{
"cells": [
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"cell_type": "markdown",
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"source": [
"\n",
"\n",
"\n",
"# Trigonometric Interpolation\n",
"\n",
"### Modules - Curve Fitting\n",
"\n",
"By Jonas Tjemsland, Andreas Krogen, Håkon Ånes and Jon Andreas Støvneng\n",
"\n",
"Last edited: January 26th 2018 \n",
"\n",
"___"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Introduction\n",
"\n",
"A trigonometric polynomial of degree $K$ can be written as a sum of sines and cosines of given periods\n",
"\n",
"$$\n",
"P_K(t)=a_0 + \\sum_{k=1}^Ka_k\\cos(kt)+\\sum_{k=1}^Kb_k\\sin(kt).\n",
"$$\n",
"\n",
"This form of interpolation is especially suited for periodic functions. The goal of trigonometric interpolation is to compute the $2n+1$ coefficients $a_0,a_1,...,a_K,b_1,b_2,...,b_K$, such that the function $P_K(t)$ passes through a given set of data points. We assume here that the data points are equally spaced. One way of solving this problem is to perform a polynomial interpolation on the unit circle in the complex plane, i.e. performing polynomial interpolation on\n",
"\n",
"$$\n",
"P(t)=\\sum c_kz^t,\n",
"$$\n",
"\n",
"where $c_k=a_k+ib_k$ and $z=e^{it}$. This approach is used in [1]. Thus, the discussion regarding polynomial interpolation can to some extent be covered using trigonometric interpolation. However, the trigonometric interpolating function $P(t)$ is obviously not unique, since $e^{it} = e^{i(t + 2\\pi)} = e^{i(t + 4\\pi)} =$ ..., thus requiring further manipulation.\n",
"\n",
"For a discussion on polynomial interpolation (Lagrange, Chebyshev, Newton's divided difference, Runge's phenomenon, etc.), we suggest a look at our notebook [Polynomial Interpolation](https://nbviewer.jupyter.org/urls/www.numfys.net/media/notebooks/polynomial_interpolation.ipynb). Here, we approach the solution using Discrete Fourier Transforms (DFTs) as in [2]. Hence, some basic knowledge of DFTs will be helpful, which e.g. can be reviewed in another notebook titled [Discrete Fourier Transform and Fast Fourier Transform](https://nbviewer.jupyter.org/urls/www.numfys.net/media/notebooks/discrete_fourier_transform.ipynb).\n",
"\n",
"OK, then. As always, we start by importing necessary libraries, and set common figure parameters."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"# Import libraries\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import scipy.fftpack as fft\n",
"%matplotlib inline\n",
"\n",
"# Casting unitary numbers to real numbers will give errors\n",
"# because of numerical rounding errors. We therefore disable \n",
"# warning messages.\n",
"import warnings\n",
"warnings.filterwarnings('ignore')\n",
"\n",
"# Set common figure parameters\n",
"newparams = {'figure.figsize': (16, 6), 'axes.grid': True,\n",
" 'lines.linewidth': 1.5, 'lines.markersize': 10,\n",
" 'font.size': 14}\n",
"plt.rcParams.update(newparams)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Generalize interpolation\n",
"\n",
"Assume a given set of $n$ data points $(t_i,x_i)$ where $i=0,1,...,n-1$, and let $f_0(t), f_1(t),...,f_{n-1}(t)$ be given functions of $t$. We now require that the $n\\times n$ matrix\n",
"\n",
"$$\n",
"A=\\begin{bmatrix}\n",
"f_0(t_0)&\\cdots&f_0(t_{n-1})\\\\\n",
"\\vdots&\\ddots&\\vdots\\\\\n",
"f_{n-1}(t_0)&\\cdots&f_{n-1}(t_{n-1})\n",
"\\end{bmatrix},\n",
"$$\n",
"\n",
