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Monday, June 22, 2020

Install vim without sudo access


Sometimes, we would like to install the VIM editor in Linux, but we do not have root or sudo access. In the following, I show the complete commands to install it without root or sudo access. 

a) firstly, we download the vim for github 
	git clone https://github.com/vim/vim.git
	cd vim 
	cd src 
	make distclean 
	./configure --prefix=\$HOME/usr/local
b) Maybe, you will get those error message:
checking for tgetent()... configure: error: NOT FOUND!

we need to install the package ncurses: download the ncurses from http://ftp.gnu.org/pub/gnu/ncurses/ 
	wget http://ftp.gnu.org/pub/gnu/ncurses/ncurses-6.1.tar.gz
	tar -xvf ncurses-6.1.tar.gz
	cd ncurses-6.1
	./configure --prefix=\$HOME/usr/local
	make
	make install
vi ~/.bashrc add the following line 
	export LD_LIBRARY_PATH=\$LD_LIBRARY_PATH:\$HOME/usr/local/lib 
		source ~/.bashrc
c) locate to previous vim directory and install vim. 
	cd xx/xx/vim/
	LDFLAGS=-L\$HOME/usr/local/lib ./configure --prefix=\$HOME/usr/local
	make 
	make install
vi ~/.bashrc add the following line 
	export PATH=\$PATH:\$HOME/usr/local/bin 
	alias vi=vim
	source ~/.bashrc 

4) complete! Enjoy it!
Reference: https://askubuntu.com/questions/158344/no-terminal-library-found-when-compiling-vim https://www.vim.org/git.php
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Thursday, June 18, 2020

Runge-Kutta Method

The fourth order Runge-Kutta method (RK4) is the most widely used algorithm for solving an ordinary differential equation.
\[ dy/dx = f(x,y) \]
\[ y_{n+1} = y_n +\frac{h}{6} (k_1+k_2+k_3+k_4) \],
where
\[ k_1 = f(x_n,y_n) \]
\[ k_2 = f(x_n+\frac{h}{2}, y_n+\frac{h}{2} k_1 \]
\[ k_3 = f(x_n+\frac{h}{2}, y_n+\frac{h}{2} k_2 \]
\[ k_4 = f(x_n+h,y_n+hk_3) .\]

$k_1$ is the slope at the beginning of the interval $[x_n,x_n+h]$.
$k_2$ is the slope at the midpoint of the interval, using slope $k_1$ to determine the value of $y$ at the point $x_n+h/2$ using Euler's method. 
$k_3$ is again the slope at the midpoint, but now using the slope $k_2$ to determine the $y$ value, $y(x_0+n*h+h/2) = y(x_0+n*h)+h/2*f(x_0+n*h+h/2,y(x_0+n*h)+h/2*k1)$.
$k_4$ is the slope at the end of the interval, with its $y$ value determined using $k_3$.
  
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Tuesday, June 9, 2020

Python notes 


import numpy as np
np.power(-1.2,5./3.)
>>>RuntimeWarning: invalid value encountered in power
nan

pow(-1.2,5./3.)
>>>0.6775459407943406-1.173543993917852j

np.seterr(invalid='raise')
try:
	np.power(-1.2,5./3.)
except:
    print('error here')  


def replaceZeroes(data):
  min_nonzero = np.min(data[np.nonzero(data)])
  data[data == 0] = min_nonzero
  return data

install numpy for python2.7 
sudo apt-get install python-pip # install pip for python2 , will get pip2
/usr/bin/python2.7 -m pip install numpy==1.14.6

python setup.py install --prefix=xxx
Python.h not found
sudo apt-get install python-dev # for python2
sudo apt-get install pythonx-dev # x is version of python, i.e. 3.7
sudo apt-get install python-matplotlib # for python2
sudo apt-get install python-scipy

from scipy.misc import derivative
derivative(exp(x), 1.0, dx=1e-6)
To modify the global variable inside the function, we need add the keyword 'global' 
a=0
def fun():
	global a
    a+=1
time 
import time
t0=time.time()
time.time() - t0

numpy insert

array=np.insert(array,0,'s')


