matlab 及其工程应用 matlab and it’s engineering application 主讲教师： 胡章芳...
TRANSCRIPT
补充 : X1:inc:x2 linspace(x1,x2,N) generates N points
between x1 and x2 x = linspace(10,20,5)
x = 10.00 12.50 15.00 17.50 20.00
logspace(x1,x2) can be used for logarithmically equally spaced points
Top-down Program Design ＆ Relational and Logical Operators
CHAPTER 3BranchingStatements
And Program Design
Abstract
Sequential programs: Branches: if, switch, try/catch Loops: Top-down Program Design Relational and Logical Operators
3.1 Top-down design concept
Top-down design is the process of starting with a large task and breaking it down into smaller, more easily understandable pieces (subtasks), which perform a portion of the desired task. Each subtask may in turn be subdivided into smaller subtasks if necessary. Once the program is divided into small pieces, each piece can be coded and tested independently. We do not attempt to combine the subtasks into a complete task until each of the subtasks has been verified to work properly by itself.
Top-down Program Design process program
StartState theproblem
Define inputsand outputs
Design thealgorithm
Convert algorithminto MATLABstatements
Test theresulting program
End
Decomposition
Stepwiserefinement
steps
1.Clearly state the problem that you are trying to solve
2.Define the inputs required by the program and the outputs to be produced by the program
3.Design the algorithm that you intend to implement in the program
4.Turn the algorithm into MATLAB statement 5.Test the resulting MATLAB program
1/3 time
1/6 time
1/2 time
Testing
Test individual subtasks: unit testing Add tested components one by one and
test them together: build Alpha release: Beta release Test for all legal input data sets: standard
data sets, ground truth
A typical testing process for a large program
Start
Unit testing of individual subtasks
Successive builds(adding subtasks to the program)
Alpha release
Beta release
Minor bugs fixedFinished program
As many times as necessary
As many times as necessary
As many times as necessary
Subtasks validated separately
Subtasks combined into a single program
Worst bugs fixed
3.2 Use of Pseudocode
A hybrid mixture of MATLAB and English for defining algorithms
Independent of any programming language so it can be easily converted to any programming language
example 1 Problem: write a program that takes the
radius and height (in meters) of a cylinder tank and the amount of water (in m3) from the user and output the amount of extra space (in m3) in the tank.
Input: radius and height amount of water
Output: extra space
example 1 Design:
1. Get radius of the tank base from the user2. Get the height of the tank from the user3. Get the amount of water4. Calculate the amount of extra space5. Write the result
Step 4 is not clear enough, refine it: Calculate the capacity of the tank
(pi * radius^2 * h) extra space capacity - water
example 1 Code:
r = input('Enter the radius of the tank base:');h = input('Enter the height of the tank:');water = input('Enter the amount of water:');capacity = pi * r^2 * h;space = capacity - water;fprintf('There is %f m3 extra space in the tank', space);
example 1
Testing:Enter the radius of the tank base:2
Enter the height of the tank:5
Enter the amount of water:10
There is 52.831853 m3 extra space in the tank
Continue testing:Enter the radius of the tank base:2
Enter the height of the tank:5
Enter the amount of water:100
There is -37.168147 m3 extra space in the tank
3.3 Relational and Logical Operators3.3.1 Relational Operators
Relational operators are used to represent conditions (such as “space 0” in the water tank example)
Result of the condition is either true or false In MATLAB:
false is represented by 0 true is represented by 1 (non-zero)
The general form:
a1 op a2 a1 and a2 are: arithmetic expressions ,variables, or
strings
Op: in table 3.1(==,~=,>,>=,<,<=)
If the relationship between a1 and a2 expressed by the operator is true, then the operation returns a value of 1;
Otherwise, the operation returns a value of 0
Operation Result
3 < 4 1
3 <= 4 1
3 == 4 0
3 ~= 4 1
3 > 4 0
4 >= 4 1
‘A’ < ‘B’ 1
Scalar and array: a=[1 0;-2,1], b=0,a>b Two array a=[1 0;-2,1], b=[0 2;-2 -1],a>=b Evaluated after all arithmetic 7+3<2+11 (7+3)<(2+11)
3.3.2 Relational Operators ==and ~=
Don’t confuse equivalence (==) with assignment (=)
Relational operations have lower priority than arithmetic operations (use parentheses to be safe)
Be careful about round off errors during numeric comparisons.
