From bc8b887455080ea7dc93dbf83a1d3abeb2c564b8 Mon Sep 17 00:00:00 2001
From: kevinsung <kevinsung@users.noreply.github.com>
Date: Sat, 23 Sep 2023 01:21:21 +0000
Subject: [PATCH] deploy: 578cb50d3d50e7666761f5a1bd40f7d08d443d7c

---
 .doctrees/api/generated/ffsim.linalg.doctree  | Bin 130631 -> 128466 bytes
 .doctrees/environment.pickle                  | Bin 1511252 -> 1508209 bytes
 .../nbsphinx/tutorials/01-introduction.ipynb  |  24 ++--
 .../tutorials/02-orbital-rotation.ipynb       |  32 ++---
 .../tutorials/03-double-factorized.ipynb      |  80 ++++++------
 .doctrees/nbsphinx/tutorials/04-lucj.ipynb    |  32 ++---
 _modules/ffsim/gates/orbital_rotation.html    |  17 +--
 _modules/ffsim/linalg/givens.html             | 116 ++++++++----------
 api/generated/ffsim.html                      |   2 +-
 api/generated/ffsim.linalg.html               |  44 ++-----
 genindex.html                                 |  10 +-
 objects.inv                                   | Bin 4310 -> 4313 bytes
 searchindex.js                                |   2 +-
 tutorials/01-introduction.ipynb               |  24 ++--
 tutorials/02-orbital-rotation.ipynb           |  32 ++---
 tutorials/03-double-factorized.ipynb          |  80 ++++++------
 tutorials/04-lucj.ipynb                       |  32 ++---
 17 files changed, 246 insertions(+), 281 deletions(-)

diff --git a/.doctrees/api/generated/ffsim.linalg.doctree b/.doctrees/api/generated/ffsim.linalg.doctree
index 87cfbc122cd1801b3c2298fc6ae4d09965fc8a17..e7f0329cd7f6cf683b0ea3e5465cf4871fa75991 100644
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diff --git a/.doctrees/environment.pickle b/.doctrees/environment.pickle
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diff --git a/.doctrees/nbsphinx/tutorials/01-introduction.ipynb b/.doctrees/nbsphinx/tutorials/01-introduction.ipynb
index b8b0526e1..e7096502b 100644
--- a/.doctrees/nbsphinx/tutorials/01-introduction.ipynb
+++ b/.doctrees/nbsphinx/tutorials/01-introduction.ipynb
@@ -16,10 +16,10 @@
    "execution_count": 1,
    "metadata": {
     "execution": {
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-     "iopub.status.busy": "2023-09-22T21:03:16.279424Z",
-     "iopub.status.idle": "2023-09-22T21:03:16.582247Z",
-     "shell.execute_reply": "2023-09-22T21:03:16.581675Z"
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    },
    "outputs": [],
@@ -62,10 +62,10 @@
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@@ -92,10 +92,10 @@
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     }
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    "outputs": [],
diff --git a/.doctrees/nbsphinx/tutorials/02-orbital-rotation.ipynb b/.doctrees/nbsphinx/tutorials/02-orbital-rotation.ipynb
index 7ee0c5f50..d6b907b41 100644
--- a/.doctrees/nbsphinx/tutorials/02-orbital-rotation.ipynb
+++ b/.doctrees/nbsphinx/tutorials/02-orbital-rotation.ipynb
@@ -43,10 +43,10 @@
    "execution_count": 1,
    "metadata": {
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@@ -111,10 +111,10 @@
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@@ -160,10 +160,10 @@
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@@ -203,10 +203,10 @@
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     }
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    "outputs": [],
diff --git a/.doctrees/nbsphinx/tutorials/03-double-factorized.ipynb b/.doctrees/nbsphinx/tutorials/03-double-factorized.ipynb
index 1f6dd43d9..260ffc4b5 100644
--- a/.doctrees/nbsphinx/tutorials/03-double-factorized.ipynb
+++ b/.doctrees/nbsphinx/tutorials/03-double-factorized.ipynb
@@ -43,10 +43,10 @@
    "execution_count": 1,
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     }
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@@ -93,10 +93,10 @@
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     }
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    "outputs": [
@@ -227,10 +227,10 @@
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@@ -285,10 +285,10 @@
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@@ -325,10 +325,10 @@
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@@ -367,10 +367,10 @@
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     }
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@@ -409,10 +409,10 @@
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     }
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@@ -450,10 +450,10 @@
    "execution_count": 8,
    "metadata": {
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-     "shell.execute_reply": "2023-09-22T21:03:20.802363Z"
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     }
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    "outputs": [
@@ -493,10 +493,10 @@
    "execution_count": 9,
    "metadata": {
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-     "shell.execute_reply": "2023-09-22T21:03:20.838163Z"
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@@ -535,10 +535,10 @@
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     }
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    "outputs": [
diff --git a/.doctrees/nbsphinx/tutorials/04-lucj.ipynb b/.doctrees/nbsphinx/tutorials/04-lucj.ipynb
index 8edc35981..050d5e27a 100644
--- a/.doctrees/nbsphinx/tutorials/04-lucj.ipynb
+++ b/.doctrees/nbsphinx/tutorials/04-lucj.ipynb
@@ -14,10 +14,10 @@
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-     "shell.execute_reply": "2023-09-22T21:03:23.107515Z"
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     }
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    "outputs": [
@@ -80,10 +80,10 @@
    "execution_count": 2,
    "metadata": {
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-     "shell.execute_reply": "2023-09-22T21:03:23.282713Z"
+     "iopub.execute_input": "2023-09-23T01:21:17.415299Z",
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+     "shell.execute_reply": "2023-09-23T01:21:17.628276Z"
     }
    },
    "outputs": [
@@ -145,10 +145,10 @@
    "execution_count": 3,
    "metadata": {
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-     "iopub.execute_input": "2023-09-22T21:03:23.287326Z",
-     "iopub.status.busy": "2023-09-22T21:03:23.286393Z",
-     "iopub.status.idle": "2023-09-22T21:03:23.432837Z",
-     "shell.execute_reply": "2023-09-22T21:03:23.432304Z"
+     "iopub.execute_input": "2023-09-23T01:21:17.632430Z",
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+     "shell.execute_reply": "2023-09-23T01:21:17.779696Z"
     }
    },
    "outputs": [
@@ -222,10 +222,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-22T21:03:23.436955Z",
-     "iopub.status.busy": "2023-09-22T21:03:23.435969Z",
-     "iopub.status.idle": "2023-09-22T21:03:23.607950Z",
-     "shell.execute_reply": "2023-09-22T21:03:23.607426Z"
+     "iopub.execute_input": "2023-09-23T01:21:17.784386Z",
+     "iopub.status.busy": "2023-09-23T01:21:17.783238Z",
+     "iopub.status.idle": "2023-09-23T01:21:17.954821Z",
+     "shell.execute_reply": "2023-09-23T01:21:17.954247Z"
     }
    },
    "outputs": [
diff --git a/_modules/ffsim/gates/orbital_rotation.html b/_modules/ffsim/gates/orbital_rotation.html
index 4aa2318fc..4265a9e4b 100644
--- a/_modules/ffsim/gates/orbital_rotation.html
+++ b/_modules/ffsim/gates/orbital_rotation.html
@@ -314,9 +314,9 @@ <h1>Source code for ffsim.gates.orbital_rotation</h1><div class="highlight"><pre
     <span class="n">dim_b</span> <span class="o">=</span> <span class="n">comb</span><span class="p">(</span><span class="n">norb</span><span class="p">,</span> <span class="n">n_beta</span><span class="p">,</span> <span class="n">exact</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
     <span class="n">vec</span> <span class="o">=</span> <span class="n">vec</span><span class="o">.</span><span class="n">reshape</span><span class="p">((</span><span class="n">dim_a</span><span class="p">,</span> <span class="n">dim_b</span><span class="p">))</span>
     <span class="c1"># transform alpha</span>
-    <span class="k">for</span> <span class="n">givens_mat</span><span class="p">,</span> <span class="n">target_orbs</span> <span class="ow">in</span> <span class="n">givens_rotations</span><span class="p">:</span>
+    <span class="k">for</span> <span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">s</span><span class="p">),</span> <span class="n">target_orbs</span> <span class="ow">in</span> <span class="n">givens_rotations</span><span class="p">:</span>
         <span class="n">_apply_orbital_rotation_adjacent_spin_in_place</span><span class="p">(</span>
-            <span class="n">vec</span><span class="p">,</span> <span class="n">givens_mat</span><span class="o">.</span><span class="n">conj</span><span class="p">(),</span> <span class="n">target_orbs</span><span class="p">,</span> <span class="n">norb</span><span class="p">,</span> <span class="n">n_alpha</span>
+            <span class="n">vec</span><span class="p">,</span> <span class="n">c</span><span class="p">,</span> <span class="n">s</span><span class="o">.</span><span class="n">conjugate</span><span class="p">(),</span> <span class="n">target_orbs</span><span class="p">,</span> <span class="n">norb</span><span class="p">,</span> <span class="n">n_alpha</span>
         <span class="p">)</span>
     <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">phase_shift</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">phase_shifts</span><span class="p">):</span>
         <span class="n">indices</span> <span class="o">=</span> <span class="n">_one_subspace_indices</span><span class="p">(</span><span class="n">norb</span><span class="p">,</span> <span class="n">n_alpha</span><span class="p">,</span> <span class="p">(</span><span class="n">i</span><span class="p">,))</span>
@@ -325,9 +325,9 @@ <h1>Source code for ffsim.gates.orbital_rotation</h1><div class="highlight"><pre
     <span class="c1"># transform beta</span>
     <span class="c1"># transpose vector to align memory layout</span>
     <span class="n">vec</span> <span class="o">=</span> <span class="n">vec</span><span class="o">.</span><span class="n">T</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>
-    <span class="k">for</span> <span class="n">givens_mat</span><span class="p">,</span> <span class="n">target_orbs</span> <span class="ow">in</span> <span class="n">givens_rotations</span><span class="p">:</span>
+    <span class="k">for</span> <span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">s</span><span class="p">),</span> <span class="n">target_orbs</span> <span class="ow">in</span> <span class="n">givens_rotations</span><span class="p">:</span>
         <span class="n">_apply_orbital_rotation_adjacent_spin_in_place</span><span class="p">(</span>
-            <span class="n">vec</span><span class="p">,</span> <span class="n">givens_mat</span><span class="o">.</span><span class="n">conj</span><span class="p">(),</span> <span class="n">target_orbs</span><span class="p">,</span> <span class="n">norb</span><span class="p">,</span> <span class="n">n_beta</span>
+            <span class="n">vec</span><span class="p">,</span> <span class="n">c</span><span class="p">,</span> <span class="n">s</span><span class="o">.</span><span class="n">conjugate</span><span class="p">(),</span> <span class="n">target_orbs</span><span class="p">,</span> <span class="n">norb</span><span class="p">,</span> <span class="n">n_beta</span>
         <span class="p">)</span>
     <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">phase_shift</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">phase_shifts</span><span class="p">):</span>
         <span class="n">indices</span> <span class="o">=</span> <span class="n">_one_subspace_indices</span><span class="p">(</span><span class="n">norb</span><span class="p">,</span> <span class="n">n_beta</span><span class="p">,</span> <span class="p">(</span><span class="n">i</span><span class="p">,))</span>
@@ -337,7 +337,12 @@ <h1>Source code for ffsim.gates.orbital_rotation</h1><div class="highlight"><pre
 
