774 lines
474 KiB
Plaintext
774 lines
474 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Populating the interactive namespace from numpy and matplotlib\n"
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]
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}
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],
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"source": [
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"%pylab inline"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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"import scipy\n",
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"import itertools"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [],
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"source": [
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"rect = lambda x: (np.abs(x) <= 1/2) * 1"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# 1d"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## логика"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [],
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"source": [
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"def swap_halves(a):\n",
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" n = len(a)\n",
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" assert n % 2 == 0\n",
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" \n",
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" m = n // 2\n",
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" \n",
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" b = a\n",
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" b = np.r_[\n",
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" b[m:],\n",
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" b[:m],\n",
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" ]\n",
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" \n",
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" return b\n",
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"\n",
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"def left_right_pad(a, m):\n",
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" n = len(a)\n",
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" \n",
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" assert n % 2 == 0\n",
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" assert m % 2 == 0\n",
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" assert m >= n\n",
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" \n",
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" l = (m - n) // 2\n",
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" r = l + n\n",
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" \n",
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" b = np.zeros(m, dtype=a.dtype)\n",
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" b[l:r] = a\n",
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" \n",
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" return b\n",
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"\n",
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"def left_right_unpad(b, n):\n",
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" m = len(b)\n",
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" \n",
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" assert n % 2 == 0\n",
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" assert m % 2 == 0\n",
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" assert m >= n\n",
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" \n",
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" l = (m - n) // 2\n",
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" r = l + n\n",
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" \n",
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" return b[l:r]"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {},
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"outputs": [],
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"source": [
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"def finite_fourier_1(xs1, ys1, m):\n",
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" n = len(xs1)\n",
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" assert n % 2 == 0\n",
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" assert m % 2 == 0\n",
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"\n",
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" a1 = xs1[-1]\n",
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" h_x1 = xs1[1] - xs1[0]\n",
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"\n",
