How Can You Draw from a PDF in Python Without the CDF?

In summary, drawing from a PDF in Python without the use of CDF can be achieved by using the PyPDF2 library. This library allows users to extract text, images, and other data from a PDF file and use it in their Python code. Additionally, the Matplotlib library can be used to visualize and draw on PDFs, providing a wide range of options for manipulating and using PDF content in Python.
  • #1
ergospherical
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Some python function f(x) defines an (unnormalised) pdf between x_min and x_max
and say we want to draw x randomly from this distribution

if we had the CDF F(x) and its inverse F^{-1}(x), we could take values y uniformly in [0,1], and then our random values of x would be x = F^{-1}(y).

but without the CDF is there a direct way, maybe even built into some python library?
 
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  • #3
How is this related to PDFs?
 
  • #4
Greg Bernhardt said:
How is this related to PDFs?
Probability density function
 
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  • #5
Frabjous said:
Probability density function
oh boy, I had the wrong acronym :biggrin:
 
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  • #6
ergospherical said:
but without the CDF is there a direct way, maybe even built into some python library?
Yes, a generalised version of rejection sampling (which allows for support over ## [-\infty, +\infty] ##) as pointed to by @f95toli is available as scipy.stats.sampling.RatioUniforms as well as other methods including some based on numerical integration and inversion of the PDF to get the CDF which is then interpolated.
 
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  • #7
That is an interesting idea. I'd gone ahead and implemented a method based on the inverse cumulative density function, which is a bit cumbersome, namely

- define the pdf, i.e. pdf = lambda x: __some function of x__
- calculate the cdf, i.e. cdf = lambda x: quad(pdf, 0, x)[0]
- invert the cdf, i.e. return fsolve(lambda x: cdf(x) - random.random(), init_guess)[0]

where for init_guess I can simply feed in what is roughly the expected value.

I think it works, but I'm curious if rejection sampling would be faster (?). In particular, I'm now sampling from ##[0, \infty]## so I would need a generalized implementation.
 
  • #8
Also, if the pdf is nasty then the numerical integration can go wrong...
 
  • #9
Rejection sampling is usually quite fast. I would start there and only move to other methods if rejection sampling doesn't work.
 
  • #10
ergospherical said:
Also, if the pdf is nasty then the numerical integration can go wrong...
Yes, but a difficult integration often goes with a very small acceptance area so naive rejection sampling may be impossibly slow.

There is of course a trade-off depending on how many samples you want: if it is only a handful there is less to be gained by spending time on the integration, but if you want a few million and the acceptance is one in ## 10^9 ##...

The prebuilt SciPy routines are pretty good and easy to use, I'd experiment to see what works best.
 

FAQ: How Can You Draw from a PDF in Python Without the CDF?

What libraries can be used to draw from a PDF in Python without using the CDF?

Several libraries can be used to draw from a PDF in Python without relying on the CDF. Some popular choices include PyMuPDF (also known as fitz), PDFMiner, and PyPDF2. These libraries allow for reading, extracting, and manipulating PDF content programmatically.

How can I extract text from a PDF using Python?

To extract text from a PDF, you can use the PyMuPDF library. First, install it using `pip install pymupdf`. Then, use the following code snippet to extract text:

import fitzpdf_document = "example.pdf"doc = fitz.open(pdf_document)for page_num in range(len(doc)):    page = doc.load_page(page_num)    text = page.get_text("text")    print(text)
This code will print the text from each page of the PDF.

How can I extract images from a PDF using Python?

To extract images from a PDF, you can use the PyMuPDF library. Here's an example:

import fitzpdf_document = "example.pdf"doc = fitz.open(pdf_document)for page_num in range(len(doc)):    page = doc.load_page(page_num)    images = page.get_images(full=True)    for img_index, img in enumerate(images):        xref = img[0]        base_image = doc.extract_image(xref)        image_bytes = base_image["image"]        image_ext = base_image["ext"]        with open(f"image{page_num}_{img_index}.{image_ext}", "wb") as img_file:            img_file.write(image_bytes)
This code will extract and save images from each page of the PDF.

How can I draw shapes or annotations on a PDF using Python?

To draw shapes or annotations on a PDF, you can use the PyMuPDF library. Here's an example of how to draw a rectangle:

import fitzpdf_document = "example.pdf"doc = fitz.open(pdf_document)page = doc.load_page(0)  # Load the first pagerect = fitz.Rect(100, 100, 200, 200)  # Define a rectanglepage.draw_rect(rect, color=(1, 0, 0), width=2)  # Draw a red rectangle with a line width of 2doc.save("annotated_example.pdf")
This code will draw a red rectangle on the first page of the PDF and save the modified PDF.

How can I merge multiple PDFs into one using Python?

To merge

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