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I'm currently trying to curve fit some experimental data to a simple power-law equation.
Nu = C*Re**m*Pr**(1/3)
I am trying to use the scipy.optimize.curve_fit function to do this, but am getting the error code: "Result from function call is not a proper array of floats." I don't know why I am getting this error code but I wonder if it is because I have too many arrays that I need to use for my equation.
My code is as follows
import matplotlib.pyplot as plt
import scipy.optimize as so
def function(C, m):
result = []
for i,j in zip(Re, Pr):
y = C * i ** m * j ** (1/3)
result.append(y)
return result
parameters, covariance = so.curve_fit(function, Re, Nu)
y2 = function(Re, Pr, *parameters)
print(parameters)
plt.plot(Re, Nu)
plt.plot(Re, y2)
plt.show()
Here is a graphing 3D surface fitter using curve_fit that has a 3D scatterplot, 3D surface plot, and a contour plot. Note that the initial parameter estimates are all 1.0, and this example does not use scipy's genetic algorithm to estimate initial parameter values.
import numpy, scipy, scipy.optimize
import matplotlib
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm # to colormap 3D surfaces from blue to red
import matplotlib.pyplot as plt
graphWidth = 800 # units are pixels
graphHeight = 600 # units are pixels
# 3D contour plot lines
numberOfContourLines = 16
def SurfacePlot(func, data, fittedParameters):
f = plt.figure(figsize=(graphWidth/100.0, graphHeight/100.0), dpi=100)
matplotlib.pyplot.grid(True)
axes = Axes3D(f)
x_data = data[0]
y_data = data[1]
z_data = data[2]
xModel = numpy.linspace(min(x_data), max(x_data), 20)
yModel = numpy.linspace(min(y_data), max(y_data), 20)
X, Y = numpy.meshgrid(xModel, yModel)
Z = func(numpy.array([X, Y]), *fittedParameters)
axes.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=cm.coolwarm, linewidth=1, antialiased=True)
axes.scatter(x_data, y_data, z_data) # show data along with plotted surface
axes.set_title('Surface Plot (click-drag with mouse)') # add a title for surface plot
axes.set_xlabel('X Data') # X axis data label
axes.set_ylabel('Y Data') # Y axis data label
axes.set_zlabel('Z Data') # Z axis data label
plt.show()
plt.close('all') # clean up after using pyplot or else thaere can be memory and process problems
def ContourPlot(func, data, fittedParameters):
f = plt.figure(figsize=(graphWidth/100.0, graphHeight/100.0), dpi=100)
axes = f.add_subplot(111)
x_data = data[0]
y_data = data[1]
z_data = data[2]
xModel = numpy.linspace(min(x_data), max(x_data), 20)
yModel = numpy.linspace(min(y_data), max(y_data), 20)
X, Y = numpy.meshgrid(xModel, yModel)
Z = func(numpy.array([X, Y]), *fittedParameters)
axes.plot(x_data, y_data, 'o')
axes.set_title('Contour Plot') # add a title for contour plot
axes.set_xlabel('X Data') # X axis data label
axes.set_ylabel('Y Data') # Y axis data label
CS = matplotlib.pyplot.contour(X, Y, Z, numberOfContourLines, colors='k')
matplotlib.pyplot.clabel(CS, inline=1, fontsize=10) # labels for contours
plt.show()
plt.close('all') # clean up after using pyplot or else thaere can be memory and process problems
def ScatterPlot(data):
f = plt.figure(figsize=(graphWidth/100.0, graphHeight/100.0), dpi=100)
matplotlib.pyplot.grid(True)
axes = Axes3D(f)
x_data = data[0]
y_data = data[1]
z_data = data[2]
axes.scatter(x_data, y_data, z_data)
axes.set_title('Scatter Plot (click-drag with mouse)')
axes.set_xlabel('X Data')
axes.set_ylabel('Y Data')
axes.set_zlabel('Z Data')
plt.show()
plt.close('all') # clean up after using pyplot or else thaere can be memory and process problems
def func(data, a, alpha, beta):
t = data[0]
p_p = data[1]
return a * (t**alpha) * (p_p**beta)
if __name__ == "__main__":
xData = numpy.array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0])
yData = numpy.array([11.0, 12.1, 13.0, 14.1, 15.0, 16.1, 17.0, 18.1, 90.0])
zData = numpy.array([1.1, 2.2, 3.3, 4.4, 5.5, 6.6, 7.7, 8.0, 9.9])
data = [xData, yData, zData]
initialParameters = [1.0, 1.0, 1.0] # these are the same as scipy default values in this example
# here a non-linear surface fit is made with scipy's curve_fit()
fittedParameters, pcov = scipy.optimize.curve_fit(func, [xData, yData], zData, p0 = initialParameters)
ScatterPlot(data)
SurfacePlot(func, data, fittedParameters)
ContourPlot(func, data, fittedParameters)
print('fitted prameters', fittedParameters)
modelPredictions = func(data, *fittedParameters)
absError = modelPredictions - zData
SE = numpy.square(absError) # squared errors
MSE = numpy.mean(SE) # mean squared errors
RMSE = numpy.sqrt(MSE) # Root Mean Squared Error, RMSE
Rsquared = 1.0 - (numpy.var(absError) / numpy.var(zData))
print('RMSE:', RMSE)
print('R-squared:', Rsquared)
I would like to fit a function to a 3d data.
