example of research chapter 3

How To Write The Methodology Chapter

The what, why & how explained simply (with examples).

By: Jenna Crossley (PhD) | Reviewed By: Dr. Eunice Rautenbach | September 2021 (Updated April 2023)

So, you’ve pinned down your research topic and undertaken a review of the literature – now it’s time to write up the methodology section of your dissertation, thesis or research paper . But what exactly is the methodology chapter all about – and how do you go about writing one? In this post, we’ll unpack the topic, step by step .

Overview: The Methodology Chapter

• The purpose  of the methodology chapter
• Why you need to craft this chapter (really) well
• How to write and structure the chapter
• Methodology chapter example
• Essential takeaways

What (exactly) is the methodology chapter?

The methodology chapter is where you outline the philosophical underpinnings of your research and outline the specific methodological choices you’ve made. The point of the methodology chapter is to tell the reader exactly how you designed your study and, just as importantly, why you did it this way.

Importantly, this chapter should comprehensively describe and justify all the methodological choices you made in your study. For example, the approach you took to your research (i.e., qualitative, quantitative or mixed), who  you collected data from (i.e., your sampling strategy), how you collected your data and, of course, how you analysed it. If that sounds a little intimidating, don’t worry – we’ll explain all these methodological choices in this post .

Why is the methodology chapter important?

The methodology chapter plays two important roles in your dissertation or thesis:

Firstly, it demonstrates your understanding of research theory, which is what earns you marks. A flawed research design or methodology would mean flawed results. So, this chapter is vital as it allows you to show the marker that you know what you’re doing and that your results are credible .

Secondly, the methodology chapter is what helps to make your study replicable. In other words, it allows other researchers to undertake your study using the same methodological approach, and compare their findings to yours. This is very important within academic research, as each study builds on previous studies.

The methodology chapter is also important in that it allows you to identify and discuss any methodological issues or problems you encountered (i.e., research limitations ), and to explain how you mitigated the impacts of these. Every research project has its limitations , so it’s important to acknowledge these openly and highlight your study’s value despite its limitations . Doing so demonstrates your understanding of research design, which will earn you marks. We’ll discuss limitations in a bit more detail later in this post, so stay tuned!

Need a helping hand?

How to write up the methodology chapter

First off, it’s worth noting that the exact structure and contents of the methodology chapter will vary depending on the field of research (e.g., humanities, chemistry or engineering) as well as the university . So, be sure to always check the guidelines provided by your institution for clarity and, if possible, review past dissertations from your university. Here we’re going to discuss a generic structure for a methodology chapter typically found in the sciences.

Before you start writing, it’s always a good idea to draw up a rough outline to guide your writing. Don’t just start writing without knowing what you’ll discuss where. If you do, you’ll likely end up with a disjointed, ill-flowing narrative . You’ll then waste a lot of time rewriting in an attempt to try to stitch all the pieces together. Do yourself a favour and start with the end in mind .

Section 1 – Introduction

As with all chapters in your dissertation or thesis, the methodology chapter should have a brief introduction. In this section, you should remind your readers what the focus of your study is, especially the research aims . As we’ve discussed many times on the blog, your methodology needs to align with your research aims, objectives and research questions. Therefore, it’s useful to frontload this component to remind the reader (and yourself!) what you’re trying to achieve.

In this section, you can also briefly mention how you’ll structure the chapter. This will help orient the reader and provide a bit of a roadmap so that they know what to expect. You don’t need a lot of detail here – just a brief outline will do.

Section 2 – The Methodology

The next section of your chapter is where you’ll present the actual methodology. In this section, you need to detail and justify the key methodological choices you’ve made in a logical, intuitive fashion. Importantly, this is the heart of your methodology chapter, so you need to get specific – don’t hold back on the details here. This is not one of those “less is more” situations.

Let’s take a look at the most common components you’ll likely need to cover. 

Methodological Choice #1 – Research Philosophy

Research philosophy refers to the underlying beliefs (i.e., the worldview) regarding how data about a phenomenon should be gathered , analysed and used . The research philosophy will serve as the core of your study and underpin all of the other research design choices, so it’s critically important that you understand which philosophy you’ll adopt and why you made that choice. If you’re not clear on this, take the time to get clarity before you make any further methodological choices.

While several research philosophies exist, two commonly adopted ones are positivism and interpretivism . These two sit roughly on opposite sides of the research philosophy spectrum.

Positivism states that the researcher can observe reality objectively and that there is only one reality, which exists independently of the observer. As a consequence, it is quite commonly the underlying research philosophy in quantitative studies and is oftentimes the assumed philosophy in the physical sciences.

Contrasted with this, interpretivism , which is often the underlying research philosophy in qualitative studies, assumes that the researcher performs a role in observing the world around them and that reality is unique to each observer . In other words, reality is observed subjectively .

These are just two philosophies (there are many more), but they demonstrate significantly different approaches to research and have a significant impact on all the methodological choices. Therefore, it’s vital that you clearly outline and justify your research philosophy at the beginning of your methodology chapter, as it sets the scene for everything that follows.

Methodological Choice #2 – Research Type

The next thing you would typically discuss in your methodology section is the research type. The starting point for this is to indicate whether the research you conducted is inductive or deductive .

Inductive research takes a bottom-up approach , where the researcher begins with specific observations or data and then draws general conclusions or theories from those observations. Therefore these studies tend to be exploratory in terms of approach.

Conversely , d eductive research takes a top-down approach , where the researcher starts with a theory or hypothesis and then tests it using specific observations or data. Therefore these studies tend to be confirmatory in approach.

Related to this, you’ll need to indicate whether your study adopts a qualitative, quantitative or mixed  approach. As we’ve mentioned, there’s a strong link between this choice and your research philosophy, so make sure that your choices are tightly aligned . When you write this section up, remember to clearly justify your choices, as they form the foundation of your study.

Methodological Choice #3 – Research Strategy

Next, you’ll need to discuss your research strategy (also referred to as a research design ). This methodological choice refers to the broader strategy in terms of how you’ll conduct your research, based on the aims of your study.

Several research strategies exist, including experimental , case studies , ethnography , grounded theory, action research , and phenomenology . Let’s take a look at two of these, experimental and ethnographic, to see how they contrast.

Experimental research makes use of the scientific method , where one group is the control group (in which no variables are manipulated ) and another is the experimental group (in which a specific variable is manipulated). This type of research is undertaken under strict conditions in a controlled, artificial environment (e.g., a laboratory). By having firm control over the environment, experimental research typically allows the researcher to establish causation between variables. Therefore, it can be a good choice if you have research aims that involve identifying causal relationships.

Ethnographic research , on the other hand, involves observing and capturing the experiences and perceptions of participants in their natural environment (for example, at home or in the office). In other words, in an uncontrolled environment.  Naturally, this means that this research strategy would be far less suitable if your research aims involve identifying causation, but it would be very valuable if you’re looking to explore and examine a group culture, for example.

As you can see, the right research strategy will depend largely on your research aims and research questions – in other words, what you’re trying to figure out. Therefore, as with every other methodological choice, it’s essential to justify why you chose the research strategy you did.

Methodological Choice #4 – Time Horizon

The next thing you’ll need to detail in your methodology chapter is the time horizon. There are two options here: cross-sectional and longitudinal . In other words, whether the data for your study were all collected at one point in time (cross-sectional) or at multiple points in time (longitudinal).

The choice you make here depends again on your research aims, objectives and research questions. If, for example, you aim to assess how a specific group of people’s perspectives regarding a topic change over time , you’d likely adopt a longitudinal time horizon.

Another important factor to consider is simply whether you have the time necessary to adopt a longitudinal approach (which could involve collecting data over multiple months or even years). Oftentimes, the time pressures of your degree program will force your hand into adopting a cross-sectional time horizon, so keep this in mind.

Methodological Choice #5 – Sampling Strategy

Next, you’ll need to discuss your sampling strategy . There are two main categories of sampling, probability and non-probability sampling.

