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PyMC3 failing to broadcast correct dimensions for inference

I am trying to extend the ideas of item response theory to multiple responses. Consider a marketing survey, which asks customers, "what's the deciding factor in whether or not you purchase product X?" Where answers are {0: price, 1: durability, 2: ease-of-use}.
Here is some synthetic data (rows are customers, columns are products, each cell is the class response.)
responses = np.array([
[0,1,2,1,0],
[1,1,1,1,1],
[0,0,2,2,1],
[1,1,2,2,1],
[1,1,0,0,0]
])
students = 5
questions = 5
categories = 3
with pm.Model() as model:
z_student = pm.Normal("z_student", mu=0, sigma=1, shape=(students,categories))
z_question = pm.Normal("z_question",mu=0, sigma=1, shape=(categories,questions))
# Transformed parameter
theta = pm.Deterministic("theta", tt.nnet.softmax(z_student - z_question))
# Likelihood
kij = pm.Categorical("kij", p=theta, observed=responses)
trace = pm.sample(chains=4)
az.plot_trace(trace, var_names=["z_student", "z_question"], compact=False);
This code produces the following error: ValueError: Input dimension mis-match. (input[0].shape[0] = 5, input[1].shape[0] = 3).
However, when I change the theta line to: theta = pm.Deterministic("theta", tt.nnet.softmax(z_student - z_question.transpose())) the sampler doesn't instantly failure, rather is samples wrong.
az.summary(trace)
mean sd hdi_3% hdi_97% mcse_mean mcse_sd ess_mean ess_sd ess_bulk ess_tail r_hat
z_student[0,0] 0.150 0.893 -1.620 1.752 0.012 0.013 5789.0 2327.0 5771.0 2991.0 1.0
z_student[0,1] 0.393 0.879 -1.319 1.980 0.012 0.012 5150.0 2610.0 5153.0 3195.0 1.0
z_student[0,2] -0.591 0.915 -2.254 1.108 0.011 0.012 6408.0 2737.0 6415.0 2830.0 1.0
z_student[1,0] -0.064 0.860 -1.676 1.538 0.011 0.014 5748.0 1942.0 5747.0 2850.0 1.0
z_student[1,1] 0.602 0.864 -0.982 2.185 0.012 0.011 4921.0 3028.0 4920.0 3269.0 1.0
z_student[1,2] -0.548 0.906 -2.218 1.137 0.012 0.012 6076.0 2870.0 6083.0 3410.0 1.0
z_student[2,0] -0.166 0.907 -1.974 1.450 0.013 0.014 4681.0 2121.0 4692.0 3108.0 1.0
z_student[2,1] -0.188 0.875 -1.776 1.472 0.011 0.014 5923.0 2073.0 5945.0 3333.0 1.0
z_student[2,2] 0.344 0.865 -1.288 1.951 0.012 0.012 4828.0 2750.0 4822.0 3039.0 1.0
z_student[3,0] -0.212 0.892 -1.980 1.395 0.011 0.013 6019.0 2504.0 5996.0 3391.0 1.0
z_student[3,1] 0.097 0.876 -1.573 1.713 0.012 0.013 5304.0 2252.0 5332.0 2971.0 1.0
z_student[3,2] 0.096 0.851 -1.583 1.645 0.011 0.012 5554.0 2678.0 5543.0 3288.0 1.0
z_student[4,0] 0.160 0.881 -1.367 1.947 0.012 0.013 5421.0 2189.0 5413.0 2927.0 1.0
z_student[4,1] 0.414 0.863 -1.255 2.026 0.012 0.012 4900.0 2548.0 4897.0 3248.0 1.0
z_student[4,2] -0.558 0.901 -2.266 1.130 0.011 0.012 6551.0 2728.0 6582.0 3142.0 1.0
z_question[0,0] -0.179 0.883 -1.795 1.488 0.011 0.015 6317.0 1769.0 6315.0 3389.0 1.0
z_question[0,1] 0.107 0.886 -1.511 1.807 0.012 0.013 5236.0 2431.0 5209.0 3503.0 1.0
z_question[0,2] 0.164 0.878 -1.450 1.834 0.012 0.013 5131.0 2248.0 5106.0 3102.0 1.0
z_question[0,3] 0.186 0.904 -1.450 1.882 0.011 0.014 6228.0 2175.0 6219.0 3335.0 1.0
z_question[0,4] -0.187 0.877 -1.790 1.508 0.011 0.014 5819.0 2089.0 5834.0 3198.0 1.0
z_question[1,0] -0.389 0.849 -1.948 1.219 0.012 0.012 4726.0 2494.0 4713.0 3146.0 1.0
z_question[1,1] -0.600 0.858 -2.249 0.946 0.012 0.011 5093.0 3247.0 5116.0 3312.0 1.0
z_question[1,2] 0.179 0.868 -1.520 1.763 0.012 0.012 5204.0 2514.0 5201.0 3418.0 1.0
z_question[1,3] -0.103 0.862 -1.683 1.561 0.013 0.013 4608.0 2212.0 4615.0 3163.0 1.0
z_question[1,4] -0.381 0.866 -2.047 1.147 0.011 0.012 6181.0 2735.0 6188.0 3038.0 1.0
z_question[2,0] 0.565 0.908 -1.125 2.337 0.012 0.012 6022.0 2879.0 6045.0 3173.0 1.0
z_question[2,1] 0.536 0.923 -1.192 2.241 0.012 0.013 6041.0 2476.0 6046.0 3059.0 1.0
z_question[2,2] -0.325 0.856 -1.918 1.289 0.012 0.012 5429.0 2741.0 5418.0 3004.0 1.0
z_question[2,3] -0.107 0.881 -1.953 1.363 0.012 0.012 5834.0 2545.0 5841.0 3332.0 1.0
z_question[2,4] 0.576 0.910 -1.202 2.253 0.011 0.013 6385.0 2606.0 6371.0 2905.0 1.0
theta[0,0] 0.360 0.173 0.072 0.685 0.003 0.002 4309.0 3774.0 4256.0 2846.0 1.0
theta[0,1] 0.528 0.182 0.208 0.857 0.003 0.002 4949.0 4563.0 4908.0 3050.0 1.0
theta[0,2] 0.113 0.104 0.001 0.304 0.001 0.001 6095.0 4045.0 7146.0 2780.0 1.0
theta[1,0] 0.216 0.144 0.007 0.477 0.002 0.002 6149.0 4576.0 6493.0 3116.0 1.0
theta[1,1] 0.678 0.168 0.381 0.962 0.002 0.002 5954.0 5954.0 6180.0 3320.0 1.0
theta[1,2] 0.107 0.100 0.000 0.294 0.001 0.001 6321.0 3863.0 7623.0 3252.0 1.0
theta[2,0] 0.234 0.150 0.010 0.509 0.002 0.002 6154.0 4352.0 6684.0 3252.0 1.0
theta[2,1] 0.230 0.152 0.005 0.506 0.002 0.001 6885.0 5424.0 6459.0 2923.0 1.0
theta[2,2] 0.536 0.186 0.194 0.858 0.002 0.002 5595.0 5250.0 5622.0 2805.0 1.0
theta[3,0] 0.239 0.157 0.007 0.526 0.002 0.002 5843.0 4627.0 5789.0 2853.0 1.0
theta[3,1] 0.381 0.178 0.065 0.703 0.003 0.002 4927.0 4377.0 5009.0 3315.0 1.0
theta[3,2] 0.380 0.174 0.069 0.692 0.003 0.002 4653.0 4176.0 4624.0 2562.0 1.0
theta[4,0] 0.361 0.175 0.057 0.668 0.002 0.002 5185.0 4637.0 5269.0 2985.0 1.0
theta[4,1] 0.527 0.184 0.186 0.852 0.003 0.002 4614.0 4445.0 4668.0 2497.0 1.0
theta[4,2] 0.111 0.100 0.002 0.303 0.001 0.001 6159.0 3978.0 7520.0 3473.0 1.0
Of note, please reference the theta values learned. Their names include: Theta[0,0]...Theta[0,2],...Theta[4,2]. So, in the first example, what PyMC3 has learned is the strength of relation between (z_student[0] - z_question[0]) and class/response 0.
