denis-bz

#!/bin/sh
# less-or-grep.sh  2014-05-25 may denis

case $1 in -h* | --h* )  # help
    exec cat <<!

To make files "live", e.g. ~/bin/todo ~/bin/books ...
add this line at the top:
    source less-or-grep.sh  # file -> less file,  file 'pattern' -> egrep
and

denis-bz

#!/usr/bin/env python
""" conjugate gradient cg( A, x, Res )
    in: A: an array, numpy dense or scipy.sparse
            or sparse LinearOperator with .matvec .rmatvec
        x: initial guess, 0 or ...
        Res = Y - A x  before calling cg()
    iter: x += step
          Res -= S  *inplace*

from Jon F. Claerbout's nice, clear

denis-bz

N-dimensional test functions for optimization, in Python.

These are the n-dim Matlab functions by A. Hedar (2005), translated to Python-numpy.
http://www-optima.amp.i.kyoto-u.ac.jp/member/student/hedar/Hedar_files/TestGO.htm
ackley dp griew levy mich perm powell power rast rosen schw sphere sum2 trid zakh .m + ellipse nesterov powellsincos

http://imgur.com/Iu9H0jk is a plot of 3 no-derivative algorithms, NLOpt LN_BOBYQA LN_PRAXIS LN_SBPLX,

denis-bz

# leastsq_bounds.py
# see also test_leastsq_bounds.py on gist.github.com/denis-bz

from __future__ import division
import numpy as np
from scipy.optimize import leastsq

__version__ = "2015-01-10 jan  denis"  # orig 2012

denis-bz

""" a simple example of ILC
    from Moore, Iterative learning control: a tutorial and big picture 2006 6p
"""
# https://en.wikipedia.org/wiki/Iterative_learning_control
# https://en.wikipedia.org/wiki/LTI_system_theory


from __future__ import division
import sys
import numpy as np

denis-bz

Mixed order interpolation

Interpolating e.g. wind or water temperature on a box grid in d dimensions usually looks at (order+1)^d neighbors of each point. Order 1, bilinear trilinear ... looks at all 2^d corners of the box around each data point; 2^d grows pretty fast. Order 0, though, looks at only 1 the nearest corner, so is blocky, discontinuous at box edges.

What's in between ? A simple method is

denis-bz

Fitline: fit a line to data, print plot trim the biggest residuals, in Python

Example:

from fitline import Fitline  # a class with functions fit(), line(), plot(), trim(), trimfit()

F = Fitline( level=.95, nbig=5, verbose=1, axis=None, xline=None )  # the defaults
F.fit( x, y )  # -> f .a .b .residuals ...

a, b = F.a, F.b # y ~= a + b * x

denis-bz

#!/usr/bin/env python2
""" nanutil.py: corr, cosine similarity, linterpol ignoring missing data (NaNs)

A "NaN" is a marker for missing data, aka NA, Not Available, in numpy / pandas data arrays.
(Technically, it's a special, "sticky" floating point value, with e.g.
NaN + anything = NaN; see https://en.wikipedia.org/wiki/NaN .)
Numpy has a handful of functions that ignore NaNs, for example
`np.nanmean([ 1, np.NaN, 3 ]) == 2`.
Here are a few more, short and straightforward:

denis-bz

source less-or-grep.sh  # this file -> less,  file 'pattern' -> egrep

Alice: "Would you tell me, please, which way I ought to go from here ?"
"That depends a good deal on where you want to get to," said the Cat.
"I don't know where ...," said Alice.
"Then it doesn't matter which way you go," said the Cat.

On the planet Earth, man had always assumed he was more intelligent than dolphins
because he had achieved so much -- the wheel, New York, wars and so on --
while all the dolphins had ever done was muck about in the water having a good time.

denis-bz

Between trapezoid and Simpson integration: frequency response

Hamming, Digital Filters pages 66-69, shows that "the frequency point of view ... sheds a new light on classical numerical integration formulas."
The plot and code below show the frequency response of T (trapezoid), S (Simpson), and some combinations like .2 T + .8 S which give a good improvement, easily.