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Merge pull request #17 from codebygarrysingh/feature/linear_algebra_vectors_matrices
Added notebook on vector operations
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‎linear-algebra-ml-ipynb/Vector_operations_dot_product.ipynb‎

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{
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"cells":[
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{
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"cell_type":"markdown",
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"source":[
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"**In this notebook we will vector operations including sum, multiplication and dot product**"
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],
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"attachments":{
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},
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"metadata":{
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"datalore":{
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"node_id":"dgS96Y5ceG7IwdE10v42in",
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"type":"MD",
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"hide_input_from_viewers":true,
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"hide_output_from_viewers":true
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}
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}
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},
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{
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"cell_type":"code",
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"source":[
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"# let's start by importing the required libraries\n",
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"\n",
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"import numpy as np\n",
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"import time"
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],
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"execution_count":18,
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"outputs":[
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],
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"metadata":{
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"datalore":{
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"node_id":"ucOqR0H3WJYR57LgKqZ9zi",
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"type":"CODE",
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"hide_input_from_viewers":true,
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"hide_output_from_viewers":true
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}
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}
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},
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{
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"cell_type":"code",
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"source":[
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"# let's take an example of a vector\n",
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"\n",
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"v = np.array([[1],[3]])\n",
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"\n",
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"v_size = v.shape[0]\n",
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"magnitude = 0 \n",
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"for i in range(v_size):\n",
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" magnitude += np.square(v[i])\n",
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"\n",
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"magnitude = np.sqrt(magnitude)\n",
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"\n",
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"print(f\"For vector {v}, magnitude is: {magnitude}\")"
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],
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"execution_count":11,
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"outputs":[
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{
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"name":"stdout",
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"text":[
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"For vector [[1]\n",
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" [3]], magnitude is: [3.16227766]\n"
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],
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"output_type":"stream"
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}
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],
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"metadata":{
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"datalore":{
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"node_id":"JhzwFPkW2YJa13VDjz28Jk",
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"type":"CODE",
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"hide_input_from_viewers":true,
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"hide_output_from_viewers":true
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}
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}
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},
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{
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"cell_type":"code",
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"source":[
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"# now let's multiply our vector with a scalar value\n",
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"\n",
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"scalar_val = 50\n",
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"magnitude_mult = 0\n",
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"v_1 = v * scalar_val\n",
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"for i in range(v_size):\n",
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" magnitude_mult += np.square(v_1[i])\n",
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"\n",
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"magnitude_mult = np.sqrt(magnitude_mult)\n",
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"\n",
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"print(f\"For vector {v_1}, magnitude is: {magnitude_mult}\")\n",
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"\n",
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"# let's also try to multiply magnitude directly by the scalar\n",
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"\n",
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"magnitude_mult_1 = magnitude * scalar_val\n",
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"\n",
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"print(f\"For vector {v_1}, magnitude is: {magnitude_mult_1}\")\n"
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],
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"execution_count":12,
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"outputs":[
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{
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"name":"stdout",
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"text":[
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"For vector [[ 50]\n",
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" [150]], magnitude is: [158.11388301]\n",
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"For vector [[ 50]\n",
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" [150]], magnitude is: [158.11388301]\n"
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],
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"output_type":"stream"
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}
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],
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"metadata":{
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"datalore":{
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"node_id":"GuaEiUgZA6dxajmOMcDDE3",
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"type":"CODE",
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"hide_input_from_viewers":true,
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"hide_output_from_viewers":true
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}
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}
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},
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{
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"cell_type":"code",
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"source":[
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"# now let's compute sum of two vectors\n",
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"\n",
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"v = np.array([[1],[3]])\n",
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"w = np.array([[4],[-1]])\n",
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"\n",
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"sum_vec = v + w\n",
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"\n",
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"print(f\"Sum of vector {v} and vector {w} is: {sum_vec}\")"
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],
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"execution_count":14,
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"outputs":[
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{
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"name":"stdout",
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"text":[
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"Sum of vector [[1]\n",
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" [3]] and vector [[ 4]\n",
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" [-1]] is: [[5]\n",
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" [2]]\n"
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],
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"output_type":"stream"
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}
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],
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"metadata":{
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"datalore":{
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"node_id":"1MJX1i41Jknz65VP8aTbfk",
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"type":"CODE",
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"hide_input_from_viewers":true,
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"hide_output_from_viewers":true
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}
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}
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},
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{
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"cell_type":"code",
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"source":[
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"# now let's compute the norm of the vector which is used interchangibly with magnitude of the vector\n",
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"\n",
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"norm_v = np.linalg.norm(v)\n",
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"\n",
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"print(f\"Norm of the vector {v} is: {norm_v}\")"
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],
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"execution_count":15,
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"outputs":[
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{
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"name":"stdout",
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"text":[
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"Norm of the vector [[1]\n",
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" [3]] is: 3.1622776601683795\n"
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],
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"output_type":"stream"
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}
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],
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"metadata":{
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"datalore":{
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"node_id":"H6V7yhIL2uCE1KPojSSzVK",
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"type":"CODE",
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"hide_input_from_viewers":true,
