Noah  Rowe

Noah Rowe


Hyper-parameter optimization using EDASpy

Tuning machine learning hyper-parameters is a tedious task we tend to postpone to the very last of the project. Hyper-parameters are everywhere are manual tuning is nearly impossible.

Imagine we have only one hyper-parameter and we want to optimize it. We would have to execute the program, script, algorithm or whatever we are tuning, N times, being N the number of possible values of the parameter. With two parameters, we would have to execute N times for each time of the second parameter, thus, N**2. And so on.

There exist lot of possibilities for hyper-parameter tuning. In this case I will explain an approach from the evolutionary algorithms. Particularly, the _Estimation of Distribution Algorithms (EDAs). _Similar to the Genetic Algorithms. The kernel of this algorithm is that iteratively, the algorithm propose some solutions from which, select the best ones that fit the cost function we want to optimize. From these selection we generate new solutions based on the normal distribution built from them. Figure 1 shows a flow diagram. In each iteration a generation with a group of solutions is sampled. This is called a generation with multiple individuals. In the selection of the best individuals, a percentage of this generation is selected (ALPHA parameter)

This type of algorithm can be used for further tasks as Feature Selection (FS) or optimization of some variables depending on some further fixed values of other variables. Future stories will talk about this topics.

Figure 1. Flow diagram of an Estimation of Distribution Algorithm (EDA).

Lets see an easy example solved using the Python package EDAspy. To install the package just do:

pip install EDAspy

We have a cost function as follows. The three hyper-parameters we want to optimize are dictionary[‘param1’], dictionary[‘param2’] and dictionary[‘param3’]. Also the cost function incorporates some weights. The algorithm must find the optimum values to the hyper-parameters in order to minimize the cost function.

weights = [20,10,-4]

def cost_function(dictionary):
    function = weights[0]*dictionary['param1']**2 + weights[1]*(np.pi/dictionary['param2']) - 2 - weights[2]*dictionary['param3']
    if function < 0:
        return 9999999
    return function

The algorithm needs as an input an initial range in which start to evaluate the solutions. Optionally, the algorithm can set a maximum and a minimum for the hyper-parameters. They are all set in a pandas table with a row for each data and a column for each hyper-parameter name. If max and min are not set, do not introduce the max and min rows.

from EDAspy.optimization.univariate import EDA_continuous as EDAc
import pandas as pd
import numpy as np

wheights = [20,10,-4]

def cost_function(dictionary):
    function = wheights[0]*dictionary['param1']**2 + wheights[1]*(np.pi/dictionary['param2']) - 2 - wheights[2]*dictionary['param3']
    if function < 0:
        return 9999999
    return function

vector = pd.DataFrame(columns=['param1', 'param2', 'param3'])
vector['data'] = ['mu', 'std', 'min', 'max']
vector = vector.set_index('data')
vector.loc['mu'] = [5, 8, 1]
vector.loc['std'] = 20
vector.loc['min'] = 0
vector.loc['max'] = 100

EDA = EDAc(SIZE_GEN=40, MAX_ITER=200, DEAD_ITER=20, ALPHA=0.7, vector=vector, aim='minimize', cost_function=cost_function)
bestcost, params, history =

#machine-learning #optimization #algorithms

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Hyper-parameter optimization using EDASpy
Chloe  Butler

Chloe Butler


Pdf2gerb: Perl Script Converts PDF Files to Gerber format


Perl script converts PDF files to Gerber format

Pdf2Gerb generates Gerber 274X photoplotting and Excellon drill files from PDFs of a PCB. Up to three PDFs are used: the top copper layer, the bottom copper layer (for 2-sided PCBs), and an optional silk screen layer. The PDFs can be created directly from any PDF drawing software, or a PDF print driver can be used to capture the Print output if the drawing software does not directly support output to PDF.

The general workflow is as follows:

  1. Design the PCB using your favorite CAD or drawing software.
  2. Print the top and bottom copper and top silk screen layers to a PDF file.
  3. Run Pdf2Gerb on the PDFs to create Gerber and Excellon files.
  4. Use a Gerber viewer to double-check the output against the original PCB design.
  5. Make adjustments as needed.
  6. Submit the files to a PCB manufacturer.

Please note that Pdf2Gerb does NOT perform DRC (Design Rule Checks), as these will vary according to individual PCB manufacturer conventions and capabilities. Also note that Pdf2Gerb is not perfect, so the output files must always be checked before submitting them. As of version 1.6, Pdf2Gerb supports most PCB elements, such as round and square pads, round holes, traces, SMD pads, ground planes, no-fill areas, and panelization. However, because it interprets the graphical output of a Print function, there are limitations in what it can recognize (or there may be bugs).

See docs/Pdf2Gerb.pdf for install/setup, config, usage, and other info.

