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AL_Fct.py
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Fri, May 10, 20:10

AL_Fct.py
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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Wed Mar 13 16:42:29 2019
@author: jecker
"""
from __future__ import division
import numpy as np
from IPython.display import display, Latex
import matplotlib.pyplot as plt
import math
import plotly
import plotly.plotly as py
import plotly.graph_objs as go
plotly.offline.init_notebook_mode(connected=True)
from IPython.core.magic import register_cell_magic
from IPython.display import HTML, display
@register_cell_magic
def bgc(color, cell=None):
script = (
"var cell = this.closest('.jp-CodeCell');"
"var editor = cell.querySelector('.jp-Editor');"
"editor.style.background='{}';"
"this.parentNode.removeChild(this)"
).format(color)
display(HTML('<img src onerror="{}">'.format(script)))
#PRINTS Equations, systems, matrix
def strEq(n,coeff):# Latex str of one equation in format a1x1+ ...+anxn or with coefficients.
Eq=''
if str(coeff)=='' or coeff==[]:
if n==1:
Eq=Eq + 'a_1x_1 = b'
elif n==2:
Eq=Eq + 'a_1x_1 + a_2x_2 = b'
else:
Eq=Eq + 'a_1x_1 + \ldots + ' + 'a_' + str(n) + 'x_'+ str(n) + '=b'
else :
if n==1:
Eq=Eq + str(round(coeff[0],3) if coeff[0] % 1 else int(coeff[0]))+ 'x_'+str(1) +\
'='+ str(round(coeff[len(coeff)-1],3) if coeff[len(coeff)-1] % 1 else int(coeff[len(coeff)-1]))
else:
Eq=Eq + str(round(coeff[0],3) if coeff[0] % 1 else int(coeff[0]))+ 'x_'+str(1)
for i in range(1,n-1):
Eq=Eq + ' + ' + str(round(coeff[i],3) if coeff[i] %1 else int(coeff[i])) + 'x_' + str(i+1)
Eq=Eq + ' + ' +str(round(coeff[len(coeff)-2],3) if coeff[len(coeff)-2] % 1 else int(coeff[len(coeff)-2]))\
+ 'x_' + str(n) + '=' + str(round(coeff[len(coeff)-1],3) if coeff[len(coeff)-1] % 1 else int(coeff[len(coeff)-1]))
return Eq
def printEq(n,coeff):# Latex Print of one equation in format a1x1+ ...+anxn or with coefficients.
texEq='$'
texEq=texEq+ strEq(n,coeff)
texEq=texEq + '$'
display(Latex(texEq))
def printSyst(m,n,MatCoeff):# Latex Print of one system of m equation in format ai1x1+ ...+ainxn=bi or with coeff in MatCoeff.
texSyst='$\\begin{cases}'
Eq_list=[]
MatCoeff=np.array(MatCoeff) #just in case it's not
for i in range(m):
if str(MatCoeff)=='':
Eq_i=''
if n==1:
Eq_i=Eq_i + 'a_{' + str(i+1) + '1}' + 'x_1 = b_' + str(i+1)
elif n==2:
Eq_i=Eq_i + 'a_{' + str(i+1) + '1}' + 'x_1 + ' + 'a_{' + str(i+1) + '2}' + 'x_2 = b_' + str(i+1)
else:
Eq_i=Eq_i + 'a_{' + str(i+1) + '1}' + 'x_1 + \ldots +' + 'a_{' + str(i+1) +str(n) + '}' + 'x_'+ str(n) + '=b_' + str(i+1)
else:
Eq_i=strEq(n,MatCoeff[i,:])
Eq_list.append(Eq_i)
texSyst=texSyst+ Eq_list[i] + '\\\\'
texSyst =texSyst+ '\\end{cases}$'
display(Latex(texSyst))
def texMatrix(A): #return tex expression of one matrix
texApre ='\\left(\\begin{array}{'
texA = ''
for i in np.asarray(A) :
texALigne = ''
texALigne = texALigne + str(round(i[0],3) if i[0] %1 else int(i[0]))
if texA == '' :
texApre = texApre + 'c'
for j in i[1:] :
if texA == '' :
texApre = texApre + 'c'
texALigne = texALigne + ' & ' + str(round(j,3) if j %1 else int(j))
texALigne = texALigne + ' \\\\'
texA = texA + texALigne
texA = texApre + '} ' + texA[:-2] + ' \\end{array}\\right)'
return texA
def printA(A) : #Print matrix
texA='$'+ texMatrix(A) + '$'
# print(texA)
display(Latex(texA))
def printEquMatrices(listOfMatrices): #list of matrices is M=[M1, M2, ..., Mn]
texEqu='$' + texMatrix(listOfMatrices[0])
for i in range(1,len(listOfMatrices)):
texEqu=texEqu+ '\\quad \\sim \\quad' + texMatrix(listOfMatrices[i])
texEqu=texEqu+ '$'
display(Latex(texEqu))
#%% Functions to enter smth
def EnterInt(n): #function enter integer.
