1645009200

# Precalculus Course: Zeros Of Polynomials - Plotting Zeros

When we are given a polynomial in factored form, we can quickly find the polynomial's zeros. Then, we can represent them as the x-intercepts of the polynomial's graph.

1652748716

## Exploratory Data Analysis Tutorial | Basics of EDA with Python

Exploratory data analysis is used by data scientists to analyze and investigate data sets and summarize their main characteristics, often employing data visualization methods. It helps determine how best to manipulate data sources to get the answers you need, making it easier for data scientists to discover patterns, spot anomalies, test a hypothesis, or check assumptions. EDA is primarily used to see what data can reveal beyond the formal modeling or hypothesis testing task and provides a better understanding of data set variables and the relationships between them. It can also help determine if the statistical techniques you are considering for data analysis are appropriate or not.

🔹 Topics Covered:
00:00:00 Basics of EDA with Python
01:40:10 Multiple Variate Analysis
02:30:26 Outlier Detection
03:44:48 Cricket World Cup Analysis using Exploratory Data Analysis

## What is Exploratory Data Analysis(EDA)?

If we want to explain EDA in simple terms, it means trying to understand the given data much better, so that we can make some sense out of it.

We can find a more formal definition in Wikipedia.

In statistics, exploratory data analysis is an approach to analyzing data sets to summarize their main characteristics, often with visual methods. A statistical model can be used or not, but primarily EDA is for seeing what the data can tell us beyond the formal modeling or hypothesis testing task.

EDA in Python uses data visualization to draw meaningful patterns and insights. It also involves the preparation of data sets for analysis by removing irregularities in the data.

Based on the results of EDA, companies also make business decisions, which can have repercussions later.

• If EDA is not done properly then it can hamper the further steps in the machine learning model building process.
• If done well, it may improve the efficacy of everything we do next.

1. Data Sourcing
2. Data Cleaning
3. Univariate analysis
4. Bivariate analysis
5. Multivariate analysis

## 1. Data Sourcing

Data Sourcing is the process of finding and loading the data into our system. Broadly there are two ways in which we can find data.

1. Private Data
2. Public Data

Private Data

As the name suggests, private data is given by private organizations. There are some security and privacy concerns attached to it. This type of data is used for mainly organizations internal analysis.

Public Data

This type of Data is available to everyone. We can find this in government websites and public organizations etc. Anyone can access this data, we do not need any special permissions or approval.

We can get public data on the following sites.

The very first step of EDA is Data Sourcing, we have seen how we can access data and load into our system. Now, the next step is how to clean the data.

## 2. Data Cleaning

After completing the Data Sourcing, the next step in the process of EDA is Data Cleaning. It is very important to get rid of the irregularities and clean the data after sourcing it into our system.

Irregularities are of different types of data.

• Missing Values
• Incorrect Format
• Anomalies/Outliers

To perform the data cleaning we are using a sample data set, which can be found here.

We are using Jupyter Notebook for analysis.

First, let’s import the necessary libraries and store the data in our system for analysis.

#import the useful libraries.
import numpy as np
import pandas as pd
import seaborn as sns
import matplotlib.pyplot as plt
%matplotlib inline

# Read the data set of "Marketing Analysis" in data.

# Printing the data
data

Now, the data set looks like this,

If we observe the above dataset, there are some discrepancies in the Column header for the first 2 rows. The correct data is from the index number 1. So, we have to fix the first two rows.

This is called Fixing the Rows and Columns. Let’s ignore the first two rows and load the data again.

#import the useful libraries.
import numpy as np
import pandas as pd
import seaborn as sns
import matplotlib.pyplot as plt
%matplotlib inline

# Read the file in data without first two rows as it is of no use.

#print the head of the data frame.

Now, the dataset looks like this, and it makes more sense.

Dataset after fixing the rows and columns

Following are the steps to be taken while Fixing Rows and Columns:

1. Delete Summary Rows and Columns in the Dataset.
2. Delete Header and Footer Rows on every page.
3. Delete Extra Rows like blank rows, page numbers, etc.
4. We can merge different columns if it makes for better understanding of the data
5. Similarly, we can also split one column into multiple columns based on our requirements or understanding.
6. Add Column names, it is very important to have column names to the dataset.

Now if we observe the above dataset, the customerid column has of no importance to our analysis, and also the jobedu column has both the information of job and education in it.

So, what we’ll do is, we’ll drop the customerid column and we’ll split the jobedu column into two other columns job and education and after that, we’ll drop the jobedu column as well.

# Drop the customer id as it is of no use.
data.drop('customerid', axis = 1, inplace = True)

#Extract job  & Education in newly from "jobedu" column.
data['job']= data["jobedu"].apply(lambda x: x.split(",")[0])
data['education']= data["jobedu"].apply(lambda x: x.split(",")[1])

# Drop the "jobedu" column from the dataframe.
data.drop('jobedu', axis = 1, inplace = True)

# Printing the Dataset
data

Now, the dataset looks like this,

Dropping Customerid and jobedu columns and adding job and education columns

Missing Values

If there are missing values in the Dataset before doing any statistical analysis, we need to handle those missing values.

There are mainly three types of missing values.

1. MCAR(Missing completely at random): These values do not depend on any other features.
2. MAR(Missing at random): These values may be dependent on some other features.
3. MNAR(Missing not at random): These missing values have some reason for why they are missing.

Let’s see which columns have missing values in the dataset.

# Checking the missing values
data.isnull().sum()

The output will be,

As we can see three columns contain missing values. Let’s see how to handle the missing values. We can handle missing values by dropping the missing records or by imputing the values.

Drop the missing Values

Let’s handle missing values in the age column.

# Dropping the records with age missing in data dataframe.
data = data[~data.age.isnull()].copy()

# Checking the missing values in the dataset.
data.isnull().sum()

Let’s check the missing values in the dataset now.

Let’s impute values to the missing values for the month column.

Since the month column is of an object type, let’s calculate the mode of that column and impute those values to the missing values.

