# Custom FigureCanvas for displaying Matplotlib output
#
# https://github.com/krischer/instaseis/blob/master/instaseis/gui/qt4mplcanvas.py
from matplotlib import rc as matplotlibrc
import matplotlib as mpl
from matplotlib.figure import Figure
from matplotlib.backends.backend_qt4agg import \
FigureCanvasQTAgg as FigureCanvas
mpl.rcParams['font.size'] = 10
matplotlibrc('figure.subplot', left=0.0, right=1.0, bottom=0.0, top=1.0)
class MyQt4MplCanvas(FigureCanvas):
"""
Class to represent the FigureCanvas widget.
"""
def __init__(self, parent=None):
# Standard Matplotlib code to generate the plot
self.fig = Figure()
# initialize the canvas where the Figure renders into
super(MyQt4MplCanvas, self).__init__(self.fig)
self.setParent(parent)
from matplotlib import rc as matplotlibrc
import matplotlib as mpl
from matplotlib.figure import Figure
from matplotlib.backends.backend_qt5agg import \
FigureCanvasQTAgg as FigureCanvas
mpl.rcParams['font.size'] = 10
matplotlibrc('figure.subplot', left=0.0, right=1.0, bottom=0.0, top=1.0)
class Qt5MplCanvas(FigureCanvas):
"""
Class to represent the FigureCanvas widget.
"""
def __init__(self, parent=None):
# Standard Matplotlib code to generate the plot
self.fig = Figure()
# initialize the canvas where the Figure renders into
super(Qt5MplCanvas, self).__init__(self.fig)
self.setParent(parent)
import os
import sys
import numpy as np # library to handle arrays like Matlab
import scipy.sparse as scysparse
from pdb import set_trace as keyboard # pdb package allows you to interrupt the python script with the keyboard() command
import spatial_discretization as sd # like include .h file in C++, calls another file
from matplotlib import pyplot as plt
from matplotlib import rc as matplotlibrc
figure_folder = "../report/"
#Latex setup
matplotlibrc('text.latex', preamble='\usepackage{color}')
matplotlibrc('text', usetex=True)
matplotlibrc('font', family='serif')
Plot_Problem1 = True
Plot_Problem2 = True
Plot_Problem3 = True
# ...
############################################################
############################################################
if Plot_Problem1:
#Definitions for ranges of l, r dx and initializations
dx_range = np.logspace(-5, 0, num=1000, base=10)
discretization_error = np.zeros((dx_range.size, 12))
dx_inverse = 1 / dx_range
x_eval = 0.0 #Evaluation point
from matplotlib import use as matplotlibuse, rc as matplotlibrc
matplotlibrc('figure.subplot', left = 0.05, right=0.98, bottom=0.10, top=0.92,
hspace=0.28)
import matplotlib as mpl
mpl.rcParams['font.size'] = 10
from matplotlib.figure import Figure
from matplotlib.backends.backend_qt4agg import FigureCanvasQTAgg as FigureCanvas
class Qt4MplCanvas(FigureCanvas):
"""
Class to represent the FigureCanvas widget.
"""
def __init__(self, parent = None):
# Standard Matplotlib code to generate the plot
self.fig = Figure()
# initialize the canvas where the Figure renders into
super(Qt4MplCanvas, self).__init__(self.fig)
self.setParent(parent)
from Tkinter import *
from matplotlib import figure, use as matplotlibuse, rc as matplotlibrc
from obspy.core.utcdatetime import UTCDateTime
matplotlibuse('TkAgg')
