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Solutions generated with MINRES-QLP #1

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Solutions generated with MINRES-QLP
amontoison Feb 25, 2021
f215714
Remove unused dependencies
amontoison Feb 25, 2021
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10 changes: 9 additions & 1 deletion README.md
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Original file line number Diff line number Diff line change
Expand Up @@ -36,7 +36,7 @@ to be cut off and I was not able to un-archive it or repair it.
If you know of a way to repair it, or better yet, have done it, please consider
submitting a pull request!

## Solutions
## Solutions generated with MATLAB

Because each problem is rank deficient, the solution we elected to report
is the minimum least-squares solution, i.e., among all the least-squares
Expand All @@ -61,6 +61,14 @@ For this reason, the solutions are named, e.g., `small_scaled_mls.rb`.
The Matlab code writes the solutions as simple vectors in a text file.
The matrices, right-hand sides and solutions are subsequently converted to Rutherford-Boeing format using the Julia package [`HarwellRutherfordBoeing.jl`](https://github.com/JuliaSparse/HarwellRutherfordBoeing.jl).

## Solutions generated with Julia

Each solution was generated by the Krylov method [`minres_qlp`](https://github.com/JuliaSmoothOptimizers/Krylov.jl) applied on the normal equations.
The computations are performed in quadruple precision.

Each minimum least-squares solution was generated using the Julia script
`write_mls.jl` found under `julia`. Solutions are stored in `mls\krylov` folder.

## References

Here are the original references for this test set.
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35 changes: 35 additions & 0 deletions julia/write_mls.jl
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@@ -0,0 +1,35 @@
using BenchmarkTools, HarwellRutherfordBoeing
using LinearAlgebra, SparseArrays, DelimitedFiles
using Krylov, Quadmath

function scale_ls!(A)
n, m = size(A)
s = ones(m)
for j = 1 : m
i = A.colptr[j]
k = A.colptr[j+1] - 1
nj = (i ≤ k) ? norm(A.nzval[i:k]) : 0.0
if nj > 0.0
A.nzval[i:k] ./= nj
s[j] = nj
end
end
return s
end

for pb in ("small", "small2", "medium", "medium2", "large", "large2", "very", "very2")
print("$pb: ")
A = RutherfordBoeingData("../rb/$(pb).rb").data
b = HarwellBoeingMatrix("../hb/$(pb).hb").rhs[:]
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HB = HarwellBoeingMatrix("../rb/$(pb).rb")
A = HB.matrix
b = HB.rhs[:,1]

is not working.

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You have to read a hb file.

s = scale_ls!(A)
A = Float128.(A)
b = Float128.(b)
M = A' * A
rhs = A' * b
x, stats = minres_qlp(M, rhs, rtol=Float128(1e-20), atol=Float128(1e-25))
println("✓")
x = Float64.(x)
open("../mls/krylov/$(pb)_scaled_mls.txt", "w") do io
writedlm(io, x)
end
end
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