Circular law states the eigenvalues of a matrix with random entries of mean 0 and variance 1/n are approximately uniformly distributed in the unit disk of the complex plane. To see this, create a random matrix:

n = 1000
x = randomu(seed, n, n) - 0.5
x *= sqrt(12.0 / n)

Find the eigenvalues:

eigenvalues = la_eigenproblem(x, eigenvectors=eigenvectors)

Plot them:

plot, real_part(eigenvalues), imaginary(eigenvalues), $
      psym=3, $
      xstyle=1, xrange=[-1.5, 1.5], $
      ystyle=1, yrange=[-1.5, 1.5]

This gives a plot like below:

Via the excellent John D. Cook blog. I recommend reading his site if you are interested in a combination of mathematics and Python.

IDLdoc 3.6.2 has been released! New features include:

  • Bug fix for image directive for image files in other directories specified with a relative path (fix by Dave Gellman).

  • Only copying MathJax for LaTeX-style equations if not already present.

  • Fixed crash when invalid format/markup was specified on the docformat line of a .pro file.

mgunit 1.6 has been released! New features include:

  • Fix for bug when no filename with jUnit output format

  • Recursively search directories below test suite home directory for * and * files

  • Fixed for bug in mguttestsuite_define::addTestingFolder that did not add absolute paths correctly

  • Add superclasses of test classes recursively

You can download a distribution with a .sav file and documentation, or just access the repo as needed.

This is fascinating:

People use imprecise words to describe the chance of events all the time — “It’s likely to rain,” or “There’s a real possibility they’ll launch before us,” or “It’s doubtful the nurses will strike.” Not only are such probabilistic terms subjective, but they also can have widely different interpretations. One person’s “pretty likely” is another’s “far from certain.” Our research shows just how broad these gaps in understanding can be and the types of problems that can flow from these differences in interpretation.

For example, below are probability distributions for some common phrases:

via FlowingData

I released a new version of my iOS app, Simple Checklist, today. Simple Checklist provides an easy way to track progress through checklists. I use them for my morning routine, weekly review, physical therapy, and other repeated sequences.

The release notes for 1.4.0:

  • [NEW] Dark mode
  • [NEW] iPhone X support
  • [NEW] Haptic feedback
  • [NEW] Markdown format for exported checklists
  • [FIX] Fixed order of exported checklist

Simple Checklist is available on the iOS App Store.

Mathpix is a great idea, executed well:

The Mathpix desktop app allows users to take screenshots of math equations and paste the extracted Latex, all with a single keyboard shortcut.

For example, I wrote this on a piece of paper and took a picture of it:

And Mathpix put the following text on my clipboard:

\sum _ { i = 0} ^ { n } i = \frac { n ( n + 1) } { 2}

Which is exactly right:

$$\sum _ { i = 0} ^ { n } i = \frac { n ( n + 1) } { 2}$$

Mathpix can grab anything that is displayed on your screen.

The Mac app is free on the Mac App Store and there is a corresponding iOS app which is free with in-app purchase.

IDL 8.7 was released recently. The listed features are:

  • ROUTINE_DIR function that returns the directory for the file containing the calling routine
  • asynchronous job classes
  • a few miscellaneous other updates

The asynchronous job classes look interesting:

The IDLAsync classes allow you to specify units of work to execute asynchronously outside the main IDL session. To do this, create an IDLAsyncQueue and one or more IDLAsyncJob objects that encapsulate the work to be performed. As jobs are added to the queue, they will be executed at some point in the future as resources are available. When a job is complete, you can retrieve its results for further use. You can also construct an IDLAsyncJoin object and pass it into the jobs on creation. If you do this, you can wait on the join object for all of the jobs it observes to be finished before continuing.

Check the release notes for more details.

HoloViews is yet another Python visualization library, but it has a different approach:

With HoloViews, instead of building a plot using direct calls to a plotting library, you first describe your data with a small amount of crucial semantic information required to make it visualizable, then you specify additional metadata as needed to determine more detailed aspects of your visualization. This approach provides immediate, automatic visualization that can be effortlessly requested at any time as your data evolves, rendered automatically by one of the supported plotting libraries (such as Bokeh or Matplotlib).

It can produce a variety of visualizations — check out its gallery to see more examples.

The IDL Usenet newsgroup has moved to a Google Group:

This Google Group is a continuation of the Usenet group comp.lang.idl-pvwave, but allows for better spam filtering. It is for discussion of the Interactive Data Language (IDL), developed by Harris Geospatial Corporation. Questions about ENVI, a geospatial analytics software written in IDL are welcome. Discussion of the similar PV-WAVE language is also allowed.