"is unitary. That is, $A^{-1}=\\overline{A}^T$. If $A$ is real, then $A^{-1}=A^T$ and the matrix is orthogonal. We now define $\\vec y=A\\vec x$, which implies that $\\vec x=\\overline A^T \\vec y$. Written in terms of sums we then have $x_j=\\sum_{k=0}^{n-1}y_k\\overline{f_k(t_j)}.$\n",
"Thus, the function\n",
"\n",
"$$\n",
"F(t)=\\sum_{k=0}^{n-1}y_k\\overline{f_k(t)},\n",
"$$\n",
"\n",
"interpolates the given data set! If $A$ is a real $n\\times n$ orthogonal matrix, then\n",
"\n",
"$$\n",
"F(t)=\\sum_{k=0}^{n-1}y_kf_k(t).\n",
"$$\n",
"\n",
"Since the DFT can be written as a unitary matrix $F_n$, we can use this to interpolate a given data set."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### From discrete Fourier transform to trigonometric interpolation\n",
"\n",
"From the previously mentioned notebook on DFTs, we have an excellent algorithm, the Fast Fourier Transform (FFT) algorithm for calculating\n",
"\n",
"$$\n",
"x_j = \\frac{1}{n}\\sum_{k=0}^{n-1}y_ke^{i2\\pi kj/n},\n",
"$$\n",
"\n",
"which easily can be rewritten as\n",
"\n",
"$$\n",
"x_j=\\sum_{k=0}^{n-1}y_k\\frac{\\exp\\left[\\frac{i2\\pi k(t_j-c)}{d-c}\\right]}{n},\n",
"$$\n",
"\n",
"where $t_j=c+j(d-c)/n$ for $j = 0, 1, ..., n-1$ for a given interval $[c,d]$. Assume that $\\vec x = (x_0,x_1,...,x_{n-1})$ is a known set of data points. Then the complex function\n",
"\n",
"$$\n",
"Q(t)=\\frac{1}{n}\\sum_{k=0}^{n-1}y_k\\exp\\left[\\frac{i2\\pi k(t-c)}{d-c}\\right]\n",
"$$\n",
"\n",
"satisfies $Q(t_j)=x_j$ for $j=0,1,...,n-1$. In other words, $Q(t)$ interpolates the set $\\{(x_j,t_j); \\,j=0,1,...,n-1\\}$, and the interpolation coefficients are found by the Fourier transform! Note that $t_i$ has to be equally spaced. This is generally not required, but it simplifies matters."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"def trigInterp(x, c=0, d=1, N=100):\n",
" \"\"\"Calculates a trigonometric polynomial of degree n-1 that interpolates\n",
" a set of n complex (or real) data points. The data points can be written\n",
" as (t_i,x_i), i=0,1,2,..., where t_i are equally spaced on the interval\n",
" [c,d].\n",
" \n",
" :x: complex or float numpy array. Data points.\n",
" :c: float. Start value t-axis. t[0].\n",
" :d: float. End value t-axis. t[N-1].\n",
" :N: int. Number of function evaluations of the interpolating function.\n",
" :returns: complex64 numpy array. Second axis of the interpolating function.\n",
" \"\"\"\n",
" t = np.linspace(c, d, N) # t-values, first axis\n",
" n = len(x) # Number of data points\n",
" y = fft.fft(x) # Interpolating coefficients\n",
" \n",
" # Evaluate sum\n",
" Q = np.zeros(N, np.complex64)\n",
" for k in range(0, n):\n",
" Q = Q + y[k]*np.exp(2j*np.pi*k*(t-c)/(d-c))\n",
" \n",
" return Q/n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's try with an example. For simplicity, we let the data points $\\vec x$ be real, although the above function can be used for complex data points as well."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
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PYDOAS0KIi1CaMB+CkvDFoeE5t9b9UM7NYbW+lUCZ49oTSlLbIEGWUn4I4G3118cB5Knn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\nem+X1nmFYeEAUoKZ/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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = np.random.randint(-10, 10, 10) # Data points\n",
"c, d = 1, 2 # Interval for t\n",
"N = 200 # Number of function evaluations\n",
"\n",
"# Calculate interpolation curve\n",
"Q = trigInterp(x, c, d, N)\n",
"\n",
"# Plot results\n",
"plt.figure()\n",
"plt.plot(np.linspace(c, d, len(Q)), Q, label=r'Interpolation curve, $Q(t)$')\n",
