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fnoble/BMW ambiguities_MatrixBuild (4).ipynb

Created March 28, 2019 08:57
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BMW ambiguities_MatrixBuild (4).ipynb
{
"cells": [
{
"cell_type": "code",
"execution_count": 84,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import pandas as pd\n",
"from scipy.stats import norm\n",
"import matplotlib\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline \n",
"\n",
"L1 = 0.19\n",
"L2 = 0.24\n",
"class Satellite:\n",
" def __init__(self, el=0, az=0):\n",
" self.el = np.deg2rad(el)\n",
" self.az = np.deg2rad(az)\n",
" self.unit_vector = np.array( [np.cos(self.el)*np.sin(self.az), \n",
" np.cos(self.el)*np.cos(self.az),\n",
" np.sin(self.el)] ).transpose()\n",
" def get_g_row(self):\n",
" return -1. * self.unit_vector.transpose()\n",
" \n",
" def get_g_row_dual_freq(self):\n",
" sat_row = self.get_g_row()\n",
" matrix_block = np.array(np.vstack((sat_row, sat_row)))\n",
" return matrix_block\n",
" \n",
" def get_g_row_dual_freq_and_clock_bias(self):\n",
" # two rows, one for each frequency, each row is direction cosines + a (receiver clock) bias\n",
" first_row = np.hstack((self.get_g_row(), [1, 0]))\n",
" second_row = np.hstack((self.get_g_row(), [0, 1]))\n",
" # return the matrix block (2 rows, 5 columns) for directions + bias\n",
" matrix_block = np.array(np.vstack((first_row, second_row)))\n",
" assert matrix_block.shape == (2, 5)\n",
" return matrix_block\n",
"\n",
"class MatrixG:\n",
" def __init__(self, list_satellites):\n",
" self.n_satellites = len(list_satellites)\n",
" # each element is a row vector\n",
" # dual frequency, so 2 rows per satellite\n",
" for one_satellite in list_satellites:\n",
" one_satellite.get_g_row()\n",
" self.G = np.array( [one_satellite.get_g_row_dual_freq() for one_satellite in list_satellites] ).reshape(self.n_satellites*2,-1)\n",
" self.G_with_receiver_clock_biases = np.array( [one_satellite.get_g_row_dual_freq_and_clock_bias() for one_satellite in list_satellites] ).reshape(self.n_satellites*2,-1)\n",
" \n",
" def get_G(self):\n",
" return self.G\n",
" \n",
" def get_G_with_receiver_clock_biases(self):\n",
" return self.G_with_receiver_clock_biases\n",
" \n",
" def get_n_satellites(self):\n",
" return self.n_satellites\n",
"\n",
"class MatrixA:\n",
" def __init__(self, matrix_G):\n",
" n_satellites = matrix_G.get_n_satellites()\n",
" n_biases = 0\n",
" \n",
" top_left_block = np.identity(3) # position\n",
" top_right_block = np.zeros((3, 2*n_satellites+n_biases)) # cross-terms position <--> ambiguities\n",
" bottom_right_block = np.identity(2*n_satellites)\n",
" for i in range(2*n_satellites):\n",
" bottom_right_block[i,i] = L2 if (i % 2 != 0) else L1\n",
"# bottom_right_block[0:2:n_sats*2,0:2:n_sats*2] = 1*lambda\n",
" # ambiguities\n",
" #bottom_left_block = matrix_G.get_G_with_receiver_clock_biases()\n",
" bottom_left_block = matrix_G.get_G()\n",
"\n",
" self.A = np.block([[ top_left_block, top_right_block ],\n",
" [ bottom_left_block, bottom_right_block ]])\n",
"\n",
"\n",
" def get_A(self):\n",
" return self.A\n",
" \n",
"class MatrixR():\n",
" # R matrix (noise)\n",
" def __init__(self, sig_x, sig_y, sig_z, sig_phi, correlation_term=0.2, n_satellites=9, n_biases=2):\n",
" # TODO warning --> non-diag terms should be corr coeff times sigma_i times sigma_j for elem ij with i!=j\n",
" top_left_block = np.full((3+n_biases, 3+n_biases), correlation_term*sig_x*sig_x)\n",
" top_left_block[0,0] = sig_x**2\n",
" top_left_block[1,1] = sig_y**2\n",
" top_left_block[2,2] = sig_z**2\n",
"\n",
" # TODO CHECK\n",
" ## actually, we dont need those clock noises in R!\n",
"# if n_biases == 2:\n",
"# top_left_block[3:5, 0:4] = 0.\n",
"# top_left_block[0:4, 3:5] = 0.\n",
"# top_left_block[3,3] = 0.001**2 # receiver clock noise assumed zero?\n",
"# top_left_block[4,4] = 0.001**2 # receiver clock noise assumed zero?\n",
"# else:\n",
"# print('ERROR we only support two biases here!')\n",
" \n",
" top_right_block = np.full((3+n_biases, n_satellites*2), 0.)\n",
" bottom_left_block = np.full((2*n_satellites, 3+n_biases), 0.)\n",
" \n",
"# bottom_right_block = np.full((n_satellites, n_satellites), correlation_term)\n",
" # 5 mm for carrier phase sigma\n",
" bottom_right_block = np.diag([2 * sig_phi**2] * n_satellites*2)\n",
" self.R = np.block([\n",
" [ top_left_block, top_right_block ],\n",
" [ bottom_left_block, bottom_right_block ]])\n",
"\n",
" def get_R(self):\n",
" return self.R\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 85,
"metadata": {},
"outputs": [],
"source": [
"# M=np.identity(5)\n",
"# for i in range(5):\n",
"# M[i,i] = L2 if (i % 2 != 0) else L1\n",
"# M"
]
},
{
"cell_type": "code",
"execution_count": 204,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"9\n"
]
}
],
"source": [
"# number of satellites == 9\n",
"satellites = [\n",
" Satellite(el=89, az=0.),\n",
" Satellite(el=60, az=-45.),\n",
" Satellite(el=60, az=45.),\n",
" Satellite(el=60, az=135.),\n",
" Satellite(el=60, az=-135.),\n",
" Satellite(el=20, az=0.),\n",
" Satellite(el=20, az=90.),\n",
" Satellite(el=20, az=179.),\n",
" Satellite(el=20, az=-90.)\n",
"]\n",
"\n",
"satellites = satellites[0:]\n",
"print(len(satellites))\n",
"\n",
"# cosine + receiver clock bias matrix\n",
"matrixG_object = MatrixG(satellites)\n",
"G = matrixG_object.get_G()\n",
"\n",
"# you need matrix G to build matrix A\n",