# Find the mode of month in data
month_mode = data.month.mode()[0]

# Fill the missing values with mode value of month in data.
data.month.fillna(month_mode, inplace = True)

# Let's see the null values in the month column.
data.month.isnull().sum()

Now output is,

# Mode of month is
'may, 2017'
# Null values in month column after imputing with mode
0

Handling the missing values in the Response column. Since, our target column is Response Column, if we impute the values to this column it’ll affect our analysis. So, it is better to drop the missing values from Response Column.

#drop the records with response missing in data.
data = data[~data.response.isnull()].copy()
# Calculate the missing values in each column of data frame
data.isnull().sum()

Let’s check whether the missing values in the dataset have been handled or not,

All the missing values have been handled

We can also, fill the missing values as ‘NaN’ so that while doing any statistical analysis, it won’t affect the outcome.

Handling Outliers

We have seen how to fix missing values, now let’s see how to handle outliers in the dataset.

Outliers are the values that are far beyond the next nearest data points.

There are two types of outliers:

1. Univariate outliers: Univariate outliers are the data points whose values lie beyond the range of expected values based on one variable.
2. Multivariate outliers: While plotting data, some values of one variable may not lie beyond the expected range, but when you plot the data with some other variable, these values may lie far from the expected value.

So, after understanding the causes of these outliers, we can handle them by dropping those records or imputing with the values or leaving them as is, if it makes more sense.

Standardizing Values

To perform data analysis on a set of values, we have to make sure the values in the same column should be on the same scale. For example, if the data contains the values of the top speed of different companies’ cars, then the whole column should be either in meters/sec scale or miles/sec scale.

Now, that we are clear on how to source and clean the data, let’s see how we can analyze the data.

## 3. Univariate Analysis

If we analyze data over a single variable/column from a dataset, it is known as Univariate Analysis.

Categorical Unordered Univariate Analysis:

An unordered variable is a categorical variable that has no defined order. If we take our data as an example, the job column in the dataset is divided into many sub-categories like technician, blue-collar, services, management, etc. There is no weight or measure given to any value in the ‘job’ column.

Now, let’s analyze the job category by using plots. Since Job is a category, we will plot the bar plot.

# Let's calculate the percentage of each job status category.
data.job.value_counts(normalize=True)

#plot the bar graph of percentage job categories
data.job.value_counts(normalize=True).plot.barh()
plt.show()

The output looks like this,

By the above bar plot, we can infer that the data set contains more number of blue-collar workers compared to other categories.

Categorical Ordered Univariate Analysis:

Ordered variables are those variables that have a natural rank of order. Some examples of categorical ordered variables from our dataset are:

• Month: Jan, Feb, March……
• Education: Primary, Secondary,……

Now, let’s analyze the Education Variable from the dataset. Since we’ve already seen a bar plot, let’s see how a Pie Chart looks like.

#calculate the percentage of each education category.
data.education.value_counts(normalize=True)

#plot the pie chart of education categories
data.education.value_counts(normalize=True).plot.pie()
plt.show()

The output will be,

By the above analysis, we can infer that the data set has a large number of them belongs to secondary education after that tertiary and next primary. Also, a very small percentage of them have been unknown.

This is how we analyze univariate categorical analysis. If the column or variable is of numerical then we’ll analyze by calculating its mean, median, std, etc. We can get those values by using the describe function.

data.salary.describe()

The output will be,

## 4. Bivariate Analysis

If we analyze data by taking two variables/columns into consideration from a dataset, it is known as Bivariate Analysis.

a) Numeric-Numeric Analysis:

Analyzing the two numeric variables from a dataset is known as numeric-numeric analysis. We can analyze it in three different ways.

• Scatter Plot
• Pair Plot
• Correlation Matrix

Scatter Plot

Let’s take three columns ‘Balance’, ‘Age’ and ‘Salary’ from our dataset and see what we can infer by plotting to scatter plot between salary balance and age balance

#plot the scatter plot of balance and salary variable in data
plt.scatter(data.salary,data.balance)
plt.show()

#plot the scatter plot of balance and age variable in data
data.plot.scatter(x="age",y="balance")
plt.show()

Now, the scatter plots looks like,

Pair Plot

Now, let’s plot Pair Plots for the three columns we used in plotting Scatter plots. We’ll use the seaborn library for plotting Pair Plots.

#plot the pair plot of salary, balance and age in data dataframe.
sns.pairplot(data = data, vars=['salary','balance','age'])
plt.show()

The Pair Plot looks like this,

Correlation Matrix

Since we cannot use more than two variables as x-axis and y-axis in Scatter and Pair Plots, it is difficult to see the relation between three numerical variables in a single graph. In those cases, we’ll use the correlation matrix.

# Creating a matrix using age, salry, balance as rows and columns
data[['age','salary','balance']].corr()

#plot the correlation matrix of salary, balance and age in data dataframe.
sns.heatmap(data[['age','salary','balance']].corr(), annot=True, cmap = 'Reds')
plt.show()

First, we created a matrix using age, salary, and balance. After that, we are plotting the heatmap using the seaborn library of the matrix.

b) Numeric - Categorical Analysis

Analyzing the one numeric variable and one categorical variable from a dataset is known as numeric-categorical analysis. We analyze them mainly using mean, median, and box plots.

Let’s take salary and response columns from our dataset.

First check for mean value using groupby

#groupby the response to find the mean of the salary with response no & yes separately.
data.groupby('response')['salary'].mean()

The output will be,

There is not much of a difference between the yes and no response based on the salary.

Let’s calculate the median,

#groupby the response to find the median of the salary with response no & yes separately.
data.groupby('response')['salary'].median()

The output will be,

By both mean and median we can say that the response of yes and no remains the same irrespective of the person’s salary. But, is it truly behaving like that, let’s plot the box plot for them and check the behavior.

#plot the box plot of salary for yes & no responses.
sns.boxplot(data.response, data.salary)
plt.show()

The box plot looks like this,

As we can see, when we plot the Box Plot, it paints a very different picture compared to mean and median. The IQR for customers who gave a positive response is on the higher salary side.