"plt.plot(np.linspace(c, d, len(x), False), x, 'mo', label='Data points, $x_k$')\n",
"plt.xlabel('$t$'), plt.ylabel('$x$'), plt.title('Trigonometric interpolation')\n",
"plt.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Improve the algorithm – exploit periodicity and remove high frequencies\n",
"\n",
"Using Euler's formula we can write $Q(t)=P(t)+iI(t)$. In the following discussions we are going to assume that the elements $x_j$ are real, such that $Q(t)=P(t)$, and let $y_k=a_k+ib_k$. The following discussion can be applied to $I(t)$ as well. From the definition of the DFT, it is clear that $y_0$ has to be real and $y_{n-k} = \\overline{ y_k}$ if every element in $x$ are real. Moreover, we can exploit the periodicity $\\cos(2\\pi n-r)=\\cos(r)$ and $\\sin(2\\pi n-r)=-\\sin(r)$ to make a more effective algorithm for calculating the interpolation curve. It should by now be clear that the trigonometric interpolating polynomial is not unique, as explained in the introduction.\n",
"\n",
"The interpolation curve becomes\n",
"\n",
"$$\n",
"Q(t)=P_n(t)=\\frac{1}{n}\\sum_{k=0}^{n-1}\\left(a_k \\cos\\frac{2\\pi k(t-c)}{d-c}-b_k \\sin\\frac{2\\pi k(t-c)}{d-c}\\right).\n",
"$$\n",
"\n",
"If $n$ is even, we can simlify this as\n",
"\n",
"$$\n",
"P_{n,\\text{even}}(t)=\\frac{a_0}{n}+\\frac{2}{n}\\sum_{k=1}^{n/2-1}\\left(a_k \\cos\\frac{2\\pi k(t-c)}{d-c}-b_k \\sin\\frac{2\\pi k(t-c)}{d-c}\\right)+\\frac{a_{n/2}}{\\sqrt n}\\cos \\frac{n\\pi(t-c)}{d-c},\n",
"$$\n",
"\n",
"thus halving the number of calculations needed. Note that this interpolating polynomial is not the same as in the previous section. All the shorter periods are not included, and thus the result will be somewhat smoother. If $n$ is odd the interpolation curve becomes\n",
"\n",
"$$\n",
"P_{n,\\text{odd}}(t)=\\frac{a_0}{n}+\\frac{2}{n}\\sum_{k=1}^{(n-1)/2}\\left(a_k \\cos\\frac{2\\pi k(t-c)}{d-c}-b_k \\sin\\frac{2\\pi k(t-c)}{d-c}\\right).\n",
"$$\n",
"\n",
"These expressions can be evaluated and plotted as before. We can however do better. We are going to view the coefficients of $P(t)$ as coefficients of an $N\\geq n$ order trigonometric polynomial. In other words, $P_n(t)=P_N(t)$, where we set $a_k=b_k=0$ for $k=n/2+1,n/2+1,...,N/2$ and $a_k+ib_k=y_k$ for $k=0,1,...,n/2$. If we perform an inverse Fourier transform of $\\frac{N}{n}P_N(t)$, we get $N$ data points lying on $P(t)$! Let's do that and see how it performs."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"def fastTrigInterp(x,c,d,N=100):\n",
" \"\"\" Calculates a trigonometric polynomial of degree n/2 (n even) or\n",
" (n-1)/2 (n odd) that interpolates a set of n real data points. The\n",
" data points can be written as (t_i,x_i), i=0,1,2,..., where t_i are \n",
" equally spaced on the interval [c,d].\n",
" \n",
" :x: complex or float numpy array. Data points.\n",
" :c: float. Start value t-axis. t[0].\n",
" :d: float. End value t-axis. t[N-1].\n",
" :N: int. Number of function evaluations of the interpolating function.\n",
" :returns: float numpy array. Second axis of the interpolating function.\n",
" \"\"\"\n",
" n = len(x) # Number of data points\n",
" y = fft.fft(x) # Interpolating coefficients\n",
" \n",
" # Interpolating coefficients as viewed as a\n",
" # trigonometric polynomial of order N.\n",
" yp = np.zeros(N, np.complex64)\n",
" yp[0:int(n/2)] = y[0:int(n/2)]\n",
" yp[N - int(n/2):N] = y[int(n/2):n]\n",
"\n",
" return np.real(fft.ifft(yp))*N/n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's try out our new interpolation function on the same data set as above."
