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  • Creating a Predicate Builder extension method

    - by Rippo
    I have a Kendo UI Grid that I am currently allowing filtering on multiple columns. I am wondering if there is a an alternative approach removing the outer switch statement? Basically I want to able to create an extension method so I can filter on a IQueryable<T> and I want to drop the outer case statement so I don't have to switch column names. private static IQueryable<Contact> FilterContactList(FilterDescriptor filter, IQueryable<Contact> contactList) { switch (filter.Member) { case "Name": switch (filter.Operator) { case FilterOperator.StartsWith: contactList = contactList.Where(w => w.Firstname.StartsWith(filter.Value.ToString()) || w.Lastname.StartsWith(filter.Value.ToString()) || (w.Firstname + " " + w.Lastname).StartsWith(filter.Value.ToString())); break; case FilterOperator.Contains: contactList = contactList.Where(w => w.Firstname.Contains(filter.Value.ToString()) || w.Lastname.Contains(filter.Value.ToString()) || (w.Firstname + " " + w.Lastname).Contains( filter.Value.ToString())); break; case FilterOperator.IsEqualTo: contactList = contactList.Where(w => w.Firstname == filter.Value.ToString() || w.Lastname == filter.Value.ToString() || (w.Firstname + " " + w.Lastname) == filter.Value.ToString()); break; } break; case "Company": switch (filter.Operator) { case FilterOperator.StartsWith: contactList = contactList.Where(w => w.Company.StartsWith(filter.Value.ToString())); break; case FilterOperator.Contains: contactList = contactList.Where(w => w.Company.Contains(filter.Value.ToString())); break; case FilterOperator.IsEqualTo: contactList = contactList.Where(w => w.Company == filter.Value.ToString()); break; } break; } return contactList; } Some additional information, I am using NHibernate Linq. Also another problem is that the "Name" column on my grid is actually "Firstname" + " " + "LastName" on my contact entity. We can also assume that all filterable columns will be strings.

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  • java.lang.IllegalArgumentException: Method must not be null

    - by abc
    Nested in org.springframework.beans.factory.BeanCreationException: Error creating bean with name 'org.springframework.beans.factory.config.PropertyPlaceholderConfigurer#0': Initialization of bean failed; nested exception is java.lang.IllegalArgumentException: Method must not be null:java.lang.IllegalArgumentException: Method must not be null i am getting this deployment error while deploying my application. java -version java version "1.6.0_20" Java(TM) SE Runtime Environment (build 1.6.0_20-b02) Java HotSpot(TM) Server VM (build 16.3-b01, mixed mode) while the same build gets deployed successfully in the same server jetty 6.1.3 with following conf. java version "1.6.0_17" spring version used is 2.5.6.SEC01 how to overcome, googling didnt work? 2010-05-13 15:53:20.903::WARN: Failed startup of context org.mortbay.jetty.webapp.WebAppContext@9ad840{/caw,jar:file:/home/jigar/jetty-6.1.3/webapps/caw.war!/} org.springframework.beans.factory.BeanCreationException: Error creating bean with name 'org.springframework.beans.factory.config.PropertyPlaceholderConfigurer#0': Initialization of bean failed; nested exception is java.lang.IllegalArgumentException: Method must not be null at org.springframework.beans.factory.support.AbstractAutowireCapableBeanFactory.doCreateBean(AbstractAutowireCapableBeanFactory.java:480) at org.springframework.beans.factory.support.AbstractAutowireCapableBeanFactory$1.run(AbstractAutowireCapableBeanFactory.java:409) at java.security.AccessController.doPrivileged(Native Method) at org.springframework.beans.factory.support.AbstractAutowireCapableBeanFactory.createBean(AbstractAutowireCapableBeanFactory.java:380) at org.springframework.beans.factory.support.AbstractBeanFactory$1.getObject(AbstractBeanFactory.java:264) at org.springframework.beans.factory.support.DefaultSingletonBeanRegistry.getSingleton(DefaultSingletonBeanRegistry.java:222) at org.springframework.beans.factory.support.AbstractBeanFactory.doGetBean(AbstractBeanFactory.java:261) at org.springframework.beans.factory.support.AbstractBeanFactory.getBean(AbstractBeanFactory.java:185) at org.springframework.beans.factory.support.AbstractBeanFactory.getBean(AbstractBeanFactory.java:164) at org.springframework.context.support.AbstractApplicationContext.invokeBeanFactoryPostProcessors(AbstractApplicationContext.java:515) at org.springframework.context.support.AbstractApplicationContext.refresh(AbstractApplicationContext.java:362) at org.springframework.web.context.ContextLoader.createWebApplicationContext(ContextLoader.java:255) at org.springframework.web.context.ContextLoader.initWebApplicationContext(ContextLoader.java:199) at org.springframework.web.context.ContextLoaderListener.contextInitialized(ContextLoaderListener.java:45) at org.mortbay.jetty.handler.ContextHandler.startContext(ContextHandler.java:530) at org.mortbay.jetty.servlet.Context.startContext(Context.java:135) at org.mortbay.jetty.webapp.WebAppContext.startContext(WebAppContext.java:1218) at org.mortbay.jetty.handler.ContextHandler.doStart(ContextHandler.java:500) at org.mortbay.jetty.webapp.WebAppContext.doStart(WebAppContext.java:448) at org.mortbay.component.AbstractLifeCycle.start(AbstractLifeCycle.java:40) at org.mortbay.jetty.handler.HandlerCollection.doStart(HandlerCollection.java:147) at org.mortbay.jetty.handler.ContextHandlerCollection.doStart(ContextHandlerCollection.java:161) at org.mortbay.component.AbstractLifeCycle.start(AbstractLifeCycle.java:40) at org.mortbay.jetty.handler.HandlerCollection.doStart(HandlerCollection.java:147) at org.mortbay.component.AbstractLifeCycle.start(AbstractLifeCycle.java:40) at org.mortbay.jetty.handler.HandlerWrapper.doStart(HandlerWrapper.java:117) at org.mortbay.jetty.Server.doStart(Server.java:210) at org.mortbay.component.AbstractLifeCycle.start(AbstractLifeCycle.java:40) at org.mortbay.xml.XmlConfiguration.main(XmlConfiguration.java:929) at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method) at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:39) at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:25) at java.lang.reflect.Method.invoke(Method.java:597) at org.mortbay.start.Main.invokeMain(Main.java:183) at org.mortbay.start.Main.start(Main.java:497) at org.mortbay.start.Main.main(Main.java:115) Caused by: java.lang.IllegalArgumentException: Method must not be null at org.springframework.util.Assert.notNull(Assert.java:112) at org.springframework.core.BridgeMethodResolver.findBridgedMethod(BridgeMethodResolver.java:63) at org.springframework.beans.GenericTypeAwarePropertyDescriptor.<init>(GenericTypeAwarePropertyDescriptor.java:58) at org.springframework.beans.CachedIntrospectionResults.<init>(CachedIntrospectionResults.java:250) at org.springframework.beans.CachedIntrospectionResults.forClass(CachedIntrospectionResults.java:144) at org.springframework.beans.BeanWrapperImpl.getCachedIntrospectionResults(BeanWrapperImpl.java:252) at org.springframework.beans.BeanWrapperImpl.getPropertyDescriptorInternal(BeanWrapperImpl.java:282) at org.springframework.beans.BeanWrapperImpl.isWritableProperty(BeanWrapperImpl.java:333) at org.springframework.beans.factory.support.AbstractAutowireCapableBeanFactory.applyPropertyValues(AbstractAutowireCapableBeanFactory.java:1247) at org.springframework.beans.factory.support.AbstractAutowireCapableBeanFactory.populateBean(AbstractAutowireCapableBeanFactory.java:1010) at org.springframework.beans.factory.support.AbstractAutowireCapableBeanFactory.doCreateBean(AbstractAutowireCapableBeanFactory.java:472) ... 35 more 2010-05-13 15:53:20.906::WARN: Nested in org.springframework.beans.factory.BeanCreationException: Error creating bean with name 'org.springframework.beans.factory.config.PropertyPlaceholderConfigurer#0': Initialization of bean failed; nested exception is java.lang.IllegalArgumentException: Method must not be null: java.lang.IllegalArgumentException: Method must not be null at org.springframework.util.Assert.notNull(Assert.java:112) at org.springframework.core.BridgeMethodResolver.findBridgedMethod(BridgeMethodResolver.java:63) at org.springframework.beans.GenericTypeAwarePropertyDescriptor.<init>(GenericTypeAwarePropertyDescriptor.java:58) at org.springframework.beans.CachedIntrospectionResults.<init>(CachedIntrospectionResults.java:250) at org.springframework.beans.CachedIntrospectionResults.forClass(CachedIntrospectionResults.java:144) at org.springframework.beans.BeanWrapperImpl.getCachedIntrospectionResults(BeanWrapperImpl.java:252) at org.springframework.beans.BeanWrapperImpl.getPropertyDescriptorInternal(BeanWrapperImpl.java:282) at org.springframework.beans.BeanWrapperImpl.isWritableProperty(BeanWrapperImpl.java:333) at org.springframework.beans.factory.support.AbstractAutowireCapableBeanFactory.applyPropertyValues(AbstractAutowireCapableBeanFactory.java:1247) at org.springframework.beans.factory.support.AbstractAutowireCapableBeanFactory.populateBean(AbstractAutowireCapableBeanFactory.java:1010) at org.springframework.beans.factory.support.AbstractAutowireCapableBeanFactory.doCreateBean(AbstractAutowireCapableBeanFactory.java:472) at org.springframework.beans.factory.support.AbstractAutowireCapableBeanFactory$1.run(AbstractAutowireCapableBeanFactory.java:409) at java.security.AccessController.doPrivileged(Native Method) at org.springframework.beans.factory.support.AbstractAutowireCapableBeanFactory.createBean(AbstractAutowireCapableBeanFactory.java:380) at org.springframework.beans.factory.support.AbstractBeanFactory$1.getObject(AbstractBeanFactory.java:264) at org.springframework.beans.factory.support.DefaultSingletonBeanRegistry.getSingleton(DefaultSingletonBeanRegistry.java:222) at org.springframework.beans.factory.support.AbstractBeanFactory.doGetBean(AbstractBeanFactory.java:261) at org.springframework.beans.factory.support.AbstractBeanFactory.getBean(AbstractBeanFactory.java:185) at org.springframework.beans.factory.support.AbstractBeanFactory.getBean(AbstractBeanFactory.java:164) at org.springframework.context.support.AbstractApplicationContext.invokeBeanFactoryPostProcessors(AbstractApplicationContext.java:515) at org.springframework.context.support.AbstractApplicationContext.refresh(AbstractApplicationContext.java:362) at org.springframework.web.context.ContextLoader.createWebApplicationContext(ContextLoader.java:255) at org.springframework.web.context.ContextLoader.initWebApplicationContext(ContextLoader.java:199) at org.springframework.web.context.ContextLoaderListener.contextInitialized(ContextLoaderListener.java:45) at org.mortbay.jetty.handler.ContextHandler.startContext(ContextHandler.java:530) at org.mortbay.jetty.servlet.Context.startContext(Context.java:135) at org.mortbay.jetty.webapp.WebAppContext.startContext(WebAppContext.java:1218) at org.mortbay.jetty.handler.ContextHandler.doStart(ContextHandler.java:500) at org.mortbay.jetty.webapp.WebAppContext.doStart(WebAppContext.java:448) at org.mortbay.component.AbstractLifeCycle.start(AbstractLifeCycle.java:40) at org.mortbay.jetty.handler.HandlerCollection.doStart(HandlerCollection.java:147) at org.mortbay.jetty.handler.ContextHandlerCollection.doStart(ContextHandlerCollection.java:161) at org.mortbay.component.AbstractLifeCycle.start(AbstractLifeCycle.java:40) at org.mortbay.jetty.handler.HandlerCollection.doStart(HandlerCollection.java:147) at org.mortbay.component.AbstractLifeCycle.start(AbstractLifeCycle.java:40) at org.mortbay.jetty.handler.HandlerWrapper.doStart(HandlerWrapper.java:117) at org.mortbay.jetty.Server.doStart(Server.java:210) at org.mortbay.component.AbstractLifeCycle.start(AbstractLifeCycle.java:40) at org.mortbay.xml.XmlConfiguration.main(XmlConfiguration.java:929) at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method) at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:39) at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:25) at java.lang.reflect.Method.invoke(Method.java:597) at org.mortbay.start.Main.invokeMain(Main.java:183) at org.mortbay.start.Main.start(Main.java:497) at org.mortbay.start.Main.main(Main.java:115) 2010-05-13 15:53:20.964::INFO: Started SelectChannelConnector @ 0.0.0.0:8090