This is how we analyze Numeric-Categorical variables, we use mean, median, and Box Plots to draw some sort of conclusions.

c) Categorical — Categorical Analysis

Since our target variable/column is the Response rate, we’ll see how the different categories like Education, Marital Status, etc., are associated with the Response column. So instead of ‘Yes’ and ‘No’ we will convert them into ‘1’ and ‘0’, by doing that we’ll get the “Response Rate”.

#create response_rate of numerical data type where response "yes"= 1, "no"= 0
data['response_rate'] = np.where(data.response=='yes',1,0)
data.response_rate.value_counts()

The output looks like this,

Let’s see how the response rate varies for different categories in marital status.

#plot the bar graph of marital status with average value of response_rate
data.groupby('marital')['response_rate'].mean().plot.bar()
plt.show()

The graph looks like this,

By the above graph, we can infer that the positive response is more for Single status members in the data set. Similarly, we can plot the graphs for Loan vs Response rate, Housing Loans vs Response rate, etc.

## 5. Multivariate Analysis

If we analyze data by taking more than two variables/columns into consideration from a dataset, it is known as Multivariate Analysis.

Let’s see how ‘Education’, ‘Marital’, and ‘Response_rate’ vary with each other.

First, we’ll create a pivot table with the three columns and after that, we’ll create a heatmap.

result = pd.pivot_table(data=data, index='education', columns='marital',values='response_rate')
print(result)

#create heat map of education vs marital vs response_rate
sns.heatmap(result, annot=True, cmap = 'RdYlGn', center=0.117)
plt.show()

The Pivot table and heatmap looks like this,

Based on the Heatmap we can infer that the married people with primary education are less likely to respond positively for the survey and single people with tertiary education are most likely to respond positively to the survey.

Similarly, we can plot the graphs for Job vs marital vs response, Education vs poutcome vs response, etc.

Conclusion

This is how we’ll do Exploratory Data Analysis. Exploratory Data Analysis (EDA) helps us to look beyond the data. The more we explore the data, the more the insights we draw from it. As a data analyst, almost 80% of our time will be spent understanding data and solving various business problems through EDA.

Thank you for reading and Happy Coding!!!

#dataanalysis #python

1561523460

## Matplotlib Cheat Sheet: Plotting in Python

This Matplotlib cheat sheet introduces you to the basics that you need to plot your data with Python and includes code samples.

Data visualization and storytelling with your data are essential skills that every data scientist needs to communicate insights gained from analyses effectively to any audience out there.

For most beginners, the first package that they use to get in touch with data visualization and storytelling is, naturally, Matplotlib: it is a Python 2D plotting library that enables users to make publication-quality figures. But, what might be even more convincing is the fact that other packages, such as Pandas, intend to build more plotting integration with Matplotlib as time goes on.

However, what might slow down beginners is the fact that this package is pretty extensive. There is so much that you can do with it and it might be hard to still keep a structure when you're learning how to work with Matplotlib.

DataCamp has created a Matplotlib cheat sheet for those who might already know how to use the package to their advantage to make beautiful plots in Python, but that still want to keep a one-page reference handy. Of course, for those who don't know how to work with Matplotlib, this might be the extra push be convinced and to finally get started with data visualization in Python.

You'll see that this cheat sheet presents you with the six basic steps that you can go through to make beautiful plots.

Check out the infographic by clicking on the button below:

With this handy reference, you'll familiarize yourself in no time with the basics of Matplotlib: you'll learn how you can prepare your data, create a new plot, use some basic plotting routines to your advantage, add customizations to your plots, and save, show and close the plots that you make.

What might have looked difficult before will definitely be more clear once you start using this cheat sheet! Use it in combination with the Matplotlib Gallery, the documentation.

Matplotlib

Matplotlib is a Python 2D plotting library which produces publication-quality figures in a variety of hardcopy formats and interactive environments across platforms.

## Prepare the Data

### 1D Data

>>> import numpy as np
>>> x = np.linspace(0, 10, 100)
>>> y = np.cos(x)
>>> z = np.sin(x)

### 2D Data or Images

>>> data = 2 * np.random.random((10, 10))
>>> data2 = 3 * np.random.random((10, 10))
>>> Y, X = np.mgrid[-3:3:100j, -3:3:100j]
>>> U = 1 X** 2 + Y
>>> V = 1 + X Y**2
>>> from matplotlib.cbook import get_sample_data

## Create Plot

>>> import matplotlib.pyplot as plt

### Figure

>>> fig = plt.figure()
>>> fig2 = plt.figure(figsize=plt.figaspect(2.0))

### Axes

>>> fig3, axes = plt.subplots(nrows=2,ncols=2)
>>> fig4, axes2 = plt.subplots(ncols=3)

## Save Plot

>>> plt.savefig('foo.png') #Save figures
>>> plt.savefig('foo.png',  transparent=True) #Save transparent figures

>>> plt.show()

## 1D Data

>>> fig, ax = plt.subplots()
>>> lines = ax.plot(x,y) #Draw points with lines or markers connecting them
>>> ax.scatter(x,y) #Draw unconnected points, scaled or colored
>>> axes[0,0].bar([1,2,3],[3,4,5]) #Plot vertical rectangles (constant width)
>>> axes[1,0].barh([0.5,1,2.5],[0,1,2]) #Plot horiontal rectangles (constant height)
>>> axes[1,1].axhline(0.45) #Draw a horizontal line across axes
>>> axes[0,1].axvline(0.65) #Draw a vertical line across axes
>>> ax.fill(x,y,color='blue') #Draw filled polygons
>>> ax.fill_between(x,y,color='yellow') #Fill between y values and 0

