# TransportMaps.Maps.ListCompositeTransportMapBase¶

## Module Contents¶

### Classes¶

 ListCompositeTransportMap Composition of transport maps $$T({\bf x}) := T_1 \circ T_2 \circ \ldots \circ T_k({\bf x})$$. CompositeTransportMap Composition of two transport maps $$T({\bf x}) := T_1 \circ T_2$$.
class TransportMaps.Maps.ListCompositeTransportMapBase.ListCompositeTransportMap(**kwargs)[source]

Composition of transport maps $$T({\bf x}) := T_1 \circ T_2 \circ \ldots \circ T_k({\bf x})$$.

inverse(x, *args, **kwargs)[source]
Parameters:

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

Returns:

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

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

Parameters:

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

Returns:

(ndarray [$$m,d,d$$]) – gradient matrices for every evaluation point.

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

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

Parameters:
Returns:

(ndarray [$$m,d,d,d$$]) – Hessian matrices for every evaluation point and every dimension.

Raises:

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

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

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

Parameters:
Returns:

(ndarray [$$m,d,d,d$$]) – action of the Hessian matrices for every evaluation point and every dimension.

Raises:

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

Compute: $$\log \det \nabla_{\bf x} T({\bf x}, {\bf a})$$.

For the transport maps $$T_1,T_2$$,

$\log \det \nabla_{\bf x} (T_1 \circ T_2)({\bf x}) = \log \det \nabla_{\bf x} T_1 ({\bf y}) + \log \det \nabla_{\bf x} T_2({\bf x})$

where $${\bf y} = T_2({\bf x})$$.

Parameters:
Returns:

(ndarray [$$m$$]) – $$\log \det \nabla_{\bf x} T({\bf x}, {\bf a})$$ at every evaluation point

Compute: $$\nabla_{\bf x} \log \det \nabla_{\bf x} T({\bf x}, {\bf a})$$

Parameters:
Returns:

(ndarray [$$m,d$$]) – $$\nabla_{\bf x} \log \det \nabla_{\bf x} T({\bf x}, {\bf a})$$ at every evaluation point

Raises:

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

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

Parameters:
Returns:

(ndarray [$$m$$]) – $$\log \det \nabla_{\bf x} T^{-1}({\bf x}, {\bf a})$$ at every evaluation point

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

Parameters:
Returns:

(ndarray [$$m$$]) – $$\nabla_{\bf x} \log \det \nabla_{\bf x} T^{-1}({\bf x}, {\bf a})$$ at every evaluation point

class TransportMaps.Maps.ListCompositeTransportMapBase.CompositeTransportMap(t1, t2)[source]

Composition of two transport maps $$T({\bf x}) := T_1 \circ T_2$$.

Compute: $$\nabla^2_{\bf x} \log \det \nabla_{\bf x} T({\bf x})$$

For the transport maps $$T_1,T_2$$,

$\nabla^2_{\bf x} \log \det \nabla_{\bf x} (T_1 \circ T_2) = \left[ \nabla^2_{\bf x} \log \det (\nabla_{\bf x} T_1 \circ T_2) \cdot \nabla_{\bf x} T_2 + \nabla_{\bf x} \log \det \nabla_{\bf x} T_2 \right] \cdot (\nabla_{\bf x} T_2) + \nabla_{\bf x} \log \det (\nabla_{\bf x} T_1 \circ T_2) \cdot \nabla^2_{\bf x} T_2 + \nabla^2_{\bf x} \log \det \nabla_{\bf x} T_2$
Parameters:
Returns:

(ndarray [$$m,d,d$$]) – $$\nabla^2_{\bf x} \log \det \nabla_{\bf x} T({\bf x})$$ at every evaluation point

Raises:

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

log_det_grad_x() and grad_x_log_det_grad_x().

Compute: $$\langle\nabla^2_{\bf x} \log \det \nabla_{\bf x} T({\bf x}), \delta{\bf x}\rangle$$

Parameters:
Returns:

(ndarray [$$m,d$$]) –

$$\langle\nabla^2_{\bf x} \log \det \nabla_{\bf x} T({\bf x}), \delta{\bf x}\rangle$$ at every evaluation point

Raises:

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

Compute: $$\nabla^2_{\bf x} \log \det \nabla_{\bf x} T^{-1}({\bf x})$$

Parameters:
Returns:

(ndarray [$$m,d,d$$]) – $$\nabla^2_{\bf x} \log \det \nabla_{\bf x} T^{-1}({\bf x})$$ at every evaluation point

Raises:

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

log_det_grad_x() and grad_x_log_det_grad_x().

Compute: $$\langle\nabla^2_{\bf x} \log \det \nabla_{\bf x} T^{-1}({\bf x}), \delta{\bf x}\rangle$$

Parameters:
Returns:

(ndarray [$$m,d,d$$]) – $$\langle\nabla^2_{\bf x} \log \det \nabla_{\bf x} T^{-1}({\bf x}), \delta{\bf x}\rangle$$ at every evaluation point

Raises:

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

log_det_grad_x() and grad_x_log_det_grad_x().