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# Managing Forms in Collect¶

For an overview on forms and form design, see Intro to Forms in ODK.

A blank form is a .xml file containing a form definition consistent with the XForm specification. Blank forms can be created using ODK Build or XLSForm.

In order to fill out forms with survey participants, you must first load blank forms into the Collect App.

If you have connected ODK Collect to a server or Google Drive:

1. Select Get blank forms on the app home screen to browse available forms and download them to your device.

• If you are using ODK Aggregate, you will see a list of available forms. Select the ones you would like download, and tap Get Selected.

Note

• If you are using Google Drive, the Get Blank Form screen will display the folders in your Google Drive account and any XML documents. Select and download the forms you want.

Warning

All XML documents in Google Drive will appear in Collect. XML documents will be listed even if they are not valid XForms.

And you can actually download any XML document, even if it isn't a real XForm.

But you can't Fill Out a non-form.

#### Loading forms with adb¶

You can load forms directly from a computer to your device via USB, using Android Debug Bridge.

\$ adb push path/to/form.xml /sdcard/odk/forms/form.xml

You can also download forms to your device via a web browser, and move them to the odk/forms/ directory, using the device's file manager (Settings -> Storage & USB -> Explore).

1. Go to the Settings menu () on your device and find Storage & USB

2. From the internal storage screen, select Explore to open the file manager.

If a form includes images or other media, those files have to be loaded to the device along with the form.

Media files should be placed in a folder labeled form-name-media.

• When using ODK Aggregate, the form upload prompt includes instructions to upload the -media folder. The files are downloaded automatically when fetching forms from Aggregate.
• When using Google Drive, the -media folder should be uploaded to the same location as the form. If you share forms with another user, you need to share the parent folder which contains a form and a folder with media files. Sharing both of them separately wouldn't be enough.
• If loading forms directly to your device, the -media folder needs to be placed in the sdcard/odk/forms directory, alongside the form itself.

## Editing Saved Forms¶

Completed (filled-in) form instances can be edited after they have been saved.

1. Select Edit Saved Form

2. Select a form by name

This will reopen the form instance, which you are then free to edit. Form instances are listed by name, which is one reason it can be helpful to name the form instance after filling it out.

Note

• Sent forms will not appear in the Edit Saved Forms list.
• Sent forms, will be available for viewing in View Sent Forms list, along with the details which cannot be edited.
• You may freely edit Saved and Finalized forms.

## Transferring Finalized Forms¶

To perform analysis on data collected with the Collect app, you will need to get the filled forms off of the devices. Generally, this is done by uploading them to an ODK server or Google Sheets. To do this, you will first need to configure a server.

In some cases, you may want to pull filled forms directly from a device. This can be simpler than setting up a server if you are only using a small number of devices or when there is no Internet access. It can also be helpful to recover from submission failures.

### Sending Finalized Forms to a Server¶

If you are connected to a server or Google Drive Account, use Send Finalized Forms to upload Finalized form instances.

Uploading a filled form from within the Collect app marks that form as sent. Sent forms are no longer editable, but they remain viewable until they are deleted.

Note

Blank values in the form are sent to google sheets as cells with a space and not as empty cells. When you are testing for empty cells, you might not get the correct results. To make sure you get the correct results, you could:

• Use the TRIM function in the google sheets to remove the leading and trailing spaces from the cells.
• Define empty cell in your tests to be a cell that is either empty or contains a single space.

Values from questions: text, select_multiple and barcode will be preceded by an apostrophe. This prevents Google Sheets from guessing at the data type and applying a format that may not be appropriate (e.g. making 1940 10 5 into a date when it actually is the value of a select multiple). Raw values may be used in any kind of computation and the apostrophes only are visible when editing a value. You may choose to manually apply a format for certain columns if desired.

Note

Using Google Drive as a server, filled forms are sent to the first sheet in a given spreadsheet, no matter what its name is. If you use one spreadsheet to keep a form definition and to collect filled forms make sure the sheet you expect to be filled is in the first place.

### Sending Previously-Sent Forms¶

If you can't find a submission that you expect on your server or need to re-send a submission for other reasons, you can change the view of the Send Finalized Forms screen to show both sent and unsent forms.

To show sent and unsent forms:
⋮ ‣ Change View ‣ Show Sent and Unsent Forms

### Pulling Forms into Briefcase¶

ODK Briefcase is a desktop application that can be used to pull filled forms to your local computer. You will first need to transfer the filled forms to your computer. This will not update the state of the form to Sent.

## Deleting Forms¶

You can delete Blank forms as well as filled forms in any state (Saved, Finalized, or Sent). Deleting Blank forms or filled forms in Saved or Finalized state removes every trace of that form definition or filled form. Deleting a Sent form deletes the form contents but metadata associated with it including the deletion date and the instance name are maintained for display in the View Sent Form list.

1. Select Delete Saved Form on the app home screen.

2. Select the Saved Forms or Blank Forms tab.

Note

Deleted Forms are listed in the View Sent Forms page, but cannot be viewed. They are indicated with the crossed-out eye icon.

### Deleting Forms with adb¶

You can also delete form instances directly with Android Debug Bridge. They are stored in sdcard/odk/instances, with a directory for each instance.


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# Finding the smallest positive missing number in array of integers contains negative and duplicates number

I found this solution but I don't understand it. Can anyone explain the idea behind it ?

A O(n) time and O(1) extra space solution:
The idea is similar to this post. We use array elements as index. To mark presence of an element x, we change the value at the index x to negative. But this approach doesn’t work if there are non-positive (-ve and 0) numbers. So we segregate positive from negative numbers as first step and then apply the approach.

Following is the two step algorithm.

1. Segregate positive numbers from others i.e., move all non-positive numbers to left side. In the following code, segregate() function does this part.

2. Now we can ignore non-positive elements and consider only the part of array which contains all positive elements. We traverse the array containing all positive numbers and to mark presence of an element x, we change the sign of value at index x to negative. We traverse the array again and print the first index which has positive value.

• You should copy relevant part because links tend to rot. Besides, it is far better to narrow down question, to exclude parts that you do understand.
– Evil
Jun 23 '18 at 23:57

After the first part, we have an array $A[1],\ldots,A[n]$ of positive numbers, and we want to find the smallest positive integer which is not present. We create a new Boolean array $B[1],\ldots,B[n]$ initialized to false. We go over all elements in $A$, and whenever we find an element $i \leq n$, we set $B[i]$ to true. We then find the smallest index $i$ such that $B[i]$ is false - this is the smallest positive integer which is not present. If all elements of $B$ are true, then $n+1$ is the smallest positive integer not present (why?).
As an optimization, we store the array $B$ by modulating the sign of elements in $A$: to represent $B[i]$ being false we use a positive sign for $A[i]$, and to represent $B[i]$ being true we use a negative sign for $A[i]$.

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# The Project

One fateful day while I was bored during a lecture, I decided to sign up for email messages from each Senate campaign during the 2018 election cycle.1 A lot of people study the impact of political advertisements on various outcomes, and I thought some interesting trends might emerge in the email blasts that campaigns send out.

# The Data

I signed up using a new email address, and only filled out the required fields to get on mailing lists. I used my real name, the zip code 00000, and a phone number of all zeros. The data for what information I gave to each campaign is on Github. I felt kind of bad signing up for volunteer lists with false information, which were the only email option for some campaigns. The data turned out to be pretty interesting though, so I think next cycle for the presidential election I will try to get on a more comprehensive set of emails by signing up for the House races too and providing zip codes and phone numbers in the relevant district.2

I found the candidates and campaign websites from RealClearPolitics’s Senate map. I started signing up for emails on 6/6/2018, but didn’t sign up for every senate race until 10/9/2018. In the last month before the election (October 6 through November 6 inclusive) I received 2,650 emails from 50 unique campaigns. Some campaigns did not have an option to signup for an email list on their website and some may have filtered out my email address because the zip code and/or phone number were clearly not accurate. Much of the analysis below compares emails from Democrats and Republicans, so I further filter the emails down to races where I received at least one email from both party’s candidates. The final number is 2,397 emails and 44 campaigns. Most analysis uses this sample, and I will specify when that is not the case.

# Who is sending emails and when?

I received emails from both parties in the following states: AZ, FL, IN, MA, MD, MI, MN, MO, MS, ND, NE, NJ, NV, NY, OH, PA, TN, TX, USA, UT, VA, VT, WA, WY. A notable omission is West Virginia, where I only received emails from Joe Manchin. Below I show the number of emails I received each day from each party.

What immediately jumped out to me was that the democratic candidates send significantly more emails (and for some reason campaigns send the fewest emails on Wednesdays). Next, I tally the number of emails I received from each candidate, and show the races where I received at least 100 emails in total.

State Party Campaign Total Emails
NV D Jacky Rosen 352
NV R Dean Heller 147
FL D Bill Nelson 237
FL R Rick Scott 7
MO R Josh Hawley 30
ND D Heidi Heitkamp 176
ND R Kevin Cramer 29
AZ D Kyrsten Sinema 96
AZ R Martha McSally 69
IN D Joe Donnelly 106
IN R Mike Braun 50
USA D DNC 59
USA R RNC 73
MN D Amy Klobuchar 19
MN D Tina Smith 62
MN R Karin Housely 38

Jacky Rosen, Bill Nelson, Claire McCaskill, Heidi Heitkamp, and Joe Donnely (all democrats) sent over 100 emails during the relevant time-frame. Dean Heller was the only republican who sent me over 100 emails. In general, Democrats sent more emails than their Republican opponents. However, I certainly would not be surprised if my sample was biased. People who signed up with in-state addresses probably received more emails than I did. I don’t know how sophisticated campaigns are with targeting their emails, but I would be shocked if they did not focus efforts like Get Out the Vote campaigns on people with addresses in their district. I do wonder, though, if there is a connection between the fundraising strategies and email strategies of each party. If Democrats rely more on smaller donations from many individuals, they might need to send more emails to everyone who expresses interest in their campaign. Republicans who either self-fund or court fewer donations from wealthier individuals might simply not have much to gain from emailing out-of-state individuals.