#Pdf2Gerb config settings:
#Put this file in same folder/directory as itself (global settings),
#or copy to another folder/directory with PDFs if you want PCB-specific settings.
#There is only one user of this file, so we don't need a custom package or namespace.
#NOTE: all constants defined in here will be added to main namespace.
#package pdf2gerb_cfg;

use strict; #trap undef vars (easier debug)
use warnings; #other useful info (easier debug)

#configurable settings:
#change values here instead of in main file

use constant WANT_COLORS => ($^O !~ m/Win/); #ANSI colors no worky on Windows? this must be set < first DebugPrint() call

#just a little warning; set realistic expectations:
#DebugPrint("${\(CYAN)} ${\(VERSION)}, $^O O/S\n${\(YELLOW)}${\(BOLD)}${\(ITALIC)}This is EXPERIMENTAL software.  \nGerber files MAY CONTAIN ERRORS.  Please CHECK them before fabrication!${\(RESET)}", 0); #if WANT_DEBUG

use constant METRIC => FALSE; #set to TRUE for metric units (only affect final numbers in output files, not internal arithmetic)
use constant APERTURE_LIMIT => 0; #34; #max #apertures to use; generate warnings if too many apertures are used (0 to not check)
use constant DRILL_FMT => '2.4'; #'2.3'; #'2.4' is the default for PCB fab; change to '2.3' for CNC

use constant WANT_DEBUG => 0; #10; #level of debug wanted; higher == more, lower == less, 0 == none
use constant GERBER_DEBUG => 0; #level of debug to include in Gerber file; DON'T USE FOR FABRICATION
use constant WANT_STREAMS => FALSE; #TRUE; #save decompressed streams to files (for debug)
use constant WANT_ALLINPUT => FALSE; #TRUE; #save entire input stream (for debug ONLY)

#DebugPrint(sprintf("${\(CYAN)}DEBUG: stdout %d, gerber %d, want streams? %d, all input? %d, O/S: $^O, Perl: $]${\(RESET)}\n", WANT_DEBUG, GERBER_DEBUG, WANT_STREAMS, WANT_ALLINPUT), 1);
#DebugPrint(sprintf("max int = %d, min int = %d\n", MAXINT, MININT), 1); 

#define standard trace and pad sizes to reduce scaling or PDF rendering errors:
#This avoids weird aperture settings and replaces them with more standardized values.
#(I'm not sure how photoplotters handle strange sizes).
#Fewer choices here gives more accurate mapping in the final Gerber files.
#units are in inches
use constant TOOL_SIZES => #add more as desired
#round or square pads (> 0) and drills (< 0):
    .010, -.001,  #tiny pads for SMD; dummy drill size (too small for practical use, but needed so StandardTool will use this entry)
    .031, -.014,  #used for vias
    .041, -.020,  #smallest non-filled plated hole
    .051, -.025,
    .056, -.029,  #useful for IC pins
    .070, -.033,
    .075, -.040,  #heavier leads
#    .090, -.043,  #NOTE: 600 dpi is not high enough resolution to reliably distinguish between .043" and .046", so choose 1 of the 2 here
    .100, -.046,
    .115, -.052,
    .130, -.061,
    .140, -.067,
    .150, -.079,
    .175, -.088,
    .190, -.093,
    .200, -.100,
    .220, -.110,
    .160, -.125,  #useful for mounting holes
#some additional pad sizes without holes (repeat a previous hole size if you just want the pad size):
    .090, -.040,  #want a .090 pad option, but use dummy hole size
    .065, -.040, #.065 x .065 rect pad
    .035, -.040, #.035 x .065 rect pad
    .001,  #too thin for real traces; use only for board outlines
    .006,  #minimum real trace width; mainly used for text
    .008,  #mainly used for mid-sized text, not traces
    .010,  #minimum recommended trace width for low-current signals
    .015,  #moderate low-voltage current
    .020,  #heavier trace for power, ground (even if a lighter one is adequate)
    .030,  #heavy-current traces; be careful with these ones!
#Areas larger than the values below will be filled with parallel lines:
#This cuts down on the number of aperture sizes used.
#Set to 0 to always use an aperture or drill, regardless of size.
use constant { MAX_APERTURE => max((TOOL_SIZES)) + .004, MAX_DRILL => -min((TOOL_SIZES)) + .004 }; #max aperture and drill sizes (plus a little tolerance)
#DebugPrint(sprintf("using %d standard tool sizes: %s, max aper %.3f, max drill %.3f\n", scalar((TOOL_SIZES)), join(", ", (TOOL_SIZES)), MAX_APERTURE, MAX_DRILL), 1);

#NOTE: Compare the PDF to the original CAD file to check the accuracy of the PDF rendering and parsing!
#for example, the CAD software I used generated the following circles for holes:
#CAD hole size:   parsed PDF diameter:      error:
#  .014                .016                +.002
#  .020                .02267              +.00267
#  .025                .026                +.001
#  .029                .03167              +.00267
#  .033                .036                +.003
#  .040                .04267              +.00267
#This was usually ~ .002" - .003" too big compared to the hole as displayed in the CAD software.
#To compensate for PDF rendering errors (either during CAD Print function or PDF parsing logic), adjust the values below as needed.
#units are pixels; for example, a value of 2.4 at 600 dpi = .0004 inch, 2 at 600 dpi = .0033"
use constant
    HOLE_ADJUST => -0.004 * 600, #-2.6, #holes seemed to be slightly oversized (by .002" - .004"), so shrink them a little
    RNDPAD_ADJUST => -0.003 * 600, #-2, #-2.4, #round pads seemed to be slightly oversized, so shrink them a little
    SQRPAD_ADJUST => +0.001 * 600, #+.5, #square pads are sometimes too small by .00067, so bump them up a little
    RECTPAD_ADJUST => 0, #(pixels) rectangular pads seem to be okay? (not tested much)
    TRACE_ADJUST => 0, #(pixels) traces seemed to be okay?
    REDUCE_TOLERANCE => .001, #(inches) allow this much variation when reducing circles and rects

