def getMesh(self, ori, plan): # complete mesh for given plane
if self.zb == None: self.makeZblock()
grd = self.getFullGrid()
dx1 = grd['dx']
dy1 = grd['dy']
#print 'aq mesh',grd
xv = zeros((grd['nx'] + 1))
xv[0] = grd['x0']
xv[1:] = grd['x0'] + cumsum(dx1)
yv = zeros((grd['ny'] + 1))
yv[0] = grd['y0']
yv[1:] = grd['y0'] + cumsum(dy1)
nlay, nx, ny = shape(self.zb)
if self.getDim() in ['Xsection', 'Radial']: return meshgrid(xv, yv)
if ori == 'Z': return meshgrid(xv, yv)
elif ori == 'X':
a = yv * ones((nlay, 1))
b = self.zb[:, :, plan]
c = ones((nlay, len(yv)))
elif ori == 'Y':
a = xv * ones((nlay, 1))
b = self.zb[:, plan, :]
c = ones((nlay, len(xv)))
c[:, 1:-1] = b[:, 1:] / 2 + b[:, :-1] / 2
c[:, 0] = b[:, 0]
c[:, -1] = b[:, -1]
return a, c
def getMesh(self, ori, plan): # complete mesh for given plane
if self.zb == None:
self.makeZblock()
grd = self.getFullGrid()
dx1 = grd["dx"]
dy1 = grd["dy"]
# print 'aq mesh',grd
xv = zeros((grd["nx"] + 1))
xv[0] = grd["x0"]
xv[1:] = grd["x0"] + cumsum(dx1)
yv = zeros((grd["ny"] + 1))
yv[0] = grd["y0"]
yv[1:] = grd["y0"] + cumsum(dy1)
nlay, nx, ny = shape(self.zb)
if self.getDim() in ["Xsection", "Radial"]:
return meshgrid(xv, yv)
if ori == "Z":
return meshgrid(xv, yv)
elif ori == "X":
a = yv * ones((nlay, 1))
b = self.zb[:, :, plan]
c = ones((nlay, len(yv)))
elif ori == "Y":
a = xv * ones((nlay, 1))
b = self.zb[:, plan, :]
c = ones((nlay, len(xv)))
c[:, 1:-1] = b[:, 1:] / 2 + b[:, :-1] / 2
c[:, 0] = b[:, 0]
c[:, -1] = b[:, -1]
return a, c
def display_toroid(u0,
s0,
s1,
ds,
u_val=1,
v_val=None,
a=1,
solver=None,
show=False):
C = toroid(u_val, v_val, a) # Find the Christoffel tensor for toroid
X = solve(C, u0, s0, s1, ds, solver)
import matplotlib.pylab as plt
from mpl_toolkits.mplot3d import Axes3D
from math import pi
if v_val is None:
u = u_val # toroids
v, w = plt.meshgrid(np.linspace(-pi, pi, 250),
np.linspace(0, 2 * pi, 250))
else:
v = v_val # spherical bowls
u, w = plt.meshgrid(np.linspace(0, 2, 250),
np.linspace(0, 2 * pi, 250))
x = (a * np.sinh(u) * np.cos(w)) / (np.cosh(u) - np.cos(v))
y = (a * np.sinh(u) * np.sin(w)) / (np.cosh(u) - np.cos(v))
z = (a * np.sin(v)) / (np.cosh(u) - np.cos(v))
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.view_init(elev=90., azim=0)
# use transparent colormap
import matplotlib.cm as cm
theCM = cm.get_cmap()
theCM._init()
alphas = -.5 * np.ones(theCM.N)
theCM._lut[:-3, -1] = alphas
ax.plot_surface(x, y, z, linewidth=0, cmap=theCM)
plt.hold('on')
# plot the parametrized data on to the toroid
if v_val is None:
w, v = X[:, 0], X[:, 2]
else:
w, u = X[:, 0], X[:, 2]
x = (a * np.sinh(u) * np.cos(w)) / (np.cosh(u) - np.cos(v))
y = (a * np.sinh(u) * np.sin(w)) / (np.cosh(u) - np.cos(v))
z = (a * np.sin(v)) / (np.cosh(u) - np.cos(v))
s1_ = s1 / pi
ax.plot(x, y, z, '--r')
fig.suptitle('$s\in[%.1f\pi \, , \,%2.1f\pi]$' % (s0, s1_))
if show == True:
plt.show()
return X, plt
def display_sphere_with_geodesic(u0, s0, s1, ds):
C = Christoffel2nd_sphere()
X = solve(C, u0, s0, s1, ds)
import matplotlib.pylab as plt
from mpl_toolkits.mplot3d import Axes3D
N = X[:, 0].shape[0]
u, v = plt.meshgrid(np.linspace(0, 2 * np.pi, N),
np.linspace(0, 2 * np.pi, N))
x = np.cos(u) * np.cos(v)
y = np.sin(u) * np.cos(v)
z = np.sin(v)
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.view_init(elev=50, azim=-120)
# use transparent colormap
import matplotlib.cm as cm
theCM = cm.get_cmap()
theCM._init()
alphas = -.5 * np.ones(theCM.N)
theCM._lut[:-3, -1] = alphas
ax.plot_surface(x, y, z, linewidth=0, cmap=theCM)
plt.hold('on')
# plot the parametrized data on to the sphere
u, v = X[:, 0], X[:, 2]
x = np.cos(u) * np.cos(v)
y = np.sin(u) * np.cos(v)
z = np.sin(v)
ax.plot(x, y, z, '--r')
from math import pi
s1_ = s1 / pi
fig.suptitle('$s\in[%.1f\, , \,%2.1f\pi]$' % (s0, s1_))
plt.show()
def plot_hyperplane(X, Y, model, K, plot_id, d = 500):
I0 = np.where(Y==-1)[0]
I1 = np.where(Y==1)[0]
plt.subplot(plot_id)
plt.plot(X[I1, 0], X[I1, 1], 'og')
plt.plot(X[I0, 0], X[I0, 1], 'xb')
min_val = np.min(X, 0)
max_val = np.max(X, 0)
clf = model()
clf.train(X, Y, K)
x0_plot = np.linspace(min_val[0, 0], max_val[0, 0], d)
x1_plot = np.linspace(min_val[0, 1], max_val[0, 1], d)
[x0, x1] = plt.meshgrid(x0_plot, x1_plot);
Y_all = np.matrix(np.zeros([d, d]))
for i in range(d):
X_all = np.matrix(np.zeros([d, 2]))
X_all[:, 0] = np.matrix(x0[:, i]).T
X_all[:, 1] = np.matrix(x1[:, i]).T
Y_all[:, i] = clf.predict(X_all)
plt.contour(np.array(x0), np.array(x1), np.array(Y_all), levels = [0.0], colors = 'red')
def getMeshCentre(self, ori, plan): # mesh au milieu de la grille
if self.zb == None: self.makeZblock()
grd = self.getFullGrid()
dx1 = grd['dx']
dy1 = grd['dy']
xv = grd['x0'] + cumsum(dx1) - dx1 / 2.
yv = grd['y0'] + cumsum(dy1) - dy1 / 2.
nlay, nx, ny = shape(self.zb)
if self.getDim() in ['Xsection', 'Radial']: return meshgrid(xv, yv)
if ori == 'Z': return meshgrid(xv, yv)
elif ori == 'X':
z = self.zb[1:, :, plan] / 2 + self.zb[:-1, :, plan] / 2
return yv * ones((nlay - 1, 1)), z
elif ori == 'Y':
z = self.zb[1:, plan, :] / 2 + self.zb[:-1, plan, :] / 2
return xv * ones((nlay - 1, 1)), z
def plot_hyperplane(X, Y, model, K, plot_id, d=500):
I0 = np.where(Y == -1)[0]
I1 = np.where(Y == 1)[0]
plt.subplot(plot_id)
plt.plot(X[I1, 0], X[I1, 1], 'og')
plt.plot(X[I0, 0], X[I0, 1], 'xb')
min_val = np.min(X, 0)
max_val = np.max(X, 0)
clf = model()
clf.train(X, Y, K)
x0_plot = np.linspace(min_val[0, 0], max_val[0, 0], d)
x1_plot = np.linspace(min_val[0, 1], max_val[0, 1], d)
[x0, x1] = plt.meshgrid(x0_plot, x1_plot)
Y_all = np.matrix(np.zeros([d, d]))
for i in range(d):
X_all = np.matrix(np.zeros([d, 2]))
X_all[:, 0] = np.matrix(x0[:, i]).T
X_all[:, 1] = np.matrix(x1[:, i]).T
Y_all[:, i] = clf.predict(X_all)
plt.contour(np.array(x0),
np.array(x1),
np.array(Y_all),
levels=[0.0],
colors='red')
def plotModel2D(self,X=[],Y=[],xLabel="",yLabel="",title="",fName=""):
#fig = plt.figure(figsize=(6,4),dpi=100)
plt.close()
# 真値のプロット（クラスごとにマーカーを変更）
plt.plot(X[Y[:,0]==0,0],X[Y[:,0]==0,1],'cx',markersize=14,label="ラベル0")
plt.plot(X[Y[:,0]==1,0],X[Y[:,0]==1,1],'m.',markersize=14,label="ラベル1")
# 予測値のメッシュの計算
X1,X2 = plt.meshgrid(plt.linspace(np.min(X[:,0]),np.max(X[:,0]),50),plt.linspace(np.min(X[:,1]),np.max(X[:,1]),50))
Xmesh = np.hstack([np.reshape(X1,[-1,1]),np.reshape(X2,[-1,1])])
Pmesh,_,_ = self.predict(Xmesh)
Pmesh = np.reshape(Pmesh,X1.shape)
# 予測値のプロット
CS = plt.contourf(X1,X2,Pmesh,linewidths=2,cmap="bwr",alpha=0.3,vmin=0,vmax=1)
# カラーバー
CB = plt.colorbar(CS)
CB.ax.tick_params(labelsize=14)
# 各軸の範囲とラベルの設定
plt.xlim([np.min(X[:,0]),np.max(X[:,0])])
plt.ylim([np.min(X[:,1]),np.max(X[:,1])])
plt.title(title,fontsize=14)
plt.xlabel(xLabel,fontsize=14)
plt.ylabel(yLabel,fontsize=14)
plt.legend()
# グラフの表示またはファイルへの保存
if len(fName):
plt.savefig(fName)
else:
plt.show()
def display_toroid(u0,s0,s1,ds,u_val=1,v_val=None,a=1,solver=None,show=False):
C = toroid(u_val,v_val,a) # Find the Christoffel tensor for toroid
X = solve(C,u0,s0,s1,ds,solver)
import matplotlib.pylab as plt
from mpl_toolkits.mplot3d import Axes3D
from math import pi
if v_val is None:
u = u_val # toroids
v,w = plt.meshgrid(np.linspace(-pi,pi,250),np.linspace(0,2*pi,250))
else:
v = v_val # spherical bowls
u,w = plt.meshgrid(np.linspace(0,2,250),np.linspace(0,2*pi,250))
x = (a*np.sinh(u)*np.cos(w))/(np.cosh(u) - np.cos(v))
