RK45 in Python

Runge-Kutta 4th and 5th order adaptive ODE integrator. Generally the scipy integrators will be easier to use, unless you specifically need RK45.
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Filter numpy images with FFT, Python

Generic linear filter support is not currently built into the Python Imaging Library. This module lets you filter a numpy array against an arbitrary kernel:

>>> I = numpy.asarray(Image.open('test.jpg'))
>>> I = filter(I, [[-1,0,1],[-2,0,2],[-1,0,1]])/8+128
>>> Image.fromarray(numpy.uint8(I)).show()


The Fast Fourier Transform (FFT) is used. The FFT routine included with numpy isn't particularly fast (c.f. FFTW [1]), and in any case using the transform isn't as efficient as applying the filter naively for small filter sizes. Also, for separable kernels (e.g. the Gaussian kernel), it is often faster to perform two 1D convolutions in sequence. However, for large images and filters, using an FFT for convolution is often faster than other approaches. (If an image and filter contain a total of N pixels, then this algorithm takes O(NlogN) time, which is the fastest known time complexity algorithm for the general problem.) Public domain.

Update: A number of image filtering operations are provided in numarray (in the module numpy.numarray.nd_image), such as filtering, image morphology, distance transforms, and segmentation; see [2].

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framecap - Capture camera input with Allegro, C++

Requires OpenCV, Allegro, and pthreads. Captures frames from a webcam. Usage:

CAPTURE *cap = create_capture();
BITMAP *bmp = capture_frame(cap);

Use capture_frame_nb to capture a frame in nonblocking mode (a NULL pointer is returned if no frame is available). Should work on Mac OS X, Linux, Windows; only tested on Windows.

(Source)

pfm - Read/write 1 and 3 channel PFM files

PFM files are mxnx1 or mxnx3 arrays of floats. C++ code to read/write the format (public domain).
(Source)

OpenCV camera and AVI input

To convert a video to a format that OpenCV can read:

  $ mencoder in.avi -ovc raw -vf format=i420 -o out.avi

This is necessary because OpenCV uses platform specific video libraries, and the intersection of their supported formats is DIB/I420/IYUV. To capture input from a camera or an AVI file, use the following C++ code: [1]. To capture frames in a nonblocking manner in Python, use: [2] with Gary Bishop's cvtypes [3].

Burrows-Wheeler transform in Python

def bwt(s):
  s = s + '\0'
  return ''.join([x[-1] for x in
         sorted([s[i:] + s[:i] for i in range(len(s))])])

def ibwt(s):
  L = [''] * len(s)
  for i in range(len(s)):
    L = sorted([s[i] + L[i] for i in range(len(s))])
  return [x for x in L if x.endswith('\0')][0][:-1]

The Burrows-Wheeler transform [1] is an invertible mathematical transformation which tends to clump related sequences of data together; hence it is useful as a pre-pass for some compression algorithms. The BWT domain in the above code excludes the null character; to include the null character, modify the transformation to also output the row of sorted([s[i:] + s[:i]...]) on which s occurs, then in IBWT simply return this row after the for loop. The Python code above is not particularly fast.

How to put a video on the Web

Install FFMPEG [1], use ffmpeg -i in.avi out.swf, then place <embed src="out.swf" width="400" height="300" loop="false" quality="high"></embed> in your HTML. Optionally, use the -s argument after -i in FFMPEG to change the resolution. If you want playback controls, output to a .flv file instead, download FlowPlayer [1], and modify their example HTML to point to your .flv video.

Ubuntu Linux postinstall notes

After installing an operating system, there are always a zillion changes I have to make to get the operating system operational. I'm new to Linux, so I thought I'd post up a list of changes I made after installing Ubuntu to help out others. These are mostly basic changes such as enabling all software packages, choosing a fast repository, mounting FAT32 drives, making Ctrl+Alt+Del bring up a task manager, installing multimedia software, changing the system DPI, trying to disable the trash feature, and adding an Open Terminal option to the desktop.
(Document)

Eigenvectors of 3x3 symmetric matrix

A C++ source and header file to compute eigenvectors/values of a 3x3 symmetric matrix. Potentially easier than installing EISPACK, LAPACK, or Gandalf if you only need this single function. Takes about 6000 clock cycles per call on my Pentium 4. Public domain. [1]