I read the data with pandas:
df = pd.read_csv('data.csv')
Ca = df.Ca
q = df.q
L = df.L0
Then, I define my 3d function (z=f(x,y)) as:
def func(q, Ca, l0, v0, beta):
return l0 + q*v0*(1+beta/(q*Ca))
then I use curve_fit to find the best fit parameters:
from scipy.optimize import curve_fit
guess = (1,1,1)
popt, pcov = curve_fit(func, q,Ca,L, guess)
And it gives me the following errors:
ValueError: `sigma` has incorrect shape.
Do you know what is the mistake and how to solve it?
Thanks a lot for your help
Here is a graphical 3D fitter with 3D scatter plot, 3D surface plot, and 3D contour plot.
import numpy, scipy, scipy.optimize
import matplotlib
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm # to colormap 3D surfaces from blue to red
import matplotlib.pyplot as plt
graphWidth = 800 # units are pixels
graphHeight = 600 # units are pixels
# 3D contour plot lines
numberOfContourLines = 16
def SurfacePlot(func, data, fittedParameters):
f = plt.figure(figsize=(graphWidth/100.0, graphHeight/100.0), dpi=100)
matplotlib.pyplot.grid(True)
axes = Axes3D(f)
x_data = data[0]
y_data = data[1]
z_data = data[2]
xModel = numpy.linspace(min(x_data), max(x_data), 20)
yModel = numpy.linspace(min(y_data), max(y_data), 20)
X, Y = numpy.meshgrid(xModel, yModel)
Z = func(numpy.array([X, Y]), *fittedParameters)
axes.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=cm.coolwarm, linewidth=1, antialiased=True)
axes.scatter(x_data, y_data, z_data) # show data along with plotted surface
axes.set_title('Surface Plot (click-drag with mouse)') # add a title for surface plot
axes.set_xlabel('X Data') # X axis data label
axes.set_ylabel('Y Data') # Y axis data label
axes.set_zlabel('Z Data') # Z axis data label
plt.show()
plt.close('all') # clean up after using pyplot or else thaere can be memory and process problems
def ContourPlot(func, data, fittedParameters):
f = plt.figure(figsize=(graphWidth/100.0, graphHeight/100.0), dpi=100)
axes = f.add_subplot(111)
x_data = data[0]
y_data = data[1]
z_data = data[2]
xModel = numpy.linspace(min(x_data), max(x_data), 20)
yModel = numpy.linspace(min(y_data), max(y_data), 20)
X, Y = numpy.meshgrid(xModel, yModel)
Z = func(numpy.array([X, Y]), *fittedParameters)
axes.plot(x_data, y_data, 'o')
axes.set_title('Contour Plot') # add a title for contour plot
axes.set_xlabel('X Data') # X axis data label
axes.set_ylabel('Y Data') # Y axis data label
CS = matplotlib.pyplot.contour(X, Y, Z, numberOfContourLines, colors='k')
matplotlib.pyplot.clabel(CS, inline=1, fontsize=10) # labels for contours
plt.show()
plt.close('all') # clean up after using pyplot or else thaere can be memory and process problems
def ScatterPlot(data):
f = plt.figure(figsize=(graphWidth/100.0, graphHeight/100.0), dpi=100)
matplotlib.pyplot.grid(True)
axes = Axes3D(f)
x_data = data[0]
y_data = data[1]
z_data = data[2]
axes.scatter(x_data, y_data, z_data)
axes.set_title('Scatter Plot (click-drag with mouse)')
axes.set_xlabel('X Data')
axes.set_ylabel('Y Data')
axes.set_zlabel('Z Data')
plt.show()
plt.close('all') # clean up after using pyplot or else thaere can be memory and process problems
def func(data, a, alpha, beta):
x = data[0]
y = data[1]
return a * (x**alpha) * (y**beta)
if __name__ == "__main__":
xData = numpy.array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0])
yData = numpy.array([11.0, 12.1, 13.0, 14.1, 15.0, 16.1, 17.0, 18.1, 90.0])
zData = numpy.array([1.1, 2.2, 3.3, 4.4, 5.5, 6.6, 7.7, 8.0, 9.9])