y = (a*np.sinh(u)*np.sin(w))/(np.cosh(u) - np.cos(v))
z = (a*np.sin(v))/(np.cosh(u) - np.cos(v))
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.view_init(elev=90., azim=0)
# use transparent colormap
import matplotlib.cm as cm
theCM = cm.get_cmap()
theCM._init()
alphas = -.5*np.ones(theCM.N)
theCM._lut[:-3,-1] = alphas
ax.plot_surface(x,y,z,linewidth=0,cmap=theCM)
plt.hold('on')
# plot the parametrized data on to the toroid
if v_val is None:
w,v = X[:,0], X[:,2]
else:
w,u = X[:,0], X[:,2]
x = (a*np.sinh(u)*np.cos(w))/(np.cosh(u) - np.cos(v))
y = (a*np.sinh(u)*np.sin(w))/(np.cosh(u) - np.cos(v))
z = (a*np.sin(v))/(np.cosh(u) - np.cos(v))
s1_ = s1/pi
ax.plot(x,y,z,'--r')
fig.suptitle('$s\in[%.1f\pi \, , \,%2.1f\pi]$'%(s0,s1_))
if show == True:
plt.show()
return X,plt
def draw(self):
x = np.arange(0, self.h_x, self.del_x)
y = np.arange(0, self.h_y, self.del_y)
X, Y = plt.meshgrid(x, y)
Z = self.map
plt.pcolor(X, Y, Z)
plt.colorbar()
plt.show()
def getMeshCentre(self, ori, plan): # mesh au milieu de la grille
if self.zb == None:
self.makeZblock()
grd = self.getFullGrid()
dx1 = grd["dx"]
dy1 = grd["dy"]
xv = grd["x0"] + cumsum(dx1) - dx1 / 2.0
yv = grd["y0"] + cumsum(dy1) - dy1 / 2.0
nlay, nx, ny = shape(self.zb)
if self.getDim() in ["Xsection", "Radial"]:
return meshgrid(xv, yv)
if ori == "Z":
return meshgrid(xv, yv)
elif ori == "X":
z = self.zb[1:, :, plan] / 2 + self.zb[:-1, :, plan] / 2
return yv * ones((nlay - 1, 1)), z
elif ori == "Y":
z = self.zb[1:, plan, :] / 2 + self.zb[:-1, plan, :] / 2
return xv * ones((nlay - 1, 1)), z
def draw_fit(self):
Ri = rotmat(self.grid_angle)
X, Y = lab.meshgrid(range(-50, 50), range(-50, 50))
X, Y = X * self.grid_spacing + self.grid_orig[0], Y * self.grid_spacing + self.grid_orig[1]
inferred_grid_pts = np.hstack([np.reshape(X, (-1,1)), np.reshape(Y, (-1,1))])
inferred_grid_pts = [Ri * np.reshape(p,(-1,1)) for p in inferred_grid_pts]
with_grid = self.img.copy()
for p in inferred_grid_pts:
cv2.circle(with_grid, tuple(p), 4, 200, 4)
show(with_grid)
def convert_depth_to_uvd(depth):
v, u = pylab.meshgrid(range(0, depth.shape[0], 1),
range(0, depth.shape[1], 1),
indexing='ij')
v = np.asarray(v, 'uint16')[:, :, np.newaxis]
u = np.asarray(u, 'uint16')[:, :, np.newaxis]
depth = depth[:, :, np.newaxis]
uvd = np.concatenate((u, v, depth), axis=2)
# print v.shape,u.shape,uvd.shape
return uvd
def getEpais(self):
if self.zb == None: self.makeZblock()
ep = self.zb[:-1, :, :] - self.zb[1:, :, :]
if self.getDim() in ['Xsection', 'Radial']:
grd = self.getFullGrid()
dx, dy = grd['dx'], grd['dy']
a, ep = meshgrid(ones((len(dx))), dy[::-1])
ep = reshape(ep, (len(dy), 1, len(dx)))
if self.getTypeAq() == 'libre':
hd = self.model.Ecoulement.getMfHead(0)
ep[0, :, :] = hd - self.zb[1, :, :]
return ep
def getEpais(self):
if self.zb == None:
self.makeZblock()
ep = self.zb[:-1, :, :] - self.zb[1:, :, :]
if self.getDim() in ["Xsection", "Radial"]:
grd = self.getFullGrid()
dx, dy = grd["dx"], grd["dy"]
a, ep = meshgrid(ones((len(dx))), dy[::-1])
ep = reshape(ep, (len(dy), 1, len(dx)))
if self.getTypeAq() == "libre":
hd = self.model.Ecoulement.getMfHead(0)
ep[0, :, :] = hd - self.zb[1, :, :]
return ep
def draw2(self):
x = np.arange(0, self.h_x + 1, self.del_x)
y = np.arange(0, self.h_y + 1, self.del_y)
X, Y = plt.meshgrid(x, y)
Z = self.u.reshape([self.x_div, self.y_div])
plt.xlabel("x")
plt.ylabel("y")
# plt.xlim([0, self.h_x])
# plt.ylim([0, self.h_y])
plt.pcolor(X, Y, Z.T)
plt.colorbar()
plt.show()
def draw3D2(self):
x = np.arange(0, self.h_x, self.del_x)
y = np.arange(0, self.h_y, self.del_y)
X, Y = plt.meshgrid(x, y)
Z = self.u.reshape([self.x_div, self.y_div])
fig = plt.figure()
ax = Axes3D(fig)
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.plot_wireframe(X, Y, Z)
plt.show()
def histogram2d(x, y, bins=10, range=None, normed=False, weights=None,
log = False,
filename = None,
**formating):
hist, x, y = numpy.histogram2d(x, y, bins, range, normed, weights)
if log is True:
hist = numpy.log(hist)
X, Y = pylab.meshgrid(x,y)
pylab.pcolor(X, Y,hist.transpose())
pylab.colorbar()
doFormating(**formating)
pylab.show()
if filename is not None:
pylab.savefig(filename)
pylab.clf()
def histogram2d(x, y, bins=10, range=None, normed=False, weights=None,
log = False,
filename = None,
**formating):
hist, x, y = numpy.histogram2d(x, y, bins, range, normed, weights)
if log is True:
hist = numpy.log(hist)
X, Y = pylab.meshgrid(x,y)
pylab.pcolor(X, Y,hist.transpose())
pylab.colorbar()
doFormating(**formating)
pylab.show()
if filename is not None:
pylab.savefig(filename)
pylab.clf()
def display_mobius_strip(u0, s0, s1, ds, solver=None, show=False):
C = mobius_strip() # Find the Christoffel tensor for mobius strip
X = solve(C, u0, s0, s1, ds, solver)
import matplotlib.pylab as plt
from mpl_toolkits.mplot3d import Axes3D
u, v = plt.meshgrid(np.linspace(-2 * np.pi, np.pi, 250),
np.linspace(-np.pi, np.pi, 250))
x = (1 + np.cos(u / 2.) * v / 2.) * np.cos(u)
y = (1 + np.cos(u / 2.) * v / 2.) * np.sin(u)
z = np.sin(u / 2.) * v / 2.
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.view_init(elev=10, azim=81)
# use transparent colormap
import matplotlib.cm as cm
theCM = cm.get_cmap()
theCM._init()
alphas = -.5 * np.ones(theCM.N)
theCM._lut[:-3, -1] = alphas
ax.plot_surface(x, y, z, linewidth=0, cmap=theCM)
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_zlabel('z')
plt.hold('on')
# plot the parametrized data on to the catenoid
u, v = X[:, 0], X[:, 2]
x = (1 + np.cos(u / 2.) * v / 2.) * np.cos(u)
y = (1 + np.cos(u / 2.) * v / 2.) * np.sin(u)
z = np.sin(u / 2.) * v / 2.
ax.plot(x, y, z, '--r')
s0_ = s0 / np.pi
s1_ = s1 / np.pi
fig.suptitle(
"$s\in[%1.f,%1.f\pi]$ , $u = %.1f$ , $u' = %.1f$, $v = %.1f$ , $v' = %.1f$"
% (s0, s1_, u0[0], u0[1], u0[2], u0[3]))
if show == True:
plt.show()
return X, plt
def display_torus(u0, s0, s1, ds, a=1, c=2, solver=None, show=False):
C = torus(a, c) # Find the Christoffel tensor for the torus
X = solve(C, u0, s0, s1, ds, solver)
import matplotlib.pylab as plt
from mpl_toolkits.mplot3d import Axes3D
N = X[:, 0].shape[0]
u, v = plt.meshgrid(np.linspace(0, 2 * np.pi, 250),
np.linspace(0, 2 * np.pi, 250))
x = (c + a * np.cos(v)) * np.cos(u)
y = (c + a * np.cos(v)) * np.sin(u)
z = np.sin(v)
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.view_init(elev=-60, azim=100)
# use transparent colormap -> negative
import matplotlib.cm as cm
theCM = cm.get_cmap()
theCM._init()
alphas = 2 * np.ones(theCM.N)
theCM._lut[:-3, -1] = alphas
ax.plot_surface(x, y, z, linewidth=0, cmap=theCM)
plt.hold('on')
# plot the parametrized data on to the torus
u, v = X[:, 0], X[:, 2]
x = (c + a * np.cos(v)) * np.cos(u)
y = (c + a * np.cos(v)) * np.sin(u)
z = np.sin(v)
ax.plot(x, y, z, '--r')
s1_ = s1 / pi
fig.suptitle(
"$s\in[%1.f,%1.f\pi]$ , $u = %.1f$ , $u' = %.1f$, $v = %.1f$ , $v' = %.1f$"
% (s0, s1_, u0[0], u0[1], u0[2], u0[3]))
if show == True:
plt.show()
return X, plt
def display_mobius_strip(u0,s0,s1,ds,solver=None,show=False):
C = mobius_strip() # Find the Christoffel tensor for mobius strip
X = solve(C,u0,s0,s1,ds,solver)
import matplotlib.pylab as plt
from mpl_toolkits.mplot3d import Axes3D
u,v = plt.meshgrid(np.linspace(-2*np.pi,np.pi,250),np.linspace(-np.pi,np.pi,250))
x = (1 + np.cos(u/2.)*v/2.)*np.cos(u)
y = (1 + np.cos(u/2.)*v/2.)*np.sin(u)
z = np.sin(u/2.)*v/2.
