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correct Huber formula
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python/benchmark/benchmark_Huber/README.md

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@@ -20,19 +20,19 @@ In this case, the ElasticHuber can be rewritten as a ReHLine optimization with
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```math
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\mathbf{S} \leftarrow
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\begin{pmatrix}
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-\sqrt{\frac{2}{n\lambda_2}} \mathbf{1}^\intercal_n & \mathbf{0}^\intercal_d \\
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\sqrt{\frac{2}{n\lambda_2}} \mathbf{1}^\intercal_n & \mathbf{0}^\intercal_d \\
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-\sqrt{\frac{1}{n\lambda_2}} \mathbf{1}^\intercal_n & \mathbf{0}^\intercal_d \\
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\sqrt{\frac{1}{n\lambda_2}} \mathbf{1}^\intercal_n & \mathbf{0}^\intercal_d \\
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\end{pmatrix}, \quad
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\mathbf{T} \leftarrow
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\begin{pmatrix}
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\sqrt{\frac{2}{n\lambda_2}} \mathbf{y}^\intercal & \mathbf{0}^\intercal_d \\
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-\sqrt{\frac{2}{n\lambda_2}} \mathbf{y}^\intercal & \mathbf{0}^\intercal_d \\
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\sqrt{\frac{1}{n\lambda_2}} \mathbf{y}^\intercal & \mathbf{0}^\intercal_d \\
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-\sqrt{\frac{1}{n\lambda_2}} \mathbf{y}^\intercal & \mathbf{0}^\intercal_d \\
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\end{pmatrix}, \quad
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\mathbf{\tau} \leftarrow
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\begin{pmatrix}
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\kappa \mathbf{1}^\intercal_n & \mathbf{0}^\intercal_d \\
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\kappa \sqrt{\frac{1}{n\lambda_2}} \mathbf{1}^\intercal_n & \mathbf{0}^\intercal_d \\
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\\
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\kappa \mathbf{1}^\intercal_n & \mathbf{0}^\intercal_d \\
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\kappa \sqrt{\frac{1}{n\lambda_2}} \mathbf{1}^\intercal_n & \mathbf{0}^\intercal_d \\
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\end{pmatrix},
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```
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