Please tell me how to convert numpy to sympy.
unit vector
not numpy. sympy only
import numpy as np
x = (2,0,0)
print("#",x)
y = np.array(list(x))
z = y/np.linalg.norm(y.astype('float'))
print("#",tuple(z))
# (2, 0, 0)
# (1.0, 0.0, 0.0)
I tried:
from sympy import *
def myUnitVector(myPoint3D):
myL=myPoint3D.distance((0, 0))
return Point3D(myPoint3D.x/myL,myPoint3D.y/myL,myPoint3D.z/myL)
x = (1,1,1)
print("#",Point3D(x))
print("#",myUnitVector(Point3D(x)))
print("#",myUnitVector(Point3D(x)).evalf())
print("#",myUnitVector(Point3D(x)).distance((0, 0)))
print("#",myUnitVector(Point3D(x)).evalf().distance((0, 0)))
# Point3D(1, 1, 1)
# Point3D(sqrt(3)/3, sqrt(3)/3, sqrt(3)/3)
# Point3D(0.577350269189626, 0.577350269189626, 0.577350269189626)
# 1
# 1.00000000000000
Related
I want to fit some data to obtain the minimum (both x and y), but when I use UnivariateSpline it will generate an error: 'ValueError: x must be increasing if s > 0'
This is my code:
import matplotlib.pyplot as plt
from scipy.interpolate import UnivariateSpline
import numpy as np
import pandas as pd
list_dist=pd.read_csv('C:/.../dist.txt')
dist=list_dist['Distanze']
ar_dist=np.array(dist)
list_energy=pd.read_csv('C:/.../energy.txt')
energy=list_energy['Energie']
ar_energy=np.array(energy)
x = ar_dist
y = ar_energy
print(x)
print(y)
s = UnivariateSpline(x, y)
xs = np.linspace(0, 10, 10000)
ys = s(xs)
ys_min=np.min(ys)
ys_min_pos=np.argmin(ys)
xs_min=xs[ys_min_pos]
print('UnivariateSpline: ', '\n', 'dist_min: ',xs_min , '\t', 'en_min: ', '\t',ys_min)
plt.plot(x, y, 'o')
plt.plot(xs, ys)
plt.show()
I have a function f(x,y) where t is a parameter. I'm trying to plot the function where t = 1 for x and y values ranging from -5 to 5. The plot doesn't render.
import sympy as sp
import numpy as np
import matplotlib.pyplot as plt
%matplotlib notebook
C = sv.CoordSys3D("")
x, y, z = C.base_scalars()
t = sp.symbols("t")
f = sp.sin(2*sp.pi*t)*sp.exp(-(x-3*sp.sin(sp.pi*t))**2 -(y-3*sp.cos(sp.pi*t))**2)
fig = plt.figure(figsize=(6, 6))
ax = fig.add_subplot(projection='3d')
X = np.linspace(-5,5,100)
Y = np.linspace(-5,5,100)
xvals, yvals = np.meshgrid(X,Y)
zvals = sp.lambdify((x,y),f.subs(t,1),"numpy")(xvals,yvals)
ax.plot_surface(xvals,yvals,zvals)
plt.show()
I get an error 'int' object has no attribute 'ndim' which I don't know how to solve.
The problem is that when you execute f.subs(t,1) it returns a number (zero in this case). So, f=0 is the expression that you are going to lambdify. Let's see the function generated by lambdify:
import inspect
print(inspect.getsource(sp.lambdify((x,y),f.subs(t,1),"numpy")))
# def _lambdifygenerated(Dummy_25, Dummy_24):
# return 0
So, no matter the values and shape of xvals and yvals, that numerical function will always return 0, which is an integer number.
However, ax.plot_surface requires zvals to have the same shape as xvals or yval. Luckily, we can easily fix that with a simple if statement:
import sympy as sp
import sympy.vector as sv
import numpy as np
import matplotlib.pyplot as plt
C = sv.CoordSys3D("")
x, y, z = C.base_scalars()
t = sp.symbols("t")
f = sp.sin(2*sp.pi*t)*sp.exp(-(x-3*sp.sin(sp.pi*t))**2 -(y-3*sp.cos(sp.pi*t))**2)
fig = plt.figure(figsize=(6, 6))
ax = fig.add_subplot(projection='3d')
X = np.linspace(-5,5,100)
Y = np.linspace(-5,5,100)
xvals, yvals = np.meshgrid(X,Y)
zvals = sp.lambdify((x,y),f.subs(t,1),"numpy")(xvals,yvals)
# if zvals is just a number, create a proper matrix
if not isinstance(zvals, np.ndarray):
zvals = zvals * np.ones_like(xvals)
ax.plot_surface(xvals,yvals,zvals)
plt.show()
The fact that this doesn't render is bug in lambdify that it doesn't work well for constant expressions.
