Matlab Chapter 3, with some basic skill., Slides of Computer Science

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Chapter 4 Loops

• The while Loop

• The for Loop

• Logical Arrays and Vectorization

• Additional Examples

4.1 The while Loop

• A while loop is a block of statement

– Repeating indefinitely as long as some

condition is satisfied.

while expression

end

Code block

while expr

end

pseudcode

A fatal (致命的) flaw (缺點)

• We did not completely test the program for

all possible types of inputs

– Division-by-zero error

4.2 The for Loop

• The for loop is a loop

– Executing a block of statements a specified number of

times.

for index = expr

Statement 1

Statement n

end

Body

index is the loop variable and expr is the loop control expression

expr = first:incr:last

for i = 1:10 Statement

… Statement n

end

for i = 1:2:10 Statement 1

… Statement n

end

i=10 i=

index is the loop variable and expr is the loop control expression expr = first:incr:last for i = 1: Stat eme nt 1 … Stat eme end^ nt n

for i = 1:2: Stat eme nt 1 … Stat eme end^ nt n

i=10 i=

for i = [5 9 7] Stat eme nt 1 … Stat eme end^ nt n

i=

for i = [1 2 3; 4 5 6] Statement 1 … Statement n end      =  6 i^3 Loop index can be a vector

Example 4.3—Calculating the Day of Year (Page 158)

• • ordinary years: 1~365leap years: 1~
  • – YearsYears evenly divisible by evenly divisible by 400100 are leap yearsbut not by 400 are not leap years
  • – All years divisible byAll other years are not leap years 4 but not by 100. are leap years
• Input – year, month, day
• Is leap year? – mod, if, elseif, else, end
• Compute day of year – for ii = 1:month- 1
  • switch (ii), case(1, 3, 5, 7, 8, 10, 12)

Detail of for operation

• • Indent the bodies of loopsDon’t modify the loop index within the body of a loop
• Preallocating arrays – arr = 1:4; %=[1 2 3 4]
  • – arr(8) = 6;When an array is extended %=[1 2 3 4 0 0 0 6]
    • • Create a new arrayCopy the contents of the old array to the new longer array
    • • Add the new value to the arrayDelete the old array
  • – Vary timeSolution -consuming for long arrays
• Vectorizing Arrays^ •^ Array is preallocated to its maximum size before the loop
• Vectorization^ –^ Vectorized more than^15 times faster than the^ for^ loop
  • Replacing loops by vectorized satements

for ii = 1:100 square(ii) = ii^2; square_root = ii^(1/2); cube_root(ii) = ii^(1/3); end ii = 1:100 square(ii) = ii.^2; square_root = ii.^(1/2); cube_root(ii) = ii.^(1/3);

300 separate lines of code

4 lines of code

The break and continue statements

• break
  • Terminates the execution of a loop
  • Passes control to the next statement after the end of the loop
• continue
  • Terminates the current pass through the loop
  • Returns control to the top of the loop

for ii = 1:5 if ii == 3; end^ break; end^ fprintf(‘ii = %d\n’, ii); disp([‘End of loop!’])

test_break ii = 1 ii = 2 End of loop!

for ii = 1:5 if ii == 3; end^ continue; end^ fprintf(‘ii = %d\n’, ii); disp([‘End of loop!’])

test_continue ii = 1 ii = 2 ii = 4 ii = 5 End of loop!

Nesting Loops

• If one loop is completely inside another one,

the two loops are called nested loops

for ii = 1:3 for jj = 1: product = ii * jj; fprintf(‘%d * %d = %d\n’, ii, jj, product); end^ end

test_nested_loops 1 * 1 = 1 1 * 2 = 2 1 * 3 = 3 2 * 1 = 2 2 * 2 = 4 2 * 3 = 6 3 * 1 = 3 3 * 2 = 6 3 * 3 = 9

4.3 Logical Arrays and Vectorization

• Logical arrays have a very important special property - They can serve as a mask for arithmetic operations - A mask is an array that selects the elements of another array for use in an operation. - The specified operation will be applied to the selected elements, and not to the remaining elements.

This is a very fast and very clever way

of performing an operation on a subset of an array

without needing loops and branches

for ii = 1:size(a,1) for jj = 1:size(a,2) if a(ii,jj) > 5; a(ii,jj) = sqrt(a(ii,jj)); end ;product = ii * jj; end^ ;fprintf(‘%d * %d = %d\n’, ii, jj, product); end

Vectorized approach is faster b = a > 5; a(b) = sqrt(a(b));