Probability sampling involves a random (and therefore representative) selection of participants from a population, whereas non-probability sampling entails selecting participants in a non-random  (and therefore non-representative) manner. For example, selecting participants based on ease of access (this is called a convenience sample).

The right sampling approach depends largely on what you’re trying to achieve in your study. Specifically, whether you trying to develop findings that are generalisable to a population or not. Practicalities and resource constraints also play a large role here, as it can oftentimes be challenging to gain access to a truly random sample. In the video below, we explore some of the most common sampling strategies.

Methodological Choice #6 – Data Collection Method

Next up, you’ll need to explain how you’ll go about collecting the necessary data for your study. Your data collection method (or methods) will depend on the type of data that you plan to collect – in other words, qualitative or quantitative data.

Typically, quantitative research relies on surveys , data generated by lab equipment, analytics software or existing datasets. Qualitative research, on the other hand, often makes use of collection methods such as interviews , focus groups , participant observations, and ethnography.

So, as you can see, there is a tight link between this section and the design choices you outlined in earlier sections. Strong alignment between these sections, as well as your research aims and questions is therefore very important.

Methodological Choice #7 – Data Analysis Methods/Techniques

The final major methodological choice that you need to address is that of analysis techniques . In other words, how you’ll go about analysing your date once you’ve collected it. Here it’s important to be very specific about your analysis methods and/or techniques – don’t leave any room for interpretation. Also, as with all choices in this chapter, you need to justify each choice you make.

What exactly you discuss here will depend largely on the type of study you’re conducting (i.e., qualitative, quantitative, or mixed methods). For qualitative studies, common analysis methods include content analysis , thematic analysis and discourse analysis . In the video below, we explain each of these in plain language.

For quantitative studies, you’ll almost always make use of descriptive statistics , and in many cases, you’ll also use inferential statistical techniques (e.g., correlation and regression analysis). In the video below, we unpack some of the core concepts involved in descriptive and inferential statistics.

In this section of your methodology chapter, it’s also important to discuss how you prepared your data for analysis, and what software you used (if any). For example, quantitative data will often require some initial preparation such as removing duplicates or incomplete responses . Similarly, qualitative data will often require transcription and perhaps even translation. As always, remember to state both what you did and why you did it.

Section 3 – The Methodological Limitations

With the key methodological choices outlined and justified, the next step is to discuss the limitations of your design. No research methodology is perfect – there will always be trade-offs between the “ideal” methodology and what’s practical and viable, given your constraints. Therefore, this section of your methodology chapter is where you’ll discuss the trade-offs you had to make, and why these were justified given the context.

Methodological limitations can vary greatly from study to study, ranging from common issues such as time and budget constraints to issues of sample or selection bias . For example, you may find that you didn’t manage to draw in enough respondents to achieve the desired sample size (and therefore, statistically significant results), or your sample may be skewed heavily towards a certain demographic, thereby negatively impacting representativeness .

In this section, it’s important to be critical of the shortcomings of your study. There’s no use trying to hide them (your marker will be aware of them regardless). By being critical, you’ll demonstrate to your marker that you have a strong understanding of research theory, so don’t be shy here. At the same time, don’t beat your study to death . State the limitations, why these were justified, how you mitigated their impacts to the best degree possible, and how your study still provides value despite these limitations .

Section 4 – Concluding Summary

Finally, it’s time to wrap up the methodology chapter with a brief concluding summary. In this section, you’ll want to concisely summarise what you’ve presented in the chapter. Here, it can be a good idea to use a figure to summarise the key decisions, especially if your university recommends using a specific model (for example, Saunders’ Research Onion ).

Importantly, this section needs to be brief – a paragraph or two maximum (it’s a summary, after all). Also, make sure that when you write up your concluding summary, you include only what you’ve already discussed in your chapter; don’t add any new information.

Methodology Chapter Example

In the video below, we walk you through an example of a high-quality research methodology chapter from a dissertation. We also unpack our free methodology chapter template so that you can see how best to structure your chapter.

Wrapping Up

And there you have it – the methodology chapter in a nutshell. As we’ve mentioned, the exact contents and structure of this chapter can vary between universities , so be sure to check in with your institution before you start writing. If possible, try to find dissertations or theses from former students of your specific degree program – this will give you a strong indication of the expectations and norms when it comes to the methodology chapter (and all the other chapters!).

Also, remember the golden rule of the methodology chapter – justify every choice ! Make sure that you clearly explain the “why” for every “what”, and reference credible methodology textbooks or academic sources to back up your justifications.

If you need a helping hand with your research methodology (or any other component of your research), be sure to check out our private coaching service , where we hold your hand through every step of the research journey. Until next time, good luck!

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This post was based on one of our popular Research Bootcamps . If you're working on a research project, you'll definitely want to check this out ...

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Methodology

• How to Write a Literature Review | Guide, Examples, & Templates

How to Write a Literature Review | Guide, Examples, & Templates

Published on January 2, 2023 by Shona McCombes . Revised on September 11, 2023.

What is a literature review? A literature review is a survey of scholarly sources on a specific topic. It provides an overview of current knowledge, allowing you to identify relevant theories, methods, and gaps in the existing research that you can later apply to your paper, thesis, or dissertation topic .

There are five key steps to writing a literature review:

• Search for relevant literature
• Evaluate sources
• Identify themes, debates, and gaps
• Outline the structure
• Write your literature review

A good literature review doesn’t just summarize sources—it analyzes, synthesizes , and critically evaluates to give a clear picture of the state of knowledge on the subject.

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Table of contents

What is the purpose of a literature review, examples of literature reviews, step 1 – search for relevant literature, step 2 – evaluate and select sources, step 3 – identify themes, debates, and gaps, step 4 – outline your literature review’s structure, step 5 – write your literature review, free lecture slides, other interesting articles, frequently asked questions, introduction.

• Quick Run-through
• Step 1 & 2

When you write a thesis , dissertation , or research paper , you will likely have to conduct a literature review to situate your research within existing knowledge. The literature review gives you a chance to:

• Demonstrate your familiarity with the topic and its scholarly context
• Develop a theoretical framework and methodology for your research
• Position your work in relation to other researchers and theorists
• Show how your research addresses a gap or contributes to a debate
• Evaluate the current state of research and demonstrate your knowledge of the scholarly debates around your topic.

Writing literature reviews is a particularly important skill if you want to apply for graduate school or pursue a career in research. We’ve written a step-by-step guide that you can follow below.

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Writing literature reviews can be quite challenging! A good starting point could be to look at some examples, depending on what kind of literature review you’d like to write.

• Example literature review #1: “Why Do People Migrate? A Review of the Theoretical Literature” ( Theoretical literature review about the development of economic migration theory from the 1950s to today.)
• Example literature review #2: “Literature review as a research methodology: An overview and guidelines” ( Methodological literature review about interdisciplinary knowledge acquisition and production.)
• Example literature review #3: “The Use of Technology in English Language Learning: A Literature Review” ( Thematic literature review about the effects of technology on language acquisition.)
• Example literature review #4: “Learners’ Listening Comprehension Difficulties in English Language Learning: A Literature Review” ( Chronological literature review about how the concept of listening skills has changed over time.)

You can also check out our templates with literature review examples and sample outlines at the links below.

Download Word doc Download Google doc

Before you begin searching for literature, you need a clearly defined topic .

If you are writing the literature review section of a dissertation or research paper, you will search for literature related to your research problem and questions .

Make a list of keywords

Start by creating a list of keywords related to your research question. Include each of the key concepts or variables you’re interested in, and list any synonyms and related terms. You can add to this list as you discover new keywords in the process of your literature search.

• Social media, Facebook, Instagram, Twitter, Snapchat, TikTok
• Body image, self-perception, self-esteem, mental health
• Generation Z, teenagers, adolescents, youth

Search for relevant sources

Use your keywords to begin searching for sources. Some useful databases to search for journals and articles include:

• Your university’s library catalogue
• Google Scholar
• Project Muse (humanities and social sciences)
• Medline (life sciences and biomedicine)
• EconLit (economics)
• Inspec (physics, engineering and computer science)

You can also use boolean operators to help narrow down your search.

