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height_analysis.py
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# -*- coding: utf-8 -*-
"""
Created on Tue Feb 13 10:46:59 2018
@author: Peter G. Lane (petergwinlane@gmail.com)
"""
import csv
import math
import numpy
import numpy.linalg as linalg
# import matplotlib.pyplot as plt
def spherical_to_cartesian(spherical_coordinates):
points = spherical_coordinates.transpose()
cartesian_coordinates = numpy.ndarray(numpy.shape(points))
cartesian_coordinates[0,:] = points[0] * numpy.cos(points[1]) * numpy.sin(points[2])
cartesian_coordinates[1,:] = points[0] * numpy.sin(points[1]) * numpy.sin(points[2])
cartesian_coordinates[2,:] = points[0] * numpy.cos(points[2])
return cartesian_coordinates.transpose()
def cartesian_to_spherical(cartesian_coordinates):
points = cartesian_coordinates.transpose()
cylindrical_coordinates = numpy.ndarray(numpy.shape(points))
cylindrical_coordinates[0] = numpy.sqrt(numpy.sum(points**2), axis=1)
cylindrical_coordinates[1] = numpy.arctan(points[1], points[0])
cylindrical_coordinates[2] = numpy.arccos(points[2]/cylindrical_coordinates[0])
return cylindrical_coordinates.transpose()
def cylindrical_to_cartesian(cylindrical_coordinates):
points = cylindrical_coordinates.transpose()
cartesian_coordinates = numpy.ndarray(numpy.shape(points))
cartesian_coordinates[0] = points[0] * numpy.cos(points[1])
cartesian_coordinates[1] = points[0] * numpy.sin(points[1])
cartesian_coordinates[2] = points[2]
return cartesian_coordinates.transpose()
def cartesian_to_cylindrical(cartesian_coordinates):
points = cartesian_coordinates.transpose()
cylindrical_coordinates = numpy.ndarray(numpy.shape(points))
cylindrical_coordinates[0] = numpy.sqrt(points[0]**2 + points[1]**2)
cylindrical_coordinates[1] = numpy.arctan2(points[1], points[0])
cylindrical_coordinates[2] = points[2]
return cylindrical_coordinates.transpose()
def calculate_transform(spherical_LTCS_coordinates, cylindrical_DSCS_coordinates):
cartesian_LTCS_coordinates = spherical_to_cartesian(spherical_LTCS_coordinates)
cartesian_DSCS_coordinates = cylindrical_to_cartesian(cylindrical_DSCS_coordinates)
# calculate the LTCS-to-DSCS transform matrix
constant_vector = numpy.ones(numpy.shape(cartesian_LTCS_coordinates)[0])
X = numpy.vstack([constant_vector, cartesian_LTCS_coordinates.transpose()])
Y = numpy.vstack([constant_vector, cartesian_DSCS_coordinates.transpose()])
print('X:\n{}'.format(X))
print('Y:\n{}'.format(Y))
print('pinv(x):{}'.format(linalg.pinv(X)))
transform = numpy.dot(Y, linalg.pinv(X))
print('Transform: {}'.format(transform))
projection_matrix = numpy.dot(linalg.pinv(X), X)
print('Projection ("Hat") Matrix:\n{}'.format(projection_matrix))
Yp = numpy.dot(transform, X)
print('Yp: {}'.format(Yp))
means = numpy.mean(Y, axis=1)
print('Mean: {}'.format(means))
total_sum_of_squares = numpy.sum((Y.transpose() - means)**2, axis=0)
total_sum_of_squares[0] = 1.0e12
print('TSS: {}'.format(total_sum_of_squares))
residuals = Y - Yp
print('Residuals: {}'.format(residuals))
''' The normal R^2 is not expressive enough to indicate bad mappings.
residual_sum_of_squares = numpy.sum(residuals**2, axis=1)
print('RSS: {}'.format(residual_sum_of_squares))
# r_squared = 1 - residual_sum_of_squares / total_sum_of_squares
'''
print('1-leverage: {}'.format(1-projection_matrix.diagonal()))
predictive_residuals = residuals/(1-projection_matrix.diagonal())
print('Pred. Res.: {}'.format(predictive_residuals))
predictive_residual_sum_of_squares = numpy.sum(predictive_residuals**2, axis=1)
print('PRESS: {}'.format(predictive_residual_sum_of_squares))
predictive_r_squared = \
1 - predictive_residual_sum_of_squares/total_sum_of_squares
return (transform, predictive_r_squared)
def LTCS_to_DSCS(transform, spherical_LTCS_coordinates):
cartesian_LTCS_coordinates = spherical_to_cartesian(spherical_LTCS_coordinates)
constant_vector = numpy.ones(numpy.shape(cartesian_LTCS_coordinates)[0])
X = numpy.vstack([constant_vector, cartesian_LTCS_coordinates.transpose()])
Y = numpy.dot(transform, X)
return(cartesian_to_cylindrical(Y[1:].transpose()))
def DSCS_to_LTCS(transform, cylindrical_LTCS_coordinates):
cartesian_DSCS_coordinates = cylindrical_to_cartesian(cylindrical_LTCS_coordinates)
constant_vector = numpy.ones(numpy.shape(cartesian_DSCS_coordinates)[0])
