New machine does not use more than 1 core for linear algebra, unresponsive to changing env variables

Questions
4

Maybe this is not the answer you are looking for. Since you are in Linux and you are using conda, you should define the default channel you want to use (main or conda-forge). After that, the nub of the issue is to install MKL or OpenBLAS (depending on your processor), and yes, it might be hard. Then, please update PyMC3 and Theano and Arviz.

Now, you need to include some environment variables in your .bashrc:

export OPENBLAS_NUM_THREADS=1
export MKL_NUM_THREADS=1
export NUMEXPR_NUM_THREADS=1
export OMP_NUM_THREADS=1

You wrote GOTO, I am not familiar with that environment variable.

After this, your code:

import pymc3 as pm
import numpy as np
import arviz as az

SEED = 99138 # from random.org
np.random.seed(SEED)

length = 20 # you may want to change this
x_pos = np.linspace(0,99,length)
signal = np.random.rand(length)
u_pos = np.linspace(0, 10, 10000)

fourier_matrix_real = np.exp(np.cos(2.0*np.pi*np.outer(u_pos, x_pos)))
fourier_matrix_imag = np.exp(np.sin(2.0*np.pi*np.outer(u_pos, x_pos)))
data_real = np.dot(fourier_matrix_real, signal)
data_imag = np.dot(fourier_matrix_imag, signal)
sd = 0.1*np.sqrt(data_real**2+data_imag**2)

with pm.Model() as model:
    signal_prior = pm.Uniform('signal',lower=0,upper=1,shape=length)
    prediction_real = pm.math.dot(fourier_matrix_real, signal_prior)
    prediction_imag = pm.math.dot(fourier_matrix_imag, signal_prior)
    likelihood_real = pm.Normal('real_FT',mu=prediction_real,sd=sd,observed = data_real)
    likelihood_imag = pm.Normal('imag_FT',mu=prediction_imag,sd=sd,observed = data_real)

    posterior = pm.sample(random_seed=SEED) # pay attention to this
    
print(az.summary(posterior))

How long did it take? How many chains were sampled?

I am writing this because I don’t know if you have the best configuration for PyMC3, so the first step is to change those four variables in your .bashrc from 1 to 16 (change all of them at once). If you do those changes in the terminal, don’t forget to run source .bashrc. When you have found the optimal number (for me 1 is the optimal number, otherwise it won’t run), change this line to include the option cores:

posterior = pm.sample(random_seed=SEED, cores=1) # pay attention to this, change cores from 1 to 16

With that, I’m sure that you will find that cores=16 uses every core of your processor, in fact, if you don’t include the option cores, the number of chains will be eight (am I wrong?). Why? You said you have a new processor with eight cores, so by default PyMC3 uses that number for the number of chains to be sampled, in other words, all the cores are used when the model is being sampled. If you want to change the number of chains, use the option cores.

If I am not mistaken, PyMC3 uses one thread (although it might be one core) for one chain. Remember that you care about the chains, not the cores.