"matrixA_object = MatrixA(matrixG_object)\n",
"A = matrixA_object.get_A()\n",
"\n",
"# noise\n",
"# sigma_pos = 0.10 # 10cm\n",
"sigma_phi = 0.005 # 5mm\n",
"sigma_value = 0.25 # 25cm\n",
"\n",
"def gimme_R(sigma_value, sigma_phi, correlation_term, n_satellites, n_biases=0):\n",
" matrixR_object = MatrixR(sig_x=sigma_value,\n",
" sig_y=sigma_value,\n",
" sig_z=sigma_value,\n",
" sig_phi=sigma_phi,\n",
" correlation_term=correlation_term,\n",
" n_satellites=n_satellites,\n",
" n_biases=n_biases)\n",
"\n",
" R = matrixR_object.get_R()\n",
" return R\n",
"\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 205,
"metadata": {},
"outputs": [
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" </tr>\n",
" <tr>\n",
" <th>15</th>\n",
" <td>-0.939693</td>\n",
" <td>-5.753958e-17</td>\n",
" <td>-0.342020</td>\n",
" <td>0.00</td>\n",
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" </tr>\n",
" <tr>\n",
" <th>16</th>\n",
" <td>-0.939693</td>\n",
" <td>-5.753958e-17</td>\n",
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" <td>0.00</td>\n",
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" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" </tr>\n",
" <tr>\n",
" <th>17</th>\n",
" <td>-0.016400</td>\n",
" <td>9.395495e-01</td>\n",
" <td>-0.342020</td>\n",
" <td>0.00</td>\n",
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" </tr>\n",
" <tr>\n",
" <th>18</th>\n",
" <td>-0.016400</td>\n",
" <td>9.395495e-01</td>\n",
" <td>-0.342020</td>\n",
" <td>0.00</td>\n",
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" <td>0.24</td>\n",
" <td>0.00</td>\n",
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" </tr>\n",
" <tr>\n",
" <th>19</th>\n",
" <td>0.939693</td>\n",
" <td>-5.753958e-17</td>\n",
" <td>-0.342020</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
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" <td>0.00</td>\n",
" <td>0.19</td>\n",
" <td>0.00</td>\n",
" </tr>\n",
" <tr>\n",
" <th>20</th>\n",
" <td>0.939693</td>\n",
" <td>-5.753958e-17</td>\n",
" <td>-0.342020</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
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" <td>0.24</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>21 rows × 21 columns</p>\n",
"</div>"
],
"text/plain": [
" 0 1 2 3 4 5 6 7 8 \\\n",
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"1 0.000000 1.000000e+00 0.000000 0.00 0.00 0.00 0.00 0.00 0.00 \n",
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"3 -0.000000 -1.745241e-02 -0.999848 0.19 0.00 0.00 0.00 0.00 0.00 \n",
"4 -0.000000 -1.745241e-02 -0.999848 0.00 0.24 0.00 0.00 0.00 0.00 \n",
"5 0.353553 -3.535534e-01 -0.866025 0.00 0.00 0.19 0.00 0.00 0.00 \n",
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"7 -0.353553 -3.535534e-01 -0.866025 0.00 0.00 0.00 0.00 0.19 0.00 \n",
"8 -0.353553 -3.535534e-01 -0.866025 0.00 0.00 0.00 0.00 0.00 0.24 \n",
"9 -0.353553 3.535534e-01 -0.866025 0.00 0.00 0.00 0.00 0.00 0.00 \n",
"10 -0.353553 3.535534e-01 -0.866025 0.00 0.00 0.00 0.00 0.00 0.00 \n",
"11 0.353553 3.535534e-01 -0.866025 0.00 0.00 0.00 0.00 0.00 0.00 \n",
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"20 0.939693 -5.753958e-17 -0.342020 0.00 0.00 0.00 0.00 0.00 0.00 \n",
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"7 0.00 ... 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 \n",
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"20 0.00 ... 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.24 \n",
"\n",
"[21 rows x 21 columns]"
]
},
"execution_count": 205,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# should be (3+8, 3+8)\n",
"df = pd.DataFrame(A)\n",
"df"
]
},
{
"cell_type": "code",
"execution_count": 206,
"metadata": {},
"outputs": [
{
"data": {
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" <th>11</th>\n",
" <td>0.0000</td>\n",
" <td>0.0000</td>\n",
" <td>0.0000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>...</td>\n",
" <td>0.00005</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>12</th>\n",
" <td>0.0000</td>\n",
" <td>0.0000</td>\n",
" <td>0.0000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>...</td>\n",
" <td>0.00000</td>\n",
" <td>0.00005</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>13</th>\n",
" <td>0.0000</td>\n",
" <td>0.0000</td>\n",
" <td>0.0000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>...</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00005</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>14</th>\n",
" <td>0.0000</td>\n",
" <td>0.0000</td>\n",
" <td>0.0000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>...</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
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" <td>0.00005</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>15</th>\n",
" <td>0.0000</td>\n",
" <td>0.0000</td>\n",
" <td>0.0000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>...</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00005</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>16</th>\n",
" <td>0.0000</td>\n",
" <td>0.0000</td>\n",
" <td>0.0000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>...</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00005</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>17</th>\n",
" <td>0.0000</td>\n",
" <td>0.0000</td>\n",
" <td>0.0000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>...</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00005</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>18</th>\n",
