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We reimplement the scattering matrix calculation for GPUs with a block matrix inversion algorithm that only uses accelerator memory.
These methods are required to employ the direct inverse matrix calculation for the channel frequency response (CFR) matrix in solving the simultaneous equations.
For example, although the "household (H)" in Hokkaido has a 1.314 (income) increase ((M)) by a unit (expenditure) increase by the "local government (H)" in Hokkaido, the multiplier effects ((M_{r1})) from Hokkaido (own region) within the 1.314 (income) increase are just 0.940, based on the results of the matrix calculation for Hokkaido ISAM.15.
Step 2. Hessian matrix calculation: For a given σ value, the Hessian matrix corresponding to pixel (x i, y i ) in the candidate is calculated as follows H σ x i, y i = L xx x i, y i, σ L xy x i, y i, σ L yx x i, y i, σ L yy x i, y i, σ (8).
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This reduces the post processing time for weight matrix calculation as well as the storage space for the huge number of photon paths.
The inverse matrix calculation as in (5) for the network (3) results in slowing down the real-time computation.
As L/M increased, the percentage of execution time used for covariance matrix calculation and adaptive weight calculation increased, but the percentage of execution time for input data delay calculation decreased.
The preceding procedures for correlation matrix calculation are depicted in Figure 6. Figure 6 Correlation matrix construction.
where a is a steering vector with all ones, which is because the ultrasonic echo signals used for covariance matrix calculation are already delayed and aligned.
Then, the covariance matrix calculation with sub-aperture averaging for a specific image pixel is expressed as mathbf{Covar}(p_{s}) = frac{sum_{k=0}^{M-L} mathbf{echo}_{text{subk}}(p_{s}) mathbf{echo}_{text{subk}}^{H}(p_{s})}{M-L+1}.
The Convergence tolerance, i.e. tolerance in maximum difference, for the density matrix calculation has been set to (10^{ - 4}).
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