More website updates

We've completed another couple of website features, both for the text dictionary. First, words that are not covered in the dictionary gets colored in red which should save you some typing. In addition you can now click on words to take you to the word dictionary for that word. This lets you copy the information for the word if you like.

Take a look here if you're interested!


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Updates to the web site

We've finally managed to publish some updates to the website. In addition to behind the scenes improvements to the "plumbing" and removing som glitches, there's a new English to Arabic dictionary. This is in an early stage of development and we hope to improve it further in the coming months. Check it out here.

The word dictionary will now try to complete your typing. Hopefully this will make it more effective and easier to use. At the moment this is only for the Arabic-English dictionary.

Hope you enjoy the updates, don't hesitate to get in touch and let us know what you think about them!

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New iPhone dictionary release

We got this one out the door ahead of schedule for once, but it contains some long awaited features. This release has been about making the dictionary more friendly as an iOS application, making day-to-day usage faster and easier.

First up is support for rotation and landscape mode. This really has been an oversight on our part and is now finally done :D

Second is the support for iOS 4 features, primarily multitasking. Multitasking is a great boon for the dictionary. It is now easy to access while browsing, listening to podcasts, reading pdfs, etc.

We've also added a copy button on the detail page for quick copying of the Arabic and English word to the pasteboard.

There's now an overlay over the word table when there are nothing to display from the dictionary. We think this is a bit better than just having an empty list.

We also wanted to automatically switch to the Arabic keyboard for you when switching to the dictionary. This is currently not possible due to restrictions in the iPhone operating systems. Maybe some day in the future though ;)

Hope you enjoy this release! We're now back to planning some cool new features more concerned with the Arabic language.

Support mail outage

Regrettably our mail service went down two weeks ago, and since I was out traveling most of that time it took quite some time to get it back up again.

It should all be back in order now. But if you've tried to contact the support email address and not received a response please contact us again!

Multivariate Newtons method in Mathemathica

Using the previously mentioned Jacobian function, here's a way to do Newton's method in multiple variables.

Here's a simple vector valued function:

In: f[{x_, y_}] := {x^2 y + 1, E^x + y}

The Jacobian:

In: jacobian[f, {x, y}]

Out: {{2 x y, x^2}, {E^x, 1}}

To construct a Jacobian function that we can evaluate we have to create a Mathematica. To evaluate the derivatives in place we use other vector component names and replace them after calculating the derivative:

In: df[{x_, y_}] := jacobian[f, {a, b}] /. {a -> x, b -> y}

With the Jacobian function it's easy to set up the iteration with FixedPointList and an anonymous function:

In: FixedPointList[(# - Inverse[df[#]].f[#]) &, {-0.7, -2.5}, 20]

Out: {{-0.7, -2.5}, ... , {0.703467, -2.02075}}

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Jacobian function for Mathematica

Following up on the vector valued functions, here's a way to compute Jacobian matrices for them:

In: jacobian[f_, c_] := Transpose[Map[D[f[c], #] &, c]]

You need to pass in a list of components for the vector argument along with the vector valued function:

In: f[{x_, y_}] := {2 x^2 y, x*y}

In: jacobian[f, {x, y}]

Out: {{4 x y, y}, {2 x^2, x}}

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One way to use vector valued functions in Mathematica

Struggling with some homework recently, I needed to do iteration on vector valued functions to find fix points. One way to do this is to pass a list/vector with the components as function arguments, and return the list/vector valued result.

For example:

f[{x_, y_}] := {1.01 x - 3*10^-5*x*y, 0.98 y + 10^-5*x*y}

The fix point iteration can then be handled by FixedPointList:

FixedPointList[f, {1000, 100}, 1000]

Plotting the result componentwise:

ListLinePlot[{%%[[All, 1]], %%[[All, 2]]}]