The big question now is how to save the posts from the old newsgroup.

iTerm2 is a macOS terminal emulator with a lot of extra features. In particular, it has a simple protocol for displaying images inline. It comes with a program imgcat that will display common image formats such as PNG, JPEG, GIF, etc. Most of the images I deal with are FITS, though. I wrote fitscat to be a handy utility to display FITS images, as well as to print basic information about the FITS file such as a listing of extensions or an extension header.

For example, fitscat can display an image in an extension, as seen below:

There are options to specify a minimum and maximum value for scaling, as well as to use a simple filter such square root.

Also, fitscat can also print basic information about a FITS file, such as a listing of extensions:

CoMP$ fitscat --list 20150624.170419.comp.1074.iqu.5.fts
Filename: 20150624.170419.comp.1074.iqu.5.fts
No.    Name      Ver    Type      Cards   Dimensions   Format
  0  PRIMARY       1 PrimaryHDU      67   ()
  1  I, 1074.38    1 ImageHDU        33   (620, 620)   float32
  2  I, 1074.50    1 ImageHDU        33   (620, 620)   float32
  3  I, 1074.62    1 ImageHDU        33   (620, 620)   float32
  4  I, 1074.74    1 ImageHDU        33   (620, 620)   float32
  5  I, 1074.86    1 ImageHDU        33   (620, 620)   float32
  6  Q, 1074.38    1 ImageHDU        33   (620, 620)   float32
  7  Q, 1074.50    1 ImageHDU        33   (620, 620)   float32
  8  Q, 1074.62    1 ImageHDU        33   (620, 620)   float32
  9  Q, 1074.74    1 ImageHDU        33   (620, 620)   float32
 10  Q, 1074.86    1 ImageHDU        33   (620, 620)   float32
 11  U, 1074.38    1 ImageHDU        33   (620, 620)   float32
 12  U, 1074.50    1 ImageHDU        33   (620, 620)   float32
 13  U, 1074.62    1 ImageHDU        33   (620, 620)   float32
 14  U, 1074.74    1 ImageHDU        33   (620, 620)   float32
 15  U, 1074.86    1 ImageHDU        33   (620, 620)   float32

Or display a header:

CoMP$ fitscat --header -e 3 20150624.170419.comp.1074.iqu.5.fts
XTENSION= 'IMAGE   '           /extension type
BITPIX  =                  -32 /bits per data value
NAXIS   =                    2 /number of axes
NAXIS1  =                  620 /
NAXIS2  =                  620 /
PCOUNT  =                    0 /
GCOUNT  =                    1 /
EXTNAME = 'I, 1074.62'         /
WAVELENG=             1074.620 / WAVELENGTH OF OBS (NM)
EXPOSURE=               250.00 / EXPOSURE TIME (MILLISEC)
NAVERAGE=                   16 / Number of images averaged together
FILTER  =                    1 / FILTER WHEEL POSITION (1-8)
LCVR1TMP=            29.639999 / DEGREES CELSIUS
LCVR2TMP=            33.429001 /
LCVR3TMP=            33.715000 /
LCVR4TMP=            33.738998 /
LCVR5TMP=            33.618999 /
LCVR6TMP=            28.847000 /
NDFILTER=                    8 / ND 1=.1, 2=.3, 3=.5, 4=1, 5=2, 6=3, 7=4, 8=cle
BACKGRND=               13.154 / Median of masked line center background
BASETEMP=               33.599 / BASE PLATE TEMP (C)
OPTRTEMP=               33.306 / OPTICAL RAIL TEMP (C)
FILTTEMP=               35.000 / ILX FILTER TEMPERATURE (C)
FLATFILE= '20150624.070023.FTS' / Name of flat field file
INHERIT =                    T /
DISPMIN =                 0.00 / Minimum data value
DISPMAX =                 5.00 / Maximum data value
DISPEXP =                 0.50 / Exponent value for scaling

The full interface of fitscat is shown below:

$ fitscat --help
usage: fitscat [-h] [--min MIN] [--max MAX] [--debug] [-d] [-l] [-r]
               [-e EXTEN_NO] [-f FILTER] [-s SLICE]

fitscat - a FITS query/display program

positional arguments:
  filename              FITS file to query

optional arguments:
  -h, --help            show this help message and exit
  --min MIN             min for scaling
  --max MAX             max for scaling
  --debug               set to debug
  -d, --display         set to display
  -l, --list            set to list HDUs
  -r, --header          set to display header
  -e EXTEN_NO, --exten_no EXTEN_NO
                        specify extension
  -f FILTER, --filter FILTER
                        specify filter (default: none)
  -s SLICE, --slice SLICE
                        specify slice of data array to display

Source code for the Python script is available on GitHub. The script is compatible with Python 2 and 3, but requires standard scientific Python packages AstroPy, NumPy, and PIL.

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