myriad

Given Y = 1/i calculate the next Y

I’m generating the following sequence , :
$$y_i = 1/i$$

where :

$$i = 1 \dots \infty$$
Given that I have the calculated-value at point x :

$$y_x$$

how should I calculate the next value $$y_{x+1}$$

I don’t know the index ‘x‘, I know only the calculated value.

For example, if $$y_x = 0.167$$ then $$y_{x+1} = 0.143$$ i.e. 1/6 implies 1/7

After a calculation I keep only the calculated value, not the current index.

Here is the formula :

$$ y_{x+n} = \frac {1} {{\frac 1 {y_{x}}}+n}$$

Detailed solution :

$$y_x = k; k= {\frac 1x}; x = {\frac 1k}$$

$$ y_{x+n} = \frac {1} {x+n} = \frac {1} {{\frac 1k}+n} = \frac {1} {{\frac 1 {y_{x}}}+n}$$

2022-03-02 by myriad math 0

Slices, Ranges and getitem()

One annoyance when implementing __getitem__() is debugging the slice syntax interactively .. Below you can see an example.

First you create a dummy class with simple method that print its arguments.

Then you can experiment.

class Blah: 
  def __getitem__(self,*args): 
    print(args) 
    return args

b = Blah()
b[1]
b[2:5]
b[::2,2:11:2]

s = b[::3]

print()

#filling the indices
ind = s[0].indices(12)
print(f'indices: {s[0]} => {ind}')

#make it a range
rng = range(*s[0].indices(12))
print(f'range: {rng}')

for i in rng: print(i)

(1,)
(slice(2, 5, None),)
((slice(None, None, 2), slice(2, 11, 2)),)
(slice(None, None, 3),)

indecies: slice(None, None, 3) => (0, 12, 3)
range: range(0, 12, 3)
0
3
6
9

In addition inside your method you can convert a slice to a range by using the .indices() method … and then use them to do processing in a loop.

2022-02-18 by myriad python 0

Cython: Tips and tricks

if you have more tricks comment below …

The last couple of days I started learning Cython …

What is Cython ?

Cython is compiled language that seamlesly integrates C with Python, plus more …

C, Cython, Python

The nice thing about is that the learning curve is very gradual. You can start w/o even changing your Python code.
Simply compiling it may speed up your script.

The next step is to start using Cython-the-language constructs.
Those include :

Declaring the type of the variables
Specifying who and how to call Functions/methods
Extension types : Classes which are implemented using Struct, instead of Dict allowing the dispatch resolution to happen at compile time, rather than runtime.

And finally you have the syntax to integrate directly C/C++ libraries and code.

Now on the

tips and tricks …

Creaing an array

Use 1D array instead of lists or numpy array whenever you can.
Red somewhere it is twice as fast than numpy.
In addition you can dynamically .resize() it in-place.

Here is the fastest way to create empty/zeroth array. First you need to have array templates prepared :

from cpython cimport array

cdef iARY = array.array('i') #integer
cdef IARY = array.array('I') #unsigned integer
cdef fARY = array.array('f') #float
cdef dARY = array.array('d') #double

then :

cdef ary = array.clone(fARY, size, 1)

Other options are :

cdef ary = array.array('f')
array.resize(ary, size)
array.zero(ary)

slower variant, but works on other types too :

cdef ary = array.array('f')
array.resize(ary, size)
ary[:] = 0

Accessing array elements

Here are several ways to access elements of array … from slower to faster.

ary[i] = value
ary._f[i] = value
#fastest, cause access the union struct directly
ary.data.as_floats[i] = value

the last one sped some portions of my code by ~30 times.

There are variations of the example above depending on the type :

_f, _i, _u …..
as_floats, as_ints, as_uints …..

A different len()

from cpython.object cimport Py_SIZE
#does not work on range()
cdef inline unsigned int clen(obj): return Py_SIZE(obj)

generates cleaner code, it should be faster. cpdef’d version is slower, which is expected.

type vs isinstance

if you have to do type checks use “type is …” instead of isinstance(), especially if you do several of them.

: x=type(5) 

: %timeit x is int
27.2 ns ± 4.12 ns per loop (mean ± std. dev. of 7 runs, 10000000 loops each)

: %timeit x is float
26.4 ns ± 0.731 ns per loop (mean ± std. dev. of 7 runs, 10000000 loops each)

: %timeit isinstance(5,int) 
52.6 ns ± 0.237 ns per loop (mean ± std. dev. of 7 runs, 10000000 loops each)

: %timeit isinstance(5,float) 
74.2 ns ± 1.28 ns per loop (mean ± std. dev. of 7 runs, 10000000 loops each)

: %timeit isinstance(x,int)                                                                                                                                           
71.5 ns ± 0.357 ns per loop (mean ± std. dev. of 7 runs, 10000000 loops each)

: %timeit isinstance(x,float)                                                                                                                                         
81 ns ± 1.32 ns per loop (mean ± std. dev. of 7 runs, 10000000 loops each)

---

: %timeit type(5) is int                                                                                                                                              
55 ns ± 0.487 ns per loop (mean ± std. dev. of 7 runs, 10000000 loops each)

: %timeit type(5) == int                                                                                                                                              
57.6 ns ± 1.59 ns per loop (mean ± std. dev. of 7 runs, 10000000 loops each)

: %timeit type(5) is float                                                                                                                                            
58 ns ± 1.26 ns per loop (mean ± std. dev. of 7 runs, 10000000 loops each)

2022-02-09 by myriad cython python 0

Python : How to check if variable is X ?