" <td>0.0000</td>\n",
" <td>0.0000</td>\n",
" <td>0.0000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>...</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00005</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>19</th>\n",
" <td>0.0000</td>\n",
" <td>0.0000</td>\n",
" <td>0.0000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>...</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00005</td>\n",
" <td>0.00000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>20</th>\n",
" <td>0.0000</td>\n",
" <td>0.0000</td>\n",
" <td>0.0000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>...</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
" <td>0.00000</td>\n",
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" <td>0.00000</td>\n",
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" <td>0.00000</td>\n",
" <td>0.00005</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>21 rows × 21 columns</p>\n",
"</div>"
],
"text/plain": [
" 0 1 2 3 4 5 6 7 \\\n",
"0 0.0225 0.0045 0.0045 0.00000 0.00000 0.00000 0.00000 0.00000 \n",
"1 0.0045 0.0225 0.0045 0.00000 0.00000 0.00000 0.00000 0.00000 \n",
"2 0.0045 0.0045 0.0225 0.00000 0.00000 0.00000 0.00000 0.00000 \n",
"3 0.0000 0.0000 0.0000 0.00005 0.00000 0.00000 0.00000 0.00000 \n",
"4 0.0000 0.0000 0.0000 0.00000 0.00005 0.00000 0.00000 0.00000 \n",
"5 0.0000 0.0000 0.0000 0.00000 0.00000 0.00005 0.00000 0.00000 \n",
"6 0.0000 0.0000 0.0000 0.00000 0.00000 0.00000 0.00005 0.00000 \n",
"7 0.0000 0.0000 0.0000 0.00000 0.00000 0.00000 0.00000 0.00005 \n",
"8 0.0000 0.0000 0.0000 0.00000 0.00000 0.00000 0.00000 0.00000 \n",
"9 0.0000 0.0000 0.0000 0.00000 0.00000 0.00000 0.00000 0.00000 \n",
"10 0.0000 0.0000 0.0000 0.00000 0.00000 0.00000 0.00000 0.00000 \n",
"11 0.0000 0.0000 0.0000 0.00000 0.00000 0.00000 0.00000 0.00000 \n",
"12 0.0000 0.0000 0.0000 0.00000 0.00000 0.00000 0.00000 0.00000 \n",
"13 0.0000 0.0000 0.0000 0.00000 0.00000 0.00000 0.00000 0.00000 \n",
"14 0.0000 0.0000 0.0000 0.00000 0.00000 0.00000 0.00000 0.00000 \n",
"15 0.0000 0.0000 0.0000 0.00000 0.00000 0.00000 0.00000 0.00000 \n",
"16 0.0000 0.0000 0.0000 0.00000 0.00000 0.00000 0.00000 0.00000 \n",
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"19 0.0000 0.0000 0.0000 0.00000 0.00000 0.00000 0.00000 0.00000 \n",
"20 0.0000 0.0000 0.0000 0.00000 0.00000 0.00000 0.00000 0.00000 \n",
"\n",
" 8 9 ... 11 12 13 14 15 \\\n",
"0 0.00000 0.00000 ... 0.00000 0.00000 0.00000 0.00000 0.00000 \n",
"1 0.00000 0.00000 ... 0.00000 0.00000 0.00000 0.00000 0.00000 \n",
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"6 0.00000 0.00000 ... 0.00000 0.00000 0.00000 0.00000 0.00000 \n",
"7 0.00000 0.00000 ... 0.00000 0.00000 0.00000 0.00000 0.00000 \n",
"8 0.00005 0.00000 ... 0.00000 0.00000 0.00000 0.00000 0.00000 \n",
"9 0.00000 0.00005 ... 0.00000 0.00000 0.00000 0.00000 0.00000 \n",
"10 0.00000 0.00000 ... 0.00000 0.00000 0.00000 0.00000 0.00000 \n",
"11 0.00000 0.00000 ... 0.00005 0.00000 0.00000 0.00000 0.00000 \n",
"12 0.00000 0.00000 ... 0.00000 0.00005 0.00000 0.00000 0.00000 \n",
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"15 0.00000 0.00000 ... 0.00000 0.00000 0.00000 0.00000 0.00005 \n",
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"18 0.00000 0.00000 ... 0.00000 0.00000 0.00000 0.00000 0.00000 \n",
"19 0.00000 0.00000 ... 0.00000 0.00000 0.00000 0.00000 0.00000 \n",
"20 0.00000 0.00000 ... 0.00000 0.00000 0.00000 0.00000 0.00000 \n",
"\n",
" 16 17 18 19 20 \n",
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"1 0.00000 0.00000 0.00000 0.00000 0.00000 \n",
"2 0.00000 0.00000 0.00000 0.00000 0.00000 \n",
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"20 0.00000 0.00000 0.00000 0.00000 0.00005 \n",
"\n",
"[21 rows x 21 columns]"
]
},
"execution_count": 206,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# print(len(satellites))\n",
"R = gimme_R(sigma_value=0.15, sigma_phi=0.005, correlation_term=0.2, n_satellites=len(satellites), n_biases=0)\n",
"# should be \n",
"df = pd.DataFrame(R)\n",
"df"
]
},
{
"cell_type": "code",
"execution_count": 207,
"metadata": {},
"outputs": [
{
"data": {
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" <th></th>\n",
" <th>0</th>\n",
" <th>1</th>\n",
" <th>2</th>\n",
" <th>3</th>\n",
" <th>4</th>\n",
" <th>5</th>\n",
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" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>0.000000</td>\n",
" <td>1.000000e+00</td>\n",
" <td>0.000000</td>\n",
" <td>0.00</td>\n",
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" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
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" <th>2</th>\n",
" <td>0.000000</td>\n",
" <td>0.000000e+00</td>\n",
" <td>1.000000</td>\n",
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" <th>3</th>\n",
" <td>-0.000000</td>\n",
" <td>-1.745241e-02</td>\n",
" <td>-0.999848</td>\n",
" <td>0.19</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
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" <td>0.00</td>\n",
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" <td>0.00</td>\n",
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" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>-0.353553</td>\n",
" <td>-3.535534e-01</td>\n",
" <td>-0.866025</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.24</td>\n",
