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- The DirectXMath API provides SIMD-friendly C types and functions for common linear algebra and graphics math operations common to DirectX applications. The library provides optimized versions for Windows 32-bit (x86), Windows 64-bit (x64), and Windows on ARM/ARM64 through SSE, AVX, and ARM-NEON intrinsics support in the Visual C compiler.
- DirectMath 1.0.2 Graphical Analysis 3.1 Magic Graph 1.1 MathType 5.2 NumLock Calculator 3.21 PracticCalc 3.7.41 ProKon 10.0h SciFace MuPAD Pro 2.5.2 SunCalculator 5.7.2 Uniplot 4.0.3 Wolfarm Research Calculator Center.
- Click the image to download the full size infographic (2000 x 5005 dpi) Regardless of how “nerdy” you may consider yourself, talking about planes and axes of movement can make your brain twist into a thousand knots!
E-learning tool for Lineair Algebra
Wouter Pasman, Frederik W. Jansen
Linear Algebra has always been a problem for computer science students. Only half of the students in our bachelor porgramme pass their examination for the Linear Algebra course at the first try. Also during the re-sits in the subsequent years, a substantial number of students are not successful in preparing themselves for the examination and fail over and over again.
To improve the chance of successful passing the re-examinations we looked at e-learning systems that could support self-study and help students to improve their compentences. We did not find an e-learning system suitable for Linear Algebra, although the interface of MathXpert1 for exercising calculus comes close to what we were looking for but it only covers a minor part of the Linear Algebra domain and it will not be expanded. Another interesting system isDirectmath2 which is not an e-learning system as such but supports mathematical formula manipulation using a rule set implemented on top of Mathematica. Inspired by this approach but we built a new front end using standard Mathematica functions and we implemented a ruleset for Linear Algebra on top of Mathematica.
The system works as follows. The students selects an exercise which appears in the left window (Figure 1). The exercise is assignment 1.11 from the book of Lay3: Solve the system
Figure 1. The window with the equation (left) and the rule-window (right). As long as the students makes no selection there are no operations to be applied.
After making a selection in the formula (e.g. the whole equation or just a row) the system offers a list of operations that can be performed on the selection. If we select the whole set of equations then we enter situation of figure 2.
Direct Math Definition
Figure 2. After the selection in the left window the operations that are applicable on this selection appear in the right window.
By selecting one of the operations, e.g. rule 'Make augmented Matrix' te system turns the equation set in the augmented matrix form (figure 3).
Figure 3. The result of the operation is the starting point for the next selection and operation.
After a number of steps we reach the situation of figure 4.
Figure 4. Subsequents steps towards the solution.
At some points the user has to give extra information, e.g. to specify a multiplier. Then a dialogue box appears, see figure 5. Also error messages or dialog boxes may appear when an operation is selected but can not be applied directly (figure 6). The error message quotes the term that is addressed (figure 7).
Figure 5. Dialog box to ask for additional parameters | Figure 6. Some direct feedback is given when an operation can not be applied yet. |
Figure 7. The error messages contain helpful information and quotes of the equation.
Experiments have shown that students can quickly grasp the logic of the interface and can after some learning complete exercises faster than with pen and paper. The system emphasizes training of the 'strategy' and avoids the extensive manual work of the equation rewriting (this is done by the system).So the students learn how to handle problems on a strategic level and the actual mechanics are assumed to be understood for the moment. In all cases, the system directly starts with an equation. Exercises with a more theoretic approach such as 'proof that the following system of equations is solvable' still have to be put into the appropriate equation before any operation can be applied.
As the student enters the operations one by one in the system, the system can track the student on his way to the solution. If we could specify the strategy a priori to the system, then the system could deduce whether a correct path to the solution has been taken. This would allow the system to give hints and feedback to the student when he takes the wrong direction or does not know how to proceed. Although there may be only a limited number of overall strategies to solve a problem, all possible sequences of elementary operations may still lead to an explosion of possible paths. It would be cumbersome to enter all these possible sequences by hand. We have developed a strategy language and a parser to specify a strategy in a compact way and to allow automatic interpretion and classification of all possible routes that the student takes as whether they are part of one of the specified strategies. By describing the strategy on a high abstraction level (using linear algebra concepts) the system can also give feedback on a more appropriate level then by only stating: 'wrong operation, this does not lead to a solution'.
The development of the strategy language and parser is part of the SURF-project 'Intelligent Feedback'. The project is a cooperation between Open University, TU Eindhoven and TU Delft. The SURF-project also includes an evaluation phase and a further development of the rule set.
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DirectXMath provides a math solution optimized for Windows.
Direct Math
In this section
| Topic | Description |
|---|---|
| Getting Started | The DirectXMath Library implements an optimal and portable interface for arithmetic and linear algebra operations on single-precision floating-point vectors (2D, 3D, and 4D) or matrices (3×3 and 4×4). |
| What's New | The DirectXMath library is based on the XNA Math C++ SIMD library version 2.04. Here we describe how DirectXMath differs from XNA Math and how DirectXMath versions differ. |
| Code Migration | This overview describes the changes required to migrate existing code using the XNA Math library to the DirectXMath library. |
| Working with D3DXMath | D3DXMath is a math helper library for Direct3D applications. |
| Code Optimization | This topic describes optimization considerations and strategies with the DirectXMath Library. |
| Library Internals | This topic describes the internal design of the DirectXMath library. |
Direct Math Meaning
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