#Also, my CAD's Print function or the PDF print driver I used was a little off for circles, so define some additional adjustment values here:
#Values are added to X/Y coordinates; units are pixels; for example, a value of 1 at 600 dpi would be ~= .002 inch
use constant
    CIRCLE_ADJUST_MINY => -0.001 * 600, #-1, #circles were a little too high, so nudge them a little lower
    CIRCLE_ADJUST_MAXX => +0.001 * 600, #+1, #circles were a little too far to the left, so nudge them a little to the right
    SUBST_CIRCLE_CLIPRECT => FALSE, #generate circle and substitute for clip rects (to compensate for the way some CAD software draws circles)
    WANT_CLIPRECT => TRUE, #FALSE, #AI doesn't need clip rect at all? should be on normally?
    RECT_COMPLETION => FALSE, #TRUE, #fill in 4th side of rect when 3 sides found

#allow .012 clearance around pads for solder mask:
#This value effectively adjusts pad sizes in the TOOL_SIZES list above (only for solder mask layers).
use constant SOLDER_MARGIN => +.012; #units are inches

#line join/cap styles:
use constant
    CAP_NONE => 0, #butt (none); line is exact length
    CAP_ROUND => 1, #round cap/join; line overhangs by a semi-circle at either end
    CAP_SQUARE => 2, #square cap/join; line overhangs by a half square on either end
    CAP_OVERRIDE => FALSE, #cap style overrides drawing logic
#number of elements in each shape type:
use constant
    RECT_SHAPELEN => 6, #x0, y0, x1, y1, count, "rect" (start, end corners)
    LINE_SHAPELEN => 6, #x0, y0, x1, y1, count, "line" (line seg)
    CURVE_SHAPELEN => 10, #xstart, ystart, x0, y0, x1, y1, xend, yend, count, "curve" (bezier 2 points)
    CIRCLE_SHAPELEN => 5, #x, y, 5, count, "circle" (center + radius)
#const my %SHAPELEN =
#Readonly my %SHAPELEN =>
    rect => RECT_SHAPELEN,
    line => LINE_SHAPELEN,
    curve => CURVE_SHAPELEN,
    circle => CIRCLE_SHAPELEN,

#This will repeat the entire body the number of times indicated along the X or Y axes (files grow accordingly).
#Display elements that overhang PCB boundary can be squashed or left as-is (typically text or other silk screen markings).
#Set "overhangs" TRUE to allow overhangs, FALSE to truncate them.
#xpad and ypad allow margins to be added around outer edge of panelized PCB.
use constant PANELIZE => {'x' => 1, 'y' => 1, 'xpad' => 0, 'ypad' => 0, 'overhangs' => TRUE}; #number of times to repeat in X and Y directions

# Set this to 1 if you need TurboCAD support.
#$turboCAD = FALSE; #is this still needed as an option?

#CIRCAD pad generation uses an appropriate aperture, then moves it (stroke) "a little" - we use this to find pads and distinguish them from PCB holes. 
use constant PAD_STROKE => 0.3; #0.0005 * 600; #units are pixels
#convert very short traces to pads or holes:
use constant TRACE_MINLEN => .001; #units are inches
#use constant ALWAYS_XY => TRUE; #FALSE; #force XY even if X or Y doesn't change; NOTE: needs to be TRUE for all pads to show in FlatCAM and ViewPlot
use constant REMOVE_POLARITY => FALSE; #TRUE; #set to remove subtractive (negative) polarity; NOTE: must be FALSE for ground planes

#PDF uses "points", each point = 1/72 inch
#combined with a PDF scale factor of .12, this gives 600 dpi resolution (1/72 * .12 = 600 dpi)
use constant INCHES_PER_POINT => 1/72; #0.0138888889; #multiply point-size by this to get inches

# The precision used when computing a bezier curve. Higher numbers are more precise but slower (and generate larger files).
#$bezierPrecision = 100;
use constant BEZIER_PRECISION => 36; #100; #use const; reduced for faster rendering (mainly used for silk screen and thermal pads)

# Ground planes and silk screen or larger copper rectangles or circles are filled line-by-line using this resolution.
use constant FILL_WIDTH => .01; #fill at most 0.01 inch at a time

# The max number of characters to read into memory
use constant MAX_BYTES => 10 * M; #bumped up to 10 MB, use const

use constant DUP_DRILL1 => TRUE; #FALSE; #kludge: ViewPlot doesn't load drill files that are too small so duplicate first tool

my $runtime = time(); #Time::HiRes::gettimeofday(); #measure my execution time

print STDERR "Loaded config settings from '${\(__FILE__)}'.\n";
1; #last value must be truthful to indicate successful load


#use Package::Constants;
#use Exporter qw(import); #

#my $caller = "pdf2gerb::";

