{
"cells": [
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"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# EART 70013 \n",
" \n",
"# Geophysical Inversion \n",
" \n",
"## Lecture 2 - Homework Solutions "
]
},
{
"cell_type": "markdown",
"metadata": {
"toc": true
},
"source": [
"Table of Contents
\n",
""
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import scipy.linalg as sl\n",
"from pprint import pprint\n",
"import scipy.interpolate as si\n",
"from mpl_toolkits.mplot3d import Axes3D"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Homework"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Homework - Optimisation - simple example\n",
"\n",
"Consider the problem from the lecture\n",
"$$ \n",
"f(\\boldsymbol{x}) = \n",
"1+2x + 4y + x^2+2xy+3y^2\n",
"$$\n",
"\n",
"Compute the gradient vector, and by setting it equal to zero and writing as a matrix equation,\n",
"solve for the stationary point. \n",
"\n",
"Plot the function via a contour plot in 2D, and add the stationay point you've computed to verify it is indeed a minima (refer to the image from the lecture)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Solution \n",
"\n",
"The gradient vector is\n",
"\n",
"$$\\nabla f= \n",
"\\begin{pmatrix}\n",
"2 + 2x + 2y\\\\\n",
"4 + 2x + 6y\n",
"\\end{pmatrix}\n",
"$$\n",
"\n",
"We can write this as a linear system:\n",
"\n",
"$$\n",
"\\nabla f = \\begin{pmatrix}\n",
"2 & 2\\\\\n",
"2 & 6\n",
"\\end{pmatrix}\n",
"\\begin{pmatrix}\n",
"x\\\\\n",
"y\n",
"\\end{pmatrix}\n",
"+\n",
"\\begin{pmatrix}\n",
"2\\\\\n",
"4\n",
"\\end{pmatrix}\n",
"$$\n",
"\n",
"So $\\nabla f = 0$ when \n",
"\n",
"$$\n",
"\\begin{pmatrix}\n",
"2 & 2\\\\\n",
"2 & 6\n",
"\\end{pmatrix}\n",
"\\begin{pmatrix}\n",
"x\\\\\n",
"y\n",
"\\end{pmatrix}\n",
"=\n",
"\\begin{pmatrix}\n",
"-2\\\\\n",
"-4\n",
"\\end{pmatrix}\n",
"$$\n",
"\n",
"Let's use a contour plot to visualise the function in 2D, solve for the minimum (the stationary point) and plot it:"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[]"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
},
{
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\n",
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