This is not the effect I wish to accomplish, I want to learn a 3D tensor accounting for every possible {student, question, category} pairing; there should be 74 thetas, not 15, where Theta[0,0,0] refers to the learned value {student_0, question_0, response_0}. However, my code is currently not accomplishing this effect.
Any ideas?
Edit: More recently, I've built a function in Theano to demonstrate my goal:
responses = np.array([
[0,1,2,2,2],
[0,1,2,1,1],
[0,1,2,0,0],
[0,1,2,0,1],
[0,1,2,1,0]
])
students = 5
questions = 5
categories = 3
a = tensor.matrix()
b = tensor.matrix()
elem_sub = a[0,0] - b[0,0], a[0,1] - b[1,0], a[0,2] - b[2,0]
function = theano.function([a,b], elem_sub)
with pm.Model() as model:
z_student = pm.Normal("student_dim1", mu=0, sigma=1, shape=(students,categories))
z_question = pm.Normal("question_dim1", mu=0, sigma=1, shape=(categories,questions))
# Transformed parameter
theta = pm.Deterministic("theta", tt.nnet.softmax(function(z_student,z_question)))
# Likelihood
kij = pm.Categorical("kij", p=theta, observed=responses)
However, the following error is triggered:
TypeError: Bad input argument with name "z_student" to theano function with name "<ipython-input-2-2a16f255dca1>:23" at index 0 (0-based).
Backtrace when that variable is created:
.
.
.
Expected an array-like object, but found a Variable: maybe you are trying to call a function on a (possibly shared) variable instead of a numeric array?

extract formula from OLS Regression Results

My Goal is: Extracting the formula (not only the coefs) after a linear regression done with statsmodel.
Context :
I have a pandas dataframe ,
df
x y z
0 0.0 2.0 54.200
1 0.0 2.2 70.160
2 0.0 2.4 89.000
3 0.0 2.6 110.960
i 'am doing a linear regression using statsmodels.api (2 variables, polynomial degree=3) , i'am happy with this regression.
OLS Regression Results
==============================================================================
Dep. Variable: z R-squared: 1.000
Model: OLS Adj. R-squared: 1.000
Method: Least Squares F-statistic: 2.193e+29
Date: Sun, 31 May 2020 Prob (F-statistic): 0.00
Time: 22:04:49 Log-Likelihood: 9444.6
No. Observations: 400 AIC: -1.887e+04
Df Residuals: 390 BIC: -1.883e+04
Df Model: 9
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const 0.2000 3.33e-11 6.01e+09 0.000 0.200 0.200
x1 2.0000 1.16e-11 1.72e+11 0.000 2.000 2.000
x2 1.0000 2.63e-11 3.8e+10 0.000 1.000 1.000
x3 4.0000 3.85e-12 1.04e+12 0.000 4.000 4.000
x4 12.0000 4.36e-12 2.75e+12 0.000 12.000 12.000
x5 3.0000 6.81e-12 4.41e+11 0.000 3.000 3.000
x6 6.0000 5.74e-13 1.05e+13 0.000 6.000 6.000
x7 13.0000 4.99e-13 2.6e+13 0.000 13.000 13.000
x8 14.0000 4.99e-13 2.81e+13 0.000 14.000 14.000
x9 5.0000 5.74e-13 8.71e+12 0.000 5.000 5.000
==============================================================================
Omnibus: 25.163 Durbin-Watson: 0.038
Prob(Omnibus): 0.000 Jarque-Bera (JB): 28.834
Skew: -0.655 Prob(JB): 5.48e-07
Kurtosis: 2.872 Cond. No. 6.66e+03
==============================================================================
I need to implement that outside of python , (ms excel) , I would like to know the formula.
I know it is polynomial deg3 , but I wondering how to know which coeff apply to which term of
the equation. Something like that :
For exemple : x7 coeef is the coeff for x³ ,y², x²y , ... ?
Note: this is a simplify version of my problem , in reallity I have 3 variables , deg:3 so 20 coefs.
This is a simpler exemple of code to get started with my case:
# %% Question extract formula from linear regresion coeff
#Import
import numpy as np # version : '1.18.1'
import pandas as pd # version'1.0.0'
import statsmodels.api as sm # version : '0.10.1'
from sklearn.preprocessing import PolynomialFeatures
from itertools import product
#%% Creating the dummies datas
def function_for_df(row):
x= row['x']
y= row['y']
return unknow_function(x,y)
def unknow_function(x,y):
"""
This is to generate the datas , of course in reality I do not know the formula
"""
r =0.2+ \
6*x**3+4*x**2+2*x+ \
5*y**3+3*y**2+1*y+ \
12*x*y + 13*x**2*y+ 14*x*y**2
return r
# input data
x_input = np.arange(0, 4 , 0.2)
y_input = np.arange(2, 6 , 0.2)
# create a simple dataframe with dummies datas
df = pd.DataFrame(list(product(x_input, y_input)), columns=['x', 'y'])
df['z'] = df.apply(function_for_df, axis=1)
# In the reality I start from there !
#%% creating the model
X = df[['x','y']].astype(float) #
Y = df['z'].astype(float)
polynomial_features_final= PolynomialFeatures(degree=3)
X3 = polynomial_features_final.fit_transform(X)
model = sm.OLS(Y, X3).fit()
predictions = model.predict(X3)
print_model = model.summary()
print(print_model)
#%% using the model to make predictions, no problem
def model_predict(x_sample, y_samples):
df_input = pd.DataFrame({ "x":x_sample, "y":y_samples }, index=[0])
X_input = polynomial_features_final.fit_transform(df_input)
prediction = model.predict(X_input)
return prediction
print("prediction for x=2, y=3.2 :" ,model_predict(2 ,3.2))
# How to extract the formula for the "model" ?
#Thanks
Side notes:
A desciption like the one given by pasty ModelDesc will be fine:
from patsy import ModelDesc
ModelDesc.from_formula("y ~ x")
# or even better :
desc = ModelDesc.from_formula("y ~ (a + b + c + d) ** 2")
desc.describe()
But i 'am not able to make the bridge between my model and patsy.ModelDesc.
Thanks for your help.

As Josef said in the comment, i had to look at : sklearn PolynomialFeature .
