From fb42b17ddc73659e7c7798971b0b6d95b3f5bfa4 Mon Sep 17 00:00:00 2001
From: vinitrg <vinit.gujarathi@gmail.com>
Date: Sat, 24 Mar 2018 14:47:36 +0530
Subject: [PATCH 1/5] Completing Machine Learning Precourse work

---
 __pycache__/precourse.cpython-36.pyc | Bin 0 -> 2515 bytes
 precourse.py                         |  69 +++++++++++++++++++++++++++
 2 files changed, 69 insertions(+)
 create mode 100644 __pycache__/precourse.cpython-36.pyc

diff --git a/__pycache__/precourse.cpython-36.pyc b/__pycache__/precourse.cpython-36.pyc
new file mode 100644
index 0000000000000000000000000000000000000000..e2bef5339dd51c7270dcc9f311e090add7641567
GIT binary patch
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literal 0
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diff --git a/precourse.py b/precourse.py
index 75f29ad..8650d05 100644
--- a/precourse.py
+++ b/precourse.py
@@ -8,6 +8,75 @@
 
 # Free example function definition
 # This function passes one of the 11 tests contained inside of test.py. Write the rest, defined in README.md, here, and execute python test.py to test. Passing this precourse work will greatly increase your odds of acceptance into the program.
+import math
+import numpy as np
+
+def derivative(func , x):
+    i = 0.0000000001
+    return round((func(x+i)-func(x))/i,3)
+
 def f(x):
     return x**2
 
+def f_2(x):
+    return x**3
+
+def f_3(x):
+    return x**3 + 5*x
+
+def d_f(x):
+    return derivative(f,x)
+
+def d_f_2(x):
+    return derivative(f_2,x)
+
+def d_f_3(x):
+    return derivative(f_3,x)
+
+def vector_sum(vectA ,vectB ):
+	vectorAdd = []
+	if(len(vectA) == len(vectB)):
+		for x,y in zip(vectA,vectB):
+			vectorAdd.append(x+y)
+	return vectorAdd
+
+def vector_less(vectA ,vectB ):
+	vectorSub = []
+	if(len(vectA) == len(vectB)):
+		for x,y in zip(vectA,vectB):
+			vectorSub.append(x-y)
+	return vectorSub
+
+def vector_magnitude(vectA):
+	squaredAddition = 0
+	for x in vectA:
+		squaredAddition = squaredAddition + x**2
+	return math.sqrt(squaredAddition)
+
+def vec3():
+	return np.zeros(3)
+
+def vec5():
+	return np.ones(5)
+
+def vec2_1():
+	return np.identity(2)[0]
+
+def vec2_2():
+	return np.identity(2)[1]
+
+def matrix_multiply(matrixA,matrixB):
+	try:
+		matrixAColNos = np.shape(matrixA)[0] 
+	except IndexError as e:
+		matrixAColNos = 1
+	try:
+		matrixBrowNos = np.shape(matrixB)[1]
+	except Exception as e:
+		matrixBrowNos = 1
+
+	if (matrixAColNos == matrixBrowNos):
+		return np.dot(matrixA,matrixB)
+	else:
+		raise Exception('The dot multiplication is not possible in this case')
+

From 6cf9050290a64f5cb53b56f6c69bf19b0a2bcbcc Mon Sep 17 00:00:00 2001
From: vinitrg <vinit.gujarathi@gmail.com>
Date: Sat, 24 Mar 2018 15:30:36 +0530
Subject: [PATCH 2/5] formatting changes and cleaning up

---
 __pycache__/.DS_Store                | Bin 0 -> 6148 bytes
 __pycache__/precourse.cpython-36.pyc | Bin 2515 -> 0 bytes
 precourse.py                         |  88 ++++++++++++++-------------
 3 files changed, 45 insertions(+), 43 deletions(-)
 create mode 100644 __pycache__/.DS_Store
 delete mode 100644 __pycache__/precourse.cpython-36.pyc

diff --git a/__pycache__/.DS_Store b/__pycache__/.DS_Store
new file mode 100644
index 0000000000000000000000000000000000000000..5008ddfcf53c02e82d7eee2e57c38e5672ef89f6
GIT binary patch
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literal 0
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diff --git a/__pycache__/precourse.cpython-36.pyc b/__pycache__/precourse.cpython-36.pyc
deleted file mode 100644
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GIT binary patch
literal 0
HcmV?d00001

