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using MatrixDepot
using PyPlot
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matrixdepot()
show all the symmetric and pos-def matrices in the collection
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matrixdepot("symmetric", "pos-def")
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matrixdepot("magic")
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A = matrixdepot("magic", 5)
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matrixdepot("magic", Float32, 5)
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A magic square is an arrangement of n^2 distinct numbers in a n-by-n square matrix such that the numbers in each row, each column, and the numbers on the diagonal and anti-diagonal all add up to the same number.
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sum(A,1)
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sum(A,2)
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sum(diag(A))
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p = [5:-1:1]
sum(diag(A[:,p]))
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matshow(A)
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B = matrixdepot("wilkinson", 12)
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matshow(full(B))
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matrixdepot("rando", Bool, 6)
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We set the precision of BigFloat and generate matrices of arbitrary precision.
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set_bigfloat_precision(200)
H = matrixdepot("hilb", BigFloat, 5)
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PolarFact is a Julia package for computing the matrix polar decomposition. It includes algorithms like Newton's method (:newton), the QDWH method (:qdwh), a hybrid Newton's method (:hybrid) and the
Halley method (:halley).
We can use Matrix Depot to compare the performance of these algorithms.
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Pkg.add("PolarFact")
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using PolarFact
Compare the number of iterations of four polar decomposition algorithms
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n = length(matrixdepot("inverse", "symmetric"))
niters = zeros(4, n)
for (i,mat) in enumerate(matrixdepot("inverse", "symmetric"))
A = matrixdepot(mat, Float64, 12)
A = full(A)
r_newton = polarfact(A, alg = :newton)
r_qdwh = polarfact(A, alg = :qdwh)
r_hybird = polarfact(A, alg = :hybrid)
r_halley = polarfact(A, alg = :halley)
niters[1, i] = r_newton.niters
niters[2, i] = r_qdwh.niters
niters[3, i] = r_hybird.niters
niters[4, i] = r_halley.niters
end
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plt.figure()
for i in 1:4
x = [1:n]
y = niters[i,:][:]
plt.plot(x,y, ".-")
plt.hold("on")
end
plt.xlabel("test matrices")
plt.ylabel("number of iterations")
plt.legend(["newton", "qdwh", "hybird", "halley"])
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We first run MatrixDepot.update(), which download two html matrix name lists.
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MatrixDepot.update()
Matrix Depot first check if the matrix is on the matrix data list before downloading it.
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MatrixDepot.get("Collection/somematrix")
HB/1138_bus (undirected graph drawing, UF Sparse Matrix Collection, Tim Davis and Yifan Hu)
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MatrixDepot.get("HB/1138_bus")
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matrixdepot()
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matrixdepot("HB/1138_bus")
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A = matrixdepot("HB/1138_bus", :r)
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spy(A)
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show all the downloaded matrices
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matrixdepot("data")
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Add a property for all the matrix representation of graphs
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@addproperty graphs = ["California", "ca-HepTh", "wb-cs-stanford", "G66"]
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matrixdepot("graphs")
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