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" fft_arg = ys1\n",
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" fft_arg = left_right_pad(fft_arg, m)\n",
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" fft_arg = swap_halves(fft_arg)\n",
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" \n",
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" fft_res = np.fft.fft(fft_arg)\n",
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" ys2 = fft_res * h_x1\n",
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" ys2 = swap_halves(ys2)\n",
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" ys2 = left_right_unpad(ys2, n)\n",
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"\n",
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"\n",
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" a2 = n ** 2 / (4 * a1 * m)\n",
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" xs2 = np.linspace(-a2, a2, n)\n",
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" \n",
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" return xs2, ys2"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {},
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"outputs": [],
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"source": [
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"def finite_fourier_2(xs1, ys1, xs2):\n",
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" n = len(xs1)\n",
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" h_x1 = xs1[1] - xs1[0]\n",
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" \n",
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" # first dimension - x\n",
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" x_2d = np.broadcast_to(xs1[:, np.newaxis], (n, n))\n",
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" \n",
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" # second dimension - u\n",
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" u_2d = np.broadcast_to(xs2[np.newaxis, :], (n, n))\n",
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" \n",
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" # exp values\n",
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" A = np.exp((-2 * np.pi * 1j) * x_2d * u_2d)\n",
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" \n",
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" # scale rows by f(x)\n",
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" A = A * np.broadcast_to(ys1[:, np.newaxis], (n, n))\n",
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"\n",
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" int_weights = np.ones(n)\n",
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" int_weights[0] = 1/2\n",
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" int_weights[-1] = 1/2\n",
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" int_weights *= h_x1\n",
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" \n",
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" # scale rows by int_weights\n",
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" A = A * np.broadcast_to(int_weights[:, np.newaxis], (n, n))\n",
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"\n",
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" ys2 = np.sum(A, axis=0)\n",
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" \n",
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" return ys2"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## примеры"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 41,
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"metadata": {},
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"outputs": [],
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"source": [
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"f = lambda x: np.exp(-x**2)\n",
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"F = lambda x: np.sqrt(np.pi) * np.exp(-x**2 * np.pi**2)\n",
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"\n",
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"a = 5\n",
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"b_given = 1.6"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 70,
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"metadata": {},
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"outputs": [],
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"source": [
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"f = np.sinc\n",
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"F = rect\n",
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"\n",
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"a = 5\n",