data = [xData, yData, zData]
initialParameters = [1.0, 1.0, 1.0] # these are the same as scipy default values in this example
# here a non-linear surface fit is made with scipy's curve_fit()
fittedParameters, pcov = scipy.optimize.curve_fit(func, [xData, yData], zData, p0 = initialParameters)
ScatterPlot(data)
SurfacePlot(func, data, fittedParameters)
ContourPlot(func, data, fittedParameters)
print('fitted prameters', fittedParameters)
modelPredictions = func(data, *fittedParameters)
absError = modelPredictions - zData
SE = numpy.square(absError) # squared errors
MSE = numpy.mean(SE) # mean squared errors
RMSE = numpy.sqrt(MSE) # Root Mean Squared Error, RMSE
Rsquared = 1.0 - (numpy.var(absError) / numpy.var(zData))
print('RMSE:', RMSE)
print('R-squared:', Rsquared)
I was given a set of raw datum and have to model it by means of some machine learning techniques. After some research, I decided to do with the method of linear approximation.
Description of the equation.
z - depth (meters)
T(z) - temperature at the depth z
T(zᵢ) - temperature at the depth zᵢ
T₀ - temperature at the surface (It is constant and known)
K - coefficient of geothermal gradient (How the temperature changes with respect to the depth)
Mᵢ - flow rate of the liquid at the depth zᵢ
As it is shown from the equation we can find the temperature of the liquid in the any depth of the well bore.
I have list of depths, temperature and the flow rate of the liquid. I have to model an equation according to these datum by means of python3. Currently I use matplotlib library for such type of calculations.
Here is an example of non-linear multiple regression in Python 3, this should easily be adapted to your multiple regression problem.
import numpy, scipy, scipy.optimize
import matplotlib
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm # to colormap 3D surfaces from blue to red
import matplotlib.pyplot as plt
graphWidth = 800 # units are pixels
graphHeight = 600 # units are pixels
# 3D contour plot lines
numberOfContourLines = 16
def SurfacePlot(func, data, fittedParameters):
f = plt.figure(figsize=(graphWidth/100.0, graphHeight/100.0), dpi=100)
matplotlib.pyplot.grid(True)
axes = Axes3D(f)
x_data = data[0]
y_data = data[1]
z_data = data[2]
xModel = numpy.linspace(min(x_data), max(x_data), 20)
yModel = numpy.linspace(min(y_data), max(y_data), 20)
X, Y = numpy.meshgrid(xModel, yModel)
Z = func(numpy.array([X, Y]), *fittedParameters)
axes.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=cm.coolwarm, linewidth=1, antialiased=True)
axes.scatter(x_data, y_data, z_data) # show data along with plotted surface
axes.set_title('Surface Plot (click-drag with mouse)') # add a title for surface plot
axes.set_xlabel('X Data') # X axis data label
axes.set_ylabel('Y Data') # Y axis data label
axes.set_zlabel('Z Data') # Z axis data label
plt.show()
plt.close('all') # clean up after using pyplot or else thaere can be memory and process problems
def ContourPlot(func, data, fittedParameters):
f = plt.figure(figsize=(graphWidth/100.0, graphHeight/100.0), dpi=100)
axes = f.add_subplot(111)
x_data = data[0]
y_data = data[1]
z_data = data[2]
xModel = numpy.linspace(min(x_data), max(x_data), 20)
yModel = numpy.linspace(min(y_data), max(y_data), 20)
X, Y = numpy.meshgrid(xModel, yModel)
Z = func(numpy.array([X, Y]), *fittedParameters)
axes.plot(x_data, y_data, 'o')
axes.set_title('Contour Plot') # add a title for contour plot
axes.set_xlabel('X Data') # X axis data label