# Email Content

Next, I will analyze the content of the emails. The word clouds above show each word sized proportionally to the amount of times it was used in the email. Both party’s emails frequently used words like senate, vote, and fight, but some differences are already apparent. Here I do unfortunately need to filter the dataset down more. Many of the emails that were sent came in a format that did not download or parse into human-readable text well. I tried to extract the text from all emails, but some (particularly ones with odd formatting or with pictures of text) I could not parse properly. The number of emails analyzed in this section is only 2,043.

Word clouds are a useful visualization, but I will use a statistical technique, the relative risk ratio, to characterize the difference in word-usage between Republican and Democratic emails.

The chart above merits some further explanation. For each word, I calculated the proportion of Democratic emails that used the word and the proportion of Republican emails that used the word. Then, I took the ratio of those two quantities, often referred to as the relative risk ratio. To put everything on a comparable scale, if Republican emails used the word more frequently, I multiplied the proportion by -1 and took the inverse. So if the ratio is equal to R and positive, then Democratic emails used the word R times more frequently. If the ratio is equal to R and negative, then Republican emails used the word R times more frequently. I show the 15 words with the largest ratio for each party.3

Something that I noticed quickly is that election-specific terms from races where the Democrat sent many more emails than the Republican have high risk ratios: “Las Vegas”, “Scott” (Bill Nelson referring to his opponent Rick Scott), and “FL” are all in the top 15 for democrats. “ActBlue” is an organization that helps Democrats fundraise. “politicalemaild” is a truncated version of the email address I provided to campaigns.

I was not surprised that the words “borders” and “conservative” are in the top for Republicans, but I was quite surprised by “web” and “website” showing up in the top 15. “Liberal” is used frequently as a pejorative by Republicans, but apparently Democrats do not use the word anywhere near as frequently when messaging their own supporters.

Of course, words that are used by one party and never used by the other will have a risk ratio of plus or minus infinity. The problem with looking at all of those words is that they often are spelling or parsing errors that happen once or twice for one party and never for the other. To account for that, I show only the 10 most frequently used words that are never used by the opposing party.

Democratic
Republican
Word Emails Using Word Proportion Using Word Emails Using Word Proportion Using Word
youd 625 0.287 0 0.000
mitch 307 0.141 0 0.000
mcconnell 299 0.138 0 0.000
environment 262 0.121 0 0.000
fivethirtyeight 224 0.103 0 0.000
silvers 217 0.100 0 0.000
nelson 212 0.098 0 0.000
melbourne 210 0.097 0 0.000
whitmire 210 0.097 0 0.000
floridas 198 0.091 0 0.000
inherit 0 0.000 74 0.079
nrcc 0 0.000 66 0.071
chuck 0 0.000 62 0.067
complaints 0 0.000 60 0.064
devoted 0 0.000 60 0.064
conservatives 0 0.000 57 0.061
suggestions 0 0.000 57 0.061
schumer 0 0.000 54 0.058
charitable 0 0.000 53 0.057

Again, “Florida’s” and “Nelson” show up as top democratic words never used by republicans because I received many emails from Bill Nelson’s campaign and almost none from Rick Scott’s. I was surprised that no Republican emails used the word “you’d.” One potential explanation is that Democrats use more personal apeals in their emails, which is further evidenced by the fact that Democrats used my email address more than republicans. Democrats referenced “Silver’s” “FiveThirtyEight” website in over 200 emails, while Republicans never mentioned either him or the website.

Besides the words that are used most differently, I was also curious how some specific words showed up in emails. Below I tabulate the usage of a few select words. Specifically, I was interested in which politicians get mentioned by each party, some campaign issues, and party signifiers.

Democratic
Republican
Word Emails Using Word Proportion Using Word Emails Using Word Proportion Using Word Signed Risk Ratio
trump 365 0.168 183 0.196 -1.170
obama 27 0.012 27 0.029 -2.333
pelosi 0 0.000 38 0.041 NA
mcconnell 299 0.138 0 0.000 NA
caravan 0 0.000 5 0.005 NA
kavanaugh 54 0.025 60 0.064 -2.592
radical 4 0.002 68 0.073 -39.655
conservative 3 0.001 136 0.146 -105.745
liberal 1 0.000 112 0.120 -261.253
progressive 25 0.011 14 0.015 -1.306

While Trump and Obama were mentioned in about 30% of emails by both Democrats and Republicans, congressional leaders were almost exclusively mentioned by the opposing party. Democrats mentioned Mitch McConnell in about 16.5% of their emails, while he was never mentioned by Republicans. Republicans mentioned Nancy Pelosi in about 9% of their emails, while she was mentioned in only 0.5% of democratic emails. This seems to lend truth to the impression I got from news coverage that Republicans ran against Pelosi and Democrats ran against McConnell.

# Email Sentiment

How did the sentiment of emails differ by party? Here I will rely on some of the built-in dictionaries in the tidytext package in R. Sentiment analysis generally refers to matching each word with some sentiment, either on a positive or negative scale or to some (short) list of topics. A review of the dictionaries that I will be using is here.

The simplest way to find the sentiment of a document is to use a dictionary that maps words to whether they express a positive or negative sentiment, give each positive word a weight of +1 and each negative word a weight of -1, then find the average for each document. The chart below does just that. Note that the bounds are at plus or minus 1 because I only take the average over words with a sentiment attached to them.

I plotted a density histogram because I received many more democratic than republican emails. The total area of the bars is scaled to sum to one for each party. The results look pretty interesting. For both parties, the distribution of sentiment is concentrated at 0.5, which corresponds to emails that use 75% positive words and 25% negative words. Democratic emails are more concentrated at this value, and the sentiment of Republican emails is more spread out with additional concentrations at plus or minus 1 (all positive or all negative words).

Next I try a slightly more complicated sentiment analysis. I use a dictionary that maps words to (potentially multiple) of the following sentiments: trust, fear, negative, sadness, anger, surprise, positive, disgust, joy, and anticipation. Then, I calculate the proportion of words with the given sentiment among words that had any sentiment for each email and plot a histogram of the results. There are a lot of charts below, but I think they all tell the same story. The overall sentiment of the words used by each party are extremely similar. If all you knew about a campaign email was the sentiment score reported below, it would be extremely hard to correctly guess the party of the candidate.

# Classification

Overall, it looks like certain words can give away the political alignment of the email, but the sentiment cannot. However, that conclusion just comes from examining the histograms. A more sophisticated method to measure how well sentiment can identify political text is to fit a prediction model, then test how well it works on a held-out set. If the information about sentiment improves predictive power, then there is evidence that the parties speak to their supporters differently. A recent working paper by Gentzcow, Shapiro, and Taddy measure political polarization by how accurately speeches on the floor of Congress can identify the partisan alignment of the speaker.4 The classification accuracy results here can be interpreted similarly. I will use the two most straightforward techniques that I know of for this task: logistic regression and leave-one-out cross validation (LOOCV).

Logistic regression is a standard method to fit a model to a binary outcome. What I want to do is estimate the probability that an email is from a Democrat as a function of the sentiment scores. A linear relationship will not work because probabilities need to be between zero and one. Logistic regression assumes that the log of the odds of an event (the probability of an email being Democratic divided by the probability of the email being Republican) is a linear function of the explanatory variables. Because of this change in perspective, interpreting the coefficients of a logistic regression is a little bit harder.5 It is still the case, however, that positive coefficients mean an increase in the explanatory variable is associated with an increase in the probability that the dependent variable equals one, so the interpretation of the sign of the coefficient remains the same.

Leave-one-out cross-validation is an evaluation method where a model is fit on all data points except one, then the model is asked to predict the value at the held-out data point, and finally the prediction and observed value are compared. In my application, I code the event that an email comes from a democratic campaign as a one and the event that an email comes from a republican campaign as a zero. If the model predicts that an email is from a Democratic campaign with probability greater than 0.5, I classify it as a Democratic email and as a Republican email otherwise. The LOOCV error rate is the number of miss-classified emails divided by the number of emails.

The explanatory variables I use are all the variables charted above (the average of positive and negative sentiment, called “Email Sentiment”, and each of the categorical sentiments) and the number of sentiment words in each email. To see if results were being driven by a single sentiment, I fit a univariate model with each term individually and a full model with all of the variables included. The results of the univaraite regressions are shown below.

Model Coefficient Intercept LOOCV Error Rate
Email Sentiment 0.084**
(0.03)
0.663***
(0.016)
30.4%
Trust -0.735***
(0.086)
1.018***
(0.039)
28.4%
Fear -0.454***
(0.126)
0.746***
(0.017)
30.3%
Negative 0.391***
(0.097)
0.596***
(0.027)
30.4%
(0.142)
0.569***
(0.021)
30.4%
Anger 0.023
(0.128)
0.693***
(0.019)
30.4%
Surprise 0.228
(0.145)
0.67***
(0.019)
30.4%
Positive -1.26***
(0.073)
1.263***
(0.034)
27.7%
Disgust -0.611**
(0.187)
0.73***
(0.015)
30.2%
Joy -1.692***
(0.109)
0.926***
(0.018)
27.1%
Anticipation -0.883***
(0.107)
0.871***
(0.024)
30.1%
Number of Sentiment Words 0
(0.001)
0.692***
(0.024)
30.4%
Note:
* p<0.05; ** p<0.01; *** p<0.001

While the error rates appear low, they actually are not much better than random chance. Of the 1,880 emails with sentiment data, 69.6% of them are from democratic campaigns. So if you just guessed that every email was Democratic, you would be wrong 30.4% of the time. An equivalent interpretation is that if you randomly classified 69.6% of the emails as Democratic and the rest as Republican, you would expect to have an error rate of 30.4%. Even for some of the sentiments with statistically significant coefficients, their prediction accuracy is no better than random chance. The full model, however, does have some predictive power. The results are shown below.