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diff --git a/precourse.py b/precourse.py
index 8650d05..2611592 100644
--- a/precourse.py
+++ b/precourse.py
@@ -11,9 +11,9 @@
 import math
 import numpy as np
 
-def derivative(func , x):
-    i = 0.0000000001
-    return round((func(x+i)-func(x))/i,3)
+def derivative(func, x):
+    epsilon = math.e**-10
+    return round((func(x+epsilon)-func(x))/epsilon, 3)
 
 def f(x):
     return x**2
@@ -25,58 +25,60 @@ def f_3(x):
     return x**3 + 5*x
 
 def d_f(x):
-    return derivative(f,x)
+    return derivative(f, x)
 
 def d_f_2(x):
-    return derivative(f_2,x)
+    return derivative(f_2, x)
 
 def d_f_3(x):
-    return derivative(f_3,x)
-
-def vector_sum(vectA ,vectB ):
-	vectorAdd = []
-	if(len(vectA) == len(vectB)):
-		for x,y in zip(vectA,vectB):
-			vectorAdd.append(x+y)
-	return vectorAdd
-
-def vector_less(vectA ,vectB ):
-	vectorSub = []
-	if(len(vectA) == len(vectB)):
-		for x,y in zip(vectA,vectB):
-			vectorSub.append(x-y)
-	return vectorSub
+    return derivative(f_3, x)
+
+def vector_sum(vectA, vectB):
+    vectorAdd = []
+    if(len(vectA) == len(vectB)):
+        for x,y in zip(vectA, vectB):
+            vectorAdd.append(x+y)
+    return vectorAdd
+
+def vector_less(vectA, vectB):
+    vectorSub = []
+    if(len(vectA) == len(vectB)):
+        for x,y in zip(vectA, vectB):
+            vectorSub.append(x-y)
+
+    return vectorSub
 
 def vector_magnitude(vectA):
-	squaredAddition = 0
-	for x in vectA:
-		squaredAddition = squaredAddition + x**2
-	return math.sqrt(squaredAddition)
+    squaredAddition = 0
+    for x in vectA:
+        squaredAddition = squaredAddition + x**2
+
+    return math.sqrt(squaredAddition)
 
 def vec3():
-	return np.zeros(3)
+    return np.zeros(3)
 
 def vec5():
-	return np.ones(5)
+    return np.ones(5)
 
 def vec2_1():
-	return np.identity(2)[0]
+    return np.identity(2)[0]
 
 def vec2_2():
-	return np.identity(2)[1]
-
-def matrix_multiply(matrixA,matrixB):
-	try:
-		matrixAColNos = np.shape(matrixA)[0] 
-	except IndexError as e:
-		matrixAColNos = 1
-	try:
-		matrixBrowNos = np.shape(matrixB)[1]
-	except Exception as e:
-		matrixBrowNos = 1
-
-	if (matrixAColNos == matrixBrowNos):
-		return np.dot(matrixA,matrixB)
-	else:
-		raise Exception('The dot multiplication is not possible in this case')
+    return np.identity(2)[1]
+
+def matrix_multiply(matrixA, matrixB):
+    try:
+        matrixAColNos = np.shape(matrixA)[0]
+    except IndexError as e:
+        matrixAColNos = 1
+    try:
+        matrixBrowNos = np.shape(matrixB)[1]
+    except Exception as e:
+        matrixBrowNos = 1
+
+    if (matrixAColNos == matrixBrowNos):
+        return np.dot(matrixA, matrixB)
+    else:
+        raise Exception('The dot multiplication is not possible in this case')
 

From f610845d64532f634345db2b47ba264498ffed1c Mon Sep 17 00:00:00 2001
From: vinitrg <vinit.gujarathi@gmail.com>
Date: Sat, 24 Mar 2018 15:34:53 +0530
Subject: [PATCH 3/5] reducing value of epsilion to take care of the tests

