From 248c5130de9e8451d49480a6ba94c5511fd14e87 Mon Sep 17 00:00:00 2001
From: Thibaut Lunet <thibaut.lunet@unige.ch>
Date: Mon, 19 Mar 2018 00:34:01 +0100
Subject: [PATCH] TL : added some first example scripts
---
examples/numpy/csv-read-interpol-plot.py | 50 ++++
examples/numpy/data.csv | 302 +++++++++++++++++++++++
examples/scipy/jacobMultiDim.py | 233 +++++++++++++++++
3 files changed, 585 insertions(+)
create mode 100644 examples/numpy/csv-read-interpol-plot.py
create mode 100644 examples/numpy/data.csv
create mode 100644 examples/scipy/jacobMultiDim.py
diff --git a/examples/numpy/csv-read-interpol-plot.py b/examples/numpy/csv-read-interpol-plot.py
new file mode 100644
index 0000000..d887dce
--- /dev/null
+++ b/examples/numpy/csv-read-interpol-plot.py
@@ -0,0 +1,50 @@
+# -*- coding: utf-8 -*-
+"""
+Created on Thu Jun 25 17:28:03 2015
+
+Python script for post-processing data stored in a csv file
+
+@author: lunet
+"""
+# Importing all required libraries
+import numpy as np
+import matplotlib.pyplot as plt
+
+# Get data from the csv file
+data = np.genfromtxt('data.csv',dtype=float,delimiter=',',names=True)
+
+# Getting the fields
+times = data['Time']
+pressures = data['Pressure']
+velocities = data['Velocity']
+
+# Interpoling data to suppress measurement error
+polyDeg = 25
+# getting the coefficient of the best polynomial fit
+pressuresPolyCoeff = np.polyfit(times,pressures,polyDeg)
+velocitiesPolyCoeff = np.polyfit(times,velocities,polyDeg)
+
+# Constructing the polynomial with the coefficients
+pressuresPoly=np.poly1d(pressuresPolyCoeff)
+velocitiesPoly=np.poly1d(velocitiesPolyCoeff)
+
+# Evaluate the polynomial at each time
+pressuresInter = pressuresPoly(times)
+velocitiesInter = velocitiesPoly(times)
+
+# Plotting all data
+plt.figure()
+plt.subplot(211)
+plt.plot(times,pressures,'b',label="Measurements")
+plt.plot(times,pressuresInter,'r',label="Interpolation")
+plt.xlabel('Time')
+plt.ylabel('Pressure')
+plt.title('Comparison between measured and interpolated fields')
+plt.legend(loc=4)
+plt.subplot(212)
+plt.plot(times,velocities,'b',label="Measurements")
+plt.plot(times,velocitiesInter,'r',label="Interpolation")
+plt.xlabel('Time')
+plt.ylabel('Velocity')
+plt.legend(loc=1)
+plt.show()
\ No newline at end of file
diff --git a/examples/numpy/data.csv b/examples/numpy/data.csv
new file mode 100644
index 0000000..d6bb50e
--- /dev/null
+++ b/examples/numpy/data.csv
@@ -0,0 +1,302 @@
+Time,Pressure,Velocity
+0,0.3301958987,3.3338040438
+0.1,0.4168124765,3.4942511735
+0.2,0.4199741904,3.3318186404
+0.3,0.3999769621,3.4085712565
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+0.6,0.3371851687,3.3642938982
+0.7,0.382838647,3.4543539478
+0.8,0.3801052262,3.3437793355
+0.9,0.3977826942,3.4440860511
+1,0.443507798,3.4928140727
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diff --git a/examples/scipy/jacobMultiDim.py b/examples/scipy/jacobMultiDim.py
new file mode 100644
index 0000000..c3fcc80
--- /dev/null
+++ b/examples/scipy/jacobMultiDim.py
@@ -0,0 +1,233 @@
+#!/usr/bin/env python2
+# -*- coding: utf-8 -*-
+"""
+Created on Tue May 23 13:29:54 2017
+
+@author: t.lunet
+"""
+import numpy as np
+import scipy.linalg as spl
+import matplotlib.pyplot as plt