matplotlibrc('figure.subplot', right=0.95, bottom=0.07,
top=0.97) # set default
from matplotlib.backends.backend_tkagg import FigureCanvasTkAgg, \
NavigationToolbar2TkAgg
from obspy.core import UTCDateTime, Stream, Trace
#from obspy.imaging.waveform import _getMinMaxList as minmaxlist
from obspy.seishub import Client
import inspect
import numpy as np
from obspy.core import read
import os
import pickle
import sys
import time
import tkColorChooser
import tkFileDialog
################################################################################
## GLOBAL CONFIGURATION VARIABLES
# Maximum time span allowed to be retrieved via Seishub in seconds.
MAX_SPAN = 60 * 60
SERVER = "http://teide:8080"
################################################################################
class Seishub(object):
import package_version as _package_version
__version__ = _package_version.version
__author__ = _package_version.author
__date__ = _package_version.date
__credits__ = _package_version.credits
#- Import numpy/Numeric/numarray as appropriate:
import num_settings as num
from num_settings import N
#- Import matplotlib (must be in this order):
from matplotlib import rc as matplotlibrc
#matplotlibrc('font',**{'family':'sans-serif','sans-serif':['Helvetica']})
matplotlibrc('text', usetex=True)
import pylab
import matplotlib
from matplotlib.toolkits.basemap import Basemap
#- Other imports that then are used as module variables:
import copy
import Scientific.IO.NetCDF as S
import shutil
import tempfile
from where_close import where_close
#-------------------- Module Function: nice_levels --------------------
from matplotlib import use as matplotlibuse, rc as matplotlibrc
matplotlibrc('figure.subplot', left = 0.05, right=0.95, bottom=0.05, top=0.95)
import matplotlib as mpl
mpl.rcParams['font.size'] = 10
from matplotlib.figure import Figure
from matplotlib.backends.backend_qt4agg import FigureCanvasQTAgg as FigureCanvas
class Qt4MplCanvas(FigureCanvas):
"""
Class to represent the FigureCanvas widget.
"""
def __init__(self, parent = None):
# Standard Matplotlib code to generate the plot
self.fig = Figure()
# initialize the canvas where the Figure renders into
super(Qt4MplCanvas, self).__init__(self.fig)
self.setParent(parent)
__author__ = _package_version.author
__date__ = _package_version.date
__credits__ = _package_version.credits
#- Import numpy/Numeric/numarray as appropriate:
import num_settings as num
from num_settings import N
#- Import matplotlib (must be in this order):
from matplotlib import rc as matplotlibrc
#matplotlibrc('font',**{'family':'sans-serif','sans-serif':['Helvetica']})
matplotlibrc('text', usetex=True)
import pylab
import matplotlib
from matplotlib.toolkits.basemap import Basemap
#- Other imports that then are used as module variables:
import copy
import Scientific.IO.NetCDF as S
import shutil
import tempfile
from where_close import where_close
import sys
import numpy as np
import scipy
import pylab as plt
from pdb import set_trace as keyboard
from matplotlib import rc as matplotlibrc
# Extracting PI constant
PI = np.pi
# LaTeX setup
matplotlibrc('text.latex', preamble='\usepackage{color}')
matplotlibrc('text',usetex=True)
matplotlibrc('font', family='serif')
figure_folder = "../report/"
Nx = 101
x = np.linspace(0,2*PI,Nx)
y_cos = np.cos(x)
y_sin = np.sin(x)
Plot_CosineAndSine = 'y'
Plot_SomethingElse = 'y'
if Plot_CosineAndSine == 'y':
figure_name = "cosine_and_sine.pdf"
figwidth = 18
figheight = 6
from matplotlib import use as matplotlibuse, rc as matplotlibrc
matplotlibrc('figure.subplot',
left=0.05,
right=0.98,
bottom=0.10,
top=0.92,
hspace=0.28)
import matplotlib as mpl
mpl.rcParams['font.size'] = 10
from matplotlib.figure import Figure
from matplotlib.backends.backend_qt4agg import FigureCanvasQTAgg as FigureCanvas
class Qt4MplCanvas(FigureCanvas):
"""
Class to represent the FigureCanvas widget.
"""
def __init__(self, parent=None):
# Standard Matplotlib code to generate the plot
self.fig = Figure()
# initialize the canvas where the Figure renders into
super(Qt4MplCanvas, self).__init__(self.fig)
self.setParent(parent)
from Tkinter import *
from matplotlib import figure, use as matplotlibuse, rc as matplotlibrc
from obspy.core.utcdatetime import UTCDateTime
matplotlibuse('TkAgg')
matplotlibrc('figure.subplot', right=0.95, bottom=0.07, top=0.97) # set default
from matplotlib.backends.backend_tkagg import FigureCanvasTkAgg, \
NavigationToolbar2TkAgg
from obspy.core import UTCDateTime, Stream, Trace
#from obspy.imaging.waveform import _getMinMaxList as minmaxlist
from obspy.seishub import Client
import inspect
import numpy as np
from obspy.core import read
import os
import pickle
import sys
import time
import tkColorChooser
import tkFileDialog
################################################################################
## GLOBAL CONFIGURATION VARIABLES
# Maximum time span allowed to be retrieved via Seishub in seconds.
MAX_SPAN = 60 * 60
SERVER = "http://teide:8080"
################################################################################
class Seishub(object):
def __init__(self):
def test(N, mesh_no):
figure_folder = "../report/figures/"
# N = total number of points surrouding a centroid AND including the centroid itself
mesh_abs_tol = 10**(-8)
xc, yc = 0., 0. # centroid location
# Analytical functions
phi = lambda X, Y: np.cos(2 * X - 2 * Y - np.pi / 4.) + X + Y
dphi_dx = lambda X, Y: 1. - 2. * np.sin(2 * X - 2 * Y - np.pi / 4.)
dphi_dy = lambda X, Y: 1. - 2. * np.sin(2 * Y - 2 * X + np.pi / 4.)
d2phi_dx2 = lambda X, Y: -4. * np.cos(2 * X - 2 * Y - np.pi / 4.)
d2phi_dy2 = lambda X, Y: -4. * np.cos(2 * Y - 2 * X + np.pi / 4.)