Make sure to read the abstract to find out whether an article is relevant to your question. When you find a useful book or article, you can check the bibliography to find other relevant sources.

You likely won’t be able to read absolutely everything that has been written on your topic, so it will be necessary to evaluate which sources are most relevant to your research question.

For each publication, ask yourself:

• What question or problem is the author addressing?
• What are the key concepts and how are they defined?
• What are the key theories, models, and methods?
• Does the research use established frameworks or take an innovative approach?
• What are the results and conclusions of the study?
• How does the publication relate to other literature in the field? Does it confirm, add to, or challenge established knowledge?
• What are the strengths and weaknesses of the research?

Make sure the sources you use are credible , and make sure you read any landmark studies and major theories in your field of research.

You can use our template to summarize and evaluate sources you’re thinking about using. Click on either button below to download.

Take notes and cite your sources

As you read, you should also begin the writing process. Take notes that you can later incorporate into the text of your literature review.

It is important to keep track of your sources with citations to avoid plagiarism . It can be helpful to make an annotated bibliography , where you compile full citation information and write a paragraph of summary and analysis for each source. This helps you remember what you read and saves time later in the process.

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To begin organizing your literature review’s argument and structure, be sure you understand the connections and relationships between the sources you’ve read. Based on your reading and notes, you can look for:

• Trends and patterns (in theory, method or results): do certain approaches become more or less popular over time?
• Themes: what questions or concepts recur across the literature?
• Debates, conflicts and contradictions: where do sources disagree?
• Pivotal publications: are there any influential theories or studies that changed the direction of the field?
• Gaps: what is missing from the literature? Are there weaknesses that need to be addressed?

This step will help you work out the structure of your literature review and (if applicable) show how your own research will contribute to existing knowledge.

• Most research has focused on young women.
• There is an increasing interest in the visual aspects of social media.
• But there is still a lack of robust research on highly visual platforms like Instagram and Snapchat—this is a gap that you could address in your own research.

There are various approaches to organizing the body of a literature review. Depending on the length of your literature review, you can combine several of these strategies (for example, your overall structure might be thematic, but each theme is discussed chronologically).

Chronological

The simplest approach is to trace the development of the topic over time. However, if you choose this strategy, be careful to avoid simply listing and summarizing sources in order.

Try to analyze patterns, turning points and key debates that have shaped the direction of the field. Give your interpretation of how and why certain developments occurred.

If you have found some recurring central themes, you can organize your literature review into subsections that address different aspects of the topic.

For example, if you are reviewing literature about inequalities in migrant health outcomes, key themes might include healthcare policy, language barriers, cultural attitudes, legal status, and economic access.

Methodological

If you draw your sources from different disciplines or fields that use a variety of research methods , you might want to compare the results and conclusions that emerge from different approaches. For example:

• Look at what results have emerged in qualitative versus quantitative research
• Discuss how the topic has been approached by empirical versus theoretical scholarship
• Divide the literature into sociological, historical, and cultural sources

Theoretical

A literature review is often the foundation for a theoretical framework . You can use it to discuss various theories, models, and definitions of key concepts.

You might argue for the relevance of a specific theoretical approach, or combine various theoretical concepts to create a framework for your research.

Like any other academic text , your literature review should have an introduction , a main body, and a conclusion . What you include in each depends on the objective of your literature review.

The introduction should clearly establish the focus and purpose of the literature review.

Depending on the length of your literature review, you might want to divide the body into subsections. You can use a subheading for each theme, time period, or methodological approach.

As you write, you can follow these tips:

• Summarize and synthesize: give an overview of the main points of each source and combine them into a coherent whole
• Analyze and interpret: don’t just paraphrase other researchers — add your own interpretations where possible, discussing the significance of findings in relation to the literature as a whole
• Critically evaluate: mention the strengths and weaknesses of your sources
• Write in well-structured paragraphs: use transition words and topic sentences to draw connections, comparisons and contrasts

In the conclusion, you should summarize the key findings you have taken from the literature and emphasize their significance.

When you’ve finished writing and revising your literature review, don’t forget to proofread thoroughly before submitting. Not a language expert? Check out Scribbr’s professional proofreading services !

This article has been adapted into lecture slides that you can use to teach your students about writing a literature review.

Scribbr slides are free to use, customize, and distribute for educational purposes.

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If you want to know more about the research process , methodology , research bias , or statistics , make sure to check out some of our other articles with explanations and examples.

• Sampling methods
• Simple random sampling
• Stratified sampling
• Cluster sampling
• Likert scales
• Reproducibility

 Statistics

• Null hypothesis
• Statistical power
• Probability distribution
• Effect size
• Poisson distribution

Research bias

• Optimism bias
• Cognitive bias
• Implicit bias
• Hawthorne effect
• Anchoring bias
• Explicit bias

A literature review is a survey of scholarly sources (such as books, journal articles, and theses) related to a specific topic or research question .

It is often written as part of a thesis, dissertation , or research paper , in order to situate your work in relation to existing knowledge.

There are several reasons to conduct a literature review at the beginning of a research project:

• To familiarize yourself with the current state of knowledge on your topic
• To ensure that you’re not just repeating what others have already done
• To identify gaps in knowledge and unresolved problems that your research can address
• To develop your theoretical framework and methodology
• To provide an overview of the key findings and debates on the topic

Writing the literature review shows your reader how your work relates to existing research and what new insights it will contribute.

The literature review usually comes near the beginning of your thesis or dissertation . After the introduction , it grounds your research in a scholarly field and leads directly to your theoretical framework or methodology .

A literature review is a survey of credible sources on a topic, often used in dissertations , theses, and research papers . Literature reviews give an overview of knowledge on a subject, helping you identify relevant theories and methods, as well as gaps in existing research. Literature reviews are set up similarly to other  academic texts , with an introduction , a main body, and a conclusion .

An  annotated bibliography is a list of  source references that has a short description (called an annotation ) for each of the sources. It is often assigned as part of the research process for a  paper .  

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Research Design

• First Online: 13 April 2022

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• Yanmei Li 3 &
• Sumei Zhang 4  

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This chapter introduces methods to design the research. Research design is the blueprint of how to conduct research from conception to completion. It requires careful crafts to ensure success. The initial step of research design is to theorize key concepts of the research questions, operationalize the variables used to measure the key concepts, and carefully identify the levels of measurements for all the key variables. After theorization of the key concepts, a thorough literature search and synthetization is imperative to explore extant studies related to the research questions. The purpose of literature review is to retrieve ideas, replicate studies, or fill the gap for issues and theories that extant research has (or has not) investigated.

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Opoku, A., Ahmed, V., & Akotia, J. (2016). Choosing an appropriate research methodology and method. In V. Ahmed, A. Opoku, & Z. Aziz (Eds.), Research methodology in the built environment: A selection of case studies . Routledge.

Pickering, C., Johnson, M., & Byrne, J. (2021). Using systematic quantitative literature reviews for urban analysis. In S. Baum (Ed.). Methods in Urban Analysis (Cities Research Series) (pp. 29–49) . Singapore: Springer.