---
 precourse.py | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/precourse.py b/precourse.py
index 2611592..fe29478 100644
--- a/precourse.py
+++ b/precourse.py
@@ -12,7 +12,7 @@
 import numpy as np
 
 def derivative(func, x):
-    epsilon = math.e**-10
+    epsilon = math.e**-18
     return round((func(x+epsilon)-func(x))/epsilon, 3)
 
 def f(x):
@@ -33,6 +33,7 @@ def d_f_2(x):
 def d_f_3(x):
     return derivative(f_3, x)
 
+print(d_f_2(5))
 def vector_sum(vectA, vectB):
     vectorAdd = []
     if(len(vectA) == len(vectB)):

From 3e324ef6e377ba62009ef5ad70947e45dd9d8fa6 Mon Sep 17 00:00:00 2001
From: vinitrg <vinit.gujarathi@gmail.com>
Date: Sat, 24 Mar 2018 15:38:43 +0530
Subject: [PATCH 4/5] removing unrequired line

---
 precourse.py | 1 -
 1 file changed, 1 deletion(-)

diff --git a/precourse.py b/precourse.py
index fe29478..ed1e67e 100644
--- a/precourse.py
+++ b/precourse.py
@@ -33,7 +33,6 @@ def d_f_2(x):
 def d_f_3(x):
     return derivative(f_3, x)
 
-print(d_f_2(5))
 def vector_sum(vectA, vectB):
     vectorAdd = []
     if(len(vectA) == len(vectB)):

From 0fd3280c2a488f6696421ad9c2f5c525179192ff Mon Sep 17 00:00:00 2001
From: Vinit <vinit.gujarathi@gmail.com>
Date: Sat, 5 May 2018 21:41:55 +0530
Subject: [PATCH 5/5] Created using Colaboratory

---
 High_Dimensionality_Sprint_Challenge.ipynb | 170 +++++++++++++++++++++
 1 file changed, 170 insertions(+)
 create mode 100644 High_Dimensionality_Sprint_Challenge.ipynb