# Exact values
phi_exact = phi(xc, yc)
dphidx_exact = dphi_dx(xc, yc)
dphidy_exact = dphi_dy(xc, yc)
d2phidx2_exact = d2phi_dx2(xc, yc)
d2phidy2_exact = d2phi_dy2(xc, yc)
error = {
'phi_x': [],
'phi_y': [],
'dphi_dx': [],
'dphi_dy': [],
'd2phi_dx2': [],
'd2phi_dy2': []
}
mesh_size = np.logspace(1., -5, 100) #
for delta_x in mesh_size:
delta_y = np.abs(dphidx_exact / dphidy_exact * delta_x)
## Around a Circle
theta = np.linspace(0., 2 * np.pi, N - 1, endpoint=False)
theta_off = 0. * np.pi / 3.
xn, yn = delta_x * np.cos(theta +
theta_off), delta_y * np.sin(theta +
theta_off)
## Manual Input
# xn = np.array([-3.0/2.0*delta_x,-delta_x/2.0,delta_x/2.0,+3.0/2.0*delta_x, -delta_x/2.0,delta_x/2.0,-delta_x/2.0,delta_x/2.0])
# yn = np.array([0., 0. ,0. ,0., delta_y,delta_y,-delta_y,-delta_y])
n_nodes = len(xn)
xc_eff = xc + np.random.randn() * mesh_abs_tol #*delta_x
yc_eff = yc + np.random.randn() * mesh_abs_tol #*delta_y
xn += np.random.randn(n_nodes) * mesh_abs_tol
yn += np.random.randn(n_nodes) * mesh_abs_tol
phi_num_x, dphidx_num, d2phidx2_num = fit.BiVarPolyFit_X(
xc_eff, yc_eff, xn, yn, phi(xn, yn))
phi_num_y, dphidy_num, d2phidy2_num = fit.BiVarPolyFit_Y(
xc_eff, yc_eff, xn, yn, phi(xn, yn))
if delta_x == mesh_size[-1]:
weights_dx = np.zeros(n_nodes)
weights_dy = np.zeros(n_nodes)
weights_dx2 = np.zeros(n_nodes)
weights_dy2 = np.zeros(n_nodes)
for ino in range(0, n_nodes):
phi_base = np.zeros(n_nodes)
phi_base[ino] = 1.0
_, weights_dx[ino], weights_dx2[ino] = fit.BiVarPolyFit_X(
xc_eff, yc_eff, xn, yn, phi_base)
_, weights_dy[ino], weights_dy2[ino] = fit.BiVarPolyFit_Y(
xc_eff, yc_eff, xn, yn, phi_base)
error['phi_x'].append(np.abs(phi_exact - phi_num_x))
error['phi_y'].append(np.abs(phi_exact - phi_num_y))
error['dphi_dx'].append(np.abs(dphidx_exact - dphidx_num))
error['dphi_dy'].append(np.abs(dphidy_exact - dphidy_num))
error['d2phi_dx2'].append(np.abs(d2phidx2_exact - d2phidx2_num))
error['d2phi_dy2'].append(np.abs(d2phidy2_exact - d2phidy2_num))
#set_trace()
#############################################
############### Plotting ####################
#############################################
# LaTeX preamble
from matplotlib import rc as matplotlibrc
matplotlibrc('text.latex', preamble='\usepackage{color}')
matplotlibrc('text', usetex=True)
matplotlibrc('font', family='serif')
# Reference decay rates
ref_error_2nd = mesh_size * mesh_size
ref_error_2nd /= ref_error_2nd[0]
ref_error_1nd = mesh_size
ref_error_1nd /= ref_error_1nd[0]
inv_mesh_size = 1. / mesh_size
########################################
figwidth, figheight = 8, 8
lineWidth = 3
fontSize = 25
gcafontSize = 21
fig = plt.figure(0, (figwidth, figheight))
ax = fig.add_subplot(1, 1, 1)
ax.plot(xn / delta_x, yn / delta_y, 'ko', markersize=12)
ax.plot(xc / delta_x, yc / delta_y, 'x', markersize=12)
ax.set_xlabel(r"$1/h$", fontsize=fontSize)
ax.set_xlabel(r"$x/\Delta x$", fontsize=fontSize)
ax.set_ylabel(r"$y/\Delta y$", fontsize=fontSize)
plt.setp(ax.get_xticklabels(), fontsize=gcafontSize)
plt.setp(ax.get_yticklabels(), fontsize=gcafontSize)
ax.grid(True)
plt.tight_layout()
plt.savefig('Points_Arragement.pdf')
plt.close()
