# TransportMaps.Maps.InverseTransportMapBase¶

## Module Contents¶

### Classes¶

 InverseTransportMap Given the transport map $$T$$, define $$S=T^{-1}$$.
class TransportMaps.Maps.InverseTransportMapBase.InverseTransportMap(**kwargs)[source]

Given the transport map $$T$$, define $$S=T^{-1}$$.

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

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

• precomp (dict) – dictionary of precomputed values

• idxs_slice (slice) – if precomputed values are present, this parameter indicates at which of the points to evaluate. The number of indices represented by idxs_slice must match x.shape[0].

Returns:

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

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

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

• precomp (dict) – dictionary of precomputed values

• idxs_slice (slice) – if precomputed values are present, this parameter indicates at which of the points to evaluate. The number of indices represented by idxs_slice must match x.shape[0].

Returns:

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

[Abstract] Compute: $$\nabla^2_{\bf x} \log \det \nabla_{\bf x} T({\bf x}, {\bf a})$$

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

• precomp (dict) – dictionary of precomputed values

• idxs_slice (slice) – if precomputed values are present, this parameter indicates at which of the points to evaluate. The number of indices represented by idxs_slice must match x.shape[0].

Returns:

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

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

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

• precomp (dict) – dictionary of precomputed values

• idxs_slice (slice) – if precomputed values are present, this parameter indicates at which of the points to evaluate. The number of indices represented by idxs_slice must match x.shape[0].

Returns:

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

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

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

• precomp (dict) – dictionary of precomputed values

• idxs_slice (slice) – if precomputed values are present, this parameter indicates at which of the points to evaluate. The number of indices represented by idxs_slice must match x.shape[0].

Returns:

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

[Abstract] Compute: $$\nabla^2_{\bf x} \log \det \nabla_{\bf x} T^{-1}({\bf x}, {\bf a})$$
• x (ndarray [$$m,d$$]) – evaluation points
• precomp (dict) – dictionary of precomputed values
• idxs_slice (slice) – if precomputed values are present, this parameter indicates at which of the points to evaluate. The number of indices represented by idxs_slice must match x.shape[0].
(ndarray [$$m,d,d$$]) – $$\nabla^2_{\bf x} \log \det \nabla_{\bf x} T^{-1}({\bf x}, {\bf a})$$ at every evaluation point