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EECS 1541 -- Introduction to Computing for the Physical Sciences

Constants

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• Recall that variables are used to store values that might change

• Constants are values that cannot be changed at any time. Some constants that are pre-defined in MATLAB are:

EECS 1541 -- Introduction to Computing for the Physical Sciences

Constants

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• What will be the final answer of the following expression?

EECS 1541 -- Introduction to Computing for the Physical Sciences

>> 2 * pi + - + pi

ans =

3.1416

Random numbers

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• Several built-in functions in MATLAB to generate random numbers such as:

• The simplest built-in random function is “rand”

EECS 1541 -- Introduction to Computing for the Physical Sciences

rand - generate a random number between 0 and 1.

randi(max) - generate a random integer: 1 ≤ x ≤ max.

randi([min,max]) - generate a random integer: min ≤ x ≤ max.

 returns an n-by-n matrix of pseudorandom normal values

Random numbers

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• Example:

• Note that there is no input argument required for the “rand” function

>> rand

ans =

0.8715

• Since “rand” returns a random real number between 0 and 1, how do we generate a random integer greater than or equal to 0 but less than 10 (i.e. 0 ≤ x < 10)?

EECS 1541 -- Introduction to Computing for the Physical Sciences

Rounding functions

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• Rounding functions:

fix - Round towards zero.

floor - Round towards minus infinity.

ceil - Round towards plus infinity.

round - Round towards nearest integer.

EECS 1541 -- Introduction to Computing for the Physical Sciences

• Example: >> fix(3.1415)

ans =

3

• Example: >> floor(-3.1415)

ans =

- 4

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Rounding functions

EECS 1541 -- Introduction to Computing for the Physical Sciences

• Example: >> ceil(3.1415)

ans =

4

• Example: >> round(-3.1415)

ans =

- 3

• Rounding functions:

fix - Round towards zero.

floor - Round towards minus infinity.

ceil - Round towards plus infinity.

round - Round towards nearest integer.

Random numbers

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• Recall: how do we generate a random integer greater than or equal to 0 but less than 10 (i.e. 0 ≤ x < 10)?

>> fix(rand*10)

• One method: We can combine the “fix” and “rand” functions

rand*10 gives a random number between 0 and 10

fix rounds “down” the random number to an integer

EECS 1541 -- Introduction to Computing for the Physical Sciences

Relational Expressions

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• Expressions that are conceptually either true or false are called relational expressions, or Boolean or logical expressions

• “true” is represented by the logical value 1, and “false” is represented by the logical value 0

EECS 1541 -- Introduction to Computing for the Physical Sciences

Relational Expressions: relational operators

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• The relational operators in MATLAB are:

Operator name

> greater than

>= greater than or equal to

< less than

<= less than or equal to

== equal to

~= not equal to

EECS 1541 -- Introduction to Computing for the Physical Sciences

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• Example:

Relational Expressions: relational operators

• Example:

>> 10 < 8 - 5

ans =

EECS 1541 -- Introduction to Computing for the Physical Sciences

>> (10 < 8) - 5

ans =

-5

0

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• Example:

Relational Expressions: relational operators

>> 9 > 8 > 7 > 6

ans =

EECS 1541 -- Introduction to Computing for the Physical Sciences

0

Relational Expressions

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• Comparing characters (e.g. a, b, c) is also possible. Characters are compared using their ASCII equivalent value

EECS 1541 -- Introduction to Computing for the Physical Sciences

• Example: >> ‘a’ < ‘d’

ans =

1

Relational Expressions: logical operators

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• The logical operators in MATLAB are:

Operator name

|| or

&& and

~ not

• The “or” logical operator will output a true value if either or both of the operands are true.

• The “and” logical operator will output a true value only if both of the operands are true.

EECS 1541 -- Introduction to Computing for the Physical Sciences

Relational Expressions: logical operators

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• The || and && operators in MATLAB are also known as short-circuit operators.

• This means that if the result of the expression can be determined from the first part, then the second part will not even be evaluated.

EECS 1541 -- Introduction to Computing for the Physical Sciences

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• Example: >> 3 < 8 || 3 > 8

ans =

Relational Expressions: logical operators

• Example: >> 10 < 8 - 5 && 3 < 8

ans =

1

0

EECS 1541 -- Introduction to Computing for the Physical Sciences

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• Example: >> (10 < 8) -5 || 3 > 8

ans =

Relational Expressions: logical operators

• Example: >> ‘b’ < ‘c’ - 1 && 3 < 8

ans =

1

0

EECS 1541 -- Introduction to Computing for the Physical Sciences

Relational Expressions: logical operators

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• Summary: Truth Table for logical operators:

x y ~x x || y x && y

True True False True True

True False False True False

false false true false False

EECS 1541 -- Introduction to Computing for the Physical Sciences

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• One of the popular built-in functions in MATLAB is the “plot” function:

Built-in Functions: Plotting functions

>> help plot

• Plotting 2-D or 3-D graphs is a powerful function provided in MATLAB.

EECS 1541 -- Introduction to Computing for the Physical Sciences

• We will look into more details about plotting graphs in MATLAB in Chapter 3 and Lab #2.