Then I found this answer :
PolynomialFeatures(degree=3).get_feature_names()
In the context :
#%% creating the model
X = df[['x','y']].astype(float) #
Y = df['z'].astype(float)
polynomial_features_final= PolynomialFeatures(degree=3)
#X3 = polynomial_features_final.fit_transform(X)
X3 = polynomial_features_final.fit_transform(df[['x', 'y']].to_numpy())
model = sm.OLS(Y, X3).fit()
predictions = model.predict(X3)
print_model = model.summary()
print(print_model)
print("\n-- ONE SOLUTION --\n Coef and Term name :")
results = list(zip(model.params, polynomial_features_final.get_feature_names()))
print(results)

You can fit the model using Patsy formula language using statsmodels.formula.api
For instance, you can have:
import statsmodels.formula.api as smf
# You do not need fit_transform to generate poly features in df
# You can specify the model using vectorized functions, many transformations are supported
model = smf.ols(formula='z ~ x*y + I(x**2)*I(y**2) + I(x**3)*I(y**3)', data=df).fit()
print_model = model.summary()
print(print_model)
OLS Regression Results
==============================================================================
Dep. Variable: z R-squared: 1.000
Model: OLS Adj. R-squared: 1.000
Method: Least Squares F-statistic: 4.193e+05
Date: Tue, 15 Feb 2022 Prob (F-statistic): 0.00
Time: 16:53:19 Log-Likelihood: -1478.1
No. Observations: 400 AIC: 2976.
Df Residuals: 390 BIC: 3016.
Df Model: 9
Covariance Type: nonrobust
=======================================================================================
coef std err t P>|t| [0.025 0.975]
---------------------------------------------------------------------------------------
Intercept 229.3425 23.994 9.558 0.000 182.168 276.517
x -180.0081 11.822 -15.226 0.000 -203.251 -156.765
y -136.2619 19.039 -7.157 0.000 -173.694 -98.830
x:y 118.0431 2.864 41.210 0.000 112.411 123.675
I(x ** 2) 31.2537 4.257 7.341 0.000 22.884 39.624
I(y ** 2) 22.5973 4.986 4.532 0.000 12.795 32.399
I(x ** 2):I(y ** 2) 1.4176 0.213 6.671 0.000 1.000 1.835
I(x ** 3) 4.7562 0.595 7.991 0.000 3.586 5.926
I(y ** 3) 4.7601 0.423 11.250 0.000 3.928 5.592
I(x ** 3):I(y ** 3) 0.0166 0.006 2.915 0.004 0.005 0.028
==============================================================================
Omnibus: 28.012 Durbin-Watson: 0.182
Prob(Omnibus): 0.000 Jarque-Bera (JB): 71.076
Skew: -0.311 Prob(JB): 3.68e-16
Kurtosis: 4.969 Cond. No. 1.32e+05
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.32e+05. This might indicate that there are
strong multicollinearity or other numerical problems.
print(model.params)
Intercept 229.342451
x -180.008082
y -136.261886
x:y 118.043098
I(x ** 2) 31.253705
I(y ** 2) 22.597298
I(x ** 2):I(y ** 2) 1.417551
I(x ** 3) 4.756205
I(y ** 3) 4.760144
I(x ** 3):I(y ** 3) 0.016611
dtype: float64
Then by simple print(model.params), you will have a natural bridge between the model and patsy.ModelDesc (here that is analogous to the formula definition)
Notes: Raw polynomial used here in the demo. You may switch to using orthogonal polynomials. That will help explain the contribution of each term to variance in the outcome, ref to StackExchange

Difference in Linear Regression using Statsmodels between Patsy version and Dummy lists version

I am having differences in the coefficient values and coefficient errors using smf.ols and sm.OLS functions of statsmodels. Even though matematically, they should be the same regression formula and give the same results.
I have done a 100% reproducible example of my question, the dataframe df can be downloaded from here: https://drive.google.com/drive/folders/1i67wztkrAeEZH2tv2hyOlgxG7N80V3pI?usp=sharing
Case 1: Linear Model using Patsy from Statsmodels
# First we load the libraries:
import statsmodels.api as sm
import statsmodels.formula.api as smf
import random
import pandas as pd
# We define a specific seed to have the same results:
random.seed(1234)
# Now we read the data that can be downloaded from Google Drive link provided above:
df = pd.read_csv("/Users/user/Documents/example/cars.csv", sep = "|")
# We create the linear regression:
lm1 = smf.ols('price ~ make + fuel_system + engine_type + num_of_doors + bore + compression_ratio + height + peak_rpm + 1', data = df)
# We see the results:
lm1.fit().summary()
The result of lm1 is:
OLS Regression Results
==============================================================================
Dep. Variable: price R-squared: 0.894
Model: OLS Adj. R-squared: 0.868
Method: Least Squares F-statistic: 35.54
Date: Mon, 18 Feb 2019 Prob (F-statistic): 5.24e-62
Time: 17:19:14 Log-Likelihood: -1899.7
No. Observations: 205 AIC: 3879.
Df Residuals: 165 BIC: 4012.
Df Model: 39
Covariance Type: nonrobust
=========================================================================================
coef std err t P>|t| [0.025 0.975]
-----------------------------------------------------------------------------------------
Intercept 1.592e+04 1.21e+04 1.320 0.189 -7898.396 3.97e+04
make[T.audi] 6519.7045 2371.807 2.749 0.007 1836.700 1.12e+04
make[T.bmw] 1.427e+04 2292.551 6.223 0.000 9740.771 1.88e+04
make[T.chevrolet] -571.8236 2860.026 -0.200 0.842 -6218.788 5075.141
make[T.dodge] -1186.3430 2261.240 -0.525 0.601 -5651.039 3278.353
make[T.honda] 2779.6496 2891.626 0.961 0.338 -2929.709 8489.009
make[T.isuzu] 3098.9677 2592.645 1.195 0.234 -2020.069 8218.004
make[T.jaguar] 1.752e+04 2416.313 7.252 0.000 1.28e+04 2.23e+04
make[T.mazda] 306.6568 2134.567 0.144 0.886 -3907.929 4521.243
make[T.mercedes-benz] 1.698e+04 2320.871 7.318 0.000 1.24e+04 2.16e+04
make[T.mercury] 2958.1002 3605.739 0.820 0.413 -4161.236 1.01e+04
make[T.mitsubishi] -1188.8337 2284.697 -0.520 0.604 -5699.844 3322.176
make[T.nissan] -1211.5463 2073.422 -0.584 0.560 -5305.405 2882.312
make[T.peugot] 3057.0217 4255.809 0.718 0.474 -5345.841 1.15e+04
make[T.plymouth] -894.5921 2332.746 -0.383 0.702 -5500.473 3711.289
make[T.porsche] 9558.8747 3688.038 2.592 0.010 2277.044 1.68e+04
make[T.renault] -2124.9722 2847.536 -0.746 0.457 -7747.277 3497.333
make[T.saab] 3490.5333 2319.189 1.505 0.134 -1088.579 8069.645
make[T.subaru] -1.636e+04 4002.796 -4.087 0.000 -2.43e+04 -8456.659
make[T.toyota] -770.9677 1911.754 -0.403 0.687 -4545.623 3003.688
make[T.volkswagen] 406.9179 2219.714 0.183 0.855 -3975.788 4789.623
make[T.volvo] 5433.7129 2397.030 2.267 0.025 700.907 1.02e+04
fuel_system[T.2bbl] 2142.1594 2232.214 0.960 0.339 -2265.226 6549.545
fuel_system[T.4bbl] 464.1109 3999.976 0.116 0.908 -7433.624 8361.846
fuel_system[T.idi] 1.991e+04 6622.812 3.007 0.003 6837.439 3.3e+04
fuel_system[T.mfi] 3716.5201 3936.805 0.944 0.347 -4056.488 1.15e+04
fuel_system[T.mpfi] 3964.1109 2267.538 1.748 0.082 -513.019 8441.241
fuel_system[T.spdi] 3240.0003 2719.925 1.191 0.235 -2130.344 8610.344
fuel_system[T.spfi] 932.1959 4019.476 0.232 0.817 -7004.041 8868.433
engine_type[T.dohcv] -1.208e+04 4205.826 -2.872 0.005 -2.04e+04 -3773.504
engine_type[T.l] -4833.9860 3763.812 -1.284 0.201 -1.23e+04 2597.456
engine_type[T.ohc] -4038.8848 1213.598 -3.328 0.001 -6435.067 -1642.702
engine_type[T.ohcf] 9618.9281 3504.600 2.745 0.007 2699.286 1.65e+04
engine_type[T.ohcv] 3051.7629 1445.185 2.112 0.036 198.323 5905.203
engine_type[T.rotor] 1403.9928 3217.402 0.436 0.663 -4948.593 7756.579
num_of_doors[T.two] -419.9640 521.754 -0.805 0.422 -1450.139 610.211
bore 3993.4308 1373.487 2.908 0.004 1281.556 6705.306
compression_ratio -1200.5665 460.681 -2.606 0.010 -2110.156 -290.977
height -80.7141 146.219 -0.552 0.582 -369.417 207.988
peak_rpm -0.5903 0.790 -0.747 0.456 -2.150 0.970
==============================================================================
Omnibus: 65.777 Durbin-Watson: 1.217
Prob(Omnibus): 0.000 Jarque-Bera (JB): 399.594
Skew: 1.059 Prob(JB): 1.70e-87
Kurtosis: 9.504 Cond. No. 3.26e+05
==============================================================================
Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 3.26e+05. This might indicate that there are
strong multicollinearity or other numerical problems.
