Hi, I’m trying to use a simple OLS solution to an overdetermined linear system using MKL and LinearAlgebra, with coefficient matrix
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M = [200000 0 0 (2e5)^2 0; 0 0 0 0 0; 0 0 0 0 0; 0 0 0 0 0; 0 2e5 0 0 (2e5)^2; 0 0 3e5 0 (3e5)^2]
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and observation
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y = [2e5 0 0 0 4e5 9e5]
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When I try to get the ols solution of the system with
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(M’ * M)^(-1) * M’ * y’
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the output is
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5×1 Matrix{Float64}:
1.9780612128670327
3.969978473845913
2.0318402149168833
9.652545605920437e-6
5.091301176166074e-6
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but this is incorrect. In particular, if I first store the result
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u = (M’ * M)^(-1) * M’
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and then compute
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u * y’
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the output is instead
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5×1 Matrix{Float64}:
1.3066744941170327
0.645027301970913
1.7964886524168833
1.436876312377322e-5
-5.193294015312655e-6
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Any pointers on what I am doing wrong/why this is happening?