docs!: implement relativistic K-matrix

.cspell.json

@@ -112,6 +112,7 @@
         "darkred",
         "displaystyle",
         "dotprint",
+        "elif",
         "evaluatable",
         "expertsystem",
         "facecolor",
@@ -160,6 +161,7 @@
         "pcolormesh",
         "pdg's",
         "phsp",
+        "pmatrix",
         "preorder",
         "py's",
         "pygments",

.pre-commit-config.yaml

@@ -49,6 +49,7 @@ repos:
             docs/report/005.*|
             docs/report/006.*|
             docs/report/007.*|
+            docs/report/009.*|
             demo/.*
           )$
 

docs/report/005.ipynb

@@ -22,7 +22,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "This report investigates how to implement non-relativistic $K$-matrix dynamics with {doc}`SymPy <sympy:index>`. The non-relativistic case is simplest and allows us to check whether the case $n_R=1, n=1$ (single resonance, single channel) reduces to a non-relativistic Breit-Wigner function.[^1] We followed the physics as described by {pdg-review}`Resonances` and {cite}`chungPartialWaveAnalysis1995,petersPartialWaveAnalysis2004,meyerMatrixTutorial2008`.\n",
+    "This report investigates how to implement non-relativistic $K$-matrix dynamics with {doc}`SymPy <sympy:index>`. The non-relativistic case is simplest and allows us to check whether the case $n_R=1, n=1$ (single resonance, single channel) reduces to a non-relativistic Breit-Wigner function.[^1] We followed the physics as described by {pdg-review}`Resonances` and {cite}`chungPartialWaveAnalysis1995,petersPartialWaveAnalysis2004,meyerMatrixTutorial2008`. For the relativistic version, see {doc}`/report/009`.\n",
     "\n",
     "[^1]: Of course, there is no need to work with matrices in this $1 \\times 1$ case. To keeps things general, however, we keep using matrices.\n",
     "\n",
@@ -462,7 +462,7 @@
     "    m0_values = m0_values[1:-1]\n",
     "\n",
     "    def set_default_values():\n",
-    "        sliders.set_ranges({\"i\": (0, n_resonances - 1)})\n",
+    "        sliders.set_ranges({\"i\": (0, n_channels - 1)})\n",
     "        for R in range(n_resonances):\n",
     "            # ranges\n",
     "            sliders.set_ranges({f\"m{R}\": (0, 3, 100)})\n",
@@ -488,6 +488,9 @@
     "        sharex=True,\n",
     "        tight_layout=True,\n",
     "    )\n",
+    "    fig.canvas.toolbar_visible = False\n",
+    "    fig.canvas.header_visible = False\n",
+    "    fig.canvas.footer_visible = False\n",
     "    if not title:\n",
     "        title = (\n",
     "            fR\"${n_channels} \\times {n_channels}$ $K$-matrix\"\n",
@@ -527,19 +530,28 @@
     "\n",
     "    # 3D plot\n",
     "    def plot3(**kwargs):\n",
+    "        imag_real = kwargs.pop(\"imag_real\")\n",
     "        Z = np_expr(plot_domain_complex, **kwargs)\n",
-    "        Z_imag = cut_off_min(cut_off_max(Z.imag))\n",
+    "        if imag_real == \"imag\":\n",
+    "            Z_values = Z.imag\n",
+    "            ax_title = \"Re $T$\"\n",
+    "        elif imag_real == \"real\":\n",
+    "            Z_values = Z.real\n",
+    "            ax_title = \"Im $T$\"\n",
+    "        elif imag_real == \"abs\":\n",
+    "            Z_values = np.abs(Z)\n",
+    "            ax_title = \"$|T|$\"\n",
+    "        else:\n",
+    "            raise NotImplementedError\n",
+    "        Z_values = cut_off_min(cut_off_max(Z_values))\n",
     "        for ax in axes[1:]:\n",
     "            ax.clear()\n",
-    "        axes[-1].pcolormesh(X, Y, Z_imag, cmap=cm.coolwarm)\n",
-    "        if kwargs[\"i\"] == 1:\n",
-    "            axes[-1].set_title(\"Im $T$\")\n",
+    "        axes[-1].pcolormesh(X, Y, Z_values, cmap=cm.coolwarm)\n",
+    "        i = kwargs[\"i\"]\n",
+    "        if n_channels == 1:\n",
+    "            axes[-1].set_title(ax_title)\n",
     "        else:\n",
-    "            axes[-1].set_title(f\"Im $T$, channel {i}\")\n",
-    "        if len(axes) == 3:\n",
-    "            Z_real = cut_off_min(cut_off_max(Z.real))\n",
-    "            axes[-2].pcolormesh(X, Y, Z_real, cmap=cm.coolwarm)\n",
-    "            axes[-2].set_title(\"Re $T$\")\n",
+    "            axes[-1].set_title(f\"{ax_title}, channel {i}\")\n",
     "        for ax in axes[1:]:\n",
     "            ax.axhline(0, linewidth=0.5, c=\"black\", linestyle=\"dotted\")\n",
     "            for R in range(n_resonances):\n",
@@ -560,6 +572,14 @@
     "        axes[-1].set_xlabel(\"Re $m$\")\n",
     "        fig.canvas.draw_idle()\n",
     "\n",
+    "    # Create switch for imag/real/abs\n",
+    "    name = \"imag_real\"\n",
+    "    sliders._sliders[name] = ipywidgets.RadioButtons(\n",
+    "        options=[\"imag\", \"real\", \"abs\"],\n",
+    "        description=\"$s$-plane plot\",\n",
+    "    )\n",
+    "    sliders._arg_to_symbol[name] = name\n",
+    "\n",
     "    # Create GUI\n",
     "    sliders_copy = dict(sliders)\n",
     "    h_boxes = []\n",
@@ -576,32 +596,31 @@
     "    remaining_sliders = sorted(\n",
     "        sliders_copy.values(), key=lambda s: s.description\n",
     "    )\n",
+    "    if n_channels == 1:\n",
+    "        remaining_sliders.remove(sliders[\"i\"])\n",
     "    ui = ipywidgets.VBox(h_boxes + remaining_sliders)\n",
     "    output = ipywidgets.interactive_output(plot3, controls=sliders)\n",
     "    display(ui, output)"
    ]
   },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "{{ run_interactive }}"
-   ]
-  },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {
-    "tags": [
-     "remove-output",
-     "hide-input"
-    ]
+    "tags": []
    },
    "outputs": [],
    "source": [
     "plot_k_matrix(n_resonances=3, n_channels=1)"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "{{ run_interactive }}"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
@@ -621,19 +640,11 @@
     "    display(Image(output_file))"
    ]
   },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "{{ run_interactive }}"
-   ]
-  },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {
     "tags": [
-     "hide-input",
      "remove-output"
     ]
    },
@@ -642,6 +653,13 @@
     "plot_k_matrix(n_resonances=2, n_channels=2)"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "{{ run_interactive }}"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,