"""
Case 2: Linear Model using Dummy Variables from Statsmodels as well
# We define a specific seed to have the same results:
random.seed(1234)
# First we check what `object` type variables we have in our dataset:
df.dtypes
# We create a list where we save the `object` type variables names:
object = ['make',
'fuel_system',
'engine_type',
'num_of_doors'
]
# Now we convert those object variables to numeric with get_dummies function to have 1 unique numeric dataframe:
df_num = pd.get_dummies(df, columns = object)
# We ensure the dataframe is numeric casting all values to float64:
df_num = df_num[df_num.columns].apply(pd.to_numeric, errors='coerce', axis = 1)
# We define the predictive variables dataset:
X = df_num.drop('price', axis = 1)
# We define the response variable values:
y = df_num.price.values
# We add a constant as we did in the previous example (adding "+1" to Patsy):
Xc = sm.add_constant(X) # Adds a constant to the model
# We create the linear model and obtain results:
lm2 = sm.OLS(y, Xc)
lm2.fit().summary()
The result of lm2 is:
OLS Regression Results
==============================================================================
Dep. Variable: y R-squared: 0.894
Model: OLS Adj. R-squared: 0.868
Method: Least Squares F-statistic: 35.54
Date: Mon, 18 Feb 2019 Prob (F-statistic): 5.24e-62
Time: 17:28:16 Log-Likelihood: -1899.7
No. Observations: 205 AIC: 3879.
Df Residuals: 165 BIC: 4012.
Df Model: 39
Covariance Type: nonrobust
======================================================================================
coef std err t P>|t| [0.025 0.975]
--------------------------------------------------------------------------------------
const 1.205e+04 6811.094 1.769 0.079 -1398.490 2.55e+04
bore 3993.4308 1373.487 2.908 0.004 1281.556 6705.306
compression_ratio -1200.5665 460.681 -2.606 0.010 -2110.156 -290.977
height -80.7141 146.219 -0.552 0.582 -369.417 207.988
peak_rpm -0.5903 0.790 -0.747 0.456 -2.150 0.970
make_alfa-romero -2273.9631 1865.185 -1.219 0.225 -5956.669 1408.743
make_audi 4245.7414 1324.140 3.206 0.002 1631.299 6860.184
make_bmw 1.199e+04 1232.635 9.730 0.000 9559.555 1.44e+04
make_chevrolet -2845.7867 1976.730 -1.440 0.152 -6748.733 1057.160
make_dodge -3460.3061 1170.966 -2.955 0.004 -5772.315 -1148.297
make_honda 505.6865 2049.865 0.247 0.805 -3541.661 4553.034
make_isuzu 825.0045 1706.160 0.484 0.629 -2543.716 4193.725
make_jaguar 1.525e+04 1903.813 8.010 0.000 1.15e+04 1.9e+04
make_mazda -1967.3063 982.179 -2.003 0.047 -3906.564 -28.048
make_mercedes-benz 1.471e+04 1423.004 10.338 0.000 1.19e+04 1.75e+04
make_mercury 684.1370 2913.361 0.235 0.815 -5068.136 6436.410
make_mitsubishi -3462.7968 1221.018 -2.836 0.005 -5873.631 -1051.963
make_nissan -3485.5094 946.316 -3.683 0.000 -5353.958 -1617.060
make_peugot 783.0586 3513.296 0.223 0.824 -6153.754 7719.871
make_plymouth -3168.5552 1293.376 -2.450 0.015 -5722.256 -614.854
make_porsche 7284.9115 2853.174 2.553 0.012 1651.475 1.29e+04
make_renault -4398.9354 2037.945 -2.159 0.032 -8422.747 -375.124
make_saab 1216.5702 1487.192 0.818 0.415 -1719.810 4152.950
make_subaru -1.863e+04 3263.524 -5.710 0.000 -2.51e+04 -1.22e+04
make_toyota -3044.9308 776.059 -3.924 0.000 -4577.218 -1512.644
make_volkswagen -1867.0452 1170.975 -1.594 0.113 -4179.072 444.981
make_volvo 3159.7498 1327.405 2.380 0.018 538.862 5780.638
fuel_system_1bbl -2790.4092 2230.161 -1.251 0.213 -7193.740 1612.922
fuel_system_2bbl -648.2498 1094.525 -0.592 0.554 -2809.330 1512.830
fuel_system_4bbl -2326.2983 3094.703 -0.752 0.453 -8436.621 3784.024
fuel_system_idi 1.712e+04 6154.806 2.782 0.006 4971.083 2.93e+04
fuel_system_mfi 926.1109 3063.134 0.302 0.763 -5121.881 6974.102
fuel_system_mpfi 1173.7017 1186.125 0.990 0.324 -1168.238 3515.642
fuel_system_spdi 449.5911 1827.318 0.246 0.806 -3158.349 4057.531
fuel_system_spfi -1858.2133 3111.596 -0.597 0.551 -8001.891 4285.464
engine_type_dohc 2703.6445 1803.080 1.499 0.136 -856.440 6263.729
engine_type_dohcv -9374.0342 3504.717 -2.675 0.008 -1.63e+04 -2454.161
engine_type_l -2130.3416 3357.283 -0.635 0.527 -8759.115 4498.431
engine_type_ohc -1335.2404 1454.047 -0.918 0.360 -4206.177 1535.696
engine_type_ohcf 1.232e+04 2850.883 4.322 0.000 6693.659 1.8e+04
engine_type_ohcv 5755.4074 1669.627 3.447 0.001 2458.820 9051.995
engine_type_rotor 4107.6373 3032.223 1.355 0.177 -1879.323 1.01e+04
num_of_doors_four 6234.8048 3491.722 1.786 0.076 -659.410 1.31e+04
num_of_doors_two 5814.8408 3337.588 1.742 0.083 -775.045 1.24e+04
==============================================================================
Omnibus: 65.777 Durbin-Watson: 1.217
Prob(Omnibus): 0.000 Jarque-Bera (JB): 399.594
Skew: 1.059 Prob(JB): 1.70e-87
Kurtosis: 9.504 Cond. No. 1.01e+16
==============================================================================
Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The smallest eigenvalue is 5.38e-23. This might indicate that there are
strong multicollinearity problems or that the design matrix is singular.