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.view_init(elev=10, azim=81)
# use transparent colormap
import matplotlib.cm as cm
theCM = cm.get_cmap()
theCM._init()
alphas = -.5*np.ones(theCM.N)
theCM._lut[:-3,-1] = alphas
ax.plot_surface(x,y,z,linewidth=0,cmap=theCM)
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_zlabel('z')
plt.hold('on')
# plot the parametrized data on to the catenoid
u,v = X[:,0], X[:,2]
x = (1 + np.cos(u/2.)*v/2.)*np.cos(u)
y = (1 + np.cos(u/2.)*v/2.)*np.sin(u)
z = np.sin(u/2.)*v/2.
ax.plot(x,y,z,'--r')
s0_ = s0/np.pi
s1_ = s1/np.pi
fig.suptitle("$s\in[%1.f,%1.f\pi]$ , $u = %.1f$ , $u' = %.1f$, $v = %.1f$ , $v' = %.1f$"%(s0,s1_,u0[0],u0[1],u0[2],u0[3]))
if show == True:
plt.show()
return X,plt
def display_catenoid(u0, s0, s1, ds, solver=None, show=False):
C = catenoid() # Find the Christoffel tensor for cylindrical catenoid
X = solve(C, u0, s0, s1, ds, solver)
import matplotlib.pylab as plt
from mpl_toolkits.mplot3d import Axes3D
N = X[:, 0].shape[0]
u, v = plt.meshgrid(np.linspace(-np.pi, np.pi, 150),
np.linspace(-np.pi, np.pi, 150))
x = np.cos(u) - v * np.sin(u)
y = np.sin(u) + v * np.cos(u)
z = v
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.view_init(elev=20, azim=-163)
# use transparent colormap
import matplotlib.cm as cm
theCM = cm.get_cmap()
theCM._init()
alphas = -.5 * np.ones(theCM.N)
theCM._lut[:-3, -1] = alphas
ax.plot_surface(x, y, z, linewidth=0, cmap=theCM)
plt.hold('on')
# plot the parametrized data on to the catenoid
u, v = X[:, 0], X[:, 2]
x = np.cos(u) - v * np.sin(u)
y = np.sin(u) + v * np.cos(u)
z = v
ax.plot(x, y, z, '--r')
s0_ = s0 / np.pi
s1_ = s1 / np.pi
fig.suptitle("$s\in[%.1f\pi,%.1f\pi]$ , $u' = %.1f$ , $v' = %.2f$" %
(s0_, s1_, u0[1], u0[3]))
if show == True:
plt.show()
return X, plt
def display_egg_carton(u0, s0, s1, ds, solver=None, show=False):
C = egg_carton() # Find the Christoffel tensor for egg carton surface
X = solve(C, u0, s0, s1, ds, solver)
import matplotlib.pylab as plt
from mpl_toolkits.mplot3d import Axes3D
from math import pi
N = X[:, 0].shape[0]
u, v = plt.meshgrid(np.linspace(s0, s1, N), np.linspace(s0, s1, N))
x = u
y = v
z = np.sin(u) * np.cos(v)
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.view_init(elev=90., azim=0)
# use transparent colormap
import matplotlib.cm as cm
theCM = cm.get_cmap()
theCM._init()
alphas = -.5 * np.ones(theCM.N)
theCM._lut[:-3, -1] = alphas
ax.plot_surface(x, y, z, linewidth=0, cmap=theCM)
plt.hold('on')
# plot the parametrized data on to the egg carton
u, v = X[:, 0], X[:, 2]
x = u
y = v
z = np.sin(u) * np.cos(v)
s0_ = s0 / pi
s1_ = s1 / pi
ax.plot(x, y, z, '--r')
fig.suptitle('$s\in[%.1f\pi \, , \,%2.1f\pi]$' % (s0_, s1_))
if show == True:
plt.show()
return X, plt
def display_sphere(u0, s0, s1, ds, solver=None, metric=None, show=False):
if metric == 'flat':
C = flat_sphere()
if u0[0] == 0 or u0[2] == 0:
print 'Division by zero may occur for provided values of u(s0) and v(s0)'
else:
C = sphere()
X = solve(C, u0, s0, s1, ds, solver)
import matplotlib.pylab as plt
from mpl_toolkits.mplot3d import Axes3D
u, v = plt.meshgrid(np.linspace(0, 2 * np.pi, 250),
np.linspace(0, 2 * np.pi, 250))
x = np.cos(u) * np.cos(v)
y = np.sin(u) * np.cos(v)
z = np.sin(v)
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
if metric == 'flat':
ax.view_init(elev=90., azim=0)
else:
ax.view_init(elev=0., azim=13)
ax.plot_surface(x, y, z, linewidth=0, cmap='Pastel1')
plt.hold('on')
# plot the parametrized data on to the sphere
u, v = X[:, 0], X[:, 2]
x = np.cos(u) * np.cos(v)
y = np.sin(u) * np.cos(v)
z = np.sin(v)
ax.plot(x, y, z, '--r')
from math import pi
s1_ = s1 / pi
fig.suptitle("$s\in[%1.f,%1.f\pi]$ , $u' = %.1f$ , $v' = %.1f$" %
(s0, s1_, u0[1], u0[3]))
if show == True:
plt.show()
return X, plt
def display_egg_carton(u0,s0,s1,ds,solver=None,show=False):
C = egg_carton() # Find the Christoffel tensor for egg carton surface
X = solve(C,u0,s0,s1,ds,solver)
import matplotlib.pylab as plt
from mpl_toolkits.mplot3d import Axes3D
from math import pi
N = X[:,0].shape[0]
u,v = plt.meshgrid(np.linspace(s0,s1,N),np.linspace(s0,s1,N))
x = u
y = v
z = np.sin(u)*np.cos(v)
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.view_init(elev=90., azim=0)
# use transparent colormap
import matplotlib.cm as cm
theCM = cm.get_cmap()
theCM._init()
alphas = -.5*np.ones(theCM.N)
theCM._lut[:-3,-1] = alphas
ax.plot_surface(x,y,z,linewidth=0,cmap=theCM)
plt.hold('on')
# plot the parametrized data on to the egg carton
u,v = X[:,0], X[:,2]
x = u
y = v
z = np.sin(u)*np.cos(v)
s0_ = s0/pi
s1_ = s1/pi
ax.plot(x,y,z,'--r')
fig.suptitle('$s\in[%.1f\pi \, , \,%2.1f\pi]$'%(s0_,s1_))
if show == True:
plt.show()
return X,plt
def display_catenoid(u0,s0,s1,ds,solver=None,show=False):
C = catenoid() # Find the Christoffel tensor for cylindrical catenoid
X = solve(C,u0,s0,s1,ds,solver)
import matplotlib.pylab as plt
from mpl_toolkits.mplot3d import Axes3D
N = X[:,0].shape[0]
u,v = plt.meshgrid(np.linspace(-np.pi,np.pi,150),np.linspace(-np.pi,np.pi,150))
x = np.cos(u) - v*np.sin(u)
y = np.sin(u) + v*np.cos(u)
z = v
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.view_init(elev=20, azim=-163)
# use transparent colormap
import matplotlib.cm as cm
theCM = cm.get_cmap()
theCM._init()
alphas = -.5*np.ones(theCM.N)
theCM._lut[:-3,-1] = alphas
ax.plot_surface(x,y,z,linewidth=0,cmap=theCM)
plt.hold('on')
# plot the parametrized data on to the catenoid
u,v = X[:,0], X[:,2]
x = np.cos(u) - v*np.sin(u)
y = np.sin(u) + v*np.cos(u)
z = v
ax.plot(x,y,z,'--r')
s0_ = s0/np.pi
s1_ = s1/np.pi
fig.suptitle("$s\in[%.1f\pi,%.1f\pi]$ , $u' = %.1f$ , $v' = %.2f$"%(s0_,s1_,u0[1],u0[3]))
if show == True:
plt.show()
return X,plt
def display_sphere(u0,s0,s1,ds,solver=None,metric=None,show=False):
if metric == 'flat':
C = flat_sphere()
if u0[0] == 0 or u0[2] == 0:
print 'Division by zero may occur for provided values of u(s0) and v(s0)'
else:
C = sphere()
X = solve(C,u0,s0,s1,ds,solver)
import matplotlib.pylab as plt
from mpl_toolkits.mplot3d import Axes3D
u,v = plt.meshgrid(np.linspace(0,2*np.pi,250),np.linspace(0,2*np.pi,250))
x = np.cos(u)*np.cos(v)
y = np.sin(u)*np.cos(v)
z = np.sin(v)
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
if metric == 'flat':
ax.view_init(elev=90., azim=0)
else:
ax.view_init(elev=0., azim=13)
ax.plot_surface(x,y,z,linewidth=0,cmap='Pastel1')
plt.hold('on')
# plot the parametrized data on to the sphere
u,v = X[:,0], X[:,2]
x = np.cos(u)*np.cos(v)
y = np.sin(u)*np.cos(v)
z = np.sin(v)
ax.plot(x,y,z,'--r')
from math import pi
s1_ = s1/pi
fig.suptitle("$s\in[%1.f,%1.f\pi]$ , $u' = %.1f$ , $v' = %.1f$"%(s0,s1_,u0[1],u0[3]))
