From 3ea5c232ff12f5704e54056131c2a6cb9b4632a9 Mon Sep 17 00:00:00 2001
From: Mirko Birbaumer <mirko.birbaumer@hslu.ch>
Date: Fri, 16 Sep 2022 12:48:30 +0000
Subject: [PATCH] added element-wise operations
---
.../Preliminaries_Numpy_Pandas.ipynb | 300 +++++++++++++++++-
1 file changed, 299 insertions(+), 1 deletion(-)
diff --git a/notebooks/Block_0/Examples script/Preliminaries_Numpy_Pandas.ipynb b/notebooks/Block_0/Examples script/Preliminaries_Numpy_Pandas.ipynb
index eb29636..a3a7307 100644
--- a/notebooks/Block_0/Examples script/Preliminaries_Numpy_Pandas.ipynb
+++ b/notebooks/Block_0/Examples script/Preliminaries_Numpy_Pandas.ipynb
@@ -752,9 +752,307 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "## 3.4 Element-wise Operations"
+ "### Changing Shapes\n",
+ "\n",
+ "Sometimes you will need to change the shape of your data without actually changing \n",
+ "its contents. For example, you may have a vector, which is one-dimensional, but need \n",
+ "a matrix, which is two-dimensional. There are two ways you can do that.\n",
+ "\n",
+ "Let's say you have the following vector:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 36,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "(4,)"
+ ]
+ },
+ "execution_count": 36,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "v = np.array([1,2,3,4])\n",
+ "v.shape"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Calling `v.shape` would return `(4,)`. But what if you want a $1\\times 4$ matrix? \n",
+ "You can accomplish that with the `reshape` function, like so:\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 37,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[1, 2, 3, 4]])"
+ ]
+ },
+ "execution_count": 37,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "x = v.reshape(1,4)\n",
+ "x"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Calling `x.shape` would return `(1,4)`. If you wanted a $4\\times 1$ matrix, you \n",
+ "could do this:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 38,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[1],\n",
+ " [2],\n",
+ " [3],\n",
+ " [4]])"
+ ]
+ },
+ "execution_count": 38,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "x = v.reshape(4,1)\n",
+ "x"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The `reshape` function works for more than just adding a dimension of size $1$. Check out its \n",
+ "documentation for more examples.\n",
+ "\n",
+ "One more thing about reshaping NumPy arrays: if you see code from experienced NumPy users, you \n",
+ "will often see them use a special slicing syntax instead of calling `reshape`. Using this \n",
+ "syntax, the previous two examples would look like this:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 39,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[1, 2, 3, 4]])"
+ ]
+ },
+ "execution_count": 39,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "x = v[None, :]\n",
+ "x"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 42,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "(4, 1)"
+ ]
+ },
+ "execution_count": 42,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "x.shape"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 40,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[1],\n",
+ " [2],\n",
+ " [3],\n",
+ " [4]])"
+ ]
+ },
+ "execution_count": 40,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "x = v[:, None]\n",
+ "x"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 43,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "(4, 1)"
+ ]
+ },
+ "execution_count": 43,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "x.shape"
]
},
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Those lines create a slice that looks at all of the items of `v` but asks NumPy to add a new dimension \n",
+ "of size $1$ for the associated axis. It may look strange to you now, but it's a common technique so \n",
+ "it's good to be aware of it. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Element-wise Operations\n",
+ "\n",
+ "#### The Python Way\n",
+ "\n",
+ "Suppose you had a list of numbers, and you wanted to add $5$ to every item in the list. \n",
+ "Without NumPy, you might do something like this:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 46,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "[6, 7, 8, 9, 10]"
+ ]
+ },
+ "execution_count": 46,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "values = [1,2,3,4,5]\n",
+ "for i in range(len(values)):\n",
+ " values[i] += 5\n",
+ " \n",
+ "values"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "That makes sense, but it's a lot of code to write and it runs slowly because \n",
+ "it's pure Python.\n",
+ "\n",
+ "__Note:__ Just in case you aren't used to using operators like `+=`, that just \n",
+ "means _add these two items and then store the result in the left item._ It is a more \n",
+ "succinct way of writing `values[i] = values[i] + 5`. The code you see in these examples \n",
+ "makes use of such operators whenever possible."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### The NumPy Way\n",
+ "\n",
+ "In NumPy, we could do the following:\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 47,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "values = [1,2,3,4,5]\n",
+ "values = np.array(values) + 5"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Creating that array may seem odd, but normally you'll be storing your data in `ndarrays` \n",
+ "anyway. So if you already had an `ndarray` named `values`, you could have just done:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
{
"cell_type": "code",
"execution_count": 4,
--
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