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Statistically Efficient Methods for Computation-Aware Uncertainty Quantification and Rare-Event Optimization

He, Shengyi

The thesis covers two fundamental topics that are important across the disciplines of operations research, statistics and even more broadly, namely stochastic optimization and uncertainty quantification, with the common theme to address both statistical accuracy and computational constraints. Here, statistical accuracy encompasses the precision of estimated solutions in stochastic optimization, as well as the tightness or reliability of confidence intervals. Computational concerns arise from rare events or expensive models, necessitating efficient sampling methods or computation procedures. In the first half of this thesis, we study stochastic optimization that involves rare events, which arises in various contexts including risk-averse decision-making and training of machine learning models. Because of the presence of rare events, crude Monte Carlo methods can be prohibitively inefficient, as it takes a sample size reciprocal to the rare-event probability to obtain valid statistical information about the rare-event. To address this issue, we investigate the use of importance sampling (IS) to reduce the required sample size. IS is commonly used to handle rare events, and the idea is to sample from an alternative distribution that hits the rare event more frequently and adjusts the estimator with a likelihood ratio to retain unbiasedness. While IS has been long studied, most of its literature focuses on estimation problems and methodologies to obtain good IS in these contexts. Contrary to these studies, the first half of this thesis provides a systematic study on the efficient use of IS in stochastic optimization. In Chapter 2, we propose an adaptive procedure that converts an efficient IS for gradient estimation to an efficient IS procedure for stochastic optimization. Then, in Chapter 3, we provide an efficient IS for gradient estimation, which serves as the input for the procedure in Chapter 2. In the second half of this thesis, we study uncertainty quantification in the sense of constructing a confidence interval (CI) for target model quantities or prediction. We are interested in the setting of expensive black-box models, which means that we are confined to using a low number of model runs, and we also lack the ability to obtain auxiliary model information such as gradients. In this case, a classical method is batching, which divides data into a few batches and then constructs a CI based on the batched estimates. Another method is the recently proposed cheap bootstrap that is constructed on a few resamples in a similar manner as batching. These methods could save computation since they do not need an accurate variability estimator which requires sufficient model evaluations to obtain. Instead, they cancel out the variability when constructing pivotal statistics, and thus obtain asymptotically valid t-distribution-based CIs with only few batches or resamples. The second half of this thesis studies several theoretical aspects of these computation-aware CI construction methods. In Chapter 4, we study the statistical optimality on CI tightness among various computation-aware CIs. Then, in Chapter 5, we study the higher-order coverage errors of batching methods. Finally, Chapter 6 is a related investigation on the higher-order coverage and correction of distributionally robust optimization (DRO) as another CI construction tool, which assumes an amount of analytical information on the model but bears similarity to Chapter 5 in terms of analysis techniques.

• Operations research
• Stochastic processes--Mathematical models
• Mathematical optimization
• Bootstrap (Statistics)
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re — Regular expression operations ¶

Source code: Lib/re/

This module provides regular expression matching operations similar to those found in Perl.

Both patterns and strings to be searched can be Unicode strings ( str ) as well as 8-bit strings ( bytes ). However, Unicode strings and 8-bit strings cannot be mixed: that is, you cannot match a Unicode string with a bytes pattern or vice-versa; similarly, when asking for a substitution, the replacement string must be of the same type as both the pattern and the search string.

Regular expressions use the backslash character ( '\' ) to indicate special forms or to allow special characters to be used without invoking their special meaning. This collides with Python’s usage of the same character for the same purpose in string literals; for example, to match a literal backslash, one might have to write '\\\\' as the pattern string, because the regular expression must be \\ , and each backslash must be expressed as \\ inside a regular Python string literal. Also, please note that any invalid escape sequences in Python’s usage of the backslash in string literals now generate a SyntaxWarning and in the future this will become a SyntaxError . This behaviour will happen even if it is a valid escape sequence for a regular expression.

The solution is to use Python’s raw string notation for regular expression patterns; backslashes are not handled in any special way in a string literal prefixed with 'r' . So r"\n" is a two-character string containing '\' and 'n' , while "\n" is a one-character string containing a newline. Usually patterns will be expressed in Python code using this raw string notation.

It is important to note that most regular expression operations are available as module-level functions and methods on compiled regular expressions . The functions are shortcuts that don’t require you to compile a regex object first, but miss some fine-tuning parameters.

The third-party regex module, which has an API compatible with the standard library re module, but offers additional functionality and a more thorough Unicode support.

Regular Expression Syntax ¶

A regular expression (or RE) specifies a set of strings that matches it; the functions in this module let you check if a particular string matches a given regular expression (or if a given regular expression matches a particular string, which comes down to the same thing).

Regular expressions can be concatenated to form new regular expressions; if A and B are both regular expressions, then AB is also a regular expression. In general, if a string p matches A and another string q matches B , the string pq will match AB. This holds unless A or B contain low precedence operations; boundary conditions between A and B ; or have numbered group references. Thus, complex expressions can easily be constructed from simpler primitive expressions like the ones described here. For details of the theory and implementation of regular expressions, consult the Friedl book [Frie09] , or almost any textbook about compiler construction.

A brief explanation of the format of regular expressions follows. For further information and a gentler presentation, consult the Regular Expression HOWTO .

Regular expressions can contain both special and ordinary characters. Most ordinary characters, like 'A' , 'a' , or '0' , are the simplest regular expressions; they simply match themselves. You can concatenate ordinary characters, so last matches the string 'last' . (In the rest of this section, we’ll write RE’s in this special style , usually without quotes, and strings to be matched 'in single quotes' .)

Some characters, like '|' or '(' , are special. Special characters either stand for classes of ordinary characters, or affect how the regular expressions around them are interpreted.

Repetition operators or quantifiers ( * , + , ? , {m,n} , etc) cannot be directly nested. This avoids ambiguity with the non-greedy modifier suffix ? , and with other modifiers in other implementations. To apply a second repetition to an inner repetition, parentheses may be used. For example, the expression (?:a{6})* matches any multiple of six 'a' characters.

The special characters are:

(Dot.) In the default mode, this matches any character except a newline. If the DOTALL flag has been specified, this matches any character including a newline.

(Caret.) Matches the start of the string, and in MULTILINE mode also matches immediately after each newline.

Matches the end of the string or just before the newline at the end of the string, and in MULTILINE mode also matches before a newline. foo matches both ‘foo’ and ‘foobar’, while the regular expression foo$ matches only ‘foo’. More interestingly, searching for foo.$ in 'foo1\nfoo2\n' matches ‘foo2’ normally, but ‘foo1’ in MULTILINE mode; searching for a single $ in 'foo\n' will find two (empty) matches: one just before the newline, and one at the end of the string.

Causes the resulting RE to match 0 or more repetitions of the preceding RE, as many repetitions as are possible. ab* will match ‘a’, ‘ab’, or ‘a’ followed by any number of ‘b’s.

Causes the resulting RE to match 1 or more repetitions of the preceding RE. ab+ will match ‘a’ followed by any non-zero number of ‘b’s; it will not match just ‘a’.

Causes the resulting RE to match 0 or 1 repetitions of the preceding RE. ab? will match either ‘a’ or ‘ab’.

The '*' , '+' , and '?' quantifiers are all greedy ; they match as much text as possible. Sometimes this behaviour isn’t desired; if the RE <.*> is matched against '<a> b <c>' , it will match the entire string, and not just '<a>' . Adding ? after the quantifier makes it perform the match in non-greedy or minimal fashion; as few characters as possible will be matched. Using the RE <.*?> will match only '<a>' .

Like the '*' , '+' , and '?' quantifiers, those where '+' is appended also match as many times as possible. However, unlike the true greedy quantifiers, these do not allow back-tracking when the expression following it fails to match. These are known as possessive quantifiers. For example, a*a will match 'aaaa' because the a* will match all 4 'a' s, but, when the final 'a' is encountered, the expression is backtracked so that in the end the a* ends up matching 3 'a' s total, and the fourth 'a' is matched by the final 'a' . However, when a*+a is used to match 'aaaa' , the a*+ will match all 4 'a' , but when the final 'a' fails to find any more characters to match, the expression cannot be backtracked and will thus fail to match. x*+ , x++ and x?+ are equivalent to (?>x*) , (?>x+) and (?>x?) correspondingly.

Added in version 3.11.

Specifies that exactly m copies of the previous RE should be matched; fewer matches cause the entire RE not to match. For example, a{6} will match exactly six 'a' characters, but not five.

