@@ -81,7 +81,7 @@ Consider now the function signatures of the symbols in :eq:`eq:djdm`. Here we ar
8181only concerned with the arguments, as these determine the sizes of the
8282resulting assembled tensors:
8383
84- .. math ::
84+ .. math ::
8585 :label:
8686
8787 \frac {\mathrm {d}\hat {J}}{\mathrm {d}m}: M\rightarrow \mathbb {R}
@@ -102,16 +102,16 @@ Instead, we define:
102102
103103.. math ::
104104 :label: eq:adjoint
105-
105+
106106 \lambda ^*(\in V\rightarrow \mathbb {R}) = -\frac {\partial J}{\partial u}\frac {\partial f}{\partial u}^{-1 }.
107107
108108 We actually solve the adjoint to this equation. That is find `\lambda \in V `
109- such that:
109+ such that:
110110
111111.. math ::
112112 :label:
113113
114- \frac {\partial f}{\partial u}^{*}(u, m; \lambda , v) =
114+ \frac {\partial f}{\partial u}^{*}(u, m; \lambda , v) =
115115 -\frac {\partial J}{\partial u}(u, m; v) \qquad \forall v \in V.
116116
117117 Note that these terms include `u `, so it is first necessary to solve
@@ -144,8 +144,8 @@ How Firedrake and Pyadjoint automate derivative calculation
144144-----------------------------------------------------------
145145
146146Firedrake automates the process in the preceding section using the methodology
147- first published in :cite: `Farrell2013 ` using the implementation in
148- `Pyadjoint <https://pyadjoint.org >`__ :cite: `Mitusch2019 `.
147+ first published in :cite: `Farrell2013 ` using the implementation in
148+ `Pyadjoint <https://pyadjoint.org >`__ :cite: `Mitusch2019 `.
149149
150150The essence of this process is:
151151
@@ -273,7 +273,7 @@ The sequence of recorded operations is stored on an object called the tape. The
273273currently active tape can be accessed by calling
274274:func: `~pyadjoint.get_working_tape `. The user usually has limited direct
275275interaction with the tape, but there is some useful information which can be
276- extracted.
276+ extracted.
277277
278278Visualising the tape
279279~~~~~~~~~~~~~~~~~~~~
@@ -289,11 +289,11 @@ are to be found on `the pygraphviz website
289289
290290.. _fig-tape :
291291
292- .. figure :: images/tape.pdf
292+ .. figure :: images/tape.svg
293293
294294 A visualisation of the Burgers equation example above shortened to a single
295295 timestep. Operations (blocks) recorded on the tape are shown as grey
296- rectangles, while taped variables are shown as ovals.
296+ rectangles, while taped variables are shown as ovals.
297297
298298The numbered blocks in the tape visualisation are as follows:
299299
@@ -423,4 +423,4 @@ themselves with this since annotated operations will return overloaded types.
423423 :filter: False
424424
425425 Farrell2013
426- Mitusch2019
426+ Mitusch2019
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