### 2D Data

>>> fig, ax = plt.subplots()
>>> im = ax.imshow(img, #Colormapped or RGB arrays
cmap= 'gist_earth',
interpolation= 'nearest',
vmin=-2,
vmax=2)
>>> axes2[0].pcolor(data2) #Pseudocolor plot of 2D array
>>> axes2[0].pcolormesh(data) #Pseudocolor plot of 2D array
>>> CS = plt.contour(Y,X,U) #Plot contours
>>> axes2[2].contourf(data1) #Plot filled contours
>>> axes2[2]= ax.clabel(CS) #Label a contour plot

### Vector Fields

>>> axes[0,1].arrow(0,0,0.5,0.5) #Add an arrow to the axes
>>> axes[1,1].quiver(y,z) #Plot a 2D field of arrows
>>> axes[0,1].streamplot(X,Y,U,V) #Plot a 2D field of arrows

### Data Distributions

>>> ax1.hist(y) #Plot a histogram
>>> ax3.boxplot(y) #Make a box and whisker plot
>>> ax3.violinplot(z)  #Make a violin plot

## Plot Anatomy & Workflow

### Plot Anatomy

y-axis

x-axis

### Workflow

The basic steps to creating plots with matplotlib are:

1 Prepare Data
2 Create Plot
3 Plot
4 Customized Plot
5 Save Plot
6 Show Plot

>>> import matplotlib.pyplot as plt
>>> x = [1,2,3,4]  #Step 1
>>> y = [10,20,25,30]
>>> fig = plt.figure() #Step 2
>>> ax = fig.add_subplot(111) #Step 3
>>> ax.plot(x, y, color= 'lightblue', linewidth=3)  #Step 3, 4
>>> ax.scatter([2,4,6],
[5,15,25],
color= 'darkgreen',
marker= '^' )
>>> ax.set_xlim(1, 6.5)
>>> plt.savefig('foo.png' ) #Step 5
>>> plt.show() #Step 6

## Close and Clear

>>> plt.cla()  #Clear an axis
>>> plt.clf(). #Clear the entire figure
>>> plt.close(). #Close a window

## Plotting Customize Plot

### Colors, Color Bars & Color Maps

>>> plt.plot(x, x, x, x**2, x, x** 3)
>>> ax.plot(x, y, alpha = 0.4)
>>> ax.plot(x, y, c= 'k')
>>> fig.colorbar(im, orientation= 'horizontal')
>>> im = ax.imshow(img,
cmap= 'seismic' )

### Markers

>>> fig, ax = plt.subplots()
>>> ax.scatter(x,y,marker= ".")
>>> ax.plot(x,y,marker= "o")

### Linestyles

>>> plt.plot(x,y,linewidth=4.0)
>>> plt.plot(x,y,ls= 'solid')
>>> plt.plot(x,y,ls= '--')
>>> plt.plot(x,y,'--' ,x**2,y**2,'-.' )
>>> plt.setp(lines,color= 'r',linewidth=4.0)

### Text & Annotations

>>> ax.text(1,
-2.1,
'Example Graph',
style= 'italic' )
>>> ax.annotate("Sine",
xy=(8, 0),
xycoords= 'data',
xytext=(10.5, 0),
textcoords= 'data',
arrowprops=dict(arrowstyle= "->",
connectionstyle="arc3"),)

### Mathtext

>>> plt.title(r '\$sigma_i=15\$', fontsize=20)

### Limits, Legends and Layouts

Limits & Autoscaling

>>> ax.axis('equal')  #Set the aspect ratio of the plot to 1
>>> ax.set(xlim=[0,10.5],ylim=[-1.5,1.5])  #Set limits for x-and y-axis
>>> ax.set_xlim(0,10.5) #Set limits for x-axis

Legends

>>> ax.set(title= 'An Example Axes',  #Set a title and x-and y-axis labels
ylabel= 'Y-Axis',
xlabel= 'X-Axis')
>>> ax.legend(loc= 'best')  #No overlapping plot elements

Ticks

>>> ax.xaxis.set(ticks=range(1,5),  #Manually set x-ticks
ticklabels=[3,100, 12,"foo" ])
>>> ax.tick_params(axis= 'y', #Make y-ticks longer and go in and out
direction= 'inout',
length=10)

Subplot Spacing

hspace=0.3,
left=0.125,
right=0.9,
top=0.9,
bottom=0.1)
>>> fig.tight_layout() #Fit subplot(s) in to the figure area

Axis Spines

>>> ax1.spines[ 'top'].set_visible(False) #Make the top axis line for a plot invisible
>>> ax1.spines['bottom' ].set_position(( 'outward',10))  #Move the bottom axis line outward

Have this Cheat Sheet at your fingertips

Original article source at https://www.datacamp.com

#matplotlib #cheatsheet #python

1667468640

## Perl Critic: The Leading Static analyzer for Perl

BUILD STATUS

NAME

Perl::Critic - Critique Perl source code for best-practices.

SYNOPSIS

use Perl::Critic;
my \$file = shift;
my \$critic = Perl::Critic->new();
my @violations = \$critic->critique(\$file);
print @violations;

DESCRIPTION

Perl::Critic is an extensible framework for creating and applying coding standards to Perl source code. Essentially, it is a static source code analysis engine. Perl::Critic is distributed with a number of Perl::Critic::Policy modules that attempt to enforce various coding guidelines. Most Policy modules are based on Damian Conway's book Perl Best Practices. However, Perl::Critic is not limited to PBP and will even support Policies that contradict Conway. You can enable, disable, and customize those Polices through the Perl::Critic interface. You can also create new Policy modules that suit your own tastes.

For a command-line interface to Perl::Critic, see the documentation for perlcritic. If you want to integrate Perl::Critic with your build process, Test::Perl::Critic provides an interface that is suitable for test programs. Also, Test::Perl::Critic::Progressive is useful for gradually applying coding standards to legacy code. For the ultimate convenience (at the expense of some flexibility) see the criticism pragma.

If you'd like to try Perl::Critic without installing anything, there is a web-service available at http://perlcritic.com. The web-service does not yet support all the configuration features that are available in the native Perl::Critic API, but it should give you a good idea of what it does.