 
 <span class="k">def</span> <span class="nf">_apply_orbital_rotation_adjacent_spin_in_place</span><span class="p">(</span>
-    <span class="n">vec</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="n">mat</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="n">target_orbs</span><span class="p">:</span> <span class="nb">tuple</span><span class="p">[</span><span class="nb">int</span><span class="p">,</span> <span class="nb">int</span><span class="p">],</span> <span class="n">norb</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">nocc</span><span class="p">:</span> <span class="nb">int</span>
+    <span class="n">vec</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span>
+    <span class="n">c</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
+    <span class="n">s</span><span class="p">:</span> <span class="nb">complex</span><span class="p">,</span>
+    <span class="n">target_orbs</span><span class="p">:</span> <span class="nb">tuple</span><span class="p">[</span><span class="nb">int</span><span class="p">,</span> <span class="nb">int</span><span class="p">],</span>
+    <span class="n">norb</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
+    <span class="n">nocc</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
 <span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
 <span class="w">    </span><span class="sd">&quot;&quot;&quot;Apply an orbital rotation to adjacent orbitals.</span>
 
@@ -353,8 +358,6 @@ <h1>Source code for ffsim.gates.orbital_rotation</h1><div class="highlight"><pre
     <span class="n">indices</span> <span class="o">=</span> <span class="n">_zero_one_subspace_indices</span><span class="p">(</span><span class="n">norb</span><span class="p">,</span> <span class="n">nocc</span><span class="p">,</span> <span class="n">target_orbs</span><span class="p">)</span>
     <span class="n">slice1</span> <span class="o">=</span> <span class="n">indices</span><span class="p">[:</span> <span class="nb">len</span><span class="p">(</span><span class="n">indices</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span><span class="p">]</span>
     <span class="n">slice2</span> <span class="o">=</span> <span class="n">indices</span><span class="p">[</span><span class="nb">len</span><span class="p">(</span><span class="n">indices</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span> <span class="p">:]</span>
-    <span class="n">c</span><span class="p">,</span> <span class="n">s</span> <span class="o">=</span> <span class="n">mat</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
-    <span class="n">c</span> <span class="o">=</span> <span class="n">c</span><span class="o">.</span><span class="n">real</span>
     <span class="n">apply_givens_rotation_in_place</span><span class="p">(</span><span class="n">vec</span><span class="p">,</span> <span class="n">c</span><span class="p">,</span> <span class="n">s</span><span class="p">,</span> <span class="n">slice1</span><span class="p">,</span> <span class="n">slice2</span><span class="p">)</span>
 
 
diff --git a/_modules/ffsim/linalg/givens.html b/_modules/ffsim/linalg/givens.html
index 29216d349..fa356b3fd 100644
--- a/_modules/ffsim/linalg/givens.html
+++ b/_modules/ffsim/linalg/givens.html
@@ -50,6 +50,8 @@ <h1>Source code for ffsim.linalg.givens</h1><div class="highlight"><pre>
 <span class="kn">from</span> <span class="nn">__future__</span> <span class="kn">import</span> <span class="n">annotations</span>
 
 <span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">from</span> <span class="nn">scipy.linalg.blas</span> <span class="kn">import</span> <span class="n">zrotg</span> <span class="k">as</span> <span class="n">zrotg_</span>
+<span class="kn">from</span> <span class="nn">scipy.linalg.lapack</span> <span class="kn">import</span> <span class="n">zrot</span>
 
 
 <div class="viewcode-block" id="apply_matrix_to_slices">
@@ -85,55 +87,24 @@ <h1>Source code for ffsim.linalg.givens</h1><div class="highlight"><pre>
 
 
 
-<div class="viewcode-block" id="givens_matrix">
-<a class="viewcode-back" href="../../../api/generated/ffsim.linalg.html#ffsim.linalg.givens.givens_matrix">[docs]</a>
-<span class="k">def</span> <span class="nf">givens_matrix</span><span class="p">(</span><span class="n">a</span><span class="p">:</span> <span class="nb">complex</span><span class="p">,</span> <span class="n">b</span><span class="p">:</span> <span class="nb">complex</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">:</span>
-<span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Compute the Givens rotation to zero out a row entry.</span>
+<div class="viewcode-block" id="zrotg">
+<a class="viewcode-back" href="../../../api/generated/ffsim.linalg.html#ffsim.linalg.givens.zrotg">[docs]</a>
+<span class="k">def</span> <span class="nf">zrotg</span><span class="p">(</span><span class="n">a</span><span class="p">:</span> <span class="nb">complex</span><span class="p">,</span> <span class="n">b</span><span class="p">:</span> <span class="nb">complex</span><span class="p">,</span> <span class="n">tol</span><span class="o">=</span><span class="mf">1e-12</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">tuple</span><span class="p">[</span><span class="nb">float</span><span class="p">,</span> <span class="nb">complex</span><span class="p">]:</span>
+<span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Safe version of the zrotg BLAS function.</span>
 
-<span class="sd">    Returns a :math:`2 \times 2` unitary matrix G that satisfies</span>
+<span class="sd">    The BLAS implementation of zrotg can return NaN values if either a or b is very</span>
+<span class="sd">    close to zero. This function detects if either a or b is close to zero up to the</span>
+<span class="sd">    specified tolerance, in which case it behaves as if it were exactly zero.</span>
 
