PDFs for Convolution with FFTW

question_code.py

import numpy as np
from scipy.signal import fftconvolve


def get_pdf(pdf_params, x):

    loc = pdf_params[0]
    unc = pdf_params[1]
    pd_loc = pdf_params[2]
    lpb = pdf_params[3]
    upb = pdf_params[4]
    pd_lpb = pdf_params[5]
    pd_upb = pdf_params[6]
    lub = pdf_params[7]
    uub = pdf_params[8]
    pd_lub = pdf_params[9]
    pd_uub = pdf_params[10]
    locs = [lpb, lub, loc, uub, upb]
    pd_locs = [pd_lpb, pd_lub, pd_loc, pd_uub, pd_upb]

    # Actual implementation of PDF
    p_x = np.where((x >= lpb) & (x <= upb),
                    np.interp(x, locs, pd_locs), 0)
    # Normalize
    pdf = p_x / np.sum(p_x)

    return pdf

pdf_x_size = 100000
# Values of X where to calculate PDF
x = np.linspace(-0.05, 1, pdf_x_size, dtype='float16') 

# Define parameters of PDFs
pdf1_params = [0.85887937, 0.14592418, 12.3069, 0.75, 1., 0.57650279, 
                0.57650279, 0.8078059, 0.95373008, 0.57650279, 0.57650279]
pdf2_params = [ 4.00e-02, 2.00e-02, 9.25e+01, -1.00e-02, 5.00e-02, 1.50e+00,
                1.50e+00, 3.00e-02, 500e-02, 1.50e+00, 1.50e+00]

# Creating the pdfs, based on parameters
pdf1 = get_pdf(pdf1_params, x)
pdf2 = get_pdf(pdf2_params, x)

# Do the convovlution with scipy.signal.fftconvolve
convolution_pdf = scipy.signal.fftconvolve(pdf1, pdf2, 'full')
convolution_pdf = convolution_pdf[0:len(pdf1)]