This example shows how to implement a hardware-efficient solution to the complex-valued matrix equation A'AX=B using the Complex Burst Matrix Solve Using Q-less QR Decomposition block.
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 = 100; % Number of rows in A n = 10; % Number of columns in A and rows in B p = 1; % Number of columns in B
For this example, use the helper function
complexRandomQlessQRMatrices to generate random matrices A and B for the problem A'AX=B. The matrices are generated such that the real and imaginary parts of the elements of A and B are between -1 and +1, and A is full rank.
rng('default') [A,B] = fixed.example.complexRandomQlessQRMatrices(m,n,p);
Use the helper function
complexQlessQRMatrixSolveFixedpointTypes 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. For more information about how datatypes are selected, see the document FixedPointMatrixLibraryDatatypesExample.pdf in the current directory.
The real and imaginary parts of the elements of A and B are between -1 and 1, so the maximum possible absolute value of any element is sqrt(2).
max_abs_A = sqrt(2); % max(abs(A(:)) max_abs_B = sqrt(2); % max(abs(B(:)) f = 24; % Fraction length (bits of precision) T = fixed.example.complexQlessQRMatrixSolveFixedpointTypes(m,n,max_abs_A,max_abs_B,f); A = cast(A,'like',T.A); B = cast(B,'like',T.B); OutputType = fixed.extractNumericType(T.X);
model = 'ComplexBurstQlessQRMatrixSolveModel'; open_system(model);
The Data Handler subsystem in this model takes complex matrices A and B as inputs. The
ready port triggers 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
ready signal, the block sets
validIn to true and sends the next row of A and B. This protocol allows data to be sent whenever a leading edge of the
ready signal is detected, ensuring that all data is processed.
Use the helper function
setModelWorkspace to add the variables defined above to the model workspace. These variables correspond to the block parameters for the Complex Burst 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,... 'numSamples',numSamples,'OutputType',OutputType);
out = sim(model);
The Complex Burst Matrix Solve Using Q-less QR Decomposition block outputs data one row at a time. When a result row is output, the block sets
validOut to true. The rows of X are output in the order they are computed, last row first, so you must reconstruct the data to interpret the results. To reconstruct the matrix X from the output data, use the helper function
X = fixed.example.matrixSolveModelOutputToArray(out.X,n,p);
To evaluate the accuracy of the Complex Burst 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 = 2.5932e-04