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"b_given = 1.6"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 56,
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"metadata": {},
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"outputs": [],
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"source": [
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"f = lambda x: np.exp(2 * np.pi * 1j * x) + np.exp(-5 * np.pi * 1j * x)\n",
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"F = lambda x: (4 * x + 3) * np.sin(8 * np.pi * x) / np.pi / (x - 1) / (2 * x + 5)\n",
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"\n",
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"a = 1\n",
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"b_given = 8"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 71,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"1.6\n"
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]
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},
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{
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"data": {
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"text/plain": [
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"<Figure size 1920x1080 with 4 Axes>"
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]
|
|
},
|
|
"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
|
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"n = 1 << 10\n",
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"m = 1 << 15\n",
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"\n",
|
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"xs1 = np.linspace(-a, a, n)\n",
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"ys1 = f(xs1)\n",
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"ys1 = np.array(ys1, dtype=complex)\n",
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"\n",
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"xs2, ys2 = finite_fourier_1(xs1, ys1, m)\n",
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"print(xs2[-1])\n",
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"\n",
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"ys3 = F(xs2)\n",
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"ys3 = np.array(ys3, dtype=complex)\n",
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"\n",
|
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"subplot(2, 2, 1)\n",
|
|
"plot(xs1, np.abs(ys1))\n",
|
|
"xlabel('x')\n",
|
|
"title('$\\\\left|f\\\\right|$')\n",
|
|
"\n",
|
|
"subplot(2, 2, 3)\n",
|
|
"plot(xs1, np.angle(ys1))\n",
|
|
"ylim(-np.pi * 1.1, np.pi * 1.1)\n",
|
|
"xlabel('x')\n",
|
|
"title('$arg f$')\n",
|
|
"\n",
|
|
"subplot(2, 2, 2)\n",
|
|
"plot(xs2, np.abs(ys2))\n",
|
|
"plot(xs2, np.abs(ys3))\n",
|
|
"xlabel('u')\n",
|
|
"title('$\\\\left|F\\\\right|$')\n",
|
|
"\n",
|
|
"subplot(2, 2, 4)\n",
|
|
"plot(xs2, np.angle(ys2))\n",
|
|
"plot(xs2, np.angle(ys3))\n",
|
|
"ylim(-np.pi * 1.1, np.pi * 1.1)\n",
|
|
"xlabel('u')\n",
|
|
"title('$arg F$')\n",
|
|
"\n",
|
|
"gcf().suptitle('FINITE FFT LIBRARY')\n",
|
|
"None"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 72,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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|
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"text/plain": [
|
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"<Figure size 1920x1080 with 4 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"xs1 = np.linspace(-a, a, n)\n",
|
|
"ys1 = vectorize(f)(xs1)\n",
|
|
"ys1 = np.array(ys1, dtype=complex)\n",
|
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"\n",
|
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"xs2 = np.linspace(-b_given, b_given, n)\n",
|
|
"ys2 = finite_fourier_2(xs1, ys1, xs2)\n",
|
|
"\n",
|
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"ys3 = F(xs2)\n",
|
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"ys3 = np.array(ys3, dtype=complex)\n",
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|
"\n",
|
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"subplot(2, 2, 1)\n",
|
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"plot(xs1, np.abs(ys1))\n",
|
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"xlabel('x')\n",
|
|
"title('$\\\\left|f\\\\right|$')\n",
|
|
"\n",
|
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"subplot(2, 2, 3)\n",
|
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"plot(xs1, np.angle(ys1))\n",
|
|
"ylim(-np.pi * 1.1, np.pi * 1.1)\n",
|
|
"xlabel('x')\n",
|
|
"title('$arg f$')\n",
|
|
"\n",
|
|
"subplot(2, 2, 2)\n",
|
|
"plot(xs2, np.abs(ys2))\n",
|
|
"plot(xs2, np.abs(ys3))\n",
|
|
"xlabel('u')\n",
