Functions and operators

(Proximal) functions and operators.

class alpaqa._alpaqa.float64.functions.L1Norm

C++ documentation alpaqa::functions::L1Norm ℓ₁-norm regularizer (with a single scalar regularization factor).

See also

alpaqa._alpaqa.float64.prox()

__init__(self: alpaqa._alpaqa.float64.functions.L1Norm, λ: float = 1) → None

property λ

Regularization factor.

class alpaqa._alpaqa.float64.functions.L1NormElementwise

C++ documentation alpaqa::functions::L1NormElementwise ℓ₁-norm regularizer (with element-wise regularization factors).

See also

alpaqa._alpaqa.float64.prox()

__init__(*args, **kwargs)

Overloaded function.

1. __init__(self: alpaqa._alpaqa.float64.functions.L1NormElementwise) -> None

2. __init__(self: alpaqa._alpaqa.float64.functions.L1NormElementwise, λ: numpy.ndarray[numpy.float64[m, 1]]) -> None

property λ

Regularization factors.

class alpaqa._alpaqa.float64.functions.NuclearNorm

C++ documentation alpaqa::functions::NuclearNorm

property U

Left singular vectors.

property V

Right singular vectors.

__init__(*args, **kwargs)

Overloaded function.

1. __init__(self: alpaqa._alpaqa.float64.functions.NuclearNorm, λ: float) -> None

2. __init__(self: alpaqa._alpaqa.float64.functions.NuclearNorm, λ: float, rows: int, cols: int) -> None

property singular_values

Vector of singular values of the last output of the prox method.

See also

alpaqa._alpaqa.float64.prox()

property singular_values_input

Vector of singular values of the last input of the prox method.

property λ

Regularization factor.

alpaqa._alpaqa.float64.prox(*args, **kwargs)

Overloaded function.

1. prox(self: alpaqa._alpaqa.float64.functions.NuclearNorm, input: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], output: numpy.ndarray[numpy.float64[m, n], flags.writeable, flags.f_contiguous], γ: float = 1) -> float

C++ documentation: alpaqa::prox Compute the proximal mapping of self at in with step size γ. This version overwrites the given output arguments.

See also

alpaqa._alpaqa.float64.prox_step()

2. prox(self: alpaqa._alpaqa.float64.functions.NuclearNorm, input: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], γ: float = 1) -> Tuple[float, numpy.ndarray[numpy.float64[m, n]]]

C++ documentation: alpaqa::prox Compute the proximal mapping of self at in with step size γ. This version returns the outputs as a tuple.

See also

alpaqa._alpaqa.float64.prox_step()

3. prox(self: alpaqa._alpaqa.float64.functions.L1Norm, input: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], output: numpy.ndarray[numpy.float64[m, n], flags.writeable, flags.f_contiguous], γ: float = 1) -> float

C++ documentation: alpaqa::prox Compute the proximal mapping of self at in with step size γ. This version overwrites the given output arguments.

See also

alpaqa._alpaqa.float64.prox_step()

4. prox(self: alpaqa._alpaqa.float64.functions.L1Norm, input: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], γ: float = 1) -> Tuple[float, numpy.ndarray[numpy.float64[m, n]]]

C++ documentation: alpaqa::prox Compute the proximal mapping of self at in with step size γ. This version returns the outputs as a tuple.

See also

alpaqa._alpaqa.float64.prox_step()

5. prox(self: alpaqa._alpaqa.float64.functions.L1NormElementwise, input: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], output: numpy.ndarray[numpy.float64[m, n], flags.writeable, flags.f_contiguous], γ: float = 1) -> float

C++ documentation: alpaqa::prox Compute the proximal mapping of self at in with step size γ. This version overwrites the given output arguments.

See also

alpaqa._alpaqa.float64.prox_step()

6. prox(self: alpaqa._alpaqa.float64.functions.L1NormElementwise, input: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], γ: float = 1) -> Tuple[float, numpy.ndarray[numpy.float64[m, n]]]

C++ documentation: alpaqa::prox Compute the proximal mapping of self at in with step size γ. This version returns the outputs as a tuple.

See also

alpaqa._alpaqa.float64.prox_step()

7. prox(self: alpaqa._alpaqa.float64.Box, input: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], output: numpy.ndarray[numpy.float64[m, n], flags.writeable, flags.f_contiguous], γ: float = 1) -> float

C++ documentation: alpaqa::prox Compute the proximal mapping of self at in with step size γ. This version overwrites the given output arguments.