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  • SPFileVersionCollection - why versions are sorted in mixed order?

    - by Janis Veinbergs
    SPFileVersionCollection and SPListItemVersionCollection versioning seems inconsistent to me. Inconsistency wouldn't be a problem to me, but sort order is. SPListItemVersionCollection I can understand versioning of ListItems as they are stored in descending order: SPContext.Current.ListItem.Versions.Count -> 5 SPContext.Current.ListItem.Versions[0].VersionId -> 1026 (2.2 latest version) SPContext.Current.ListItem.Versions[1].VersionId -> 1025 (2.1) SPContext.Current.ListItem.Versions[2].VersionId -> 1024 (2.0) ... [4].VersionId -> (oldest version) SPFileVersionCollection However I can't understand how version numbers are saved for a document library item: SPContext.Current.ListItem.File.Versions.Count -> 4 SPContext.Current.ListItem.File.Versions[0].ID -> 512 (1.0 oldest one) SPContext.Current.ListItem.File.Versions[1].ID -> 513 (1.1) SPContext.Current.ListItem.File.Versions[2].ID -> 1025 (2.1 latest version) SPContext.Current.ListItem.File.Versions[3].ID -> 1024 (2.0 (EDIT: IsCurrentVersion = True)) They are nor in ascending order, nor descending, but something mixed. Is there any reason for SharePoint team to decide to store SPFile versions like that? And do they expect that I write my own method to get latest version or is there a builtin one for that? A note: Let me point out that SPListItem.File is not null for document library items.

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  • Ruby on Rails export to csv - maintain mysql select statement order

    - by zekial
    Exporting some data from mysql to a csv file using FasterCSV. I'd like the columns in the outputted CSV to be in the same order as the select statement in my query. Example: rows = Data.find( :all, :select=>'name, age, height, weight' ) headers = rows[0].attributes.keys FasterCSV.generate do |csv| csv << headers rows.each do |r| csv << r.attributes.values end end CSV Output: height,weight,name,age 74,212,bob,23 70,201,fred,24 . . . I want the CSV columns in the same order as my select statement. Obviously the attributes method is not going to work. Any ideas on the best way to ensure that the columns in my csv file will be in the same order as the select statement? Got a lot of data and performance is an issue. The select statement is not static. I realize I could loop through column names within the rows.each loop but it seems kinda dirty.