if show == True:
plt.show()
return X,plt
def display_torus(u0,s0,s1,ds,a=1,c=2,solver=None,show=False):
C = torus(a,c) # Find the Christoffel tensor for the torus
X = solve(C,u0,s0,s1,ds,solver)
import matplotlib.pylab as plt
from mpl_toolkits.mplot3d import Axes3D
N = X[:,0].shape[0]
u,v = plt.meshgrid(np.linspace(0,2*np.pi,250),np.linspace(0,2*np.pi,250))
x = (c + a*np.cos(v))*np.cos(u)
y = (c + a*np.cos(v))*np.sin(u)
z = np.sin(v)
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.view_init(elev=-60, azim=100)
# use transparent colormap -> negative
import matplotlib.cm as cm
theCM = cm.get_cmap()
theCM._init()
alphas = 2*np.ones(theCM.N)
theCM._lut[:-3,-1] = alphas
ax.plot_surface(x,y,z,linewidth=0,cmap=theCM)
plt.hold('on')
# plot the parametrized data on to the torus
u,v = X[:,0], X[:,2]
x = (c + a*np.cos(v))*np.cos(u)
y = (c + a*np.cos(v))*np.sin(u)
z = np.sin(v)
ax.plot(x,y,z,'--r')
s1_ = s1/pi
fig.suptitle("$s\in[%1.f,%1.f\pi]$ , $u = %.1f$ , $u' = %.1f$, $v = %.1f$ , $v' = %.1f$"%(s0,s1_,u0[0],u0[1],u0[2],u0[3]))
if show == True:
plt.show()
return X,plt
def plot(V, title, save_name, elev=20., azim=30.):
#Get X,Y range
NXmax, NYmax = V.shape
x = range(0, NXmax-1, 1)
y = range(0, NYmax-1, 1)
X, Y = p.meshgrid(x,y)#Make grid
def functz(V):#Make Z for plotting
z = V[X,Y]
return z
Z = functz(V)
fig = p.figure()#Make new fig
ax = Axes3D(fig)
#Plot fewer lines
xstride, ystride = floor(max(x)/20), floor(max(y)/20)
ax.plot_wireframe(X, Y, Z, rstride=xstride, \
cstride=ystride, color = 'r')
ax.set_xlabel('X'); ax.set_ylabel('Y')
ax.set_zlabel('Potential, V(x,y)')
ax.set_xlim(0,max(x)); ax.set_ylim(0,max(y))
ax.set_title(title)
ax.contourf(X,Y,Z,11,stride=25,offset=min(Z))
ax.view_init(elev=elev, azim=azim)
p.savefig('figures/%s.png'%save_name,bbox_inches='tight')
print("Finished %s (%s.png)" % (title, save_name))
def plotSQE(sqe,viewDirectory,filename,title="S(Q,E)",lower=False,\
upper=False,TextSize=16):
pylab.clf()
pylab.axes( (0.15, 0.1, 0.8, 0.8 ) )
if upper:
for q in range(len(sqe.q)):
for e in range(len(sqe.e)):
if sqe.sqe[q,e] > upper:
sqe.sqe[q,e] = upper
if lower:
for q in range(len(sqe.q)):
for e in range(len(sqe.e)):
if sqe.sqe[q,e] < lower:
sqe.sqe[q,e] = lower
myfile = os.path.join(viewDirectory,filename)
x = sqe.q; y = sqe.e; z = numpy.transpose(sqe.sqe)
X,Y = pylab.meshgrid(x,y)
image = pylab.pcolor( X,Y, z, shading="flat")
ylabel = "E [meV]"
xlabel = "Q [1/Angstroms]"
pylab.xlim( x[0], x[-1] )
pylab.ylim( y[0], y[-1] )
pylab.xlabel( xlabel )
pylab.ylabel( ylabel )
pylab.title( title )
pylab.colorbar()
pylab.savefig( myfile )
return
T = np.column_stack([np.ones(x.size), x.reshape(x.size), y.reshape(y.size)])
T = feature_extend(T)
return predict_log_reg(T, theta).reshape(x.shape)
if __name__ == "__main__":
data = Orange.data.Table("data/data-quad.tab")
X, y, _ = data.to_numpy()
m = X.shape[0]
n = X.shape[1]
X = np.column_stack([np.ones(m), X])
X = feature_extend(X)
theta, j_hist = batch_log_reg(X, y, alpha=0.1, theta=np.zeros(X.shape[1]), max_iterations=10000)
print "Grad desc:", theta
plt.close()
grid = 30
x1 = np.linspace(min(X[:,1]), max(X[:,1]), grid)
x2 = np.linspace(min(X[:,2]), max(X[:,2]), grid)
X1, X2 = meshgrid(x1, x2)
Z = test_mesh(X1, X2, theta)
plt.pcolor(X1, X2, Z) # plt.cm.gray
plt.scatter(X[:,1], X[:,2], c=["y" if yi else "b" for yi in y])
plt.xlabel("x1")
plt.ylabel("x2")
plt.title("Logistic regression with non-linear decision boundary")
plt.savefig("0.pdf")
from numpy import ma
import os
# ----------------------------------------
# Extraindo as variaveis da saida do Hycom
# Grade 1/24°
print('------------------------------')
print(' Extraindo variáveis do HYCOM ')
print('------------------------------')
DIR = '/mnt/nfs/dpns32/data1/operador/previsao/hycom_2_2/hycom2netcdf/Ncdf/'
nc_f=DIR+'HYCOM_1_24_'+datai+'_'+dataf+'.nc'
nc_fid=Dataset(nc_f, 'r')
lat=nc_fid.variables['Latitude'][:]
lon=nc_fid.variables['Longitude'][:]
lons,lats=plab.meshgrid(lon,lat)
lat_s=float(lat_sul)
lat_n=float(lat_norte)
lat_media=-((-lat_s)+(-lat_n))/2
lat_media=str(lat_media)
u=nc_fid.variables['u_velocity'][:]
v=nc_fid.variables['v_velocity'][:]
u=np.squeeze(u);v=np.squeeze(v)
u0=np.copy(u); v0=np.copy(v)
# Criando arrays de datas e prog para as figuras
tit_horas=['00','03','06','09','12','15','18','21']
titfig=[]
for ttt in range(0,numdays,1):
aux=date_list[ttt]
dt=aux.strftime('%Y%m%d')
def imageMap(lons, lats, vals, vmin=None, vmax=None,
imageWidth=None, imageHeight=None, outFile=None,
projection='cyl', cmap=M.cm.jet, makeFigure=False,
borders=[0., -90., 360., 90.], autoBorders=True, borderSlop=10.,
meridians=[0, 360, 60], parallels=[-60, 90, 30],
**options
):
lons = normalizeLons(lons)
if vmin == 'auto': vmin = None
if vmax == 'auto': vmax = None
if imageWidth is not None: makeFigure = True
if projection is None or projection == '': projection = 'cyl'
if cmap is None or cmap == '': cmap = M.cm.jet
if isinstance(cmap, bytes) and cmap != '':
try:
cmap = eval('M.cm.' + cmap)
except:
cmap = M.cm.jet
# ensureItems(options, {'xlabel': 'Longitude (deg)', 'ylabel': 'Latitude (deg)', \
ensureItems(options, { \
'title': 'An Image Map', 'dpi': 100,
'imageWidth': imageWidth or 1024, 'imageHeight': imageHeight or 768})
if autoBorders:
borders = [min(lons), min(lats), max(lons), max(lats)]
borders = roundBorders(borders, borderSlop)
m = Basemap(borders[0], borders[1], borders[2], borders[3], \
projection=projection, lon_0=N.average([lons[0], lons[-1]]))
if makeFigure:
dpi = float(options['dpi'])
width = float(imageWidth) / dpi
if imageHeight is None:
height = width * m.aspect
else:
height = float(imageHeight) / dpi
f = M.figure(figsize=(width,height)).add_axes([0.1,0.1,0.8,0.8], frameon=True)
if vmin is not None or vmax is not None:
if vmin is None:
vmin = min(vals)
else:
vmin = float(vmin)
if vmax is None:
vmax = max(vals)
else:
vmax = float(vmax)
vrange = (vmax - vmin) / 255.
levels = N.arange(vmin, vmax, vrange/30.)
else:
levels = 30
x, y = m(*M.meshgrid(lons,lats))
c = m.contourf(x, y, vals, levels, cmap=cmap, colors=None)
m.drawcoastlines()
m.drawmeridians(list(range(meridians[0], meridians[1], meridians[2])), labels=[0,0,0,1])
m.drawparallels(list(range(parallels[0], parallels[1], parallels[2])), labels=[1,1,1,1])
M.colorbar(c)
evalKeywordCmds(options)
if outFile:
M.savefig(outFile, **validCmdOptions(options, 'savefig'))
def display_multiple_geodesics(u0,s0,s1,ds,surface,with_object=True):
import matplotlib.pylab as plt
from mpl_toolkits.mplot3d import Axes3D
def solve_multiple(C,u0,s0,s1,ds,s):
from sympy.abc import u,v
print 'Running solver...'