" <td>0.00</td>\n",
" <td>...</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9</th>\n",
" <td>-0.353553</td>\n",
" <td>3.535534e-01</td>\n",
" <td>-0.866025</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.19</td>\n",
" <td>...</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" </tr>\n",
" <tr>\n",
" <th>10</th>\n",
" <td>-0.353553</td>\n",
" <td>3.535534e-01</td>\n",
" <td>-0.866025</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>...</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" </tr>\n",
" <tr>\n",
" <th>11</th>\n",
" <td>0.353553</td>\n",
" <td>3.535534e-01</td>\n",
" <td>-0.866025</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>...</td>\n",
" <td>0.19</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" </tr>\n",
" <tr>\n",
" <th>12</th>\n",
" <td>0.353553</td>\n",
" <td>3.535534e-01</td>\n",
" <td>-0.866025</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>...</td>\n",
" <td>0.00</td>\n",
" <td>0.24</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" </tr>\n",
" <tr>\n",
" <th>13</th>\n",
" <td>-0.000000</td>\n",
" <td>-9.396926e-01</td>\n",
" <td>-0.342020</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>...</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.19</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" </tr>\n",
" <tr>\n",
" <th>14</th>\n",
" <td>-0.000000</td>\n",
" <td>-9.396926e-01</td>\n",
" <td>-0.342020</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
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" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>...</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.24</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" </tr>\n",
" <tr>\n",
" <th>15</th>\n",
" <td>-0.939693</td>\n",
" <td>-5.753958e-17</td>\n",
" <td>-0.342020</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>...</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.19</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" </tr>\n",
" <tr>\n",
" <th>16</th>\n",
" <td>-0.939693</td>\n",
" <td>-5.753958e-17</td>\n",
" <td>-0.342020</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>...</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.24</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" </tr>\n",
" <tr>\n",
" <th>17</th>\n",
" <td>-0.016400</td>\n",
" <td>9.395495e-01</td>\n",
" <td>-0.342020</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>...</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.19</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" </tr>\n",
" <tr>\n",
" <th>18</th>\n",
" <td>-0.016400</td>\n",
" <td>9.395495e-01</td>\n",
" <td>-0.342020</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>...</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.24</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" </tr>\n",
" <tr>\n",
" <th>19</th>\n",
" <td>0.939693</td>\n",
" <td>-5.753958e-17</td>\n",
" <td>-0.342020</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>...</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.19</td>\n",
" <td>0.00</td>\n",
" </tr>\n",
" <tr>\n",
" <th>20</th>\n",
" <td>0.939693</td>\n",
" <td>-5.753958e-17</td>\n",
" <td>-0.342020</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>...</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0.24</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>21 rows × 21 columns</p>\n",
"</div>"
],
"text/plain": [
" 0 1 2 3 4 5 6 7 8 \\\n",
"0 1.000000 0.000000e+00 0.000000 0.00 0.00 0.00 0.00 0.00 0.00 \n",
"1 0.000000 1.000000e+00 0.000000 0.00 0.00 0.00 0.00 0.00 0.00 \n",
"2 0.000000 0.000000e+00 1.000000 0.00 0.00 0.00 0.00 0.00 0.00 \n",
"3 -0.000000 -1.745241e-02 -0.999848 0.19 0.00 0.00 0.00 0.00 0.00 \n",
"4 -0.000000 -1.745241e-02 -0.999848 0.00 0.24 0.00 0.00 0.00 0.00 \n",
"5 0.353553 -3.535534e-01 -0.866025 0.00 0.00 0.19 0.00 0.00 0.00 \n",
"6 0.353553 -3.535534e-01 -0.866025 0.00 0.00 0.00 0.24 0.00 0.00 \n",
"7 -0.353553 -3.535534e-01 -0.866025 0.00 0.00 0.00 0.00 0.19 0.00 \n",
"8 -0.353553 -3.535534e-01 -0.866025 0.00 0.00 0.00 0.00 0.00 0.24 \n",
"9 -0.353553 3.535534e-01 -0.866025 0.00 0.00 0.00 0.00 0.00 0.00 \n",
"10 -0.353553 3.535534e-01 -0.866025 0.00 0.00 0.00 0.00 0.00 0.00 \n",
"11 0.353553 3.535534e-01 -0.866025 0.00 0.00 0.00 0.00 0.00 0.00 \n",
"12 0.353553 3.535534e-01 -0.866025 0.00 0.00 0.00 0.00 0.00 0.00 \n",
"13 -0.000000 -9.396926e-01 -0.342020 0.00 0.00 0.00 0.00 0.00 0.00 \n",
"14 -0.000000 -9.396926e-01 -0.342020 0.00 0.00 0.00 0.00 0.00 0.00 \n",
"15 -0.939693 -5.753958e-17 -0.342020 0.00 0.00 0.00 0.00 0.00 0.00 \n",
"16 -0.939693 -5.753958e-17 -0.342020 0.00 0.00 0.00 0.00 0.00 0.00 \n",
"17 -0.016400 9.395495e-01 -0.342020 0.00 0.00 0.00 0.00 0.00 0.00 \n",
"18 -0.016400 9.395495e-01 -0.342020 0.00 0.00 0.00 0.00 0.00 0.00 \n",
"19 0.939693 -5.753958e-17 -0.342020 0.00 0.00 0.00 0.00 0.00 0.00 \n",
"20 0.939693 -5.753958e-17 -0.342020 0.00 0.00 0.00 0.00 0.00 0.00 \n",
"\n",
" 9 ... 11 12 13 14 15 16 17 18 19 20 \n",
"0 0.00 ... 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 \n",
"1 0.00 ... 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 \n",
"2 0.00 ... 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 \n",
"3 0.00 ... 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 \n",
"4 0.00 ... 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 \n",
"5 0.00 ... 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 \n",