Also, ActivePerl includes a very slick graphical interface to Perl-Critic called perlcritic-gui. You can get a free community edition of ActivePerl from http://www.activestate.com.

PREREQUISITES

Perl::Critic runs on Perl back to Perl 5.6.1. It relies on the PPI module to do the heavy work of parsing Perl.

INTERFACE SUPPORT

The Perl::Critic module is considered to be a public class. Any changes to its interface will go through a deprecation cycle.

CONSTRUCTOR

new( [ -profile => \$FILE, -severity => \$N, -theme => \$string, -include => \@PATTERNS, -exclude => \@PATTERNS, -top => \$N, -only => \$B, -profile-strictness => \$PROFILE_STRICTNESS_{WARN|FATAL|QUIET}, -force => \$B, -verbose => \$N ], -color => \$B, -pager => \$string, -allow-unsafe => \$B, -criticism-fatal => \$B)

new()

Returns a reference to a new Perl::Critic object. Most arguments are just passed directly into Perl::Critic::Config, but I have described them here as well. The default value for all arguments can be defined in your .perlcriticrc file. See the "CONFIGURATION" section for more information about that. All arguments are optional key-value pairs as follows:

-profile is a path to a configuration file. If \$FILE is not defined, Perl::Critic::Config attempts to find a .perlcriticrc configuration file in the current directory, and then in your home directory. Alternatively, you can set the PERLCRITIC environment variable to point to a file in another location. If a configuration file can't be found, or if \$FILE is an empty string, then all Policies will be loaded with their default configuration. See "CONFIGURATION" for more information.

-severity is the minimum severity level. Only Policy modules that have a severity greater than \$N will be applied. Severity values are integers ranging from 1 (least severe violations) to 5 (most severe violations). The default is 5. For a given -profile, decreasing the -severity will usually reveal more Policy violations. You can set the default value for this option in your .perlcriticrc file. Users can redefine the severity level for any Policy in their .perlcriticrc file. See "CONFIGURATION" for more information.

If it is difficult for you to remember whether severity "5" is the most or least restrictive level, then you can use one of these named values:

SEVERITY NAME   ...is equivalent to...   SEVERITY NUMBER
--------------------------------------------------------
-severity => 'gentle'                     -severity => 5
-severity => 'stern'                      -severity => 4
-severity => 'harsh'                      -severity => 3
-severity => 'cruel'                      -severity => 2
-severity => 'brutal'                     -severity => 1

The names reflect how severely the code is criticized: a gentle criticism reports only the most severe violations, and so on down to a brutal criticism which reports even the most minor violations.

-theme is special expression that determines which Policies to apply based on their respective themes. For example, the following would load only Policies that have a 'bugs' AND 'pbp' theme:

my \$critic = Perl::Critic->new( -theme => 'bugs && pbp' );

Unless the -severity option is explicitly given, setting -theme silently causes the -severity to be set to 1. You can set the default value for this option in your .perlcriticrc file. See the "POLICY THEMES" section for more information about themes.

-include is a reference to a list of string @PATTERNS. Policy modules that match at least one m/\$PATTERN/ixms will always be loaded, irrespective of all other settings. For example:

my \$critic = Perl::Critic->new(-include => ['layout'], -severity => 4);

This would cause Perl::Critic to apply all the CodeLayout::* Policy modules even though they have a severity level that is less than 4. You can set the default value for this option in your .perlcriticrc file. You can also use -include in conjunction with the -exclude option. Note that -exclude takes precedence over -include when a Policy matches both patterns.

-exclude is a reference to a list of string @PATTERNS. Policy modules that match at least one m/\$PATTERN/ixms will not be loaded, irrespective of all other settings. For example:

my \$critic = Perl::Critic->new(-exclude => ['strict'], -severity => 1);

This would cause Perl::Critic to not apply the RequireUseStrict and ProhibitNoStrict Policy modules even though they have a severity level that is greater than 1. You can set the default value for this option in your .perlcriticrc file. You can also use -exclude in conjunction with the -include option. Note that -exclude takes precedence over -include when a Policy matches both patterns.

-single-policy is a string PATTERN. Only one policy that matches m/\$PATTERN/ixms will be used. Policies that do not match will be excluded. This option has precedence over the -severity, -theme, -include, -exclude, and -only options. You can set the default value for this option in your .perlcriticrc file.

-top is the maximum number of Violations to return when ranked by their severity levels. This must be a positive integer. Violations are still returned in the order that they occur within the file. Unless the -severity option is explicitly given, setting -top silently causes the -severity to be set to 1. You can set the default value for this option in your .perlcriticrc file.

-only is a boolean value. If set to a true value, Perl::Critic will only choose from Policies that are mentioned in the user's profile. If set to a false value (which is the default), then Perl::Critic chooses from all the Policies that it finds at your site. You can set the default value for this option in your .perlcriticrc file.

-profile-strictness is an enumerated value, one of "\$PROFILE_STRICTNESS_WARN" in Perl::Critic::Utils::Constants (the default), "\$PROFILE_STRICTNESS_FATAL" in Perl::Critic::Utils::Constants, and "\$PROFILE_STRICTNESS_QUIET" in Perl::Critic::Utils::Constants. If set to "\$PROFILE_STRICTNESS_FATAL" in Perl::Critic::Utils::Constants, Perl::Critic will make certain warnings about problems found in a .perlcriticrc or file specified via the -profile option fatal. For example, Perl::Critic normally only warns about profiles referring to non-existent Policies, but this value makes this situation fatal. Correspondingly, "\$PROFILE_STRICTNESS_QUIET" in Perl::Critic::Utils::Constants makes Perl::Critic shut up about these things.

-force is a boolean value that controls whether Perl::Critic observes the magical "## no critic" annotations in your code. If set to a true value, Perl::Critic will analyze all code. If set to a false value (which is the default) Perl::Critic will ignore code that is tagged with these annotations. See "BENDING THE RULES" for more information. You can set the default value for this option in your .perlcriticrc file.