Your real problem though is that the expression you are trying to plot is just zero:
In [5]: f
Out[5]:
2 2
- (x_ - 3⋅sin(π⋅t)) - (y_ - 3⋅cos(π⋅t))
ℯ ⋅sin(2⋅π⋅t)
In [6]: f.subs(t, 1)
Out[6]: 0
In order to create a 3d plot using plot_surface and wireframe I wrote this (looking here around)
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from matplotlib import rc
from matplotlib.ticker import MultipleLocator
import matplotlib.ticker as mticker
import numpy as np
from matplotlib.ticker import FormatStrFormatter
def log_tick_formatter(val, pos=None):
return f"10$^{{{int(val)}}}$"
data=np.genfromtxt('jpdfomegal2_90.dat')
x_len= len(np.unique(data[:, 0]))
y_len= len(np.unique(data[:, 1]))
X = data[:, 0].reshape(x_len, y_len)
Y = data[:, 1].reshape(x_len, y_len)
Z = data[:, 2].reshape(x_len, y_len)
#identify lowest non-negative Z value Zmin>0
Zmin = np.where(Z > 0, Z, np.inf).min()
Zmax = Z.max()
#and substitute zero with a slightly lower value than Zmin
Z[Z==0] = 0.9 * Zmin
#log transformation because the conversion in 3D
#does not work well in matplotlib
Zlog = np.log10(Z)
rc('font',family='palatino')
rc('font',size=18)
fig = plt.figure(figsize=(12,8))
#ax = fig.add_subplot(projection='3d')
ax = Axes3D(fig)
ax.set_xlim3d(0,15)
ax.set_zlim3d(np.floor(np.log10(Zmin))-1, np.ceil(np.log10(10)))
ax.zaxis.set_major_formatter(mticker.FuncFormatter(log_tick_formatter))
ax.zaxis.set_major_locator(mticker.MaxNLocator(integer=True))
rc('font',family='palatino')
rc('font',size=18)
tmp_planes = ax.zaxis._PLANES
ax.zaxis._PLANES = ( tmp_planes[2], tmp_planes[3],
tmp_planes[0], tmp_planes[1],
tmp_planes[4], tmp_planes[5])
ax.set_xlabel('$\omega^2 /<\omega^2>$')
ax.xaxis.labelpad = 10
ax.yaxis.labelpad = 10
ax.set_ylabel('cos$(\omega,\lambda^2)$')
ax.zaxis.set_rotate_label(False) # disable automatic rotation
ax.zaxis.labelpad = 10
ax.set_zlabel('')
ax.view_init(elev=17, azim=-60)
ax.grid(False)
ax.xaxis.pane.set_edgecolor('black')
ax.yaxis.pane.set_edgecolor('black')
ax.zaxis.pane.set_edgecolor('black')
ax.xaxis.pane.fill = False
ax.yaxis.pane.fill = False
ax.zaxis.pane.fill = False
ax.xaxis.set_major_locator(MultipleLocator(2))
ax.yaxis.set_major_locator(MultipleLocator(0.2))
ax.zaxis.set_major_locator(MultipleLocator(1))
#not sure this axis scaling routine is really necessary
scale_x = 1
scale_y = 1
scale_z = 0.8
ax.get_proj = lambda: np.dot(Axes3D.get_proj(ax), np.diag([scale_x, scale_y, scale_z, 1]))
ax.contour(X, Y, np.log10(Z), 4, lw=0.1, colors="k", linestyles="--", offset=np.floor(np.log10(Zmin))-1)#-7)
surf = ax.plot_surface(X, Y, np.log10(Z), cmap="binary", lw=0.1,alpha=0.5)
ax.plot_wireframe(X, Y, np.log10(Z),linewidth=1,color='k')
ax.contour(X, Y, np.log10(Z), 4, lw=0.1, colors="k", linestyles="solid")
fig.colorbar(surf, shrink=0.5, aspect=20)
plt.tight_layout()
plt.savefig('jpdf_lambda2_90.png', bbox_inches='tight')
plt.show()
the problem is related to the "minorticks" along zaxis .. I obtain this :
but I would have this format and ticks in the axis
Does somebody clarify how to obtain it and as well I did not find a way to use the log scale in pyplot 3d
There's an open bug on log-scaling in 3D plots, and it looks like there won't be a fix any time soon.
You can use a matplotlib.ticker.FixedLocator to add the z-axis minor ticks, as shown below.
I didn't have your data, so I've plotted an arbitrary surface.