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"hide_output_from_viewers":true
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}
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}
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},
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{
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"cell_type":"code",
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"source":[
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"# now let's calculate the dot product of two vectors\n",
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"# dot product is a scalar computation of two vectors to determine projection of one vector on another\n",
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"A = np.array([[1, 2], [3, 4]])\n",
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"B = np.array([[5, 6], [7, 8]])\n",
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"# Matrix multiplication\n",
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"result = np.dot(A, B)\n",
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"#dot_prod = np.dot(v.reshape(1,2),w)\n",
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"\n",
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"print(f\"Dot product of vector {v} and vector {w} is: {result}\")\n"
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],
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"execution_count":19,
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"outputs":[
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{
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"name":"stdout",
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"text":[
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"Dot product of vector [[1]\n",
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" [3]] and vector [[ 4]\n",
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" [-1]] is: [[19 22]\n",
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" [43 50]]\n"
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],
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"output_type":"stream"
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}
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],
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"metadata":{
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"datalore":{
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"node_id":"9s7AC3oL8F7ger2VRhPinZ",
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"type":"CODE",
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"hide_input_from_viewers":true,
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"hide_output_from_viewers":true
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}
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}
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},
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{
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"cell_type":"code",
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"source":[
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"# let's calculate dot product of two vectors using np dot function and @ operator\n",
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"\n",
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"a = np.random.rand(1000000)\n",
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"b = np.random.rand(1000000)\n",
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"\n",
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"time_start = time.time()\n",
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"dot_prod = np.dot(a,b)\n",
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"time_stop = time.time()\n",
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"\n",
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"print(f\"Time taken to calculate dot_product {dot_prod} is : {time_stop-time_start}\")"
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],
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"execution_count":20,
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"outputs":[
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{
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"name":"stdout",
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"text":[
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"Time taken to calculate dot_product 250203.84421967238 is : 0.004907131195068359\n"
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],
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"output_type":"stream"
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}
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],
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"metadata":{
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"datalore":{
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"node_id":"ls1tyiR92aV3qRo57qjwu6",
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"type":"CODE",
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"hide_input_from_viewers":true,
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"hide_output_from_viewers":true
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}
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}
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},
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{
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"cell_type":"code",
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"source":[
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"# let's calculate dot product of two vectors using np dot function and @ operator\n",
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"\n",
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"a = np.random.rand(1000000)\n",
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"b = np.random.rand(1000000)\n",
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"\n",
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"time_start = time.time()\n",
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"dot_prod = a @ b\n",
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"time_stop = time.time()\n",
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"\n",
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"print(f\"Time taken to calculate dot_product {dot_prod} is : {time_stop-time_start}\")"
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],
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"execution_count":22,
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"outputs":[
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{
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"name":"stdout",
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"text":[
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"Time taken to calculate dot_product 249861.64146470415 is : 0.0008220672607421875\n"
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],
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"output_type":"stream"
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}
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],
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"metadata":{
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"datalore":{
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"node_id":"PIlt0vE8K227CHzZSC9bmu",
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"type":"CODE",
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"hide_input_from_viewers":true,
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"hide_output_from_viewers":true
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}
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}
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},
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{
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"cell_type":"code",
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"source":[
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"# Calculating vector similarity is one of the fundamental concepts of NLP \n",
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"\n",
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"A = np.array([[1, 2], [3, 4]])\n",
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"B = np.array([[5, 6], [7, 8]])\n",
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"\n",
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"dot_prod = np.dot(A, B)\n",
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"\n",
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"vect_sim = dot_prod\/(np.linalg.norm(A)*np.linalg.norm(B))\n",
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"\n",
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"print(f\"Vector similarity between A & B is: {vect_sim}\")"
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],
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"execution_count":24,
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"outputs":[
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{
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"name":"stdout",
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"text":[
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"Vector similarity between A & B is: [[0.26297735 0.30450009]\n",
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" [0.59515927 0.69204567]]\n"
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],
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"output_type":"stream"
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}
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],
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"metadata":{
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"datalore":{
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"node_id":"lA3fnPUHZcqmeuyxiDTK53",
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"type":"CODE",
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"hide_input_from_viewers":true,
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"hide_output_from_viewers":true
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}
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}
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},
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{
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"cell_type":"markdown",
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"source":[
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"**Vector similarity is used in many practical applications from NLPs to Classification to Reccommendations**"
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],
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"attachments":{
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},
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"metadata":{
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"datalore":{
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"node_id":"OO7npmOt1sYII3rQ9gTkF2",
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"type":"MD",
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"hide_input_from_viewers":true,
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"hide_output_from_viewers":true
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}
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}
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}
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],
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"metadata":{
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"kernelspec":{
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"display_name":"Python",
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"language":"python",
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"name":"python"
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},
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"datalore":{
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"computation_mode":"JUPYTER",
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"package_manager":"pip",
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"base_environment":"default",
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"packages":[
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],
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"report_row_ids":[
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],
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"version":3
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}
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},
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"nbformat":4,
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"nbformat_minor":4
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}

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