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"E296 学生教程文件"是一个针对E296课程的学生们提供的教学资源压缩包，其中包含了一系列与学习相关的材料。这个压缩包的主要目标是辅助学生理解和掌握特定的知识点，可能是一个课程项目或者实验指导。 "Tutorial Files for E296 Students.zip"这个名字暗示了这是一组专为E296课程设计的教程文件，可能包含了课件、代码示例、练习题和解答等，旨在帮助学生深入学习课程内容。这个压缩包可能包含了逐步的教学步骤，以便学生们按照指示操作，从而提升他们的编程技能和理论理解。 "matlab"表明这个压缩包的核心内容与MATLAB软件有关。MATLAB是一款广泛应用于工程、科学计算和数据分析的高级编程环境。它支持矩阵和数组运算，是处理数值计算、符号计算、数据可视化、图像处理以及算法开发的理想工具。在E296课程中，MATLAB可能被用来教授科学计算方法、信号处理、控制系统或其他相关主题。【压缩包子文件的文件名称列表】： 1. "MATLABTutorial1_student-master"：这看起来是一个MATLAB教程的第一部分，可能是为学生定制的。"master"可能指的是主分支或完整版，意味着这是整个教程系列的基础部分。这个文件夹可能包括了源代码、解释文档、练习和解决方案，旨在引导学生熟悉MATLAB的基本语法和常用功能。 2. "新建文件夹"：这个文件夹的名字没有具体说明，但通常意味着它可能包含了未命名或新增的教程内容。这可能包含了与MATLAB教程相关的其他材料，如额外的练习、案例研究、扩展话题或是项目文件。 E296课程的学生可以通过这个压缩包学习如何使用MATLAB进行各种计算任务。他们将从MATLABTutorial1_student-master开始，逐步了解和实践MATLAB的基本操作，然后通过"新建文件夹"中的内容进一步深化理解，可能涉及更复杂的概念或实际应用。整个过程旨在提高学生的编程技能，并使他们能够在MATLAB环境中解决实际问题。

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Tutorial Files for E296 Studnets.zip （7个子文件）

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新建文件夹

E296MA

Dr. Gabriel Gomez

GSI Spencer Frank

Fall 2017

MATLAB Tutorial 1 - Solving Linear Systems, Plotting

and Visualization, and Objects

MATLAB is a user-friendly computational tool used throughout academia and industry.

It has countless powerful toolboxes, and allows the user to quickly write code to expedite

mathematical computation. The advantage of MATLAB over other scientiﬁc computing

software, such as Python, is the ease of use. For example, almost all the necessary software

packages are built into MATLAB and rarely does the user need to load particular packages.

This make computation fast and easy.

In this tutorial, we will go over:

1. Importing Data

2. Visualization (2D and 3D)

3. Curve ﬁtting

4. Solving linear systems

5. Object Oriented Programming

Download Tutorial from gitHub

1. Create a github account at github.com

2. search for spencerf/MATLABtutorial1

3. clone (or fork) the gitHub repository to your local folder

4. Open MATLABTutorial1.pdf

1 Data Import, Visualization, Curve Fitting

1.1 Data Import and Visualization

Import data from the internet by pasting the following into Matlab:

api = ’ http : / / cli ma te da ta ap i . worldbank . org / climateweb / r e s t /v1/ ’ ;

u r l = [ a p i ’ country / cru / t as / year /USA ’ ] ;

S = webread ( u r l ) ;

This will load a structured array S with information about the year and the temperature

data. This data can be extracted with the following syntax

ye a rs = [ S . yea r ] ;

temps = [ S . data ] ;

temps = 9/5 ∗ temps + 3 2 ; %Convert to Fahre n h e i t

y e a r s t o p l o t = datetime ( years , 1 , 1 ) ; %Convert year s t o ’ datetime ’

Note that the brackets are necessary with this type of structured array. Without the brackets

you will only access the last data entry. The last two lines convert the temperature data to

Fahrenheit and convert the year data to a standard datetime format that can be directly

read by MATLAB.

To plot the data

%P lo t data

fi gure

plot ( y e a r s t o p l o t , temps , ’ ok ’ ) ;

t i t l e ( ’USA Average Temperature 1901−2012 ’ )

xlabel ( ’ Year ’ )

ylabel ( ’ Temperature (ˆ{\ c i r c }F) ’ )

xmin = y e a r s t o p l o t ( 1 ) ;

xmax = y e a r s t o p l o t (end ) ;

xlim ( [ xmin xmax ] )

1920 1940 1960 1980 2000

Year

42.5

43.5

44.5

45.5

46.5

Temperature (

USA Average Temperature 1901-2012

1.2 Split Data into Training and Test Set

In order to text the prediction capabilities of a model, it is important to segment out two

sets of data. The training data consists of the data that we will use to ‘train’ our model.