return sc.odeint(f,u0,s,args=(C,u,v))
def display_multiple_catenoid(u0,s0,s1,ds,C,s):
X = solve_multiple(C,u0,s0,s1,ds,s)
plt.hold('on')
# plot the parametrized data on to the catenoid
u,v = X[:,0], X[:,2]
x = np.cos(u) - v*np.sin(u)
y = np.sin(u) + v*np.cos(u)
z = v
ax.plot(x,y,z,'--r')
return plt
def display_multiple_egg_carton(u0,s0,s1,ds,C,s):
X = solve_multiple(C,u0,s0,s1,ds,s)
plt.hold('on')
# plot the parametrized data on to the egg carton
u,v = X[:,0], X[:,2]
x = u
y = v
z = np.sin(u)*np.cos(v)
ax.plot(x,y,z,'--r')
return plt
def display_multiple_sphere(u0,s0,s1,ds,C,s):
X = solve_multiple(C,u0,s0,s1,ds,s)
plt.hold('on')
# plot the parametrized data on to the sphere
u,v = X[:,0], X[:,2]
x = np.cos(u)*np.cos(v)
y = np.sin(u)*np.cos(v)
z = np.sin(v)
ax.plot(x,y,z,'--r')
return plt
def display_multiple_torus(u0,s0,s1,ds,C,s):
X = solve_multiple(C,u0,s0,s1,ds,s)
plt.hold('on')
# plot the parametrized data on to the sphere
u,v = X[:,0], X[:,2]
x = (2 + 1*np.cos(v))*np.cos(u)
y = (2 + 1*np.cos(v))*np.sin(u)
z = np.sin(v)
ax.plot(x,y,z,'--r')
return plt
u0_range = np.arange(s0,s1+ds,ds)
N = u0_range.shape[0]
fig = plt.figure()
if surface == 'catenoid':
if with_object:
u,v = plt.meshgrid(np.linspace(-np.pi,np.pi,150),np.linspace(-np.pi,np.pi,150))
x = np.cos(u) - v*np.sin(u)
y = np.sin(u) + v*np.cos(u)
z = v
C = catenoid()
elif surface == 'egg_carton':
if with_object:
u,v = plt.meshgrid(np.linspace(-4,4,250),np.linspace(-4,4,250))
x = u
y = v
z = np.sin(u)*np.cos(v)
C = egg_carton()
elif surface == 'sphere':
if with_object:
u,v = plt.meshgrid(np.linspace(0,2*np.pi,250),np.linspace(0,2*np.pi,250))
x = np.cos(u)*np.cos(v)
y = np.sin(u)*np.cos(v)
z = np.sin(v)
C = sphere()
elif surface == 'torus':
if with_object:
u,v = plt.meshgrid(np.linspace(0,2*np.pi,150),np.linspace(0,2*np.pi,150))
x = (2 + 1*np.cos(v))*np.cos(u)
y = (2 + 1*np.cos(v))*np.sin(u)
z = np.sin(v)
C = torus()
ax = fig.add_subplot(111, projection='3d')
ax.view_init(azim=65, elev=67)
if with_object:
theCM = 'Pastel1'
ax.plot_surface(x,y,z,linewidth=0,cmap=theCM)
plt.hold('on')
if surface == 'catenoid':
for u_val in u0_range:
u0[3] = u_val
plt = display_multiple_catenoid(u0,s0,s1,ds,C,u0_range)
elif surface == 'egg_carton':
for u_val in u0_range:
u0[0] = u_val
plt = display_multiple_egg_carton(u0,s0,s1,ds,C,u0_range)
elif surface == 'sphere':
for u_val in u0_range:
u0[0] = u_val
plt = display_multiple_sphere(u0,s0,s1,ds,C,u0_range)
elif surface == 'torus':
for u_val in u0_range:
u0[0] = u_val # alternate v0 values
plt = display_multiple_torus(u0,s0,s1,ds,C,u0_range)
from math import pi
s0_ = s0#/pi
s1_ = s1/pi
fig.suptitle("$s\in[%1.f,%1.f\pi]$ , $u' = %.1f$ , $v = %.1f$ , $v' = %.1f$"%(s0_,s1_,u0[1],u0[2],u0[3]))
plt.show()
def sub_lba_dist(lists_action, lists_cmd, options):
# Local Variables: plot_fontsize, lists_action, i, idx_write, save_figure, lba_size_set, stat_record, idx_read, section_name, X, y, x, plot_figure, lba_stat_array, options, Y, lists_cmd
# Function calls: subplot, plot, lba_size_dist, set, gcf, figure, title, zlabel, isfield, findall, mesh, sub_lba_dist, colorbar, meshgrid, xlabel, ylabel, generate_ppt, saveas, isempty, find
#% stat_record=sub_lba_dist(lists_action,lists_cmd,options)
#% --> calcuate the size distribution
#% inputs
#% lists_action: n samples x 2 array for arrival time and completion time;
#% lists_cmd: n samples x 3 for LBA, size, flags ( (0 write, 1 read))
#% access_type: 0 write, 1 read, 2 all
#% options: control parameters
#% lba_size_set: how many LBA range sets
#%
#% outputs
#% lba_stat_array: cells structure; LBA statistics for write/read/all
#%
#% contact [email protected] for questions
if hasattr(options, 'plot_fontsize'):
plot_fontsize = options.plot_fontsize
else:
plot_fontsize = 10
if hasattr(options, 'save_figure'):
save_figure = options.save_figure
else:
save_figure = 1
if hasattr(options, 'plot_figure'):
plot_figure = options.plot_figure
else:
plot_figure = 1
if hasattr(options, 'lba_size_set'):
lba_size_set = options.lba_size_set
else:
options.lba_size_set = 50
plot_figure = options.plot_figure
#%5: LBA vs time;
if plot_figure == 1:
idx_read = np.nonzero((lists_cmd[:, 2] == 1))
idx_write = np.nonzero((lists_cmd[:, 2] == 0))
plt.figure
plt.subplot(2., 1., 1.)
plt.plot(lists_action[(idx_read), 0],
lists_cmd[(idx_read), 0],
'r*',
markersize=1)
plt.ylabel('LBA')
plt.title('read')
plt.subplot(2., 1., 2.)
plt.plot(lists_action[(idx_write), 0],
lists_cmd[(idx_write), 0],
'b+',
markersize=1)
plt.ylabel('LBA')
plt.xlabel('time (s)')
plt.title('write')
plt.savefig('lba_all.eps')
plt.savefig('lba_all.jpg')
lba_stat_array = []
for i in np.arange(3):
print(i)
stat_record = lba_size_dist2(lists_cmd, i, options)
if plot_figure == 1:
x = np.arange(1, 1025)
y = stat_record.lba_size_idx
if len(y) <= 1:
continue
fig = plt.figure()
ax = Axes3D(fig)
[X, Y] = plt.meshgrid(x, y)
ax.plot_surface(X, Y, (stat_record.lba_size_dist))
plt.set_cmap('hot')
ax.set_ylabel('LBA Range')
ax.set_xlabel('Request size')
ax.set_zlabel('Frequency')
if i == 0.:
ax.set_title('LBA & Size Disribution - Write ')
elif i == 1.:
ax.set_title('LBA & Size Disribution - Read ')
else:
ax.set_title('LBA & Size Disribution - Combined ')
# set((plt.gcf, '-property', 'FontSize'), 'FontSize', plot_fontsize)
# plt.grid()
if i == 1:
plt.savefig('lba_size_freq_read.eps', format="eps")
plt.savefig('lba_size_freq_read.jpg')
elif i == 0:
plt.savefig('lba_size_freq_write.eps', format="eps")
plt.savefig('lba_size_freq_write.jpg')
else:
plt.savefig('lba_size_freq_com.eps', format="eps")
plt.savefig('lba_size_freq_com.jpg')
plt.show()
lba_stat_array.append(stat_record)
# if options.export_report:
# options.section_name = 'LBA Distribution'
# generate_ppt(options)
return lba_stat_array
def visualize(self):
if self.log == 1:
f = open('calc.log','w')
f.close()
configure_output("calc.log")
x_1 = float(self.coor1_x.GetValue())
y_1 = float(self.coor1_y.GetValue())
z_1 = float(self.coor1_z.GetValue())
x_2 = float(self.coor2_x.GetValue())
y_2 = float(self.coor2_y.GetValue())
z_2 = float(self.coor2_z.GetValue())
z_pos = float(self.z_pos.GetValue())
mol = Molecule('h2',[(self.atom_no_1,(y_1,x_1,z_1)),
(self.atom_no_2,(y_2,x_2,z_2))],
units='Angstrom')
bf_name = self.Bf_box.GetValue()
#Why?
if bf_name == "sto-3g":
bf_name = "sto-3g"
elif bf_name == "6-31g":
bf_name = "6-31g"
elif bf_name == "3-21g":
bf_name = "3-21g"
elif bf_name == "6-31g**":
bf_name = "6-31g**"
elif bf_name == "6-31g**++":
bf_name = "6-31g**++"
elif bf_name == "6-311g**":
bf_name = "6-311g**"
elif bf_name == "6-311g++(2d,2p)":
bf_name = "6-311g++(2d,2p)"
elif bf_name == "6-311g++(3d,3p)":
bf_name = "6-311g++(3d,3p)"
elif bf_name == "6-311g++(3df,3pd)":
bf_name = "6-311g++(3df,3pd)"
elif bf_name == "sto-6g":
bf_name = "sto-6g"
elif bf_name == "lacvp":
bf_name = "lacvp"
elif bf_name == "cc-pvdz":
bf_name = "cc-pvdz"
elif bf_name == "cc-pvtz":
bf_name = "cc-pvtz"
elif bf_name == "dzvp":
bf_name = "dzvp"
en,orbe,orbs = rhf(mol,basis_data=bf_name)
self.console_box.SetValue('energy=%f' % en)
bfs = getbasis(mol,bf_name)
delta = 0.1
c_range = 5.0
#setting for visualize
x = np.arange(-1*c_range,c_range,delta)
y = np.arange(-1*c_range,c_range,delta)
X,Y = p.meshgrid(x,y)
Z = np.zeros((len(X),len(Y)))
Z_2 = np.zeros((len(X),len(Y)))
#print C matrix
#print "C=",orbs
#bounding = self.orb_bound_box.GetValue()
#calculate wave function
for k,bf in enumerate(bfs.bfs):
for i,x1 in enumerate(x):
for j,y1 in enumerate(y):
#calculate wave function
#basic function multiply
#if bounding == "boundary":
Z[i,j] += bf.amp(x1,y1,z_pos) * orbs[k,0]
#else:
# Z[i,j] += bf.amp(x1,y1,z_pos) * orbs[k,1]
if self.log == 1:
with open('calc.log','a') as f_handle:
f_handle.write("\norbs is\n")
np.savetxt(f_handle,orbs)
f_handle.write("\norbe is\n")
np.savetxt(f_handle,orbe)
##### visualize #####
fig = p.figure()
ax = Axes3D(fig)
#ax.plot_surface(X,Y,Z)
ax.plot_wireframe(X,Y,Z,color = 'b')
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
p.show()
print('Esperando o ww3 terminar em alguma máquina')
time.sleep(60)
# ---------------------
# Definindo Diretorios
savedir = '/home/operador/ondogramas/ww3_418/ww3' + mod + '/ww3ant' + str(
cyc) + '/'
savedir2 = '/home/operador/grads/produtos_operantar/' + str(cyc) + 'hmg/'
# ----------------------------------------
# Extraindo as variaveis da saida do WW3
nc_fid = Dataset(nc_f, 'r')
lat = nc_fid.variables['latitude'][:]
lon = nc_fid.variables['longitude'][:]
lon = lon - 360
lon_grid, lat_grid = plab.meshgrid(lon, lat)
grid = pr.geometry.GridDefinition(lats=lat_grid, lons=lon_grid)
hs = nc_fid.variables['hs'][:]
dire = nc_fid.variables['dir'][:]
dp = nc_fid.variables['dp'][:]
u_wnd = nc_fid.variables['uwnd'][:]
v_wnd = nc_fid.variables['vwnd'][:]
prg = np.size(u_wnd)
freqpeak = nc_fid.variables['fp'][:] #wave peak frequency
perpeak = 1 / freqpeak
# Pontos Derrota Ilhas Órcades:
lat_pd = [-62.50, -62.167, -61.833, -61.50, -61.167, -60.833, -60.50]
lon_pd = [-58.00, -56.00, -54.00, -52.00, -50.00, -48.00, -46.00]
swath = pr.geometry.SwathDefinition(lons=lon_pd, lats=lat_pd)
def jointplot(X,Y,xlabel=None,ylabel=None,binsim=40,binsh=20,contour=True):
"""
Plots the joint distribution of posteriors for X1 and X2, including the 1D
histograms showing the median and standard deviations.
