Matlab作业1

Matlab Worksheet 1

Part A

1. Get into Matlab: Use the diary command to record your activity in to a file: diary mydiary01.doc before you start your work. (And diary off to switch off your diary when you finish your work.)

At the Command Window assign a v alue x=10, then use the Up Key ↑ to repeat the expression, editing it to show the effect of using a semicolon （分号） after the 10, namely x=10;

Answers:

2. Confirm whether the following names of variables are acceptable: a) Velocity Yes No

b) Velocity1 Yes No

c) Velocity.1 Yes No

d) Velocity_1 Yes No

e) Velocity-01 Yes No

f) velocityONE Yes No

g) 1velocity Yes No

3. Assign two scalar variables （标量） x and y values x=1.5, y=2.3, then construct Matlab expressions for the following: a) y x y x z +=35 b) ()3/27y x z = c) ()

y e x x z 25106

/111log -???????+-= d) )2cos()2sin(x e y x z x ππ+-=

Answers:

4. Assign two variables with complex values u=2+3j and v=4+10j and then construct expression for:

a) v

u b) j uv 2+ c) j u 2 d) u j ve π2- Answers:

5. Use the colon operator : to assign numerical values between 0 and 1 to vector array variable a in steps of 0.1.

Answer: x=0:0.1:1

https://www.360docs.net/doc/ad17587527.html,e linspace function to assign 20 values to vector variable y between 20 and 30. Answer: x=linspace(20,30,20)

7.Assign 20 values to a variable h increasing logarithmically（用对数） between 10

and 1000.

Next, use the colon operator to assign the first 10 elements of h to a variable p. Answers: h=log10(linspace(10,1000,20))

p=h(1:10)

8.Create 6 element row vector z with values 1.0 1.2 1.6 -1.7 1.8 1.9, then construct

an expression for the sum of the 2nd 4th and 6th elements of z.

Answers: v=[1.0 1.2 1.6 -1.7 1.8 1.9];

u=[0;0;0;1;0;1];

z=v*u

https://www.360docs.net/doc/ad17587527.html,e the colon operator to create a vector array x between 10 and -10in steps of -1,

and second, an array vector y between 20 and -20 in steps -2 .

a)Add x and y, b) subtract 10x from 5y.（5y-10x）

Answers: x=-10:1:10;

y=-20:2:20;

z1=x+y

z2=5*y-10*x

https://www.360docs.net/doc/ad17587527.html,e the size,length, who and whos commands to establish the size and length of x

and y from Question 9, and use transpose operator ’ to convert vector x from

Question 9.

Answers: x=-10:1:10;

y=-20:2:20;

z1=x+y

z2=5*y-10*x

size(x)

length(x)

who

whos

x'

11.Show that if w=[ 2i 3i 3+i] the .’ operator creates the transpose. What effect does the

operator ’ applied to w have on its own?

Answer: w=[ 2i 3i 3+i]

w'

w.'

w =

0 + 2.0000i 0 + 3.0000i 3.0000 + 1.0000i

ans =

0 - 2.0000i

0 - 3.0000i

3.0000 - 1.0000i

ans =

0 + 2.0000i

0 + 3.0000i

3.0000 + 1.0000i

https://www.360docs.net/doc/ad17587527.html,e the ones function to create a 4 by 6 array of 1’s. Considering just the sha pe of

the resulting array, what do the expression ones(3), ones(5) and ones(7) all have in common?

Answer: ones(4,6)

ones(3)

ones(5)

ones(7)

Ones（3） is 3 by 3

Ones (5) is 5 by 5

13.Create using the rand function a 5 by 4 random matrix and assign it to matrix array

variable A and observe carefully what A(:,3) A(1:2) and A(3,[2 4]) mean.