"6 0.00 ... 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 \n",
"7 0.00 ... 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 \n",
"8 0.00 ... 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 \n",
"9 0.19 ... 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 \n",
"10 0.00 ... 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 \n",
"11 0.00 ... 0.19 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 \n",
"12 0.00 ... 0.00 0.24 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 \n",
"13 0.00 ... 0.00 0.00 0.19 0.00 0.00 0.00 0.00 0.00 0.00 0.00 \n",
"14 0.00 ... 0.00 0.00 0.00 0.24 0.00 0.00 0.00 0.00 0.00 0.00 \n",
"15 0.00 ... 0.00 0.00 0.00 0.00 0.19 0.00 0.00 0.00 0.00 0.00 \n",
"16 0.00 ... 0.00 0.00 0.00 0.00 0.00 0.24 0.00 0.00 0.00 0.00 \n",
"17 0.00 ... 0.00 0.00 0.00 0.00 0.00 0.00 0.19 0.00 0.00 0.00 \n",
"18 0.00 ... 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.24 0.00 0.00 \n",
"19 0.00 ... 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.19 0.00 \n",
"20 0.00 ... 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.24 \n",
"\n",
"[21 rows x 21 columns]"
]
},
"execution_count": 207,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df = pd.DataFrame(A)\n",
"df"
]
},
{
"cell_type": "code",
"execution_count": 208,
"metadata": {},
"outputs": [],
"source": [
"# i think obs_error_sigma is like ~sigma_URE\n",
"def get_covariance_matrix_estimate(A, R, obs_error_sigma=1.0):\n",
" W = np.linalg.inv(R)\n",
" GWGt = np.dot(A.transpose(), np.dot(W, A))\n",
" return obs_error_sigma * np.linalg.inv(GWGt)\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 209,
"metadata": {},
"outputs": [],
"source": [
"Q = get_covariance_matrix_estimate(A, R, obs_error_sigma=1.0)"
]
},
{
"cell_type": "code",
"execution_count": 210,
"metadata": {},
"outputs": [
{
"data": {
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" <tr>\n",
" <th>3</th>\n",
" <td>0.024094</td>\n",
" <td>0.025747</td>\n",
" <td>0.118816</td>\n",
" <td>0.629004</td>\n",
" <td>0.496865</td>\n",
" <td>0.544645</td>\n",
" <td>0.431177</td>\n",
" <td>0.634313</td>\n",
" <td>0.502165</td>\n",
" <td>0.538492</td>\n",
" <td>...</td>\n",
" <td>0.448823</td>\n",
" <td>0.355318</td>\n",
" <td>0.341222</td>\n",
" <td>0.270134</td>\n",
" <td>0.333045</td>\n",
" <td>0.263660</td>\n",
" <td>0.088641</td>\n",
" <td>0.070174</td>\n",
" <td>0.094719</td>\n",
" <td>0.074986</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>0.019074</td>\n",
" <td>0.020383</td>\n",
" <td>0.094063</td>\n",
" <td>0.496865</td>\n",
" <td>0.394220</td>\n",
" <td>0.431177</td>\n",
" <td>0.341349</td>\n",
" <td>0.502165</td>\n",
" <td>0.397547</td>\n",
" <td>0.426306</td>\n",
" <td>...</td>\n",
" <td>0.355318</td>\n",
" <td>0.281294</td>\n",
" <td>0.270134</td>\n",
" <td>0.213856</td>\n",
" <td>0.263660</td>\n",
" <td>0.208731</td>\n",
" <td>0.070174</td>\n",
" <td>0.055555</td>\n",
" <td>0.074986</td>\n",
" <td>0.059364</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>-0.012983</td>\n",
" <td>0.054006</td>\n",
" <td>0.102556</td>\n",
" <td>0.544645</td>\n",
" <td>0.431177</td>\n",
" <td>0.593490</td>\n",
" <td>0.468750</td>\n",
" <td>0.543786</td>\n",
" <td>0.430497</td>\n",
" <td>0.342798</td>\n",
" <td>...</td>\n",
" <td>0.391117</td>\n",
" <td>0.309634</td>\n",
" <td>0.451710</td>\n",
" <td>0.357603</td>\n",
" <td>0.120398</td>\n",
" <td>0.095315</td>\n",
" <td>-0.083567</td>\n",
" <td>-0.066158</td>\n",
" <td>0.248824</td>\n",
" <td>0.196985</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>-0.010279</td>\n",
" <td>0.042754</td>\n",
" <td>0.081190</td>\n",
" <td>0.431177</td>\n",
" <td>0.341349</td>\n",
" <td>0.468750</td>\n",
" <td>0.371962</td>\n",
" <td>0.430497</td>\n",
" <td>0.340810</td>\n",
" <td>0.271382</td>\n",
" <td>...</td>\n",
" <td>0.309634</td>\n",
" <td>0.245127</td>\n",
" <td>0.357603</td>\n",
" <td>0.283103</td>\n",
" <td>0.095315</td>\n",
" <td>0.075458</td>\n",
" <td>-0.066158</td>\n",
" <td>-0.052375</td>\n",
" <td>0.196985</td>\n",
" <td>0.155947</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7</th>\n",
" <td>0.070753</td>\n",
" <td>0.070753</td>\n",
" <td>0.119303</td>\n",
" <td>0.634313</td>\n",
" <td>0.502165</td>\n",
" <td>0.543786</td>\n",
" <td>0.430497</td>\n",
" <td>0.808486</td>\n",
" <td>0.638955</td>\n",
" <td>0.543786</td>\n",
" <td>...</td>\n",
" <td>0.280471</td>\n",
" <td>0.222039</td>\n",
" <td>0.564684</td>\n",
" <td>0.447042</td>\n",
" <td>0.564684</td>\n",
" <td>0.447042</td>\n",
" <td>-0.129008</td>\n",
" <td>-0.102131</td>\n",
" <td>-0.135168</td>\n",
" <td>-0.107008</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>0.056013</td>\n",
" <td>0.056013</td>\n",
" <td>0.094448</td>\n",
" <td>0.502165</td>\n",
" <td>0.397547</td>\n",
" <td>0.430497</td>\n",
" <td>0.340810</td>\n",
" <td>0.638955</td>\n",
" <td>0.506707</td>\n",
" <td>0.430497</td>\n",
" <td>...</td>\n",
" <td>0.222039</td>\n",
" <td>0.175781</td>\n",
" <td>0.447042</td>\n",
" <td>0.353908</td>\n",
" <td>0.447042</td>\n",
" <td>0.353908</td>\n",
" <td>-0.102131</td>\n",
" <td>-0.080854</td>\n",
" <td>-0.107008</td>\n",
" <td>-0.084715</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9</th>\n",
" <td>0.054006</td>\n",
" <td>-0.012983</td>\n",
" <td>0.102556</td>\n",
" <td>0.538492</td>\n",
" <td>0.426306</td>\n",
" <td>0.342798</td>\n",
" <td>0.271382</td>\n",
" <td>0.543786</td>\n",
" <td>0.430497</td>\n",
" <td>0.593490</td>\n",