Example: a=0; b=sin(pi) a==b abs(a-b)<1.0e-14 (you can represent “x == y” as “abs(x-y) < 1.0
e-14”)
3.3.3 Logical Operators
More complex conditions can be represented by combining relational operations using logic operators
l1 op l2 Logical operators:
& AND| ORxor Exclusive OR~ NOT
Logical Operators
input and or xor not
a b a & b a | b xor(a,b) ~a
0 0 0 0 0 1
0 1 0 1 1 1
1 0 0 1 1 0
1 1 1 1 0 0
Scalar and array: a=[1 0; 0,1], b=0,a&b Two array a=[1 0; 0,1], b=[1 1; 0 0],a|b
Operator Hierarchy
Processing order of operations: 1.parenthesis (starting from the innermost) 2.exponentials (left to right) 3.multiplications and divisions (left to right) 4.additions and subtractions (left to right) 5.relational operators (left to right) 6.~ operators 7.& operators (left to right) 8.| operators (left to right)
example 2 Assume that the following variables are initialized with the valu
es shown, and calculate the result of the specified expressions,
value1=1, value2=0, value3=-10
3.3.4 Logical Functions
Table 3.4 ischar(a) isempty(a) isinf(a) isnan(a) isnumeric(a)
…… Quiz 3.1
3.4 Branches
Branches are used to select and execute specific sections of the code while skipping other sections
Selection of different sections depend on a condition statement
We will learn: if statement switch statement
3.4.1-1 Branches: “if” Statement
if ( condition ),statement 1
statement 2
...
end
condition
statementgroup
true
false
statement
group
if
end
Example 1 Examples:
if ( r <= 0 ), disp( [ ‘Radius must be positive’ ] );end
if ( ( grade < 0 ) | ( grade > 100 ) ), disp( [ ‘Grade must be in [0,100] range’ ] );end
if isinf( result ), disp( ‘Result is infinite’ );end
Example 2 Water tank example:
r = input('Enter the radius of the tank base (in meters):');if ( r <= 0 ), error( ‘Radius must be positive' );endh = input('Enter the height of the tank (in meters):');if ( h <= 0 ), error( ‘Height must be positive' );endw = input('Enter the amount of water (in m3):');if ( w <= 0 ), error( ‘Amount of water must be positive' );endcapacity = pi * r^2 * h;space = capacity - w;if ( space > 0 ), disp( [ 'There is ' num2str(space) ' m3 extra space' ] );
else disp( 'Tank is full' );end
3.4.1-2 Branches: “if-else” Statement
if ( condition ),statement 1statement 2...
elsestatement 1statement 2...
end
condition
statementgroup 1
true false
statementgroup 2
statement
group 1
statement
group 2
if
end
3.4.1-3 Branches: “if-elseif-else” Statement
if ( condition 1 ),statement 1statement 2...
elseif ( condition 2 ),statement 1statement 2...
elsestatement 1statement 2...
