# Systolic 4x4 Matrix QR Decomposition Xiangfeng Wang Mark Chen.

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Systolic 4x4 Matrix QR Decomposition Xiangfeng Wang Mark Chen

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

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

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.

QR Decomposition

 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.

QR Decomposition

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

sinecosine X’Y’ x=1, y=2,  = actan(1/2) = 0.4636, sin  = 0.4472, cos  = 0.8944 y’= 2.2361, x’ = 1.0646e-004, time for the calculation ~25 cycles

Generating and Applying the Rotation

Simulation

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