# TransportMaps.Maps.AffineMapBase¶

## Module Contents¶

### Classes¶

 AffineMap Affine map $$T[{\bf c},{\bf L}]({\bf x})={\bf c} + {\bf L}{\bf x}$$ LinearMap Affine map $$T[{\bf c},{\bf L}]({\bf x})={\bf c} + {\bf L}{\bf x}$$
class TransportMaps.Maps.AffineMapBase.AffineMap(**kwargs)[source]

Affine map $$T[{\bf c},{\bf L}]({\bf x})={\bf c} + {\bf L}{\bf x}$$

property Linv[source]
property c[source]

The constant term $${\bf c}$$

property L[source]

The linear term $${\bf L}$$

property coeffs[source]

Returns the constant and linear term of the linear map.

Returns:

(ndarray) –

flattened array of coefficients

evaluate(x, *args, **kwargs)[source]

Evaluate the map at the points $${\bf x} \in \mathbb{R}^{m \times d_{\text{in}}}$$.

Parameters:

x (ndarray [$$m,d_{\text{in}}$$]) – evaluation points

Returns:

(ndarray [$$m,d_{\text{out}}$$]) – transformed points

Raises:

ValueError – if $$d_{\text{in}}$$ does not match the dimension of the transport map.

Evaluate the gradient (constant for linear maps)

Parameters:

x (ndarray [$$m,d_{\text{in}}$$]) – evaluation points

Returns:

(ndarray [$$m, d_{\text{out}},d_{\text{in}}$$]) –

gradient matrix (constant at every evaluation point).

Raises:

ValueError – if $$d_{\text{in}}$$ does not match the dimension of the transport map.

Evaluate the function and gradient (constant for linear maps)

Parameters:

x (ndarray [$$m,d_{\text{in}}$$]) – evaluation points

Returns:

(tuple) –

Raises:

ValueError – if $$d_{\text{in}}$$ does not match the dimension of the transport map.

hess_x(x, *args, **kwargs)[source]

Evaluate the Hessian for the linear map (zero)

Parameters:

x (ndarray [$$m,d_{\text{in}}$$]) – evaluation points

Returns:

(ndarray [$$m,d_{\text{out},d_{\text{in}},d_{\text{in}}$$]) – Hessian matrix (zero everywhere).

Raises:

ValueError – if $$d_{\text{in}}$$ does not match the dimension of the transport map.

action_hess_x(x, dx, *args, **kwargs)[source]

Evaluate the action of the Hessian for the linear map (zero)

Parameters:
Returns:

(ndarray [$$m,d_{\text{out}},d_{\text{in}}$$]) –

action of the Hessian matrix (zero everywhere).

Raises:

ValueError – if $$d_{\text{in}}$$ does not match the dimension of the transport map.

inverse(y, *args, **kwargs)[source]

Compute the pseudoinverse map $$\hat{T}^{-1}({\bf y},{\bf a})$$

Parameters:

y (ndarray [$$m,d$$]) – evaluation points

Returns:

(ndarray [$$m,d$$]) – $$\hat{T}^{-1}({\bf y},{\bf a})$$ for every evaluation point

Compute $$\nabla_{\bf x} \hat{T}^{-1}({\bf x},{\bf a})$$.

Parameters:

x (ndarray [$$m,d$$]) – evaluation points

Returns:

(ndarray [$$d,d$$]) – gradient matrix (constant at every evaluation point).

Raises:

ValueError – if $$d$$ does not match the dimension of the transport map.

hess_x_inverse(x, *args, **kwargs)[source]

Compute $$\nabla^2_{\bf x} \hat{T}^{-1}({\bf x},{\bf a})$$.

Parameters:

x (ndarray [$$m,d$$]) – evaluation points

Returns:

(ndarray [$$d,d,d$$]) – Hessian matrix (zero everywhere).

Raises:

ValueError – if $$d$$ does not match the dimension of the transport map.

action_hess_x_inverse(x, dx, *args, **kwargs)[source]

Compute $$\langle\nabla^2_{\bf x} \hat{T}^{-1}({\bf x},{\bf a}), \delta{\bf x}\rangle$$.

Parameters:
Returns:

(ndarray [$$d,d$$]) – action of Hessian matrix (zero everywhere).

Raises:

ValueError – if $$d$$ does not match the dimension of the transport map.

class TransportMaps.Maps.AffineMapBase.LinearMap(c, L, Linv=None)[source]

Bases: AffineMap

Affine map $$T[{\bf c},{\bf L}]({\bf x})={\bf c} + {\bf L}{\bf x}$$