|
|
"title('$\\\\left|F\\\\right|$')\n",
|
|
"\n",
|
|
"subplot(2, 2, 4)\n",
|
|
"plot(xs2, np.angle(ys2))\n",
|
|
"plot(xs2, np.angle(ys3))\n",
|
|
"ylim(-np.pi * 1.1, np.pi * 1.1)\n",
|
|
"xlabel('u')\n",
|
|
"title('$arg F$')\n",
|
|
"\n",
|
|
"gcf().suptitle('INTEGRAL FFT')\n",
|
|
"None"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"# 2d"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"## логика"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 10,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"def swap_halves_2d(a):\n",
|
|
" n = len(a)\n",
|
|
" assert n % 2 == 0\n",
|
|
" \n",
|
|
" m = n // 2\n",
|
|
" \n",
|
|
" b = a\n",
|
|
" b = np.r_[\n",
|
|
" b[m:, :],\n",
|
|
" b[:m, :],\n",
|
|
" ]\n",
|
|
" b = np.c_[\n",
|
|
" b[:, m:],\n",
|
|
" b[:, :m],\n",
|
|
" ]\n",
|
|
" \n",
|
|
" return b\n",
|
|
"\n",
|
|
"def left_right_pad_2d(a, m):\n",
|
|
" n = len(a)\n",
|
|
" \n",
|
|
" assert n % 2 == 0\n",
|
|
" assert m % 2 == 0\n",
|
|
" assert m >= n\n",
|
|
" \n",
|
|
" l = (m - n) // 2\n",
|
|
" r = l + n\n",
|
|
" \n",
|
|
" b = np.zeros((m, m), dtype=a.dtype)\n",
|
|
" b[l:r, l:r] = a\n",
|
|
" \n",
|
|
" return b\n",
|
|
"\n",
|
|
"def left_right_unpad_2d(b, n):\n",
|
|
" m = len(b)\n",
|
|
" \n",
|
|
" assert n % 2 == 0\n",
|
|
" assert m % 2 == 0\n",
|
|
" assert m >= n\n",
|
|
" \n",
|
|
" l = (m - n) // 2\n",
|
|
" r = l + n\n",
|
|
" \n",
|
|
" return b[l:r, l:r]"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 11,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"def finite_fourier_1_2d(xs1, ys1, m):\n",
|
|
" n = len(xs1)\n",
|
|
" assert n % 2 == 0\n",
|
|
" assert m % 2 == 0\n",
|
|
"\n",
|
|
" a1 = xs1[-1]\n",
|
|
" h_x1 = xs1[1] - xs1[0]\n",
|
|
"\n",
|
|
" fft_arg = ys1\n",
|
|
" fft_arg = left_right_pad_2d(fft_arg, m)\n",
|
|
" fft_arg = swap_halves_2d(fft_arg)\n",
|
|
" \n",
|
|
" fft_res = np.fft.fft2(fft_arg)\n",
|
|
" ys2 = fft_res * h_x1 * h_x1\n",
|
|
" ys2 = swap_halves_2d(ys2)\n",
|
|
" ys2 = left_right_unpad_2d(ys2, n)\n",
|
|
"\n",
|
|
"\n",
|
|
" a2 = n ** 2 / (4 * a1 * m)\n",
|
|
" xs2 = np.linspace(-a2, a2, n)\n",
|
|
" \n",
|
|
" return xs2, ys2"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 17,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"def finite_fourier_2_2d(xs1, ys1, xs2):\n",
|
|
" n = len(xs1)\n",
|
|
" h_x1 = xs1[1] - xs1[0]\n",
|
|
" \n",
|
|
" shape = (n, n, n, n)\n",
|
|
" \n",
|
|
" # first dimension - x\n",
|
|
" x_4d = np.broadcast_to(xs1[:, np.newaxis, np.newaxis, np.newaxis], shape)\n",
|
|
" # second dimension - y\n",
|
|
" y_4d = np.broadcast_to(xs1[np.newaxis, :, np.newaxis, np.newaxis], shape)\n",
|
|
" \n",
|
|
" # third dimension - u\n",
|
|
" u_4d = np.broadcast_to(xs2[np.newaxis, np.newaxis, :, np.newaxis], shape)\n",
|
|
" # forth dimension - v\n",
|
|
" v_4d = np.broadcast_to(xs2[np.newaxis, np.newaxis, np.newaxis, :], shape)\n",
|
|
" \n",
|
|
" # exp values\n",
|
|
" A = np.exp((-2 * np.pi * 1j) * (x_4d * u_4d + y_4d * v_4d))\n",
|
|
" \n",
|
|
" # scale d1 and d2 by f(x, y)\n",
|
|
" A = A * np.broadcast_to(ys1[:, :, np.newaxis, np.newaxis], shape)\n",
|
|
"\n",
|
|
" int_weights = np.ones(n)\n",
|
|
" int_weights[0] = 1/2\n",
|
|
" int_weights[-1] = 1/2\n",
|
|
" int_weights *= h_x1\n",
|
|
" \n",
|
|
" # scale d1 by int_weights\n",
|
|
" A = A * np.broadcast_to(int_weights[:, np.newaxis, np.newaxis, np.newaxis], shape)\n",
|
|
" # scale d2 by int_weights\n",
|
|
" A = A * np.broadcast_to(int_weights[np.newaxis, :, np.newaxis, np.newaxis], shape)\n",
|
|
"\n",
|
|
" A = np.sum(A, axis=0)\n",
|
|
" A = np.sum(A, axis=0)\n",
|
|
" \n",
|
|
" return A"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"## примеры"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 36,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"f_2d = lambda a: np.exp(-(a[:, :, 0]**2 + a[:, :, 1]**2))\n",
|
|
"F_2d = lambda a: np.pi * np.exp(-(a[:, :, 0]**2 + a[:, :, 1]**2) * np.pi**2)\n",
|
|
"\n",
|
|
"y1_max = 1\n",
|
|
"y2_max = np.pi"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 81,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"f_2d = lambda a: np.sinc(a[:, :, 0]) * np.sinc(a[:, :, 1])\n",
|
|
"F_2d = lambda a: rect(a[:, :, 0]) * rect(a[:, :, 1])\n",
|
|
"\n",
|
|
"y1_max = 1\n",
|
|
"y2_max = 1\n",
|
|
"\n",
|
|
"a = 5\n",
|
|
"b = 0.8"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 76,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"f_1d = lambda x: np.exp(2 * np.pi * 1j * x) + np.exp(-5 * np.pi * 1j * x)\n",
|
|
"F_1d = lambda x: (4 * x + 3) * np.sin(8 * np.pi * x) / np.pi / (x - 1) / (2 * x + 5)\n",
|
|
"\n",
|
|
"\n",
|
|
"f_2d = lambda a: f_1d(a[:, :, 0]) * f_1d(a[:, :, 1])\n",