-<span class="sd">    .. math::</span>
-
-<span class="sd">        G</span>
-<span class="sd">        \begin{pmatrix}</span>
-<span class="sd">            a \\</span>
-<span class="sd">            b</span>
-<span class="sd">        \end{pmatrix}</span>
-<span class="sd">        =</span>
-<span class="sd">        \begin{pmatrix}</span>
-<span class="sd">            r \\</span>
-<span class="sd">            0</span>
-<span class="sd">        \end{pmatrix}</span>
-
-<span class="sd">    where :math:`r` is a complex number.</span>
-
-<span class="sd">    References:</span>
-<span class="sd">        - `&lt;https://en.wikipedia.org/wiki/Givens_rotation#Stable_calculation&gt;`_</span>
-<span class="sd">        - `&lt;https://www.netlib.org/lapack/lawnspdf/lawn148.pdf&gt;`_</span>
-
-<span class="sd">    Args:</span>
-<span class="sd">        a: A complex number representing the first row entry</span>
-<span class="sd">        b: A complex number representing the second row entry</span>
-
-<span class="sd">    Returns:</span>
-<span class="sd">        The Givens rotation matrix.</span>
+<span class="sd">    Note that in contrast to `scipy.linalg.blas.zrotg`, this function returns c as a</span>
+<span class="sd">    float rather than a complex.</span>
 <span class="sd">    &quot;&quot;&quot;</span>
-    <span class="c1"># Handle case that a is zero</span>
-    <span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">isclose</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">):</span>
-        <span class="n">cosine</span> <span class="o">=</span> <span class="mf">0.0</span>
-        <span class="n">sine</span> <span class="o">=</span> <span class="mf">1.0</span>
-    <span class="c1"># Handle case that b is zero and a is nonzero</span>
-    <span class="k">elif</span> <span class="n">np</span><span class="o">.</span><span class="n">isclose</span><span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">):</span>
-        <span class="n">cosine</span> <span class="o">=</span> <span class="mf">1.0</span>
-        <span class="n">sine</span> <span class="o">=</span> <span class="mf">0.0</span>
-    <span class="c1"># Handle case that a and b are both nonzero</span>
-    <span class="k">else</span><span class="p">:</span>
-        <span class="n">hypotenuse</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">hypot</span><span class="p">(</span><span class="nb">abs</span><span class="p">(</span><span class="n">a</span><span class="p">),</span> <span class="nb">abs</span><span class="p">(</span><span class="n">b</span><span class="p">))</span>
-        <span class="n">cosine</span> <span class="o">=</span> <span class="nb">abs</span><span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="o">/</span> <span class="n">hypotenuse</span>
-        <span class="n">sign_a</span> <span class="o">=</span> <span class="n">a</span> <span class="o">/</span> <span class="nb">abs</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
-        <span class="n">sine</span> <span class="o">=</span> <span class="n">sign_a</span> <span class="o">*</span> <span class="n">b</span><span class="o">.</span><span class="n">conjugate</span><span class="p">()</span> <span class="o">/</span> <span class="n">hypotenuse</span>
-
-    <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="n">cosine</span><span class="p">,</span> <span class="n">sine</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="n">sine</span><span class="o">.</span><span class="n">conjugate</span><span class="p">(),</span> <span class="n">cosine</span><span class="p">]])</span></div>
+    <span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">isclose</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="n">atol</span><span class="o">=</span><span class="n">tol</span><span class="p">):</span>
+        <span class="k">return</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mi">1</span> <span class="o">+</span> <span class="mi">0</span><span class="n">j</span>
+    <span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">isclose</span><span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="n">atol</span><span class="o">=</span><span class="n">tol</span><span class="p">):</span>
+        <span class="k">return</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mi">0</span><span class="n">j</span>
+    <span class="n">c</span><span class="p">,</span> <span class="n">s</span> <span class="o">=</span> <span class="n">zrotg_</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span>
+    <span class="k">return</span> <span class="n">c</span><span class="o">.</span><span class="n">real</span><span class="p">,</span> <span class="n">s</span></div>
 
 
 
@@ -141,12 +112,12 @@ <h1>Source code for ffsim.linalg.givens</h1><div class="highlight"><pre>
 <a class="viewcode-back" href="../../../api/generated/ffsim.linalg.html#ffsim.linalg.givens.givens_decomposition">[docs]</a>
 <span class="k">def</span> <span class="nf">givens_decomposition</span><span class="p">(</span>
     <span class="n">mat</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span>
-<span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">tuple</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">tuple</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">[</span><span class="nb">int</span><span class="p">,</span> <span class="nb">int</span><span class="p">]]],</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">]:</span>
+<span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">tuple</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">tuple</span><span class="p">[</span><span class="nb">tuple</span><span class="p">[</span><span class="nb">float</span><span class="p">,</span> <span class="nb">complex</span><span class="p">],</span> <span class="nb">tuple</span><span class="p">[</span><span class="nb">int</span><span class="p">,</span> <span class="nb">int</span><span class="p">]]],</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">]:</span>
 <span class="w">    </span><span class="sd">&quot;&quot;&quot;Givens rotation decomposition of a unitary matrix.&quot;&quot;&quot;</span>
     <span class="n">n</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">shape</span>
-    <span class="n">current_matrix</span> <span class="o">=</span> <span class="n">mat</span>
+    <span class="n">current_matrix</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="nb">complex</span><span class="p">,</span> <span class="n">copy</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
     <span class="n">left_rotations</span> <span class="o">=</span> <span class="p">[]</span>
-    <span class="n">right_rotations</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">tuple</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">[</span><span class="nb">int</span><span class="p">,</span> <span class="nb">int</span><span class="p">]]]</span> <span class="o">=</span> <span class="p">[]</span>
+    <span class="n">right_rotations</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">tuple</span><span class="p">[</span><span class="nb">tuple</span><span class="p">[</span><span class="nb">float</span><span class="p">,</span> <span class="nb">complex</span><span class="p">],</span> <span class="nb">tuple</span><span class="p">[</span><span class="nb">int</span><span class="p">,</span> <span class="nb">int</span><span class="p">]]]</span> <span class="o">=</span> <span class="p">[]</span>
 