while type(n)!=int:
try:
n=int(n)
if n<=0:
print("Le nombre ne peut pas être négatif!")
print("Entrez à nouveau : ")
n=input()
except:
print("Ce n'est pas un entier!")
print("Entrez à nouveau :")
n=input()
n=int(n)
return n
def EnterListReal(n): #function enter list of real numbers.
coeff=input()
while type(coeff)!=list:
try:
coeff=[float(eval(x)) for x in coeff.split(',')]
if len(coeff)!=n+1:
print("Vous n'avez pas entré le bon nombre de réels!")
print("Entrez à nouveau : ")
coeff=input()
except:
print("Ce n'est pas le bon format!")
print("Entrez à nouveau")
coeff=input()
#coeff[abs(coeff)<1e-15]=0 #ensures that 0 is 0.
return coeff
#%%Verify if sol is the solution of the equation with coefficients coeff
def SolOfEq(sol,coeff, i):
A = np.asarray(coeff[0:len(coeff)-1])
if abs(np.dot(A,sol)-coeff[len(coeff)-1])<1e-10:
print("La suite entrée est une solution de l'équation", i)
else:
print("La suite entrée n'est pas une solution de l'équation",i)
return abs(np.dot(A,sol)-coeff[len(coeff)-1])<1e-10
def SolOfSyst(solution,MatriceCoeff,m):
MatriceCoeff=np.array(MatriceCoeff)
isSol=[SolOfEq(solution, MatriceCoeff[i,:],i+1) for i in range(0,m)]
if all(isSol[i]==True for i in range(len(isSol))):
print("C'est une solution du système")
else:
print("Ce n'est pas une solution du système")
#%%Plots using plotly
def Plot2DSys(xL,xR,p,MatCoeff): # small values for p allows for dots to be seen
MatCoeff=np.array(MatCoeff)
x=np.linspace(xL,xR,p)
legend=[]
data=[]
for i in range(1,len(MatCoeff)+1):
trace=go.Scatter(x=x, y= (MatCoeff[i-1,2]-MatCoeff[i-1,0]*x)/MatCoeff[i-1,1], name='Droite %d'%i)
data.append(trace)
fig = go.Figure(data=data)
plotly.offline.iplot(fig)
def Plot3DSys(xL,xR,p,MatCoeff): # small values for p allows for dots to be seen
MatCoeff=np.array(MatCoeff)
x=np.linspace(xL,xR,p)
legend=[]
data=[]
for i in range(1,len(MatCoeff)+1):
trace=go.Scatter(x=x, y= (MatCoeff[i-1,2]-MatCoeff[i-1,0]*x)/MatCoeff[i-1,1], name='Droite %d'%i)
data.append(trace)
fig = go.Figure(data=data)
plotly.offline.iplot(fig)
#%%Echelonnage
def echZero(indice, M): #echelonne la matrice pour mettre les zeros dans les lignes du bas. M (matrice ou array) et Mat (list) pas le même format.
Mat=M[indice==False,:].ravel()
Mat=np.concatenate([Mat,M[indice==True,:].ravel()])
Mat=Mat.reshape(len(M), len(M[0,:]))
return Mat
def Eij(M, i,j): #matrice elementaire, echange la ligne i avec la ligne j
M[[i,j],:]=M[[j,i],:]
return M
def Ealpha(M, i, alpha): # matrice elementaire, multiple la ligne i par le scalaire alpha
M[i,:]=alpha*M[i,:]
return M
def Eijalpha(M, i,j, alpha): # matrice elementaire, AJOUTE à la ligne i alpha *ligne j. Attention alpha + ou -
M[i,:]=M[i,:] + alpha *M[j,:]
return M
def echelonMat(MatCoeff):
Mat=np.array(MatCoeff)
Mat=Mat.astype(float) # in case the array in int instead of float.
numPivot=0
for i in range(len(Mat)):
j=i
while all(abs(Mat[j:,i])<1e-15) and j!=len(Mat[0,:])-1: #if column (or rest of) is zero, take next column
j+=1
if j==len(Mat[0,:])-1:
print("La matrice est sous la forme échelonnée")
printEquMatrices([MatCoeff, Mat])
break
if abs(Mat[i,j])<1e-15:
Mat[i,j]=0
zero=abs(Mat[i:,j])<1e-15
M= echZero(zero,Mat[i:,:] )
Mat[i:,:]=M
Mat=Ealpha(Mat, i,1/Mat[i,j] ) #normalement Mat[i,i]!=0
for k in range(i+1,len(MatCoeff)):
Mat=Eijalpha(Mat, k,i, -Mat[k,j])
#Mat[k,:]=[0 if abs(Mat[k,l])<1e-15 else Mat[k,l] for l in range(len(MatCoeff[0,:]))]
numPivot+=1
Mat[abs(Mat)<1e-15]=0
printA(np.asmatrix(Mat))

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