My daughter got a hand-me-down GeForce GS8400 from a friend at school. That's like a $45 video card, yet is presumably advanced enough to support Cuda, and therefore PyCuda. What's that? http://documen.tician.de/pycuda/ We keep getting back to numpy arrays as a basis for computer graphics. Linear algebra with numpy.matrix looks like a good way to go in a digital math class.
From Cut-the-Knot, this 9x9 invertible matrix:
import numpy as np
A result of cutting and pasting:
m = """1 1 1 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 0 1 1 1 0 1 0 1 1 1 0 0 0 1 1 0 1 0 1 1 1 0 1 0 1 1 0 0 0 1 1 1 0 1 0 0 1 1 0 1 1 1 1 0 1 1 0 1 0 1 0 0 0 1 0 1 1 1 1 1""".split()
Convert to integers:
mat = np.matrix(np.array([int(x) for x in m]).reshape(9,9)) mat matrix([[1, 1, 1, 1, 1, 0, 1, 0, 0], [0, 1, 0, 1, 0, 1, 1, 0, 1], [1, 1, 1, 0, 1, 1, 1, 0, 1], [0, 1, 1, 1, 0, 0, 0, 1, 1], [0, 1, 0, 1, 1, 1, 0, 1, 0], [1, 1, 0, 0, 0, 1, 1, 1, 0], [1, 0, 0, 1, 1, 0, 1, 1, 1], [1, 0, 1, 1, 0, 1, 0, 1, 0], [0, 0, 1, 0, 1, 1, 1, 1, 1]])
Getting the inverse is now as simple as:
print np.round(mat.I, 2) # that's mat.I with I for Inverse
[[-0.17 -0.23 0.48 -0.07 -0.12 0.11 0.32 0.27 -0.51] [ 0.07 -0.07 0.2 0.33 0.2 0.27 -0.2 -0.33 -0.27] [ 0.32 -0.12 -0.04 0.2 -0.24 -0.12 -0.36 0.2 0.32] [ 0.23 0.37 -0.32 -0.07 0.08 -0.29 0.12 0.27 -0.11] [ 0.08 -0.28 0.24 -0.2 0.44 -0.28 0.16 -0.2 0.08] [-0.27 0.27 0.2 -0.33 0.2 -0.07 -0.2 0.33 0.07] [ 0.48 0.32 -0.56 -0.2 -0.36 0.32 -0.04 -0.2 0.48] [-0.11 -0.29 -0.32 0.27 0.08 0.37 0.12 -0.07 0.23] [-0.51 0.11 0.48 0.27 -0.12 -0.23 0.32 -0.07 -0.17]] http://www.cut-the-knot.org/explain_game.shtml Connecting the dots twixt Pycuda and numpy: http://documen.tician.de/pycuda/array.html#pycuda.gpuarray.GPUArray Perry Greenfield has had much to do with getting Python going at the Space Telescope Science Institute (STScI). We invited him to give a lightning talk during my class, but he was stuck in Amsterdam owing to the volcanic ash problem in Iceland. http://www.scipy.org/wikis/topical_software/Tutorial http://stsdas.stsci.edu/perry/pydatatut.pdf (144 pages by Perry Greenfield and Robert Jedrzejewski -- about analyzing astronomical imagery in Python with numpy, pyfits, numdisplay etc.). Numpy has a lot in common with IDL, an inhouse analysis language for many on the Hubble project. In sharing research data with the wider public however, it's easier if the files might be worked on by free and open source software. IDL ain't cheap. http://www.cfa.harvard.edu/~jbattat/computer/python/science/idl-numpy.html Speaking of Cuda (used to code for the GPU vs. the CPU), there's a PyopenCL as well, also by Andreas Klöckner. http://developer.amd.com/GPU/ATISTREAMSDK/pages/TutorialOpenCL.aspx Kirby