     <span class="c1"># compute left and right Givens rotations</span>
     <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">):</span>
@@ -157,18 +128,22 @@ <h1>Source code for ffsim.linalg.givens</h1><div class="highlight"><pre>
                 <span class="n">row</span> <span class="o">=</span> <span class="n">n</span> <span class="o">-</span> <span class="n">j</span> <span class="o">-</span> <span class="mi">1</span>
                 <span class="k">if</span> <span class="ow">not</span> <span class="n">np</span><span class="o">.</span><span class="n">isclose</span><span class="p">(</span><span class="n">current_matrix</span><span class="p">[</span><span class="n">row</span><span class="p">,</span> <span class="n">target_index</span><span class="p">],</span> <span class="mf">0.0</span><span class="p">):</span>
                     <span class="c1"># zero out element at target index in given row</span>
-                    <span class="n">givens_mat</span> <span class="o">=</span> <span class="n">givens_matrix</span><span class="p">(</span>
+                    <span class="n">c</span><span class="p">,</span> <span class="n">s</span> <span class="o">=</span> <span class="n">zrotg</span><span class="p">(</span>
                         <span class="n">current_matrix</span><span class="p">[</span><span class="n">row</span><span class="p">,</span> <span class="n">target_index</span> <span class="o">+</span> <span class="mi">1</span><span class="p">],</span>
                         <span class="n">current_matrix</span><span class="p">[</span><span class="n">row</span><span class="p">,</span> <span class="n">target_index</span><span class="p">],</span>
                     <span class="p">)</span>
-                    <span class="n">right_rotations</span><span class="o">.</span><span class="n">append</span><span class="p">(</span>
-                        <span class="p">(</span><span class="n">givens_mat</span><span class="p">,</span> <span class="p">(</span><span class="n">target_index</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">target_index</span><span class="p">))</span>
-                    <span class="p">)</span>
-                    <span class="n">current_matrix</span> <span class="o">=</span> <span class="n">apply_matrix_to_slices</span><span class="p">(</span>
-                        <span class="n">current_matrix</span><span class="p">,</span>
-                        <span class="n">givens_mat</span><span class="p">,</span>
-                        <span class="p">[(</span><span class="bp">Ellipsis</span><span class="p">,</span> <span class="n">target_index</span> <span class="o">+</span> <span class="mi">1</span><span class="p">),</span> <span class="p">(</span><span class="bp">Ellipsis</span><span class="p">,</span> <span class="n">target_index</span><span class="p">)],</span>
+                    <span class="n">right_rotations</span><span class="o">.</span><span class="n">append</span><span class="p">(((</span><span class="n">c</span><span class="p">,</span> <span class="n">s</span><span class="p">),</span> <span class="p">(</span><span class="n">target_index</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">target_index</span><span class="p">)))</span>
+                    <span class="n">current_matrix</span> <span class="o">=</span> <span class="n">current_matrix</span><span class="o">.</span><span class="n">T</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>
+                    <span class="p">(</span>
+                        <span class="n">current_matrix</span><span class="p">[</span><span class="n">target_index</span> <span class="o">+</span> <span class="mi">1</span><span class="p">],</span>
+                        <span class="n">current_matrix</span><span class="p">[</span><span class="n">target_index</span><span class="p">],</span>
+                    <span class="p">)</span> <span class="o">=</span> <span class="n">zrot</span><span class="p">(</span>
+                        <span class="n">current_matrix</span><span class="p">[</span><span class="n">target_index</span> <span class="o">+</span> <span class="mi">1</span><span class="p">],</span>
+                        <span class="n">current_matrix</span><span class="p">[</span><span class="n">target_index</span><span class="p">],</span>
+                        <span class="n">c</span><span class="p">,</span>
+                        <span class="n">s</span><span class="p">,</span>
                     <span class="p">)</span>
+                    <span class="n">current_matrix</span> <span class="o">=</span> <span class="n">current_matrix</span><span class="o">.</span><span class="n">T</span>
         <span class="k">else</span><span class="p">:</span>
             <span class="c1"># rotate rows by left multiplication</span>
             <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
@@ -176,24 +151,31 @@ <h1>Source code for ffsim.linalg.givens</h1><div class="highlight"><pre>
                 <span class="n">col</span> <span class="o">=</span> <span class="n">j</span>
                 <span class="k">if</span> <span class="ow">not</span> <span class="n">np</span><span class="o">.</span><span class="n">isclose</span><span class="p">(</span><span class="n">current_matrix</span><span class="p">[</span><span class="n">target_index</span><span class="p">,</span> <span class="n">col</span><span class="p">],</span> <span class="mf">0.0</span><span class="p">):</span>
                     <span class="c1"># zero out element at target index in given column</span>
-                    <span class="n">givens_mat</span> <span class="o">=</span> <span class="n">givens_matrix</span><span class="p">(</span>
+                    <span class="n">c</span><span class="p">,</span> <span class="n">s</span> <span class="o">=</span> <span class="n">zrotg</span><span class="p">(</span>
                         <span class="n">current_matrix</span><span class="p">[</span><span class="n">target_index</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">col</span><span class="p">],</span>
                         <span class="n">current_matrix</span><span class="p">[</span><span class="n">target_index</span><span class="p">,</span> <span class="n">col</span><span class="p">],</span>
                     <span class="p">)</span>
-                    <span class="n">left_rotations</span><span class="o">.</span><span class="n">append</span><span class="p">(</span>
-                        <span class="p">(</span><span class="n">givens_mat</span><span class="p">,</span> <span class="p">(</span><span class="n">target_index</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">target_index</span><span class="p">))</span>
-                    <span class="p">)</span>
-                    <span class="n">current_matrix</span> <span class="o">=</span> <span class="n">apply_matrix_to_slices</span><span class="p">(</span>
-                        <span class="n">current_matrix</span><span class="p">,</span> <span class="n">givens_mat</span><span class="p">,</span> <span class="p">[</span><span class="n">target_index</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">target_index</span><span class="p">]</span>
+                    <span class="n">left_rotations</span><span class="o">.</span><span class="n">append</span><span class="p">(((</span><span class="n">c</span><span class="p">,</span> <span class="n">s</span><span class="p">),</span> <span class="p">(</span><span class="n">target_index</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">target_index</span><span class="p">)))</span>
+                    <span class="p">(</span>
+                        <span class="n">current_matrix</span><span class="p">[</span><span class="n">target_index</span> <span class="o">-</span> <span class="mi">1</span><span class="p">],</span>
+                        <span class="n">current_matrix</span><span class="p">[</span><span class="n">target_index</span><span class="p">],</span>
+                    <span class="p">)</span> <span class="o">=</span> <span class="n">zrot</span><span class="p">(</span>
+                        <span class="n">current_matrix</span><span class="p">[</span><span class="n">target_index</span> <span class="o">-</span> <span class="mi">1</span><span class="p">],</span>
+                        <span class="n">current_matrix</span><span class="p">[</span><span class="n">target_index</span><span class="p">],</span>