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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FWyI3J1uWju6A0aQx9uswbqXevkahEEIIIYQoOUmKhRBVyps/HSM+KY3PHmuL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\n+wK99A6nQuvayIORneqyJPQ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+bCeRcUl6hwVAZFwSD322k+/2XeS5exuxbHQHWVO3DIzK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\nSZKkZlmKJUmSJEnNshRLkiRJkpr1L7FcjoQHC10aAAAAAElFTkSuQmCC\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Calculate interpolation curve\n",
"xp = fastTrigInterp(x, c, d, N)\n",
"\n",
"# Plot results\n",
"plt.figure()\n",
"plt.plot(np.linspace(c, d, N, False), xp, label=r'Interpolation curve, $Q(t)$')\n",
"plt.plot(np.linspace(c, d, len(x), False), x, 'mo', label='Data points, $x_k$')\n",
"plt.xlabel('$t$'), plt.ylabel('$x$'), plt.title('Trigonometric interpolation')\n",
"plt.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"By exploiting the periodicity of the data points and excluding the higher frequencies we clearly see that the interpolation curve $Q(t)$ is smoother, and hence fits the data points \"better\" than our previous $Q(t)$ curve.\n",
"\n",
"### Least squares fitting\n",
"\n",
"When the number of data points becomes large, it is unusual to fit a model function exactly. Then, we are often instead interested in fitting an approximated curve. This is often done when analyzing measurements.\n",
"\n",
"The least squares problem [4] for this setup can be formulated as follows. Given a linear system $A_m\\vec x=\\vec y$ of $m$ equations, find a vector $\\vec x$ that minimizes $||\\vec y-A\\vec x||$. In other words, we have an inconsistent system of $m$ equations that we want to solve \"as best as possible\". It can be shown that for every _linear_ system $A_m\\vec x=\\vec y$, the corresponding _normal_ system $A_m^TA_m\\vec x = A_m^T \\vec y$ is consistent. Moreover, all solutions of the normal system are least squares solutions of $A_m\\vec x=\\vec y$.\n",
"\n",
"Let's apply this to the generalized interpolation above. $A_m$ is then the matrix of the first $m$ rows of $A$. Since $A$ is unitary (and orthogonal if $A$ is real), the column vectors and row vectors of $A$ form orthonormal sets. Likewise, the column vectors and row vectors of $A_m$ will form orthonormal sets. Thus, the normal equation becomes\n",
"\n",
"$$\n",
"A_m^TA_m\\vec x = I\\vec x = \\vec x = A_m^T \\vec y.\n",
"$$\n",
"\n",
"This means that the least squares solution for $F_n(t)=\\sum_{k=0}^{n-1}y_kf_k(t)$ using only the first $m$ equations is\n",
"\n",
"$$\n",
"F_m(t)=\\sum_{k=0}^{m-1}y_kf_k(t).\n",
"$$\n",
"\n",
"For the case of trigonometric interpolation, this means that the least squares solution of degree $m$ is simply done by filtering out the $n-m$ terms of the highest frequencies. These arguments hold for both functions `trigInterp` and `fastTrigInterp` above. We are now going to create a function calculating the least squares solution, based on the latter."