Variable Coefficient
Email Sentiment 0.99***
(0.2)
Trust -6.511***
(0.704)
Fear -8.376***
(1.04)
Negative -2.256*
(0.945)
(1.148)
Anger 3.013**
(1.117)
Surprise 1.201
(1.106)
Positive -7.824***
(0.68)
Disgust -7.099***
(1.263)
Joy -3.985***
(1.089)
Anticipation -1.123
(0.773)
Number of Sentiment Words -0.002
(0.004)
Intercept 8.438***
(0.646)
Note:
* p<0.05; ** p<0.01; *** p<0.001. LOOCV Error Rate: 21.6%

The error rate for the full model is 21.6%, an improvement over random chance by a factor of about 2/3. By using all of the sentiments together, emails can be classified better than by simply guessing that every email is democratic.

Emails with higher positive average sentiment, or more sadness and anger words are more likely to be democratic emails. Emails with more trust, fear, negative, positive, disgust, or joy words are more likely to be from republican candidates. Democrats might tend to describe the previous Congress with words that convey anger or sadness, while Republicans would use positive, joy, or trust words. The fact that Republican emails also use more disgust and fear words is evidence against that explanation though, or at least is evidence that the truth is more complicated.

# Further Work

The classification and cross-validation methods that I used are certainly simpler versions of where the state of the art is. I would not be surprised if more information could be extracted from the text or the sentiments with more sophisticated tools. Something that I haven’t explored, but could be quite interesting, is using the text itself rather than the sentiment to classify emails. The difficulty is that text data is very high dimensional: there were far more unique words used than emails sent. Regression with more variables than observations tends to overfit the estimation data and produce poor out-of-sample predictions. There are also some words that are very predictive, but not predictive in an “interesting” way. Emails always mention the candidate’s name, frequently include a link to the campaign’s donation page or list their mailing address. Clearly, you can immediately know the party of the sender from those features. But those predictions are also not very interesting.

With unlimited time and resources, what I would like to do is extract from the emails some measures of the general language each party uses and then use those features to classify the email. If those features classify accurately, then there is evidence for divergence in how the parties speak to their supporters. That result has implications for trying to convince people to change their political beliefs and how to talk to people from across the isle. Presenting convincing arguments to partisans of each party probably requires speaking their language in some sense, and campaign emails are potentially a useful data source for learning that language.

1. This project may have been entierly inspired by the fact that I really liked the title.

2. The code and data are on Github here: https://github.com/g-tierney/political_emails.

3. I also removed all non-alphanumeric characters from each word.

5. Technically, a one unit increase in the explanatory variable increases the odds that an event occurs by $$e^\beta$$ where $$\beta$$ is the estimated logit coefficient.


text:
• ### Announcements

#### Archived

This topic is now archived and is closed to further replies.

# Re-using transformed vertices

## Recommended Posts

I have the situation with my terrain engine where I want to use the same vertex data with multiple calls to DrawIndexedPrimitive, with different index data e.g pseudo:
do
{
do
{
DrawIndexedPrimitive()
} some no. of times
}for each chunk of vertex data

Now since after the draw call the vertex data is transformed I have to re-copy it (typically I have ~2000 vertices with blocks of a few 100 indexed triangles at a time) which is very inefficient especially since I have to keep locking to copy it. I want to copy the vertices across once then somehow keep them untransformed afterwards. Is this possible? I guess an alternative would be to use them as post-transformed with rhw after but this would involve re-formating the vertices and switching FVF lots which is ugly!
Read about my game, project #1 NEW (18th December)2 new screenshots, one from the engine and one from the level editor
John 3:16 [edited by - d000hg on March 7, 2003 6:58:21 AM]

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The T&L in PC graphics hardware is write/push only I''m afraid - AFAIK there is often never even a complete list of transformed vertices available to the hardware - i.e. it does them after primitive assembly.

About all you can do is use any spare CPU cycles you have and do something like ProcessVertices() to transform once (PV is always done in software) and then copy the result into your buffer multiple times as necessary.

Since the vertices aren''t changing for your multiple passes, there''s no reason there should be multiple copies of the vertex data though!

--
Simon O''Connor
Creative Asylum Ltd
www.creative-asylum.com

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I should explain my algo better:
As the triangle count isn''t known, I store vertices used in rendering in blocks of ~2000 using stl::vector. Because I use different textures for different ground types (sand,grass etc) I have different triangles using these vertices for multiple textures, so I also store blocks of indexing data for each texture for each block of vertices. However if I made the blocks for indexing large, this means that just one extra triangle uses a whole new block. So I make indexing blocks small to reduce wastage. This means that a block of indices may use many index blocks for each texture. I render by texture so this means for one vertex block I want to render many index blocks without reloading vertex data. I CAN just copy all the index data across from multiple blocks into a larger IB, but then I''m rendering like 4K polys in one call.

I don''t want the vertices to be transformed after calling DrawPrimitive - is there not some way of forcing the data in the VB to be unchanged after the call?

Failing that, would using processvertices once and using transformed vrtices be quicker than having to potentially recalculate each vertex 4-6 times. In SW vertex processing I''m guessing yes, but what about Vs HW?

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quote:
Original post by d000hg
I don''t want the vertices to be transformed after calling DrawPrimitive - is there not some way of forcing the data in the VB to be unchanged after the call?

Every time you pass untransformed vertices to Draw*Primitive, then they''ll be transformed (& lit) before rendering. That''s just the way T&L (& vshader) 3D hardware works.

The contents of the source VB you pass to Draw*Primitive aren''t ever changed by the Draw*Primitive call - that''s the point it''s one way, the vertices in the source VB are input only, the chip or even the SW T&L pipe doesn''t transform the vertices and overwrite the source buffer.

quote:
Failing that, would using processvertices once and using transformed vrtices be quicker than having to potentially recalculate each vertex 4-6 times. In SW vertex processing I''m guessing yes, but what about Vs HW?

That''s one of those cases where ideally your code should be performing runtime profiling of itself during the first few frames to decide which is the best strategy. Failing that you''ll have to test with your specific app. Complexity of shader, how many lights, whether things like NORMALIZENORMALS are enabled, CPU load, efficiency of your dynamic locking etc all affect whether a single PV() followed by multiple Draw*Primitive()s from the transformed result is faster than multiple Draw*Primitive() calls with untransformed data.

What I will say though is most of the time the T&L on modern chips is very starved of data by most apps, there''s a lot of underused power there - so the multiple DrawPrimitive()s from the same buffer won''t be anywhere near as bad as you''re assuming.

--
Simon O''Connor
Creative Asylum Ltd
www.creative-asylum.com

##### Share on other sites
quote:
The contents of the source VB you pass to Draw*Primitive aren''t ever changed by the Draw*Primitive call - that''s the point it''s one way, the vertices in the source VB are input only, the chip or even the SW T&L pipe doesn''t transform the vertices and overwrite the source buffer.
Really? I assumed that''s why it didn''t work properly?
So I can say load 10 vertices, then call DrawIndexedPrim for indices 1,2,3. Then in a second call to drawindexedprimitive, without touching the VB, I can say draw with indices 3,4,5 without vertex #3 being changed by the previous call?
quote:
What I will say though is most of the time the T&L on modern chips is very starved of data by most apps, there''s a lot of underused power there - so the multiple DrawPrimitive()s from the same buffer won''t be anywhere near as bad as you''re assuming.
I''m not actually bothered about the data being transformed often, I jsut don''t want to reload the VB many times as that IS slow. I''ll check out why it screwed up I guess. Though I am aiming for this to run on SW T&L cards...