#sub cfg
#    my $proto = shift;
#    my $class = ref($proto) || $proto;
#    my $settings =
#    {
#        $WANT_DEBUG => 990, #10; #level of debug wanted; higher == more, lower == less, 0 == none
#    };
#    bless($settings, $class);
#    return $settings;

#use constant HELLO => "hi there2"; #"main::HELLO" => "hi there";
#use constant GOODBYE => 14; #"main::GOODBYE" => 12;

#print STDERR "read cfg file\n";

#our @EXPORT_OK = Package::Constants->list(__PACKAGE__); #; NOTE: "_OK" skips short/common names

#print STDERR scalar(@EXPORT_OK) . " consts exported:\n";
#foreach(@EXPORT_OK) { print STDERR "$_\n"; }
#my $val = main::thing("xyz");
#print STDERR "caller gave me $val\n";
#foreach my $arg (@ARGV) { print STDERR "arg $arg\n"; }

Download Details:

Author: swannman
Source Code:

License: GPL-3.0 license


Why Use WordPress? What Can You Do With WordPress?

Can you use WordPress for anything other than blogging? To your surprise, yes. WordPress is more than just a blogging tool, and it has helped thousands of websites and web applications to thrive. The use of WordPress powers around 40% of online projects, and today in our blog, we would visit some amazing uses of WordPress other than blogging.
What Is The Use Of WordPress?

WordPress is the most popular website platform in the world. It is the first choice of businesses that want to set a feature-rich and dynamic Content Management System. So, if you ask what WordPress is used for, the answer is – everything. It is a super-flexible, feature-rich and secure platform that offers everything to build unique websites and applications. Let’s start knowing them:

1. Multiple Websites Under A Single Installation
WordPress Multisite allows you to develop multiple sites from a single WordPress installation. You can download WordPress and start building websites you want to launch under a single server. Literally speaking, you can handle hundreds of sites from one single dashboard, which now needs applause.
It is a highly efficient platform that allows you to easily run several websites under the same login credentials. One of the best things about WordPress is the themes it has to offer. You can simply download them and plugin for various sites and save space on sites without losing their speed.

2. WordPress Social Network
WordPress can be used for high-end projects such as Social Media Network. If you don’t have the money and patience to hire a coder and invest months in building a feature-rich social media site, go for WordPress. It is one of the most amazing uses of WordPress. Its stunning CMS is unbeatable. And you can build sites as good as Facebook or Reddit etc. It can just make the process a lot easier.
To set up a social media network, you would have to download a WordPress Plugin called BuddyPress. It would allow you to connect a community page with ease and would provide all the necessary features of a community or social media. It has direct messaging, activity stream, user groups, extended profiles, and so much more. You just have to download and configure it.
If BuddyPress doesn’t meet all your needs, don’t give up on your dreams. You can try out WP Symposium or PeepSo. There are also several themes you can use to build a social network.

3. Create A Forum For Your Brand’s Community
Communities are very important for your business. They help you stay in constant connection with your users and consumers. And allow you to turn them into a loyal customer base. Meanwhile, there are many good technologies that can be used for building a community page – the good old WordPress is still the best.
It is the best community development technology. If you want to build your online community, you need to consider all the amazing features you get with WordPress. Plugins such as BB Press is an open-source, template-driven PHP/ MySQL forum software. It is very simple and doesn’t hamper the experience of the website.
Other tools such as wpFoRo and Asgaros Forum are equally good for creating a community blog. They are lightweight tools that are easy to manage and integrate with your WordPress site easily. However, there is only one tiny problem; you need to have some technical knowledge to build a WordPress Community blog page.

4. Shortcodes
Since we gave you a problem in the previous section, we would also give you a perfect solution for it. You might not know to code, but you have shortcodes. Shortcodes help you execute functions without having to code. It is an easy way to build an amazing website, add new features, customize plugins easily. They are short lines of code, and rather than memorizing multiple lines; you can have zero technical knowledge and start building a feature-rich website or application.
There are also plugins like Shortcoder, Shortcodes Ultimate, and the Basics available on WordPress that can be used, and you would not even have to remember the shortcodes.

5. Build Online Stores
If you still think about why to use WordPress, use it to build an online store. You can start selling your goods online and start selling. It is an affordable technology that helps you build a feature-rich eCommerce store with WordPress.
WooCommerce is an extension of WordPress and is one of the most used eCommerce solutions. WooCommerce holds a 28% share of the global market and is one of the best ways to set up an online store. It allows you to build user-friendly and professional online stores and has thousands of free and paid extensions. Moreover as an open-source platform, and you don’t have to pay for the license.
Apart from WooCommerce, there are Easy Digital Downloads, iThemes Exchange, Shopify eCommerce plugin, and so much more available.

6. Security Features
WordPress takes security very seriously. It offers tons of external solutions that help you in safeguarding your WordPress site. While there is no way to ensure 100% security, it provides regular updates with security patches and provides several plugins to help with backups, two-factor authorization, and more.
By choosing hosting providers like WP Engine, you can improve the security of the website. It helps in threat detection, manage patching and updates, and internal security audits for the customers, and so much more.

