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Python numerical integration performance

Out of the box performance of python numerical integration is poor. Here we present three python versions of the trapezoidal rule.

Python code (naive version)

import math
import time

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Install sofware dependencies

#export pkgmngt=dnf
export pkgmngt=apt
sudo $pkgmngt update && sudo $pkgmngt install tree exa zsh wget curl unzip fontconfig -y

Font Install

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! --------------------------------------------------------
! compile command line:
! ifort -O2 -i8 -mcmodel=medium -qmkl=parallel ./hermitianEigen-small.f90 -o ./hermitianEigen-small  ${MKLROOT}/lib/intel64/libmkl_lapack95_ilp64.a -L${MKLROOT}/lib/intel64 -lpthread -lm -ldl
! --------------------------------------------------------

program hermitianEigen

    use, intrinsic :: iso_fortran_env
    use lapack95, only: heevd

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Purpose

To benchmark Python (Numpy) default procedure to find all eigenvalues and eigenvectors of a complex (hermitian) matrix and compare the results with Fortran using either MKL and OpenBLAS libraries.

Python code

import time
import numpy as np

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! --------------------------------------------------------------------------------------
!
! 01. Purpose: Solves a simple eigenvalue/eigenvector problem in order to check
!     for the zheev thread locking bug #1560
!     https://github.com/xianyi/OpenBLAS/issues/1560
!
! 02. Compile and build
!
! export MAX_THREADS=4
! export OPENBLAS_NUM_THREADS=$MAX_THREADS

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Install Intel Compilers on Windows via WSL2

Note: This step-by-step tutorial assumes that you already have a Linux distribution (Debian, Ubuntu...) installed on your WSL environment.

Update your package repository inside WSL2

sudo apt update

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Timed Openblas library build

cd /tmp
libver=0.3.21
wget https://github.com/xianyi/OpenBLAS/releases/download/v$libver/OpenBLAS-$libver.tar.gz
tar xf OpenBLAS-$libver.tar.gz
cd OpenBLAS-$libver

export USE_THREAD=1

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cat <<EOF > $HOME/.minirc.dfl
pu localecho        Yes
pu addlinefeed      Yes
pu linewrap         Yes
pu addcarreturn     Yes
EOF

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2022-03-27

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'''
Dados os dois anos abaixo, este programa exibe todas as datas 
que são tanto palíndromas (capicuas) como ambigramas (rotacionais).
'''

ANO_INI = 2000
ANO_FIM = 2100

import datetime as dt