axes.set_ylabel('Y Data') # Y axis data label
CS = matplotlib.pyplot.contour(X, Y, Z, numberOfContourLines, colors='k')
matplotlib.pyplot.clabel(CS, inline=1, fontsize=10) # labels for contours
plt.show()
plt.close('all') # clean up after using pyplot or else thaere can be memory and process problems
def ScatterPlot(data):
f = plt.figure(figsize=(graphWidth/100.0, graphHeight/100.0), dpi=100)
matplotlib.pyplot.grid(True)
axes = Axes3D(f)
x_data = data[0]
y_data = data[1]
z_data = data[2]
axes.scatter(x_data, y_data, z_data)
axes.set_title('Scatter Plot (click-drag with mouse)')
axes.set_xlabel('X Data')
axes.set_ylabel('Y Data')
axes.set_zlabel('Z Data')
plt.show()
plt.close('all') # clean up after using pyplot or else thaere can be memory and process problems
def func(data, a, alpha, beta):
t = data[0]
p_p = data[1]
return a * (t**alpha) * (p_p**beta)
if __name__ == "__main__":
xData = numpy.array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0])
yData = numpy.array([11.0, 12.1, 13.0, 14.1, 15.0, 16.1, 17.0, 18.1, 90.0])
zData = numpy.array([1.1, 2.2, 3.3, 4.4, 5.5, 6.6, 7.7, 8.0, 9.9])
data = [xData, yData, zData]
# this example uses curve_fit()'s default initial paramter values
fittedParameters, pcov = scipy.optimize.curve_fit(func, [xData, yData], zData)
ScatterPlot(data)
SurfacePlot(func, data, fittedParameters)
ContourPlot(func, data, fittedParameters)
print('fitted prameters', fittedParameters)
I am working with a confusion matrix (Figure A)
How can I make my ticks to start from 1 to 3 instead of 0 to 2?
I tried adding a +1 in tick_marks. But it does not work (Figure B)
Check my code:
import itertools
cm = confusion_matrix(y_test, y_pred)
np.set_printoptions(precision=2)
print('Confusion matrix, without normalization')
print(cm)
plt.figure()
plot_confusion_matrix(cm)
def plot_confusion_matrix(cm, title='Confusion matrix', cmap=plt.cm.Oranges):
plt.imshow(cm, interpolation='nearest', cmap=cmap)
plt.title(title)
plt.colorbar()
tick_marks = np.arange(len(iris.target_names)) + 1
plt.xticks(tick_marks, rotation=45)
plt.yticks(tick_marks)
thresh = cm.max() / 2.
for i, j in itertools.product(range(cm.shape[0]), range(cm.shape[1])):
plt.text(j, i, cm[i, j],
horizontalalignment="center",
color="white" if cm[i, j] > thresh else "black")
plt.tight_layout()
plt.ylabel('True label')
plt.xlabel('Predicted label')
Figure A:
Figure B
You should get the axis of the plt and change the xtick_labels (if that's what you intend to do):
import itertools
import numpy as np
import matplotlib.pyplot as plt
from sklearn import svm, datasets
from sklearn.model_selection import train_test_split
from sklearn.metrics import confusion_matrix
# import some data to play with
iris = datasets.load_iris()
X = iris.data
y = iris.target
class_names = iris.target_names
# Split the data into a training set and a test set
X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=0)
# Run classifier, using a model that is too regularized (C too low) to see
# the impact on the results
classifier = svm.SVC(kernel='linear', C=0.01)
y_pred = classifier.fit(X_train, y_train).predict(X_test)
def plot_confusion_matrix(cm, title='Confusion matrix', cmap=plt.cm.Oranges):
plt.imshow(cm, interpolation='nearest', cmap=cmap)
plt.title(title)
plt.colorbar()
tick_marks = np.arange(len(iris.target_names))
plt.xticks(tick_marks, rotation=45)
ax = plt.gca()
ax.set_xticklabels((ax.get_xticks() +1).astype(str))
plt.yticks(tick_marks)
thresh = cm.max() / 2.