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Soochow Journal of Mathematics

 Short Title: Soochow J. Math. Publisher: Soochow University, Department of Mathematics, Taipei, Taiwan ISSN: 0250-3255 Online: http://sjm.math.scu.edu.tw/mp/scu/02PastIssue.asphttp://mathlab.math.scu.edu.tw/mp/scu/02PastIssue.asp Predecessor: Soochow Journal of Mathematics and Natural Sciences Comments: No longer indexed; Publication suspended
 Documents Indexed: 984 Publications (1978–2007)
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 105 Differential geometry (53-XX) 93 General topology (54-XX) 88 Functional analysis (46-XX) 87 Functions of a complex variable (30-XX) 82 Real functions (26-XX) 66 Probability theory and stochastic processes (60-XX) 61 Operator theory (47-XX) 54 Group theory and generalizations (20-XX) 52 Statistics (62-XX) 45 Ordinary differential equations (34-XX) 43 Approximations and expansions (41-XX) 37 Information and communication theory, circuits (94-XX) 36 Computer science (68-XX) 35 Order, lattices, ordered algebraic structures (06-XX) 35 Sequences, series, summability (40-XX) 34 Associative rings and algebras (16-XX) 30 Numerical analysis (65-XX) 28 Special functions (33-XX) 27 Operations research, mathematical programming (90-XX) 24 Partial differential equations (35-XX) 20 Mathematical logic and foundations (03-XX) 20 Combinatorics (05-XX) 18 Harmonic analysis on Euclidean spaces (42-XX) 16 Number theory (11-XX) 16 Difference and functional equations (39-XX) 16 Calculus of variations and optimal control; optimization (49-XX) 15 Measure and integration (28-XX) 14 Biology and other natural sciences (92-XX) 12 Linear and multilinear algebra; matrix theory (15-XX) 12 Geometry (51-XX) 10 General algebraic systems (08-XX) 10 Global analysis, analysis on manifolds (58-XX) 8 Several complex variables and analytic spaces (32-XX) 8 Integral equations (45-XX) 6 Abstract harmonic analysis (43-XX) 6 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Nonassociative rings and algebras (17-XX) 5 Topological groups, Lie groups (22-XX) 5 Potential theory (31-XX) 5 Dynamical systems and ergodic theory (37-XX) 5 Convex and discrete geometry (52-XX) 5 Manifolds and cell complexes (57-XX) 4 General and overarching topics; collections (00-XX) 4 Systems theory; control (93-XX) 3 Category theory; homological algebra (18-XX) 3 Integral transforms, operational calculus (44-XX) 3 Algebraic topology (55-XX) 3 Mechanics of deformable solids (74-XX) 3 Fluid mechanics (76-XX) 2 History and biography (01-XX) 2 Commutative algebra (13-XX) 2 Algebraic geometry (14-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Field theory and polynomials (12-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Quantum theory (81-XX) 1 Relativity and gravitational theory (83-XX) 1 Geophysics (86-XX)

