From aa85c6892a331082ce4617bc2e07a8d7b09c90b2 Mon Sep 17 00:00:00 2001
From: Matheus Gomes Cordeiro <matheusgomescord@gmail.com>
Date: Mon, 18 Nov 2024 13:35:51 -0300
Subject: [PATCH] Criado usando o Colab

---
 examples/speed_tests_numba_and_cython.ipynb | 21 ++++++++++++++++-----
 1 file changed, 16 insertions(+), 5 deletions(-)

diff --git a/examples/speed_tests_numba_and_cython.ipynb b/examples/speed_tests_numba_and_cython.ipynb
index 1392f15..1649f7a 100644
--- a/examples/speed_tests_numba_and_cython.ipynb
+++ b/examples/speed_tests_numba_and_cython.ipynb
@@ -87,6 +87,18 @@
         "%matplotlib inline"
       ]
     },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "## Performance Comparison: Mr Mustard vs. Fast Wave for Single Fock & Single Position Wavefunctions\n",
+        "---\n",
+        "$$$$\n",
+        "**Explanation:** This analysis evaluates the computational efficiency of three approaches—Mr Mustard, Fast Wave (Numba), and Fast Wave (Cython)—for calculating the squared amplitude $|\\psi_n(x)|^2$ of a Single Fock & Single Position Wavefunction $\\psi_n(x)$. The Single Fock & Single Position wavefunction, $\\psi_{i}(x)$, maps a scalar input $x$ to a scalar output. Execution times for each method are plotted to facilitate comparison."
+      ],
+      "metadata": {
+        "id": "f3JX7gvQA77f"
+      }
+    },
     {
       "cell_type": "code",
       "execution_count": null,
@@ -112,7 +124,6 @@
         }
       ],
       "source": [
-        "#@title Comparing Mr Mustard's speed to Fast Wave (Single Fock & Single Position; real values)\n",
         "n = 30 #@param\n",
         "x_max = 5.0 #@param\n",
         "x_min = -5.0 #@param\n",
@@ -164,8 +175,10 @@
         "id": "j4MOFicqZYF6"
       },
       "source": [
-        "\n",
-        "[Scptt: add text to explain the difference between the first comparison \"single fock, signle position\" and the second comparison \"single fock, multile position\".]"
+        "## Performance Comparison: Mr Mustard vs. Fast Wave for Single Fock & Multiple Position Wavefunctions\n",
+        "---\n",
+        "$$$$\n",
+        "**Explanation:** This analysis evaluates the computational efficiency of three approaches—Mr Mustard, Fast Wave (Numba), and Fast Wave (Cython)—for calculating the squared amplitude $|\\psi_n(X_{m})|^2$ of a Single Fock & Multiple Position Wavefunction $\\psi_n(X_{m})$. The Single Fock & Multiple Position wavefunction, $\\psi_{i}(X)$, maps an array of position inputs $X_{m}$ to an array of corresponding outputs: $[\\psi_{i}(x_{1}), \\psi_{i}(x_{2}), ..., \\psi_{i}(x_{m})]$. Execution times for each method are plotted to facilitate comparison."
       ]
     },
     {
@@ -193,8 +206,6 @@
         }
       ],
       "source": [
-        "#@title Comparing Mr Mustard's speed to Fast Wave (Single Fock & Multiple Position; real values)\n",
-        "\n",
         "n = 50 #@param\n",
         "x_max = 5.0 #@param\n",
         "x_min = -5.0 #@param\n",