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from matplotlib import rc
from matplotlib.ticker import MultipleLocator, FixedLocator
import matplotlib.ticker as mticker
import numpy as np
from matplotlib.ticker import FormatStrFormatter
def log_tick_formatter(val, pos=None):
return f"10$^{{{int(val)}}}$"
x = np.linspace(1,15,15)
y = np.linspace(0,1,15)
X, Y = np.meshgrid(x, y)
Z = 1 + X**2 * Y**2
#identify lowest non-negative Z value Zmin>0
Zmin = np.where(Z > 0, Z, np.inf).min()
Zmax = Z.max()
#and substitute zero with a slightly lower value than Zmin
Z[Z==0] = 0.9 * Zmin
rc('font',family='palatino')
rc('font',size=18)
fig = plt.figure(figsize=(12,8))
ax = Axes3D(fig, auto_add_to_figure=False)
fig.add_axes(ax)
ax.set_xlim3d(0,15)
ax.set_zlim3d(np.floor(np.log10(Zmin))-1, np.ceil(np.log10(Zmax)))
ax.zaxis.set_major_formatter(mticker.FuncFormatter(log_tick_formatter))
tmp_planes = ax.zaxis._PLANES
ax.zaxis._PLANES = ( tmp_planes[2], tmp_planes[3],
tmp_planes[0], tmp_planes[1],
tmp_planes[4], tmp_planes[5])
ax.set_xlabel('$\omega^2 /<\omega^2>$')
ax.xaxis.labelpad = 10
ax.yaxis.labelpad = 10
ax.set_ylabel('cos$(\omega,\lambda^2)$')
ax.zaxis.set_rotate_label(False) # disable automatic rotation
ax.zaxis.labelpad = 10
ax.set_zlabel('')
ax.view_init(elev=17, azim=-60)
ax.grid(False)
ax.xaxis.pane.set_edgecolor('black')
ax.yaxis.pane.set_edgecolor('black')
ax.zaxis.pane.set_edgecolor('black')
ax.xaxis.pane.fill = False
ax.yaxis.pane.fill = False
ax.zaxis.pane.fill = False
ax.xaxis.set_major_locator(MultipleLocator(2))
ax.yaxis.set_major_locator(MultipleLocator(0.2))
ax.zaxis.set_major_locator(MultipleLocator(1))
# Z minor ticks
zminorticks = []
zaxmin, zaxmax = ax.get_zlim()
for zorder in np.arange(np.floor(zaxmin),
np.ceil(zaxmax)):
zminorticks.extend(np.log10(np.linspace(2,9,8)) + zorder)
ax.zaxis.set_minor_locator(FixedLocator(zminorticks))
#not sure this axis scaling routine is really necessary
scale_x = 1
scale_y = 1
scale_z = 0.8
ax.get_proj = lambda: np.dot(Axes3D.get_proj(ax), np.diag([scale_x, scale_y, scale_z, 1]))
ax.contour(X, Y, np.log10(Z), 4, colors="k", linestyles="--", offset=np.floor(np.log10(Zmin))-1)#-7)
surf = ax.plot_surface(X, Y, np.log10(Z), cmap="binary", lw=0.1,alpha=0.5)
ax.plot_wireframe(X, Y, np.log10(Z),linewidth=1,color='k')
ax.contour(X, Y, np.log10(Z), 4, colors="k", linestyles="solid")
fig.colorbar(surf, shrink=0.5, aspect=20)
# get a warning that Axes3D is incompatible with tight_layout()
# plt.tight_layout()
# for saving
# fig.savefig('log3d.png')
plt.show()
I may be misunderstanding how numpy.ma.masked_where() works, but it doesn't seem to work properly with matplotlib hist2d().
In the code below, I create an ndarray, mask it, then plot the original and masked ndarrays with matplotlib.pyplot.plot(). This works.
However, when I try to plot both with matplotlib.pyplot.hist2d(), the mask doesn't seem to be taken into account. I have tested this with matplot lib 1.3.1 and 3.2.1, and with numpy 1.18.5.
Any suggestions?