Citations contained in zbMATH Open

378 Publications have been cited 1,808 times in 1,614 Documents Cited by Year
On some generalized difference sequence spaces. Zbl 0841.46006
Et, Mikail; Çolak, Rifat
1995
Some open problems and conjectures on submanifolds of finite type. Zbl 0749.53037
Chen, Bang-Yen
1991
Some inequalities of Hadamard type. Zbl 0834.26009
Dragomir, Sever Silvestru; Pečarić, Josip E.; Persson, L. E.
1995
A report on submanifolds of finite type. Zbl 0867.53001
Chen, Bang-Yen
1996
Some new Cesàro sequence spaces of non-absolute type which include the spaces $$c_0$$ and $$c$$. Zbl 1085.46500
Şengönül, Mehmet; Başar, Feyzi
2005
A fixed point theorem in a generalized metric space. Zbl 1137.54024
Das, Pratulananda; Dey, Lakshmi Kanta
2007
On a new type of generalized difference Cesàro sequence spaces. Zbl 1093.46507
Tripathy, Binod Chandra; Esi, Ayhan; Tripathy, Balakrushna
2005
On finite dimensional 2-normed spaces. Zbl 1003.46007
2001
On $$I$$-convergent double sequences. Zbl 1083.40002
Tripathy, Balakrushna; Tripathy, Binod Chandra
2005
A new Hilbert’s type integral inequality. Zbl 1137.26310
Yang, Bicheng
2007
$$R$$-weak commutativity and common fixed points. Zbl 0918.54038
Pant, R. P.
1999
The minimal translation surfaces in Euclidean space. Zbl 0799.53009
Verstraelen, L.; Walrave, J.; Yaprak, S.
1994
Geometry of warped products as Riemannian submanifolds and related problems. Zbl 1012.53051
Chen, Bang-Yen
2002
On the Nash equilibrium. Zbl 0721.90017
Chang, Shiow-Yu
1990
An Ostrowski type inequality for double integrals and applications for cubature formulae. Zbl 0987.26015
Barnett, N. S.; Dragomir, S. S.
2001
Refinement of an inequality of Grüss type for Riemann-Stieltjes integral. Zbl 1061.26019
Liu, Zheng
2004
Remarks on multivalued nonexpansive mappings. Zbl 0826.47037
López Acedo, Genaro; Xu, Hong-Kun
1995
New sufficient conditions for starlike and univalent functions. Zbl 0843.30024
Ponnusamy, S.; Rajasekaran, S.
1995
On curvature properties of quasi-Einstein hypersurfaces in semi-Euclidean spaces. Zbl 1008.53020
Deszcz, Ryszard; Hotloś, Marian; Ṣentürk, Zerrin
2001
On a class of sequences related to the $$\ell^p$$ space defined by Orlicz functions. Zbl 1046.46007
Tripathy, Binod Chandra; Mahanta, Sabita
2003
Generalized difference sequence spaces defined by a modulus function in a locally convex space. Zbl 1085.46501
Altin, Yavuz; Et, Mikail
2005
On some subclass of semisymmetric manifolds. Zbl 1007.53018
Kowalczyk, Dorota
2001
Qualitative behavior of higher order difference equation. Zbl 1144.39012
Elabbasy, E. M.; El-Metwally, H.; Elsayed, E. M.
2007
On simultaneous approximation by Szász-beta operators. Zbl 0846.41022
Gupta, Vijay; Srivastava, G. S.; Sahai, A.
1995
On Legrende curves in 3-dimensional normal almost contact metric manifolds. Zbl 1144.53041
Wełyczko, Joanna
2007
Submanifolds with planar normal sections. Zbl 0485.53004
Chen, Bang-Yen
1981
Generalized difference paranormed statistically convergent sequences defined by Orlicz function in a locally convex space. Zbl 1066.40005
Tripathy, Binod Chandra
2004
Totally umbilical submanifolds. Zbl 0442.53051
Chen, Bang-Yen
1980
A generalization of the HGA inequalities. Zbl 0462.26009
Wang, Chung-Lie
1980
Fixed point theorems for multi-valued increasing operators in partial ordered spaces. Zbl 1084.47046
Feng, Yuqiang; Liu, Sanyang
2004
Non-primitive words in the language $$p^ +q^ +$$. Zbl 0813.68127
Shyr, H. J.; Yu, S. S.
1994
On statistical convergence of generalized difference sequences. Zbl 1058.40001
Işik, Mahmut
2004
On the upper bound estimate of Cochrane sums. Zbl 1016.11038
Zhang, Wenpeng; Yi, Yuan
2002
Fixed point theorem for compatible mappings satisfying a contractive condition of integral type. Zbl 1135.54026
Kumar, Sanjay; Chugh, Renu; Kumar, Ramesh
2007
Noncompatible mappings and common fixed points. Zbl 0945.54033
Pant, R. P.
2000
Ruled surfaces with finite type Gauss map in Minkowski spaces. Zbl 0976.53020
Kim, Young Ho; Yoon, Dae Won
2000
On Legendre curves in Riemannian and Lorentzian Sasaki spaces. Zbl 1013.53016
Belkhelfa, M.; Hirică, I. E.; Rosca, R.; Verstraelen, L.
2002
Some properties of overlapping order and related languages. Zbl 0691.68077
Hsu, S. C.; Ito, M.; Shyr, H. J.
1989
Symmetry properties of Sasakian space forms. Zbl 1087.53021
Belkhelfa, Mohamed; Deszcz, Ryszard; Verstraelen, Leopold
2005
A generalization of KKM principle and its applications. Zbl 0747.47033
Chang, S. Y.
1989
On Simpson’s quadrature formula for Lipschitzian mappings and applications. Zbl 0938.26014
Dragomir, Sever Silvestru
1999
Constant-ratio hypersurfaces. Zbl 1007.53006
Chen, Bang-Yen
2001
On a typical topology induced by a grill. Zbl 1152.54310
Roy, B.; Mukherjee, M. N.
2007
Mapping properties of analytic function defined by hypergeometric function. II. Zbl 0964.30007
Shukla, Nalini; Shukla, Pratibha
1999
Classification of space-times satisfying some pseudo-symmetry type conditions. Zbl 1082.53019
Deszcz, R.; Haesen, S.; Verstraelen, L.
2004
Strongly almost convergent sequences defined by a modulus and uniformly statistical convergence. Zbl 0808.40007
Pehlivan, Serpil
1994
McKean-Vlasov equations with discontinuous coefficients. Zbl 0817.60071
Chiang, Tzuu-Shuh
1994
Existence and controllability results for multivalued semilinear differential equations with nonlocal conditions. Zbl 1033.34068
Benchohra, M.; Ntouyas, S. K.
2003
Convolution calculus and applications to stochastic differential equations. Zbl 1029.60055
Ben Chrouda, Mohamed; El Oued, Mohamed; Ouerdiane, Habib
2002
c-prime fuzzy ideals of nearrings. Zbl 1140.16020
Kedukodi, Babushri Srinivas; Bhavanari, Satyanarayana; Kuncham, Syam Prasad
2007
Semi-regular spaces. Zbl 0527.54017
Dorsett, Charles
1982
Partition graphs. Zbl 0655.05055
Detemple, Duane; Harary, Frank; Robertson, Jack
1987
Unitary operators on the space of $$L^ 2$$-functions over abstract Wiener spaces. Zbl 0661.46042
Lee, Yuh-Jia
1987
Exterior concurrent vector fields on Riemannian manifolds. I: Some general results. Zbl 0692.53004
Petrović, M.; Rosca, R.; Verstraelen, L.
1989
Perturbation of the Drazin inverse. Zbl 0997.15003
Castro González, N.; Koliha, J. J.; Straškraba, I.
2001
Generalized Gross heat equation with noises. Zbl 1113.60066
Barhoumi, Abdessatar; Kuo, Hui-Hsiung; Ouerdiane, Habib
2006
A characterization of prime and semiprime ideals of groupoids in terms of fuzzy subsets. Zbl 0999.20057
Kehayopulu, Niovi; Xie, Xiang-Yun; Tsingelis, Michael
2001
Statistically convergent double sequence spaces defined by Orlicz functions. Zbl 1122.40001
Tripathy, Binod Chandra; Sarma, Bipul
2006
A new Ostrowski type inequality for double integrals. Zbl 1119.26027
Pachpatte, B. G.
2006
Four-dimensional matrix characterization of absolute summability. Zbl 1061.40004
Patterson, Richard F.
2004
Minimal generating systems for fuzzy ideals. Zbl 0835.13008
Jaballah, Ali; Mordeson, John N.
1995
Nuclei on $$z$$-frames. Zbl 0863.54017
Zhao, Dongsheng
1996
Vector valued paranormed bounded and null sequence spaces associated with multiplier sequences. Zbl 1043.46013
Tripathy, Binod Chandra; Sen, Mausumi
2003
On certain sufficient condition for starlike functions. Zbl 1043.30007
Liu, Mingsheng
2003
On left derivations of BCI-algebras. Zbl 1137.06302
Abujabal, Hamza A. S.; Al-Shehri, Nora O.
2007
Functions whose composition with Baire class one functions are Baire class one. Zbl 1137.26300
Zhao, Dongsheng
2007
Some results on common fixed point in fuzzy metric spaces. Zbl 1137.54308
Som, Tanmoy
2007
Local and global uniqueness theorems on fractional integro-differential equations via Bihari’s and Gronwall’s inequalities. Zbl 1137.26301
Momani, Shaher; Jameel, Ahlam; Al-Azawi, Sora
2007
Some properties of dense languages. Zbl 0586.68062
Shyr, H. J.; Tseng, Din-Chang
1984
Iterative solutions of coupled matrix convolution equations. Zbl 1137.65070
2007
On weakly quasi-conformally symmetric manifolds. Zbl 1091.53017
Shaikh, A. A.; Baishya, Kanak Kanti
2005
A new common fixed point principle. Zbl 0991.54051
Pant, R. P.
2001
On 3-dimensional LP-Sasakian manifolds. Zbl 0980.53057
Shaikh, A. A.; De, U. C.
2000
On Bihari like integral and discrete inequalities. Zbl 0745.26013
Pachpatte, B. G.
1991
The classification of homogeneous continua. Zbl 0780.54033
Lewis, Wayne
1992
Iterative construction of fixed points of multi-valued operators of the accretive type. II. Zbl 0911.47058
Osilike, M. O.
1998
Short-time asymptotics of the heat kernel of the Laplacian of a general doubly connected domain in $$\mathbb{R}^2$$ with Robin boundary conditions. Zbl 0920.35031
Zayed, E. M. E.
1999
Some properties of two integral operators. Zbl 0923.30010
Li, Jian Lin
1999
The classification of 3-dimensional locally homogeneous Blaschke hypersurfaces with nondiagonalizable affine shape operators. Zbl 1118.53009
Ooguri, Masahiro
2006
Approximations in hypernear-rings. Zbl 1111.16043
Zhan, Jianming; Ma, Xueling
2006
Separation axioms in ordered spaces. Zbl 1064.54048
Das, Phullendu
2004
The geometry of eye and brain. Zbl 1131.92303
Verstraelen, Leopold
2004
Homogeneous hypersurfaces with non diagonalisable, rank one shape operators. Zbl 0827.53011
Magid, Martin; Vrancken, Luc
1995
Algebraic surfaces associated to arrangements of conics. Zbl 0862.14024
Tang, Lizhong
1995
On $$\Gamma$$-semigroup with the right and left unities. Zbl 0802.20053
Dutta, T. K.; Adhikari, N. C.
1993
On nearly conformally symmetric warped product spacetimes. Zbl 0796.53019
Gȩbarowski, Andrzej
1994
Matrix transformations between certain sequence spaces of $$X_p$$ and $$\ell_p$$. Zbl 0960.40002
Başar, Feyzi
2000
An M/G/1 type queue with time-homogeneous breakdowns and deterministic repair times. Zbl 1022.60086
2003
Common fixed points for fuzzy mappings using generalised altering distances. Zbl 1068.54043
Choudhury, Binayak S.; Dutta, P. N.
2005
Another proof on a theorem of Lyndon and Schützenberger in a free monoid. Zbl 0412.20053
Chu, Danny D.; Town, Hsiang-Sheng
1978
Iterative construction of fixed points of multi-valued operators of the accretive type. Zbl 0868.47033
Osilike, M. O.
1996
Isomorphisms between leaf preserving diffeomorphism groups. Zbl 0869.58004
Rybicki, Tomasz
1996
Mihai, Vochita; Sengupta, Ambar N.
2007
Languages defined by some partial orders. Zbl 0537.68078
Day, Ping Hwei; Shyr, H. J.
1983
On a type of Sasakian manifold. Zbl 0707.53039
Chaki, M. C.; Tarafdar, Manjusha
1990
Global existence for semilinear stochastic delay evolution equations with nonlocal conditions. Zbl 0997.34078
Balasubramaniam, P.; Ntouyas, S. K.
2001
On certain classes of multivalent functions with negative coefficients. Zbl 0512.30010
Shukla, S. L.; Dashrath
1982
Certain bitopological concepts in a bispace. Zbl 0985.54028
Lahiri, B. K.; Das, Pratulananda
2001
Some properties of a quarter symmetric metric connection on a Riemannian manifold. Zbl 0747.53021
Mukhopadhyay, S.; Roy, A. K.; Barua, B.
1991
Oscillation and global attractivity in the discrete Lasota-Wazewska model. Zbl 0930.39012
Chen, Ming-Po; Yu, J. S.
1999
A fixed point theorem in a generalized metric space. Zbl 1137.54024
Das, Pratulananda; Dey, Lakshmi Kanta
2007
A new Hilbert’s type integral inequality. Zbl 1137.26310
Yang, Bicheng
2007
Qualitative behavior of higher order difference equation. Zbl 1144.39012
Elabbasy, E. M.; El-Metwally, H.; Elsayed, E. M.
2007
On Legrende curves in 3-dimensional normal almost contact metric manifolds. Zbl 1144.53041
Wełyczko, Joanna
2007
Fixed point theorem for compatible mappings satisfying a contractive condition of integral type. Zbl 1135.54026
Kumar, Sanjay; Chugh, Renu; Kumar, Ramesh
2007
On a typical topology induced by a grill. Zbl 1152.54310
Roy, B.; Mukherjee, M. N.
2007
c-prime fuzzy ideals of nearrings. Zbl 1140.16020
Kedukodi, Babushri Srinivas; Bhavanari, Satyanarayana; Kuncham, Syam Prasad
2007
On left derivations of BCI-algebras. Zbl 1137.06302
Abujabal, Hamza A. S.; Al-Shehri, Nora O.
2007
Functions whose composition with Baire class one functions are Baire class one. Zbl 1137.26300
Zhao, Dongsheng
2007
Some results on common fixed point in fuzzy metric spaces. Zbl 1137.54308
Som, Tanmoy
2007
Local and global uniqueness theorems on fractional integro-differential equations via Bihari’s and Gronwall’s inequalities. Zbl 1137.26301
Momani, Shaher; Jameel, Ahlam; Al-Azawi, Sora
2007
Iterative solutions of coupled matrix convolution equations. Zbl 1137.65070
2007
Mihai, Vochita; Sengupta, Ambar N.
2007
Meromorphic functions of relative order $$(p,q)$$. Zbl 1134.30019
Banerjee, Dibyendu; Jana, Srimanta
2007
Fixed points in fuzzy metric space for noncompatible maps. Zbl 1147.47058
Pant, Vyomesh; Pant, R. P.
2007
Hypersurfaces with constant mean curvature in a locally symmetric manifold. Zbl 1132.53032
Wang, Mei-Jiao; Hong, Yi
2007
On higher-order conditions for strict efficiency. Zbl 1194.90114
Luu Do Van; Kien Pham Trung
2007
On weakly precontinuous functions in bitological spaces. Zbl 1146.54005
Noiri, Takashi; Popa, Valeriu
2007
Classification of Lagrangian surfaces of constant curvature in complex hyperbolic plane. II. Zbl 1139.53039
Chen, Bang-Yen
2007
Examples of $$\mathcal{K}\mathcal{C}$$-maps and $$\mathcal{K}\mathcal{D}$$-maps on abstract convex spaces. Zbl 1144.47040
Park, Sehie
2007
Common fixed points and best approximation in convex metric spaces. Zbl 1149.47043
Beg, Ismat; Abbas, Mujahid
2007
Statistically convergent and Cesàrio summable double sequences of fuzzy real numbers. Zbl 1142.40301
Tripathy, Binod Chandra; Dutta, Amar Jyoti
2007
A study on certain class of analytic functions defined by Ruscheweyh derivative. Zbl 1130.30009
Attiya, A. A.; Aouf, M. K.
2007
Green’s relations in ordered groupoids in terms of fuzzy subsets. Zbl 1144.06007
Kehayopulu, Niovi; Tsingelis, Michael
2007
Common fixed point theorems via an implicit relation and new properties. Zbl 1137.54324
Aliouche, Abdelkrim
2007
Gao’s constants of Lorentz sequence spaces. Zbl 1148.46016
Cui, Huanhuan; Wang, Fenghui
2007
A new Hilbert-type integral inequality and its reverse. Zbl 1152.26024
Xie, Zitian; Zeng, Zheng
2007
On some difference sequences defined by a sequence of Orlicz functions. Zbl 1144.46300
2007
Even dimensional submanifolds of spheres with nonnegative curvature operator. Zbl 1148.53310
Kechagias, Nondas E.
2007
A unified approach to fractional calculus pertaining to $$H$$-functions. Zbl 1149.26011
Chaudrasia, V. B. L.; Srivastava, Amber
2007
Some coefficient inequalities for certain subclasses of analytic functions with respect to $$k$$-symmetric points. Zbl 1130.30015
Wang, Zhi-Gang; Gao, Chun-Yi; Yuan, Shao-Mou
2007
Numerical study of heat transfer over permeable stretching surface with variable viscosity and thermal diffusivity in uniform magnetic field. Zbl 1246.76021
Al-Harbi, Saleh M.
2007
Convergence conditions and closed maps. Zbl 1128.54002
Goel, Asha; Garg, G. L.
2007
$$(1,2)\alpha$$-open sets based on bitopological separation axioms. Zbl 1145.54027
Jafari, Saeid; Lellis Thivagar, M.; Athisaya Ponmani, S.
2007
New Chebyshev type inequalities involving functions of two and three variables. Zbl 1137.26308
Pachpatte, B. G.
2007
Additive groups of self-injective rings. Zbl 1139.20053
Feigelstock, Shalom
2007
The effect of the skewing distribution on skew-symmetric families. Zbl 1137.60308
Umbach, Dale
2007
On new separation axioms via $$\lambda$$-open sets. II. Zbl 1151.54326
Rajesh, N.
2007
Argument estimates of certain meromorphically $$P$$-valent functions. Zbl 1136.30305
Lashin, A. Y.
2007
Generalized Gross heat equation with noises. Zbl 1113.60066
Barhoumi, Abdessatar; Kuo, Hui-Hsiung; Ouerdiane, Habib
2006
Statistically convergent double sequence spaces defined by Orlicz functions. Zbl 1122.40001
Tripathy, Binod Chandra; Sarma, Bipul
2006
A new Ostrowski type inequality for double integrals. Zbl 1119.26027
Pachpatte, B. G.
2006
The classification of 3-dimensional locally homogeneous Blaschke hypersurfaces with nondiagonalizable affine shape operators. Zbl 1118.53009
Ooguri, Masahiro
2006
Approximations in hypernear-rings. Zbl 1111.16043
Zhan, Jianming; Ma, Xueling
2006
Periodicity and stability of a discrete time periodic $$n$$-species Lotka-Volterra competition system with feedback controls and deviating arguments. Zbl 1134.93023
Chen, Xiaoxing; Chen, Fengde
2006
On $$L_p$$-inverse theorem for a linear combination of a new sequence of linear positive operators. Zbl 1110.41012
Agrawal, P. N.; Mohammad, Ali J.
2006
On pseudo projective $$\Phi$$-recurrent Kenmotsu manifolds. Zbl 1113.53021
2006
The nonsequential approximate solutions in problems of asymptotic analysis. Zbl 1122.28004
Chentsov, A. G.
2006
On fuzzy real-valued double sequence spaces. Zbl 1111.40002
Tripathy, Binod Chandra; Dutta, Amar Jyoti
2006
On involutory BCK-algebras. Zbl 1111.06012
Huang, Yisheng
2006
On some weaker forms of $$B^*$$-continuity for multifunction. Zbl 1107.54013
Ganguly, D. K.; Mitra, Chandrani
2006
A neighborhood condition for vertices at distance two implying Hamiltonicity. Zbl 1108.05059
Zhao, Kewen; Liu, Bolian
2006
On certain classes of functions associated with multivalently analytic and multivalently meromorphic functions. Zbl 1114.30009
Irmak, H.; Raina, R. K.
2006
Divisible is injective. Zbl 1113.16005
Feigelstock, Shalom
2006
Mixed type duality for a variational problem with strong pseudoindex constraints. Zbl 1148.49302
Husain, I.; Ahmed, A.
2006
On functions with strongly preclosed graphs. Zbl 1108.54301
2006
Erratum on the article: Stability of the characteristic vector field of a Sasakian manifold. Zbl 1106.53304
Borrelli, Vincent
2006
Simply connected Lie subgroups of the unipotent Lie group of order 4. Zbl 1111.22009
Benjumea, J. C.; Echarte, F. J.; Núñez, J.; Tenorio, A. F.
2006
$$*$$-topology and generalized open sets. Zbl 1114.54002
2006
A note on certain character sums. Zbl 1230.11100
Liu, Huaning; Zhang, Wenpeng
2006
The fiducial inference on the two-parameter exponential distribution. Zbl 1119.62101
Wang, Min; Zhang, Baoxue; Xu, Xingzhong
2006
Some results on exact sequences of semi modules analogues to module theory. Zbl 1108.16044
Bhambri, S. K.; Kant Dubey, Manish
2006
Some new Cesàro sequence spaces of non-absolute type which include the spaces $$c_0$$ and $$c$$. Zbl 1085.46500
Şengönül, Mehmet; Başar, Feyzi
2005
On a new type of generalized difference Cesàro sequence spaces. Zbl 1093.46507
Tripathy, Binod Chandra; Esi, Ayhan; Tripathy, Balakrushna
2005
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text:
Linear regression models assume that the output variable $Y$ can be explained (or reasonably approximated) as a linear combination of the input vector $X$:

where

• $\beta_j$ are the parameters of the model.
• $X_j$ can come from quantitative inputs, interactions between variables, qualitative inputs (in the form of dummy variables) or others.

# Least squares method

The most common method to estimate $\beta$ from the training data is the least squares, where the coefficients that minimize the residual sum of squares

RSS has two crucial properties worth expliciting. First, squaring the differences ignores the direction of the differences, and hence negative differences cannot offset positive diferences. Second, the square assigns a higher importance to big errors. We can rewrite RSS in matrix form as

To minimize RSS, we differentiate this quadratic function with respect to $\beta$

and, assuming $\textbf X$ has full column rank and hence $\textbf X^T\textbf X$ is positive definite, we set the first derivative to zero

This allows to obtain a unique solution

If $\textbf X$ is not full rank i.e. its columns are not linearly independent, then $\textbf X^T \textbf X$ is singular, and the least squares coefficients $\hat \beta$ are not uniquely defined.

## Least squares as BLUE

### Variance of the estimates

The data we use is no more than a sample of all the possible cases. Hence, a different training data will lead to a different set of $\hat \beta$. If we assume that the observations $y_i$ are uncorrelated and have constant variance $\sigma^2$, and that the $x_i$ are fixed (non-random), the variance in the $\hat \beta$ is

If we also assume that the a lineal model is correct for the mean, and that deviations of $y$ around its expectation are additive and Gaussian ($\varepsilon \tilde{} N(0,\sigma^2)$),

Regarding $\sigma^2$, we can use an unbiased estimator

which follows a $\chi^2$ distribution.

With these properties we can define confidence intervals for the parameters $\beta_j$. We do so by using a Z-score to test if each coefficient $\beta_j = 0$:

where $v_j$ is the $j$th diagonal element of $(\textbf X^T\textbf X)^{-1}$. $z_j$ is distributed as $t_{N-p-1}$.

### The Gauss-Markov theorem

Let’s focus on the estimation of any linear combination of the parameters $\theta=a^T \beta$ (e.g. the predictions $f(x_0)=x_0^T\beta$). The least squares estimate is

If the model is linear, we can prove that $a^T\hat \beta$ is an unbiased estimator i.e. the expected value does not differ from the true value of the parameter being estimated:

Not only that, but the Gauss-Markov theorem states that the parameters $\hat \beta$ are the best linear unbiased estimator (BLUE), as its variance is the smallest. Let’s dig a bit into this. The mean squared error (MSE) of an estimator $\hat \theta$ in estimating $\theta$ is

where $Var(\hat \theta)$ is the variance, and $[E(\hat \theta - \theta)]^2$ the squared bias. Hence, among unbiased estimators (those where $[E(\hat \theta - \theta)]^2 = 0$), least squares estimator is the best one, as its variance, and hence the prediction error, are the smallest.

## Limitations

There are two main reservations about least squares estimates. The first one is about prediction accuracy: despite least squared being the best among unbiased estimators, there are biased estimators with better prediction accuracy (lower MSE). They achieve so by accepting some bias to reduce variance e.g. constraining the size of the model, setting coefficients to 0 and hence achieving lower variance than least squares. The second one is interpretation: least squares takes all the input variables as predictors, which complicates the understanding of the model.

# Subset selection

Some methods couple variable subset selection to the linear regression, discarding input variables:

• Best-subset selection: finds, for each $k \in {0,1,…,p}$ the subset of $k$ variables that gives the smallest residual sum of squares. Choosing $k$ is not trivial; usually the one that minimizes the estimate of the expected predicted error. There is an obvious computational burden, and when $p>40$ this approach becomes unfeasible.
• Forward- and backward-stepwise selection: these are heuristic approaches to the problem of subset selection with high $p$. In forward-stepwise selection we start with an intercept at $\bar y$, and sequentially add the variable that best improves the fit. In the other end, backward-stepwise selection starts with the full model, and sequentially deletes the predictor that has least impact on the fit. In both cases, we end up with a sequence of models of different sizes $k$ that we need to study.
• Forward stagewise selection: it also starts with the intercept, and iteratively, finds the variable most correlated with the current residual. Then, it fits a linear regression of the residual to this variable and the coefficient is added to the model. As opposed to forward-stepwise selection, the coefficients of the rest of the variables are not changed when a new one is added. These steps are repeated until no more variables are correlated with the residuals. Forward stagewise selection is slower, but might present advantages in high dimensional settings.

However, those methods often exhibit high variance and do not reduce prediction error.

