1. 응용 전산 및 실습 MATLAB – Chapter 3 행렬연산
위덕대학교 에너지전기공학부
이 성 환
Chapter 3
Uiduk University

2. MATLAB – Scripting M-File
REVIEW
MATLAB 메뉴의 File  New  M-File 선택
M-File Editor 가 실행되며 다음과 같이 화면에 나타남
원하는 MATLAB 명령어 입력 (명령어 입력 시 절대 한글을 사용하지 말 것!)
File  Save 를 선택하고 원하는 경로에 원하는 파일 이름으로 저장 (파일 이름에 절대 한글을 쓰지 말 것!)
Debug  Run 을 선택하여 생성한 M-File을 실행하면 MATLAB Command Window에 결과가 나타남
Chapter 3
Uiduk University

3. MATLAB – Enhancing M-File
REVIEW
Keyword / Function
Meaning
Example ;
Suppress output
radius = 5; %
Comment
radius = 5; % 반지름 값
disp(variable)
Display results without identifying variable names
disp(radius)
echo
Control the ‘Command Window’ echoing of script file commands
input
Prompt user for input
radius = input(‘반지름을 입력하세요> ‘);
pause
Pause until user presses any key
pause(n)
Pause for n seconds, then continue
pause(3)
fprintf(format, var1, var2,,,)
Print msg
fprintf(‘계산이 완료되었습니다.’);
fprintf(‘반지름은 %f 입니다.\n’, radius);
waitforbuttonpress
Pause until user presses mouse button or keyboard key
Chapter 3
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4. MATLAB – Array Definition MATLAB – Array Calculation
REVIEW
Keyword
Meaning
[ ]
배열의 시작과 끝 ;
행 구분 ,
열 구분
MATLAB – Array Calculation
Operation
Symbol
Example
Addition, a + b +
A + B
Subtraction, a – b -
A – B
Multiplication, a • b *
A * B
Division, a  b
/ or inv()
A / B = A * inv(B)
Exponentiation, ab ^
A ^ 2
Transposition, aT ‘ A’
Chapter 3
Uiduk University

5. MATLAB – Solving Linear Equations
REVIEW
EX6) Solving the following linear equations
>> A = [1, -1, 2; 3, 2, 9; 0, 1, -4]
A =
>> B = [10; 9; 3]
B = 10 9 3
>> x = inv(A) * B
x =
6.4783
Chapter 3
Uiduk University

6. MATLAB – Scalar and Array Operation
REVIEW
Element-By-Element Operation
Representative Data
Scalar Addition
Scalar Multiplication
Array Addition
Array Multiplication
Array Division
Array Exponentiation
Chapter 3
Uiduk University

7. MATLAB – Standard Arrays
REVIEW
Keyword
Description
ones(n)
ones(m, n)
Create n x n arrays containing all ones
Create m x n arrays containing all ones
zeros(n)
zeros(m, n)
Create n x n arrays containing all zeros
Create m x n arrays containing all zeros
eye(n, n)
eye(m, n)
Produce n x n identity matrices
Produce m x n identity matrices
rand(n)
rand(m, n)
Uniformly distributed n x n random arrays
Uniformly distributed m x n random arrays
randn(n)
randn(m, n)
Zero-mean, unit-variance normal distribution n x n, m x n random arrays
size(A)
Return row & column size
Chapter 3
Uiduk University

8. MATLAB – Easy Array Construction
Array Construction Technique
Description
x = [ 2, 2*pi, sqrt(5), 2-3j ]
Create row vector x containing element specified
x = first : last
Create row vector x starting with first, counting by one, ending at or before last
x = first : increment : last
Create row vector x starting with first, counting by increment, ending at or before last
x = linspace(first, last, n)
Create row vector x starting with first, ending at last, having n elements
x = logspace(first, last, n)
Create logarithmically-spaced row vector x starting with 10first, ending at 10last, having n elements
Chapter 3
Uiduk University

9. MATLAB – Easy Array Construction
EX1)
>> c = [1, 6, 9, 7]
c =
>> a = 1 : 5
a =
>> b = 1 : 2 : 7
b =
>> x = (0 : 0.1 : 0.3) * pi
x =
EX2)
>> d = [ 1:2:5, 1, 0, 1 ]
d =
>> a = 1 : 3, b = 1 : 2 : 7
a =
b =
>> c = [ b, a ]
c =
EX3)
>> x = linspace(2, 6, 3)
x =
>> x = logspace(0, 2, 11)
Chapter 3
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10. MATLAB – Complex Array’s Transpose Pitfall
>> d = a + i * a
d =
i i i
>> e = d’ % Complex conjugate transpose of d
e = i i i
>> f = d.’ % Dot transpose = Transpose of d i i i
Chapter 3
Uiduk University

11. MATLAB – Array Addressing
Description
A(r, c)
Indicates the elements by the r’th row and the c’th column
A(r, : )
Addresses a subarray within A defined by the index vector of desired rows in r and all columns
A( : , c)
Addresses a subarray within A defined by all rows and the index vector of desired columns in c
A( a : b , c : d)
Addresses a subarray within A intersected by the rows from a to b and the columns from c to d
Chapter 2
Uiduk University

12. MATLAB – Array Addressing
EX5)
>> A = [1, 2, 3; 4, 5, 6; 7, 8, 9]
A =
>> A(3, 3) = 0
>> A(2, 6) = 1 % extends array A
EX6)
>> A( : , 4) = 4
A =
>> B = A(1 : 2, 2 : 3)
B =
>> A( :, 2) = [ ] % removes 2nd column
Chapter 3
Uiduk University

13. MATLAB – Array Addressing
EX7)
>> A = [1, 2, 3; 4, 5, 6; 7, 8, 9]
A =
>> B = [1, 4, 7]
B =
>> A(2, : ) = B % substitutes 2nd row
Chapter 3
Uiduk University

14. MATLAB – Array Manipulation
Function
Description
rot90(A)
rot90(A, k)
Rotates vector A by 90 degrees
Rotates vector A by 90 degrees * k (k > 0 = ccw, k < 0 = cw)
flipud(A)
Flips array in up-down direction
fliplr(A)
Flips array in the left-right direction
triu(A)
Extracts upper triangular part
tril(A)
Extracts lower triangular part
diag(A)
Extracts diagonal elements
cross(A, B)
Outer product of A and B :
dot(A, B)
= sum(A.*B)
Inner product of A and B :
Chapter 3
Uiduk University

15. MATLAB – Array Manipulation
EX8)
>> A = [1, 2, 3; 4, 5, 6; 7, 8, 9]
A =
>> flipud(A)
ans =
>> fliplr(A)
EX9)
>> rot90(A)
ans =
>> diag(A) 1 5 9
>> diag(ans)
EX10)
>> triu(A)
ans =
>> A = [1, 2, 3];
>> B = [4, 5, 6];
>> dot(A, B) 32
>> cross(A, B)
Chapter 3
Uiduk University

16. MATLAB – Reading From Data File
<< mat.txt>> 파일의 내용
>> load mat.txt
>> t = mat( : , 1); % 시간 벡터
>> x = mat( : , 2); % 변위 벡터
>> v = mat( : , 3); % 속도 벡터
>> a = mat( : , 4); % 가속도 벡터
Chapter 3
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17. MATLAB – Multidimensional Arrays
>> A = zeros(2, 3) % start with a 2-D array
A =
>> A( : , : , 2) = ones(2, 3) % add a second page to go 3-D !
A( : , : , 1) =
A( : , : , 2) =
Chapter 3
Uiduk University