Implement Hardware-Efficient Real Partial-Systolic Matrix Solve Using Q-less QR Decomposition
This example shows how to implement a hardware-efficient solution to the real-valued matrix equation A'AX=B using the Real Partial-Systolic Matrix Solve Using Q-less QR Decomposition block.
Define Matrix Dimensions
Specify the number of rows in matrix A, the number of columns in matrix A and rows in B, and the number of columns in matrix B.
m = 300; % Number of rows in A n = 10; % Number of columns in A and rows in B p = 1; % Number of columns in B
Generate Matrices
For this example, use the helper function realRandomQlessQRMatrices
to generate random matrices A and B for the problem A'AX=B. The matrices are generated such that the elements of A and B are between -1 and +1, and A is full rank.
rng('default')
[A,B] = fixed.example.realRandomQlessQRMatrices(m,n,p);
Select Fixed-Point Data Types
Use the helper function realQlessQRMatrixSolveFixedpointTypes
to select fixed-point data types for input matrices A and B, and output X such that there is a low probability of overflow during the computation.
max_abs_A = 1; % Upper bound on max(abs(A(:)) max_abs_B = 1; % Upper bound on max(abs(B(:)) precisionBits = 24; % Number of bits of precision T = fixed.realQlessQRMatrixSolveFixedpointTypes(m,n,max_abs_A,max_abs_B,precisionBits); A = cast(A,'like',T.A); B = cast(B,'like',T.B); OutputType = fixed.extractNumericType(T.X);
Open the Model
model = 'RealPartialSystolicQlessQRMatrixSolveModel';
open_system(model);
The Data Handler subsystem in this model takes real matrices A and B as inputs. The readyA
and readyB
ports trigger the Data Handler. After sending a true validIn signal, there may be some delay before ready is set to false. When the Data Handler detects the leading edge of the readyA
signal, the block sets validInA
to true and sends the next row of A. When the Data Handler detects the leading edge of the readyB
signal, the block sets validInB
to true and sends the next matrix B. This protocol allows data to be sent whenever a leading edge of a ready signal is detected, ensuring that all data is processed.
Set Variables in the Model Workspace
Use the helper function setModelWorkspace
to add the variables defined above to the model workspace. These variables correspond to the block parameters for the Real Partial-Systolic Matrix Solve Using Q-less QR Decomposition block.
numSamples = 1; % Number of samples fixed.example.setModelWorkspace(model,'A',A,'B',B,'m',m,'n',n,'p',p,... 'regularizationParameter',0,... 'numSamples',numSamples,'OutputType',OutputType);
Simulate the Model
out = sim(model);
Construct the Solution from the Output Data
The Real Partial-Systolic Matrix Solve Using Q-less QR Decomposition block outputs matrix X at each time step. When a valid result matrix is output, the block sets validOut
to true.
X = out.X;
Verify the Accuracy of the Output
To evaluate the accuracy of the Real Partial-Systolic Matrix Solve Using Q-less QR Decomposition block, compute the relative error.
relative_error = norm(double(A'*A*X - B))/norm(double(B)) %#ok<NOPTS>
relative_error = 8.6289e-05