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  • The ORDER BY clause is invalid in views, inline functions, derived tables, subqueries, and common ta

    - by zurna
    I get "The ORDER BY clause is invalid in views, inline functions, derived tables, subqueries, and common table expressions, unless TOP or FOR XML is also specified." error with the following code. I initially had two tables, ADSAREAS & CATEGORIES. I started receiving this error when I removed CATEGORIES table. Select Case SIDX Case "ID" : SQLCONT1 = " AdsAreasID" Case "Page" : SQLCONT1 = " AdsAreasName" Case Else : SQLCONT1 = " AdsAreasID" End Select Select Case SORD Case "asc" : SQLCONT2 = " ASC" Case "desc" : SQLCONT2 = " DESC" Case Else : SQLCONT2 = " ASC" End Select ''# search feature ---> Select Case SEARCHFIELD Case "ID" : SQLSFIELD = "AND AdsAreasID" Case "Ads Areas" : SQLSFIELD = "AND AdsAreasName" Case Else : SQLSFIELD = "" End Select Select Case SEARCHOPER Case "eq" : SQLSOPER = " = " & SEARCHSTRING Case "ne" : SQLSOPER = " <> " & SEARCHSTRING Case "lt" : SQLSOPER = " <" & SEARCHSTRING Case "le" : SQLSOPER = " <= " & SEARCHSTRING Case "gt" : SQLSOPER = " >" & SEARCHSTRING Case "ge" : SQLSOPER = " >= " & SEARCHSTRING Case "bw" : SQLSOPER = " LIKE '" & SEARCHSTRING & "%' " Case "ew" : SQLSOPER = " LIKE '%" & SEARCHSTRING & "' " Case "cn" : SQLSOPER = " LIKE '%" & SEARCHSTRING & "%' " Case Else : SQLSOPER = "" End Select ''# search feature ---> SQL = "SELECT * FROM ( SELECT A.AdsAreasID, A.AdsAreasName, ROW_NUMBER() OVER (ORDER BY A.AdsAreasID) As Row" SQL = SQL & " FROM ADSAREAS A" SQL = SQL & " WHERE Row > ("& RecordsPageSize - RecordsPerPage &") AND Row <= ("& RecordsPageSize &") ORDER BY" & SQLCONT1 & SQLCONT2 Set objXML = objConn.Execute(SQL)

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  • jQuery "Autcomplete" plugin is messing up the order of my data

    - by Max Williams
    I'm using Jorn Zaefferer's Autocomplete plugin on a couple of different pages. In both instances, the order of displayed strings is a little bit messed up. Example 1: array of strings: basically they are in alphabetical order except for General Knowledge which has been pushed to the top: General Knowledge,Art and Design,Business Studies,Citizenship,Design and Technology,English,Geography,History,ICT,Mathematics,MFL French,MFL German,MFL Spanish,Music,Physical Education,PSHE,Religious Education,Science,Something Else Displayed strings: General Knowledge,Geography,Art and Design,Business Studies,Citizenship,Design and Technology,English,History,ICT,Mathematics,MFL French,MFL German,MFL Spanish,Music,Physical Education,PSHE,Religious Education,Science,Something Else Note that Geography has been pushed to be the second item, after General Knowledge. The rest are all fine. Example 2: array of strings: as above but with Cross-curricular instead of General Knowledge. Cross-curricular,Art and Design,Business Studies,Citizenship,Design and Technology,English,Geography,History,ICT,Mathematics,MFL French,MFL German,MFL Spanish,Music,Physical Education,PSHE,Religious Education,Science,Something Else Displayed strings: Cross-curricular,Citizenship,Art and Design,Business Studies,Design and Technology,English,Geography,History,ICT,Mathematics,MFL French,MFL German,MFL Spanish,Music,Physical Education,PSHE,Religious Education,Science,Something Else Here, Citizenship has been pushed to the number 2 position. I've experimented a little, and it seems like there's a bug saying "put things that start with the same letter as the first item after the first item and leave the rest alone". Kind of mystifying. I've tried a bit of debugging by triggering alerts inside the autocomplete plugin code but everywhere i can see, it's using the correct order. it seems to be just when its rendered out that it goes wrong. Any ideas anyone? max

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  • IWshShortcut Target Resolution in Windows 7

    - by Dan Walker
    I've got some code to read shortcuts using the Windows Script Host, but it appears to have a problem in Windows 7. When reading shortcuts, if there is an environment variable in the target path, it resolves to the wrong drive. For example, the shortcut to Notepad resolves to D:\Windows\system32\notepad.exe instead of C:\Windows\system32\notepad.exe. The problem is not with my computer's settings, because the shortcut works just fine, and when looking at the value for %SystemRoot%, it shows C:\Windows. Any ideas as to what could be the problem, or alternatively, what a different method of reading shortcuts would be? Thanks, Dan

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  • Machine Learning Algorithm for Predicting Order of Events?

    - by user213060
    Simple machine learning question. Probably numerous ways to solve this: There is an infinite stream of 4 possible events: 'event_1', 'event_2', 'event_4', 'event_4' The events do not come in in completely random order. We will assume that there are some complex patterns to the order that most events come in, and the rest of the events are just random. We do not know the patterns ahead of time though. After each event is received, I want to predict what the next event will be based on the order that events have come in in the past. The predictor will then be told what the next event actually was: Predictor=new_predictor() prev_event=False while True: event=get_event() if prev_event is not False: Predictor.last_event_was(prev_event) predicted_event=Predictor.predict_next_event(event) The question arises of how long of a history that the predictor should maintain, since maintaining infinite history will not be possible. I'll leave this up to you to answer. The answer can't be infinte though for practicality. So I believe that the predictions will have to be done with some kind of rolling history. Adding a new event and expiring an old event should therefore be rather efficient, and not require rebuilding the entire predictor model, for example. Specific code, instead of research papers, would add for me immense value to your responses. Python or C libraries are nice, but anything will do. Thanks! Update: And what if more than one event can happen simultaneously on each round. Does that change the solution?

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  • Best approach to storing image pixels in bottom-up order in Java

    - by finnw
    I have an array of bytes representing an image in Windows BMP format and I would like my library to present it to the Java application as a BufferedImage, without copying the pixel data. The main problem is that all implementations of Raster in the JDK store image pixels in top-down, left-to-right order whereas BMP pixel data is stored bottom-up, left-to-right. If this is not compensated for, the resulting image will be flipped vertically. The most obvious "solution" is to set the SampleModel's scanlineStride property to a negative value and change the band offsets (or the DataBuffer's array offset) to point to the top-left pixel, i.e. the first pixel of the last line in the array. Unfortunately this does not work because all of the SampleModel constructors throw an exception if given a negative scanlineStride argument. I am currently working around it by forcing the scanlineStride field to a negative value using reflection, but I would like to do it in a cleaner and more portable way if possible. e.g. is there another way to fool the Raster or SampleModel into arranging the pixels in bottom-up order but without breaking encapsulation? Or is there a library somewhere that will wrap the Raster and SampleModel, presenting the pixel rows in reverse order? I would prefer to avoid the following approaches: Copying the whole image (for performance reasons. The code must process hundreds of large (= 1Mpixels) images per second and although the whole image must be available to the application, it will normally access only a tiny (but hard-to-predict) portion of the image.) Modifying the DataBuffer to perform coordinate transformation (this actually works but is another "dirty" solution because the buffer should not need to know about the scanline/pixel layout.) Re-implementing the Raster and/or SampleModel interfaces from scratch (but I have a hunch that I will be unable to avoid this.)

