docs update

docs/CHANGELOG.md

@@ -7,7 +7,9 @@ Remember to align the itemized text with the first line of an item within a list
 
 ## EMLP 0.8.0 (Unreleased)
 
-<!-- * New features:
-  * {func}`jax.scipy.stats.chi2` is now available as a distribution with logpdf and pdf methods.
-  * {func}`jax.scipy.stats.betabinom` is now available as a distribution with logpmf and pmf methods.
-  * -->
+* New features:
+  * Fallback autograd jvp implementation of drho to make implementing new reps easier.
+  * Mixed group representations (now working and tested)
+  * Experimental support of complex groups and representations
+* Bug Fixes:
+  * Element ordering of mixed groups is now correctly maintained in the soln

docs/index.rst

@@ -22,8 +22,8 @@ A type system for the automated construction of equivariant layers.
    :maxdepth: 1
    :caption: Advanced Features
 
-   notebooks/mixed_tensors.md
    notebooks/new_representations.md
+   notebooks/mixed_tensors.md
    notebooks/multilinear_maps.md
 
 .. toctree::

docs/notebooks/new_representations.ipynb

@@ -11,7 +11,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "As our solver treats objects very generally, implementing new representations is surprisingly easy. To implement a new [`Representation`](https://emlp.readthedocs.io/en/latest/package/emlp.solver.representation.html#emlp.models.solver.representation.Rep) you need to implement `size()` which is the dimension of the representation, `rho(M)` which is a mapping from the group elements to the representation matrix, as well `__eq__` and `__hash__` to distinguish different representations. It's also a good idea to implement a `__str__` function to improve readability. All representations implemented this way should have the `.G` attribute specifying the symmetry group.\n",
+    "As our solver treats objects very generally, implementing new representations is surprisingly easy. To implement a new [Representation](https://emlp.readthedocs.io/en/latest/package/emlp.solver.representation.html#emlp.models.solver.representation.Rep) you need to implement `size()` which is the dimension of the representation, `rho(M)` which is a mapping from the group elements to the representation matrix, as well `__eq__` and `__hash__` to distinguish different representations. It's also a good idea to implement a `__str__` function to improve readability. All representations implemented this way should have the `.G` attribute specifying the symmetry group.\n",
     "\n",
     "The implementation also requires you to specify whether the representation is regular (whether `rho(M)` outputs a permutaiton matrix) with the `is_regular` attribute, and also the `.T` property that returns the dual of the representation. We plan on removing these two requirements in a later release."
    ]

docs/notebooks/quickstart.ipynb

@@ -731,7 +731,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Representations that have many copies or multiplicity of a given representation type, such as for the many channels in a neural network, are simply examples of the $\\oplus$ operator (`+` in python). The `rep.symmetric_basis()` and `rep.symmetric_projector()` can return lazy matrices $Q$ and $P=QQ^T$ when the representations are composite (or when the representation is specified lazily). [implementation change is making this much slower than normal, using smaller values]"
+    "Representations that have many copies or multiplicity of a given representation type, such as for the many channels in a neural network, are simply examples of the $\\oplus$ operator (`+` in python). The `rep.symmetric_basis()` and `rep.symmetric_projector()` can return lazy matrices $Q$ and $P=QQ^T$ when the representations are composite (or when the representation is specified lazily). These Lazy matrices are modeled after [scipy LinearOperators](https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.LinearOperator.html). By exploiting structure in the matrices via fast matrix vector multiplies (MVMs), it can be possible to work with extremely large matrices."
    ]
   },
   {
@@ -770,7 +770,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "These Lazy matrices are modeled after [scipy LinearOperators](https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.LinearOperator.html). Unfortunately the larger matrices are harder to visualize as for the matrix above we need 84000 different colors! We are happy to field suggestions for visualizing very large bases."
+    "Unfortunately the larger matrices are harder to visualize as for the matrix above we need 84000 different colors! We are happy to field suggestions for visualizing very large bases."
    ]
   },
   {