########################################
figwidth, figheight = 14, 12
fig = plt.figure(1, (figwidth, figheight))
ax = fig.add_subplot(2, 3, 1)
error_plot = error['phi_x']
ax.loglog(inv_mesh_size, error_plot, linewidth=lineWidth)
ax.loglog(inv_mesh_size, ref_error_1nd * error_plot[0], ':k')
ax.loglog(inv_mesh_size, 1e-1 * ref_error_2nd * error_plot[0], ':k')
ax.set_title(r"X direction interpolation", fontsize=gcafontSize)
plt.setp(ax.get_xticklabels(), fontsize=gcafontSize)
plt.setp(ax.get_yticklabels(), fontsize=gcafontSize)
ax.set_xlabel(r"$1/h$", fontsize=fontSize)
ax.set_ylabel(r"error", fontsize=fontSize)
ax.grid(True)
ax = fig.add_subplot(2, 3, 2)
error_plot = error['dphi_dx']
ax.loglog(inv_mesh_size, error_plot, linewidth=lineWidth)
ax.loglog(inv_mesh_size, ref_error_1nd * error_plot[0], ':k')
ax.loglog(inv_mesh_size, 1e-1 * ref_error_2nd * error_plot[0], ':k')
ax.set_title(r"dphi/dx", fontsize=gcafontSize)
plt.setp(ax.get_xticklabels(), fontsize=gcafontSize)
plt.setp(ax.get_yticklabels(), fontsize=gcafontSize)
ax.set_xlabel(r"$1/h$", fontsize=fontSize)
ax.grid(True)
ax = fig.add_subplot(2, 3, 3)
error_plot = error['d2phi_dx2']
ax.loglog(inv_mesh_size, error_plot, linewidth=lineWidth)
ax.loglog(inv_mesh_size, ref_error_1nd * error_plot[0], ':k')
ax.loglog(inv_mesh_size, 1e-1 * ref_error_2nd * error_plot[0], ':k')
ax.set_title(r"d2phi/dx2", fontsize=gcafontSize)
plt.setp(ax.get_xticklabels(), fontsize=gcafontSize)
plt.setp(ax.get_yticklabels(), fontsize=gcafontSize)
ax.set_xlabel(r"$1/h$", fontsize=fontSize)
ax.grid(True)
ax = fig.add_subplot(2, 3, 4)
error_plot = error['phi_y']
ax.loglog(inv_mesh_size, error_plot, linewidth=lineWidth)
ax.loglog(inv_mesh_size, ref_error_1nd * error_plot[0], ':k')
ax.loglog(inv_mesh_size, 1e-1 * ref_error_2nd * error_plot[0], ':k')
ax.set_title(r"Y direction interpolation", fontsize=gcafontSize)
plt.setp(ax.get_xticklabels(), fontsize=gcafontSize)
plt.setp(ax.get_yticklabels(), fontsize=gcafontSize)
ax.set_xlabel(r"$1/h$", fontsize=fontSize)
ax.set_ylabel(r"error", fontsize=fontSize)
ax.grid(True)
ax = fig.add_subplot(2, 3, 5)
error_plot = error['dphi_dy']
ax.loglog(inv_mesh_size, error_plot, linewidth=lineWidth)
ax.loglog(inv_mesh_size, ref_error_1nd * error_plot[0], ':k')
ax.loglog(inv_mesh_size, 1e-1 * ref_error_2nd * error_plot[0], ':k')
ax.set_title(r"dphi/dy", fontsize=gcafontSize)
plt.setp(ax.get_xticklabels(), fontsize=gcafontSize)
plt.setp(ax.get_yticklabels(), fontsize=gcafontSize)
ax.set_xlabel(r"$1/h$", fontsize=fontSize)
ax.grid(True)
ax = fig.add_subplot(2, 3, 6)
error_plot = error['d2phi_dy2']
ax.loglog(inv_mesh_size, error_plot, linewidth=lineWidth)
ax.loglog(inv_mesh_size, ref_error_1nd * error_plot[0], ':k')
ax.loglog(inv_mesh_size, 1e-1 * ref_error_2nd * error_plot[0], ':k')
ax.set_title(r"d2phi/dy2", fontsize=gcafontSize)
plt.setp(ax.get_xticklabels(), fontsize=gcafontSize)
plt.setp(ax.get_yticklabels(), fontsize=gcafontSize)
ax.set_xlabel(r"$1/h$", fontsize=fontSize)
ax.grid(True)
fig_name = figure_folder + 'Mesh ' + str(
mesh_no) + ', Error_vs_invMeshSize (N=' + str(N) + ').pdf'
plt.tight_layout()
plt.show()
plt.savefig(fig_name)
plt.close()
