[SOLVED] 代写 math python COMP1730/COMP6730 Programming for Scientists

COMP1730/COMP6730 Programming for Scientists
Data: Values, types and expressions.

Lecture outline
* Data and data types.
* Expressions: computing values. * Variables: remembering values.

What is “data”?
* The number of students currently enrolled in the course.
* The words typed into a web search engine.
* A time series of total rainfall in Canberra for the month of June since 1971.
* An elevation map of Australia.
* Most (scientific) applications of computing involve summarising or deriving information from data.

Example: Data analysis
* In 2018, enrolment in COMP1730/6730, at its peak, was 530 students. In 2019, the enrolment (so far) is 483 students. How big a decrease, in percent, is this?
* The decrease is: 530 – 483
* as a fraction of the 2018 number:
(530 – 483) / 530 * in percent: ((530 – 483) / 530) * 100

Expressions
* ((530 – 483) / 530) * 100isan expression;
* it evaluates to 8.867924528301886;
* 483, 530, 100 and 8.867924528301886 are
all values.
* In interactive mode, the python interpreter will
print the result of evaluating an expression:
>>> ((530 – 483) / 530) * 100
8.867924528301886
(with one exception, which we’ll see later).

python syntax (recap)
* A python program is a sequence of statements: – import a module;
– function definition;
– function call expression.
– Every function call is an expression. – …and more we’ll see later.
* Comment: # to end-of-line. * Whitespace:
– end-of-line ends statement (except for function definition, which ends at the end of the suite);
– indentation defines extent of (function) suite.

python expressions
* Expressions are built up of: – constants (“literals”);
– variables;
– operators; and – function calls.
* When an expression is executed, it evaluates to a value (a.k.a. the return value).
* Expressions can act as statements (the return value is ignored), but statements cannot act as expressions.

Continuation
* end-of-line marks the end of a statement. * Except that,
– adding a “” at the end makes the statement continue onto the next line, e.g.,
(2 ** 0) + (2 ** 1) + (2 ** 2) + (2 ** 3) + (2 ** 4)
– an expression enclosed in parentheses continues to the closing parenthesis, e.g.,
math.sqrt((x2 – x1) ** 2 +
(y2 – y1) ** 2)

Values and Types

Every value has a type
* Value (data) types in python:
– Integers (type int)
– Floating-point numbers (type float) – Strings (type str)
– Truth values (type bool)
– …and many more we’ll see later.
* Types determine what we can do with values (and sometimes what the result is).

* The type function tells us the type of a value:
>>> type(2)

>>> type(2 / 3)

>>> type(“zero”)

>>> type(“1”)

>>> type(1 < 0)

Numeric types
* Integers (type int) represent positive and negative whole numbers (0, 1, 2, −1, −17, 4096, . . .).
* Values of type int have no inherent size limit.
>>> 2 ** (2 ** 2)
16
>>> 2 ** (2 ** (2 ** 2))
65536
>>> 2 ** (2 ** (2 ** (2 ** 2)))
…
* Note: Can’t use commas to “format” integers (must write 1282736, not 1,282,736).

* Floating-point numbers (type float) represent decimal numbers.
* Values of type float have limited range and limited precision.
– Min/max value: ±1.79 · 10308.
– Smallest non-zero value: 2.22 · 10−308. – Smallest value > 1: 1 + 2.22 · 10−16.
(These are typical limits; actual limits depend on
the python implementation.)
* Type float also has special values ± inf
(infinity) and nan (not a number).
* More about floating-point numbers and their
limitations in a coming lecture.

* Every decimal number is a float: >>> type(1.5 – 0.5)

>>> type(1.0)

* The result of division is always a float: >>> type(4 / 2)

* floats can be written (and are sometimes printed) in “scientific notation”:
– 2.99e8 means 2.99 · 108.
– 6.626e-34 means 6.626 · 10−34 – 1e308 means 1 · 10308.

Strings
* Strings (type str) represent text.
* A string literal is enclosed in single or double
quote marks:
>>> “Hello world”
’Hello world’
>>> ’4″ long’
’4″ long’
– A string can contain other types of quote mark, but not the one used to delimit it.
* More about strings in a coming lecture.

Type conversion
* Explicit conversions use the type name like a function:
>>> int(2.0)
>>> float(” -1.05″)
>>> str(0.75 * 1.75)
* Conversion from str to number only works if the string contains (only) a numeric literal.
* Conversion from int to float is automatic. – E.g., int times float becomes a float.

Expressions: Operators and Functions

Numeric operators in python
+, -, *, / **
// %
standard arithmetic
power (x ** n means xn) floor division
remainder
* Some operators can be applied also to values of other (non-numeric) types, but with a different meaning (this is called “operator overloading”).
* We’ll see more operators later in the course.

Precedence
* There is an order of precedence on operators, that determines how an expression is read:
– 2*3-1 means (2*3)-1, not 2*(3-1). – -1**5 means -(1**5), not (-1)**5.
* Operators with equal precedence associate left: – d/2*pi means (d/2)*pi, not d/(2*pi)
* …except exponentiation, which associates right.
* Whenever it is not obvious, use parentheses to make it clear.

Math functions
* The math module provides standard math functions, such as square root, logarithm, trigonometric functions, etc.
>>> import math
>>> help(math) # read documentation
…
>>> math.sqrt(3 ** 2 + 4 ** 2)
5.0
* Almost all math functions take and return values of type float.

Comparison operators
<, >, <=, >= ==
!=
ordering (strict and non-strict) equality (note double ’=’ sign) not equal
* Can compare two values of the same type (for almost any type).
* Comparisons return a truth value (type bool), which is either True or False.
* Caution: Conversion from any type to type bool happens automatically, but the result may not be what you expect.

Variables

Variables
* A variable is a name that is associated with a value in the program.
– The python interpreter stores name–value associations in a namespace.
(More about namespaces later in the course.)
* A variable can be an expression: evaluating it returns the associated value.
* A name–value association is created by the first assignment to the name.

Valid names in python (reminder)
* A (function or variable) name in python may contain letters, numbers and underscores ( ), but must begin with a letter or undescore.
* Reserved words cannot be used as names.
* Names are case sensitive: upper and lower case letters are not the same.
– Length Of Rope and length of rope are different names.

Variable assignment
* A variable assignment is written var name = expression
– Reminder: Equality is written == (two =’s). – Assignment is a statement.
* When executing an assignment, the interpreter 1. evaluates the right-hand side expression;
2. associates the left-hand side name with the
resulting value.

Programming problem
* Triangulation: Given the distance AB (the baseline) and the angles to a common landmark C, calculate a new baseline
BC=AB sinα sin(α + β)
E
Cεφ γ
δ
β
B
D
α
A

The print function
* print prints text to the console:
>>> print(“The answer is:”, 42)
The answer is: 42
– Non-text arguments are converted to type str before printing.
– print takes a variable number of arguments, and prints them all followed by a newline.
* Print the result, and intermediate steps, when a program is run in script mode.