"""
As we can see, some variables like height have the same coefficient. Nevertheless some others don't (level isuzu from variable make, level ohc of engine_type or the independent term, etc.). Shouldn't it be the same result for both outputs? What am I missing here or doing wrong?
Thanks in advance for your help.
P.D. As clarified by #sukhbinder, even using Patsy formula without independent
term (putting "-1" in the formula, as Patsy incorporates it by
default) and eliminating independent term from dummy formulation, I
receive different results.

The reason why the results do not match is because Statsmodels does a pre-selection on predictive variables depending on high multicollinearity.
Exactly the same results are accomplished going through descriptive summary of the regression and identifying variables missing:
deletex = [
'make_alfa-romero',
'fuel_system_1bbl',
'engine_type_dohc',
'num_of_doors_four'
]
df_num.drop( deletex, axis = 1, inplace = True)
df_num = df_num[df_num.columns].apply(pd.to_numeric, errors='coerce', axis = 1)
X = df_num.drop('price', axis = 1)
y = df_num.price.values
Xc = sm.add_constant(X) # Adds a constant to the model
random.seed(1234)
linear_regression = sm.OLS(y, Xc)
linear_regression.fit().summary()
Which prints the result:
OLS Regression Results
==============================================================================
Dep. Variable: y R-squared: 0.894
Model: OLS Adj. R-squared: 0.868
Method: Least Squares F-statistic: 35.54
Date: Thu, 21 Feb 2019 Prob (F-statistic): 5.24e-62
Time: 18:16:08 Log-Likelihood: -1899.7
No. Observations: 205 AIC: 3879.
Df Residuals: 165 BIC: 4012.
Df Model: 39
Covariance Type: nonrobust
======================================================================================
coef std err t P>|t| [0.025 0.975]
--------------------------------------------------------------------------------------
const 1.592e+04 1.21e+04 1.320 0.189 -7898.396 3.97e+04
bore 3993.4308 1373.487 2.908 0.004 1281.556 6705.306
compression_ratio -1200.5665 460.681 -2.606 0.010 -2110.156 -290.977
height -80.7141 146.219 -0.552 0.582 -369.417 207.988
peak_rpm -0.5903 0.790 -0.747 0.456 -2.150 0.970
make_audi 6519.7045 2371.807 2.749 0.007 1836.700 1.12e+04
make_bmw 1.427e+04 2292.551 6.223 0.000 9740.771 1.88e+04
make_chevrolet -571.8236 2860.026 -0.200 0.842 -6218.788 5075.141
make_dodge -1186.3430 2261.240 -0.525 0.601 -5651.039 3278.353
make_honda 2779.6496 2891.626 0.961 0.338 -2929.709 8489.009
make_isuzu 3098.9677 2592.645 1.195 0.234 -2020.069 8218.004
make_jaguar 1.752e+04 2416.313 7.252 0.000 1.28e+04 2.23e+04
make_mazda 306.6568 2134.567 0.144 0.886 -3907.929 4521.243
make_mercedes-benz 1.698e+04 2320.871 7.318 0.000 1.24e+04 2.16e+04
make_mercury 2958.1002 3605.739 0.820 0.413 -4161.236 1.01e+04
make_mitsubishi -1188.8337 2284.697 -0.520 0.604 -5699.844 3322.176
make_nissan -1211.5463 2073.422 -0.584 0.560 -5305.405 2882.312
make_peugot 3057.0217 4255.809 0.718 0.474 -5345.841 1.15e+04
make_plymouth -894.5921 2332.746 -0.383 0.702 -5500.473 3711.289
make_porsche 9558.8747 3688.038 2.592 0.010 2277.044 1.68e+04
make_renault -2124.9722 2847.536 -0.746 0.457 -7747.277 3497.333
make_saab 3490.5333 2319.189 1.505 0.134 -1088.579 8069.645
make_subaru -1.636e+04 4002.796 -4.087 0.000 -2.43e+04 -8456.659
make_toyota -770.9677 1911.754 -0.403 0.687 -4545.623 3003.688
make_volkswagen 406.9179 2219.714 0.183 0.855 -3975.788 4789.623
make_volvo 5433.7129 2397.030 2.267 0.025 700.907 1.02e+04
fuel_system_2bbl 2142.1594 2232.214 0.960 0.339 -2265.226 6549.545
fuel_system_4bbl 464.1109 3999.976 0.116 0.908 -7433.624 8361.846
fuel_system_idi 1.991e+04 6622.812 3.007 0.003 6837.439 3.3e+04
fuel_system_mfi 3716.5201 3936.805 0.944 0.347 -4056.488 1.15e+04
fuel_system_mpfi 3964.1109 2267.538 1.748 0.082 -513.019 8441.241
fuel_system_spdi 3240.0003 2719.925 1.191 0.235 -2130.344 8610.344
fuel_system_spfi 932.1959 4019.476 0.232 0.817 -7004.041 8868.433
engine_type_dohcv -1.208e+04 4205.826 -2.872 0.005 -2.04e+04 -3773.504
engine_type_l -4833.9860 3763.812 -1.284 0.201 -1.23e+04 2597.456
engine_type_ohc -4038.8848 1213.598 -3.328 0.001 -6435.067 -1642.702
engine_type_ohcf 9618.9281 3504.600 2.745 0.007 2699.286 1.65e+04
engine_type_ohcv 3051.7629 1445.185 2.112 0.036 198.323 5905.203
engine_type_rotor 1403.9928 3217.402 0.436 0.663 -4948.593 7756.579
num_of_doors_two -419.9640 521.754 -0.805 0.422 -1450.139 610.211
==============================================================================
Omnibus: 65.777 Durbin-Watson: 1.217
Prob(Omnibus): 0.000 Jarque-Bera (JB): 399.594
Skew: 1.059 Prob(JB): 1.70e-87
Kurtosis: 9.504 Cond. No. 3.26e+05
==============================================================================
Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 3.26e+05. This might indicate that there are
strong multicollinearity or other numerical problems.
Results that is completely equal to the first call with Statsmodels:
random.seed(1234)
lm_python = smf.ols('price ~ make + fuel_system + engine_type + num_of_doors + bore + compression_ratio + height + peak_rpm + 1', data = df)
lm_python.fit().summary()
OLS Regression Results
==============================================================================
Dep. Variable: price R-squared: 0.894
Model: OLS Adj. R-squared: 0.868
Method: Least Squares F-statistic: 35.54
Date: Thu, 21 Feb 2019 Prob (F-statistic): 5.24e-62
Time: 18:17:37 Log-Likelihood: -1899.7
No. Observations: 205 AIC: 3879.