The work that went in creating this nice method is shown, step by step, in
the ipython notebook "error contours.ipynb". Sources of inspiration:
- http://python4mpia.github.io/intro/quick-tour.html
- http://stackoverflow.com/questions/12301071/multidimensional-confidence-intervals
Usage:
>>> jointplot(M.rtr.trace(),M.mdot.trace(),xlabel='$\log \ r_{\\rm tr}$', ylabel='$\log \ \dot{m}$')
gives the following plot.
.. figure:: ../figures/jointplot.png
:scale: 100 %
:alt: Two-dimensional kernel density distribution.
Two-dimensional kernel density distribution, along with one-dimensional histograms of each distribution.
"""
import scipy.stats
# Generates 2D histogram for image
histt, xt, yt = numpy.histogram2d(X, Y, bins=[binsim,binsim], normed=False)
histt = numpy.transpose(histt) # Beware: numpy switches axes, so switch back.
# assigns correct proportions to subplots
fig=pylab.figure()
gs = pylab.GridSpec(2, 2, width_ratios=[3,1], height_ratios=[1,3], wspace=0.001, hspace=0.001)
con=pylab.subplot(gs[2])
histx=pylab.subplot(gs[0], sharex=con)
histy=pylab.subplot(gs[3], sharey=con)
# Image
con.imshow(histt,extent=[xt[0],xt[-1], yt[0],yt[-1]],origin='lower',cmap=pylab.cm.gray_r,aspect='auto')
# Overplot with error contours 1,2 sigma
if contour==True:
pdf = scipy.stats.gaussian_kde([X, Y])
x,y = pylab.meshgrid(xt,yt)
z = numpy.array(pdf.evaluate([x.flatten(),y.flatten()])).reshape(x.shape)
# the [61,15] values were obtained by trial and error until the joint confidence
# contours matched the confidence intervals from the individual X,Y
s=scipy.stats.scoreatpercentile(pdf(pdf.resample(1000)), [61,15])
cs=con.contour(x,y,z, levels=s, extent=[x[0],x[-1], y[0],y[-1]], linestyles=['-','-','-'], colors=['black','blue'])
# use dictionary in order to assign your own labels to the contours.
#fmtdict = {s[0]:r'$1\sigma$',s[1]:r'$2\sigma$'}
#con.clabel(cs, fmt=fmtdict, inline=True, fontsize=20)
if xlabel!=None: con.set_xlabel(xlabel)
if ylabel!=None: con.set_ylabel(ylabel)
# X-axis histogram
histx.hist(X, binsh, histtype='stepfilled',facecolor='lightblue')
pylab.setp(histx.get_xticklabels(), visible=False) # no X label
pylab.setp(histx.get_yticklabels(), visible=False) # no Y label
# Vertical lines with median and 1sigma confidence
yax=histx.set_ylim()
histx.plot([numpy.median(X),numpy.median(X)],[yax[0],yax[1]],'k-',linewidth=2) # median
xsd=scipy.stats.scoreatpercentile(X, [15.87,84.13])
histx.plot([xsd[0],xsd[0]],[yax[0],yax[1]],'k--') # -1sd
histx.plot([xsd[-1],xsd[-1]],[yax[0],yax[1]],'k--') # +1sd
# Y-axis histogram
histy.hist(Y, binsh, histtype='stepfilled', orientation='horizontal',facecolor='lightyellow')
pylab.setp(histy.get_yticklabels(), visible=False) # no Y label
pylab.setp(histy.get_xticklabels(), visible=False) # no X label
# Vertical lines with median and 1sigma confidence
xax=histy.set_xlim()
histy.plot([xax[0],xax[1]],[numpy.median(Y),numpy.median(Y)],'k-',linewidth=2) # median
ysd=scipy.stats.scoreatpercentile(Y, [15.87,84.13])
histy.plot([xax[0],xax[1]],[ysd[0],ysd[0]],'k--') # -1sd
histy.plot([xax[0],xax[1]],[ysd[-1],ysd[-1]],'k--') # +1sd
#Synaptic parameters, corresponding to a NetCon synapse built into NEURON
synapseParameters = {
'idx' : 0, # insert synapse on index "0", the soma
'e' : 0., # reversal potential of synapse
'syntype' : 'Exp2Syn', # conductance based double-exponential synapse
'tau1' : 1.0, # Time constant, rise
'tau2' : 1.0, # Time constant, decay
'weight' : 0.05, # Synaptic weight
'record_current' : True, # Will enable synapse current recording
}
#Generate the grid in xz-plane over which we calculate local field potentials
x = pl.linspace(-50, 50, 11)
z = pl.linspace(-50, 50, 11)
X, Z = pl.meshgrid(x, z)
y = pl.zeros(X.size)
#define parameters for extracellular recording electrode, using optional method
electrodeParameters = {
'sigma' : 0.3, # extracellular conductivity
'x' : X.reshape(-1), # x,y,z-coordinates of contact points
'y' : y,
'z' : Z.reshape(-1),
'method' : 'som_as_point', #treat soma segment as sphere source
}
################################################################################
# Main simulation procedure, setting up extracellular electrode, cell, synapse
################################################################################
def plot_chi2(model, data, fit_result=None, limits=None,
disregard_correlation=False,
npoints=(100, 100), stddev_max=3, fmt='%d',
linewidth=2):
"""Plot chi**2 contours and linear fit approxiation
Note that chi**2 is related to likelihood in the following way:
L = exp(-(1/2)*chi**2)
This means that log(L) and chi**2 are identical up to a factor (-2).
"""
import matplotlib.pylab as plt
# Unpack model and fit result
f, p, c = model
# popt, pcov
if disregard_correlation:
fit_result[1] = set_off_diagonal_to_zero(fit_result[1])
# If no limits are given, compute a good choice from fit_result
# Set up a grid of points in parameter space
p1_lim = limits[0]
p2_lim = limits[1]
p1 = np.linspace(p1_lim[0], p1_lim[1], npoints[0])
p2 = np.linspace(p2_lim[0], p2_lim[1], npoints[1])
P1, P2 = plt.meshgrid(p1, p2)
# Compute chi**2 (called chi2) for each grid point
# Looping can probably be avoided, but I don't know how.
x2 = np.empty_like(P1) # real chi**2
x2lin = np.empty_like(P1) # linear chi**2 approximation
for i1 in range(p1.size):
for i2 in range(p2.size):