Read More

#use of wordpress #use wordpress for business website #use wordpress for website #what is use of wordpress #why use wordpress #why use wordpress to build a website

Using Singular Value Separation in Python and Numpy (linalg.svd)

In this pythonn - Numpy tutorial we will learn about Numpy linalg.svd: Singular Value Decomposition in Python. In mathematics, a singular value decomposition (SVD) of a matrix refers to the factorization of a matrix into three separate matrices. It is a more generalized version of an eigenvalue decomposition of matrices. It is further related to the polar decompositions.

In Python, it is easy to calculate the singular decomposition of a complex or a real matrix using the numerical python or the numpy library. The numpy library consists of various linear algebraic functions including one for calculating the singular value decomposition of a matrix.

In machine learning models, singular value decomposition is widely used to train models and in neural networks. It helps in improving accuracy and in reducing the noise in data. Singular value decomposition transforms one vector into another without them necessarily having the same dimension. Hence, it makes matrix manipulation in vector spaces easier and efficient. It is also used in regression analysis.

Syntax of Numpy linalg.svd() function

The function that calculates the singular value decomposition of a matrix in python belongs to the numpy module, named linalg.svd() .

The syntax of the numpy linalg.svd () is as follows:

numpy.linalg.svd(A, full_matrices=True, compute_uv=True, hermitian=False)

You can customize the true and false boolean values based on your requirements.

The parameters of the function are given below:

  • A->array_like: This is the required matrix whose singular value decomposition is being calculated. It can be real or complex as required. It’s dimension should be >= 2.
  • full_matrices->boolean value(optional): If set to true, then the Hermitian transpose of the given matrix is a square, if it’s false then it isn’t.
  • compute_uv->boolen value(optional): It determines whether the Hermitian transpose is to be calculated or not in addition to the singular value decomposition.
  • hermitian->boolean value(optional): The given matrix is considered hermitian(that is symmetric, with real values) which might provide a more efficient method for computation.

The function returns three types of matrices based on the parameters mentioned above:

  • S->array_like: The vector containing the singular values in the descending order with dimensions same as the original matrix.
  • u->array_like: This is an optional solution that is returned when compute_uv is set to True. It is a set of vectors with singular values.
  • v-> array_like: Set of unitary arrays only returned when compute_uv is set to True.

It raises a LinALgError when the singular values diverse.

Prerequisites for setup

Before we dive into the examples, make sure you have the numpy module installed in your local system. This is required for using linear algebraic functions like the one discussed in this article. Run the following command in your terminal.

pip install numpy

That’s all you need right now, let’s look at how we will implement the code in the next section.

To calculate Singular Value Decomposition (SVD) in Python, use the NumPy library’s linalg.svd() function. Its syntax is numpy.linalg.svd(A, full_matrices=True, compute_uv=True, hermitian=False), where A is the matrix for which SVD is being calculated. It returns three matrices: S, U, and V.

Example 1: Calculating the Singular Value Decomposition of a 3×3 Matrix

In this first example we will take a 3X3 matrix and compute its singular value decomposition in the following way:

#importing the numpy module
import numpy as np
#using the numpy.array() function to create an array
#calculatin all three matrices for the output
#using the numpy linalg.svd function
u,s,v=np.linalg.svd(A, compute_uv=True)
#displaying the result
print("the output is=")
print('s(the singular value) = ',s)
print('u = ',u)
print('v = ',v)

The output will be:

the output is=
s(the singular value) =  [3.36962067e+01 2.13673903e+00 8.83684950e-16]
u =  [[-0.21483724  0.88723069  0.40824829]
 [-0.52058739  0.24964395 -0.81649658]
 [-0.82633754 -0.38794278  0.40824829]]
v =  [[-0.47967118 -0.57236779 -0.66506441]
 [-0.77669099 -0.07568647  0.62531805]
 [-0.40824829  0.81649658 -0.40824829]]

Example 1

Example 1

Example 2: Calculating the Singular Value Decomposition of a Random Matrix

In this example, we will be using the numpy.random.randint() function to create a random matrix. Let’s get into it!

#importing the numpy module
import numpy as np
#using the numpy.array() function to craete an array
A=np.random.randint(5, 200, size=(3,3))
#display the created matrix
print("The input matrix is=",A)
#calculatin all three matrices for the output
#using the numpy linalg.svd function
u,s,v=np.linalg.svd(A, compute_uv=True)
#displaying the result
print("the output is=")
print('s(the singular value) = ',s)
print('u = ',u)
print('v = ',v)

The output will be as follows:

The input matrix is= [[ 36  74 101]
 [104 129 185]
 [139 121 112]]
the output is=
s(the singular value) =  [348.32979681  61.03199722  10.12165841]
u =  [[-0.3635535  -0.48363012 -0.79619769]
 [-0.70916514 -0.41054007  0.57318554]
 [-0.60408084  0.77301925 -0.19372034]]
v =  [[-0.49036384 -0.54970618 -0.67628871]
 [ 0.77570499  0.0784348  -0.62620264]
 [ 0.39727203 -0.83166766  0.38794824]]

Example 2

Example 2

Suggested: Numpy linalg.eigvalsh: A Guide to Eigenvalue Computation.