See also

alpaqa._alpaqa.float64.prox_step()

8. prox(self: alpaqa._alpaqa.float64.Box, input: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], γ: float = 1) -> Tuple[float, numpy.ndarray[numpy.float64[m, n]]]

C++ documentation: alpaqa::prox Compute the proximal mapping of self at in with step size γ. This version returns the outputs as a tuple.

See also

alpaqa._alpaqa.float64.prox_step()

alpaqa._alpaqa.float64.prox_step(*args, **kwargs)

Overloaded function.

1. prox_step(self: alpaqa._alpaqa.float64.functions.NuclearNorm, input: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], input_step: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], output: numpy.ndarray[numpy.float64[m, n], flags.writeable, flags.f_contiguous], output_step: numpy.ndarray[numpy.float64[m, n], flags.writeable, flags.f_contiguous], γ: float = 1, γ_step: float = -1) -> float

C++ documentation: alpaqa::prox_step Compute a generalized forward-backward step. This version overwrites the given output arguments.

See also

alpaqa._alpaqa.float64.prox()

2. prox_step(self: alpaqa._alpaqa.float64.functions.NuclearNorm, input: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], input_step: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], γ: float = 1, γ_step: float = -1) -> Tuple[float, numpy.ndarray[numpy.float64[m, n]], numpy.ndarray[numpy.float64[m, n]]]

C++ documentation: alpaqa::prox_step Compute a generalized forward-backward step. This version returns the outputs as a tuple.

See also

alpaqa._alpaqa.float64.prox()

3. prox_step(self: alpaqa._alpaqa.float64.functions.L1Norm, input: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], input_step: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], output: numpy.ndarray[numpy.float64[m, n], flags.writeable, flags.f_contiguous], output_step: numpy.ndarray[numpy.float64[m, n], flags.writeable, flags.f_contiguous], γ: float = 1, γ_step: float = -1) -> float

C++ documentation: alpaqa::prox_step Compute a generalized forward-backward step. This version overwrites the given output arguments.

See also

alpaqa._alpaqa.float64.prox()

4. prox_step(self: alpaqa._alpaqa.float64.functions.L1Norm, input: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], input_step: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], γ: float = 1, γ_step: float = -1) -> Tuple[float, numpy.ndarray[numpy.float64[m, n]], numpy.ndarray[numpy.float64[m, n]]]

C++ documentation: alpaqa::prox_step Compute a generalized forward-backward step. This version returns the outputs as a tuple.

See also

alpaqa._alpaqa.float64.prox()

5. prox_step(self: alpaqa._alpaqa.float64.functions.L1NormElementwise, input: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], input_step: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], output: numpy.ndarray[numpy.float64[m, n], flags.writeable, flags.f_contiguous], output_step: numpy.ndarray[numpy.float64[m, n], flags.writeable, flags.f_contiguous], γ: float = 1, γ_step: float = -1) -> float

C++ documentation: alpaqa::prox_step Compute a generalized forward-backward step. This version overwrites the given output arguments.

See also

alpaqa._alpaqa.float64.prox()

6. prox_step(self: alpaqa._alpaqa.float64.functions.L1NormElementwise, input: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], input_step: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], γ: float = 1, γ_step: float = -1) -> Tuple[float, numpy.ndarray[numpy.float64[m, n]], numpy.ndarray[numpy.float64[m, n]]]

C++ documentation: alpaqa::prox_step Compute a generalized forward-backward step. This version returns the outputs as a tuple.

See also

alpaqa._alpaqa.float64.prox()

7. prox_step(self: alpaqa._alpaqa.float64.Box, input: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], input_step: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], output: numpy.ndarray[numpy.float64[m, n], flags.writeable, flags.f_contiguous], output_step: numpy.ndarray[numpy.float64[m, n], flags.writeable, flags.f_contiguous], γ: float = 1, γ_step: float = -1) -> float

C++ documentation: alpaqa::prox_step Compute a generalized forward-backward step. This version overwrites the given output arguments.

See also

alpaqa._alpaqa.float64.prox()

8. prox_step(self: alpaqa._alpaqa.float64.Box, input: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], input_step: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], γ: float = 1, γ_step: float = -1) -> Tuple[float, numpy.ndarray[numpy.float64[m, n]], numpy.ndarray[numpy.float64[m, n]]]

C++ documentation: alpaqa::prox_step Compute a generalized forward-backward step. This version returns the outputs as a tuple.

See also

alpaqa._alpaqa.float64.prox()