for i, j in itertools.product(range(cm.shape[0]), range(cm.shape[1])):
plt.text(j, i, cm[i, j],
horizontalalignment="center",
color="white" if cm[i, j] > thresh else "black")
plt.tight_layout()
plt.ylabel('True label')
plt.xlabel('Predicted label')
cm = confusion_matrix(y_test, y_pred)
np.set_printoptions(precision=2)
print('Confusion matrix, without normalization')
print(cm)
fig, ax = plt.subplots()
plot_confusion_matrix(cm)
plt.show()
result:
I faced a similar problem: When I wanted to use custom labels for my classes, either the squared boxes went out of bounds or the labels were being offset, as you show here.
If you have multiple labels (>7), then first you need to explicitly set the tick frequency to one using plticker.MultipleLocator. Then you simply set the x and y ticklabels without mentioning the ticks (To not set the xticks and yticks is important. If you do so, the imshow/matshow part gets chopped off at the top.) Add the following lines inside the plot_confusion_matrix function.
import matplotlib.ticker as plticker
fig = plt.figure()
ax = fig.add_subplot(111)
cax = ax.matshow(cm,cmap=cmap)
fig.colorbar(cax)
loc = plticker.MultipleLocator(base=1.0)
ax.xaxis.set_major_locator(loc)
ax.yaxis.set_major_locator(loc)
ax.set_yticklabels(['']+iris.target_names)
ax.set_xticklabels(['']+iris.target_names)
I am trying to learn a little about nearest neighbour matching. Below you see two scatter plots. The first shows the real data. I trying to use scikit-learn's NN-classifier to identify the white observations. The second scatter plot shows my achievement - which is entirely useless, as you can see.
I don't get why that is the case? It seems that the white observations are closely related and different fromt the other observations. What is happening here?
Here is what I do:
# import neccessary packages
import pandas as pd
import numpy as np
import sklearn as skl
from sklearn.cross_validation import train_test_split as tts
import matplotlib.pyplot as plt
from sklearn import neighbors
from matplotlib.colors import ListedColormap
# import data and give a little overview
sample = pd.read_stata('real_data_1.dta')
s = sample
print(s.dtypes)
print(s.shape)
# Nearest Neighboor
print(__doc__)
n_neighbors = 1
X = np.array((s.t_ums_ma, s.t_matauf)).reshape(918, 2)
y = np.array(s.matauf_measure)
plt.scatter(s.t_ums_ma,s.t_matauf, c=s.matauf_measure, label='Nordan Scatter', color='b', s=25, marker="o")
plt.xlabel('crisis')
plt.ylabel('current debt')
plt.title('Interesting Graph\nCheck it out')
plt.legend()
plt.gray()
plt.show()
X_train, X_test, y_train, y_test = tts(X, y, test_size = 1)
h = 0.02
# Create color maps
cmap_light = ListedColormap(['#FFAAAA', '#AAFFAA', '#AAAAFF'])
cmap_bold = ListedColormap(['#FF0000', '#00FF00', '#0000FF'])
for weights in ['uniform', 'distance']:
# we create an instance of Neighbours Classifier and fit the data.
clf = neighbors.KNeighborsClassifier(n_neighbors, weights=weights)
clf.fit(X, y)
# Plot the decision boundary. For that, we will assign a color to each
# point in the mesh [x_min, m_max]x[y_min, y_max].
x_min, x_max = X_train[:, 0].min() - 0.01, X[:, 0].max() + 0.01
y_min, y_max = X_train[:, 1].min() - 0.01, X[:, 1].max() + 0.01
xx, yy = np.meshgrid(np.arange(x_min, x_max, h),
np.arange(y_min, y_max, h))
Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
# Put the result into a color plot
Z = Z.reshape(xx.shape)
plt.figure()
plt.pcolormesh(xx, yy, Z, cmap=cmap_light)
# Plot also the training points
plt.scatter(X[:, 0], X[:, 1], c=y, cmap=cmap_bold)
plt.xlim(xx.min(), xx.max())
plt.ylim(yy.min(), yy.max())
plt.title("3-Class classification (k = %i, weights = '%s')"
% (n_neighbors, weights))
plt.show()
Any help is greatly appreciated! Best /R