Df Residuals: 165 BIC: 4012.
Df Model: 39
Covariance Type: nonrobust
=========================================================================================
coef std err t P>|t| [0.025 0.975]
-----------------------------------------------------------------------------------------
Intercept 1.592e+04 1.21e+04 1.320 0.189 -7898.396 3.97e+04
make[T.audi] 6519.7045 2371.807 2.749 0.007 1836.700 1.12e+04
make[T.bmw] 1.427e+04 2292.551 6.223 0.000 9740.771 1.88e+04
make[T.chevrolet] -571.8236 2860.026 -0.200 0.842 -6218.788 5075.141
make[T.dodge] -1186.3430 2261.240 -0.525 0.601 -5651.039 3278.353
make[T.honda] 2779.6496 2891.626 0.961 0.338 -2929.709 8489.009
make[T.isuzu] 3098.9677 2592.645 1.195 0.234 -2020.069 8218.004
make[T.jaguar] 1.752e+04 2416.313 7.252 0.000 1.28e+04 2.23e+04
make[T.mazda] 306.6568 2134.567 0.144 0.886 -3907.929 4521.243
make[T.mercedes-benz] 1.698e+04 2320.871 7.318 0.000 1.24e+04 2.16e+04
make[T.mercury] 2958.1002 3605.739 0.820 0.413 -4161.236 1.01e+04
make[T.mitsubishi] -1188.8337 2284.697 -0.520 0.604 -5699.844 3322.176
make[T.nissan] -1211.5463 2073.422 -0.584 0.560 -5305.405 2882.312
make[T.peugot] 3057.0217 4255.809 0.718 0.474 -5345.841 1.15e+04
make[T.plymouth] -894.5921 2332.746 -0.383 0.702 -5500.473 3711.289
make[T.porsche] 9558.8747 3688.038 2.592 0.010 2277.044 1.68e+04
make[T.renault] -2124.9722 2847.536 -0.746 0.457 -7747.277 3497.333
make[T.saab] 3490.5333 2319.189 1.505 0.134 -1088.579 8069.645
make[T.subaru] -1.636e+04 4002.796 -4.087 0.000 -2.43e+04 -8456.659
make[T.toyota] -770.9677 1911.754 -0.403 0.687 -4545.623 3003.688
make[T.volkswagen] 406.9179 2219.714 0.183 0.855 -3975.788 4789.623
make[T.volvo] 5433.7129 2397.030 2.267 0.025 700.907 1.02e+04
fuel_system[T.2bbl] 2142.1594 2232.214 0.960 0.339 -2265.226 6549.545
fuel_system[T.4bbl] 464.1109 3999.976 0.116 0.908 -7433.624 8361.846
fuel_system[T.idi] 1.991e+04 6622.812 3.007 0.003 6837.439 3.3e+04
fuel_system[T.mfi] 3716.5201 3936.805 0.944 0.347 -4056.488 1.15e+04
fuel_system[T.mpfi] 3964.1109 2267.538 1.748 0.082 -513.019 8441.241
fuel_system[T.spdi] 3240.0003 2719.925 1.191 0.235 -2130.344 8610.344
fuel_system[T.spfi] 932.1959 4019.476 0.232 0.817 -7004.041 8868.433
engine_type[T.dohcv] -1.208e+04 4205.826 -2.872 0.005 -2.04e+04 -3773.504
engine_type[T.l] -4833.9860 3763.812 -1.284 0.201 -1.23e+04 2597.456
engine_type[T.ohc] -4038.8848 1213.598 -3.328 0.001 -6435.067 -1642.702
engine_type[T.ohcf] 9618.9281 3504.600 2.745 0.007 2699.286 1.65e+04
engine_type[T.ohcv] 3051.7629 1445.185 2.112 0.036 198.323 5905.203
engine_type[T.rotor] 1403.9928 3217.402 0.436 0.663 -4948.593 7756.579
num_of_doors[T.two] -419.9640 521.754 -0.805 0.422 -1450.139 610.211
bore 3993.4308 1373.487 2.908 0.004 1281.556 6705.306
compression_ratio -1200.5665 460.681 -2.606 0.010 -2110.156 -290.977
height -80.7141 146.219 -0.552 0.582 -369.417 207.988
peak_rpm -0.5903 0.790 -0.747 0.456 -2.150 0.970
==============================================================================
Omnibus: 65.777 Durbin-Watson: 1.217
Prob(Omnibus): 0.000 Jarque-Bera (JB): 399.594
Skew: 1.059 Prob(JB): 1.70e-87
Kurtosis: 9.504 Cond. No. 3.26e+05
==============================================================================
There is the need to check correspondence in predictive variables as pd.get_dummies does an extensive obtaining of all dummy variables, and Statsmodels applies an N-1 levels inside the categorical variable selection.

PyTorch next(iter(training_loader)) extremely slow, simple data, can't num_workers?

Here x_dat and y_dat are just really long 1-dimensional tensors.
class FunctionDataset(Dataset):
def __init__(self):
x_dat, y_dat = data_product()
self.length = len(x_dat)
self.y_dat = y_dat
self.x_dat = x_dat
def __getitem__(self, index):
sample = self.x_dat[index]
label = self.y_dat[index]
return sample, label
def __len__(self):
return self.length
...
data_set = FunctionDataset()
...
training_sampler = SubsetRandomSampler(train_indices)
validation_sampler = SubsetRandomSampler(validation_indices)
training_loader = DataLoader(data_set, sampler=training_sampler, batch_size=params['batch_size'], shuffle=False)
validation_loader = DataLoader(data_set, sampler=validation_sampler, batch_size=valid_size, shuffle=False)
I have also tried pinning the memory for the two loaders. Setting num_workers to > 0 gives me run-time errors between the processes (like EOF error and interruption errors). I get my batch with:
x_val, target = next(iter(training_loader))
The entire data-set would fit into memory/gpu but I would like to emulate batches for this experiment. Profiling my process gives me the following:
16276989 function calls (16254744 primitive calls) in 38.779 seconds
Ordered by: cumulative time
ncalls tottime percall cumtime percall filename:lineno(function)
1745/1 0.028 0.000 38.780 38.780 {built-in method builtins.exec}
1 0.052 0.052 38.780 38.780 simple aprox.py:3(<module>)
1 0.000 0.000 36.900 36.900 simple aprox.py:519(exploreHeatmap)
1 0.000 0.000 36.900 36.900 simple aprox.py:497(optFromSample)
1 0.033 0.033 36.900 36.900 simple aprox.py:274(train)
705/483 0.001 0.000 34.495 0.071 {built-in method builtins.next}
222 1.525 0.007 34.493 0.155 dataloader.py:311(__next__)
222 0.851 0.004 12.752 0.057 dataloader.py:314(<listcomp>)
3016001 11.901 0.000 11.901 0.000 simple aprox.py:176(__getitem__)
21 0.010 0.000 10.891 0.519 simple aprox.py:413(validationError)
443 1.380 0.003 9.664 0.022 sampler.py:136(__iter__)
663/221 2.209 0.003 8.652 0.039 dataloader.py:151(default_collate)
221 0.070 0.000 6.441 0.029 dataloader.py:187(<listcomp>)
442 6.369 0.014 6.369 0.014 {built-in method stack}
3060221 2.799 0.000 5.890 0.000 sampler.py:68(<genexpr>)
3060000 3.091 0.000 3.091 0.000 tensor.py:382(<lambda>)
222 0.001 0.000 1.985 0.009 sampler.py:67(__iter__)
222 1.982 0.009 1.982 0.009 {built-in method randperm}
663/221 0.002 0.000 1.901 0.009 dataloader.py:192(pin_memory_batch)
221 0.000 0.000 1.899 0.009 dataloader.py:200(<listcomp>)
....