+
+# Matplotlib : do not fill marker in plot
+plt.rcParams['markers.fillstyle'] = 'none'
+
+# Number of point in each direction
+nX = 12
+nY = 12
+nZ = 12
+
+# Velocity in each direction
+cX = 1.0
+cY = 1.0
+cZ = 1.0
+
+# Discretization scheme in each direction
+schemeX = 'U1'
+schemeY = 'U1'
+schemeZ = 'U1'
+
+# Script actions
+plotMatrix = False
+saveFig = False
+
+# Initial velocity fields
+u01D = np.ones(nX)
+u02D = np.ones((nX, nY)).ravel()
+u03D = np.ones((nX, nY, nZ)).ravel()
+
+# Stencils
+stencilU1 = [-1, 1, 0]
+stencilC2 = [-0.5, 0, 0.5]
+stencilU3 = [1./6, -6./6, 3./6, 2./6, 0]
+
+dicoStencil = {'U1': ['$1^{st}$ order Upwind', stencilU1],
+ 'C2': ['$2^{nd}$ order Centered', stencilC2],
+ 'U3': ['$3^{rd}$ order Upwind', stencilU3]}
+
+stencilXName = dicoStencil[schemeX][0]
+stencilYName = dicoStencil[schemeY][0]
+stencilZName = dicoStencil[schemeZ][0]
+
+stencilX = dicoStencil[schemeX][1]
+stencilY = dicoStencil[schemeY][1]
+stencilZ = dicoStencil[schemeZ][1]
+
+iSX = (len(stencilX)-1)//2
+iSY = (len(stencilY)-1)//2
+iSZ = (len(stencilZ)-1)//2
+
+
+def rhs1D(u):
+ """
+ Define a 1D Right Hand Side (RHS) for the advection operator
+
+ .. math::
+ f(u) = c_x \\frac{\\partial u}{\\partial x}
+
+ Parameter
+ ---------
+ u : numpy.ndarray
+ The 1D vector, to evaluate the space derivative from,
+ of size :math:`n_x`
+
+ Returns
+ -------
+ uEval : numpy.ndarray
+ The 1D derivative of u
+ """
+ u1D = u.reshape((nX))
+ uEval = np.zeros_like(u1D)
+ for i in range(len(stencilX)):
+ uEval -= stencilX[i]*np.roll(u1D, iSX-i, axis=0)*cX
+
+ return uEval.ravel()
+
+
+def rhs2D(u):
+ """
+ Define a 2D Right Hand Side (RHS) for the advection operator
+
+ .. math::
+ f(u) = c_x \\frac{\\partial u}{\\partial x} +
+ c_y \\frac{\\partial u}{\\partial y}
+
+ Parameter
+ ---------
+ u : numpy.ndarray
+ The 2D vector, to evaluate the space derivative from,
+ of size :math:`n_x.n_y`
+
+ Returns
+ -------
+ uEval : numpy.ndarray
+ The 2D derivative of u
+ """
+ u2D = u.reshape((nX, nY))
+ uEval = np.zeros_like(u2D)
+
+ for i in range(len(stencilX)):
+ uEval -= stencilX[i]*np.roll(u2D, iSX-i, axis=0)*cX
+ for i in range(len(stencilY)):
+ uEval -= stencilY[i]*np.roll(u2D, iSY-i, axis=1)*cY
+
+ return uEval.ravel()
+
+
+def rhs3D(u):
+ """
+ Define a 3D Right Hand Side (RHS) for the advection operator
+
+ .. math::
+ f(u) = c_x \\frac{\\partial u}{\\partial x} +
+ c_y \\frac{\\partial u}{\\partial y} +
+ c_z \\frac{\\partial u}{\\partial z}
+
+ Parameter
+ ---------
+ u : numpy.ndarray
+ The 3D vector, to evaluate the space derivative from,
+ of size :math:`n_x.n_y.n_z`
+
+ Returns
+ -------
+ uEval : numpy.ndarray
+ The 3D derivative of u
+ """
+ u3D = u.reshape((nX, nY, nZ))
+ uEval = np.zeros_like(u3D)
+
+ for i in range(len(stencilX)):
+ uEval -= stencilX[i]*np.roll(u3D, iSX-i, axis=0)*cX
+ for i in range(len(stencilY)):
+ uEval -= stencilY[i]*np.roll(u3D, iSY-i, axis=1)*cY
+ for i in range(len(stencilZ)):
+ uEval -= stencilZ[i]*np.roll(u3D, iSZ-i, axis=2)*cZ
+
+ return uEval.ravel()
+
+
+def computeJacobian(u, rhs):
+ """
+ Compute the Jacobi matrix of a given RHS function, by computing the
+ partial derivative with finite difference for every element of the
+ vectorial basis.
