Download presentation

Presentation is loading. Please wait.

Published byErin Stelling Modified about 1 year ago

1
Systolic 4x4 Matrix QR Decomposition Xiangfeng Wang Mark Chen

2
Matrix Triangularization Given matrix A ij To triangularize A, we find a square orthogonal matrix Q and left multiply it with A.

3
Matrix Triangularization For example, given Q 23 Left multiplying Q 23 with A will zero the A 32 value.

4
Matrix Triangularization Using this principle, by setting up our Q correctly Left multiplying this Q with A will eliminate all value below the main diagonal of A.

5
QR Decomposition

6
The circular cell simply “reflects” or changes the direction of the data flow The square cell performs two functions. For token values (marked with a *), it will perform the sine and cosine values and store it. For all other values it will apply the sine and cosine values and then pass it along its respective path.

7
QR Decomposition

8
Generating the Sine and Cosine Sine Cosine x y X’ Y’ y’ = x*c + y*s x ’ = y*c – x*s

9
sinecosine X’Y’ x=1, y=2, = actan(1/2) = , sin = , cos = y’= , x’ = e-004, time for the calculation ~25 cycles

10
Generating and Applying the Rotation

11
Simulation

12
We finished one computational unit. We will build the whole System and figure out the right timing…

Similar presentations

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google