+                        <span class="n">c</span><span class="p">,</span>
+                        <span class="n">s</span><span class="p">,</span>
                     <span class="p">)</span>
 
     <span class="c1"># convert left rotations to right rotations</span>
-    <span class="k">for</span> <span class="n">givens_mat</span><span class="p">,</span> <span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">)</span> <span class="ow">in</span> <span class="nb">reversed</span><span class="p">(</span><span class="n">left_rotations</span><span class="p">):</span>
-        <span class="n">givens_mat</span> <span class="o">=</span> <span class="n">givens_mat</span><span class="o">.</span><span class="n">T</span><span class="o">.</span><span class="n">conj</span><span class="p">()</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">mat</span><span class="o">.</span><span class="n">dtype</span><span class="p">,</span> <span class="n">copy</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
+    <span class="k">for</span> <span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">s</span><span class="p">),</span> <span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">)</span> <span class="ow">in</span> <span class="nb">reversed</span><span class="p">(</span><span class="n">left_rotations</span><span class="p">):</span>
+        <span class="n">c</span><span class="p">,</span> <span class="n">s</span> <span class="o">=</span> <span class="n">zrotg</span><span class="p">(</span><span class="n">c</span> <span class="o">*</span> <span class="n">current_matrix</span><span class="p">[</span><span class="n">j</span><span class="p">,</span> <span class="n">j</span><span class="p">],</span> <span class="n">s</span><span class="o">.</span><span class="n">conjugate</span><span class="p">()</span> <span class="o">*</span> <span class="n">current_matrix</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">i</span><span class="p">])</span>
+        <span class="n">right_rotations</span><span class="o">.</span><span class="n">append</span><span class="p">(((</span><span class="n">c</span><span class="p">,</span> <span class="o">-</span><span class="n">s</span><span class="o">.</span><span class="n">conjugate</span><span class="p">()),</span> <span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">)))</span>
+
+        <span class="n">givens_mat</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="n">c</span><span class="p">,</span> <span class="o">-</span><span class="n">s</span><span class="p">],</span> <span class="p">[</span><span class="n">s</span><span class="o">.</span><span class="n">conjugate</span><span class="p">(),</span> <span class="n">c</span><span class="p">]])</span>
         <span class="n">givens_mat</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">*=</span> <span class="n">current_matrix</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">i</span><span class="p">]</span>
         <span class="n">givens_mat</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">]</span> <span class="o">*=</span> <span class="n">current_matrix</span><span class="p">[</span><span class="n">j</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span>
-        <span class="n">new_givens_mat</span> <span class="o">=</span> <span class="n">givens_matrix</span><span class="p">(</span><span class="n">givens_mat</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">givens_mat</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>
-        <span class="n">right_rotations</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="n">new_givens_mat</span><span class="o">.</span><span class="n">T</span><span class="p">,</span> <span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">)))</span>
+        <span class="n">c</span><span class="p">,</span> <span class="n">s</span> <span class="o">=</span> <span class="n">zrotg</span><span class="p">(</span><span class="n">givens_mat</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">givens_mat</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>
+        <span class="n">new_givens_mat</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="n">c</span><span class="p">,</span> <span class="n">s</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="n">s</span><span class="o">.</span><span class="n">conjugate</span><span class="p">(),</span> <span class="n">c</span><span class="p">]])</span>
         <span class="n">phase_matrix</span> <span class="o">=</span> <span class="n">givens_mat</span> <span class="o">@</span> <span class="n">new_givens_mat</span>
         <span class="n">current_matrix</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">phase_matrix</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span>
         <span class="n">current_matrix</span><span class="p">[</span><span class="n">j</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">phase_matrix</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span>
diff --git a/api/generated/ffsim.html b/api/generated/ffsim.html
index 2df89f45c..07b2ebc65 100644
--- a/api/generated/ffsim.html
+++ b/api/generated/ffsim.html
@@ -135,7 +135,7 @@ <h2>Subpackages<a class="headerlink" href="#subpackages" title="Link to this hea
 <li class="toctree-l2"><a class="reference internal" href="ffsim.linalg.html#module-ffsim.linalg.givens">ffsim.linalg.givens module</a><ul>
 <li class="toctree-l3"><a class="reference internal" href="ffsim.linalg.html#ffsim.linalg.givens.apply_matrix_to_slices"><code class="docutils literal notranslate"><span class="pre">apply_matrix_to_slices()</span></code></a></li>
 <li class="toctree-l3"><a class="reference internal" href="ffsim.linalg.html#ffsim.linalg.givens.givens_decomposition"><code class="docutils literal notranslate"><span class="pre">givens_decomposition()</span></code></a></li>
-<li class="toctree-l3"><a class="reference internal" href="ffsim.linalg.html#ffsim.linalg.givens.givens_matrix"><code class="docutils literal notranslate"><span class="pre">givens_matrix()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="ffsim.linalg.html#ffsim.linalg.givens.zrotg"><code class="docutils literal notranslate"><span class="pre">zrotg()</span></code></a></li>
 </ul>
 </li>
 <li class="toctree-l2"><a class="reference internal" href="ffsim.linalg.html#module-ffsim.linalg.linalg">ffsim.linalg.linalg module</a><ul>
diff --git a/api/generated/ffsim.linalg.html b/api/generated/ffsim.linalg.html
index 514c5d761..1a3f4fb60 100644
--- a/api/generated/ffsim.linalg.html
+++ b/api/generated/ffsim.linalg.html
@@ -250,45 +250,23 @@ <h2>Submodules<a class="headerlink" href="#submodules" title="Link to this headi
 <dd><p>Givens rotation decomposition of a unitary matrix.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><code class="xref py py-class docutils literal notranslate"><span class="pre">tuple</span></code>[<code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code>[<code class="xref py py-class docutils literal notranslate"><span class="pre">tuple</span></code>[<code class="xref py py-class docutils literal notranslate"><span class="pre">ndarray</span></code>, <code class="xref py py-class docutils literal notranslate"><span class="pre">tuple</span></code>[<code class="xref py py-class docutils literal notranslate"><span class="pre">int</span></code>, <code class="xref py py-class docutils literal notranslate"><span class="pre">int</span></code>]]], <code class="xref py py-class docutils literal notranslate"><span class="pre">ndarray</span></code>]</p>
+<dd class="field-odd"><p><code class="xref py py-class docutils literal notranslate"><span class="pre">tuple</span></code>[<code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code>[<code class="xref py py-class docutils literal notranslate"><span class="pre">tuple</span></code>[<code class="xref py py-class docutils literal notranslate"><span class="pre">tuple</span></code>[<code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code>, <code class="xref py py-class docutils literal notranslate"><span class="pre">complex</span></code>], <code class="xref py py-class docutils literal notranslate"><span class="pre">tuple</span></code>[<code class="xref py py-class docutils literal notranslate"><span class="pre">int</span></code>, <code class="xref py py-class docutils literal notranslate"><span class="pre">int</span></code>]]], <code class="xref py py-class docutils literal notranslate"><span class="pre">ndarray</span></code>]</p>
 </dd>
 </dl>
 </dd></dl>
 