if any(x>5 for x in range(-2,20)):
	print('one element >5')
fill matrix with same element 
np.full((2,2),1)
construct matrix 
from scipy.sparse import diags
diagonals = [[1, 2, 3, 4], [1, 2, 3], [1, 2]]
diags(diagonals, [0, -1, 2]).toarray()
diags([1,1],[-1,1],shape=(3,4)).toarray()
print numpy narray nice 
def matprint(mat, fmt="g"):
    col_maxes = [max([len(("{:"+fmt+"}").format(x)) for x in col]) for col in mat.T]
    for x in mat:
        for i, y in enumerate(x):
            print(("{:"+str(col_maxes[i])+fmt+"}").format(y), end="  ")
        print("")

print(np.array2string(A, suppress_small=True, formatter={'float': '{:0.4f}'.format}))
pip update package 
pip install package-name -U --user



a=[1,2,3,4]
a[1:-1] will give 2,3 doesn't include last element 3!
a[1:4] or a[1:] will give 2,3,4 
a[-1] give 4



a=[2]*number # initialize list with same value 2
b=np.full((1,3),2) #give array([[2, 2, 2]])
b[0] give array([2, 2, 2])
c=np.full((3),2) give array([2, 2, 2])
c[0] give 2

insert one row into numpy array 
a=np.zeros((2,2))
#line 1 is the line before to insert, 0 is the axis 
a=np.insert(1,np.array((2,2)),0)
give
array([[ 0.,  0.],
       [ 2.,  2.],
       [ 0.,  0.]])

row_number,col_number = a_array.shape
row_number = len(a_array)

sympy.latex() converts mathematical expressions into Latex equations.


check varible type is numpy.float64
isinstance(numpy.float64(1.3), numpy.float64) 
>>> True
plot odd numbers subplot in matplotlib 
fig, axes = plt.subplots(2, 3, figsize=(20, 10))
fig.delaxes(ax=axes(2,2))
we will get 5 subplots. matplotlib subplot tight_layout 
fig.tight_layout(rect=[0, 0.03, 1, 0.95])
save arrays to file 
import numpy
list1 = [1, 2, 3, 4]
list2 = [0.45, 0.98, 0.89, 0.21]
dat = numpy.array([list1, list2])
dat = dat.T
numpy.savetxt('data.txt', dat, delimiter = ',')




Reference:
https://stackoverflow.com/questions/3419082/write-multiple-numpy-arrays-to-file
https://docs.scipy.org/doc/scipy/reference/generated/scipy.misc.derivative.html
https://gist.github.com/braingineer/d801735dac07ff3ac4d746e1f218ab75
https://stackoverflow.com/questions/8298797/inserting-a-row-at-a-specific-location-in-a-2d-array-in-numpy
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Monday, June 8, 2020

Test two float number if equal

math.isclose(a,b,rel_tol=1e-9,abs_tol=0)
rel_tol is the relative tolerance – it is the maximum allowed difference between a and b, relative to the larger absolute value of a or b.
abs_tol is the minimum absolute tolerance
the result will be: abs(a-b) <= max(rel_tol * max(abs(a), abs(b)), abs_tol)
Return True if the values a and b are close to each other and False otherwise.

  
  import math
  import sys
  print(math.isclose(0.3,0.3+1e-7,rel_tol=sys.float_info.epsilon,abs_tol=0))

bool CompareDoubles2 (double A, double B) 
{
   diff = A - B;
   return (diff < EPSILON) && (-diff < EPSILON);
}
Reference: https://stackoverflow.com/questions/17333/what-is-the-most-effective-way-for-float-and-double-comparison
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Sunday, June 7, 2020

Install scipy 1.4.1

Here is the method to install Scipy 1.4.1.

python3 -m pip install --upgrade pip
pip3 install pybind11
pip3 install --no-cache --upgrade scipy  or pip3 install --upgrade scipy==1.4.1

Reference:
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Saturday, June 6, 2020

Numerical solve the ordinary differential equation with python

Some excellent instructions are listed below.
It is real very easy to get it.


 Just do it!

multiple shooting
A First Course in Ordinary Differential Equations (book)

newton method

henyey relaxation

Finite Difference Schemes from 1st to 4th order

Implicit Euler method

SUite of Nonlinear and DIfferential/ALgebraic Equation Solvers

Solving differential equations using modified Picard iteration

sympy
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