# Shrinkage methods

## Ridge regression

Ridge regression shrinks the regression coefficients by imposing a penalty on their size:

where $\lambda\geq0$ is the complexity parameter that controls the size of the model: the larger $\lambda$, the greater the shrinkage, the higher the tendency of the coefficients towards zero. Note that the intersection $\beta_0$ is left out of the penalty term. A more explicit way of displaying the size constraint is

subject to $\sum_{j=1}^p\beta_j^2\leq t$. Rewriting it in matrix form we can see the ridge regression solutions:

where $\textbf I$ is the $p \times p$ identity matrix.

# Generalized linear models

Generalized linear models (GLM) are a sub-family of generalized additive models, which take the following form

 where the $f_j$’s are unspecified smooth (“nonparametric”) functions which we will estimate simultaneously. The conditional mean $\mu(X)$ (e.g. $\mu(X)=P(Y=1 X)$ for a binary reponse) is relaed to the additive function of the predictors via a link function $g$:

# PUT SOMEWHERE

## Regularization methods

Several regularization methods have been proposed for ill-posed problems i.e. those where one or more of the following properties don’t apply:

• A solution exists
• The solution is unique
• The solution’s behavior changes continuously with the initial conditions.

# Fitting a logistic reg through an iterative solution

We look for an estimate a parameter vector beta $\hat{\beta}$ that maximizes the likelihood of the model. Iterative solutions follow this algorithm:

1. Select $\hat{\beta}_0$, an initial guess for $\hat{\beta}$.
2. Get a new $\hat{\beta}$ using a polynomial approximation of the likelihood.
3. Calculate $C = \hat{\beta} - \hat{\beta}_0$.
4. Repeat until $C < k$, where $k$ is a convergence criterion.

# References

• Hastie, T., Tibshirani, R., & Friedman, J. (2009). The Elements of Statistical Learning. New York, NY: Springer New York. https://doi.org/10.1007/978-0-387-84858-7
• Wikipedia


text:
2 Tutorial: Exporting a Subsystem as a dSPACE Application - MapleSim Help

2 Tutorial: Exporting a Subsystem as a dSPACE Application

This tutorial guides you through the process of creating a dSPACE model using the dSPACE DS1104 Real-Time Application template from a pure closed-loop simulation model.

It is a rapid control prototyping application, where the controller runs in real-time on the DS1104 board in order to control a real system.

2.1 Overview of the Plant to Control

The model simulates a DC Motor speed controller. The system is composed of the following real components:

 • The DC Motor itself, which includes a gear (ratio=30)
 • The H-bridge driver, allowing the bi-directional control of the motor. This component also provides a current measurement output with a 377 µA/A sensitivity, connected in series with a 2 kΩ resistor
 • A Transistor-Transistor Logic (TTL) incremental encoder with 300 lines. This encoder is attached to the motor shaft (the rotor), not to the gear shaft. Thus, there are 9000 lines (300*30) per revolution

2.2 Overview of the Initial Closed-loop Simulation Model

The initial closed-loop simulation model (DC Motor Control Start Tutorial) is located in the dSPACE Connector Examples palette under the Libraries tab. Click DC Motor Control Start Tutorial to open the model in MapleSim.

The main components are (from right to left):

 • The DC Motor subsystem. You can explore this model to see the different parameters of the motor.
 • A H-bridge subsystem, based on ideal switch and diode components. The H-bridge, supplied with a 12V voltage source, provides the required power to the motor. Each switch is driven by an on/off signal output by the SignMagn subsystem.
 • The SignMagn subsystem computes the switching logic in order to drive the H-bridge in the "Sign/Magnitude mode".
 • The DutyCycle subsystem transforms the voltage command (output of the PID controller) into a direction and a duty cycle signal, required by the Sign/Magnitude drive mode.
 • A PID controller which maintains the real motor speed as closely as possible to the reference.
 • A Pulse component which outputs a square pulse as a reference speed.

Run this model and look at the result.

2.3 Preparing the Model for Export

The model you opened in the previous section is not ready to export, mainly because it does not precisely reflect the real sensors and their interaction with the input and output components of the dSPACE DS1104 board. Next, you will add modeling components for the incremental encoder and the current sensor. You will also group into a subsystem all the components needed in the Controller application that will run in real-time on the DS1104 board.

The output of the incremental encoder are pulses corresponding to the angular position of the rotor. In the real-time application, you will connect this sensor to the incremental encoder input of the DS1104 board. The encoder input driver of the DS1104 gives the angular position and the position difference between two time steps. Use this delta position to compute the speed.

To add the incremental encoder model

 1 Select, and then delete the line between the DCMotor speed output and the minus input of the Feedback component.
 2 Add a Gain component (from the Signal Blocks > Common palette) to the right of the DCMotor subsystem.

 3 Transform the Gain component into a subsystem (that is, select the Gain component, then select the Edit menu, and then select Create Subsystem). Name the subsystem IncEncoder.
 4 Double-click on this subsystem to open it.
 5 Connect the input and output of the Gain component to the subsystem boundary. Name the input Speed and name the output DeltaPos.
 6 Select the Gain component, and then enter $\frac{9000\cdot 0.001}{2\cdot \mathrm{\pi }}$ for the gain value (k). Since there are 9000 lines per revolution and the sample time of the application will be 1 ms, we have to multiply the real speed by $\frac{9000\cdot 0.001}{2\cdot \mathrm{π}}$ in order to get the delta position value.

 8 Connect the DCMotor speed output to the input of the IncEncoder subsystem.

Processing the Incremental Encoder Capture Signal in the Real-time Application

In the real-time application, you will need to transform the incremental encoder capture signal of the DS1104 board (delta position) into a quantity corresponding to the motor speed. For this you just need to add another gain component with a value which is the inverse of the one you set up in the previous section.

To process the incremental encoder capture signal

 1 Add a Gain component (from the Signal Blocks > Common palette) near the minus input of the Feedback component (at the left of the PID subsystem).

 2 Transform the newly added Gain component into a subsystem (that is, select the Gain component, then select the Edit menu, and then select Create Subsystem). Name the subsystem IncEncoderScaling.
 3 Double-click on this subsystem to open it.
 4 Connect the input and output of the Gain component to the subsystem boundary. Name the input DeltaPos and name the output Speed.
 5 Select the Gain component, and then enter $\frac{2\cdot \mathrm{\pi }}{9000\cdot 0.001}$ for the gain value (k).

 7 Connect the output of the IncEncoder subsystem to the input of the IncEncoderScaling subsystem.
 8 Connect the output of the IncEncoderScaling subsystem to the minus input of the Feedback component.

Converting the Controller to a Subsystem

By converting your entire model or part of your model into a subsystem, you identify which parts of the model you want to export to a dSPACE application. In this example, you will group the controller components into a subsystem.

To convert the controller into a subsystem

 1 Using the selection tool ( ) located above the Model Workspace, draw a box around the controller components in the model.

 2 From the Edit menu, select Create Subsystem.
 3 In the Create Subsystem dialog box, enter Controller as the subsystem name.
 4 Click OK. A Controller subsystem is displayed in the Model Workspace.

 5 Double-click the Controller subsystem and modify the names of the inputs and outputs as follows:
 • First input (connected to the Feedback component): SpeedReference
 • Second input (connected to the IncEncoderScaling subsystem): DeltaPos
 • First output (first output of the DutyCycle subsystem): Direction
 • Second output (second output of the DutyCycle subsystem): DutyCycle

For the real-time application, connect the current sensor output to an analog input of the DS1104 board in order to monitor the current in the drive. To save time, the current sensor model is already included in this model. It is called CurrentMeas and can be found under the Project tab, in the Definitions > Subsystems palette.

To add the current sensor model

 2 Under the Project tab, navigate to the Definitions > Subsystems palette, and then drag the CurrentMeas subsystem to the Model Workspace. Place the CurrentMeas subsystem below the DCMotor subsystem.
 3 Delete the current probe connected to the DCMotor subsystem in the model.
 4 Connect the current output of the DCMotor subsystem to the input of the CurrentMeas subsystem.

Processing the current sensor ADC signal in the real-time application

In the real-time application, connect the output of the current sensor to an ADC input of the DS1104 board and transform the signal into a quantity corresponding to the motor current. For this you just need to add a scaling gain block in the controller subsystem.

To process the current sensor ADC signal

 1 Double-click the Controller subsystem to open it.
 2 Add a Gain component (from the Libraries > Signal Blocks > Common palette) below the other blocks of this subsystem.

 3 Connect the input of this Gain block to the left border of the subsystem, and then name the input Imeas.
 4 Connect the output of Gain component to the right border of the subsystem, and then name the output Current.

Note: The current value will not be used in the controller (you just want to monitor it), so you will not connect it to any block of the controller. However, in order to generate code, you cannot leave the output of the Gain component unconnected.

 5 Select the Gain component, and then enter $\frac{1}{2000\cdot 377\cdot {10}^{-6}}$ for the gain value (k).

Note: The sensitivity is 377 µA/A, and you get your value from the voltage measurement across a 2 kΩ resistor. This results in a scaling value of $\frac{1}{2000\cdot 377\cdot {10}^{-6}}$ .

 6 Connect the output of the IncEncoderScaling subsystem to the right border of the subsystem, and then name the output Speed. This allows you to monitor the motor speed in the real-time application.
 7 Delete the three probes. They will be added to Controller subsystem outputs in step 10.

 9 Connect the third input of the Controller subsystem to the output of the CurrentMeas subsystem.
 10 Add probes to the first and second outputs of the Controller subsystem.

Optional: You can add probes to the third and fourth outputs of the Controller subsystem to display their values during a MapleSim simulation.