import math
import numpy as np
import time
import sys
import numpy.ma as ma
import matplotlib
import matplotlib.pyplot as plt
from scipy.stats import expon, poisson, uniform, norm
print(matplotlib.__version__, np.__version__)
nSiz=10000
maxx, maxy = 1.0, 10.0
x, y, z = uniform.rvs(scale=maxx, size=nSiz), uniform.rvs(scale=maxy, size=nSiz), norm.rvs(scale=1.0, size=nSiz)
binx, biny = np.linspace(0, maxx, 20), np.linspace(0, maxy, 20)
d = np.array([(xx, yy, zz) for xx, yy, zz in zip(x, y, z)], dtype=[('X', 'f4'), ('Y', 'f4'), ('Z', 'f4')])
print("Col titles: " + str(d.dtype.names))
dc = ma.masked_where(d['X'] < 0.5, d) # Mask data
fig, axx = plt.subplots(2, 2, figsize=(10, 10), dpi=300)
ax = axx.ravel()
ax[0].plot(d['X'], d['Y'], 'bv', ms=3)
ax[1].plot(dc['X'], dc['Y'], 'ro', ms=6, alpha=0.1) ### Mask seems to work
ax[2].hist2d(d['X'], d['Y'], bins=[binx, biny], cmap='Blues')
ax[3].hist2d(dc['X'], dc['Y'], bins=[binx, biny], cmap='Blues') ### Mask doesn't seem to work
for axx in ax:
axx.set_xlabel(d.dtype.names[0], fontsize = 15)
axx.set_ylabel(d.dtype.names[1], fontsize = 15)
axx.set_xlim(0.0, maxx)
axx.set_ylim(0.0, maxy)
ax[0].set_title('No cut')
ax[1].set_title('Cut')
plt.show()
The last plot is incorrect:
Turns out a simple solution in my case is not to use:
dc = ma.masked_where(d['X'] < 0.5, d)
but instead to simply replace that command with:
dc = d[d['X'] < 0.5]
That does the job for me (though I still don't know the purpose of numpy.ma.masked_where()).
I have the following matplotlib script. I want to replace the points on the plot with images. Let's say 'red.png' for the red points and 'blue.png' for the blue points. How can I adjust the following to plot these images instead of the default points?
from scipy import linalg
import numpy as np
import pylab as pl
import matplotlib as mpl
import matplotlib.image as image
from sklearn.qda import QDA
###############################################################################
# load sample dataset
from sklearn.datasets import load_iris
iris = load_iris()
X = iris.data[:, 0:2] # Take only 2 dimensions
y = iris.target
X = X[y > 0]
y = y[y > 0]
y -= 1
target_names = iris.target_names[1:]
###############################################################################
# QDA
qda = QDA()
y_pred = qda.fit(X, y, store_covariances=True).predict(X)
###############################################################################
# Plot results
# constants
dpi = 72; imageSize = (32,32)
# read in our png file
im_red = image.imread('red.png')
im_blue = image.imread('blue.png')
def plot_ellipse(splot, mean, cov, color):
v, w = linalg.eigh(cov)
u = w[0] / linalg.norm(w[0])
angle = np.arctan(u[1] / u[0])
angle = 180 * angle / np.pi # convert to degrees
# filled gaussian at 2 standard deviation
ell = mpl.patches.Ellipse(mean, 2 * v[0] ** 0.5, 2 * v[1] ** 0.5,
180 + angle, color=color)
ell.set_clip_box(splot.bbox)
ell.set_alpha(0.5)
splot.add_artist(ell)
xx, yy = np.meshgrid(np.linspace(4, 8.5, 200), np.linspace(1.5, 4.5, 200))
X_grid = np.c_[xx.ravel(), yy.ravel()]
zz_qda = qda.predict_proba(X_grid)[:, 1].reshape(xx.shape)
pl.figure()
splot = pl.subplot(1, 1, 1)
pl.contourf(xx, yy, zz_qda > 0.5, alpha=0.5)
pl.scatter(X[y == 0, 0], X[y == 0, 1], c='b', label=target_names[0])
pl.scatter(X[y == 1, 0], X[y == 1, 1], c='r', label=target_names[1])
pl.contour(xx, yy, zz_qda, [0.5], linewidths=2., colors='k')
print(xx)
pl.axis('tight')
pl.show()
You can plot images instead of markers in a figure using BboxImage as in this tutorial.
from matplotlib import pyplot as plt
from matplotlib.image import BboxImage
from matplotlib.transforms import Bbox, TransformedBbox
# Load images.
redMarker = plt.imread('red.jpg')
blueMarker = plt.imread('blue.jpg')
# Data
blueX = [1, 2, 3, 4]
blueY = [1, 3, 5, 2]
redX = [1, 2, 3, 4]
redY = [3, 2, 3, 4]
# Create figure
fig = plt.figure()
ax = fig.add_subplot(111)
# Plots an image at each x and y location.
def plotImage(xData, yData, im):
for x, y in zip(xData, yData):
bb = Bbox.from_bounds(x,y,1,1)
bb2 = TransformedBbox(bb,ax.transData)
bbox_image = BboxImage(bb2,
norm = None,
origin=None,
clip_on=False)
bbox_image.set_data(im)
ax.add_artist(bbox_image)
plotImage(blueX, blueY, blueMarker)
plotImage(redX, redY, redMarker)
# Set the x and y limits
ax.set_ylim(0,6)
ax.set_xlim(0,6)
plt.show()