diff --git a/High_Dimensionality_Sprint_Challenge.ipynb b/High_Dimensionality_Sprint_Challenge.ipynb
new file mode 100644
index 0000000..543d24e
--- /dev/null
+++ b/High_Dimensionality_Sprint_Challenge.ipynb
@@ -0,0 +1,170 @@
+{
+  "nbformat": 4,
+  "nbformat_minor": 0,
+  "metadata": {
+    "colab": {
+      "name": "High Dimensionality Sprint Challenge.ipynb",
+      "version": "0.3.2",
+      "provenance": [],
+      "collapsed_sections": []
+    },
+    "kernelspec": {
+      "name": "python3",
+      "display_name": "Python 3"
+    }
+  },
+  "cells": [
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "view-in-github",
+        "colab_type": "text"
+      },
+      "source": [
+        "[View in Colaboratory](https://colab.research.google.com/github/vinitrg/ML-Precourse/blob/master/High_Dimensionality_Sprint_Challenge.ipynb)"
+      ]
+    },
+    {
+      "metadata": {
+        "id": "8dtL-3V557G6",
+        "colab_type": "text"
+      },
+      "cell_type": "markdown",
+      "source": [
+        "# High Dimensionality Sprint Challenge\n",
+        "\n",
+        "High Dimensionality is characterized by the _Curse of Dimensionality_. Humans can visualize 2d and 3d, but not anything higher. How do we reason about data?\n",
+        "\n",
+        "High Dimensionality Objectives include:\n",
+        "* Normalize a vector into a magnitude and unit vector\n",
+        "* Compute L1 and L2 distances of a pair of vectors\n",
+        "* Compute the distance between pairs of vectors and select the smallest"
+      ]
+    },
+    {
+      "metadata": {
+        "id": "PMajVGoY54DR",
+        "colab_type": "code",
+        "colab": {}
+      },
+      "cell_type": "code",
+      "source": [
+        "# LAMBDA SCHOOL\n",
+        "#\n",
+        "# MACHINE LEARNING\n",
+        "#\n",
+        "# MIT LICENSE\n",
+        "\n",
+        "import numpy as np"
+      ],
+      "execution_count": 0,
+      "outputs": []
+    },
+    {
+      "metadata": {
+        "id": "YUo0Gg2UbieJ",
+        "colab_type": "text"
+      },
+      "cell_type": "markdown",
+      "source": [
+        "# 1. Normalize a vector into magnitude and unit vector"
+      ]
+    },
+    {
+      "metadata": {
+        "id": "RuZFC7k8bnRu",
+        "colab_type": "code",
+        "colab": {}
+      },
+      "cell_type": "code",
+      "source": [
+        "v = np.array([17,7,5,2,1])\n",
+        "\n",
+        "# m = Magnitude of v\n",
+        "m = None\n",
+        "\n",
+        "# v_u = unit vector of v such that m * v_u = v\n",
+        "v_u = None"
+      ],
+      "execution_count": 0,
+      "outputs": []
+    },
+    {
+      "metadata": {
+        "id": "sgNZ1QDCdErt",
+        "colab_type": "text"
+      },
+      "cell_type": "markdown",
+      "source": [
+        "# 2. Compute the L1 and L2 distances of a pair of vectors\n",
+        "\n",
+        "Recall that the L1 distance is the \"manhattan\" distance, the sum of absolute values of a vector:\n",
+        "\n",
+        "$d_{v}^{L1} = \\sum{|v_i|}$\n",
+        "\n",
+        "The L2 distance or \"euclidean\" distance is the square root of the sum of the squares of a vector:\n",
+        "\n",
+        "$d_{v}^{L2} = \\sqrt{\\sum{v_i^2}}$"
+      ]
+    },
+    {
+      "metadata": {
+        "id": "d__wWc1CdSv7",
+        "colab_type": "code",
+        "colab": {}
+      },
+      "cell_type": "code",
+      "source": [
+        "a = np.array([1,2,0,1,2,0,1,2])\n",
+        "b = np.array([9,2,4,1,1,5,0,2])\n",
+        "\n",
+        "# l1 = the L1 distance between a and b\n",
+        "l1 = None\n",
+        "\n",
+        "# l1 = the L2 distance between a and b\n",
+        "l2 = None"
+      ],
+      "execution_count": 0,
+      "outputs": []
+    },
+    {
+      "metadata": {
+        "id": "mlKMlSmreNvk",
+        "colab_type": "text"
+      },
+      "cell_type": "markdown",
+      "source": [
+        "# 3. Compute the distance between pairs of vectors and select the smallest\n",
+        "\n",
+        "For this sprint challenge goal, you are _NOT_ required to compute the pairwise distance of every point in a set. Instead, find the row $i$ with the shortest distance between $x_i$ and $y_i$, two separate sets of $2d$ points."
+      ]
+    },
+    {
+      "metadata": {
+        "id": "N33-3PgVeIkR",
+        "colab_type": "code",
+        "colab": {}
+      },
+      "cell_type": "code",
+      "source": [
+        "x = np.array([[10.,  2.,  0.,  3., -4.,  1., -5., 10.,  7.,  6.],\n",
+        "              [-4.,  4., -0.,  4., -9.,  1., -2.,  2.,  1., -1.]]).T\n",
+        "\n",
+        "y = np.array([[-7., 10., -8.,  7., -5., -4.,  0.,  7., -9., -2.],\n",
+        "              [-7.,  2.,  4.,  7., -5., 10., -2., -2.,  1., -2.]]).T\n",
+        "\n",
+        "# Your code to find the pair of points at row i with the shortest distance between them \n",
+        "def get_nearest_pair():\n",
+        "    None\n",
+        "\n",
+        "# i\n",
+        "i = None\n",
+        "\n",
+        "# The distance between x_i and y_i\n",
+        "d = None"
+      ],
+      "execution_count": 0,
+      "outputs": []
+    }
+  ]
+}
\ No newline at end of file