Answer:

A=rand([5,4])

A(:,3) %提取第三列元素

A(1:2) %提取第一行前两个元素

A(3,[2 4]) %提取第三行第二第四个元素

A =

0.6787 0.1712 0.0971 0.0344

0.7577 0.7060 0.8235 0.4387

0.7431 0.0318 0.6948 0.3816

0.3922 0.2769 0.3171 0.7655

0.6555 0.0462 0.9502 0.7952

ans =

0.0971

0.8235

0.6948

0.3171

0.9502

ans =

0.6787 0.7577

ans =

0.0318 0.3816

https://www.360docs.net/doc/ad17587527.html,ing array subscripts, create an expression for the sum of the element in the top

right-hand-corner（右上角） of A and the bottom left-hand-corner of A（左下

角）. Also assign the 2nd column（列） of A to a column vector b, and assign the 3rd row of A to a row vector d（行）.

Answer: A=rand([5,4])

A(1,4)+A(5,1)

b=A(:,2)

d=A(3,:)

>>diary off to switch off your diary now.

15. Using the colon operator, assign a row vector array t, values between 0 and 10 in steps of 0.01. Use the ; operator to prevent displaying the information. Obtain the term-by-term values of functions:

a) t e z 05.0-= b) )sin(05.0t e z t π-= c) )2cos()sin(05.0t t e z t ππ-=

Answers:

t=0:0.01:10; z=exp(-0.05 *t)

t=0:0.01:10; z=exp(-0.05 *t) .*sin(pi*t)

t=0:0.01:10; z=exp(-0.05 *t) .*sin(pi*t).*cos(2*pi*t)

16. For Question 15 c), use the plot function to plot the value z against t. And use xlabel and ylabel to label the t axis ‘time’ and z axis ‘Response’ and use title to give your figure a title. Copy the figure into your mydiary01.doc (from the figure edit menu, select copy, then open mydiary01.doc and paste in the figure as an object).

Answers:

t=0:0.01:10;

z=exp(-0.05 *t) .*sin(pi*t).*cos(2*pi*t);

plot(t,z);

xlabel('time');

ylabel('reponse');

title('time and reponse');

Part B

1.Create a new Script m-file, called myfirst.m, to assign values to three vector arrays

a, b, and c; add each component together and assign to array d, where

A=[ 1, 2, 3], b=[4 5 6], c=[7 8 9]. Run myfirst.m. Examine the variable values in

the WorkSpace . Edit myfirst.m to change variable b to b=[10 20 30]. Re-run myfirst.m

Answers:

A=[ 1, 2, 3];

b=[4 5 6] ;

c=[7 8 9];

A+b+c

2.Create a function m-file, called myfun.m, that accepts two arrays x and y as

arguments（自变量）, and produces the sum of x and y, and gives as the function output, the maximum of x+y.

Answer: function[A]=myfun(x,y)

sum=x+y;

A=max(sum);

end

3.Modify your script m-file myfirst.m by calling in it myfun.m twice, namely with a

and b as parameters in the argument list, and second with parameters b and c. Run myfirst.mand afterwards. Examine the WorkSpace variable values.

Answers:

a=[1 2 3];

b=[4 5 6] ;

c=[7 8 9];

A1=myfun(a,b)

A=myfun(b,c)

4. Modify your script m-file myfirst.m by introducing variables A and B. Assign

scalar values A=1, B=2. Declare A and B as global variables both in myfirst.m and myfun.m. Modify myfun.m by adding A and B to the maximum value of x+y.

Answers:

global A;

global B;

A=1;

B=2;

a=[1 2 3];

b=[4 5 6] ;

c=[7 8 9];

A1=myfun(a,b)

A2=myfun(b,c)

function[S]=myfun(x,y)

global A;

global B;

sum=x+y+A+B;

S=max(sum);

end

5.Create a script m-file and, using a pair of nested（嵌套的）for loops, assign to a

5 by 5 matrix array A, values equal to the sum of the subscripts（下标之和）.

Ensure that the array is first cleared before the loops and afterwards display the array values. Run the m-file.