+
+ Parameter
+ ---------
+ u : numpy.ndarray
+ The initial vector, where to evaluate
+ """
+ n = u.size
+ uPerturb = u.copy()
+ jacobian = np.empty((n, n))
+ uEval0 = rhs(u)
+ eps = 1e-8
+ for i in range(n):
+ uPerturb[i] += eps
+ jacobian[:, i] = rhs(uPerturb)
+ jacobian[:, i] -= uEval0
+ jacobian[:, i] /= eps
+ uPerturb[i] = u[i]
+ return jacobian
+
+# Compute the Jacobie matrix of each RHS function
+print('Compute 1D Jacobi matrix')
+A1D = computeJacobian(u01D, rhs1D)
+print('Compute 2D Jacobi matrix')
+A2D = computeJacobian(u02D, rhs2D)
+print('Compute 3D Jacobi matrix')
+A3D = computeJacobian(u03D, rhs3D)
+
+# Eventually plot the Jacobi matrices
+if plotMatrix:
+ plt.figure('1D')
+ plt.imshow(A1D)
+ plt.colorbar()
+
+ plt.figure('2D')
+ plt.imshow(A2D)
+ plt.colorbar()
+
+ plt.figure('3D')
+ plt.imshow(A3D)
+ plt.colorbar()
+
+# Compute the eigenvalues of each Jacobi matrix
+print('Compute eigenvalues of 1D Jacobi matrix')
+lam1D = spl.eigvals(A1D)
+print('Compute eigenvalues of 2D Jacobi matrix')
+lam2D = spl.eigvals(A2D)
+print('Compute eigenvalues of 3D Jacobi matrix')
+lam3D = spl.eigvals(A3D)
+print('Done, ploting ...')
+
+# Plot the eigenvalues
+plt.figure('Eigenvalues')
+plt.axvline(0, c='gray', ls='--', lw=1.0)
+plt.axhline(0, c='gray', ls='--', lw=1.0)
+plt.plot(lam1D.real, lam1D.imag, 's', label='1D', ms=12.0, mfc=None)
+plt.plot(lam2D.real, lam2D.imag, 'o', label='2D', ms=8.0, mfc=None)
+plt.plot(lam3D.real, lam3D.imag, '*', label='3D', ms=6.0, mfc=None)
+plt.axis('equal')
+plt.legend()
+plt.xlabel('$\\mathcal{R}(\\lambda)$') # Use $...$ for latex output
+plt.ylabel('$\\mathcal{I}(\\lambda)$')
+
+# Define figure title
+if stencilXName == stencilYName and stencilYName == stencilZName:
+ stencilName = stencilXName
+else:
+ stencilName = '{}(x), {}(y), {}(z)'.format(
+ stencilXName, stencilYName, stencilXName)
+
+plt.title('Eigenvalues of '+stencilName+' operator (Advection)\n' +
+ 'cX={}, cY={}, cZ={}'.format(cX, cY, cZ))
+
+# Eventually save figure
+if saveFig:
+ if schemeX == schemeY and schemeY == schemeZ:
+ scheme = schemeX
+ else:
+ scheme = schemeX+schemeY+schemeZ
+ plt.savefig('eigenvalues{}.pdf'.format(scheme), bbox_inches='tight')
--
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