-verbose can be a positive integer (from 1 to 11), or a literal format specification. See Perl::Critic::Violation for an explanation of format specifications. You can set the default value for this option in your .perlcriticrc file.

-unsafe directs Perl::Critic to allow the use of Policies that are marked as "unsafe" by the author. Such policies may compile untrusted code or do other nefarious things.

-color and -pager are not used by Perl::Critic but is provided for the benefit of perlcritic.

-criticism-fatal is not used by Perl::Critic but is provided for the benefit of criticism.

-color-severity-highest, -color-severity-high, -color-severity- medium, -color-severity-low, and -color-severity-lowest are not used by Perl::Critic, but are provided for the benefit of perlcritic. Each is set to the Term::ANSIColor color specification to be used to display violations of the corresponding severity.

-files-with-violations and -files-without-violations are not used by Perl::Critic, but are provided for the benefit of perlcritic, to cause only the relevant filenames to be displayed.

METHODS

critique( \$source_code )

Runs the \$source_code through the Perl::Critic engine using all the Policies that have been loaded into this engine. If \$source_code is a scalar reference, then it is treated as a string of actual Perl code. If \$source_code is a reference to an instance of PPI::Document, then that instance is used directly. Otherwise, it is treated as a path to a local file containing Perl code. This method returns a list of Perl::Critic::Violation objects for each violation of the loaded Policies. The list is sorted in the order that the Violations appear in the code. If there are no violations, this method returns an empty list.

add_policy( -policy => \$policy_name, -params => \%param_hash )

Creates a Policy object and loads it into this Critic. If the object cannot be instantiated, it will throw a fatal exception. Otherwise, it returns a reference to this Critic.

-policy is the name of a Perl::Critic::Policy subclass module. The 'Perl::Critic::Policy' portion of the name can be omitted for brevity. This argument is required.

-params is an optional reference to a hash of Policy parameters. The contents of this hash reference will be passed into to the constructor of the Policy module. See the documentation in the relevant Policy module for a description of the arguments it supports.

policies()

Returns a list containing references to all the Policy objects that have been loaded into this engine. Objects will be in the order that they were loaded.

config()

Returns the Perl::Critic::Config object that was created for or given to this Critic.

statistics()

Returns the Perl::Critic::Statistics object that was created for this Critic. The Statistics object accumulates data for all files that are analyzed by this Critic.

FUNCTIONAL INTERFACE

For those folks who prefer to have a functional interface, The critique method can be exported on request and called as a static function. If the first argument is a hashref, its contents are used to construct a new Perl::Critic object internally. The keys of that hash should be the same as those supported by the Perl::Critic::new() method. Here are some examples:

use Perl::Critic qw(critique);

# Use default parameters...
@violations = critique( \$some_file );

# Use custom parameters...
@violations = critique( {-severity => 2}, \$some_file );

# As a one-liner
%> perl -MPerl::Critic=critique -e 'print critique(shift)' some_file.pm

None of the other object-methods are currently supported as static functions. Sorry.

CONFIGURATION

Most of the settings for Perl::Critic and each of the Policy modules can be controlled by a configuration file. The default configuration file is called .perlcriticrc. Perl::Critic will look for this file in the current directory first, and then in your home directory. Alternatively, you can set the PERLCRITIC environment variable to explicitly point to a different file in another location. If none of these files exist, and the -profile option is not given to the constructor, then all the modules that are found in the Perl::Critic::Policy namespace will be loaded with their default configuration.

The format of the configuration file is a series of INI-style blocks that contain key-value pairs separated by '='. Comments should start with '#' and can be placed on a separate line or after the name-value pairs if you desire.

Default settings for Perl::Critic itself can be set before the first named block. For example, putting any or all of these at the top of your configuration file will set the default value for the corresponding constructor argument.

severity  = 3                                     #Integer or named level
only      = 1                                     #Zero or One
force     = 0                                     #Zero or One
verbose   = 4                                     #Integer or format spec
top       = 50                                    #A positive integer
theme     = (pbp || security) && bugs             #A theme expression
include   = NamingConventions ClassHierarchies    #Space-delimited list
exclude   = Variables  Modules::RequirePackage    #Space-delimited list
criticism-fatal = 1                               #Zero or One
color     = 1                                     #Zero or One
allow-unsafe = 1                                  #Zero or One
pager     = less                                  #pager to pipe output to

The remainder of the configuration file is a series of blocks like this:

[Perl::Critic::Policy::Category::PolicyName]
severity = 1
set_themes = foo bar
maximum_violations_per_document = 57
arg1 = value1
arg2 = value2

Perl::Critic::Policy::Category::PolicyName is the full name of a module that implements the policy. The Policy modules distributed with Perl::Critic have been grouped into categories according to the table of contents in Damian Conway's book Perl Best Practices. For brevity, you can omit the 'Perl::Critic::Policy' part of the module name.

severity is the level of importance you wish to assign to the Policy. All Policy modules are defined with a default severity value ranging from 1 (least severe) to 5 (most severe). However, you may disagree with the default severity and choose to give it a higher or lower severity, based on your own coding philosophy. You can set the severity to an integer from 1 to 5, or use one of the equivalent names:

SEVERITY NAME ...is equivalent to... SEVERITY NUMBER
----------------------------------------------------
gentle                                             5
stern                                              4
harsh                                              3
cruel                                              2
brutal                                             1

The names reflect how severely the code is criticized: a gentle criticism reports only the most severe violations, and so on down to a brutal criticism which reports even the most minor violations.

set_themes sets the theme for the Policy and overrides its default theme. The argument is a string of one or more whitespace-delimited alphanumeric words. Themes are case-insensitive. See "POLICY THEMES" for more information.

add_themes appends to the default themes for this Policy. The argument is a string of one or more whitespace-delimited words. Themes are case- insensitive. See "POLICY THEMES" for more information.

maximum_violations_per_document limits the number of Violations the Policy will return for a given document. Some Policies have a default limit; see the documentation for the individual Policies to see whether there is one. To force a Policy to not have a limit, specify "no_limit" or the empty string for the value of this parameter.