 <dl class="py function">
-<dt class="sig sig-object py" id="ffsim.linalg.givens.givens_matrix">
-<span class="sig-prename descclassname"><span class="pre">ffsim.linalg.givens.</span></span><span class="sig-name descname"><span class="pre">givens_matrix</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">a</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">b</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/ffsim/linalg/givens.html#givens_matrix"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ffsim.linalg.givens.givens_matrix" title="Link to this definition">¶</a></dt>
-<dd><p>Compute the Givens rotation to zero out a row entry.</p>
-<p>Returns a <span class="math notranslate nohighlight">\(2 \times 2\)</span> unitary matrix G that satisfies</p>
-<div class="math notranslate nohighlight">
-\[\begin{split}G
-\begin{pmatrix}
-    a \\
-    b
-\end{pmatrix}
-=
-\begin{pmatrix}
-    r \\
-    0
-\end{pmatrix}\end{split}\]</div>
-<p>where <span class="math notranslate nohighlight">\(r\)</span> is a complex number.</p>
-<p class="rubric">References</p>
-<ul class="simple">
-<li><p><a class="reference external" href="https://en.wikipedia.org/wiki/Givens_rotation#Stable_calculation">https://en.wikipedia.org/wiki/Givens_rotation#Stable_calculation</a></p></li>
-<li><p><a class="reference external" href="https://www.netlib.org/lapack/lawnspdf/lawn148.pdf">https://www.netlib.org/lapack/lawnspdf/lawn148.pdf</a></p></li>
-</ul>
+<dt class="sig sig-object py" id="ffsim.linalg.givens.zrotg">
+<span class="sig-prename descclassname"><span class="pre">ffsim.linalg.givens.</span></span><span class="sig-name descname"><span class="pre">zrotg</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">a</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">b</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-12</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/ffsim/linalg/givens.html#zrotg"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ffsim.linalg.givens.zrotg" title="Link to this definition">¶</a></dt>
+<dd><p>Safe version of the zrotg BLAS function.</p>
+<p>The BLAS implementation of zrotg can return NaN values if either a or b is very
+close to zero. This function detects if either a or b is close to zero up to the
+specified tolerance, in which case it behaves as if it were exactly zero.</p>
+<p>Note that in contrast to <cite>scipy.linalg.blas.zrotg</cite>, this function returns c as a
+float rather than a complex.</p>
 <dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>a</strong> (<code class="xref py py-class docutils literal notranslate"><span class="pre">complex</span></code>) – A complex number representing the first row entry</p></li>
-<li><p><strong>b</strong> (<code class="xref py py-class docutils literal notranslate"><span class="pre">complex</span></code>) – A complex number representing the second row entry</p></li>
-</ul>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><code class="xref py py-class docutils literal notranslate"><span class="pre">ndarray</span></code></p>
-</dd>
-<dt class="field-odd">Returns<span class="colon">:</span></dt>
-<dd class="field-odd"><p>The Givens rotation matrix.</p>
+<dt class="field-odd">Return type<span class="colon">:</span></dt>
+<dd class="field-odd"><p><code class="xref py py-class docutils literal notranslate"><span class="pre">tuple</span></code>[<code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code>, <code class="xref py py-class docutils literal notranslate"><span class="pre">complex</span></code>]</p>
 </dd>
 </dl>
 </dd></dl>
diff --git a/genindex.html b/genindex.html
index 1bb8daf4d..6da1b5f8f 100644
--- a/genindex.html
+++ b/genindex.html
@@ -456,14 +456,12 @@ <h2 id="G">G</h2>
 <table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%; vertical-align: top;"><ul>
       <li><a href="api/generated/ffsim.gates.html#ffsim.gates.orbital_rotation.gen_orbital_rotation_index">gen_orbital_rotation_index() (in module ffsim.gates.orbital_rotation)</a>
-</li>
-      <li><a href="api/generated/ffsim.slow.gates.html#ffsim.slow.gates.orbital_rotation.gen_orbital_rotation_index_in_place_slow">gen_orbital_rotation_index_in_place_slow() (in module ffsim.slow.gates.orbital_rotation)</a>
 </li>
   </ul></td>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="api/generated/ffsim.linalg.html#ffsim.linalg.givens.givens_decomposition">givens_decomposition() (in module ffsim.linalg.givens)</a>
+      <li><a href="api/generated/ffsim.slow.gates.html#ffsim.slow.gates.orbital_rotation.gen_orbital_rotation_index_in_place_slow">gen_orbital_rotation_index_in_place_slow() (in module ffsim.slow.gates.orbital_rotation)</a>
 </li>
-      <li><a href="api/generated/ffsim.linalg.html#ffsim.linalg.givens.givens_matrix">givens_matrix() (in module ffsim.linalg.givens)</a>
+      <li><a href="api/generated/ffsim.linalg.html#ffsim.linalg.givens.givens_decomposition">givens_decomposition() (in module ffsim.linalg.givens)</a>
 </li>
   </ul></td>
 </tr></table>
@@ -761,6 +759,10 @@ <h2 id="Z">Z</h2>
 <table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%; vertical-align: top;"><ul>
       <li><a href="api/generated/ffsim.hamiltonians.html#ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.z_representation">z_representation (ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian attribute)</a>
+</li>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="api/generated/ffsim.linalg.html#ffsim.linalg.givens.zrotg">zrotg() (in module ffsim.linalg.givens)</a>
 </li>
   </ul></td>
 </tr></table>
diff --git a/objects.inv b/objects.inv
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diff --git a/searchindex.js b/searchindex.js
index 105867ffd..5db4b8740 100644
--- a/searchindex.js
+++ b/searchindex.js
@@ -1 +1 @@
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\ No newline at end of file
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"ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.to_z_representation"]], "two_body_tensor (ffsim.hamiltonians.molecular_hamiltonian.molecularhamiltonian attribute)": [[3, "ffsim.hamiltonians.molecular_hamiltonian.MolecularHamiltonian.two_body_tensor"]], "z_representation (ffsim.hamiltonians.double_factorized_hamiltonian.doublefactorizedhamiltonian attribute)": [[3, "ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.z_representation"]], "apply_matrix_to_slices() (in module ffsim.linalg.givens)": [[4, "ffsim.linalg.givens.apply_matrix_to_slices"]], "double_factorized() (in module ffsim.linalg.double_factorized)": [[4, "ffsim.linalg.double_factorized.double_factorized"]], "double_factorized_t2() (in module ffsim.linalg.double_factorized)": [[4, "ffsim.linalg.double_factorized.double_factorized_t2"]], "expm_multiply_taylor() (in module ffsim.linalg.linalg)": [[4, "ffsim.linalg.linalg.expm_multiply_taylor"]], "ffsim.linalg": [[4, "module-ffsim.linalg"]], "ffsim.linalg.double_factorized": [[4, "module-ffsim.linalg.double_factorized"]], "ffsim.linalg.givens": [[4, "module-ffsim.linalg.givens"]], "ffsim.linalg.linalg": [[4, "module-ffsim.linalg.linalg"]], "ffsim.linalg.predicates": [[4, "module-ffsim.linalg.predicates"]], "givens_decomposition() (in module ffsim.linalg.givens)": [[4, "ffsim.linalg.givens.givens_decomposition"]], "is_antihermitian() (in module ffsim.linalg.predicates)": [[4, "ffsim.linalg.predicates.is_antihermitian"]], "is_hermitian() (in module ffsim.linalg.predicates)": [[4, "ffsim.linalg.predicates.is_hermitian"]], "is_orthogonal() (in module ffsim.linalg.predicates)": [[4, "ffsim.linalg.predicates.is_orthogonal"]], "is_real_symmetric() (in module ffsim.linalg.predicates)": [[4, "ffsim.linalg.predicates.is_real_symmetric"]], "is_special_orthogonal() (in module ffsim.linalg.predicates)": [[4, "ffsim.linalg.predicates.is_special_orthogonal"]], "is_unitary() (in module ffsim.linalg.predicates)": [[4, "ffsim.linalg.predicates.is_unitary"]], "lup() (in module ffsim.linalg.linalg)": [[4, "ffsim.linalg.linalg.lup"]], "modified_cholesky() (in module ffsim.linalg.double_factorized)": [[4, "ffsim.linalg.double_factorized.modified_cholesky"]], "optimal_diag_coulomb_mats() (in module ffsim.linalg.double_factorized)": [[4, "ffsim.linalg.double_factorized.optimal_diag_coulomb_mats"]], "zrotg() (in module ffsim.linalg.givens)": [[4, "ffsim.linalg.givens.zrotg"]], "supportslinearoperator (class in ffsim.protocols.linear_operator)": [[5, "ffsim.protocols.linear_operator.SupportsLinearOperator"]], "supportstrace (class in ffsim.protocols.trace)": [[5, "ffsim.protocols.trace.SupportsTrace"]], "ffsim.protocols": [[5, "module-ffsim.protocols"]], "ffsim.protocols.linear_operator": [[5, "module-ffsim.protocols.linear_operator"]], "ffsim.protocols.trace": [[5, "module-ffsim.protocols.trace"]], "linear_operator() (in