Causes the resulting RE to match from m to n repetitions of the preceding RE, attempting to match as many repetitions as possible. For example, a{3,5} will match from 3 to 5 'a' characters. Omitting m specifies a lower bound of zero, and omitting n specifies an infinite upper bound. As an example, a{4,}b will match 'aaaab' or a thousand 'a' characters followed by a 'b' , but not 'aaab' . The comma may not be omitted or the modifier would be confused with the previously described form.

Causes the resulting RE to match from m to n repetitions of the preceding RE, attempting to match as few repetitions as possible. This is the non-greedy version of the previous quantifier. For example, on the 6-character string 'aaaaaa' , a{3,5} will match 5 'a' characters, while a{3,5}? will only match 3 characters.

Causes the resulting RE to match from m to n repetitions of the preceding RE, attempting to match as many repetitions as possible without establishing any backtracking points. This is the possessive version of the quantifier above. For example, on the 6-character string 'aaaaaa' , a{3,5}+aa attempt to match 5 'a' characters, then, requiring 2 more 'a' s, will need more characters than available and thus fail, while a{3,5}aa will match with a{3,5} capturing 5, then 4 'a' s by backtracking and then the final 2 'a' s are matched by the final aa in the pattern. x{m,n}+ is equivalent to (?>x{m,n}) .

Either escapes special characters (permitting you to match characters like '*' , '?' , and so forth), or signals a special sequence; special sequences are discussed below.

If you’re not using a raw string to express the pattern, remember that Python also uses the backslash as an escape sequence in string literals; if the escape sequence isn’t recognized by Python’s parser, the backslash and subsequent character are included in the resulting string. However, if Python would recognize the resulting sequence, the backslash should be repeated twice. This is complicated and hard to understand, so it’s highly recommended that you use raw strings for all but the simplest expressions.

Used to indicate a set of characters. In a set:

Characters can be listed individually, e.g. [amk] will match 'a' , 'm' , or 'k' .

Ranges of characters can be indicated by giving two characters and separating them by a '-' , for example [a-z] will match any lowercase ASCII letter, [0-5][0-9] will match all the two-digits numbers from 00 to 59 , and [0-9A-Fa-f] will match any hexadecimal digit. If - is escaped (e.g. [a\-z] ) or if it’s placed as the first or last character (e.g. [-a] or [a-] ), it will match a literal '-' .

Special characters lose their special meaning inside sets. For example, [(+*)] will match any of the literal characters '(' , '+' , '*' , or ')' .

Character classes such as \w or \S (defined below) are also accepted inside a set, although the characters they match depend on the flags used.

Characters that are not within a range can be matched by complementing the set. If the first character of the set is '^' , all the characters that are not in the set will be matched. For example, [^5] will match any character except '5' , and [^^] will match any character except '^' . ^ has no special meaning if it’s not the first character in the set.

To match a literal ']' inside a set, precede it with a backslash, or place it at the beginning of the set. For example, both [()[\]{}] and []()[{}] will match a right bracket, as well as left bracket, braces, and parentheses.

Support of nested sets and set operations as in Unicode Technical Standard #18 might be added in the future. This would change the syntax, so to facilitate this change a FutureWarning will be raised in ambiguous cases for the time being. That includes sets starting with a literal '[' or containing literal character sequences '--' , '&&' , '~~' , and '||' . To avoid a warning escape them with a backslash.

Changed in version 3.7: FutureWarning is raised if a character set contains constructs that will change semantically in the future.

A|B , where A and B can be arbitrary REs, creates a regular expression that will match either A or B . An arbitrary number of REs can be separated by the '|' in this way. This can be used inside groups (see below) as well. As the target string is scanned, REs separated by '|' are tried from left to right. When one pattern completely matches, that branch is accepted. This means that once A matches, B will not be tested further, even if it would produce a longer overall match. In other words, the '|' operator is never greedy. To match a literal '|' , use \| , or enclose it inside a character class, as in [|] .

Matches whatever regular expression is inside the parentheses, and indicates the start and end of a group; the contents of a group can be retrieved after a match has been performed, and can be matched later in the string with the \number special sequence, described below. To match the literals '(' or ')' , use \( or \) , or enclose them inside a character class: [(] , [)] .

This is an extension notation (a '?' following a '(' is not meaningful otherwise). The first character after the '?' determines what the meaning and further syntax of the construct is. Extensions usually do not create a new group; (?P<name>...) is the only exception to this rule. Following are the currently supported extensions.

(One or more letters from the set 'a' , 'i' , 'L' , 'm' , 's' , 'u' , 'x' .) The group matches the empty string; the letters set the corresponding flags for the entire regular expression:

re.A (ASCII-only matching)

re.I (ignore case)

re.L (locale dependent)

re.M (multi-line)

re.S (dot matches all)

re.U (Unicode matching)

re.X (verbose)

(The flags are described in Module Contents .) This is useful if you wish to include the flags as part of the regular expression, instead of passing a flag argument to the re.compile() function. Flags should be used first in the expression string.

Changed in version 3.11: This construction can only be used at the start of the expression.

A non-capturing version of regular parentheses. Matches whatever regular expression is inside the parentheses, but the substring matched by the group cannot be retrieved after performing a match or referenced later in the pattern.

(Zero or more letters from the set 'a' , 'i' , 'L' , 'm' , 's' , 'u' , 'x' , optionally followed by '-' followed by one or more letters from the 'i' , 'm' , 's' , 'x' .) The letters set or remove the corresponding flags for the part of the expression:

(The flags are described in Module Contents .)

The letters 'a' , 'L' and 'u' are mutually exclusive when used as inline flags, so they can’t be combined or follow '-' . Instead, when one of them appears in an inline group, it overrides the matching mode in the enclosing group. In Unicode patterns (?a:...) switches to ASCII-only matching, and (?u:...) switches to Unicode matching (default). In bytes patterns (?L:...) switches to locale dependent matching, and (?a:...) switches to ASCII-only matching (default). This override is only in effect for the narrow inline group, and the original matching mode is restored outside of the group.

Added in version 3.6.

Changed in version 3.7: The letters 'a' , 'L' and 'u' also can be used in a group.

Attempts to match ... as if it was a separate regular expression, and if successful, continues to match the rest of the pattern following it. If the subsequent pattern fails to match, the stack can only be unwound to a point before the (?>...) because once exited, the expression, known as an atomic group , has thrown away all stack points within itself. Thus, (?>.*). would never match anything because first the .* would match all characters possible, then, having nothing left to match, the final . would fail to match. Since there are no stack points saved in the Atomic Group, and there is no stack point before it, the entire expression would thus fail to match.

Similar to regular parentheses, but the substring matched by the group is accessible via the symbolic group name name . Group names must be valid Python identifiers, and in bytes patterns they can only contain bytes in the ASCII range. Each group name must be defined only once within a regular expression. A symbolic group is also a numbered group, just as if the group were not named.

Named groups can be referenced in three contexts. If the pattern is (?P<quote>['"]).*?(?P=quote) (i.e. matching a string quoted with either single or double quotes):

Changed in version 3.12: In bytes patterns, group name can only contain bytes in the ASCII range ( b'\x00' - b'\x7f' ).

A backreference to a named group; it matches whatever text was matched by the earlier group named name .

A comment; the contents of the parentheses are simply ignored.

Matches if ... matches next, but doesn’t consume any of the string. This is called a lookahead assertion . For example, Isaac (?=Asimov) will match 'Isaac ' only if it’s followed by 'Asimov' .

Matches if ... doesn’t match next. This is a negative lookahead assertion . For example, Isaac (?!Asimov) will match 'Isaac ' only if it’s not followed by 'Asimov' .

Matches if the current position in the string is preceded by a match for ... that ends at the current position. This is called a positive lookbehind assertion . (?<=abc)def will find a match in 'abcdef' , since the lookbehind will back up 3 characters and check if the contained pattern matches. The contained pattern must only match strings of some fixed length, meaning that abc or a|b are allowed, but a* and a{3,4} are not. Note that patterns which start with positive lookbehind assertions will not match at the beginning of the string being searched; you will most likely want to use the search() function rather than the match() function:

This example looks for a word following a hyphen:

Changed in version 3.5: Added support for group references of fixed length.