Suggesting the data loader is immensely slow compared to the remaining activity of my experiment (training the model and lots of other computations etc.). What's going wrong and what would be the best way to speed this up?

When retrieving a batch with
x, y = next(iter(training_loader))
you actually create a new instance of dataloader iterator at each call (!) See this thread for more infotrmation.
What you should do instead is create the iterator once (per epoch):
training_loader_iter = iter(training_loader)
and then call next for each batch on the iterator
for i in range(num_batches_in_epoch):
x, y = next(training_loader_iter)
I had similar issue before, and this also made the EOF errors you experience when using multiple workers go away.

3D Surface Colormap in Python

There's another problem I'm facing now. I have a data file like the following:
# Time THR-1 ALA-2 PRO-3 VAL-4 PRO-5 MET-6 PRO-7 ASP-8 LEU-9 LYS-10 ASN-11 VAL-12 LYS-13 SER-14 LYS-15 ILE-16 GLY-17 SER-18 THR-19 GLU-20 ASN-21 LEU-22 LYS-23 HIS-24 GLN-25 PRO-26 GLY-27 GLY-28 GLY-29 LYS-30 VAL-31 GLN-32 ILE-33 ILE-34 ASN-35 LYS-36 LYS-37 LEU-38 ASP-39 LEU-40 SER-41 ASN-42 VAL-43 GLN-44 SER-45 LYS-46 CYS-47 GLY-48 SER-49 LYS-50 ASP-51 ASN-52 ILE-53 LYS-54 HIS-55 VAL-56 PRO-57 GLY-58 GLY-59 GLY-60 SER-61 VAL-62 GLN-63 ILE-64 VAL-65 TYR-66 LYS-67 PRO-68 VAL-69 ASP-70 LEU-71 SER-72 LYS-73 VAL-74 THR-75 SER-76 LYS-77 CYS-78 GLY-79 SER-80 LEU-81 GLY-82 ASN-83 ILE-84 HIS-85 HIS-86 LYS-87 PRO-88 GLY-89 GLY-90 GLY-91 GLN-92 VAL-93 GLU-94 VAL-95 LYS-96 SER-97 GLU-98 LYS-99 LEU-100 ASP-101 PHE-102 LYS-103 ASP-104 ARG-105 VAL-106 GLN-107 SER-108 LYS-109 ILE-110 GLY-111 SER-112 LEU-113 ASP-114 ASN-115 ILE-116 THR-117 HIS-118 VAL-119 PRO-120 GLY-121 GLY-122 GLY-123 ASN-124 DA-1 DA-2 DA-3 DC-4 DA-5 DT-6 DG-7 DT-8 DT-9 DA-10 DA-11 DA-12 DC-13 DA-14 DT-15 DG-16 DT-17 DT-18 DT-19 DA-1 DA-2 DA-3 DC-4 DA-5 DT-6 DG-7 DT-8 DT-9 DT-10 DA-11 DA-12 DC-13 DA-14 DT-15 DG-16 DT-17 DT-18 DT-19
0.000 84.841 0.274 8.595 -4.939 1.713 -1.704 0.768 -127.825 5.554 108.207 5.297 8.390 212.124 2.830 39.479 8.168 0.458 8.848 6.897 -83.882 29.016 9.647 308.856 6.400 32.481 11.327 10.372 0.247 -3.669 45.391 7.648 -6.990 16.870 11.946 18.778 29.161 127.841 -1.885 -49.943 4.716 6.552 16.029 4.803 7.307 5.423 35.449 -1.362 0.703 0.817 5.544 -14.168 -2.450 0.138 10.984 2.680 -0.238 -0.204 -1.814 -0.273 0.971 -0.256 2.553 -1.172 0.337 0.659 -3.890 8.570 1.180 2.319 -10.711 0.433 0.320 7.904 -0.021 1.672 -0.895 -1.804 -0.317 0.233 0.013 1.462 -1.310 -3.139 -1.453 -4.536 0.559 59.050 -10.891 3.089 5.579 9.818 6.599 -1.635 -34.622 2.576 14.145 9.062 -82.518 51.319 -5.944 -42.734 -0.065 5.200 -18.819 -1.670 0.354 -0.142 -0.938 -4.108 -0.582 -0.511 -0.452 0.763 -21.291 2.587 -5.088 -0.458 5.958 -0.746 -0.587 0.600 6.134 9.432 -47.476 0.517 -0.958 -1.246 0.005 -1.422 -5.105 -2.815 -6.459 -1.618 56.055 117.408 92.845 60.554 -6.065 -9.293 -3.752 -5.407 -1.491 -4.924 -0.944 13.894 32.688 15.937 2.866 -0.934 25.169 1.291 -5.292 -8.727 5.852 -8.092 -40.334 -18.542 0.468 -6.011 -2.043 -1.305 -0.959
10.000 127.315 0.993 15.230 12.627 0.804 0.642 -2.810 -101.634 5.500 114.097 3.368 9.100 162.819 -10.033 39.935 6.920 9.887 9.732 4.997 -79.368 25.134 -5.714 307.359 5.781 34.996 8.885 7.234 -5.875 -0.094 31.674 3.963 -8.064 14.720 12.726 25.431 25.011 108.108 -0.293 -63.815 4.442 1.071 12.768 2.871 1.451 2.179 30.666 -2.066 0.995 1.496 3.384 -1.398 -0.776 -0.101 5.159 1.092 -0.829 -0.205 -0.125 1.054 0.574 -0.291 1.106 0.875 -1.106 -1.955 1.153 4.273 0.628 1.305 -5.547 0.755 0.126 3.704 0.925 0.074 -0.516 3.643 -0.133 -0.064 0.717 0.547 0.197 -0.408 -0.912 -1.296 0.508 35.027 -3.056 10.216 5.885 8.755 -0.792 -1.442 -28.498 2.122 6.803 1.344 -58.583 47.395 -2.332 -32.863 -2.826 5.311 -23.087 6.478 -0.205 0.288 -0.373 4.358 0.362 -1.010 -0.352 2.271 -13.406 -2.747 -4.616 -2.275 3.943 -4.391 -7.063 -0.599 3.081 12.778 -40.043 0.327 -1.940 -2.012 2.592 2.909 1.041 0.658 -0.868 -3.206 16.355 109.843 107.372 63.801 8.499 0.931 2.639 -0.884 0.214 1.880 -2.379 8.408 12.583 10.883 23.083 7.955 31.277 0.539 3.992 -0.887 12.925 -4.248 -31.420 -4.812 1.125 3.287 -0.532 -0.438 0.291
20.000 84.636 5.538 15.954 10.437 0.439 1.773 -1.913 -96.625 5.704 132.598 -0.572 6.877 174.628 -9.400 32.417 -0.264 3.812 6.175 5.056 -62.617 25.479 -1.171 288.031 8.114 37.636 10.461 4.612 -3.521 -0.335 37.957 6.596 -11.250 12.510 11.557 21.128 37.344 135.293 -2.163 -80.896 0.912 1.963 1.101 2.815 6.051 5.374 28.443 0.905 1.734 0.813 5.060 -1.365 1.653 -0.415 4.862 1.758 -0.572 -0.339 0.423 0.759 1.036 -0.543 0.783 0.102 -0.971 -1.529 -1.595 5.519 0.587 1.306 -2.813 0.605 0.761 4.542 0.698 0.767 -0.050 2.201 -0.084 0.563 0.357 0.422 0.642 0.588 -1.426 -1.375 1.455 31.332 -3.390 16.696 15.616 13.449 0.096 -2.711 -24.804 1.969 4.095 2.078 -58.303 47.776 -1.047 -22.013 -2.270 4.204 -11.059 3.952 0.382 -0.863 0.010 3.473 0.375 -1.301 -0.037 1.396 -14.392 -2.887 -5.915 -2.315 5.888 -3.365 -5.950 -2.439 4.814 7.125 -46.399 4.393 5.939 -0.508 2.461 2.562 -0.717 4.225 3.642 4.664 27.859 104.835 114.077 74.730 8.410 1.862 0.061 -1.288 -1.181 2.106 4.346 9.017 29.050 -5.088 14.618 4.149 5.062 1.369 15.083 9.537 18.306 -1.165 -8.966 3.864 3.523 7.232 4.275 1.888 4.708