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  • How to add a specific method to a particular scope in Visual Studion 2005

    - by pragadheesh
    Hi, In my visual studio project (C++), when i copy a method(meth1) of a particular scope say 'scope1' and paste it in the same code area, it is getting pasted in General Scope. i.e I want to add a method into a particular scope but when i try it is getting added in general scope. How can i solve this? For eg: There is an existing method: void add(int a, int b) { .... } This method is in File scope. i.e limited for that file. Now i want to add another method add2 in the same file scope. So I copied the existing add method and pasted it. void add2(int a, int b) { .... } But this method is getting added in the global scope and not in the file scope.

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  • HTTP POST prarameters order / REST urls

    - by pq
    Let's say that I'm uploading a large file via a POST HTTP request. Let's also say that I have another parameter (other than the file) that names the resource which the file is updating. The resource cannot be not part of the URL the way you can do it with REST (e.g. foo.com/bar/123). Let's say this is due to a combination of technical and political reasons. The server needs to ignore the file if the resource name is invalid or, say, the IP address and/or the logged in user are not authorized to update the resource. Looks like, if this POST came from an HTML form that contains the resource name first and file field second, for most (all?) browsers, this order is preserved in the POST request. But it would be naive to fully rely on that, no? In other words the order of HTTP parameters is insignificant and a client is free to construct the POST in any order. Isn't that true? Which means that, at least in theory, the server may end up storing the whole large file before it can deny the request. It seems to me that this is a clear case where RESTful urls have an advantage, since you don't have to look at the POST content to perform certain authorization/error checking on the request. Do you agree? What are your thoughts, experiences?

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  • Call a macro every time any method is called - Objective C

    - by Jacob Relkin
    Hi, I wrote a debug macro that prints to the console the passed-in string whenever the global kDebug flag == YES. I need to print out the name of a method and it's classname whenever any method is called. That works fine when i painstakingly go through every method and write the name of the class and the method in a string. Is there any special handler that gets called when any method in Objective-C is called, and if so, is there a way i can somehow override it to call my debug macro?? The entire purpose of this is so that I don't have to go through every method in my code and hand-code the method signature in the debug macro call. Thanks

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  • Order in many to many relation in Django model

    - by Pietro Speroni
    I am writing a small website to store the papers I have written. The relation papers<- author is important, but the order of the name of the authors (which one is First Author, which one is second order, and so on) is also important. I am just learning Django so I don't know much. In any case so far I have done: from django.db import models class author(models.Model): Name = models.CharField(max_length=60) URLField = models.URLField(verify_exists=True, null=True, blank=True) def __unicode__(self): return self.Name class topic(models.Model): TopicName = models.CharField(max_length=60) def __unicode__(self): return self.TopicName class publication(models.Model): Title = models.CharField(max_length=100) Authors = models.ManyToManyField(author, null=True, blank=True) Content = models.TextField() Notes = models.TextField(blank=True) Abstract = models.TextField(blank=True) pub_date = models.DateField('date published') TimeInsertion = models.DateTimeField(auto_now=True) URLField = models.URLField(verify_exists=True,null=True, blank=True) Topic = models.ManyToManyField(topic, null=True, blank=True) def __unicode__(self): return self.Title This work fine in the sense that I now can define who the authors are. But I cannot order them. How should I do that? Of course I could add a series of relations: first author, second author,... but it would be ugly, and would not be flexible. Any better idea? Thanks

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  • Java split giving opposite order of arabic characters

    - by MuhammadA
    I am splitting the following string using \\| in java (android) using the IntelliJ 12 IDE. Everything is fine except the last part, somehow the split picks them up in the opposite order : As you can see the real positioning 34,35,36 is correct and according to the string, but when it gets picked out into split part no 5 its in the wrong order, 36,35,34 ... Any way I can get them to be in the right order? My Code: public ArrayList<Book> getBooksFromDatFile(Context context, String fileName) { ArrayList<Book> books = new ArrayList<Book>(); try { // load csv from assets InputStream is = context.getAssets().open(fileName); try { BufferedReader reader = new BufferedReader(new InputStreamReader(is)); String line; while ((line = reader.readLine()) != null) { String[] RowData = line.split("\\|"); books.add(new Book(RowData[0], RowData[1], RowData[2], RowData[3], RowData[4], RowData[5])); } } catch (IOException ex) { Log.e(TAG, "Error parsing csv file!"); } finally { try { is.close(); } catch (IOException e) { Log.e(TAG, "Error closing input stream!"); } } } catch (IOException ex) { Log.e(TAG, "Error reading .dat file from assets!"); } return books; }

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  • Algorithm to produce Cartesian product of arrays in depth-first order

    - by Yuri Gadow
    I'm looking for an example of how, in Ruby, a C like language, or pseudo code, to create the Cartesian product of a variable number of arrays of integers, each of differing length, and step through the results in a particular order: So given, [1,2,3],[1,2,3],[1,2,3]: [1, 1, 1] [2, 1, 1] [1, 2, 1] [1, 1, 2] [2, 2, 1] [1, 2, 2] [2, 1, 2] [2, 2, 2] [3, 1, 1] [1, 3, 1] etc. Instead of the typical result I've seen (including the example I give below): [1, 1, 1] [2, 1, 1] [3, 1, 1] [1, 2, 1] [2, 2, 1] [3, 2, 1] [1, 3, 1] [2, 3, 1] etc. The problem with this example is that the third position isn't explored at all until all combinations of of the first two are tried. In the code that uses this, that means even though the right answer is generally (the much larger equivalent of) 1,1,2 it will examine a few million possibilities instead of just a few thousand before finding it. I'm dealing with result sets of one million to hundreds of millions, so generating them and then sorting isn't doable here and would defeat the reason for ordering them in the first example, which is to find the correct answer sooner and so break out of the cartesian product generation earlier. Just in case it helps clarify any of the above, here's how I do this now (this has correct results and right performance, but not the order I want, i.e., it creates results as in the second listing above): def cartesian(a_of_a) a_of_a_len = a_of_a.size result = Array.new(a_of_a_len) j, k, a2, a2_len = nil, nil, nil, nil i = 0 while 1 do j, k = i, 0 while k < a_of_a_len a2 = a_of_a[k] a2_len = a2.size result[k] = a2[j % a2_len] j /= a2_len k += 1 end return if j > 0 yield result i += 1 end end UPDATE: I didn't make it very clear that I'm after a solution where all the combinations of 1,2 are examined before 3 is added in, then all 3 and 1, then all 3, 2 and 1, then all 3,2. In other words, explore all earlier combinations "horizontally" before "vertically." The precise order in which those possibilities are explored, i.e., 1,1,2 or 2,1,1, doesn't matter, just that all 2 and 1 are explored before mixing in 3 and so on.