# Note the weird numpy indexing order.
# i2,i1 seems wrong, but is correct:
# TODO: implement
pass
# x2 [i2, i1] = chi2 ((p1[i1], p2[i2]), c, f, data)
# x2lin[i2, i1] = chi2_lin((p1[i1], p2[i2]), fit_result)
# Set the most likely point to chi**2 = 0
x2 -= x2.min()
# Use sqrt scale
# x2 = np.sqrt(x2)
# x2lin = np.sqrt(x2lin)
# Plot likelihood as color landscape
x2_image = plt.pcolor(P1, P2, x2, vmin=0,
vmax=stddev_max ** 2, cmap='gray')
plt.colorbar()
# Add marker at the minimum
plt.plot(fit_result[0][0], fit_result[0][1],
marker='*', markersize=12, color='r')
# Add contour of real likelihood
contour_levels = np.arange(1, stddev_max + 1) ** 2
x2_cont = plt.contour(P1, P2, x2, contour_levels,
colors='r', linewidths=linewidth)
plt.clabel(x2_cont, inline=1, fontsize=10,
linewidths=linewidth, fmt=fmt)
# Overplot linear approximation as contours
x2lin_cont = plt.contour(P1, P2, x2lin, contour_levels,
colors='b', linewidths=linewidth)
plt.clabel(x2lin_cont, inline=1, fontsize=10,
linewidths=linewidth, fmt=fmt)
# Add colorbar and labels
# axcb = plt.colorbar()
# axcb.set_label(r'$\chi^2$', size=15)
plt.xlabel('Parameter P1')
plt.ylabel('Parameter P2')
plt.axis(p1_lim + p2_lim)
def show(
self,
typ="s1",
k=0,
N=-1,
M=-1,
kmax=1000,
seuildb=50,
titre="SHC",
xl=True,
yl=True,
fontsize=14,
dB=True,
cmap=plt.cm.hot_r,
anim=True,
):
""" show coeff
Parameters
----------
typ : string
default ('s1')
's1' shape 1 (Nf , N , M )
's2' shape 2 (Nf , N*M )
's3' shape 3 (Nf , K ) T ( K x 2 )
k : integer
frequency index default 0
N, M = maximal value for degree, mode respectively
(not to be defined if 's2' or 's3')
"""
fa = np.linspace(self.fmin, self.fmax, self.Nf)
if typ == "s1":
if N == -1:
N = self.N1
if M == -1:
M = self.M1
Mg, Ng = plt.meshgrid(np.arange(M), np.arange(N))
if anim:
fig = plt.gcf()
ax = fig.gca()
v = np.abs(self.s1[k, 0:N, 0:M])
if dB:
v = 20 * np.log10(v)
p = plt.scatter(Mg, Ng, c=v, s=30, cmap=cmap, linewidth=0, vmin=-seuildb, vmax=0)
plt.colorbar()
plt.draw()
else:
v = np.abs(self.s1[k, 0:N, 0:M])
if dB:
vdB = 20 * np.log10(v + 1e-15)
plt.scatter(Mg, Ng, c=vdB, s=30, cmap=cmap, linewidth=0, vmin=-seuildb, vmax=0)
plt.title(titre)
plt.colorbar()
else:
plt.scatter(Mg, Ng, c=v, s=30, cmap=cmap, linewidth=0)
plt.title(titre)
plt.colorbar()
if xl:
plt.xlabel("m", fontsize=fontsize)
if yl:
plt.ylabel("n", fontsize=fontsize)
if typ == "s2":
if np.shape(self.s2)[1] <= 1:
plt.plot(fa, 10 * np.log10(abs(self.s2[:, 0])))
else:
K = np.shape(self.s2)[1]
kmax = min(kmax, K)
db = 20 * np.log10(abs(self.s2[:, 0:kmax] + 1e-15))
col = 1 - (db > -seuildb) * (db + seuildb) / seuildb
#
# gray
#
# pcolor(np.arange(K+1)[0:kmax],self.fa,col,cmap=cm.gray_r,vmin=0.0,vmax=1.0)
#
# color
#
plt.pcolor(np.arange(K + 1)[0:kmax], fa, col, cmap=plt.cm.hot, vmin=0.0, vmax=1.0)
if xl:
plt.xlabel("index", fontsize=fontsize)
if yl:
plt.ylabel("Frequency (GHz)", fontsize=fontsize)
if typ == "s3":
if np.shape(self.s3)[1] <= 1:
plt.plot(fa, 10 * np.log10(abs(self.s3[:, 0])))
else:
K = np.shape(self.s3)[1]
kmax = min(kmax, K)
db = 20 * np.log10(abs(self.s3[:, 0:kmax] + 1e-15))
col = 1 - (db > -seuildb) * (db + seuildb) / seuildb
plt.pcolor(np.arange(K + 1)[0:kmax], fa, col, cmap=plt.cm.hot, vmin=0.0, vmax=1.0)
if xl:
plt.xlabel("index", fontsize=fontsize)
if yl:
plt.ylabel("Frequency (GHz)", fontsize=fontsize)
# echelle=[str(0), str(-10), str(-20), str(-30), str(-40), str(-50)]
if (typ == "s2") | (typ == "s3"):
echelle = [
str(0),
str(-seuildb + 40),
str(-seuildb + 30),
str(-seuildb + 20),
str(-seuildb + 10),
str(-seuildb),
]
cbar = plt.colorbar(ticks=[0, 0.2, 0.4, 0.6, 0.8, 1])
cbar.ax.set_yticklabels(echelle)
cbar.ax.set_ylim(1, 0)
for t in cbar.ax.get_yticklabels():
t.set_fontsize(fontsize)
plt.xticks(fontsize=fontsize)
plt.yticks(fontsize=fontsize)
plt.title(titre, fontsize=fontsize + 2)
x0 = -0.5
for j in range(0,100):
x = x0+j*0.01
eps = 0.006
if (y <= sq3*(x+0.25) and x<0.) or (y<-sq3*(x-0.25) and x >= 0):
grid[i,j] = 0
else: if(y <= sq3/4. + 0.01): V[i,j] = 0.0 # Triangle tip
for iter in range(1,Niter): # Iterate
if(iter%50 == 0): print('Working, iteration', iter, 'out of', Niter)
contour() # keep one side at 1000V
for i in range(1, Nmax-2):
for j in range(1,Nmax-2):
if grid[i,j]==0.: # interior points
V[i,j] = 0.25*(V[i+1,j]+V[i-1,j]+V[i,j+1]+V[i,j-1])
x = range(0, Nmax-1, 2)
y = range(0, Nmax, 2) # Plot every other point
X, Y = p.meshgrid(x,y)
def functz(V): # Function returns V(x, y)
z = V[X,Y]
return z
Z = functz(V)
fig = p.figure() # Create figure
ax = Axes3D(fig) # Plot axes
ax.plot_wireframe(X, Y, Z, color = 'r') # Red wireframe
ax.set_title('Potential within Triangle (Rotatable)')
ax.set_xlabel('X') # Label axes
ax.set_ylabel('Y')
ax.set_zlabel('Potential')
p.show() # Display fig
for i in range(1, N - 1):
u[i][j][2] = 2. * u[i][j][1] - u[i][j][0] + ratio * (
u[i + 1][j][1] + u[i - 1][j][1] + u[i][j + 1][1] +
u[i][j - 1][1] - 4. * u[i][j][1])
u[:][:][0] = u[:][:][1] # Reset past
u[:][:][1] = u[:][:][2] # Reset present
for j in range(0, N):
for i in range(0, N):
v[i][j] = u[i][j][2] # Convert to 2D for matplotlib
return v
v = vibration(tim)
x1 = range(0, N)
y1 = range(0, N)
X, Y = p.meshgrid(x1, y1)
def functz(v):
z = v[X, Y]
return z
Z = functz(v)
fig = p.figure()
ax = Axes3D(fig)
ax.plot_wireframe(X, Y, Z, color='r')
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_zlabel('u(x,y)')
p.show()
tt = time.time()
analysis.run()
print "Elapsed time: ", time.time()-tt, "seconds"
raw_data = {}
X = set()
Y = set()
for c in analysis.driver.recorders[0].get_iterator():
raw_data[(c['paraboloid.x'],c['paraboloid.y'])] = c['paraboloid.f_xy']
X.add(c['paraboloid.x'])
Y.add(c['paraboloid.y'])
X = sorted(list(X))
Y = sorted(list(Y))
xi, yi = p.meshgrid(X, Y)
zi = []
for x in X:
row = []
for y in Y:
row.append(raw_data[(x, y)])
zi.append(row)
zi = array(zi)
fig = p.figure()
ax = p3.Axes3D(fig)
ax.plot_surface(xi, yi, zi, rstride=1, cstride=1, cmap=cm.jet, linewidth=0)
p.show()
# find probability of that acceleration actually occuring in a flying fly
def find_alpha (arr, n, bins):
alpha = np.zeros(arr.shape)
for i in range(arr.shape[0]):
for j in range(arr.shape[1]):
index = np.argmin( np.abs(bins - arr[i,j]) )
a = n[index]
alpha[i,j] = a
return alpha
mesh_x,mesh_y = pylab.meshgrid( np.linspace(-.01,-.0001,300), np.linspace(.0001,.1,300) )
c = accel(mesh_x, mesh_y)
alpha = find_alpha(c, n, bins)
alpha = alpha - alpha.max()/2
alpha = np.sin(np.pi/2 * (alpha / alpha.max()) )
cm = colormap.ScalarMappable(cmap='gray')
rgb = cm.to_rgba(-1*np.exp(c))
rgba = rgb
['u', 'spl', 'dt', 'dx', 'fac', 'epsilon', 'j_start',
'j_end', 'num_x', 't_steps_betw_plt'],
type_converters=converters.blitz)
spl_ma = np.ma.array(spl, mask=np.isnan(spl), fill_value=0)
cmap = p.cm.ocean
cmap.set_bad(color='k',alpha=1)
#-- X coordinates
x = list(range(0, num_x, x_skip))
#-- Y coordinates
y = list(range(0, mt, t_steps_betw_plt))
#-- 2D grids with X and Y coordinates
X, Y = p.meshgrid(x, y)
def functz(spl):
z = spl[X, Y]
return z
#s = surf(x, y, 20*spl)
#fig = p.figure(1) # create figure
#fig.clf()
#ax = Axes3D(fig) # plot axes
#ax.plot_surface(X*dx*x_skip, Y*dt*t_steps_betw_plt, spl[X, Y],
# cmap=p.cm.bone)# color = 'r') # red wireframe
#ax.plot_surface(X*dx*x_skip, Y*dt*t_steps_betw_plt, spl[X, Y],
# cmap=p.cm.bone)# color = 'r') # red
#ax.set_xlabel('Positon') # label axes
#ax.set_ylabel('Time')
#ax.set_zlabel('Disturbance')
def meshgrid_of(A):
x = range(np.shape(A)[0])
y = range(np.shape(A)[1])
xx, yy = p.meshgrid(x, y)
return xx, yy
def show(self,
typ='s1',
k=0,
N=-1,
M=-1,
kmax=1000,
seuildb=50,
titre='SHC',
xl=True,
yl=True,
fontsize=14,
dB=True,
cmap=plt.cm.hot_r,
anim=True):
""" show coeff
Parameters
----------
typ : string
default ('s1')
's1' shape 1 (Nf , N , M )
's2' shape 2 (Nf , N*M )
's3' shape 3 (Nf , K ) T ( K x 2 )
k : integer
frequency index default 0
N, M = maximal value for degree, mode respectively
(not to be defined if 's2' or 's3')
"""
fa = np.linspace(self.fmin, self.fmax, self.Nf)
if typ == 's1':
if N == -1:
N = self.N1
if M == -1:
M = self.M1
Mg, Ng = plt.meshgrid(np.arange(M), np.arange(N))
if anim:
fig = plt.gcf()
ax = fig.gca()
