Package parsimony :: Package datasets :: Package simulate :: Module grad

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Module grad

source code

Created on Thu Sep 26 12:06:07 2013

Author: Tommy Löfstedt, Edouard Duchesnay

License: BSD 3-clause.

Classes

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Function

SmoothedL1

L2Squared

NesterovFunction

TotalVariation

GroupLasso

SmoothedTotalVariation

SmoothedGroupLasso

SmoothedGroupTotalVariation

Functions

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grad_l1(beta, rng=RandomUniform(-1,1))
Sub-gradient of the function

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grad_l1mu(beta, mu)
Gradient of the function

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grad_l2(beta, rng=RandomUniform(0,1))
Sub-gradient of the function

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grad_l2_squared(beta, rng=None)
Gradient of the function

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grad_tv(beta, A, rng=RandomUniform(0,1))

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grad_gl(beta, A, rng=RandomUniform(-1,1))

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grad_tvmu(beta, A, mu)

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grad_glmu(beta, A, mu)

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grad_grouptvmu(beta, A, mu)

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_Nesterov_GroupTV_project(a)
Projection onto the compact space of the smoothed Group TV function.

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_Nesterov_grad(beta, A, rng=RandomUniform(-1,1), grad_norm=<function grad_l2 at 0x32d49b0>)

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_Nesterov_grad_smoothed(A, alpha)

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_Nestetov_alpha(beta, A, mu, proj)
Dual variable of the Nesterov function.

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_Nesterov_project(alpha)

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_Nesterov_TV_project(alpha)
Projection onto the compact space of the smoothed TV function.

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Variables

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__package__ = 'parsimony.datasets.simulate'

Function Details

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grad_l1(beta, rng=RandomUniform(-1,1))

source code

Sub-gradient of the function

    f(x) = |x|_1,

where |x|_1 is the L1-norm.

grad_l1mu(beta, mu)

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Gradient of the function

    f(x) = L1(mu, x),

where L1(mu, x) is the Nesterov smoothed L1-norm.

grad_l2(beta, rng=RandomUniform(0,1))

source code

Sub-gradient of the function

    f(x) = |x|_2,

where |x|_2 is the L2-norm.

grad_l2_squared(beta, rng=None)

source code

Gradient of the function

    f(x) = (1 / 2) * |x|²_2,

where |x|²_2 is the squared L2-norm.