The remaining key-value pairs are configuration parameters that will be passed into the constructor for that Policy. The constructors for most Policy objects do not support arguments, and those that do should have reasonable defaults. See the documentation on the appropriate Policy module for more details.

Instead of redefining the severity for a given Policy, you can completely disable a Policy by prepending a '-' to the name of the module in your configuration file. In this manner, the Policy will never be loaded, regardless of the -severity given to the Perl::Critic constructor.

A simple configuration might look like this:

#--------------------------------------------------------------
# I think these are really important, so always load them

[TestingAndDebugging::RequireUseStrict]
severity = 5

[TestingAndDebugging::RequireUseWarnings]
severity = 5

#--------------------------------------------------------------
# I think these are less important, so only load when asked

[Variables::ProhibitPackageVars]
severity = 2

[ControlStructures::ProhibitPostfixControls]
allow = if unless  # My custom configuration
severity = cruel   # Same as "severity = 2"

#--------------------------------------------------------------
# Give these policies a custom theme.  I can activate just
# these policies by saying `perlcritic -theme larry`

[Modules::RequireFilenameMatchesPackage]

[TestingAndDebugging::RequireTestLables]

#--------------------------------------------------------------
# I do not agree with these at all, so never load them

[-NamingConventions::Capitalization]
[-ValuesAndExpressions::ProhibitMagicNumbers]

#--------------------------------------------------------------
# For all other Policies, I accept the default severity,
# so no additional configuration is required for them.

For additional configuration examples, see the perlcriticrc file that is included in this examples directory of this distribution.

Damian Conway's own Perl::Critic configuration is also included in this distribution as examples/perlcriticrc-conway.

THE POLICIES

A large number of Policy modules are distributed with Perl::Critic. They are described briefly in the companion document Perl::Critic::PolicySummary and in more detail in the individual modules themselves. Say "perlcritic -doc PATTERN" to see the perldoc for all Policy modules that match the regex m/PATTERN/ixms

There are a number of distributions of additional policies on CPAN. If Perl::Critic doesn't contain a policy that you want, some one may have already written it. See the "SEE ALSO" section below for a list of some of these distributions.

POLICY THEMES

Each Policy is defined with one or more "themes". Themes can be used to create arbitrary groups of Policies. They are intended to provide an alternative mechanism for selecting your preferred set of Policies. For example, you may wish disable a certain subset of Policies when analyzing test programs. Conversely, you may wish to enable only a specific subset of Policies when analyzing modules.

The Policies that ship with Perl::Critic have been broken into the following themes. This is just our attempt to provide some basic logical groupings. You are free to invent new themes that suit your needs.

THEME             DESCRIPTION
--------------------------------------------------------------------------
core              All policies that ship with Perl::Critic
pbp               Policies that come directly from "Perl Best Practices"
bugs              Policies that that prevent or reveal bugs
certrec           Policies that CERT recommends
certrule          Policies that CERT considers rules
maintenance       Policies that affect the long-term health of the code
cosmetic          Policies that only have a superficial effect
complexity        Policies that specifically relate to code complexity
security          Policies that relate to security issues
tests             Policies that are specific to test programs

Any Policy may fit into multiple themes. Say "perlcritic -list" to get a listing of all available Policies and the themes that are associated with each one. You can also change the theme for any Policy in your .perlcriticrc file. See the "CONFIGURATION" section for more information about that.

Using the -theme option, you can create an arbitrarily complex rule that determines which Policies will be loaded. Precedence is the same as regular Perl code, and you can use parentheses to enforce precedence as well. Supported operators are:

Operator    Alternative    Example
-----------------------------------------------------------------
&&          and            'pbp && core'
||          or             'pbp || (bugs && security)'
!           not            'pbp && ! (portability || complexity)'

Theme names are case-insensitive. If the -theme is set to an empty string, then it evaluates as true all Policies.

BENDING THE RULES

Perl::Critic takes a hard-line approach to your code: either you comply or you don't. In the real world, it is not always practical (nor even possible) to fully comply with coding standards. In such cases, it is wise to show that you are knowingly violating the standards and that you have a Damn Good Reason (DGR) for doing so.

To help with those situations, you can direct Perl::Critic to ignore certain lines or blocks of code by using annotations:

require 'LegacyLibaray1.pl';  ## no critic
require 'LegacyLibrary2.pl';  ## no critic

for my \$element (@list) {

## no critic

\$foo = "";               #Violates 'ProhibitEmptyQuotes'
\$barf = bar() if \$foo;   #Violates 'ProhibitPostfixControls'
#Some more evil code...

## use critic

#Some good code...
do_something(\$_);
}

The "## no critic" annotations direct Perl::Critic to ignore the remaining lines of code until a "## use critic" annotation is found. If the "## no critic" annotation is on the same line as a code statement, then only that line of code is overlooked. To direct perlcritic to ignore the "## no critic" annotations, use the --force option.

A bare "## no critic" annotation disables all the active Policies. If you wish to disable only specific Policies, add a list of Policy names as arguments, just as you would for the "no strict" or "no warnings" pragmas. For example, this would disable the ProhibitEmptyQuotes and ProhibitPostfixControls policies until the end of the block or until the next "## use critic" annotation (whichever comes first):

## no critic (EmptyQuotes, PostfixControls)

# Now exempt from ValuesAndExpressions::ProhibitEmptyQuotes
\$foo = "";

# Now exempt ControlStructures::ProhibitPostfixControls
\$barf = bar() if \$foo;

# Still subjected to ValuesAndExpression::RequireNumberSeparators
\$long_int = 10000000000;

Since the Policy names are matched against the "## no critic" arguments as regular expressions, you can abbreviate the Policy names or disable an entire family of Policies in one shot like this:

## no critic (NamingConventions)

# Now exempt from NamingConventions::Capitalization
my \$camelHumpVar = 'foo';

# Now exempt from NamingConventions::Capitalization
sub camelHumpSub {}

The argument list must be enclosed in parentheses or brackets and must contain one or more comma-separated barewords (e.g. don't use quotes). The "## no critic" annotations can be nested, and Policies named by an inner annotation will be disabled along with those already disabled an outer annotation.