" <td>...</td>\n",
" <td>0.391117</td>\n",
" <td>0.309634</td>\n",
" <td>0.120398</td>\n",
" <td>0.095315</td>\n",
" <td>0.451710</td>\n",
" <td>0.357603</td>\n",
" <td>0.253475</td>\n",
" <td>0.200668</td>\n",
" <td>-0.082488</td>\n",
" <td>-0.065303</td>\n",
" </tr>\n",
" <tr>\n",
" <th>10</th>\n",
" <td>0.042754</td>\n",
" <td>-0.010279</td>\n",
" <td>0.081190</td>\n",
" <td>0.426306</td>\n",
" <td>0.337492</td>\n",
" <td>0.271382</td>\n",
" <td>0.214844</td>\n",
" <td>0.430497</td>\n",
" <td>0.340810</td>\n",
" <td>0.468750</td>\n",
" <td>...</td>\n",
" <td>0.309634</td>\n",
" <td>0.245127</td>\n",
" <td>0.095315</td>\n",
" <td>0.075458</td>\n",
" <td>0.357603</td>\n",
" <td>0.283103</td>\n",
" <td>0.200668</td>\n",
" <td>0.158862</td>\n",
" <td>-0.065303</td>\n",
" <td>-0.051698</td>\n",
" </tr>\n",
" <tr>\n",
" <th>11</th>\n",
" <td>-0.029731</td>\n",
" <td>-0.029731</td>\n",
" <td>0.085808</td>\n",
" <td>0.448823</td>\n",
" <td>0.355318</td>\n",
" <td>0.391117</td>\n",
" <td>0.309634</td>\n",
" <td>0.280471</td>\n",
" <td>0.222039</td>\n",
" <td>0.391117</td>\n",
" <td>...</td>\n",
" <td>0.503148</td>\n",
" <td>0.397229</td>\n",
" <td>0.007424</td>\n",
" <td>0.005877</td>\n",
" <td>0.007424</td>\n",
" <td>0.005877</td>\n",
" <td>0.298916</td>\n",
" <td>0.236642</td>\n",
" <td>0.301505</td>\n",
" <td>0.238691</td>\n",
" </tr>\n",
" <tr>\n",
" <th>12</th>\n",
" <td>-0.023537</td>\n",
" <td>-0.023537</td>\n",
" <td>0.067932</td>\n",
" <td>0.355318</td>\n",
" <td>0.281294</td>\n",
" <td>0.309634</td>\n",
" <td>0.245127</td>\n",
" <td>0.222039</td>\n",
" <td>0.175781</td>\n",
" <td>0.309634</td>\n",
" <td>...</td>\n",
" <td>0.397229</td>\n",
" <td>0.315341</td>\n",
" <td>0.005877</td>\n",
" <td>0.004653</td>\n",
" <td>0.005877</td>\n",
" <td>0.004653</td>\n",
" <td>0.236642</td>\n",
" <td>0.187341</td>\n",
" <td>0.238691</td>\n",
" <td>0.188964</td>\n",
" </tr>\n",
" <tr>\n",
" <th>13</th>\n",
" <td>0.030356</td>\n",
" <td>0.119380</td>\n",
" <td>0.062758</td>\n",
" <td>0.341222</td>\n",
" <td>0.270134</td>\n",
" <td>0.451710</td>\n",
" <td>0.357603</td>\n",
" <td>0.564684</td>\n",
" <td>0.447042</td>\n",
" <td>0.120398</td>\n",
" <td>...</td>\n",
" <td>0.007424</td>\n",
" <td>0.005877</td>\n",
" <td>0.704780</td>\n",
" <td>0.556854</td>\n",
" <td>0.263106</td>\n",
" <td>0.208293</td>\n",
" <td>-0.474741</td>\n",
" <td>-0.375837</td>\n",
" <td>-0.037163</td>\n",
" <td>-0.029421</td>\n",
" </tr>\n",
" <tr>\n",
" <th>14</th>\n",
" <td>0.024032</td>\n",
" <td>0.094509</td>\n",
" <td>0.049684</td>\n",
" <td>0.270134</td>\n",
" <td>0.213856</td>\n",
" <td>0.357603</td>\n",
" <td>0.283103</td>\n",
" <td>0.447042</td>\n",
" <td>0.353908</td>\n",
" <td>0.095315</td>\n",
" <td>...</td>\n",
" <td>0.005877</td>\n",
" <td>0.004653</td>\n",
" <td>0.556854</td>\n",
" <td>0.441711</td>\n",
" <td>0.208293</td>\n",
" <td>0.164898</td>\n",
" <td>-0.375837</td>\n",
" <td>-0.297538</td>\n",
" <td>-0.029421</td>\n",
" <td>-0.023292</td>\n",
" </tr>\n",
" <tr>\n",
" <th>15</th>\n",
" <td>0.119380</td>\n",
" <td>0.030356</td>\n",
" <td>0.062758</td>\n",
" <td>0.333045</td>\n",
" <td>0.263660</td>\n",
" <td>0.120398</td>\n",
" <td>0.095315</td>\n",
" <td>0.564684</td>\n",
" <td>0.447042</td>\n",
" <td>0.451710</td>\n",
" <td>...</td>\n",
" <td>0.007424</td>\n",
" <td>0.005877</td>\n",
" <td>0.263106</td>\n",
" <td>0.208293</td>\n",
" <td>0.704780</td>\n",
" <td>0.556854</td>\n",
" <td>-0.026836</td>\n",
" <td>-0.021245</td>\n",
" <td>-0.477452</td>\n",
" <td>-0.377982</td>\n",
" </tr>\n",
" <tr>\n",
" <th>16</th>\n",
" <td>0.094509</td>\n",
" <td>0.024032</td>\n",
" <td>0.049684</td>\n",
" <td>0.263660</td>\n",
" <td>0.208731</td>\n",
" <td>0.095315</td>\n",
" <td>0.075458</td>\n",
" <td>0.447042</td>\n",
" <td>0.353908</td>\n",
" <td>0.357603</td>\n",
" <td>...</td>\n",
" <td>0.005877</td>\n",
" <td>0.004653</td>\n",
" <td>0.208293</td>\n",
" <td>0.164898</td>\n",
" <td>0.556854</td>\n",
" <td>0.441711</td>\n",
" <td>-0.021245</td>\n",
" <td>-0.016819</td>\n",
" <td>-0.377982</td>\n",
" <td>-0.299236</td>\n",
" </tr>\n",
" <tr>\n",
" <th>17</th>\n",
" <td>-0.012210</td>\n",
" <td>-0.102774</td>\n",
" <td>0.018638</td>\n",
" <td>0.088641</td>\n",
" <td>0.070174</td>\n",
" <td>-0.083567</td>\n",
" <td>-0.066158</td>\n",
" <td>-0.129008</td>\n",
" <td>-0.102131</td>\n",
" <td>0.253475</td>\n",
" <td>...</td>\n",
" <td>0.298916</td>\n",
" <td>0.236642</td>\n",
" <td>-0.474741</td>\n",
" <td>-0.375837</td>\n",
" <td>-0.026836</td>\n",
" <td>-0.021245</td>\n",
" <td>0.542097</td>\n",
" <td>0.428064</td>\n",
" <td>0.093938</td>\n",
" <td>0.074368</td>\n",
" </tr>\n",
" <tr>\n",
" <th>18</th>\n",
" <td>-0.009666</td>\n",
" <td>-0.081362</td>\n",
" <td>0.014755</td>\n",
" <td>0.070174</td>\n",
" <td>0.055555</td>\n",
" <td>-0.066158</td>\n",
" <td>-0.052375</td>\n",
" <td>-0.102131</td>\n",
" <td>-0.080854</td>\n",
" <td>0.200668</td>\n",
" <td>...</td>\n",
" <td>0.236642</td>\n",
" <td>0.187341</td>\n",
" <td>-0.375837</td>\n",
" <td>-0.297538</td>\n",
" <td>-0.021245</td>\n",
" <td>-0.016819</td>\n",
" <td>0.428064</td>\n",
" <td>0.339752</td>\n",
" <td>0.074368</td>\n",
" <td>0.058874</td>\n",
" </tr>\n",
" <tr>\n",
" <th>19</th>\n",
" <td>-0.103179</td>\n",
" <td>-0.014155</td>\n",
" <td>0.018247</td>\n",
" <td>0.094719</td>\n",
" <td>0.074986</td>\n",
" <td>0.248824</td>\n",
" <td>0.196985</td>\n",
" <td>-0.135168</td>\n",
" <td>-0.107008</td>\n",
