我想在python中编写符合曲线的下面代码：
df_day$col1=fitted(lm(df$col1~1+sin(2*pi*t/365.25)+cos(2*pi*t/365.25)))
我不知道如何在python中编写拟合曲线。我真的很感激任何帮助。
答案 0 :(得分：0)
如果你安装了scipy和matplotlib，这里有一个Python 3示例，它将适合数据，打印出拟合统计数据，并以95％置信区间绘制模型。它需要pyeq3拟合库，可以使用命令＆＃34; pip install pyeq3＆＃34;进行安装。
import os, sys, inspect
import numpy, scipy, matplotlib
import matplotlib.pyplot as plt
import pyeq3
##########################################################
# setup section
# this code requires a capital letter "X" instead of the original letter "t"
# to designate the data to be fitted.
# note that the fitted parameters are named "A" and "B" in this example
functionString = '1 + A*sin(2*pi*X/365.25) + B*cos(2*pi*X/365.25)'
dataString = '''
X Y # lines of text that do not begin with a number are ignored
5.357 0.376
5.457 0.489
5.797 0.874
5.936 1.049
6.161 1.327
6.697 2.054
6.731 2.077
6.775 2.138
8.442 4.744
9.769 7.068
9.861 7.104
'''
##########################################################
# pyeq3 fitting section
# note that the constructor is passed the function string here
equation = pyeq3.Models_2D.UserDefinedFunction.UserDefinedFunction(inUserFunctionString = functionString)
# note that True is passed here to indicate weighted data, for unwighted pass False
pyeq3.dataConvertorService().ConvertAndSortColumnarASCII(dataString, equation, False)
print("Fitting data...")
equation.Solve()
##########################################################
# text output section for fitted parameter values
print("Equation:", equation.GetDisplayName(), str(equation.GetDimensionality()) + "D")
print("Fitting target of", equation.fittingTargetDictionary[equation.fittingTarget], '=', equation.CalculateAllDataFittingTarget(equation.solvedCoefficients))
print("Fitted Parameters:")
for i in range(len(equation.solvedCoefficients)):
print(" %s = %-.16E" % (equation.GetCoefficientDesignators()[i], equation.solvedCoefficients[i]))
print()
##########################################################
# calculate absolute, relative, and percent errors from the fit
equation.CalculateModelErrors(equation.solvedCoefficients, equation.dataCache.allDataCacheDictionary)
##########################################################
# this section prints information on each individual data point
for i in range(len(equation.dataCache.allDataCacheDictionary['DependentData'])):
print('X:', equation.dataCache.allDataCacheDictionary['IndependentData'][0][i],)
print('Y:', equation.dataCache.allDataCacheDictionary['DependentData'][i],)
print('Model:', equation.modelPredictions[i],)
print('Abs. Error:', equation.modelAbsoluteError[i],)
if not equation.dataCache.DependentDataContainsZeroFlag:
print('Rel. Error:', equation.modelRelativeError[i],)
print('Percent Error:', equation.modelPercentError[i])
else:
print()
print()
##########################################################
# overall fit and parameter statistics output section
equation.CalculateCoefficientAndFitStatistics()
if equation.upperCoefficientBounds or equation.lowerCoefficientBounds:
print('You entered coefficient bounds. Parameter statistics may')
print('not be valid for parameter values at or near the bounds.')