30.000 91.953 11.008 15.794 12.043 0.596 4.611 1.048 -70.764 7.475 72.100 1.360 6.891 150.455 -7.180 11.932 4.845 9.519 6.184 4.684 -57.283 24.797 0.393 275.626 14.021 22.233 10.877 0.934 -7.551 -2.439 27.929 5.098 -6.797 12.784 12.140 19.698 25.762 108.882 0.267 -54.801 1.470 2.139 1.302 1.996 2.021 3.090 22.690 0.669 1.347 0.113 5.378 -1.570 0.585 -0.143 1.156 -0.050 -1.086 0.148 -0.017 -0.417 -0.201 -1.304 0.808 -0.950 -0.958 -1.741 0.200 2.846 0.633 1.279 -3.693 0.338 -1.058 3.651 0.009 0.202 -1.009 0.037 -0.245 -0.183 -0.615 0.192 -0.386 0.426 -1.800 -2.009 0.496 33.517 -4.213 15.421 16.942 14.559 0.109 -2.553 -25.113 1.199 2.074 -0.265 -56.399 40.657 -0.746 -24.020 -1.986 3.400 -9.631 1.384 0.502 -1.001 0.547 2.622 -0.201 -1.062 -0.916 0.493 -14.621 -2.660 -4.459 -1.066 3.788 -4.289 -7.086 2.460 5.341 8.759 -39.474 -0.051 2.116 0.498 1.267 0.728 1.071 1.155 0.824 3.214 32.413 124.028 144.011 80.795 11.199 5.365 1.969 0.659 2.780 2.311 1.671 14.244 33.170 -6.859 -6.106 13.690 4.742 0.645 17.301 12.245 15.829 -11.976 -22.289 3.100 1.725 5.538 5.041 3.517 -0.205
40.000 149.956 11.453 22.603 13.125 1.909 5.563 1.533 -90.126 5.479 90.590 4.141 6.652 173.681 -3.703 24.551 3.012 10.247 12.607 7.241 -64.707 21.636 -0.285 276.445 6.223 29.727 8.346 5.092 -5.591 -2.969 27.881 3.581 -6.824 13.884 11.709 21.034 25.732 104.610 -0.237 -54.221 1.960 1.674 2.394 1.727 6.499 3.453 25.335 0.636 0.754 -0.591 5.789 -3.344 1.182 -0.366 0.810 0.901 -0.625 -0.997 -0.241 0.214 0.311 -0.312 0.498 -1.336 -0.911 -1.210 -2.459 3.182 0.599 0.713 -4.273 0.326 0.522 3.207 0.312 0.830 -0.558 1.351 -0.017 0.569 -0.367 0.966 -0.637 -2.392 -2.722 -3.405 0.818 39.708 -2.537 16.297 14.229 10.427 0.837 -1.855 -24.033 0.996 5.579 -1.055 -65.068 48.891 -2.411 -21.785 -2.094 1.285 -3.668 1.264 0.463 0.070 -0.034 2.779 0.115 -0.947 1.107 0.337 -16.009 -3.881 -5.203 -1.503 0.358 -4.410 -8.007 -1.383 10.872 17.390 -47.147 1.140 -2.218 -0.597 -0.312 0.685 1.781 5.662 1.917 1.504 32.806 123.230 132.991 68.245 11.523 3.048 0.389 -0.890 0.170 2.100 1.166 11.693 31.756 2.595 19.844 24.565 30.414 11.828 18.563 22.426 20.596 -13.383 -18.574 -2.142 4.737 1.680 0.071 3.983 -0.001
For which, I'm trying to plot a 3D colormap with time in the x-axis, number of columns in the y-axis and their respective values in the z-axis.
I have written the following code to extract data from the file and to plot it:
#!/usr/bin/python
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from matplotlib import cm
from matplotlib.ticker import LinearLocator, FormatStrFormatter
import numpy as np
data = np.loadtxt('contrib_pol.dat', skiprows=1)
x = data[:,0]
y = range(1,len(data[0,:]))
z = []
fig=plt.figure()
ax=fig.gca(projection='3d')
for r, row in enumerate(data):
for c, col in enumerate(row[1:], start=1):
z.append(col)
surf = ax.plot_surface(x, y, z, cmap=cm.coolwarm,
linewidth=0, antialiased=False)
plt.show()
And I'm having the errors:
Traceback (most recent call last):
File "./barplot.py", line 31, in <module>
linewidth=0, antialiased=False)
File "/usr/lib/python2.7/dist-packages/mpl_toolkits/mplot3d/axes3d.py", line 1586, in plot_surface
X, Y, Z = np.broadcast_arrays(X, Y, Z)
File "/home/microbio/.local/lib/python2.7/site-packages/numpy/lib/stride_tricks.py", line 250, in broadcast_arrays
shape = _broadcast_shape(*args)
File "/home/microbio/.local/lib/python2.7/site-packages/numpy/lib/stride_tricks.py", line 185, in _broadcast_shape
b = np.broadcast(*args[:32])
ValueError: shape mismatch: objects cannot be broadcast to a single shape
Can you help???

Check the docstring of plot_surface, it states that you need to supply the data as 2D-arrays. With two additional lines of code, you can make it work using numpy.meshgrid to get the base grid, and a numpy.reshape to get your z value in the right format.
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from matplotlib import cm
from matplotlib.ticker import LinearLocator, FormatStrFormatter
import numpy as np
data = np.loadtxt('contrib_pol.dat', skiprows=1)
x = data[:,0]
y = range(1,len(data[0,:]))
z = []
fig=plt.figure()
ax=fig.gca(projection='3d')
for r, row in enumerate(data):
for c, col in enumerate(row[1:], start=1):
z.append(col)
# generate the grid
xx, yy = np.meshgrid(x, y)
# reshaping your data to match the grid shape
zz = np.reshape(z, (len(y), len(x)))
surf = ax.plot_surface(xx, yy, zz, cmap=cm.coolwarm,
linewidth=0, antialiased=False)
plt.show()