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [],
"source": [
"def leastSquaresTrig(x, m, c=0, d=1, N=100):\n",
" \"\"\"Calculates a least squares trigonometric polynomial fit of degree\n",
" about m/2 of n real data points. The data points can be written as\n",
" (t_i,x_i), i=0,1,2,..., where t_i are equally spaced on the interval\n",
" [c,d].\n",
" \n",
" :x: complex or float numpy array. Data points.\n",
" :c: float. Start value t-axis. t[0].\n",
" :d: float. End value t-axis. t[N-1].\n",
" :N: int. Number of function evaluations of the fitted function.\n",
" :returns: float numpy array. Second axis of the fitted function.\n",
" \"\"\"\n",
" n = len(x) # Number of data points\n",
" if not 0<=m<=n<=N:\n",
" raise ValueError('Is 0<=m<=n<=N??')\n",
" y = fft.fft(x) # Interpolating coefficients\n",
" \n",
" # Interpolating coefficients viewed as a\n",
" # trigonometric polynomial of order N.\n",
" yp = np.zeros(N, np.complex64)\n",
" \n",
" # Use only m lowest frequencies\n",
" yp[0:int(m/2)] = y[0:int(m/2)]\n",
" yp[N - int(m/2) + 1:N] = y[n - int(m/2) + 1:n]\n",
" \n",
" # If odd m, terms corresponding to m/2 has both a sine\n",
" # and a cosine term\n",
" if (m % 2):\n",
" yp[int(m/2)] = y[int(m/2)]\n",
" # If even m, terms corresponding to m/2 has only a cosine term\n",
" else:\n",
" yp[int(m/2)] = np.real(y[int(m/2)])\n",
" if m0:\n",
" yp[N - int(m/2)] = yp[int(m/2)]\n",
" \n",
" return np.real(fft.ifft(yp))*N/n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We now perform trigonometric interpolation on the same random data points as earlier, excluding an increasing number of frequencies. As we have seen, this implies that we are finding the least squares solutions for a trigonometric polynomial of decreasing degree."
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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vGuhUA2s1RIdQL6bcPJDjWUWsf/k3LBUWR4ckhBBCCNHqSZ9iIUS7cXBXNvt+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86dsb3/PqN8xJbd3Di8KZ6DG+PwCraXrMUmJm/ZMrK/+w7bhx7CafIko7VbUVbN7tUxOPtYE9zT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\nGxsjuj6JHhqLEkk0HiVYHLm5ZDqdbPr1r2m47tpPHmwM7By+B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VMHsWrJHsp214Xsdfdv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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure()\n",
"for m in [0, 2, 5, 8, 10]:\n",
" # Calculate interpolation curve\n",
" xp = leastSquaresTrig(x, m, c, d, N)\n",
" # Plot results\n",
" plt.plot(np.linspace(c, d, len(xp), False), xp, label=r'$m=%d$' % m)\n",
"\n",
"plt.plot(np.linspace(c, d, len(x), False), x, 'mo')\n",
"plt.xlabel('$t$'), plt.ylabel('$x$')\n",
"plt.title('Least squares trigonometric fit to %d data points' % len(x))\n",
"plt.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So there you are, using the consepts introduced in this notebook it is quite easy to create a least squares algorithm to fit a trigonometric function with arbitrary frequencies.\n",
"\n",
"### References\n",
"[1] Wikipedia: Trigonometric interpolation, https://en.wikipedia.org/wiki/Trigonometric_interpolation, 02.28.2016, Acquired May 4th 2016. \n",
"[2] T. Sauer: Numerical Analysis, 2nd edition, Pearson 2013. \n",
"[3] H. Anton, C. Rorres: Elementary Linear Algebra with Supplemental Applications, 11th edition, Wiley 2015. \n",
"[4] Wikipedia: Least squares, https://en.wikipedia.org/wiki/Least_squares, Acquired May 6th 2016."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.1"
}
},
"nbformat": 4,
"nbformat_minor": 1
}