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  • How can I order by the result of a recursive SQL query

    - by Tony
    I have the following method I need to ORDER BY: def has_attachments? attachments.size > 0 || (!parent.nil? && parent.has_attachments?) end I have gotten this far: ORDER BY CASE WHEN attachments.size > 0 THEN 1 ELSE (CASE WHEN parent_id IS NULL THEN 0 ELSE (CASE message.parent ...what goes here ) END END END I may be looking at this wrong because I don't have experience with recursive SQL. Essentially I want to ORDER by whether a message or any of its parents has attachments. If it's attachment size is 0, I can stop and return a 1. If the message has an attachment size of 0, I now check to see if it has a parent. If it has no parent then there is no attachment, however if it does have a parent then I essentially have to do the same query case logic for the parent. UPDATE The table looks like this +---------------------+--------------+------+-----+---------+----------------+ | Field | Type | Null | Key | Default | Extra | +---------------------+--------------+------+-----+---------+----------------+ | id | int(11) | NO | PRI | NULL | auto_increment | | message_type_id | int(11) | NO | MUL | | | | message_priority_id | int(11) | NO | MUL | | | | message_status_id | int(11) | NO | MUL | | | | message_subject_id | int(11) | NO | MUL | | | | from_user_id | int(11) | YES | MUL | NULL | | | parent_id | int(11) | YES | MUL | NULL | | | expires_at | datetime | YES | MUL | NULL | | | subject_other | varchar(255) | YES | | NULL | | | body | text | YES | | NULL | | | created_at | datetime | NO | MUL | | | | updated_at | datetime | NO | | | | | lock_version | int(11) | NO | | 0 | | +---------------------+--------------+------+-----+---------+----------------+ Where the parent_id refers to the parent message, if it exists. Thanks!

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  • Is it possible to prevent out-of-order execution by using single volatile

    - by Yan Cheng CHEOK
    By referring article, it is using a pair of volatile to prevent out-of-order execution. I was wondering, is it possible to prevent it using single volatile? void fun_by_thread_1() { this.isNuclearFactory = true; this.factory = new NuclearFactory(); } void fun_by_thread_2() { Factory _factory = this.factory; if (this.isNuclearFactory) { // Do not operate nuclear factory!!! return; } // If out-of-order execution happens, _factory might // be NuclearFactory instance. _factory.operate(); } Factory factory = new FoodFactory(); volatile boolean isNuclearFactory = false; The reason I ask, is because I have a single guard flag (similar to isNuclearFactory flag), to guard against multiple variables (similar to many Factory). I do not wish to mark all the Factory as volatile. Or, shall I fall into the following solution? void fun_by_thread_1() { try { writer.lock(); this.isNuclearFactory = true; this.factory = new NuclearFactory(); } finally { writer.unlock(); } } void fun_by_thread_2() { try { reader.lock(); Factory _factory = this.factory; if (this.isNuclearFactory) { // Do not operate nuclear factory!!! return; } } finally { reader.unlock(); } _factory.operate(); } Factory factory = new FoodFactory(); boolean isNuclearFactory = false; P/S: I know instanceof. Factory is just an example to demonstrate of out-of-order problem.

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  • Match subpatterns in any order

    - by Yaroslav
    I have long regexp with two complicated subpatters inside. How i can match that subpatterns in any order? Simplified example: /(apple)?\s?(banana)?\s?(orange)?\s?(kiwi)?/ and i want to match both of apple banana orange kiwi apple orange banana kiwi It is very simplified example. In my case banana and orange is long complicated subpatterns and i don't want to do something like /(apple)?\s?((banana)?\s?(orange)?|(orange)?\s?(banana)?)\s?(kiwi)?/ Is it possible to group subpatterns like chars in character class? UPD Real data as requested: 14:24 26,37 Mb 108.53 01:19:02 06.07 24.39 19:39 46:00 my strings much longer, but it is significant part. Here you can see two lines what i need to match. First has two values: length (14 min 24 sec) and size 26.37 Mb. Second one has three values but in different order: size 108.53 Mb, length 01 h 19 m 02 s and date June, 07 Third one has two size and length Fourth has only length There are couple more variations and i need to parse all values. I have a regexp that pretty close except i can't figure out how to match patterns in different order without writing it twice. (?<size>\d{1,3}\[.,]\d{1,2}\s+(?:Mb)?)?\s? (?<length>(?:(?:01:)?\d{1,2}:\d{2}))?\s* (?<date>\d{2}\.\d{2}))? NOTE: that is only part of big regexp that forks fine already.

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  • ignoring elements order in xml validation against xsd

    - by segolas
    Hi, Ia processing an email and saving some header inside a xml document. I also need to validate the document against a xml schema. As the subject suggest, I need to validate ignoring the elements order but, as far as I read this seems to be impossible. Am I correct? If I put the headers in a<xsd:sequence>, the order obviously matter. If I us the order is ignored but for some strange reason this imply that the elements must occur at least once. My xml is something like this: <headers> <subject>bla bla bla</subject> <recipient>[email protected]</recipient> <recipient>rcp02domain.com</recipient> <recipient>[email protected]</recipient> </headers> but I think the final document is valid even if subject and recipient elements are swapped. There is really nothing to do?

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  • No-argument method on window.external is invoked when checking with typeof

    - by janko
    Hi, I am trying to display an HTML page with embedded JavaScript code inside a System.Windows.Forms.WebBrowser control. The JavaScript code is expected to interact with the embedding environment through the window.external object. Before invoking a method on window.external, JavaScript is supposed to check for the existance of the method. If it is not there, the code should invoke a generic fallback method. // basic idea if (typeof(window.external.MyMethod) != 'undefined') { window.external.MyMethod(args); } else { window.external.Generic("MyMethod", args); } However, checking for a no-argument method with typeof seems to invoke the method already. That is, if MyMethod accepts any positive number of arguments, the code above will work perfectly; but, if MyMethod is a no-argument method, then the expression typeof(window.external.MyMethod) will not check for its type but invoke it, too. Is there any work-around to this behavior? Can I somehow escape the expression window.external.MyMethod to prevent the method call from occurring?

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  • Android Unit Testing - Resolution & Verification Problems

    - by Bill
    I just switched the way my Android project is being built and non of my unit tests work any more...I get errors like WARN/dalvikvm(575): VFY: unable to resolve static field X in ..... WARN/dalvikvm(575): VFY: unable to find class referenced in signature These errors only come from my Unit Tests, where classes defined in it can't even see other classes defined in the unit test. Before each project had its own directory with copies of the 3rd party jar files. I've read around that Dex does weird things with references but haven't been able to figure out how to fix this problem. Is there a better way to do this? I would love to see an example of a large Android workspace where there are multiple projects, jar references, etc... Is it possible to fix this with an Order/Export tweak ? The project is structured like this: Eclipse Workspace (PROJECT_HOME classpath variable) lib 3rd-party jars android.jar Java Project A Looks in PROJECT_HOME Java Project B Looks in PROJECT_HOME Depends on project A Android Project Depends on A & B Looks in PROJECT_HOME Android Test Project Depends on A , B, Android Project Looks in PROJECT_HOME

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  • Is NFS capable of preserving order of operations?

    - by JustJeff
    I have a diskless host 'A', that has a directory NFS mounted on server 'B'. A process on A writes to two files F1 and F2 in that directory, and a process on B monitors these files for changes. Assume that B polls for changes faster than A is expected to make them. Process A seeks the head of the files, writes data, and flushes. Process B seeks the head of the files and does reads. Are there any guarantees about how the order of the changes performed by A will be detected at B? Specifically, if A alternately writes to one file, and then the other, is it reasonable to expect that B will notice alternating changes to F1 and F2? Or could B conceivably detect a series of changes on F1 and then a series on F2? I know there are a lot of assumptions embedded in the question. For instance, I am virtually certain that, even operating on just one file, if A performs 100 operations on the file, B may see a smaller number of changes that give the same result, due to NFS caching some of the actions on A before they are communicated to B. And of course there would be issues with concurrent file access even if NFS weren't involved and both the reading and the writing process were running on the same real file system. The reason I'm even putting the question up here is that it seems like most of the time, the setup described above does detect the changes at B in the same order they are made at A, but that occasionally some events come through in transposed order. So, is it worth trying to make this work? Is there some way to tune NFS to make it work, perhaps cache settings or something? Or is fine-grained behavior like this just too much expect from NFS?