Wrapping Up

In this article, we explored the concept of singular value decomposition in mathematics and how to calculate it using Python’s numpy module. We used the linalg.svd() function to compute the singular value decomposition of both given and random matrices. Numpy provides an efficient and easy-to-use method for performing linear algebra operations, making it highly valuable in machine learning, neural networks, and regression analysis. Keep exploring other linear algebraic functions in numpy to enhance your mathematical toolset in Python.

Article source at:

#python #numpy 

Josefa  Corwin

Josefa Corwin


Mailboxer: A Rails Gem to Send Messages inside A Web Application


This project is based on the need for a private message system for ging / social_stream. Instead of creating our core message system heavily dependent on our development, we are trying to implement a generic and potent messaging gem.

After looking for a good gem to use we noticed the lack of messaging gems and functionality in them. Mailboxer tries to fill this void delivering a powerful and flexible message system. It supports the use of conversations with two or more participants, sending notifications to recipients (intended to be used as system notifications “Your picture has new comments”, “John Doe has updated his document”, etc.), and emailing the messageable model (if configured to do so). It has a complete implementation of a Mailbox object for each messageable with inbox, sentbox and trash.

The gem is constantly growing and improving its functionality. As it is used with our parallel development ging / social_stream we are finding and fixing bugs continously. If you want some functionality not supported yet or marked as TODO, you can create an issue to ask for it. It will be great feedback for us, and we will know what you may find useful in the gem.

Mailboxer was born from the great, but outdated, code from lpsergi / acts_as_messageable.

We are now working to make exhaustive documentation and some wiki pages in order to make it even easier to use the gem to its full potential. Please, give us some time if you find something missing or ask for it. You can also find us on the Gitter room for this repo. Join us there to talk.


Add to your Gemfile:

gem 'mailboxer'

Then run:

$ bundle install

Run install script:

$ rails g mailboxer:install

And don't forget to migrate your database:

$ rake db:migrate

You can also generate email views:

$ rails g mailboxer:views


If upgrading from 0.11.0 to 0.12.0, run the following generators:

$ rails generate mailboxer:namespacing_compatibility
$ rails generate mailboxer:install -s

Then, migrate your database:

$ rake db:migrate

Requirements & Settings


We are now adding support for sending emails when a Notification or a Message is sent to one or more recipients. You should modify the mailboxer initializer (/config/initializer/mailboxer.rb) to edit these settings:

Mailboxer.setup do |config|
  #Enables or disables email sending for Notifications and Messages
  config.uses_emails = true
  #Configures the default `from` address for the email sent for Messages and Notifications of Mailboxer
  config.default_from = ""

You can change the way in which emails are delivered by specifying a custom implementation of notification and message mailers:

Mailboxer.setup do |config|
  config.notification_mailer = CustomNotificationMailer
  config.message_mailer = CustomMessageMailer

If you have subclassed the Mailboxer::Notification class, you can specify the mailers using a member method:

class NewDocumentNotification < Mailboxer::Notification
  def mailer_class

class NewCommentNotification < Mailboxer::Notification
  def mailer_class

Otherwise, the mailer class will be determined by appending 'Mailer' to the mailable class name.

User identities

Users must have an identity defined by a name and an email. We must ensure that Messageable models have some specific methods. These methods are:

#Returning any kind of identification you want for the model
def name
  return "You should add method :name in your Messageable model"
#Returning the email address of the model if an email should be sent for this object (Message or Notification).
#If no mail has to be sent, return nil.
def mailboxer_email(object)
  #Check if an email should be sent for that object
  #if true
  return "define_email@on_your.model"
  #if false
  #return nil

These names are explicit enough to avoid colliding with other methods, but as long as you need to change them you can do it by using mailboxer initializer (/config/initializer/mailboxer.rb). Just add or uncomment the following lines:

Mailboxer.setup do |config|
  # ...
  #Configures the methods needed by mailboxer
  config.email_method = :mailboxer_email
  config.name_method = :name
  config.notify_method = :notify
  # ...

You may change whatever you want or need. For example:

config.email_method = :notification_email
config.name_method = :display_name
config.notify_method = :notify_mailboxer

Will use the method notification_email(object) instead of mailboxer_email(object), display_name for name and notify_mailboxer for notify.

Using default or custom method names, if your model doesn't implement them, Mailboxer will use dummy methods so as to notify you of missing methods rather than crashing.

Preparing your models

In your model:

class User < ActiveRecord::Base

You are not limited to the User model. You can use Mailboxer in any other model and use it in several different models. If you have ducks and cylons in your application and you want to exchange messages as if they were the same, just add acts_as_messageable to each one and you will be able to send duck-duck, duck-cylon, cylon-duck and cylon-cylon messages. Of course, you can extend it for as many classes as you need.


class Duck < ActiveRecord::Base
class Cylon < ActiveRecord::Base

Mailboxer API

Warning for version 0.8.0

Version 0.8.0 sees Messageable#read and Messageable#unread renamed to mark_as_(un)read, and Receipt#read and Receipt#unread to is_(un)read. This may break existing applications, but read is a reserved name for Active Record, and the best pratice in this case is simply avoid using it.

How can I send a message?