This is the data that we will ﬁt a curve too. The other set of data is called the ‘test’ data.

This dataset is used to evaluate the predictive capability of our trained model.

In our case we will split the data at the year 1990; everything before 1990 will be considered

‘training’ data, and everything after 1990 will be considered ‘test’ data. You can use the

following code to segment the test and training data.

%% S p l i t data i n t o t r a i n i n g s e t and t e s t s e t

y e a r f o r t r a i n t e s t =1990;

i n d i c e s t r a i n=years<=y e a r f o r t r a i n t e s t ;

y e a r s t r a i n = y ea r s ( i n d i c e s t r a i n ) ;

te m ps tr a in = temps ( i n d i c e s t r a i n ) ;

y e a r s t o p l o t t r a i n=y e a r s t o p l o t ( i n d i c e s t r a i n ) ;

i n d i c e s t e s t=years >y e a r f o r t r a i n t e s t ;

y e a r s t e s t = ye a rs ( i n d i c e s t e s t ) ;

te mp s t e st = temps ( i n d i c e s t e s t ) ;

y e a r s t o p l o t t e s t=y e a r s t o p l o t ( i n d i c e s t e s t ) ;

1.3 Curve Fitting on Training Data

Now, we will ﬁt a model to our training data. We will use diﬀerent degree polynomials. The

simplest polynomial is a line, i.e. y=mx+b. To ﬁt a line to our data we can use the following

code:

%F i t 1−d eg re e p o l y n o m i a l

[ p 1 a l l , ˜ , mu 1 a ll ] = p o l y f i t ( y e a r s t r a i n , t e m p s train , 1 ) ;

p1temps trai n = polyval ( p 1 a l l , y e a r s t r a i n , [ ] , mu1 al l ) ; %e v a l u a t e polynomial

hold on ; xlim ( [ y e a r s t o p l o t t r a i n ( 1 ) y e a r s t o p l o t t r a i n (end ) ] ) ;

f 1 = plot ( y e a r s t o p l o t t r a i n , p 1tem ps trai n , ’ r ’ ) ;

xlim ( [ y e a r s t o p l o t t r a i n ( 1 ) y e a r s t o p l o t t r a i n (end ) ] ) ;

R s qu a re d t r ai n1=1−sum(( p1temps tr ain−t e mp s tr a i n ) . ˆ 2 ) / . . .

( ( ( length ( t em p s t r ai n )−1) ∗ var ( tem ps t r ai n ) ) )

no rm2 trai n1=norm( p1te mps train −temps t r a i n , 2 )

There is also a nice interface for curve ﬁtting in Matlab, called cftool . This is a user friendly

interface that lets you easily ﬁt data to a user-speciﬁed function. Try it out by typing cftool

into the command line.

Try: Use either polyﬁt or cftool to ﬁt 2nd and 3rd degree polynomial to the training data.

Try the center and scale option to ﬁnd a better conditioned polynomial. Plot all three

polynomials on the same axis.

Try: Obtain the R-squared value of each polynomial

Try: Obtain the 2-norm value of each ﬁtted function. The 2-norm (a.k.a. Euclidean Norm)

of a vector x

= f

− y

is ||x||

)

You should end up with a plot that looks like the following:

1910 1920 1930 1940 1950 1960 1970 1980 1990

Year

42.5

43.5

44.5

45.5

Temperature (

USA Average Temperature 1901-2012

1st-Degree

2nd-Degree

3rd-Degree

Q: Which function do you think best describes the data? Why?

1.4 Prediction

To evaluate which curve best describes the data, we need to think about not just how well

the curve describes previous data, but how well the curve describes as of yet unknown data.

To do this, we split our data into training and test sets, pretending that we do not know

what happens after the year 1990. Now, we use the test data to evaluate how well predictions

based on our curve ﬁts describe what happens in the period from 1991-2012.

To do this, we evaluate our polynomials for years 1991-2012, and compare to the actual

measured data. This can be done using the following code

%t e s t 1−degr e e polynomial

p1tem p s t e s t = polyval ( p1 , y e a r s t e s t , [ ] , mu1 ) ; %e v a l u a t e polynomial

hold on ; xlim ( [ y e a r s t o p l o t ( 1 ) y e a r s t o p l o t (end ) ] ) ;

f 1 = plot ( y e a r s t o p l o t t e s t , p 1temp s test , ’ r−∗ ’ ) ;

no r m2 test1=norm( p1tem ps test −t e m p s test , 2 )

We have also calculated the 2-norm to evaluate how well our predictions describe the test

data.

Try: Calculate predictions in the 1991-2012 period using the 2nd and 3rd degree polynomial

to the training data. Plot all three polynomials on the same axis.

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