Here is how you can check the type of a variable :

In [240]: isinstance(5, int)                                                                                                                                                 
Out[240]: True

In [241]: var = 5                                                                                                                                                            

In [242]: isinstance(var, int)                                                                                                                                               
Out[242]: True

In [243]: isinstance(var, str)                                                                                                                                               
Out[243]: False

In [244]: isinstance([1,2,3], list)                                                                                                                                          
Out[244]: True

#is it one of many types
In [245]: isinstance([1,2,3], (list,tuple))                                                                                                                                  
Out[245]: True

Here is a function you can use to check if variable is an iterator :

def is_iter(x):
  try:
    iter(x); return True
  except TypeError: return False

2022-01-29 by myriad python 0

Numpy : min/max of integer types

Here is how to find the MIN or MAX values for the Integer types in numpy :

In [235]: np.iinfo(np.int8)                                                                                                                                                  
Out[235]: iinfo(min=-128, max=127, dtype=int8)

In [236]: np.iinfo(np.int16)                                                                                                                                                 
Out[236]: iinfo(min=-32768, max=32767, dtype=int16)

In [237]: np.iinfo(np.int32)                                                                                                                                                 
Out[237]: iinfo(min=-2147483648, max=2147483647, dtype=int32)

In [238]: np.iinfo(np.int64)                                                                                                                                                 
Out[238]: iinfo(min=-9223372036854775808, max=9223372036854775807, dtype=int64)

In [239]: np.iinfo(np.int)                                                                                                                                                   
Out[239]: iinfo(min=-9223372036854775808, max=9223372036854775807, dtype=int64)

2022-01-29 by myriad numpy 0

Perl: DATA section

This is my first Perl post. I wanted to explore a less known feature of Perl which is very useful at times.

Lets say as in my case that you need to combine and then compress .js and .css files from all over the place.
What I mean is that instead of importing in your html multiple different files you want to just import one compressed javascript file and one compressed css file.

Your first instinct may be, is to create a hash and describe all files locations … but may be the simple and dirty approach is better, enter the Perl __DATA__ section.

It is very clever idea, what if you can treat part of the source code file as a different file i.e. file within a file. Simply said everything after the __DATA__ token could be accessed via the <DATA> file handle.

Saying : @array = <DATA> will slurp everything into the @array, one line per element. In the example below i’m also removing the new line symbol.

So how do we setup which files to compress ? Simple, first type __DATA__ at the end of the file and then just use any command to append the path/file spec. I used those :

ls -w1 -d $PWD/blah/*.js >> compress.pl
ls -w1 -d $PWD/blah/*.css >> compress.pl
…

… several times. Don’t forget use append >>, not overwrite >

What does the script do :

read the __DATA__ section into the @files array
filter .js and .css and create a space separated string
using the strings from above build commands to concatenate the two groups
run the tools to compress concatenated files

#!/usr/bin/env perl
use strict;

sub run {
	my $cmd = shift @_;
	print "> $cmd\n";
	qx/$cmd/
}

#concatenated files
my $cat_js = 'cat.js';
my $cat_css = 'cat.css';
my $out = 'out';
#define compress commands
my $js_cmd = "/usr/local/bin/uglifyjs -c -m -- $cat_js > $out.js";
my $css_cmd = "yui-compressor --type css $cat_css > $out.css";

#read the DATA section
my @files = map {s/\n//;$_} <DATA>;
#extract js and css file
my $js_files  = join ' ', (grep /js$/, @files);
my $css_files = join ' ', (grep /css$/, @files);

#concatenate files
my $js_cat  = "cat $js_files > $cat_js";
my $css_cat = "cat $css_files > $cat_css";

run($js_cat);
run($js_cmd);

run($css_cat);
run($css_cmd);

#ls -w1 -d $PWD/*.*  >> compress.pl

__DATA__

One more thing, what is the purpose of the first line …

Shebang

If you make the file executable and have :

#!/usr/bin/perl

#!/usr/bin/env perl

as a first line then instead of calling the script like this :

perl compress.pl

you can do it this way :

./compress.pl

2022-01-12 by myriad perl 0

Prolog: Saving the fact+rules to file

Sometimes you may wish you can save your current state to file. Here is how you do it

save(Heads,File) :- tell(File), listing(Heads), told.

you can use the same idea to save the result of other predicates to file.

2022-01-10 by myriad prolog 0

Enums

Python does not have builtin Enumerable type, but we can easily resolve this problem :

def enum(args, start=0):
	class Enum(object):
		__slots__ = args.split()
		names = {}

		def __init__(self):
			for i, key in enumerate(Enum.__slots__, start):
				self.names[i] = key
				setattr(self, key, i)

	return Enum()


e = enum('ONE TWO THREE', start=1)

print(e.ONE)
print(e.TWO)
print(e.THREE)

-----

1
2
3

2022-01-10 by myriad python 0

myriad

Given Y = 1/i calculate the next Y

Slices, Ranges and getitem()

Incremental average

Timing code execution

Cython: Tips and tricks

What is Cython ?

C, Cython, Python

tips and tricks …

Creaing an array

Accessing array elements

A different len()

type vs isinstance

Python : How to check if variable is X ?

Numpy : min/max of integer types

Perl: DATA section

Shebang

Prolog: Saving the fact+rules to file

Enums

For gifts and updates

myriad

What is Cython ?

C, Cython, Python

tips and tricks …

Creaing an array

Accessing array elements

A different len()

type vs isinstance

Shebang

Categories

Tags

For gifts and updates