module ffsim.protocols.linear_operator)": [[5, "ffsim.protocols.linear_operator.linear_operator"]], "trace() (in module ffsim.protocols.trace)": [[5, "ffsim.protocols.trace.trace"]], "ffsim.slow": [[6, "module-ffsim.slow"]], "ffsim.slow.contract": [[7, "module-ffsim.slow.contract"]], "ffsim.slow.contract.diag_coulomb": [[7, "module-ffsim.slow.contract.diag_coulomb"]], "ffsim.slow.contract.num_op_sum": [[7, "module-ffsim.slow.contract.num_op_sum"]], "apply_diag_coulomb_evolution_in_place_num_rep_numpy() (in module ffsim.slow.gates.diag_coulomb)": [[8, "ffsim.slow.gates.diag_coulomb.apply_diag_coulomb_evolution_in_place_num_rep_numpy"]], "apply_diag_coulomb_evolution_in_place_num_rep_slow() (in module ffsim.slow.gates.diag_coulomb)": [[8, "ffsim.slow.gates.diag_coulomb.apply_diag_coulomb_evolution_in_place_num_rep_slow"]], "apply_diag_coulomb_evolution_in_place_z_rep_slow() (in module ffsim.slow.gates.diag_coulomb)": [[8, "ffsim.slow.gates.diag_coulomb.apply_diag_coulomb_evolution_in_place_z_rep_slow"]], "apply_givens_rotation_in_place_slow() (in module ffsim.slow.gates.orbital_rotation)": [[8, "ffsim.slow.gates.orbital_rotation.apply_givens_rotation_in_place_slow"]], "apply_num_op_sum_evolution_in_place_slow() (in module ffsim.slow.gates.num_op_sum)": [[8, "ffsim.slow.gates.num_op_sum.apply_num_op_sum_evolution_in_place_slow"]], "apply_single_column_transformation_in_place_slow() (in module ffsim.slow.gates.orbital_rotation)": [[8, "ffsim.slow.gates.orbital_rotation.apply_single_column_transformation_in_place_slow"]], "ffsim.slow.gates": [[8, "module-ffsim.slow.gates"]], "ffsim.slow.gates.diag_coulomb": [[8, "module-ffsim.slow.gates.diag_coulomb"]], "ffsim.slow.gates.num_op_sum": [[8, "module-ffsim.slow.gates.num_op_sum"]], "ffsim.slow.gates.orbital_rotation": [[8, "module-ffsim.slow.gates.orbital_rotation"]], "gen_orbital_rotation_index_in_place_slow() (in module ffsim.slow.gates.orbital_rotation)": [[8, "ffsim.slow.gates.orbital_rotation.gen_orbital_rotation_index_in_place_slow"]], "expectation_squared_diag_coulomb() (in module ffsim.trotter.qdrift)": [[9, "ffsim.trotter.qdrift.expectation_squared_diag_coulomb"]], "ffsim.trotter": [[9, "module-ffsim.trotter"]], "ffsim.trotter.qdrift": [[9, "module-ffsim.trotter.qdrift"]], "ffsim.trotter.trotter": [[9, "module-ffsim.trotter.trotter"]], "one_body_square_decomposition() (in module ffsim.trotter.qdrift)": [[9, "ffsim.trotter.qdrift.one_body_square_decomposition"]], "qdrift_probabilities() (in module ffsim.trotter.qdrift)": [[9, "ffsim.trotter.qdrift.qdrift_probabilities"]], "simulate_qdrift_double_factorized() (in module ffsim.trotter.qdrift)": [[9, "ffsim.trotter.qdrift.simulate_qdrift_double_factorized"]], "simulate_trotter_double_factorized() (in module ffsim.trotter.trotter)": [[9, "ffsim.trotter.trotter.simulate_trotter_double_factorized"]], "spectral_norm_diag_coulomb() (in module ffsim.trotter.qdrift)": [[9, "ffsim.trotter.qdrift.spectral_norm_diag_coulomb"]], "spectral_norm_one_body_tensor() (in module ffsim.trotter.qdrift)": [[9, "ffsim.trotter.qdrift.spectral_norm_one_body_tensor"]], "variance_diag_coulomb() (in module ffsim.trotter.qdrift)": [[9, "ffsim.trotter.qdrift.variance_diag_coulomb"]], "variance_one_body_tensor() (in module ffsim.trotter.qdrift)": [[9, "ffsim.trotter.qdrift.variance_one_body_tensor"]], "ucjoperator (class in ffsim.variational.lucj)": [[10, "ffsim.variational.lucj.UCJOperator"]], "apply_ucj_operator() (in module ffsim.variational.lucj)": [[10, "ffsim.variational.lucj.apply_ucj_operator"]], "diag_coulomb_mats_alpha_alpha (ffsim.variational.lucj.ucjoperator attribute)": [[10, "ffsim.variational.lucj.UCJOperator.diag_coulomb_mats_alpha_alpha"]], "diag_coulomb_mats_alpha_beta (ffsim.variational.lucj.ucjoperator attribute)": [[10, "ffsim.variational.lucj.UCJOperator.diag_coulomb_mats_alpha_beta"]], "ffsim.variational": [[10, "module-ffsim.variational"]], "ffsim.variational.lucj": [[10, "module-ffsim.variational.lucj"]], "final_orbital_rotation (ffsim.variational.lucj.ucjoperator attribute)": [[10, "ffsim.variational.lucj.UCJOperator.final_orbital_rotation"]], "from_parameters() (ffsim.variational.lucj.ucjoperator static method)": [[10, "ffsim.variational.lucj.UCJOperator.from_parameters"]], "from_t_amplitudes() (ffsim.variational.lucj.ucjoperator static method)": [[10, "ffsim.variational.lucj.UCJOperator.from_t_amplitudes"]], "n_reps (ffsim.variational.lucj.ucjoperator property)": [[10, "ffsim.variational.lucj.UCJOperator.n_reps"]], "norb (ffsim.variational.lucj.ucjoperator property)": [[10, "ffsim.variational.lucj.UCJOperator.norb"]], "orbital_rotations (ffsim.variational.lucj.ucjoperator attribute)": [[10, "ffsim.variational.lucj.UCJOperator.orbital_rotations"]], "to_parameters() (ffsim.variational.lucj.ucjoperator method)": [[10, "ffsim.variational.lucj.UCJOperator.to_parameters"]], "to_t_amplitudes() (ffsim.variational.lucj.ucjoperator method)": [[10, "ffsim.variational.lucj.UCJOperator.to_t_amplitudes"]]}})
\ No newline at end of file
diff --git a/tutorials/01-introduction.ipynb b/tutorials/01-introduction.ipynb
index b8b0526e1..e7096502b 100644
--- a/tutorials/01-introduction.ipynb
+++ b/tutorials/01-introduction.ipynb
@@ -16,10 +16,10 @@
    "execution_count": 1,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-22T21:03:16.279811Z",
-     "iopub.status.busy": "2023-09-22T21:03:16.279424Z",
-     "iopub.status.idle": "2023-09-22T21:03:16.582247Z",
-     "shell.execute_reply": "2023-09-22T21:03:16.581675Z"
+     "iopub.execute_input": "2023-09-23T01:21:10.728516Z",
+     "iopub.status.busy": "2023-09-23T01:21:10.728159Z",
+     "iopub.status.idle": "2023-09-23T01:21:11.032417Z",
+     "shell.execute_reply": "2023-09-23T01:21:11.031854Z"
     }
    },
    "outputs": [],
@@ -62,10 +62,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-22T21:03:16.586628Z",
-     "iopub.status.busy": "2023-09-22T21:03:16.585111Z",
-     "iopub.status.idle": "2023-09-22T21:03:16.590572Z",
-     "shell.execute_reply": "2023-09-22T21:03:16.590118Z"
+     "iopub.execute_input": "2023-09-23T01:21:11.037047Z",
+     "iopub.status.busy": "2023-09-23T01:21:11.035562Z",
+     "iopub.status.idle": "2023-09-23T01:21:11.040972Z",
+     "shell.execute_reply": "2023-09-23T01:21:11.040514Z"
     }
    },
    "outputs": [],
@@ -92,10 +92,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-22T21:03:16.594310Z",
-     "iopub.status.busy": "2023-09-22T21:03:16.593415Z",
-     "iopub.status.idle": "2023-09-22T21:03:16.597294Z",
-     "shell.execute_reply": "2023-09-22T21:03:16.596845Z"
+     "iopub.execute_input": "2023-09-23T01:21:11.044733Z",
+     "iopub.status.busy": "2023-09-23T01:21:11.043841Z",
+     "iopub.status.idle": "2023-09-23T01:21:11.047740Z",
+     "shell.execute_reply": "2023-09-23T01:21:11.047295Z"
     }
    },
    "outputs": [],
diff --git a/tutorials/02-orbital-rotation.ipynb b/tutorials/02-orbital-rotation.ipynb
index 7ee0c5f50..d6b907b41 100644
--- a/tutorials/02-orbital-rotation.ipynb
+++ b/tutorials/02-orbital-rotation.ipynb
@@ -43,10 +43,10 @@
    "execution_count": 1,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-22T21:03:18.236148Z",
-     "iopub.status.busy": "2023-09-22T21:03:18.235765Z",
-     "iopub.status.idle": "2023-09-22T21:03:18.536110Z",
-     "shell.execute_reply": "2023-09-22T21:03:18.535486Z"
+     "iopub.execute_input": "2023-09-23T01:21:12.555910Z",
+     "iopub.status.busy": "2023-09-23T01:21:12.555674Z",
+     "iopub.status.idle": "2023-09-23T01:21:12.856048Z",
+     "shell.execute_reply": "2023-09-23T01:21:12.855430Z"
     }
    },
    "outputs": [],
@@ -111,10 +111,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-22T21:03:18.539935Z",
-     "iopub.status.busy": "2023-09-22T21:03:18.539625Z",
-     "iopub.status.idle": "2023-09-22T21:03:18.566180Z",
-     "shell.execute_reply": "2023-09-22T21:03:18.565631Z"
+     "iopub.execute_input": "2023-09-23T01:21:12.859974Z",
+     "iopub.status.busy": "2023-09-23T01:21:12.859457Z",
+     "iopub.status.idle": "2023-09-23T01:21:12.885192Z",
+     "shell.execute_reply": "2023-09-23T01:21:12.884669Z"
     }
    },
    "outputs": [],
@@ -160,10 +160,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-22T21:03:18.569585Z",
-     "iopub.status.busy": "2023-09-22T21:03:18.569376Z",
-     "iopub.status.idle": "2023-09-22T21:03:18.580624Z",
-     "shell.execute_reply": "2023-09-22T21:03:18.580075Z"
+     "iopub.execute_input": "2023-09-23T01:21:12.889505Z",
+     "iopub.status.busy": "2023-09-23T01:21:12.888315Z",
+     "iopub.status.idle": "2023-09-23T01:21:12.900215Z",