#alfa wants to send a message to beta
alfa.send_message(beta, "Body", "subject")

How can I read the messages of a conversation?

As a messageable, what you receive are receipts, which are associated with the message itself. You should retrieve your receipts for the conversation and get the message associated with them.

This is done this way because receipts save the information about the relation between messageable and the messages: is it read?, is it trashed?, etc.

#alfa gets the last conversation (chronologically, the first in the inbox)
conversation = alfa.mailbox.inbox.first

#alfa gets it receipts chronologically ordered.
receipts = conversation.receipts_for alfa

#using the receipts (i.e. in the view)
receipts.each do |receipt|
  message = receipt.message
  read = receipt.is_unread? #or message.is_unread?(alfa)

How can I reply to a message?

#alfa wants to reply to all in a conversation
#using a receipt
alfa.reply_to_all(receipt, "Reply body")

#using a conversation
alfa.reply_to_conversation(conversation, "Reply body")
#alfa wants to reply to the sender of a message (and ONLY the sender)
#using a receipt
alfa.reply_to_sender(receipt, "Reply body")

How can I delete a message from trash?

#delete conversations forever for one receipt (still in database)

#you can mark conversation as deleted for one participant
conversation.mark_as_deleted participant

#Mark the object as deleted for messageable
#Object can be:
  #* A Receipt
  #* A Conversation
  #* A Notification
  #* A Message
  #* An array with any of them
alfa.mark_as_deleted conversation

# get available message for specific user

How can I retrieve my conversations?

#alfa wants to retrieve all his conversations

#A wants to retrieve his inbox

#A wants to retrieve his sent conversations

#alfa wants to retrieve his trashed conversations

How can I paginate conversations?

You can use Kaminari to paginate the conversations as normal. Please, make sure you use the last version as mailboxer uses select('DISTINCT conversations.*') which was not respected before Kaminari 0.12.4 according to its changelog. Working correctly on Kaminari 0.13.0.

#Paginating all conversations using :page parameter and 9 per page
conversations =[:page]).per(9)

#Paginating received conversations using :page parameter and 9 per page
conversations =[:page]).per(9)

#Paginating sent conversations using :page parameter and 9 per page
conversations =[:page]).per(9)

#Paginating trashed conversations using :page parameter and 9 per page
conversations =[:page]).per(9)

You can take a look at the full documentation for Mailboxer in

Do you want to test Mailboxer?

Thanks to Roman Kushnir (@RKushnir) you can test Mailboxer with this sample app.

I need a GUI!

If you need a GUI you should take a look at these links:


Author: mailboxer
Source code:
License: MIT license

#ruby  #ruby-on-rails 

Phung Dang

Phung Dang


Sử dụng Phân tách giá trị số ít trong Python và Numpy (linalg.svd)

Trong hướng dẫn pythonn - Numpy này, chúng ta sẽ tìm hiểu về Numpy linalg.svd: Phân tách giá trị số ít trong Python. Trong toán học, phân tích giá trị đơn lẻ (SVD) của ma trận đề cập đến việc phân tích ma trận thành ba ma trận riêng biệt. Nó là một phiên bản tổng quát hơn của phép phân tách giá trị riêng của ma trận. Nó liên quan nhiều hơn đến sự phân hủy cực.

Trong Python, thật dễ dàng để tính toán phép phân tách số ít của một ma trận thực hoặc phức bằng cách sử dụng python số hoặc thư viện numpy. Thư viện numpy bao gồm các hàm đại số tuyến tính khác nhau, bao gồm một hàm để tính toán phân tích giá trị đơn lẻ của ma trận.

Trong các mô hình học máy , phân tách giá trị đơn lẻ được sử dụng rộng rãi để huấn luyện các mô hình và trong các mạng thần kinh. Nó giúp cải thiện độ chính xác và giảm nhiễu trong dữ liệu. Phép phân tích giá trị đơn biến đổi một vectơ thành một vectơ khác mà không nhất thiết chúng phải có cùng chiều. Do đó, nó làm cho thao tác ma trận trong không gian vectơ dễ dàng và hiệu quả hơn. Nó cũng được sử dụng trong phân tích hồi quy .

Cú pháp của hàm Numpy linalg.svd()

Hàm tính toán phân tách giá trị số ít của ma trận trong python thuộc về mô-đun numpy, có tên là linalg.svd() .

Cú pháp của numpy linalg.svd() như sau:

numpy.linalg.svd(A, full_matrices=True, compute_uv=True, hermitian=False)

Bạn có thể tùy chỉnh các giá trị boolean đúng và sai dựa trên yêu cầu của mình.

Các tham số của chức năng được đưa ra dưới đây:

  • A->array_like: Đây là ma trận bắt buộc có sự phân tách giá trị đơn lẻ đang được tính toán. Nó có thể là thực hoặc phức tạp theo yêu cầu. Kích thước của nó phải là> = 2.
  • full_matrices->boolean value(tùy chọn): Nếu được đặt thành true, thì phép chuyển vị Hermitian của ma trận đã cho là một hình vuông, nếu nó sai thì không.
  • toán_uv->giá trị boolen (tùy chọn): Nó xác định liệu phép chuyển vị Hermiti có được tính toán hay không ngoài việc phân tách giá trị số ít.
  • hermitian->giá trị boolean (tùy chọn): Ma trận đã cho được coi là hermitian (nghĩa là đối xứng, với các giá trị thực) có thể cung cấp một phương pháp tính toán hiệu quả hơn.