|
|
"F_2d = lambda a: F_1d(a[:, :, 0]) * F_1d(a[:, :, 1])\n",
|
|
"\n",
|
|
"y1_max = 2\n",
|
|
"y2_max = 1\n",
|
|
"\n",
|
|
"a = 1\n",
|
|
"b = 4"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 82,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"0.8\n"
|
|
]
|
|
},
|
|
{
|
|
"data": {
|
|
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\n",
|
|
"text/plain": [
|
|
"<Figure size 1920x1080 with 12 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"n = 1 << 6\n",
|
|
"m = 1 << 8\n",
|
|
"\n",
|
|
"xs1 = np.linspace(-a, a, n)\n",
|
|
"X1 = np.reshape(list(itertools.product(xs1, xs1)), (n, n, 2))\n",
|
|
"ys1 = f_2d(X1)\n",
|
|
"\n",
|
|
"xs2, ys2 = finite_fourier_1_2d(xs1, ys1, m)\n",
|
|
"print(xs2[-1])\n",
|
|
"X2 = np.reshape(list(itertools.product(xs2, xs2)), (n, n, 2))\n",
|
|
"\n",
|
|
"ys3 = F_2d(X2)\n",
|
|
"ys3 = np.array(ys3, dtype=complex)\n",
|
|
"\n",
|
|
"subplot(2, 3, 1)\n",
|
|
"imshow(\n",
|
|
" np.abs(ys1), \n",
|
|
" extent=[xs1[0], xs1[-1], xs1[0], xs1[-1]],\n",
|
|
" vmin=0,\n",
|
|
" vmax=y1_max,\n",
|
|
")\n",
|
|
"colorbar()\n",
|
|
"title('$\\\\left|f\\\\right|$')\n",
|
|
"\n",
|
|
"subplot(2, 3, 4)\n",
|
|
"imshow(\n",
|
|
" np.angle(ys1),\n",
|
|
" extent=[xs1[0], xs1[-1], xs1[0], xs1[-1]],\n",
|
|
" vmin=-np.pi, \n",
|
|
" vmax=np.pi,\n",
|
|
")\n",
|
|
"colorbar()\n",
|
|
"title('$arg f$')\n",
|
|
"\n",
|
|
"subplot(2, 3, 2)\n",
|
|
"imshow(\n",
|
|
" np.abs(ys2), \n",
|
|
" extent=[xs2[0], xs2[-1], xs2[0], xs2[-1]],\n",
|
|
" vmin=0,\n",
|
|
" vmax=y2_max,\n",
|
|
")\n",
|
|
"colorbar()\n",
|
|
"title('$\\\\left|\\hat F\\\\right|$')\n",
|
|
"\n",
|
|
"subplot(2, 3, 5)\n",
|
|
"imshow(\n",
|
|
" np.angle(ys2), \n",
|
|
" extent=[xs2[0], xs2[-1], xs2[0], xs2[-1]],\n",
|
|
" vmin=-np.pi, \n",
|
|
" vmax=np.pi,\n",
|
|
")\n",
|
|
"colorbar()\n",
|
|
"title('$arg \\hat F$')\n",
|
|
"\n",
|
|
"subplot(2, 3, 3)\n",
|
|
"imshow(\n",
|
|
" np.abs(ys3), \n",
|
|
" extent=[xs2[0], xs2[-1], xs2[0], xs2[-1]],\n",
|
|
" vmin=0,\n",
|
|
" vmax=y2_max,\n",
|
|
")\n",
|
|
"colorbar()\n",
|
|
"title('$\\\\left|F\\\\right|$')\n",
|
|
"\n",
|
|
"subplot(2, 3, 6)\n",
|
|
"imshow(\n",
|
|
" np.angle(ys3), \n",
|
|
" extent=[xs2[0], xs2[-1], xs2[0], xs2[-1]],\n",
|
|
" vmin=-np.pi, \n",
|
|
" vmax=np.pi,\n",
|
|
")\n",
|
|
"colorbar()\n",
|
|
"title('$arg F$')\n",
|
|
"\n",
|
|
"gcf().suptitle('FINITE FFT LIBRARY')\n",
|
|
"None"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 83,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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\n",
|
|
"text/plain": [
|
|
"<Figure size 1920x1080 with 12 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"n = 1 << 6\n",
|
|
"\n",
|
|
"xs1 = np.linspace(-a, a, n)\n",
|
|
"X1 = np.reshape(list(itertools.product(xs1, xs1)), (n, n, 2))\n",
|
|
"ys1 = f_2d(X1)\n",
|
|
"\n",
|
|
"xs2 = np.linspace(-b, b, n)\n",
|
|
"ys2 = finite_fourier_2_2d(xs1, ys1, xs2)\n",
|
|
"\n",
|
|
"ys3 = F_2d(X2)\n",
|
|
"ys3 = np.array(ys3, dtype=complex)\n",
|
|
"\n",
|
|
"subplot(2, 3, 1)\n",
|
|
"imshow(\n",
|
|
" np.abs(ys1), \n",
|
|
" extent=[xs1[0], xs1[-1], xs1[0], xs1[-1]],\n",
|
|
" vmin=0,\n",
|
|
" vmax=y1_max,\n",
|
|
")\n",
|
|
"colorbar()\n",
|
|
"title('$\\\\left|f\\\\right|$')\n",
|
|
"\n",
|
|
"subplot(2, 3, 4)\n",
|
|
"imshow(\n",
|
|
" np.angle(ys1),\n",
|
|
" extent=[xs1[0], xs1[-1], xs1[0], xs1[-1]],\n",
|
|
" vmin=-np.pi, \n",
|
|
" vmax=np.pi,\n",
|
|
")\n",
|
|
"colorbar()\n",
|
|
"title('$arg f$')\n",
|
|
"\n",
|
|
"subplot(2, 3, 2)\n",
|
|
"imshow(\n",
|
|
" np.abs(ys2), \n",
|
|
" extent=[xs2[0], xs2[-1], xs2[0], xs2[-1]],\n",
|
|
" vmin=0,\n",
|
|
" vmax=y2_max,\n",
|
|
")\n",
|
|
"colorbar()\n",
|
|
"title('$\\\\left|\\hat F\\\\right|$')\n",
|
|
"\n",
|
|
"subplot(2, 3, 5)\n",
|
|
"imshow(\n",
|
|
" np.angle(ys2), \n",
|
|
" extent=[xs2[0], xs2[-1], xs2[0], xs2[-1]],\n",
|
|
" vmin=-np.pi, \n",
|
|
" vmax=np.pi,\n",
|
|
")\n",
|
|
"colorbar()\n",
|
|
"title('$arg \\hat F$')\n",
|
|
"\n",
|
|
"subplot(2, 3, 3)\n",
|
|
"imshow(\n",
|
|
" np.abs(ys3), \n",
|
|
" extent=[xs2[0], xs2[-1], xs2[0], xs2[-1]],\n",
|
|
" vmin=0,\n",
|
|
" vmax=y2_max,\n",
|
|
")\n",
|
|
"colorbar()\n",
|
|
"title('$\\\\left|F\\\\right|$')\n",
|
|
"\n",
|
|
"subplot(2, 3, 6)\n",
|
|
"imshow(\n",
|
|
" np.angle(ys3), \n",
|
|
" extent=[xs2[0], xs2[-1], xs2[0], xs2[-1]],\n",
|
|
" vmin=-np.pi, \n",
|
|
" vmax=np.pi,\n",
|
|
")\n",
|
|
"colorbar()\n",
|
|
"title('$arg F$')\n",
|
|
"\n",
|
|
"gcf().suptitle('INTEGRAL FFT')\n",
|
|
"None"
|
|
]
|
|
}
|
|
],
|
|
"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": "3.7.2"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 2
|
|
}
|