Matches if the current position in the string is not preceded by a match for ... . This is called a negative lookbehind assertion . Similar to positive lookbehind assertions, the contained pattern must only match strings of some fixed length. Patterns which start with negative lookbehind assertions may match at the beginning of the string being searched.

Will try to match with yes-pattern if the group with given id or name exists, and with no-pattern if it doesn’t. no-pattern is optional and can be omitted. For example, (<)?(\w+@\w+(?:\.\w+)+)(?(1)>|$) is a poor email matching pattern, which will match with '<user@host.com>' as well as 'user@host.com' , but not with '<user@host.com' nor 'user@host.com>' .

Changed in version 3.12: Group id can only contain ASCII digits. In bytes patterns, group name can only contain bytes in the ASCII range ( b'\x00' - b'\x7f' ).

The special sequences consist of '\' and a character from the list below. If the ordinary character is not an ASCII digit or an ASCII letter, then the resulting RE will match the second character. For example, \$ matches the character '$' .

Matches the contents of the group of the same number. Groups are numbered starting from 1. For example, (.+) \1 matches 'the the' or '55 55' , but not 'thethe' (note the space after the group). This special sequence can only be used to match one of the first 99 groups. If the first digit of number is 0, or number is 3 octal digits long, it will not be interpreted as a group match, but as the character with octal value number . Inside the '[' and ']' of a character class, all numeric escapes are treated as characters.

Matches only at the start of the string.

Matches the empty string, but only at the beginning or end of a word. A word is defined as a sequence of word characters. Note that formally, \b is defined as the boundary between a \w and a \W character (or vice versa), or between \w and the beginning or end of the string. This means that r'\bat\b' matches 'at' , 'at.' , '(at)' , and 'as at ay' but not 'attempt' or 'atlas' .

The default word characters in Unicode (str) patterns are Unicode alphanumerics and the underscore, but this can be changed by using the ASCII flag. Word boundaries are determined by the current locale if the LOCALE flag is used.

Inside a character range, \b represents the backspace character, for compatibility with Python’s string literals.

Matches the empty string, but only when it is not at the beginning or end of a word. This means that r'at\B' matches 'athens' , 'atom' , 'attorney' , but not 'at' , 'at.' , or 'at!' . \B is the opposite of \b , so word characters in Unicode (str) patterns are Unicode alphanumerics or the underscore, although this can be changed by using the ASCII flag. Word boundaries are determined by the current locale if the LOCALE flag is used.

Matches any Unicode decimal digit (that is, any character in Unicode character category [Nd] ). This includes [0-9] , and also many other digit characters.

Matches [0-9] if the ASCII flag is used.

Matches any decimal digit in the ASCII character set; this is equivalent to [0-9] .

Matches any character which is not a decimal digit. This is the opposite of \d .

Matches [^0-9] if the ASCII flag is used.

Matches Unicode whitespace characters (which includes [ \t\n\r\f\v] , and also many other characters, for example the non-breaking spaces mandated by typography rules in many languages).

Matches [ \t\n\r\f\v] if the ASCII flag is used.

Matches characters considered whitespace in the ASCII character set; this is equivalent to [ \t\n\r\f\v] .

Matches any character which is not a whitespace character. This is the opposite of \s .

Matches [^ \t\n\r\f\v] if the ASCII flag is used.

Matches Unicode word characters; this includes all Unicode alphanumeric characters (as defined by str.isalnum() ), as well as the underscore ( _ ).

Matches [a-zA-Z0-9_] if the ASCII flag is used.

Matches characters considered alphanumeric in the ASCII character set; this is equivalent to [a-zA-Z0-9_] . If the LOCALE flag is used, matches characters considered alphanumeric in the current locale and the underscore.

Matches any character which is not a word character. This is the opposite of \w . By default, matches non-underscore ( _ ) characters for which str.isalnum() returns False .

Matches [^a-zA-Z0-9_] if the ASCII flag is used.

If the LOCALE flag is used, matches characters which are neither alphanumeric in the current locale nor the underscore.

Matches only at the end of the string.

Most of the escape sequences supported by Python string literals are also accepted by the regular expression parser:

(Note that \b is used to represent word boundaries, and means “backspace” only inside character classes.)

'\u' , '\U' , and '\N' escape sequences are only recognized in Unicode (str) patterns. In bytes patterns they are errors. Unknown escapes of ASCII letters are reserved for future use and treated as errors.

Octal escapes are included in a limited form. If the first digit is a 0, or if there are three octal digits, it is considered an octal escape. Otherwise, it is a group reference. As for string literals, octal escapes are always at most three digits in length.

Changed in version 3.3: The '\u' and '\U' escape sequences have been added.

Changed in version 3.6: Unknown escapes consisting of '\' and an ASCII letter now are errors.

Changed in version 3.8: The '\N{ name }' escape sequence has been added. As in string literals, it expands to the named Unicode character (e.g. '\N{EM DASH}' ).

Module Contents ¶

The module defines several functions, constants, and an exception. Some of the functions are simplified versions of the full featured methods for compiled regular expressions. Most non-trivial applications always use the compiled form.

Changed in version 3.6: Flag constants are now instances of RegexFlag , which is a subclass of enum.IntFlag .

An enum.IntFlag class containing the regex options listed below.

Added in version 3.11: - added to __all__

Make \w , \W , \b , \B , \d , \D , \s and \S perform ASCII-only matching instead of full Unicode matching. This is only meaningful for Unicode (str) patterns, and is ignored for bytes patterns.

Corresponds to the inline flag (?a) .

The U flag still exists for backward compatibility, but is redundant in Python 3 since matches are Unicode by default for str patterns, and Unicode matching isn’t allowed for bytes patterns. UNICODE and the inline flag (?u) are similarly redundant.

Display debug information about compiled expression.

No corresponding inline flag.

Perform case-insensitive matching; expressions like [A-Z] will also match lowercase letters. Full Unicode matching (such as Ü matching ü ) also works unless the ASCII flag is used to disable non-ASCII matches. The current locale does not change the effect of this flag unless the LOCALE flag is also used.

Corresponds to the inline flag (?i) .

Note that when the Unicode patterns [a-z] or [A-Z] are used in combination with the IGNORECASE flag, they will match the 52 ASCII letters and 4 additional non-ASCII letters: ‘İ’ (U+0130, Latin capital letter I with dot above), ‘ı’ (U+0131, Latin small letter dotless i), ‘ſ’ (U+017F, Latin small letter long s) and ‘K’ (U+212A, Kelvin sign). If the ASCII flag is used, only letters ‘a’ to ‘z’ and ‘A’ to ‘Z’ are matched.

Make \w , \W , \b , \B and case-insensitive matching dependent on the current locale. This flag can be used only with bytes patterns.

Corresponds to the inline flag (?L) .

This flag is discouraged; consider Unicode matching instead. The locale mechanism is very unreliable as it only handles one “culture” at a time and only works with 8-bit locales. Unicode matching is enabled by default for Unicode (str) patterns and it is able to handle different locales and languages.

Changed in version 3.6: LOCALE can be used only with bytes patterns and is not compatible with ASCII .

Changed in version 3.7: Compiled regular expression objects with the LOCALE flag no longer depend on the locale at compile time. Only the locale at matching time affects the result of matching.

When specified, the pattern character '^' matches at the beginning of the string and at the beginning of each line (immediately following each newline); and the pattern character '$' matches at the end of the string and at the end of each line (immediately preceding each newline). By default, '^' matches only at the beginning of the string, and '$' only at the end of the string and immediately before the newline (if any) at the end of the string.

Corresponds to the inline flag (?m) .

Indicates no flag being applied, the value is 0 . This flag may be used as a default value for a function keyword argument or as a base value that will be conditionally ORed with other flags. Example of use as a default value:

Make the '.' special character match any character at all, including a newline; without this flag, '.' will match anything except a newline.