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  • std::bind overload resolution

    - by bpw1621
    The following code works fine #include <functional> using namespace std; using namespace std::placeholders; class A { int operator()( int i, int j ) { return i - j; } }; A a; auto aBind = bind( &A::operator(), ref(a), _2, _1 ); This does not #include <functional> using namespace std; using namespace std::placeholders; class A { int operator()( int i, int j ) { return i - j; } int operator()( int i ) { return -i; } }; A a; auto aBind = bind( &A::operator(), ref(a), _2, _1 ); I have tried playing around with the syntax to try and explicitly resolve which function I want in the code that does not work without luck so far. How do I write the bind line in order to choose the call that takes the two integer arguments?

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  • undefined method `code' for nil:NilClass message with rails and a legacy database

    - by Jude Osborn
    I'm setting up a very simple rails 3 application to view data in a legacy MySQL database. The legacy database is mostly rails ORM compatible, except that foreign key fields are pluralized. For example, my "orders" table has a foreign key field to the "companies" table called "companies_id" (rather than "company_id"). So naturally I'm having to use the ":foreign_key" attribute of "belongs_to" to set the field name manually. I haven't used rails in a few years, but I'm pretty sure I'm doing everything right, yet I get the following error when trying to access "order.currency.code": undefined method `code' for nil:NilClass This is a very simple application so far. The only thing I've done is generate the application and a bunch of scaffolds for each of the legacy database tables. Then I've gone into some of the models to make adjustments to accommodate the above mentioned difference in database naming conventions, and added some fields to the views. That's it. No funny business. So my database tables look like this (relevant fields only): orders ------ id description invoice_number currencies_id currencies ---------- id code description My Order model looks like this: class Order < ActiveRecord::Base belongs_to :currency, :foreign_key=>'currencies_id' end My Currency model looks like this: class Currency < ActiveRecord::Base has_many :orders end The relevant view snippet looks like this: <% @orders.each do |order| %> <tr> <td><%= order.description %></td> <td><%= order.invoice_number %></td> <td><%= order.currency.code %></td> </tr> <% end %> I'm completely out of ideas. Any suggestions?

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  • A Taxonomy of Numerical Methods v1