Hàm trả về ba loại ma trận dựa trên các tham số được đề cập ở trên:

  • S->array_like : Vectơ chứa các giá trị số ít theo thứ tự giảm dần với kích thước giống như ma trận ban đầu.
  • u->array_like : Đây là một giải pháp tùy chọn được trả về khi compute_uv được đặt thành True. Nó là một tập hợp các vectơ có giá trị số ít.
  • v->array_like : Tập hợp các mảng đơn vị chỉ được trả về khi compute_uv được đặt thành True.

Nó làm tăng LinALgError khi các giá trị đơn lẻ đa dạng.

Điều kiện tiên quyết để thiết lập

Trước khi chúng tôi đi sâu vào các ví dụ, hãy đảm bảo rằng bạn đã cài đặt mô-đun numpy trong hệ thống cục bộ của mình. Điều này là cần thiết để sử dụng các hàm đại số tuyến tính giống như hàm được thảo luận trong bài viết này. Chạy lệnh sau trong thiết bị đầu cuối của bạn.

pip install numpy

Đó là tất cả những gì bạn cần ngay bây giờ, hãy xem cách chúng tôi sẽ triển khai mã trong phần tiếp theo.

Để tính toán Phân tách giá trị số ít (SVD) trong Python, hãy sử dụng hàm linalg.svd() của thư viện NumPy. Cú pháp của nó là numpy.linalg.svd(A, full_matrices=True, compute_uv=True, hermitian=False), trong đó A là ma trận mà SVD đang được tính toán. Nó trả về ba ma trận: S, U và V.

Ví dụ 1: Tính toán phân tích giá trị đơn lẻ của ma trận 3 × 3

Trong ví dụ đầu tiên này, chúng ta sẽ lấy một ma trận 3X3 và tính toán phân tích giá trị đơn lẻ của nó theo cách sau:

#importing the numpy module
import numpy as np
#using the numpy.array() function to create an array
#calculatin all three matrices for the output
#using the numpy linalg.svd function
u,s,v=np.linalg.svd(A, compute_uv=True)
#displaying the result
print("the output is=")
print('s(the singular value) = ',s)
print('u = ',u)
print('v = ',v)

Đầu ra sẽ là:

the output is=
s(the singular value) =  [3.36962067e+01 2.13673903e+00 8.83684950e-16]
u =  [[-0.21483724  0.88723069  0.40824829]
 [-0.52058739  0.24964395 -0.81649658]
 [-0.82633754 -0.38794278  0.40824829]]
v =  [[-0.47967118 -0.57236779 -0.66506441]
 [-0.77669099 -0.07568647  0.62531805]
 [-0.40824829  0.81649658 -0.40824829]]

ví dụ 1

ví dụ 1

Ví dụ 2: Tính toán phân tích giá trị đơn lẻ của một ma trận ngẫu nhiên

Trong ví dụ này, chúng ta sẽ sử dụng hàm numpy.random.randint() để tạo một ma trận ngẫu nhiên. Hãy đi vào nó!

#importing the numpy module
import numpy as np
#using the numpy.array() function to craete an array
A=np.random.randint(5, 200, size=(3,3))
#display the created matrix
print("The input matrix is=",A)
#calculatin all three matrices for the output
#using the numpy linalg.svd function
u,s,v=np.linalg.svd(A, compute_uv=True)
#displaying the result
print("the output is=")
print('s(the singular value) = ',s)
print('u = ',u)
print('v = ',v)

Đầu ra sẽ như sau:

The input matrix is= [[ 36  74 101]
 [104 129 185]
 [139 121 112]]
the output is=
s(the singular value) =  [348.32979681  61.03199722  10.12165841]
u =  [[-0.3635535  -0.48363012 -0.79619769]
 [-0.70916514 -0.41054007  0.57318554]
 [-0.60408084  0.77301925 -0.19372034]]
v =  [[-0.49036384 -0.54970618 -0.67628871]
 [ 0.77570499  0.0784348  -0.62620264]
 [ 0.39727203 -0.83166766  0.38794824]]

ví dụ 2

ví dụ 2

Đề xuất: Numpy linalg.eigvalsh: Hướng dẫn tính toán giá trị riêng .

kết thúc

Trong bài viết này, chúng ta đã khám phá khái niệm phân tách giá trị số ít trong toán học và cách tính toán nó bằng cách sử dụng mô-đun numpy của Python. Chúng tôi đã sử dụng hàm linalg.svd() để tính toán phân tách giá trị số ít của cả ma trận đã cho và ma trận ngẫu nhiên. Numpy cung cấp một phương pháp hiệu quả và dễ sử dụng để thực hiện các phép toán đại số tuyến tính, làm cho nó có giá trị cao trong học máy, mạng thần kinh và phân tích hồi quy. Tiếp tục khám phá các hàm đại số tuyến tính khác trong numpy để nâng cao bộ công cụ toán học của bạn trong Python.

Nguồn bài viết tại:

#python #numpy