+     "shell.execute_reply": "2023-09-23T01:21:12.899700Z"
     }
    },
    "outputs": [],
@@ -203,10 +203,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-22T21:03:18.583300Z",
-     "iopub.status.busy": "2023-09-22T21:03:18.583102Z",
-     "iopub.status.idle": "2023-09-22T21:03:18.588294Z",
-     "shell.execute_reply": "2023-09-22T21:03:18.587757Z"
+     "iopub.execute_input": "2023-09-23T01:21:12.904675Z",
+     "iopub.status.busy": "2023-09-23T01:21:12.903115Z",
+     "iopub.status.idle": "2023-09-23T01:21:12.909645Z",
+     "shell.execute_reply": "2023-09-23T01:21:12.909124Z"
     }
    },
    "outputs": [],
diff --git a/tutorials/03-double-factorized.ipynb b/tutorials/03-double-factorized.ipynb
index 1f6dd43d9..260ffc4b5 100644
--- a/tutorials/03-double-factorized.ipynb
+++ b/tutorials/03-double-factorized.ipynb
@@ -43,10 +43,10 @@
    "execution_count": 1,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-22T21:03:20.293237Z",
-     "iopub.status.busy": "2023-09-22T21:03:20.292688Z",
-     "iopub.status.idle": "2023-09-22T21:03:20.699547Z",
-     "shell.execute_reply": "2023-09-22T21:03:20.699005Z"
+     "iopub.execute_input": "2023-09-23T01:21:14.538466Z",
+     "iopub.status.busy": "2023-09-23T01:21:14.538260Z",
+     "iopub.status.idle": "2023-09-23T01:21:14.944173Z",
+     "shell.execute_reply": "2023-09-23T01:21:14.943411Z"
     }
    },
    "outputs": [
@@ -93,10 +93,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-22T21:03:20.713380Z",
-     "iopub.status.busy": "2023-09-22T21:03:20.712853Z",
-     "iopub.status.idle": "2023-09-22T21:03:20.719004Z",
-     "shell.execute_reply": "2023-09-22T21:03:20.718537Z"
+     "iopub.execute_input": "2023-09-23T01:21:14.963251Z",
+     "iopub.status.busy": "2023-09-23T01:21:14.962671Z",
+     "iopub.status.idle": "2023-09-23T01:21:14.969003Z",
+     "shell.execute_reply": "2023-09-23T01:21:14.968514Z"
     }
    },
    "outputs": [
@@ -227,10 +227,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-22T21:03:20.721657Z",
-     "iopub.status.busy": "2023-09-22T21:03:20.721273Z",
-     "iopub.status.idle": "2023-09-22T21:03:20.725738Z",
-     "shell.execute_reply": "2023-09-22T21:03:20.725283Z"
+     "iopub.execute_input": "2023-09-23T01:21:14.971924Z",
+     "iopub.status.busy": "2023-09-23T01:21:14.971350Z",
+     "iopub.status.idle": "2023-09-23T01:21:14.976136Z",
+     "shell.execute_reply": "2023-09-23T01:21:14.975672Z"
     }
    },
    "outputs": [],
@@ -285,10 +285,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-22T21:03:20.728216Z",
-     "iopub.status.busy": "2023-09-22T21:03:20.727839Z",
-     "iopub.status.idle": "2023-09-22T21:03:20.731504Z",
-     "shell.execute_reply": "2023-09-22T21:03:20.731060Z"
+     "iopub.execute_input": "2023-09-23T01:21:14.978817Z",
+     "iopub.status.busy": "2023-09-23T01:21:14.978442Z",
+     "iopub.status.idle": "2023-09-23T01:21:14.982342Z",
+     "shell.execute_reply": "2023-09-23T01:21:14.981860Z"
     }
    },
    "outputs": [],
@@ -325,10 +325,10 @@
    "execution_count": 5,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-22T21:03:20.734014Z",
-     "iopub.status.busy": "2023-09-22T21:03:20.733642Z",
-     "iopub.status.idle": "2023-09-22T21:03:20.738284Z",
-     "shell.execute_reply": "2023-09-22T21:03:20.737833Z"
+     "iopub.execute_input": "2023-09-23T01:21:14.984891Z",
+     "iopub.status.busy": "2023-09-23T01:21:14.984507Z",
+     "iopub.status.idle": "2023-09-23T01:21:14.989382Z",
+     "shell.execute_reply": "2023-09-23T01:21:14.988900Z"
     }
    },
    "outputs": [
@@ -367,10 +367,10 @@
    "execution_count": 6,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-22T21:03:20.740698Z",
-     "iopub.status.busy": "2023-09-22T21:03:20.740308Z",
-     "iopub.status.idle": "2023-09-22T21:03:20.753973Z",
-     "shell.execute_reply": "2023-09-22T21:03:20.753394Z"
+     "iopub.execute_input": "2023-09-23T01:21:14.991924Z",
+     "iopub.status.busy": "2023-09-23T01:21:14.991546Z",
+     "iopub.status.idle": "2023-09-23T01:21:15.000804Z",
+     "shell.execute_reply": "2023-09-23T01:21:15.000310Z"
     }
    },
    "outputs": [
@@ -409,10 +409,10 @@
    "execution_count": 7,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-22T21:03:20.756581Z",
-     "iopub.status.busy": "2023-09-22T21:03:20.756030Z",
-     "iopub.status.idle": "2023-09-22T21:03:20.763740Z",
-     "shell.execute_reply": "2023-09-22T21:03:20.763274Z"
+     "iopub.execute_input": "2023-09-23T01:21:15.003508Z",
+     "iopub.status.busy": "2023-09-23T01:21:15.003108Z",
+     "iopub.status.idle": "2023-09-23T01:21:15.010861Z",
+     "shell.execute_reply": "2023-09-23T01:21:15.010380Z"
     }
    },
    "outputs": [
@@ -450,10 +450,10 @@
    "execution_count": 8,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-22T21:03:20.766424Z",
-     "iopub.status.busy": "2023-09-22T21:03:20.765969Z",
-     "iopub.status.idle": "2023-09-22T21:03:20.802839Z",
-     "shell.execute_reply": "2023-09-22T21:03:20.802363Z"
+     "iopub.execute_input": "2023-09-23T01:21:15.013478Z",
+     "iopub.status.busy": "2023-09-23T01:21:15.013072Z",
+     "iopub.status.idle": "2023-09-23T01:21:15.049959Z",
+     "shell.execute_reply": "2023-09-23T01:21:15.049443Z"
     }
    },
    "outputs": [
@@ -493,10 +493,10 @@
    "execution_count": 9,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-22T21:03:20.805492Z",
-     "iopub.status.busy": "2023-09-22T21:03:20.805199Z",
-     "iopub.status.idle": "2023-09-22T21:03:20.838642Z",
-     "shell.execute_reply": "2023-09-22T21:03:20.838163Z"
+     "iopub.execute_input": "2023-09-23T01:21:15.052667Z",
+     "iopub.status.busy": "2023-09-23T01:21:15.052330Z",
+     "iopub.status.idle": "2023-09-23T01:21:15.085976Z",
+     "shell.execute_reply": "2023-09-23T01:21:15.080583Z"
     }
    },
    "outputs": [
@@ -535,10 +535,10 @@
    "execution_count": 10,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-22T21:03:20.842012Z",
-     "iopub.status.busy": "2023-09-22T21:03:20.841702Z",
-     "iopub.status.idle": "2023-09-22T21:03:20.856836Z",
-     "shell.execute_reply": "2023-09-22T21:03:20.856269Z"
+     "iopub.execute_input": "2023-09-23T01:21:15.089868Z",
+     "iopub.status.busy": "2023-09-23T01:21:15.089518Z",
+     "iopub.status.idle": "2023-09-23T01:21:15.102275Z",
+     "shell.execute_reply": "2023-09-23T01:21:15.101739Z"
     }
    },
    "outputs": [
diff --git a/tutorials/04-lucj.ipynb b/tutorials/04-lucj.ipynb
index 8edc35981..050d5e27a 100644
--- a/tutorials/04-lucj.ipynb
+++ b/tutorials/04-lucj.ipynb
@@ -14,10 +14,10 @@
    "execution_count": 1,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-22T21:03:22.734065Z",
-     "iopub.status.busy": "2023-09-22T21:03:22.733637Z",
-     "iopub.status.idle": "2023-09-22T21:03:23.108073Z",
-     "shell.execute_reply": "2023-09-22T21:03:23.107515Z"
+     "iopub.execute_input": "2023-09-23T01:21:17.005056Z",
+     "iopub.status.busy": "2023-09-23T01:21:17.004496Z",
+     "iopub.status.idle": "2023-09-23T01:21:17.411951Z",
+     "shell.execute_reply": "2023-09-23T01:21:17.411330Z"
     }
    },
    "outputs": [
@@ -80,10 +80,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-22T21:03:23.111168Z",
-     "iopub.status.busy": "2023-09-22T21:03:23.110704Z",
-     "iopub.status.idle": "2023-09-22T21:03:23.283244Z",
-     "shell.execute_reply": "2023-09-22T21:03:23.282713Z"
+     "iopub.execute_input": "2023-09-23T01:21:17.415299Z",
+     "iopub.status.busy": "2023-09-23T01:21:17.414894Z",
+     "iopub.status.idle": "2023-09-23T01:21:17.628856Z",
+     "shell.execute_reply": "2023-09-23T01:21:17.628276Z"
     }
    },
    "outputs": [
@@ -145,10 +145,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-22T21:03:23.287326Z",
-     "iopub.status.busy": "2023-09-22T21:03:23.286393Z",
-     "iopub.status.idle": "2023-09-22T21:03:23.432837Z",
-     "shell.execute_reply": "2023-09-22T21:03:23.432304Z"
+     "iopub.execute_input": "2023-09-23T01:21:17.632430Z",
+     "iopub.status.busy": "2023-09-23T01:21:17.631772Z",
+     "iopub.status.idle": "2023-09-23T01:21:17.780200Z",
+     "shell.execute_reply": "2023-09-23T01:21:17.779696Z"
     }
    },
    "outputs": [
@@ -222,10 +222,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-22T21:03:23.436955Z",
-     "iopub.status.busy": "2023-09-22T21:03:23.435969Z",
-     "iopub.status.idle": "2023-09-22T21:03:23.607950Z",
-     "shell.execute_reply": "2023-09-22T21:03:23.607426Z"
+     "iopub.execute_input": "2023-09-23T01:21:17.784386Z",
+     "iopub.status.busy": "2023-09-23T01:21:17.783238Z",
+     "iopub.status.idle": "2023-09-23T01:21:17.954821Z",
+     "shell.execute_reply": "2023-09-23T01:21:17.954247Z"
     }
    },
    "outputs": [