Y = numpy.vstack([constant_vector, cartesian_DSCS_coordinates.transpose()])
X = numpy.dot(linalg.inv(transform), Y)
return(cartesian_to_spherical(X[1:].transpose()))
# Measured Spherical LTCS Coordinates
#filename = 'reference_network_LTCS.csv'
#filename = 'reference_network_LTCS_20180504.csv'
#filename = 'reference_network_LTCS_TEST.csv'
filename = 'reference_network_IB2_LTCS.csv'
with open(filename, 'r') as file:
string_data = list(csv.reader(file, delimiter=','))
data_LTCS = numpy.ndarray((len(string_data), 3))
for index,row in enumerate(string_data):
point = list(map(lambda x: float(x), row[1:]))
data_LTCS[index,:] = point
print('Measured Spherical LTCS Coordinates (azimuth, zenith, distance):\n{}'\
.format(data_LTCS))
# Measured Cartesian LTCS Coordinates
P = spherical_to_cartesian(data_LTCS)
print('Measured Cartesian LTCS Coordinates (x, y, z (up)):\n{}'.format(P.transpose()))
mean_height = numpy.mean(P[:,2])
# relative_heights = mean_height-P[:,2]
relative_heights = P[:,2]-P[0,2]
print('Measured Relative Heights: {}'.format(relative_heights))
print('Measured Height Mean: {}'.format(numpy.mean(relative_heights)))
print('Measured Height Std. Dev.: {}'.format(numpy.std(relative_heights)))
centroid = numpy.array([numpy.mean(P[:,0]), numpy.mean(P[:,1])])
print('Measured Horizontal Centroid: {}'.format(centroid))
radii = numpy.sqrt((centroid[0]-P[:,0])**2 + (centroid[1]-P[:,1])**2)
print('Measured Horizontal Radii: {}'.format(radii))
print('Measured Horizontal Radius Mean: {}'.format(numpy.mean(radii)))
print('Measured Horizontal Radius Std. Dev.: {}'.format(numpy.std(radii)))
relative_distances = numpy.sqrt((P[:,0]-P[0,0])**2 + (P[:,1]-P[0,1])**2 + (P[:,2]-P[0,2])**2)
print('Measured Relative (B2) Distances: {}'.format(relative_distances))
print()
# Configured Cylindrical DSCS Coordinates
filename = 'reference_network_IB2.csv'
with open(filename, 'r') as file:
string_data = list(csv.reader(file, delimiter=','))
data_DSCS = numpy.ndarray((len(string_data), 3))
for index,row in enumerate(string_data):
point = list(map(lambda x: float(x), row[1:]))
data_DSCS[index,:] = point
print('Configured Cylindrical DSCS Coordinates (rho, theta, z):\n{}'.format(data_DSCS))
# Configured Cartesian DSCS Coordinates
Pp = cylindrical_to_cartesian(data_DSCS)
X_all = Pp.transpose()
print('Configured Cartesian DSCS Coordinates: (x, y (up), z)\n{}'.format(X_all))
mean_height = numpy.mean(Pp[:,1])
# relative_heights = mean_height-Pp[:,1]
relative_heights = Pp[:,1]-Pp[0,1]
print('Configured Relative Heights: {}'.format(relative_heights))
print('Configured Height Mean: {}'.format(numpy.mean(relative_heights)))
print('Configured Height Std. Dev.: {}'.format(numpy.std(relative_heights)))
centroidp = numpy.array([numpy.mean(Pp[:,0]), numpy.mean(Pp[:,2])])
print('Configured Horizontal Centroid: {}'.format(centroidp))
radiip = numpy.sqrt((centroidp[0]-Pp[:,0])**2 + (centroidp[1]-Pp[:,2])**2)
print('Configured Horizontal Radii: {}'.format(radiip))
print('Configured Horizontal Radius Mean: {}'.format(numpy.mean(radiip)))
print('Configured Horizontal Radius Std. Dev.: {}'.format(numpy.std(radiip)))
relative_distances = numpy.sqrt((Pp[:,0]-Pp[0,0])**2 + (Pp[:,1]-Pp[0,1])**2 + (Pp[:,2]-Pp[0,2])**2)
print('Configured Relative (B2) Distances: {}'.format(relative_distances))
print()
height_residuals = Pp[:,1]-P[:,2]
print('Height Residuals: {}'.format(height_residuals))
print('Height Residuals Mean: {}'.format(numpy.mean(height_residuals)))
print('Height Residuals Std. Dev.: {}'.format(numpy.std(height_residuals)))
radii_residuals = radiip-radii
print('Radii Residuals: {}'.format(radii_residuals))
print('Radii Residuals Mean: {}'.format(numpy.mean(radii_residuals)))
print('Radii Residuals Std. Dev.: {}'.format(numpy.std(radii_residuals)))
transform,r_squared = calculate_transform(data_LTCS, data_DSCS)
print('R^2 of LTCS->DSCS Transform: {}'.format(r_squared))
cartesian_data_DSCS = cylindrical_to_cartesian(data_DSCS)
transformed_DSCS = LTCS_to_DSCS(transform, data_LTCS)
cartesian_transformed_DSCS = cylindrical_to_cartesian(transformed_DSCS)
print(cartesian_data_DSCS)
print(cartesian_transformed_DSCS)
cartesian_residuals_DSCS = cartesian_data_DSCS - cartesian_transformed_DSCS
print('Cartesian DSCS Residuals: {}'.format(cartesian_residuals_DSCS))