" <td>-0.082488</td>\n",
" <td>...</td>\n",
" <td>0.301505</td>\n",
" <td>0.238691</td>\n",
" <td>-0.037163</td>\n",
" <td>-0.029421</td>\n",
" <td>-0.477452</td>\n",
" <td>-0.377982</td>\n",
" <td>0.093938</td>\n",
" <td>0.074368</td>\n",
" <td>0.544528</td>\n",
" <td>0.429988</td>\n",
" </tr>\n",
" <tr>\n",
" <th>20</th>\n",
" <td>-0.081683</td>\n",
" <td>-0.011206</td>\n",
" <td>0.014445</td>\n",
" <td>0.074986</td>\n",
" <td>0.059364</td>\n",
" <td>0.196985</td>\n",
" <td>0.155947</td>\n",
" <td>-0.107008</td>\n",
" <td>-0.084715</td>\n",
" <td>-0.065303</td>\n",
" <td>...</td>\n",
" <td>0.238691</td>\n",
" <td>0.188964</td>\n",
" <td>-0.029421</td>\n",
" <td>-0.023292</td>\n",
" <td>-0.377982</td>\n",
" <td>-0.299236</td>\n",
" <td>0.074368</td>\n",
" <td>0.058874</td>\n",
" <td>0.429988</td>\n",
" <td>0.341275</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>21 rows × 21 columns</p>\n",
"</div>"
],
"text/plain": [
" 0 1 2 3 4 5 6 \\\n",
"0 0.022500 0.004500 0.004500 0.024094 0.019074 -0.012983 -0.010279 \n",
"1 0.004500 0.022500 0.004500 0.025747 0.020383 0.054006 0.042754 \n",
"2 0.004500 0.004500 0.022500 0.118816 0.094063 0.102556 0.081190 \n",
"3 0.024094 0.025747 0.118816 0.629004 0.496865 0.544645 0.431177 \n",
"4 0.019074 0.020383 0.094063 0.496865 0.394220 0.431177 0.341349 \n",
"5 -0.012983 0.054006 0.102556 0.544645 0.431177 0.593490 0.468750 \n",
"6 -0.010279 0.042754 0.081190 0.431177 0.341349 0.468750 0.371962 \n",
"7 0.070753 0.070753 0.119303 0.634313 0.502165 0.543786 0.430497 \n",
"8 0.056013 0.056013 0.094448 0.502165 0.397547 0.430497 0.340810 \n",
"9 0.054006 -0.012983 0.102556 0.538492 0.426306 0.342798 0.271382 \n",
"10 0.042754 -0.010279 0.081190 0.426306 0.337492 0.271382 0.214844 \n",
"11 -0.029731 -0.029731 0.085808 0.448823 0.355318 0.391117 0.309634 \n",
"12 -0.023537 -0.023537 0.067932 0.355318 0.281294 0.309634 0.245127 \n",
"13 0.030356 0.119380 0.062758 0.341222 0.270134 0.451710 0.357603 \n",
"14 0.024032 0.094509 0.049684 0.270134 0.213856 0.357603 0.283103 \n",
"15 0.119380 0.030356 0.062758 0.333045 0.263660 0.120398 0.095315 \n",
"16 0.094509 0.024032 0.049684 0.263660 0.208731 0.095315 0.075458 \n",
"17 -0.012210 -0.102774 0.018638 0.088641 0.070174 -0.083567 -0.066158 \n",
"18 -0.009666 -0.081362 0.014755 0.070174 0.055555 -0.066158 -0.052375 \n",
"19 -0.103179 -0.014155 0.018247 0.094719 0.074986 0.248824 0.196985 \n",
"20 -0.081683 -0.011206 0.014445 0.074986 0.059364 0.196985 0.155947 \n",
"\n",
" 7 8 9 ... 11 12 13 \\\n",
"0 0.070753 0.056013 0.054006 ... -0.029731 -0.023537 0.030356 \n",
"1 0.070753 0.056013 -0.012983 ... -0.029731 -0.023537 0.119380 \n",
"2 0.119303 0.094448 0.102556 ... 0.085808 0.067932 0.062758 \n",
"3 0.634313 0.502165 0.538492 ... 0.448823 0.355318 0.341222 \n",
"4 0.502165 0.397547 0.426306 ... 0.355318 0.281294 0.270134 \n",
"5 0.543786 0.430497 0.342798 ... 0.391117 0.309634 0.451710 \n",
"6 0.430497 0.340810 0.271382 ... 0.309634 0.245127 0.357603 \n",
"7 0.808486 0.638955 0.543786 ... 0.280471 0.222039 0.564684 \n",
"8 0.638955 0.506707 0.430497 ... 0.222039 0.175781 0.447042 \n",
"9 0.543786 0.430497 0.593490 ... 0.391117 0.309634 0.120398 \n",
"10 0.430497 0.340810 0.468750 ... 0.309634 0.245127 0.095315 \n",
"11 0.280471 0.222039 0.391117 ... 0.503148 0.397229 0.007424 \n",
"12 0.222039 0.175781 0.309634 ... 0.397229 0.315341 0.005877 \n",
"13 0.564684 0.447042 0.120398 ... 0.007424 0.005877 0.704780 \n",
"14 0.447042 0.353908 0.095315 ... 0.005877 0.004653 0.556854 \n",
"15 0.564684 0.447042 0.451710 ... 0.007424 0.005877 0.263106 \n",
"16 0.447042 0.353908 0.357603 ... 0.005877 0.004653 0.208293 \n",
"17 -0.129008 -0.102131 0.253475 ... 0.298916 0.236642 -0.474741 \n",
"18 -0.102131 -0.080854 0.200668 ... 0.236642 0.187341 -0.375837 \n",
"19 -0.135168 -0.107008 -0.082488 ... 0.301505 0.238691 -0.037163 \n",
"20 -0.107008 -0.084715 -0.065303 ... 0.238691 0.188964 -0.029421 \n",
"\n",
" 14 15 16 17 18 19 20 \n",
"0 0.024032 0.119380 0.094509 -0.012210 -0.009666 -0.103179 -0.081683 \n",
"1 0.094509 0.030356 0.024032 -0.102774 -0.081362 -0.014155 -0.011206 \n",
"2 0.049684 0.062758 0.049684 0.018638 0.014755 0.018247 0.014445 \n",
"3 0.270134 0.333045 0.263660 0.088641 0.070174 0.094719 0.074986 \n",
"4 0.213856 0.263660 0.208731 0.070174 0.055555 0.074986 0.059364 \n",
"5 0.357603 0.120398 0.095315 -0.083567 -0.066158 0.248824 0.196985 \n",
"6 0.283103 0.095315 0.075458 -0.066158 -0.052375 0.196985 0.155947 \n",
"7 0.447042 0.564684 0.447042 -0.129008 -0.102131 -0.135168 -0.107008 \n",
"8 0.353908 0.447042 0.353908 -0.102131 -0.080854 -0.107008 -0.084715 \n",
"9 0.095315 0.451710 0.357603 0.253475 0.200668 -0.082488 -0.065303 \n",
"10 0.075458 0.357603 0.283103 0.200668 0.158862 -0.065303 -0.051698 \n",
"11 0.005877 0.007424 0.005877 0.298916 0.236642 0.301505 0.238691 \n",
"12 0.004653 0.005877 0.004653 0.236642 0.187341 0.238691 0.188964 \n",
"13 0.556854 0.263106 0.208293 -0.474741 -0.375837 -0.037163 -0.029421 \n",
"14 0.441711 0.208293 0.164898 -0.375837 -0.297538 -0.029421 -0.023292 \n",
"15 0.208293 0.704780 0.556854 -0.026836 -0.021245 -0.477452 -0.377982 \n",
"16 0.164898 0.556854 0.441711 -0.021245 -0.016819 -0.377982 -0.299236 \n",
"17 -0.375837 -0.026836 -0.021245 0.542097 0.428064 0.093938 0.074368 \n",
"18 -0.297538 -0.021245 -0.016819 0.428064 0.339752 0.074368 0.058874 \n",
"19 -0.029421 -0.477452 -0.377982 0.093938 0.074368 0.544528 0.429988 \n",
