tlm_adjoint.markers

Module Contents

class tlm_adjoint.markers.ControlsMarker(M)

Represents

\[m = m_\text{input},\]

where \(m\) is the control and \(m_\text{input}\) the input value for the control. The forward residual is defined

\[\mathcal{F} \left( m \right) = m - m_\text{input}.\]

Parameters:

M – A variable or a Sequence of variables defining the control \(m\). May be static.

adjoint_jacobian_solve(adj_X, nl_deps, B)

Compute an adjoint solution.

Parameters:

• adj_X – Either None, or a variable (if the adjoint solution has a single component) or Sequence of variables (otherwise) defining the initial guess for an iterative solve. May be modified or returned. Subclasses may replace this argument with adj_x if the adjoint solution has a single component.

• nl_deps – A Sequence of variables defining values for non-linear dependencies. Should not be modified.

• B – The right-hand-side. A variable (if the adjoint solution has a single component) or Sequence of variables (otherwise) storing the value of the right-hand-side. May be modified or returned. Subclasses may replace this argument with b if the adjoint solution has a single component.

Returns:

A variable or Sequence of variables storing the value of the adjoint solution. May return None to indicate a value of zero.

class tlm_adjoint.markers.FunctionalMarker(J)

Represents

\[J_\text{output} = J,\]

where \(J\) is the functional and \(J_\text{output}\) is the output value for the functional. The forward residual is defined

\[\mathcal{F} \left( J_\text{output}, J \right) = J_\text{output} - J.\]

Parameters:

J – A variable defining the functional \(J\).

adjoint_derivative_action(nl_deps, dep_index, adj_x)

Return the action of the adjoint of a derivative of the forward residual on the adjoint solution. This is the negative of an adjoint right-hand-side term.

Parameters:

• nl_deps – A Sequence of variables defining values for non-linear dependencies. Should not be modified.

• dep_index – An int. The derivative is defined by differentiation of the forward residual with respect to self.dependencies()[dep_index].

• adj_X – The adjoint solution. A variable if the adjoint solution has a single component, otherwise a Sequence of variables. Should not be modified. Subclasses may replace this argument with adj_x if the adjoint solution has a single component.

Returns:

The action of the adjoint of a derivative on the adjoint solution. Will be passed to subtract_adjoint_derivative_action(), and valid types depend upon the adjoint variable type. Typically this will be a variable, or a two element tuple (alpha, F), where alpha is a numbers.Complex and F a variable, with the value defined by the product of alpha and F.

adjoint_jacobian_solve(adj_x, nl_deps, b)

Compute an adjoint solution.

Parameters:

• adj_X – Either None, or a variable (if the adjoint solution has a single component) or Sequence of variables (otherwise) defining the initial guess for an iterative solve. May be modified or returned. Subclasses may replace this argument with adj_x if the adjoint solution has a single component.

• nl_deps – A Sequence of variables defining values for non-linear dependencies. Should not be modified.

• B – The right-hand-side. A variable (if the adjoint solution has a single component) or Sequence of variables (otherwise) storing the value of the right-hand-side. May be modified or returned. Subclasses may replace this argument with b if the adjoint solution has a single component.

Returns:

A variable or Sequence of variables storing the value of the adjoint solution. May return None to indicate a value of zero.