Answer:

for i=1:5

for j=1:5

A(i,j)=i+j;

end

end

A

6.Relational Operators:- Assign variables x=1 and y=2, then examine the values of

the expressions:

a)x>y, b)xy)*(x==y)?

Answer:

x=1;

y=2;

x>y

x

x==y

z=(x>y)*(x==y)

7. While loop:- Create a script m-file, and using a ‘while loop’, generate the partial sum for the series: ...31211+++π

ππ which stops adding-on terms when they are less than 1e-6 times the total sum.

Answer:

s=0;

n=1;

while s*n*pi<10^6

s=s+1/(n*pi);

n=n+1;

end

s

n

注意括号！！！

8. While loop:- Use a ‘while loop’ to keep adding array A to itself until just one of

the elements in A is greater than, but not equal to 40 where, initially ??

????=4321A .

Answer:

A=[1 2; 3 4];

sum_A=zeros(2);

while sum_A <= 40 *ones(2);

sum_A=sum_A+A;

end ;

sum_A

9. If statements:- Create a function m-file that receives variable x and y as arguments, then uses an ‘if’ statement internally （内在的） to execute the condition that: ‘if x is greater than y the function takes the value x, otherwise it takes the value y’. Test it on 2 numbers x=1 and y=1.

Answer: function [S]=myfun(x,y)

if x>y

S=x;

else

S=y;

end

10.If statements:- Create a function m-file that receives variable x, y and z as

arguments, then uses an ‘if elseif and else’ statements, generate the output va lue to be =x if first of all x>1, otherwise =y if y>10, otherwise =z if z>20, otherwise =1 if none of those conditions hold. Test it on values (100,100,100) and (0, 0,0).

Answer:

function [ m ] = Untitled8(x,y,z)

%UNTITLED8 Summary of this function goes here

% Detailed explanation goes here

function[m]=xym(x,y,z)

if x>1

m=x;

else if y>10

m=y;

else if z>20

m=z;

else

m=1;

end

end

end

end

ans =

100

ans =

1

11.Switch Statement:- Create a function with one input argument x to test whether the

expression: real(x^2) is equal to 0,1, or -1, which then displays a string stating appr opriately whether: ‘x is equal to zero’, ‘x is equal to +1 or -1’ or ‘x is equal to +j or –j’; otherwise display ‘test failed’. Test your m-file on three values: x=0, x=10 and x=j (1

=

j).

-

Answer:

switch x^2

case 0

disp('x is equal to zero');

case 1

disp('x is equal to +1 or -1');

case -1

disp('x is equal to +j or -j');

otherwise

disp('test failed');

end

x is equal to zero

test failed

x is equal to +j or –j

12. Polynomials:- Create a script m-file to generate the 5th degree polynomial （多项式）: 104322345+++++x x x x x and find all the roots. Use the plot function to plot the polynomial between x=-2 and x=2. Give the plot a title ‘A 5th degree polynomial for different domains’.

Answer:

p=[1,2,3,4,1,10];

y=roots(p)

x=-2:0.01:2;

plot(x,x.^5+2*x.^4+3*x.^3+4*x.^2+5*x+10,'r');

title('A 5th degree polynomial for different domains'); y =

-2.0000

-0.6566 + 1.6409i

-0.6566 - 1.6409i

0.6566 + 1.0815i

0.6566 - 1.0815i

A 5th degree polynomial for different domains

矩阵

Length 个数

Sort排序

C’转置

Size 显示几行几列

Ones

Zeros

Eye

Diag 矩阵对角元素提取

.*矩阵对应元素相乘

matlab里~=是不等于的意思。

matlab关系符号：

>（大于），>=（大于等于），<（小于），<=（小于等于）， ==（等于）~=（不等于）matlab逻辑符号：

&（与），|（或），~（非）， xor（异或）

save

名字只能以字母开头，或包括字母数字下划线

log(x) x的自然对数

log2(x) x的以2为底的对数

log10(x) x的以10为底的对数

复数直接用j表示

p=[1,2,3,4,1,10];

y=roots(p)

roots求根