{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"source": [
"\n",
"[*NBBinder test on a collection of notebooks about some thermodynamic properperties of water*](https://github.com/rmsrosa/nbbinder)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"source": [
"\n",
" "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"source": [
"\n",
"[<- Reading the Data](02.00-Data.ipynb) | [Water Contents](00.00-Water_Contents.ipynb) | [References](BA.00-References.ipynb) | [High-Dimensional Fittings ->](04.00-High_Dim_Fittings.ipynb)\n",
"\n",
"---\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Low-Dimensional Fittings\n",
"\n",
"We use the classical least-square method to fit low degree polynomials to the data.\n",
"\n",
"See e.g. [Golub and Van Loan (1996)](BA.00-References.ipynb) and [Trefethen and Bau III (1997)](BA.00-References.ipynb) for details on the least-square method."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Importing the libraries"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [],
"source": [
"import csv\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Loading the data\n",
"\n",
"This time we use the `csv` library to read the data from file and use `numpy` to work with the data."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Loading with csv\n",
"\n",
"We first load the data into a python list with `csv`."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
"text/plain": [
"[['temp', 'density', 'viscosity'],\n",
" ['Temperature (C)', 'Density (g/cm^3)', 'Viscosity (cm^2/s)'],\n",
" ['0', '0.9999', '0.01787'],\n",
" ['5', '1', '1.514'],\n",
" ['10', '0.9997', '1.304'],\n",
" ['15', '0.9991', '1.138'],\n",
" ['20', '0.9982', '1.004'],\n",
" ['25', '0.9971', '0.894'],\n",
" ['30', '0.9957', '0.802'],\n",
" ['35', '0.9941', '0.725'],\n",
" ['40', '0.9923', '0.659'],\n",
" ['50', '0.9881', '0.554'],\n",
" ['60', '0.9832', '0.475'],\n",
" ['70', '0.9778', '0.414'],\n",
" ['80', '0.9718', '0.366'],\n",
" ['90', '0.9653', '0.327'],\n",
" ['100', '0.9584', '0.295']]"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"file = open('water.csv',\"r\")\n",
"water_csv = list(csv.reader(file, delimiter=\",\"))\n",
"water_csv"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Header and datapoints\n",
"\n",
"We separate the header from the datapoints and have the datapoints put into a `numpy` array as follows."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"{'temp': 'Temperature (C)', 'density': 'Density (g/cm^3)', 'viscosity': 'Viscosity (cm^2/s)'}\n"
]
}
],
"source": [
"header = dict([(water_csv[0][i],water_csv[1][i]) for i in range(3)])\n",
"print(header)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[[0.000e+00 9.999e-01 1.787e-02]\n",
" [5.000e+00 1.000e+00 1.514e+00]\n",
" [1.000e+01 9.997e-01 1.304e+00]\n",
" [1.500e+01 9.991e-01 1.138e+00]\n",
" [2.000e+01 9.982e-01 1.004e+00]\n",
" [2.500e+01 9.971e-01 8.940e-01]\n",
" [3.000e+01 9.957e-01 8.020e-01]\n",
" [3.500e+01 9.941e-01 7.250e-01]\n",
" [4.000e+01 9.923e-01 6.590e-01]\n",
" [5.000e+01 9.881e-01 5.540e-01]\n",
" [6.000e+01 9.832e-01 4.750e-01]\n",
" [7.000e+01 9.778e-01 4.140e-01]\n",
" [8.000e+01 9.718e-01 3.660e-01]\n",
" [9.000e+01 9.653e-01 3.270e-01]\n",
" [1.000e+02 9.584e-01 2.950e-01]]\n"
]
}
],
"source": [
"datapoints = np.array(water_csv[2:]).astype(\"float\")\n",
"print(datapoints)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Linear approximation\n",
"\n",
"Given a set of temperature and density data in the form $(T_j, \\rho_j)$, we look for a linear relation $\\rho^{(1)}(T) = c + m T$ which is the \"best fit\" for the data. \n",
"\n",
"One way to approach this problem is to interpret the best fit as minimizing the sum of squares of the residuals. The **residual** for each $j$ measurement is\n",
"\n",
"$$\n",
"r_j = \\rho_j - \\rho^{(1)}(T_j),\n",
"$$\n",
"\n",
"and the **sum of squares of the residuals** is\n",
"\n",
"$$\n",
" \\min_{c,m\\in \\mathbb{R}} \\sum_j (\\rho_j - \\rho^{(1)}(T))^2.\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Matrix form\n",
"\n",
"This can be written in matrix form as\n",
"\n",
"$$\n",
"\\displaystyle \\min_{\\mathbf{u}\\in \\mathbb{R}^2} \\|A\\mathbf{u} - \\mathbf{f}\\|_2^2,\n",
"$$\n",
"\n",
"where $\\|\\cdot\\|_2$ is the Euclidian norm of a vector and\n",
"\n",
"$$ A = \\left[ \\begin{matrix} T_1 & 1 \\\\ \\vdots & 1 \\\\ T_n & 1 \\end{matrix}\\right], \\qquad \\mathbf{u} = \\left( \\begin{matrix} m \\\\ c \\end{matrix}\\right), \\qquad \\mathbf{f} = \\left( \\begin{matrix} \\rho_1 \\\\ \\vdots \\\\ \\rho_n \\end{matrix} \\right).\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"The matrix $A$ is a simple **Vandermonde** type matrix obtained from the temperature data, $\\mathbf{u}$ is the unknown vector with the desired coefficients for the approximation, and $\\mathbf{f}$ is the vector with the density measurements."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### The Vandermonde matrix\n",
"\n",
"We use the [`numpy`](https://docs.scipy.org/doc/numpy/) function [`numpy.vstack()`](https://docs.scipy.org/doc/numpy/reference/generated/numpy.vstack.html) to build the Vandermonde matrix $A$."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[[ 0. 1.]\n",
" [ 5. 1.]\n",
" [ 10. 1.]\n",
" [ 15. 1.]\n",
" [ 20. 1.]\n",
" [ 25. 1.]\n",
" [ 30. 1.]\n",
" [ 35. 1.]\n",
" [ 40. 1.]\n",
" [ 50. 1.]\n",
" [ 60. 1.]\n",
" [ 70. 1.]\n",
" [ 80. 1.]\n",
" [ 90. 1.]\n",
" [100. 1.]]\n"
]
}
],
"source": [
"T = datapoints[:,0]\n",
"A1 = np.vstack([T,np.ones(len(T))]).T\n",
"print(A1)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### The density measurements\n",
"\n",
"The density data is the second column of the data array."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[0.9999 1. 0.9997 0.9991 0.9982 0.9971 0.9957 0.9941 0.9923 0.9881\n",
" 0.9832 0.9778 0.9718 0.9653 0.9584]\n"
]
}
],
"source": [
"f = datapoints[:,1]\n",
"print(f)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Solution of the least-square problem for the linear approximation\n",
"\n",
"We use the `numpy` function [numpy.linagl.lstsq()](https://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.lstsq.html) to solve the least-square problem."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"-0.00041965346534652876 1.0056721122112207\n"
]
}
],
"source": [
"m, d = np.linalg.lstsq(A1, f, rcond=None)[0]\n",
"print(m,d)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Visualizing the result\n",
"\n",
"Now we plot the linear approximation along with the data to visualize the quality of the approximation"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
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\n",
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