MatrixIdentification.jl

Author: anastasia21112

benchmarks/LinearSolve/MatrixIdentification.jl

@@ -0,0 +1,95 @@
+using LinearAlgebra
+
+## compute the percentage banded for a matrix given a bandwidth
+function compute_bandedness(A, bandwidth)
+    n = size(A, 1)
+    total_band_positions = 0
+    non_zero_in_band = 0
+    bandwidth = bandwidth
+    for r in 1:n
+        for c in 1:n
+            if abs(r - c) <= bandwidth
+                total_band_positions += 1  # This position belongs to the band
+                if A[r, c] != 0
+                    non_zero_in_band += 1  # This element is non-zero in the band
+                end
+            end
+        end
+    end
+
+    percentage_filled = non_zero_in_band / total_band_positions * 100
+    return percentage_filled
+end
+
+## use the compute banded function to compute the bandedness given different bandsizes
+function isbanded(A)
+    n = size(A, 1)
+    count = 5
+    potential_band_sizes = []
+
+    while count < n - 5: 
+        push!(potential_band_sizes, count += 5)
+    end
+    
+    for bandsize in potential_band_sizes
+        percentage_filled = compute_bandedness(A, bandsize)
+        if percentage_filled >= 0.9
+            return true 
+        end
+    end
+
+    return false
+
+## compute the sparsity for a given matrix
+function compute_sparsity(A)
+    n = size(A, 1)
+    percentage_sparsity = length(nonzeros(A)) / n^2
+    return percentage_sparsity
+end
+
+## get the percentage banded for a bandwidth of 5 and percentage sparsity
+function getstructure(A::Matrix)::Any
+    percentage_banded = compute_bandedness(A, 5)
+    percentage_sparsity = compute_sparsity(A)
+
+    return (percentage_banded, percentage_sparsity)
+end
+
+## return the best type of matrix for a given sparse matrix
+function sparsestructure(A::SparseMatrixCSC)::Any
+    sym = issymmetric(A)
+    herm = ishermitian(A)
+    banded = isbanded(A)
+    posdef = isposdef(A)
+    lower_triangular = istril(A)
+    upper_triangular = istriu(A)
+
+
+    n = size(A, 1)
+
+    if banded
+        return BandedMatrix(A)
+    end
+    
+    if sym 
+       return Symmetric(A)
+    end 
+
+    if herm
+        return Hermitian(A)
+    end
+
+    if lower_triangular
+        return LowerTriangular(A)
+    end
+
+    if upper_triangular
+        return UpperTriangular(A)
+    end
+end
+
+
+
+
+
+