"20 -0.023292 -0.377982 -0.299236 0.074368 0.058874 0.429988 0.341275 \n",
"\n",
"[21 rows x 21 columns]"
]
},
"execution_count": 210,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# n_ambs=2*len(satellites)\n",
"pd.DataFrame(Q)\n",
"# Qaa = extract_Qaa_from_Q(Q)\n",
"# pd.DataFrame(extract_Qaa_from_Q(Q))\n",
"# adopp = get_ADOP(Qaa, n_ambs=n_ambs)\n",
"# print(adopp)\n",
"# ss = get_ambs_success_rate(adopp, n_ambs=n_ambs)\n",
"# print(ss)"
]
},
{
"cell_type": "code",
"execution_count": 211,
"metadata": {},
"outputs": [],
"source": [
"def extract_Qaa_from_Q(Q):\n",
" return Q[3:, 3:]\n",
"\n",
"def get_ADOP(Qaa, n_ambs=2*len(satellites)):\n",
" # abs? dets can be negative..\n",
" return np.power(np.linalg.det(Qaa), 1./(2.*n_ambs) )\n",
" \n",
"def get_ambs_success_rate(ADOP, n_ambs):\n",
" return np.power(2.*norm.cdf(1. / (2. * ADOP)) - 1., n_ambs)"
]
},
{
"cell_type": "code",
"execution_count": 212,
"metadata": {},
"outputs": [],
"source": [
"# sigma_pos_list = [0.01, 0.1, 0.15, 0.25, 0.5, 1, 10, 100]\n",
"# sigma_pos_list = [np.round(np.power(10, x), 2) for x in np.arange(-2, 2, 0.2)]\n",
"sigma_pos_list = np.arange(0.10, 5.00, 0.05 )\n",
"data = {}\n",
"nambs = 2*len(satellites) # dual frequency\n",
"for s in sigma_pos_list:\n",
" ########\n",
" # now correlation_term is valid AS LONG AS we input same sigma for x/y/z /!\\\n",
" #######\n",
" R_ = gimme_R(sigma_value=s, sigma_phi=0.01, correlation_term=0.05, n_satellites=len(satellites), n_biases=0)\n",
" Q_ = get_covariance_matrix_estimate(A=A, R=R_, obs_error_sigma=1.0)\n",
" Qaa = extract_Qaa_from_Q(Q_)\n",
" adop_ = get_ADOP(Qaa, n_ambs=nambs)\n",
" adop_prob_ = get_ambs_success_rate(ADOP=adop_, n_ambs=nambs)\n",
" data[str(s)] = {'ADOP': adop_, 'P_success': adop_prob_}"
]
},
{
"cell_type": "code",
"execution_count": 213,
"metadata": {},
"outputs": [
{
"data": {
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" <th>P_success</th>\n",
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],
"text/plain": [
" ADOP P_success\n",
"0.1 0.106057 0.999956\n",
"0.15000000000000002 0.113453 0.999811\n",
"0.20000000000000004 0.119018 0.999522\n",
"0.25000000000000006 0.123524 0.999070\n",
"0.30000000000000004 0.127333 0.998451\n",
"0.3500000000000001 0.130646 0.997669\n",
"0.40000000000000013 0.133585 0.996731\n",
"0.45000000000000007 0.136233 0.995646\n",
"0.5000000000000001 0.138646 0.994424\n",
"0.5500000000000002 0.140866 0.993075\n",
"0.6000000000000002 0.142923 0.991608\n",
"0.6500000000000001 0.144842 0.990032\n",
"0.7000000000000002 0.146642 0.988356\n",
"0.7500000000000002 0.148338 0.986589\n",
"0.8000000000000002 0.149942 0.984736\n",
"0.8500000000000002 0.151465 0.982806\n",
"0.9000000000000002 0.152915 0.980804\n",
"0.9500000000000003 0.154299 0.978736\n",
"1.0000000000000004 0.155623 0.976609\n",
"1.0500000000000003 0.156894 0.974426\n",
"1.1000000000000005 0.158115 0.972192\n",
"1.1500000000000004 0.159291 0.969912\n",
"1.2000000000000004 0.160425 0.967590\n",
"1.2500000000000004 0.161520 0.965229\n",
"1.3000000000000005 0.162579 0.962832\n",
"1.3500000000000005 0.163605 0.960403\n",
"1.4000000000000006 0.164600 0.957945\n",
"1.4500000000000006 0.165565 0.955459\n",
"1.5000000000000004 0.166503 0.952950\n",
"1.5500000000000005 0.167416 0.950418\n",
"... ... ...\n",
"3.5000000000000013 0.191757 0.847943\n",
"3.550000000000001 0.192211 0.845400\n",
"3.6000000000000014 0.192660 0.842865\n",
"3.6500000000000012 0.193103 0.840338\n",
"3.7000000000000015 0.193541 0.837821\n",
"3.7500000000000013 0.193975 0.835313\n",
"3.800000000000001 0.194404 0.832813\n",
"3.8500000000000014 0.194828 0.830323\n",
"3.9000000000000012 0.195247 0.827842\n",
"3.9500000000000015 0.195662 0.825370\n",
"4.000000000000001 0.196073 0.822908\n",
"4.050000000000002 0.196479 0.820455\n",
"4.100000000000001 0.196881 0.818012\n",
"4.150000000000001 0.197279 0.815578\n",
"4.200000000000001 0.197674 0.813154\n",
"4.250000000000001 0.198064 0.810740\n",
"4.300000000000001 0.198450 0.808336\n",
"4.350000000000001 0.198833 0.805941\n",
"4.400000000000001 0.199212 0.803556\n",
"4.450000000000001 0.199588 0.801181\n",
"4.500000000000001 0.199960 0.798815\n",
"4.550000000000001 0.200328 0.796460\n",
"4.600000000000001 0.200693 0.794114\n",
"4.650000000000001 0.201055 0.791778\n",
"4.700000000000001 0.201414 0.789452\n",
"4.750000000000001 0.201770 0.787136\n",
"4.800000000000002 0.202122 0.784830\n",
"4.850000000000001 0.202472 0.782534\n",
"4.900000000000001 0.202818 0.780248\n",
"4.950000000000001 0.203161 0.777971\n",
"\n",
"[98 rows x 2 columns]"
]
},
"execution_count": 213,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"dff = pd.DataFrame.from_dict(data, orient='index')\n",
"\n",
"dff"
]
},
{
"cell_type": "code",
"execution_count": 214,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<iframe id=\"igraph\" scrolling=\"no\" style=\"border:none;\" seamless=\"seamless\" src=\"https://plot.ly/~swiftguillaume/126.embed\" height=\"525px\" width=\"100%\"></iframe>"
],
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"<plotly.tools.PlotlyDisplay object>"
]
},
"execution_count": 214,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import cufflinks as cf\n",
"# d2 = dff.set_index('ADOP')\n",
"# d2['P_success'].iplot()\n",
"\n",
"dff['P_success'].iplot()\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
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