Some Policies like Subroutines::ProhibitExcessComplexity apply to an entire block of code. In those cases, the "## no critic" annotation must appear on the line where the violation is reported. For example:

sub complicated_function {  ## no critic (ProhibitExcessComplexity)
}

Policies such as Documentation::RequirePodSections apply to the entire document, in which case violations are reported at line 1.

Use this feature wisely. "## no critic" annotations should be used in the smallest possible scope, or only on individual lines of code. And you should always be as specific as possible about which Policies you want to disable (i.e. never use a bare "## no critic"). If Perl::Critic complains about your code, try and find a compliant solution before resorting to this feature.

THE Perl::Critic PHILOSOPHY

Coding standards are deeply personal and highly subjective. The goal of Perl::Critic is to help you write code that conforms with a set of best practices. Our primary goal is not to dictate what those practices are, but rather, to implement the practices discovered by others. Ultimately, you make the rules -- Perl::Critic is merely a tool for encouraging consistency. If there is a policy that you think is important or that we have overlooked, we would be very grateful for contributions, or you can simply load your own private set of policies into Perl::Critic.

EXTENDING THE CRITIC

The modular design of Perl::Critic is intended to facilitate the addition of new Policies. You'll need to have some understanding of PPI, but most Policy modules are pretty straightforward and only require about 20 lines of code. Please see the Perl::Critic::DEVELOPER file included in this distribution for a step-by-step demonstration of how to create new Policy modules.

If you develop any new Policy modules, feel free to send them to <team@perlcritic.com> and I'll be happy to consider putting them into the Perl::Critic distribution. Or if you would like to work on the Perl::Critic project directly, you can fork our repository at https://github.com/Perl-Critic/Perl-Critic.git.

The Perl::Critic team is also available for hire. If your organization has its own coding standards, we can create custom Policies to enforce your local guidelines. Or if your code base is prone to a particular defect pattern, we can design Policies that will help you catch those costly defects before they go into production. To discuss your needs with the Perl::Critic team, just contact <team@perlcritic.com>.

PREREQUISITES

Perl::Critic requires the following modules:

B::Keywords

Config::Tiny

Exception::Class

File::Spec

File::Spec::Unix

File::Which

IO::String

List::SomeUtils

List::Util

Module::Pluggable

Perl::Tidy

Pod::Spell

PPI

Pod::PlainText

Pod::Select

Pod::Usage

Scalar::Util

String::Format

Term::ANSIColor

Text::ParseWords

version

CONTACTING THE DEVELOPMENT TEAM

You are encouraged to subscribe to the public mailing list at https://groups.google.com/d/forum/perl-critic. At least one member of the development team is usually hanging around in irc://irc.perl.org/#perlcritic and you can follow Perl::Critic on Twitter, at https://twitter.com/perlcritic.

There are a number of distributions of additional Policies available. A few are listed here:

Perl::Critic::More

Perl::Critic::Bangs

Perl::Critic::Lax

Perl::Critic::StricterSubs

Perl::Critic::Swift

Perl::Critic::Tics

These distributions enable you to use Perl::Critic in your unit tests:

Test::Perl::Critic

Test::Perl::Critic::Progressive

There is also a distribution that will install all the Perl::Critic related modules known to the development team:

BUGS

Scrutinizing Perl code is hard for humans, let alone machines. If you find any bugs, particularly false-positives or false-negatives from a Perl::Critic::Policy, please submit them at https://github.com/Perl-Critic/Perl-Critic/issues. Thanks.

CREDITS

Adam Kennedy - For creating PPI, the heart and soul of Perl::Critic.

Damian Conway - For writing Perl Best Practices, finally :)

Chris Dolan - For contributing the best features and Policy modules.

Andy Lester - Wise sage and master of all-things-testing.

Elliot Shank - The self-proclaimed quality freak.

Giuseppe Maxia - For all the great ideas and positive encouragement.

and Sharon, my wife - For putting up with my all-night code sessions.

Thanks also to the Perl Foundation for providing a grant to support Chris Dolan's project to implement twenty PBP policies. http://www.perlfoundation.org/april_1_2007_new_grant_awards

Thanks also to this incomplete laundry list of folks who have contributed to Perl::Critic in some way: Gregory Oschwald, Mike O'Regan, Tom Hukins, Omer Gazit, Evan Zacks, Paul Howarth, Sawyer X, Christian Walde, Dave Rolsky, Jakub Wilk, Roy Ivy III, Oliver Trosien, Glenn Fowler, Matt Creenan, Alex Balhatchet, Sebastian Paaske Tørholm, Stuart A Johnston, Dan Book, Steven Humphrey, James Raspass, Nick Tonkin, Harrison Katz, Douglas Sims, Mark Fowler, Alan Berndt, Neil Bowers, Sergey Romanov, Gabor Szabo, Graham Knop, Mike Eldridge, David Steinbrunner, Kirk Kimmel, Guillaume Aubert, Dave Cross, Anirvan Chatterjee, Todd Rinaldo, Graham Ollis, Karen Etheridge, Jonas Brømsø, Olaf Alders, Jim Keenan, Slaven Rezić, Szymon Nieznański.

AUTHOR

Jeffrey Ryan Thalhammer jeff@imaginative-software.com

This program is free software; you can redistribute it and/or modify it under the same terms as Perl itself. The full text of this license can be found in the LICENSE file included with this module.

Author: Perl-Critic
Source Code: https://github.com/Perl-Critic/Perl-Critic

1645009200

## Precalculus Course: Zeros Of Polynomials - Plotting Zeros

When we are given a polynomial in factored form, we can quickly find the polynomial's zeros. Then, we can represent them as the x-intercepts of the polynomial's graph.

1593242571

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