v = np.abs(self.s1[k, 0:N, 0:M])
if dB:
v = 20 * np.log10(v)
p = plt.scatter(Mg,
Ng,
c=v,
s=30,
cmap=cmap,
linewidth=0,
vmin=-seuildb,
vmax=0)
plt.colorbar()
plt.draw()
else:
v = np.abs(self.s1[k, 0:N, 0:M])
if dB:
vdB = 20 * np.log10(v + 1e-15)
plt.scatter(Mg,
Ng,
c=vdB,
s=30,
cmap=cmap,
linewidth=0,
vmin=-seuildb,
vmax=0)
plt.title(titre)
plt.colorbar()
else:
plt.scatter(Mg, Ng, c=v, s=30, cmap=cmap, linewidth=0)
plt.title(titre)
plt.colorbar()
if xl:
plt.xlabel('m', fontsize=fontsize)
if yl:
plt.ylabel('n', fontsize=fontsize)
if typ == 's2':
if np.shape(self.s2)[1] <= 1:
plt.plot(fa, 10 * np.log10(abs(self.s2[:, 0])))
else:
K = np.shape(self.s2)[1]
kmax = min(kmax, K)
db = 20 * np.log10(abs(self.s2[:, 0:kmax] + 1e-15))
col = 1 - (db > -seuildb) * (db + seuildb) / seuildb
#
#gray
#
#pcolor(np.arange(K+1)[0:kmax],self.fa,col,cmap=cm.gray_r,vmin=0.0,vmax=1.0)
#
#color
#
plt.pcolor(np.arange(K + 1)[0:kmax],
fa,
col,
cmap=plt.cm.hot,
vmin=0.0,
vmax=1.0)
if xl:
plt.xlabel('index', fontsize=fontsize)
if yl:
plt.ylabel('Frequency (GHz)', fontsize=fontsize)
if typ == 's3':
if np.shape(self.s3)[1] <= 1:
plt.plot(fa, 10 * np.log10(abs(self.s3[:, 0])))
else:
K = np.shape(self.s3)[1]
kmax = min(kmax, K)
db = 20 * np.log10(abs(self.s3[:, 0:kmax] + 1e-15))
col = 1 - (db > -seuildb) * (db + seuildb) / seuildb
plt.pcolor(np.arange(K + 1)[0:kmax],
fa,
col,
cmap=plt.cm.hot,
vmin=0.0,
vmax=1.0)
if xl:
plt.xlabel('index', fontsize=fontsize)
if yl:
plt.ylabel('Frequency (GHz)', fontsize=fontsize)
#echelle=[str(0), str(-10), str(-20), str(-30), str(-40), str(-50)]
if (typ == 's2') | (typ == 's3'):
echelle = [
str(0),
str(-seuildb + 40),
str(-seuildb + 30),
str(-seuildb + 20),
str(-seuildb + 10),
str(-seuildb)
]
cbar = plt.colorbar(ticks=[0, 0.2, 0.4, 0.6, 0.8, 1])
cbar.ax.set_yticklabels(echelle)
cbar.ax.set_ylim(1, 0)
for t in cbar.ax.get_yticklabels():
t.set_fontsize(fontsize)
plt.xticks(fontsize=fontsize)
plt.yticks(fontsize=fontsize)
plt.title(titre, fontsize=fontsize + 2)
import numpy as np
from scipy.stats import multivariate_normal as mvn
import matplotlib.pylab as plt
from mpl_toolkits.mplot3d import Axes3D
from matplotlib.colors import LightSource
from matplotlib import cm
m = np.array([0, 0])
covs = [np.eye(2), np.array([[.5, -1.], [-1., 3]]), np.array([[2, 1], [1, 2]])]
#%%
x = np.linspace(-5, 5, 100)
y = np.linspace(-5, 5, 100)
xv, yv = plt.meshgrid(x, y)
zs = []
for c in covs:
zs.append(
mvn.pdf(np.c_[xv.flatten(), yv.flatten()], mean=m,
cov=c).reshape(xv.shape))
#%%
#ls = LightSource(270, 45)
fig, axs = plt.subplots(1,
3,
subplot_kw=dict(projection='3d'),
figsize=(11, 3))
for ax, z, c in zip(axs, zs, covs):
# rgb = ls.shade(z, cmap=cm.gist_earth, vert_exag=0.1, blend_mode='soft')
surf = ax.plot_surface(
xv,
def jointplot(X,
Y,
xlabel=None,
ylabel=None,
binsim=40,
binsh=20,
contour=True):
"""
Plots the joint distribution of posteriors for X1 and X2, including the 1D
histograms showing the median and standard deviations.
The work that went in creating this nice method is shown, step by step, in
the ipython notebook "error contours.ipynb". Sources of inspiration:
- http://python4mpia.github.io/intro/quick-tour.html
- http://stackoverflow.com/questions/12301071/multidimensional-confidence-intervals
Usage:
>>> jointplot(M.rtr.trace(),M.mdot.trace(),xlabel='$\log \ r_{\\rm tr}$', ylabel='$\log \ \dot{m}$')
gives the following plot.
.. figure:: ../figures/jointplot.png
:scale: 100 %
:alt: Two-dimensional kernel density distribution.
Two-dimensional kernel density distribution, along with one-dimensional histograms of each distribution.
"""
import scipy.stats
# Generates 2D histogram for image
histt, xt, yt = numpy.histogram2d(X,
Y,
bins=[binsim, binsim],
normed=False)
histt = numpy.transpose(
histt) # Beware: numpy switches axes, so switch back.
# assigns correct proportions to subplots
fig = pylab.figure()
gs = pylab.GridSpec(2,
2,
width_ratios=[3, 1],
height_ratios=[1, 3],
wspace=0.001,
hspace=0.001)
con = pylab.subplot(gs[2])
histx = pylab.subplot(gs[0], sharex=con)
histy = pylab.subplot(gs[3], sharey=con)
# Image
con.imshow(histt,
extent=[xt[0], xt[-1], yt[0], yt[-1]],
origin='lower',
cmap=pylab.cm.gray_r,
aspect='auto')
# Overplot with error contours 1,2 sigma
if contour == True:
pdf = scipy.stats.gaussian_kde([X, Y])
x, y = pylab.meshgrid(xt, yt)
z = numpy.array(pdf.evaluate([x.flatten(),
y.flatten()])).reshape(x.shape)
# the [61,15] values were obtained by trial and error until the joint confidence
# contours matched the confidence intervals from the individual X,Y
s = scipy.stats.scoreatpercentile(pdf(pdf.resample(1000)), [61, 15])
cs = con.contour(x,
y,
z,
levels=s,
extent=[x[0], x[-1], y[0], y[-1]],
linestyles=['-', '-', '-'],
colors=['black', 'blue'])
# use dictionary in order to assign your own labels to the contours.
#fmtdict = {s[0]:r'$1\sigma$',s[1]:r'$2\sigma$'}
#con.clabel(cs, fmt=fmtdict, inline=True, fontsize=20)
if xlabel != None: con.set_xlabel(xlabel)
if ylabel != None: con.set_ylabel(ylabel)
# X-axis histogram
histx.hist(X, binsh, histtype='stepfilled', facecolor='lightblue')
pylab.setp(histx.get_xticklabels(), visible=False) # no X label
pylab.setp(histx.get_yticklabels(), visible=False) # no Y label
# Vertical lines with median and 1sigma confidence
yax = histx.set_ylim()
histx.plot([numpy.median(X), numpy.median(X)], [yax[0], yax[1]],
'k-',
linewidth=2) # median
xsd = scipy.stats.scoreatpercentile(X, [15.87, 84.13])
histx.plot([xsd[0], xsd[0]], [yax[0], yax[1]], 'k--') # -1sd
histx.plot([xsd[-1], xsd[-1]], [yax[0], yax[1]], 'k--') # +1sd
# Y-axis histogram
histy.hist(Y,
binsh,
histtype='stepfilled',
orientation='horizontal',
facecolor='lightyellow')
pylab.setp(histy.get_yticklabels(), visible=False) # no Y label
pylab.setp(histy.get_xticklabels(), visible=False) # no X label
# Vertical lines with median and 1sigma confidence
xax = histy.set_xlim()
histy.plot([xax[0], xax[1]],
[numpy.median(Y), numpy.median(Y)],
'k-',
linewidth=2) # median
ysd = scipy.stats.scoreatpercentile(Y, [15.87, 84.13])
histy.plot([xax[0], xax[1]], [ysd[0], ysd[0]], 'k--') # -1sd
histy.plot([xax[0], xax[1]], [ysd[-1], ysd[-1]], 'k--') # +1sd
# for j in range(y_edge2+1, 90):
# V[i,j] = 0.25*(V[i+1,j]+V[i-1,j]+V[i,j+1]+V[i,j-1])
return V[i,j]
if __name__ == '__main__':
print("Initializing")
Nmax = 100; Niter = 70; V = zeros((Nmax+1, Nmax+1), float)
max_range = 90 # Required: max_range < Nmax
print("Working hard, wait for the figure while I count to 60")
voltage(100, 100, 100, 100, 30, 60, 30, 60)
finite_difference(V, 30, 60, 30, 60, max_range)
x = range(0, max_range, 2); y = range(0, max_range, 2)
X, Y = plt.meshgrid(x,y)
Z = functz(V)
fig = plt.figure()
ax = Axes3D(fig)
ax.plot_wireframe(X, Y, Z, color='r')
ax.contour(X, Y, Z, offset=0)
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Potential')
plt.show()
print("Espera mientras se construye la gráfica, cuenta hasta ...")
for k in range(0, Nmax - 1):
V[k, 0] = 100.0
for iter in range(Niter):
if iter % 10 == 0: print(iter)
for i in range(1, Nmax - 2):
for j in range(1, Nmax - 2):
V[i, j] = 0.25 * (V[i + 1, j] + V[i - 1, j] + V[i, j + 1] +
V[i, j - 1])
x = range(0, Nmax - 1, 2)
y = range(0, 50, 2)
X, Y = plt.meshgrid(x, y)
def functz(V):
z = V[X, Y]
return z
Z = functz(V)
fig = plt.figure()
ax = Axes3D(fig)
#surf = ax.plot_wireframe(X, Y, Z)
surf = ax.plot_surface(X,
Y,
Z,
# Campo electrico de una particula puntual cargada
def Electric(r, rp, q):
E = 1 / (4 * np.pi * eps0) * q * (r - rp) / np.linalg.norm(r - rp) ** 3
return E
# Permitividad del vacio
eps0 = 8.85418e-12
# Resolucion de graficas
Nres = 25
# Coordenada X
Xarray = np.linspace(0, 10, Nres)
# Coordenada Y
Yarray = np.linspace(0, 10, Nres)
# Construccion de la cuadricula
X, Y = plt.meshgrid(Xarray, Yarray)
# CONSTRUCCION DE CAMPO E Y POTENCIAL PHI, PARTICULA 1
# Carga electrica
q1 = -1
# Posicion particula
rp1 = np.array([4, 4])
# Incializacion Potencial Electrico
phi1 = np.zeros((Nres, Nres))
# Incializacion Campo Electrico
E1x = np.ones((Nres, Nres))
E1y = np.ones((Nres, Nres))
# Calculo Potencial Electrico y Campo Electrico
for i in xrange(Nres):
for j in xrange(Nres):
r = np.array([Xarray[i], Yarray[j]])