    - by JoshReuben
    Numerical Analysis – When, What, (but not how) Once you understand the Math & know C++, Numerical Methods are basically blocks of iterative & conditional math code. I found the real trick was seeing the forest for the trees – knowing which method to use for which situation. Its pretty easy to get lost in the details – so I’ve tried to organize these methods in a way that I can quickly look this up. I’ve included links to detailed explanations and to C++ code examples. I’ve tried to classify Numerical methods in the following broad categories: Solving Systems of Linear Equations Solving Non-Linear Equations Iteratively Interpolation Curve Fitting Optimization Numerical Differentiation & Integration Solving ODEs Boundary Problems Solving EigenValue problems Enjoy – I did ! Solving Systems of Linear Equations Overview Solve sets of algebraic equations with x unknowns The set is commonly in matrix form Gauss-Jordan Elimination http://en.wikipedia.org/wiki/Gauss%E2%80%93Jordan_elimination C++: http://www.codekeep.net/snippets/623f1923-e03c-4636-8c92-c9dc7aa0d3c0.aspx Produces solution of the equations & the coefficient matrix Efficient, stable 2 steps: · Forward Elimination – matrix decomposition: reduce set to triangular form (0s below the diagonal) or row echelon form. If degenerate, then there is no solution · Backward Elimination –write the original matrix as the product of ints inverse matrix & its reduced row-echelon matrix à reduce set to row canonical form & use back-substitution to find the solution to the set Elementary ops for matrix decomposition: · Row multiplication · Row switching · Add multiples of rows to other rows Use pivoting to ensure rows are ordered for achieving triangular form LU Decomposition http://en.wikipedia.org/wiki/LU_decomposition C++: http://ganeshtiwaridotcomdotnp.blogspot.co.il/2009/12/c-c-code-lu-decomposition-for-solving.html Represent the matrix as a product of lower & upper triangular matrices A modified version of GJ Elimination Advantage – can easily apply forward & backward elimination to solve triangular matrices Techniques: · Doolittle Method – sets the L matrix diagonal to unity · Crout Method - sets the U matrix diagonal to unity Note: both the L & U matrices share the same unity diagonal & can be stored compactly in the same matrix Gauss-Seidel Iteration http://en.wikipedia.org/wiki/Gauss%E2%80%93Seidel_method C++: http://www.nr.com/forum/showthread.php?t=722 Transform the linear set of equations into a single equation & then use numerical integration (as integration formulas have Sums, it is implemented iteratively). an optimization of Gauss-Jacobi: 1.5 times faster, requires 0.25 iterations to achieve the same tolerance Solving Non-Linear Equations Iteratively find roots of polynomials – there may be 0, 1 or n solutions for an n order polynomial use iterative techniques Iterative methods · used when there are no known analytical techniques · Requires set functions to be continuous & differentiable · Requires an initial seed value – choice is critical to convergence à conduct multiple runs with different starting points & then select best result · Systematic - iterate until diminishing returns, tolerance or max iteration conditions are met · bracketing techniques will always yield convergent solutions, non-bracketing methods may fail to converge Incremental method if a nonlinear function has opposite signs at 2 ends of a small interval x1 & x2, then there is likely to be a solution in their interval – solutions are detected by evaluating a function over interval steps, for a change in sign, adjusting the step size dynamically. Limitations – can miss closely spaced solutions in large intervals, cannot detect degenerate (coinciding) solutions, limited to functions that cross the x-axis, gives false positives for singularities Fixed point method http://en.wikipedia.org/wiki/Fixed-point_iteration C++: http://books.google.co.il/books?id=weYj75E_t6MC&pg=PA79&lpg=PA79&dq=fixed+point+method++c%2B%2B&source=bl&ots=LQ-5P_taoC&sig=lENUUIYBK53tZtTwNfHLy5PEWDk&hl=en&sa=X&ei=wezDUPW1J5DptQaMsIHQCw&redir_esc=y#v=onepage&q=fixed%20point%20method%20%20c%2B%2B&f=false Algebraically rearrange a solution to isolate a variable then apply incremental method Bisection method http://en.wikipedia.org/wiki/Bisection_method C++: http://numericalcomputing.wordpress.com/category/algorithms/ Bracketed - Select an initial interval, keep bisecting it ad midpoint into sub-intervals and then apply incremental method on smaller & smaller intervals – zoom in Adv: unaffected by function gradient à reliable Disadv: slow convergence False Position Method http://en.wikipedia.org/wiki/False_position_method C++: http://www.dreamincode.net/forums/topic/126100-bisection-and-false-position-methods/ Bracketed - Select an initial interval , & use the relative value of function at interval end points to select next sub-intervals (estimate how far between the end points the solution might be & subdivide based on this) Newton-Raphson method http://en.wikipedia.org/wiki/Newton's_method C++: http://www-users.cselabs.umn.edu/classes/Summer-2012/csci1113/index.php?page=./newt3 Also known as Newton's method Convenient, efficient Not bracketed – only a single initial guess is required to start iteration – requires an analytical expression for the first derivative of the function as input. Evaluates the function & its derivative at each step. Can be extended to the Newton MutiRoot method for solving multiple roots Can be easily applied to an of n-coupled set of non-linear equations – conduct a Taylor Series expansion of a function, dropping terms of order n, rewrite as a Jacobian matrix of PDs & convert to simultaneous linear equations !!! Secant Method http://en.wikipedia.org/wiki/Secant_method C++: http://forum.vcoderz.com/showthread.php?p=205230 Unlike N-R, can estimate first derivative from an initial interval (does not require root to be bracketed) instead of inputting it Since derivative is approximated, may converge slower. Is fast in practice as it does not have to evaluate the derivative at each step. Similar implementation to False Positive method Birge-Vieta Method http://mat.iitm.ac.in/home/sryedida/public_html/caimna/transcendental/polynomial%20methods/bv%20method.html C++: http://books.google.co.il/books?id=cL1boM2uyQwC&pg=SA3-PA51&lpg=SA3-PA51&dq=Birge-Vieta+Method+c%2B%2B&source=bl&ots=QZmnDTK3rC&sig=BPNcHHbpR_DKVoZXrLi4nVXD-gg&hl=en&sa=X&ei=R-_DUK2iNIjzsgbE5ID4Dg&redir_esc=y#v=onepage&q=Birge-Vieta%20Method%20c%2B%2B&f=false combines Horner's method of polynomial evaluation (transforming into lesser degree polynomials that are more computationally efficient to process) with Newton-Raphson to provide a computational speed-up Interpolation Overview Construct new data points for as close as possible fit within range of a discrete set of known points (that were obtained via sampling, experimentation) Use Taylor Series Expansion of a function f(x) around a specific value for x Linear Interpolation http://en.wikipedia.org/wiki/Linear_interpolation C++: http://www.hamaluik.com/?p=289 Straight line between 2 points à concatenate interpolants between each pair of data points Bilinear Interpolation http://en.wikipedia.org/wiki/Bilinear_interpolation C++: http://supercomputingblog.com/graphics/coding-bilinear-interpolation/2/ Extension of the linear function for interpolating functions of 2 variables – perform linear interpolation first in 1 direction, then in another. Used in image processing – e.g. texture mapping filter. Uses 4 vertices to interpolate a value within a unit cell. Lagrange Interpolation http://en.wikipedia.org/wiki/Lagrange_polynomial C++: http://www.codecogs.com/code/maths/approximation/interpolation/lagrange.php For polynomials Requires recomputation for all terms for each distinct x value – can only be applied for small number of nodes Numerically unstable Barycentric Interpolation http://epubs.siam.org/doi/pdf/10.1137/S0036144502417715 C++: http://www.gamedev.net/topic/621445-barycentric-coordinates-c-code-check/ Rearrange the terms in the equation of the Legrange interpolation by defining weight functions that are independent of the interpolated value of x Newton Divided Difference Interpolation http://en.wikipedia.org/wiki/Newton_polynomial C++: http://jee-appy.blogspot.co.il/2011/12/newton-divided-difference-interpolation.html Hermite Divided Differences: Interpolation polynomial approximation for a given set of data points in the NR form - divided differences are used to approximately calculate the various differences. For a given set of 3 data points , fit a quadratic interpolant through the data Bracketed functions allow Newton divided differences to be calculated recursively Difference table Cubic Spline Interpolation http://en.wikipedia.org/wiki/Spline_interpolation C++: https://www.marcusbannerman.co.uk/index.php/home/latestarticles/42-articles/96-cubic-spline-class.html Spline is a piecewise polynomial Provides smoothness – for interpolations with significantly varying data Use weighted coefficients to bend the function to be smooth & its 1st & 2nd derivatives are continuous through the edge points in the interval Curve Fitting A generalization of interpolating whereby given data points may contain noise à the curve does not necessarily pass through all the points Least Squares Fit http://en.wikipedia.org/wiki/Least_squares C++: http://www.ccas.ru/mmes/educat/lab04k/02/least-squares.c Residual – difference between observed value & expected value Model function is often chosen as a linear combination of the specified functions Determines: A) The model instance in which the sum of squared residuals has the least value B) param values for which model best fits data Straight Line Fit Linear correlation between independent variable and dependent variable Linear Regression http://en.wikipedia.org/wiki/Linear_regression C++: http://www.oocities.org/david_swaim/cpp/linregc.htm Special case of statistically exact extrapolation Leverage least squares Given a basis function, the sum of the residuals is determined and the corresponding gradient equation is expressed as a set of normal linear equations in matrix form that can be solved (e.g. using LU Decomposition) Can be weighted - Drop the assumption that all errors have the same significance –-> confidence of accuracy is different for each data point. Fit the function closer to points with higher weights Polynomial Fit - use a polynomial basis function Moving Average http://en.wikipedia.org/wiki/Moving_average C++: http://www.codeproject.com/Articles/17860/A-Simple-Moving-Average-Algorithm Used for smoothing (cancel fluctuations to highlight longer-term trends & cycles), time series data analysis, signal processing filters Replace each data point with average of neighbors. Can be simple (SMA), weighted (WMA), exponential (EMA). Lags behind latest data points – extra weight can be given to more recent data points. Weights can decrease arithmetically or exponentially according to distance from point. Parameters: smoothing factor, period, weight basis Optimization Overview Given function with multiple variables, find Min (or max by minimizing –f(x)) Iterative approach Efficient, but not necessarily reliable Conditions: noisy data, constraints, non-linear models Detection via sign of first derivative - Derivative of saddle points will be 