print()
print('Degress of freedom error', equation.df_e)
print('Degress of freedom regression', equation.df_r)
if equation.rmse == None:
print('Root Mean Squared Error (RMSE): n/a')
else:
print('Root Mean Squared Error (RMSE):', equation.rmse)
if equation.r2 == None:
print('R-squared: n/a')
else:
print('R-squared:', equation.r2)
if equation.r2adj == None:
print('R-squared adjusted: n/a')
else:
print('R-squared adjusted:', equation.r2adj)
if equation.Fstat == None:
print('Model F-statistic: n/a')
else:
print('Model F-statistic:', equation.Fstat)
if equation.Fpv == None:
print('Model F-statistic p-value: n/a')
else:
print('Model F-statistic p-value:', equation.Fpv)
if equation.ll == None:
print('Model log-likelihood: n/a')
else:
print('Model log-likelihood:', equation.ll)
if equation.aic == None:
print('Model AIC: n/a')
else:
print('Model AIC:', equation.aic)
if equation.bic == None:
print('Model BIC: n/a')
else:
print('Model BIC:', equation.bic)
print()
print("Individual Parameter Statistics:")
for i in range(len(equation.solvedCoefficients)):
if type(equation.tstat_beta) == type(None):
tstat = 'n/a'
else:
tstat = '%-.5E' % ( equation.tstat_beta[i])
if type(equation.pstat_beta) == type(None):
pstat = 'n/a'
else:
pstat = '%-.5E' % ( equation.pstat_beta[i])
if type(equation.sd_beta) != type(None):
print("Coefficient %s = %-.16E, std error: %-.5E" % (equation.GetCoefficientDesignators()[i], equation.solvedCoefficients[i], equation.sd_beta[i]))
else:
print("Coefficient %s = %-.16E, std error: n/a" % (equation.GetCoefficientDesignators()[i], equation.solvedCoefficients[i]))
print(" t-stat: %s, p-stat: %s, 95 percent confidence intervals: [%-.5E, %-.5E]" % (tstat, pstat, equation.ci[i][0], equation.ci[i][1]))
print()
print("Coefficient Covariance Matrix:")
for i in equation.cov_beta:
print(i)
##########################################################
# graphics output section
def ModelScatterConfidenceGraph(equation, graphWidth, graphHeight):
f = plt.figure(figsize=(graphWidth/100.0, graphHeight/100.0), dpi=100)
axes = f.add_subplot(111)
y_data = equation.dataCache.allDataCacheDictionary['DependentData']
x_data = equation.dataCache.allDataCacheDictionary['IndependentData'][0]
# first the raw data as a scatter plot
axes.plot(x_data, y_data, 'D')
# create data for the fitted equation plot
xModel = numpy.linspace(min(x_data), max(x_data))
tempcache = equation.dataCache # store the data cache
equation.dataCache = pyeq3.dataCache()
equation.dataCache.allDataCacheDictionary['IndependentData'] = numpy.array([xModel, xModel])
equation.dataCache.FindOrCreateAllDataCache(equation)
yModel = equation.CalculateModelPredictions(equation.solvedCoefficients, equation.dataCache.allDataCacheDictionary)
equation.dataCache = tempcache # restore the original data cache
# now the model as a line plot
axes.plot(xModel, yModel)
# now calculate confidence intervals
# http://support.sas.com/documentation/cdl/en/statug/63347/HTML/default/viewer.htm#statug_nlin_sect026.htm
# http://www.staff.ncl.ac.uk/tom.holderness/software/pythonlinearfit
mean_x = numpy.mean(x_data)
n = equation.nobs
t_value = scipy.stats.t.ppf(0.975, equation.df_e) # (1.0 - (a/2)) is used for two-sided t-test critical value, here a = 0.05
confs = t_value * numpy.sqrt((equation.sumOfSquaredErrors/equation.df_e)*(1.0/n + (numpy.power((xModel-mean_x),2.0)/
((numpy.sum(numpy.power(x_data,2.0)))-n*(numpy.power(mean_x,2.0))))))
# get lower and upper confidence limits based on predicted y and confidence intervals
upper = yModel + abs(confs)
lower = yModel - abs(confs)
# mask off any numbers outside the existing plot limits
booleanMask = yModel > axes.get_ylim()[0]
booleanMask &= (yModel < axes.get_ylim()[1])
# color scheme improves visibility on black background lines or points
axes.plot(xModel[booleanMask], lower[booleanMask], linestyle='solid', color='white')
axes.plot(xModel[booleanMask], upper[booleanMask], linestyle='solid', color='white')
axes.plot(xModel[booleanMask], lower[booleanMask], linestyle='dashed', color='blue')
axes.plot(xModel[booleanMask], upper[booleanMask], linestyle='dashed', color='blue')
axes.set_title('Model With 95% Confidence Intervals') # add a title
axes.set_xlabel('X Data') # X axis data label
axes.set_ylabel('Y Data') # Y axis data label
plt.show()
plt.close('all') # clean up after using pyplot
graphWidth = 800
graphHeight = 600
ModelScatterConfidenceGraph(equation, graphWidth, graphHeight)