CLN: update example notebook formatting, add custom basis to basis comparison

Author: yb6599

examples/OPTI-TWIST_constrained_sensing.ipynb

@@ -919,7 +919,7 @@
     "2. Change the `l1_penalty` parameter. This affects the strength of the regularization applied when finding sensor locations. If `n_sensors` is not passed to the `SSPOC` constructor, then the value of `l1_penalty` can affect the number of sensors that are selected. You can also tune the `threshold` parameter to further affect the sensor count.\n",
     "3. Update `n_sensors` after fitting. Use the `update_sensors` function to do so. It is recommended that you also pass in the training and test data so that the classifier can be refit using the new sensors.\n",
     "\n",
-    "See the [classification notebook](http://localhost:8888/notebooks/examples/classification.ipynb) for more information."
+    "See the [classification notebook](https://python-sensors.readthedocs.io/en/latest/examples/classification.html) for more information."
    ]
   },
   {

examples/Olivetti_constrained_sensing.ipynb

@@ -164,7 +164,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Unconstrained optimization of sensor placement:\n",
+    "## Unconstrained sensor placement:\n",
     "\n",
     "Consider the case where we treat all sensor locations as being equally viable."
    ]
@@ -469,7 +469,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## The exact_n case: "
+    "## The exact_n case"
    ]
   },
   {
@@ -913,7 +913,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Reconstruct image from test set using sensors placed via constrained (exact_n) optimizer"
+    "### Reconstruct image from test set using sensors placed via constrained (exact_n) optimizer"
    ]
   },
   {
@@ -1186,7 +1186,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## The max_n case: \n",
+    "## The max_n case\n",
     "\n",
     "#### Max_n employs the same strategy as exact_n when: (results are identical)\n",
     "- The QR optimizer (unconstrained) places more than (n_const_sensors) in the constrained region, which violates the desired constraint.\n",
@@ -1340,7 +1340,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## The predetermined case: \n",
+    "## The predetermined case\n",
     "\n",
     "- This occurs when (n_pre_sensors) locations are already specified and we want the best locations to place the remaining sensors. \n",
     "\n",
@@ -1877,7 +1877,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Reconstruct image from test set using sensors placed via predetermined optimizer"
+    "### Reconstruct image from test set using sensors placed via predetermined optimizer"
    ]
   },
   {
@@ -1986,7 +1986,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## The distance constrained case:\n",
+    "## The distance constrained case\n",
     "- This occurs when we want to place sensors a certain distance (radius (r)) away from each other.\n",
     "\n",
     "#### Suppose we want to places sensors 7 units away from each other to reconstruct the Olivetti Faces Dataset."