end
statement
group 1
condition1
statementgroup 1
true false
condition2
statementgroup 2
statementgroup 3
true
false stateme
ntgroup 2
statement
group 3
if
end
Branching Example 3.2 Example: Finding roots of the quadratic eq
uation “ax2 + bx + c = 0” Pseudocode:
d = b2 – 4ac if d > 0,
two real rootselseif d == 0, two identical rootselse two complex roots
Branching Examples% Prompt the user for the coefficients of the equation
disp ('This program solves for the roots of a quadratic ');
disp ('equation of the form A*X^2 + B*X + C = 0. ');
a = input ('Enter the coefficient A: ');b = input ('Enter the coefficient B: ');c = input ('Enter the coefficient C: ');% Calculate discriminantdiscriminant = b^2 - 4 * a * c;% Solve for the roots, depending on the value of the discriminant
if discriminant > 0 % there are two real roots, so... x1 = ( -b + sqrt(discriminant) ) / ( 2 * a ); x2 = ( -b - sqrt(discriminant) ) / ( 2 * a ); disp ('This equation has two real roots:'); fprintf ('x1 = %f\n', x1); fprintf ('x2 = %f\n', x2);elseif discriminant == 0 % there is one repeated ro
ot, so... x1 = ( -b ) / ( 2 * a ); disp ('This equation has two identical real root
s:'); fprintf ('x1 = x2 = %f\n', x1);else % there are complex roots, so ... real_part = ( -b ) / ( 2 * a ); imag_part = sqrt ( abs ( discriminant ) ) / ( 2 *
a ); disp ('This equation has complex roots:'); fprintf('x1 = %f +i %f\n', real_part, imag_part ); fprintf('x2 = %f -i %f\n', real_part, imag_part );end
Branching Examples Example: Assigning letter grades
How can we compute the letter corresponding to a given numeric grade?
Range Grade
100 grade > 95 A
95 grade > 86 B
86 grade > 76 C
76 grade > 66 D
66 grade > 0 F
Branching Examples Letter grade example:grade= input ('Enter the value of grade:');
if ( grade > 95 ), disp( ‘Grade is A’ );elseif ( grade > 86 ), disp( ‘Grade is B’ );elseif ( grade > 76 ), disp( ‘Grade is C’ );elseif ( grade > 66 ), disp( ‘Grade is D’ );else disp( ‘Grade is F’ );end
Branching Examplesif ( grade > 95 ), disp( ‘Grade is A’ );else if ( grade > 86 ), disp( ‘Grade is B’ ); else if ( grade > 76 ), disp( ‘Grade is C’ ); else if ( grade > 66 ), disp( ‘Grade is D’ ); else disp( ‘Grade is F’ ); end end endend
nested if statements
Example 3.3 -----Evaluating a Function of Tow Variable
22
2
2
),(
yx
yx
yx
yx
yxf
0
0
0
0
x
x
x
x
0
0
0
0
y
y
y
yand
and
and
and
3.4.4 “switch” Statementswitch ( expression ),case value 1, statement 1 statement 2 ...case value 2, statement 1 statement 2 ......end
statement
group 1
statement
group 2
expression is a scalar or string constant
Branches: “switch” Statementswitch ( expression ),case {value set 1}, statement 1 statement 2 ...case {value set 2}, statement 1 statement 2 ......otherwise, statement 1 statement 2 ...end
statement
group 1
statement
group 2
optional statement group that is executed if none of the cases is satisfied
Branching Examples Example: Odd or even numbers value=input('please enter the value:') switch (value), case {1,3,5,7,9}, disp( 'Odd number' ); case {2,4,6,8,10}, disp('Even number'); otherwise, disp('Out of range'); end
Branches: “try/catch” Statementtry statement 1 statement 2 ...catch statement 1 statement 2 ...end
Try Block
Catch Block
a=[1 2 3;4 5 6];
b=[7 8 9;10 11 12];
try
c=a*b
catch
d=a.*b
end
Branching Examples Example:% Initialize arraya=[1 -3 2 5];try %Try to display an element index=input('Enter subscript of element todisplay: '); disp( [ 'a(' int2str(index) ')=' num2str(a(index)) ] );catch %If we get here an error occurred disp(['Illegal subscript: ' int2str(index)]);end
Quiz 3.2
3.7 Summary
Top-down Program Design Basic types of MATLAB branches (if, switch,
try/catch) Relational and Logical Operators Additional information about plots(axis,hold s
ubplot) Control additional characteristics pf plots(bold
face,italic,superscripts,font size,font name)
3.7.1 Summary of good programming practice
1.round off 2.Follow the steps of the program design
process 3.If and switch constructs
3.7.1 MATLAB summary axis figure hold if ischar isempty iIsnan isnumeric polar subplot switch try/catch construct
Exercises
3.1 3.2 3.3 3.4 3.5 3.11 3.12