0 Local minima Bisection method Similar method for finding a root for a non-linear equation Start with an interval that contains a minimum Golden Search method http://en.wikipedia.org/wiki/Golden_section_search C++: http://www.codecogs.com/code/maths/optimization/golden.php Bisect intervals according to golden ratio 0.618.. Achieves reduction by evaluating a single function instead of 2 Newton-Raphson Method Brent method http://en.wikipedia.org/wiki/Brent's_method C++: http://people.sc.fsu.edu/~jburkardt/cpp_src/brent/brent.cpp Based on quadratic or parabolic interpolation – if the function is smooth & parabolic near to the minimum, then a parabola fitted through any 3 points should approximate the minima – fails when the 3 points are collinear , in which case the denominator is 0 Simplex Method http://en.wikipedia.org/wiki/Simplex_algorithm C++: http://www.codeguru.com/cpp/article.php/c17505/Simplex-Optimization-Algorithm-and-Implemetation-in-C-Programming.htm Find the global minima of any multi-variable function Direct search – no derivatives required At each step it maintains a non-degenerative simplex – a convex hull of n+1 vertices. Obtains the minimum for a function with n variables by evaluating the function at n-1 points, iteratively replacing the point of worst result with the point of best result, shrinking the multidimensional simplex around the best point. Point replacement involves expanding & contracting the simplex near the worst value point to determine a better replacement point Oscillation can be avoided by choosing the 2nd worst result Restart if it gets stuck Parameters: contraction & expansion factors Simulated Annealing http://en.wikipedia.org/wiki/Simulated_annealing C++: http://code.google.com/p/cppsimulatedannealing/ Analogy to heating & cooling metal to strengthen its structure Stochastic method – apply random permutation search for global minima - Avoid entrapment in local minima via hill climbing Heating schedule - Annealing schedule params: temperature, iterations at each temp, temperature delta Cooling schedule – can be linear, step-wise or exponential Differential Evolution http://en.wikipedia.org/wiki/Differential_evolution C++: http://www.amichel.com/de/doc/html/ More advanced stochastic methods analogous to biological processes: Genetic algorithms, evolution strategies Parallel direct search method against multiple discrete or continuous variables Initial population of variable vectors chosen randomly – if weighted difference vector of 2 vectors yields a lower objective function value then it replaces the comparison vector Many params: #parents, #variables, step size, crossover constant etc Convergence is slow – many more function evaluations than simulated annealing Numerical Differentiation Overview 2 approaches to finite difference methods: · A) approximate function via polynomial interpolation then differentiate · B) Taylor series approximation – additionally provides error estimate Finite Difference methods http://en.wikipedia.org/wiki/Finite_difference_method C++: http://www.wpi.edu/Pubs/ETD/Available/etd-051807-164436/unrestricted/EAMPADU.pdf Find differences between high order derivative values - Approximate differential equations by finite differences at evenly spaced data points Based on forward & backward Taylor series expansion of f(x) about x plus or minus multiples of delta h. Forward / backward difference - the sums of the series contains even derivatives and the difference of the series contains odd derivatives – coupled equations that can be solved. Provide an approximation of the derivative within a O(h^2) accuracy There is also central difference & extended central difference which has a O(h^4) accuracy Richardson Extrapolation http://en.wikipedia.org/wiki/Richardson_extrapolation C++: http://mathscoding.blogspot.co.il/2012/02/introduction-richardson-extrapolation.html A sequence acceleration method applied to finite differences Fast convergence, high accuracy O(h^4) Derivatives via Interpolation Cannot apply Finite Difference method to discrete data points at uneven intervals – so need to approximate the derivative of f(x) using the derivative of the interpolant via 3 point Lagrange Interpolation Note: the higher the order of the derivative, the lower the approximation precision Numerical Integration Estimate finite & infinite integrals of functions More accurate procedure than numerical differentiation Use when it is not possible to obtain an integral of a function analytically or when the function is not given, only the data points are Newton Cotes Methods http://en.wikipedia.org/wiki/Newton%E2%80%93Cotes_formulas C++: http://www.siafoo.net/snippet/324 For equally spaced data points Computationally easy – based on local interpolation of n rectangular strip areas that is piecewise fitted to a polynomial to get the sum total area Evaluate the integrand at n+1 evenly spaced points – approximate definite integral by Sum Weights are derived from Lagrange Basis polynomials Leverage Trapezoidal Rule for default 2nd formulas, Simpson 1/3 Rule for substituting 3 point formulas, Simpson 3/8 Rule for 4 point formulas. For 4 point formulas use Bodes Rule. Higher orders obtain more accurate results Trapezoidal Rule uses simple area, Simpsons Rule replaces the integrand f(x) with a quadratic polynomial p(x) that uses the same values as f(x) for its end points, but adds a midpoint Romberg Integration http://en.wikipedia.org/wiki/Romberg's_method C++: http://code.google.com/p/romberg-integration/downloads/detail?name=romberg.cpp&can=2&q= Combines trapezoidal rule with Richardson Extrapolation Evaluates the integrand at equally spaced points The integrand must have continuous derivatives Each R(n,m) extrapolation uses a higher order integrand polynomial replacement rule (zeroth starts with trapezoidal) à a lower triangular matrix set of equation coefficients where the bottom right term has the most accurate approximation. The process continues until the difference between 2 successive diagonal terms becomes sufficiently small. Gaussian Quadrature http://en.wikipedia.org/wiki/Gaussian_quadrature C++: http://www.alglib.net/integration/gaussianquadratures.php Data points are chosen to yield best possible accuracy – requires fewer evaluations Ability to handle singularities, functions that are difficult to evaluate The integrand can include a weighting function determined by a set of orthogonal polynomials. Points & weights are selected so that the integrand yields the exact integral if f(x) is a polynomial of degree <= 2n+1 Techniques (basically different weighting functions): · Gauss-Legendre Integration w(x)=1 · Gauss-Laguerre Integration w(x)=e^-x · Gauss-Hermite Integration w(x)=e^-x^2 · Gauss-Chebyshev Integration w(x)= 1 / Sqrt(1-x^2) Solving ODEs Use when high order differential equations cannot be solved analytically Evaluated under boundary conditions RK for systems – a high order differential equation can always be transformed into a coupled first order system of equations Euler method http://en.wikipedia.org/wiki/Euler_method C++: http://rosettacode.org/wiki/Euler_method First order Runge–Kutta method. Simple recursive method – given an initial value, calculate derivative deltas. Unstable & not very accurate (O(h) error) – not used in practice A first-order method - the local error (truncation error per step) is proportional to the square of the step size, and the global error (error at a given time) is proportional to the step size In evolving solution between data points xn & xn+1, only evaluates derivatives at beginning of interval xn à asymmetric at boundaries Higher order Runge Kutta http://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods C++: http://www.dreamincode.net/code/snippet1441.htm 2nd & 4th order RK - Introduces parameterized midpoints for more symmetric solutions à accuracy at higher computational cost Adaptive RK – RK-Fehlberg – estimate the truncation at each integration step & automatically adjust the step size to keep error within prescribed limits. At each step 2 approximations are compared – if in disagreement to a specific accuracy, the step size is reduced Boundary Value Problems Where solution of differential equations are located at 2 different values of the independent variable x à more difficult, because cannot just start at point of initial value – there may not be enough starting conditions available at the end points to produce a unique solution An n-order equation will require n boundary conditions – need to determine the missing n-1 conditions which cause the given conditions at the other boundary to be satisfied Shooting Method http://en.wikipedia.org/wiki/Shooting_method C++: http://ganeshtiwaridotcomdotnp.blogspot.co.il/2009/12/c-c-code-shooting-method-for-solving.html Iteratively guess the missing values for one end & integrate, then inspect the discrepancy with the boundary values of the other end to adjust the estimate Given the starting boundary values u1 & u2 which contain the root u, solve u given the false position method (solving the differential equation as an initial value problem via 4th order RK), then use u to solve the differential equations. Finite Difference Method For linear & non-linear systems Higher order derivatives require more computational steps – some combinations for boundary conditions may not work though Improve the accuracy by increasing the number of mesh points Solving EigenValue Problems An eigenvalue can substitute a matrix when doing matrix multiplication à convert matrix multiplication into a polynomial EigenValue For a given set of equations in matrix form, determine what are the solution eigenvalue & eigenvectors Similar Matrices - have same eigenvalues. Use orthogonal similarity transforms to reduce a matrix to diagonal form from which eigenvalue(s) & eigenvectors can be computed iteratively Jacobi method http://en.wikipedia.org/wiki/Jacobi_method C++: http://people.sc.fsu.edu/~jburkardt/classes/acs2_2008/openmp/jacobi/jacobi.html Robust but Computationally intense – use for small matrices < 10x10 Power Iteration http://en.wikipedia.org/wiki/Power_iteration For any given real symmetric matrix, generate the largest single eigenvalue & its eigenvectors Simplest method – does not compute matrix decomposition à suitable for large, sparse matrices Inverse Iteration Variation of power iteration method – generates the smallest eigenvalue from the inverse matrix Rayleigh Method http://en.wikipedia.org/wiki/Rayleigh's_method_of_dimensional_analysis Variation of power iteration method Rayleigh Quotient Method Variation of inverse iteration method Matrix Tri-diagonalization Method Use householder algorithm to reduce an NxN symmetric matrix to a tridiagonal real symmetric matrix vua N-2 orthogonal transforms     Whats Next Outside of Numerical Methods there are lots of different types of algorithms that I’ve learned over the decades: Data Mining – (I covered this briefly in a previous post: http://geekswithblogs.net/JoshReuben/archive/2007/12/31/ssas-dm-algorithms.aspx ) Search & Sort Routing Problem Solving Logical Theorem Proving Planning Probabilistic Reasoning Machine Learning Solvers (eg MIP) Bioinformatics (Sequence Alignment, Protein Folding) Quant Finance (I read Wilmott’s books – interesting) Sooner or later, I’ll cover the above topics as well.

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