Corresponds to the inline flag (?s) .

In Python 3, Unicode characters are matched by default for str patterns. This flag is therefore redundant with no effect and is only kept for backward compatibility.

See ASCII to restrict matching to ASCII characters instead.

This flag allows you to write regular expressions that look nicer and are more readable by allowing you to visually separate logical sections of the pattern and add comments. Whitespace within the pattern is ignored, except when in a character class, or when preceded by an unescaped backslash, or within tokens like *? , (?: or (?P<...> . For example, (? : and * ? are not allowed. When a line contains a # that is not in a character class and is not preceded by an unescaped backslash, all characters from the leftmost such # through the end of the line are ignored.

This means that the two following regular expression objects that match a decimal number are functionally equal:

Corresponds to the inline flag (?x) .

Functions ¶

Compile a regular expression pattern into a regular expression object , which can be used for matching using its match() , search() and other methods, described below.

The expression’s behaviour can be modified by specifying a flags value. Values can be any of the flags variables, combined using bitwise OR (the | operator).

The sequence

is equivalent to

but using re.compile() and saving the resulting regular expression object for reuse is more efficient when the expression will be used several times in a single program.

The compiled versions of the most recent patterns passed to re.compile() and the module-level matching functions are cached, so programs that use only a few regular expressions at a time needn’t worry about compiling regular expressions.

Scan through string looking for the first location where the regular expression pattern produces a match, and return a corresponding Match . Return None if no position in the string matches the pattern; note that this is different from finding a zero-length match at some point in the string.

If zero or more characters at the beginning of string match the regular expression pattern , return a corresponding Match . Return None if the string does not match the pattern; note that this is different from a zero-length match.

Note that even in MULTILINE mode, re.match() will only match at the beginning of the string and not at the beginning of each line.

If you want to locate a match anywhere in string , use search() instead (see also search() vs. match() ).

If the whole string matches the regular expression pattern , return a corresponding Match . Return None if the string does not match the pattern; note that this is different from a zero-length match.

Added in version 3.4.

Split string by the occurrences of pattern . If capturing parentheses are used in pattern , then the text of all groups in the pattern are also returned as part of the resulting list. If maxsplit is nonzero, at most maxsplit splits occur, and the remainder of the string is returned as the final element of the list.

If there are capturing groups in the separator and it matches at the start of the string, the result will start with an empty string. The same holds for the end of the string:

That way, separator components are always found at the same relative indices within the result list.

Empty matches for the pattern split the string only when not adjacent to a previous empty match.

Changed in version 3.1: Added the optional flags argument.

Changed in version 3.7: Added support of splitting on a pattern that could match an empty string.

Return all non-overlapping matches of pattern in string , as a list of strings or tuples. The string is scanned left-to-right, and matches are returned in the order found. Empty matches are included in the result.

The result depends on the number of capturing groups in the pattern. If there are no groups, return a list of strings matching the whole pattern. If there is exactly one group, return a list of strings matching that group. If multiple groups are present, return a list of tuples of strings matching the groups. Non-capturing groups do not affect the form of the result.

Changed in version 3.7: Non-empty matches can now start just after a previous empty match.

Return an iterator yielding Match objects over all non-overlapping matches for the RE pattern in string . The string is scanned left-to-right, and matches are returned in the order found. Empty matches are included in the result.

Return the string obtained by replacing the leftmost non-overlapping occurrences of pattern in string by the replacement repl . If the pattern isn’t found, string is returned unchanged. repl can be a string or a function; if it is a string, any backslash escapes in it are processed. That is, \n is converted to a single newline character, \r is converted to a carriage return, and so forth. Unknown escapes of ASCII letters are reserved for future use and treated as errors. Other unknown escapes such as \& are left alone. Backreferences, such as \6 , are replaced with the substring matched by group 6 in the pattern. For example:

If repl is a function, it is called for every non-overlapping occurrence of pattern . The function takes a single Match argument, and returns the replacement string. For example:

The pattern may be a string or a Pattern .

The optional argument count is the maximum number of pattern occurrences to be replaced; count must be a non-negative integer. If omitted or zero, all occurrences will be replaced. Empty matches for the pattern are replaced only when not adjacent to a previous empty match, so sub('x*', '-', 'abxd') returns '-a-b--d-' .

In string-type repl arguments, in addition to the character escapes and backreferences described above, \g<name> will use the substring matched by the group named name , as defined by the (?P<name>...) syntax. \g<number> uses the corresponding group number; \g<2> is therefore equivalent to \2 , but isn’t ambiguous in a replacement such as \g<2>0 . \20 would be interpreted as a reference to group 20, not a reference to group 2 followed by the literal character '0' . The backreference \g<0> substitutes in the entire substring matched by the RE.

Changed in version 3.5: Unmatched groups are replaced with an empty string.

Changed in version 3.6: Unknown escapes in pattern consisting of '\' and an ASCII letter now are errors.

Changed in version 3.7: Unknown escapes in repl consisting of '\' and an ASCII letter now are errors.

Changed in version 3.7: Empty matches for the pattern are replaced when adjacent to a previous non-empty match.

Changed in version 3.12: Group id can only contain ASCII digits. In bytes replacement strings, group name can only contain bytes in the ASCII range ( b'\x00' - b'\x7f' ).

Perform the same operation as sub() , but return a tuple (new_string, number_of_subs_made) .

Escape special characters in pattern . This is useful if you want to match an arbitrary literal string that may have regular expression metacharacters in it. For example:

This function must not be used for the replacement string in sub() and subn() , only backslashes should be escaped. For example:

Changed in version 3.3: The '_' character is no longer escaped.

Changed in version 3.7: Only characters that can have special meaning in a regular expression are escaped. As a result, '!' , '"' , '%' , "'" , ',' , '/' , ':' , ';' , '<' , '=' , '>' , '@' , and "`" are no longer escaped.

Clear the regular expression cache.

Exceptions ¶

Exception raised when a string passed to one of the functions here is not a valid regular expression (for example, it might contain unmatched parentheses) or when some other error occurs during compilation or matching. It is never an error if a string contains no match for a pattern. The error instance has the following additional attributes:

The unformatted error message.

The regular expression pattern.

The index in pattern where compilation failed (may be None ).

The line corresponding to pos (may be None ).

The column corresponding to pos (may be None ).

Changed in version 3.5: Added additional attributes.

Regular Expression Objects ¶

Compiled regular expression object returned by re.compile() .

Changed in version 3.9: re.Pattern supports [] to indicate a Unicode (str) or bytes pattern. See Generic Alias Type .

Scan through string looking for the first location where this regular expression produces a match, and return a corresponding Match . Return None if no position in the string matches the pattern; note that this is different from finding a zero-length match at some point in the string.

The optional second parameter pos gives an index in the string where the search is to start; it defaults to 0 . This is not completely equivalent to slicing the string; the '^' pattern character matches at the real beginning of the string and at positions just after a newline, but not necessarily at the index where the search is to start.

The optional parameter endpos limits how far the string will be searched; it will be as if the string is endpos characters long, so only the characters from pos to endpos - 1 will be searched for a match. If endpos is less than pos , no match will be found; otherwise, if rx is a compiled regular expression object, rx.search(string, 0, 50) is equivalent to rx.search(string[:50], 0) .

If zero or more characters at the beginning of string match this regular expression, return a corresponding Match . Return None if the string does not match the pattern; note that this is different from a zero-length match.

The optional pos and endpos parameters have the same meaning as for the search() method.

If the whole string matches this regular expression, return a corresponding Match . Return None if the string does not match the pattern; note that this is different from a zero-length match.

Identical to the split() function, using the compiled pattern.

Similar to the findall() function, using the compiled pattern, but also accepts optional pos and endpos parameters that limit the search region like for search() .

Similar to the finditer() function, using the compiled pattern, but also accepts optional pos and endpos parameters that limit the search region like for search() .

Identical to the sub() function, using the compiled pattern.