The model should be very similar to the DC Motor Control model found in the dSPACE Connector Examples palette. The Controller subsystem is now ready to be prepared for export. Note that you can still simulate this model in MapleSim.

2.4 Map the Controller subsystem inputs and outputs to the dSPACE DS1104 inputs and outputs

You will now define the mapping of the Controller subsystem inputs and outputs to the DS1104 hardware inputs and outputs, reflecting the real connection between the DS1104 and the DC Motor. This will be done using the Maple template, dSPACE DS1104 Real-Time Application, which will then be attached to the model.

To map the controller

 1 Click Templates ( ) in the Main Toolbar.
 2 From the list, select dSPACE DS1104 Real-Time Application.
 3 In the Attachment field, enter dSPACE_DS1104_Controller as the worksheet name.
 4 Click Create Attachment. Your MapleSim model is opened in Maple, in the dSPACE DS1104 Real-Time Application template.
 5 Browse to the Controller1 subsystem by selecting Controller1 from the list box next to Main above the model diagram.

 6 In the Subsystem Selection section of the template, click Load Selected Subsystem. All of the template fields are populated with information specific to the subsystem displayed in the model diagram.

You can now define the mapping between the inputs and outputs of the subsystem and the dSPACE DS1104 inputs and outputs, according to the following details:

 • The speed reference could be connected to an external signal generator signal. However, it can be interesting to run a virtual signal generator in real-time on the dSPACE board in order to tune the amplitude, frequency and/or offset directly from the dSPACE ControlDesk software. Thus, you will connect the speed reference input of the controller to a virtual square wave signal. The other choices for the virtual signals are Sine, Step or Constant.
 • The incremental encoder of the DC Motor will be connected to the first incremental encoder input of the DS1104 board.
 • Next, the current sensor of the H-Bridge will be connected to the first ADC input of the DS1104 board.
 • The direction input of the H-Bridge will be connected to the first digital output of the DS1104 board.
 • The duty cycle input of the H-Bridge will be connected to the first PWM output of the DS1104 board.
 • The current sensor signal monitored by the controller (third output of the controller) will be left unconnected.

You will proceed in two steps. First you will define all of the mapping signals, and then you will configure the input and output parameters.

To define all of the mapping signals:

 1 In the Input / Output Settings for the dSPACE DS1104 Board section, Input Mapping table, select the Main.Controller1.SpeedReference(t) signal in the list of model inputs. In the DS1104 inputs or Virtual signals list box on the right, select virtual_Square_1. This signal will be replaced in the application by a square signal generator running on the dSPACE board.
 2 In the Input Mapping table, select the Main.Controller1.DeltaPos(t) signal in the list of model inputs. In the DS1104 inputs or Virtual signals list box on the right, select DELTA_INC1, which is the delta position information given by the first incremental encoder input of the DS1104 board.
 3 In the Input Mapping table, select the Main.Controller1.Imeas(t) signal in the list of model inputs. In the DS1104 inputs or Virtual signals list box on the right, select ADCH1. This signal reads the value of the first ADC channel of the DS1104.
 4 In the Output Mapping table, select the Main.Controller1.Direction(t) signal in the list of model outputs. In the DS1104 outputs list box at the right, select Bit_ch0.

This signal sends the value computed by the application to the first digital channel of the DS1104. Note that the digital inputs and outputs of the DS1104 board can be configured either as inputs or outputs. In the present case, since the Bit_ch0 channel is defined as an output, it can no longer be used as an input. To verify this, browse to the DS1104 inputs or Virtual signals list box and look for the Bit_ch0 signal. You will see that it is marked as unavailable. If you try to connect an input signal to this channel, you will get an error message until you disconnect the channel from its output signal.

 5 In the Output Mapping table, select the Main.Controller1.DutyCycle(t) signal in the list of model outputs. In the DS1104 outputs list box on the right, select PWM_ch1. This signal will send the value computed by the application to the first single phase PWM channel of the DS1104.

The Main.Controller1.Current(t) signal is left unconnected. You can monitor it using ControlDesk.

To configure the parameters

 1 To configure the first digital I/O channel, scroll down to the Bit I/O Unit section, expand this section, and then do the following:
 • In the Initialization and Termination section, select 1 for the Initial Value (this corresponds to a forward turn of the motor).
 • In the Termination section, select Hold the current value. (You want the termination direction of the motor to be the same as it was just before the termination of the application.)

Note: The first channel, Bit_ch0, should be marked as Used as Output. All of the other channels should be marked as Not used.

 2 To configure the Incremental Encoder Interface, scroll down to the Incremental Encoder Interface section, expand this section, and then do the following:
 • In the General parameters section, select TTL for the Encoder 1 mode.
 • For the Encoder 1 reset-on-index mode, select false, since there is no index signal on this encoder.
 • In the Initialization section, leave the default value of 0 for the initial position of the encoder, since you will not be using the position capture.

 3 To configure the first single phase PWM channel, scroll down to the PWM Generation section, expand this section, and then do the following:
 • In the General Parameters section do the following:
 – Select Asymmetric as the PWM mode.
 – Enter 2 in the PWM Period (ms) text area.
 – Select Active high for PWM ch1 polarity (the polarity for the first channel).
 • In the Initialization section, enter 0 in the PWM ch1 text area. This is the initial duty cycle for the first PWM channel; the initial speed of the motor should be 0.
 • In the Termination section, select Termination value, and then enter 0 as the termination duty cycle for PWM ch1, the first PWM channel. (For safety, the termination speed of the motor should be 0.)

 4 To configure the Virtual Square Signal Generator, scroll down to the Virtual Square Signals Generator section, expand it, and then do the following in the Square 1 part of the table:
 • Enter 5 for the Amplitude.
 • Enter 0.5 for the Frequency (Hz).
 • Enter 10 for the Offset.

The I/O mapping and configuration is now complete. You can now proceed to the next step: exporting the controller to a real-time dSPACE application.

Note that you can attach more than one template of this kind if, for example, you need to define different I/O mappings for the same controller.

2.5 Exporting the Controller to a dSPACE real-time application running on the DS1104 board

In this section, you will create a dSPACE executable that can be run on a DS1104 from the Controller subsystem.

To Export the Controller

 1 Scroll down to the Step 3: Options section.
 2 In the Solver Settings area, enter 0.001 s for the Base Rate.

 3 In the Optimization Options area, select 3 (that is Full) for the Level of code optimization.

This option specifies the degree of simplification applied to the model equations during the code generation process. The full optimization option eliminates redundant variables and equations in the system.

 4 In the TRC Variables and Parameters Options section do the following:
 • Select Include the maximum number of variables.
 • Select Include the maximum number of parameters.

These options add all the possible variables and parameters in the TRC file that is generated with the dSPACE application. The TRC file is used by ControlDesk so that you can display variables and modify parameters in the real-time application as it is running.

 5 Scroll down to the Step 4: Generate dSPACE Application section of the template. Enter the following information for your real-time application:
 • In the dSPACE directory text area, enter the directory where dSPACE is installed.
 • In the Target directory text area, enter the directory where you want to store your real-time application.
 • In the Application name text area, enter the name for your real-time application.

 6 Click Generate dSPACE Application to generate the C code, the .trc file, the .sdf file and the .ppc file for your application.
 7 Open ControlDesk and load the generated application as usual. You will have access to the inputs, outputs, states and state derivatives of the application in the Model group. The parameters are in the Model Parameters subgroup, the execution time and current time can be accessed from the Task Info > Execution subgroup. Of course, this application should be connected to the real system so that you get interesting values.


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Pythagorean theorem

Calculus pythagorean

Calculus in processing ... please wait

Function : pythagorean

Summary :

The function makes it possible to verify by using the Pythagorean theorem knowing the lengths of the sides of a triangle that this is a right triangle. If the sides of the triangle depend on a variable, then the value of the variable is calculated so that the triangle is a right triangle.

Pythagorean online

Description :

The calculator by means of the pythagorean function makes it possible to know if lengths satisfy the Pythagorean theorem. If the lengths contain variables, the calculator will seek to find the values of the variables which allow to verify the Pythagorean theorem.

The Pythagorean theorem is expressed as follows: In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the opposite sides. If we consider the triangle ABC rectangle in A, if we put BC = a, AC = b, AB = c then the theorem of Pythagoras is written BC^2=AB^2+AC^2 or a^2=b^2+c^2.

The Pythagorean theorem admits a reciprocal which states : If in a triangle the square of one side is equal to the sum of the squares of the opposite sides, then the triangle is a right triangle.

Verify that a triangle is a right triangle knowing the length of its sides

The calculator makes it possible to verify that a triangle is a right triangle knowing the length of the hypotenuse and the length of the opposite sides. If it is desired, for example, to verify that there exists a right-angled triangle whose hypotenuse has length 5 and the opposite sides for length 3 and 4, enter pythagorean(3;4;5). The calculator returns 1 if the values passed in parameter make it possible to deduce that the triangle is a right triangle, 0 otherwise. The calculator returns the details of the calculations used to use the Pythagorean theorem.

Solve an equation involving the length of the sides in a right triangle

The calculator makes it possible to find the length of one side knowing the other two from the theorem of pythagoras. For example, if we look for the hypotenuse of a right triangle whose opposite sides are 3 and 4 enter pythagorean(3;4;x), the value of the hypotenuse is then calculated.

The function makes it possible to verify by using the Pythagorean theorem knowing the lengths of the sides of a triangle that this is a right triangle. If the sides of the triangle depend on a variable, then the value of the variable is calculated so that the triangle is a right triangle.

Syntax :

pythagorean(length_side_opposite;length_side_opposite;hypotenuse_length)

Examples :

Calculate online with pythagorean (Pythagorean theorem)