How to Use PostgreSQL Union and Union All Queries

This tutorial will show you how to use PostgreSQL Union and Union All queries to combine results from select statements.

#postgresql

Pdf2gerb: Perl Script Converts PDF Files to Gerber format

pdf2gerb

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:

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

#Pdf2Gerb config settings:
#Put this file in same folder/directory as pdf2gerb.pl 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 pfg2gerb.pl 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)}Pdf2Gerb.pl ${\(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
#traces:
    .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
    .012,
    .015,  #moderate low-voltage current
    .020,  #heavier trace for power, ground (even if a lighter one is adequate)
    .025,
    .030,  #heavy-current traces; be careful with these ones!
    .040,
    .050,
    .060,
    .080,
    .100,
    .120,
);
#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_MINX => 0,
    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
    CIRCLE_ADJUST_MAXY => 0,
    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 =>
our %SHAPELEN =
(
    rect => RECT_SHAPELEN,
    line => LINE_SHAPELEN,
    curve => CURVE_SHAPELEN,
    circle => CIRCLE_SHAPELEN,
);

#panelization:
#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


#############################################################################################
#junk/experiment:

#use Package::Constants;
#use Exporter qw(import); #https://perldoc.perl.org/Exporter.html

#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__); #https://www.perlmonks.org/?node_id=1072691; 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: https://github.com/swannman/pdf2gerb

License: GPL-3.0 license

#perl

Ahebwe Oscar

1620185280

How model queries work in Django

Welcome to my blog, hey everyone in this article we are going to be working with queries in Django so for any web app that you build your going to want to write a query so you can retrieve information from your database so in this article I’ll be showing you all the different ways that you can write queries and it should cover about 90% of the cases that you’ll have when you’re writing your code the other 10% depend on your specific use case you may have to get more complicated but for the most part what I cover in this article should be able to help you so let’s start with the model that I have I’ve already created it.

**Read More : **How to make Chatbot in Python.

let’s just get into this diagram that I made so in here:

django queries about Describe each parameter in Django querset

we’re making a simple query for the myModel table so we want to pull out all the information in the database so we have this variable which is gonna hold a return value and we have our myModel models so this is simply the myModel model name so whatever you named your model just make sure you specify that and we’re gonna access the objects attribute once we get that object’s attribute we can simply use the all method and this will return all the information in the database so we’re gonna start with all and then we will go into getting single items filtering that data and go to our command prompt.

Here and we’ll actually start making our queries from here to do this let’s just go ahead and run** Python manage.py shell** and I am in my project file so make sure you’re in there when you start and what this does is it gives us an interactive shell to actually start working with our data so this is a lot like the Python shell but because we did manage.py it allows us to do things a Django way and actually query our database now open up the command prompt and let’s go ahead and start making our first queries.

#django #django model queries #django orm #django queries #django query #model django query #model query #query with django

Solwin Infotech

1620729846

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.

#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

Kiwanuka Timothy

1679971140

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
A=np.array([[2,4,6],
       [8,10,12],
       [14,16,18]])
#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 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

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: https://www.askpython.com

#python #numpy

米萱萱

1680070980

在 Python 和 Numpy 中使用奇异值分离 (linalg.svd)

在此 pythonn - Numpy 教程中，我们将了解 Numpy linalg.svd：Python 中的奇异值分解。在数学中，矩阵的奇异值分解 (SVD) 是指将矩阵分解为三个单独的矩阵。它是矩阵特征值分解的更一般化版本。它进一步与极性分解有关。

在 Python 中，使用数值 python 或 numpy 库很容易计算复数或实数矩阵的奇异分解。numpy 库由各种线性代数函数组成，包括用于计算矩阵奇异值分解的函数。

在机器学习模型中，奇异值分解被广泛用于训练模型和神经网络。它有助于提高准确性和减少数据中的噪音。奇异值分解将一个向量转换为另一个向量，而它们不一定具有相同的维度。因此，它使向量空间中的矩阵操作更加容易和高效。它也用于回归分析。

Numpy linalg.svd() 函数的语法

python中计算矩阵奇异值分解的函数属于numpy模块，名为linalg.svd()。

numpy linalg.svd() 的语法如下：

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

您可以根据您的要求自定义 true 和 false 布尔值。

该函数的参数如下：

A->array_like：这是需要计算奇异值分解的矩阵。根据需要，它可以是真实的或复杂的。它的维度应该> = 2。
full_matrices->boolean value（可选）：如果设置为 true，则给定矩阵的 Hermitian 转置为正方形，如果为 false，则不是。
compute_uv->boolen value(optional)：决定是否在奇异值分解的基础上计算Hermitian转置。
hermitian->boolean value（可选）：给定的矩阵被认为是 hermitian（即对称的，具有实数值），这可能提供更有效的计算方法。

该函数根据上述参数返回三种类型的矩阵：

S->array_like：包含奇异值的向量，按降序排列，维度与原始矩阵相同。
u->array_like：这是一个可选的解决方案，当 compute_uv 设置为 True 时返回。它是一组具有奇异值的向量。
v-> array_like：单一数组集仅在 compute_uv 设置为 True 时返回。

当奇异值不同时，它会引发LinALgError 。

设置的先决条件

在深入研究示例之前，请确保您已在本地系统中安装了 numpy 模块。这是使用线性代数函数（如本文中讨论的函数）所必需的。在您的终端中运行以下命令。

pip install numpy

这就是您现在所需要的，让我们看看我们将如何在下一节中实现代码。

要在 Python 中计算奇异值分解 (SVD)，请使用 NumPy 库的 linalg.svd() 函数。它的语法是 numpy.linalg.svd(A, full_matrices=True, compute_uv=True, hermitian=False)，其中 A 是计算 SVD 的矩阵。它返回三个矩阵：S、U 和 V。

示例 1：计算 3×3 矩阵的奇异值分解

在第一个示例中，我们将采用 3X3 矩阵并按以下方式计算其奇异值分解：

#importing the numpy module
import numpy as np
#using the numpy.array() function to create an array
A=np.array([[2,4,6],
       [8,10,12],
       [14,16,18]])
#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)

输出将是：

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]]

示例 1

示例 2：计算随机矩阵的奇异值分解

在这个例子中，我们将使用numpy.random.randint()函数来创建一个随机矩阵。让我们开始吧！

#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)

输出将如下所示：

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]]

示例 2

建议：Numpy linalg.eigvalsh：特征值计算指南。

包起来

在本文中，我们探讨了数学中奇异值分解的概念以及如何使用 Python 的 numpy 模块对其进行计算。我们使用 linalg.svd() 函数来计算给定矩阵和随机矩阵的奇异值分解。Numpy 为执行线性代数运算提供了一种高效且易于使用的方法，使其在机器学习、神经网络和回归分析中具有很高的价值。继续探索 numpy 中的其他线性代数函数，以增强您在 Python 中的数学工具集。

文章来源：https: //www.askpython.com

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