Identical to the subn() function, using the compiled pattern.

The regex matching flags. This is a combination of the flags given to compile() , any (?...) inline flags in the pattern, and implicit flags such as UNICODE if the pattern is a Unicode string.

The number of capturing groups in the pattern.

A dictionary mapping any symbolic group names defined by (?P<id>) to group numbers. The dictionary is empty if no symbolic groups were used in the pattern.

The pattern string from which the pattern object was compiled.

Changed in version 3.7: Added support of copy.copy() and copy.deepcopy() . Compiled regular expression objects are considered atomic.

Match Objects ¶

Match objects always have a boolean value of True . Since match() and search() return None when there is no match, you can test whether there was a match with a simple if statement:

Match object returned by successful match es and search es.

Changed in version 3.9: re.Match supports [] to indicate a Unicode (str) or bytes match. See Generic Alias Type .

Return the string obtained by doing backslash substitution on the template string template , as done by the sub() method. Escapes such as \n are converted to the appropriate characters, and numeric backreferences ( \1 , \2 ) and named backreferences ( \g<1> , \g<name> ) are replaced by the contents of the corresponding group. The backreference \g<0> will be replaced by the entire match.

Returns one or more subgroups of the match. If there is a single argument, the result is a single string; if there are multiple arguments, the result is a tuple with one item per argument. Without arguments, group1 defaults to zero (the whole match is returned). If a groupN argument is zero, the corresponding return value is the entire matching string; if it is in the inclusive range [1..99], it is the string matching the corresponding parenthesized group. If a group number is negative or larger than the number of groups defined in the pattern, an IndexError exception is raised. If a group is contained in a part of the pattern that did not match, the corresponding result is None . If a group is contained in a part of the pattern that matched multiple times, the last match is returned.

If the regular expression uses the (?P<name>...) syntax, the groupN arguments may also be strings identifying groups by their group name. If a string argument is not used as a group name in the pattern, an IndexError exception is raised.

A moderately complicated example:

Named groups can also be referred to by their index:

If a group matches multiple times, only the last match is accessible:

This is identical to m.group(g) . This allows easier access to an individual group from a match:

Named groups are supported as well:

Return a tuple containing all the subgroups of the match, from 1 up to however many groups are in the pattern. The default argument is used for groups that did not participate in the match; it defaults to None .

For example:

If we make the decimal place and everything after it optional, not all groups might participate in the match. These groups will default to None unless the default argument is given:

Return a dictionary containing all the named subgroups of the match, keyed by the subgroup name. The default argument is used for groups that did not participate in the match; it defaults to None . For example:

Return the indices of the start and end of the substring matched by group ; group defaults to zero (meaning the whole matched substring). Return -1 if group exists but did not contribute to the match. For a match object m , and a group g that did contribute to the match, the substring matched by group g (equivalent to m.group(g) ) is

Note that m.start(group) will equal m.end(group) if group matched a null string. For example, after m = re.search('b(c?)', 'cba') , m.start(0) is 1, m.end(0) is 2, m.start(1) and m.end(1) are both 2, and m.start(2) raises an IndexError exception.

An example that will remove remove_this from email addresses:

For a match m , return the 2-tuple (m.start(group), m.end(group)) . Note that if group did not contribute to the match, this is (-1, -1) . group defaults to zero, the entire match.

The value of pos which was passed to the search() or match() method of a regex object . This is the index into the string at which the RE engine started looking for a match.

The value of endpos which was passed to the search() or match() method of a regex object . This is the index into the string beyond which the RE engine will not go.

The integer index of the last matched capturing group, or None if no group was matched at all. For example, the expressions (a)b , ((a)(b)) , and ((ab)) will have lastindex == 1 if applied to the string 'ab' , while the expression (a)(b) will have lastindex == 2 , if applied to the same string.

The name of the last matched capturing group, or None if the group didn’t have a name, or if no group was matched at all.

The regular expression object whose match() or search() method produced this match instance.

The string passed to match() or search() .

Changed in version 3.7: Added support of copy.copy() and copy.deepcopy() . Match objects are considered atomic.

Regular Expression Examples ¶

Checking for a pair ¶.

In this example, we’ll use the following helper function to display match objects a little more gracefully:

Suppose you are writing a poker program where a player’s hand is represented as a 5-character string with each character representing a card, “a” for ace, “k” for king, “q” for queen, “j” for jack, “t” for 10, and “2” through “9” representing the card with that value.

To see if a given string is a valid hand, one could do the following:

That last hand, "727ak" , contained a pair, or two of the same valued cards. To match this with a regular expression, one could use backreferences as such:

To find out what card the pair consists of, one could use the group() method of the match object in the following manner:

Simulating scanf() ¶

Python does not currently have an equivalent to scanf() . Regular expressions are generally more powerful, though also more verbose, than scanf() format strings. The table below offers some more-or-less equivalent mappings between scanf() format tokens and regular expressions.

To extract the filename and numbers from a string like

you would use a scanf() format like

The equivalent regular expression would be

search() vs. match() ¶

Python offers different primitive operations based on regular expressions:

re.match() checks for a match only at the beginning of the string

re.search() checks for a match anywhere in the string (this is what Perl does by default)

re.fullmatch() checks for entire string to be a match

Regular expressions beginning with '^' can be used with search() to restrict the match at the beginning of the string:

Note however that in MULTILINE mode match() only matches at the beginning of the string, whereas using search() with a regular expression beginning with '^' will match at the beginning of each line.

Making a Phonebook ¶

split() splits a string into a list delimited by the passed pattern. The method is invaluable for converting textual data into data structures that can be easily read and modified by Python as demonstrated in the following example that creates a phonebook.

First, here is the input. Normally it may come from a file, here we are using triple-quoted string syntax

The entries are separated by one or more newlines. Now we convert the string into a list with each nonempty line having its own entry:

Finally, split each entry into a list with first name, last name, telephone number, and address. We use the maxsplit parameter of split() because the address has spaces, our splitting pattern, in it:

The :? pattern matches the colon after the last name, so that it does not occur in the result list. With a maxsplit of 4 , we could separate the house number from the street name:

Text Munging ¶

sub() replaces every occurrence of a pattern with a string or the result of a function. This example demonstrates using sub() with a function to “munge” text, or randomize the order of all the characters in each word of a sentence except for the first and last characters:

Finding all Adverbs ¶

findall() matches all occurrences of a pattern, not just the first one as search() does. For example, if a writer wanted to find all of the adverbs in some text, they might use findall() in the following manner:

Finding all Adverbs and their Positions ¶

If one wants more information about all matches of a pattern than the matched text, finditer() is useful as it provides Match objects instead of strings. Continuing with the previous example, if a writer wanted to find all of the adverbs and their positions in some text, they would use finditer() in the following manner:

Raw String Notation ¶

Raw string notation ( r"text" ) keeps regular expressions sane. Without it, every backslash ( '\' ) in a regular expression would have to be prefixed with another one to escape it. For example, the two following lines of code are functionally identical:

When one wants to match a literal backslash, it must be escaped in the regular expression. With raw string notation, this means r"\\" . Without raw string notation, one must use "\\\\" , making the following lines of code functionally identical:

Writing a Tokenizer ¶

A tokenizer or scanner analyzes a string to categorize groups of characters. This is a useful first step in writing a compiler or interpreter.

The text categories are specified with regular expressions. The technique is to combine those into a single master regular expression and to loop over successive matches:

The tokenizer produces the following output:

Friedl, Jeffrey. Mastering Regular Expressions. 3rd ed., O’Reilly Media, 2009. The third edition of the book no longer covers Python at all, but the first edition covered writing good regular expression patterns in great detail.

Table of Contents

• Regular Expression Syntax
• Regular Expression Objects
• Match Objects
• Checking for a Pair
• Simulating scanf()
• search() vs. match()
• Making a Phonebook
• Text Munging
• Finding all Adverbs
• Finding all Adverbs and their Positions
• Raw String Notation
• Writing a Tokenizer

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