fit function

Table of contents

INSERT > Table of Contents

出現到每個section的link

Equation

ctrl + shift + e

save

save 可以選擇匯出的檔

the old way script

一樣可以藉由 publish 變成 live script ，figure要Insert

Error Handline

可以善用 error function 跟 warning function

Exception Handline (try catch end)

Exception

MATLAB:badsubscript
超過有限範圍

1. implemented with try-catch block
2. identify errors with catch ME and Exception.last
3. Throw errors with the throw function
4. rethrow errors with the rethrow function
5. assert function to identify incorrect assumptions

assert

assert(x >= 0)

如果 x < 0 就會跳出 Assertion failed.

Algorithmic complexity

measure time

1. tic toc
   tic; function(); toc

Elapsed time is 0.155401 seconds.

2. timeit
   t = timeit(@() function())

t = 0.1412

fibonacci

complexity (更多在演算法)

isequal

用來check function 是否相同

isequal(rooting_v3(v, w), rooting_v5(v, w))

efficiency

性能分析 (profile)

% 1. Turn off any existing profiling
profile off

% 2. Start profiling
profile on

% 3. Run the code
graph = {
    [2, 3],     % Neighbors of node 1
    [1, 3],     % Neighbors of node 2
    [1, 2, 4],  % Neighbors of node 3
    [3]         % Neighbors of node 4
};
result = max_clique(graph);

% 4. Stop profiling
profile off

% 5. View profiling report
profile viewer

減少同樣的code重複被執行 (多重迴圈)

第一個較好

preallocation

replace explicit looping

stop recursion

Vectorization

Any operator or function that operates on an entire vector or entire array is said to be a vector command

善用 logical indexing 的概念

rv = nthroot(v, 1:length(v));

for ii = 1:length(v)
    rv(ii) = nthroot(v(ii), ii);
end

example nthroot

repmat

Index Re-ordering

列儲存 column major
matlab儲存方式是列優先

example

version1

function A = not_preallocatable_v1(N)
% from COMPUTER PROGRAMMING WITH MATLAB, 3rd Edition, 2015
% by J. M. Fitzpatrick and A. Ledeczi
% Chapter 2, Section 4.9
ii = 0;
while rand > 1/N
   ii = ii + 1;
   for jj = 1:N
      A(ii,jj) = ii + jj^2;
   end
end

version2

function A = not_preallocatable_v2(N)
% from COMPUTER PROGRAMMING WITH MATLAB, 3rd Edition, 2015
% by J. M. Fitzpatrick and A. Ledeczi
% Chapter 2, Section 4.9
ii = 0;
while rand > 1/N
   ii = ii + 1;
   for jj = 1:N
      A(jj,ii) = ii + jj^2;
   end
end
A = A';
        

version2 比 version1 快很多，因為他是用列來儲存，雖然最後還要轉至矩陣

parfor

oop

struct

VeryCoolGuy = struct('name', [])