Code Source de version 1.2

inclut le solveur d'équations différentielles

Sou_Sapphire_Solver.py

@@ -0,0 +1,230 @@
+import numpy as np
+import matplotlib.pyplot as plt
+from functools import lru_cache
+
+'''
+
+All the differential equations were solved by hand.
+It took a while.
+
+-Souhail
+
+'''
+
+# af''+bf'+cf=0
+def DIFF_SOLVE(a,b,c,y0,derivative=False):
+    tauBC = b/c
+    tauBA = b/a
+    tau = tauBC*tauBA - 4
+    omega2 = c/a
+    if tau > 0:
+        #print('TAU - 1')
+        r1 = omega2*(-b+np.sqrt(tau/c))
+        r2 = omega2*(-b-np.sqrt(tau/c))
+        if not derivative:
+            return lambda t: y0*((r2*(np.exp(r1*t)-np.exp(r2*t))/(r2-r1))+np.exp(r2*t))
+        else:
+            return lambda t: y0*((r2*(r1*np.exp(r1*t)-r2*np.exp(r2*t))/(r2-r1))+r2*np.exp(r2*t))
+    elif tau < 0:
+        #print('TAU - 2')
+        aph = -b*omega2
+        bet = omega2*np.sqrt(-tau/c)
+        if not derivative:
+            return lambda t: y0*np.exp(aph*t)*(np.cos(bet*t)-(aph/bet)*np.sin(bet*t))
+        else:
+            return lambda t: -aph*y0*np.exp(aph*t)*np.sin(bet*t)*((aph/bet)+(bet/aph))
+    else:
+        #print('TAU - 0')
+        r0 = -b*omega2
+        if not derivative:
+            return lambda t: y0*(1-t*r0)*np.exp(r0*t)
+        else:
+            return lambda t: -y0*r0*r0*np.exp(r0*t)
+
+def EXTREMAS(arr):
+    sign = np.sign(np.diff(arr))
+    sign_d = np.where(np.diff(sign)!=0)[0] + 1
+
+    #boundary check
+    if sign[0] == -1:
+        sign_d = np.concatenate(([0],sign_d))
+    if sign[-1] == 1:
+        sign_d = np.concatenate((sign_d,[len(arr)-1]))
+
+    #the main deal
+    maxima = np.zeros_like(arr,dtype=bool)
+    minima = np.zeros_like(arr,dtype=bool)
+    for i in sign_d:
+        try:
+            if sign[i-1] == 1 and sign[i] == -1:
+                maxima[i] = True
+            elif sign[i-1] == -1 and sign[i] == 1:
+                minima[i] = True
+        except IndexError:
+            pass
+
+    return np.where(maxima)[0], np.where(minima)[0]
+
+'''
+ay''+by'+cy=g(t)
+with g(t)=Asin(w*t+phi)
+'''
+
+def LAPLACE_SOLVE(a,b,c,y0,A,w,phi,derivative=False):
+    delta = b*b-4*a*c
+    sgn = np.sign(delta)
+
+    cphi = np.cos(phi)
+    sphi = np.sin(phi)
+
+    if sgn == 1:
+        r1 = (-b+np.sqrt(delta))/(2*a)
+        r2 = (-b-np.sqrt(delta))/(2*a)
+
+        B = A*r1*sphi+A*w*cphi
+        B /= a*(r1-r2)*(r1*r1+w*w)
+        C = A*r2*sphi+A*w*cphi
+        C /= a*(r2-r1)*(r2*r2+w*w)
+        D = A*np.exp(phi*1j)
+        E = D - 2*A*cphi
+        D /= 2*a*1j*(r1-w*1j)*(r2-w*1j)
+        E /= 2*a*1j*(r1+w*1j)*(r2+w*1j)
+        F = (a*r1*y0+b*y0)/(a*(r1-r2))
+        G = (a*r2*y0+b*y0)/(a*(r2-r1))
+
+        #y(t)=
+        if not derivative:
+            return lambda t: (B+F)*np.exp(r1*t)+(C+G)*np.exp(r2*t)+(D*np.exp(w*t*1j)+E*np.exp(-w*t*1j))*np.sin(w*t)
+        #y'(t)=
+        else:
+            return lambda t: (B+F)*r1*np.exp(r1*t)+(C+G)*r2*np.exp(r2*t)+w*np.sin(w*t)*(D*(1+1j)*np.exp(w*t*1j)+E*(1-1j)*np.exp(-w*t*1j))
+
+    elif sgn == 0:
+        r = -b/(2*a)
+
+        B = -r*r*sphi-2*r*w*cphi+w*w*sphi
+        B *= (A/(a*((r*r+w*w)**2)))
+        C = r*sphi+w*cphi
+        C *= (A/(a*(r*r+w*w)))
+        D = A*np.exp(phi*1j)
+        E = D - 2*A*cphi
+        D /= 2*a*1j*((r-w*1j)**2)
+        E /= 2*a*1j*((r+w*1j)**2)
+        F = y0
+        G = (r+(b/a))*y0
+
+        #y(t)=
+        if not derivative:
+            return lambda t: (B+F+C*t+G*t)*np.exp(r*t)+np.sin(w*t)*(D*np.exp(w*t*1j)+E*np.exp(-w*t*1j))
+        #y'(t)=
+        else:
+            return lambda t: (B+F+C+G)*np.exp(r*t)+(C+G)*t*r*np.exp(r*t)+w*np.sin(w*t)*(D*(1+1j)*np.exp(w*t*1j)+E*(1-1j)*np.exp(-w*t*1j))
+
+    elif sgn == -1:
+        aph = -b/(2*a)
+        bet = np.sqrt(-delta)/(2*a)
+        r1 = aph + bet*1j
+        r2 = aph - bet*1j
+
+        B = A*(r1)*sphi+A*w*cphi
+        C = A*(r2)*sphi+A*w*cphi
+        B /= 2*a*1j*bet*(((r1)**2)+w*w)
+        C /= -2*a*1j*bet*(((r2)**2)+w*w)
+        D = A*np.exp(phi*1j)
+        E = D - 2*A*cphi
+        D /= 2*a*1j*(((aph-w*1j)**2)+bet*bet)
+        E /= 2*a*1j*(((aph+w*1j)**2)+bet*bet)
+        F = a*r1*y0+b*y0
+        G = a*r2*y0+b*y0
+        F /= 2*a*bet*1j
+        G /= 2*a*bet*1j
+
+        #y(t)=
+        if not derivative:
+            return lambda t: (B+F)*np.exp(t*r1)+(C+G)*np.exp(t*r2)+D*np.exp(w*t*1j)+E*np.exp(-w*t*1j)
+        #y'(t)=
+        else:
+            return lambda t: r1*(B+F)*np.exp(t*r1)+r2*(C+G)*np.exp(t*r2)+1j*w*(D*np.exp(w*t*1j)-E*np.exp(-w*t*1j))
+
+@lru_cache
+def LAPLACE_SOLVE_MECH(m,h,k,x0,v0,derivative=False):
+    delta = h*h-4*m*k
+    sgn = np.sign(delta)
+
+    if sgn == 1:
+        r1 = (-h+np.sqrt(delta))/(2*m)
+        r2 = (-h-np.sqrt(delta))/(2*m)
+
+        A = (m*r1*x0+m*v0+h*x0)/(m*(r1-r2))
+        B = (m*r2*x0+m*v0+h*x0)/(m*(r2-r1))
+
+        if not derivative:
+            return lambda t: A*np.exp(r1*t)+B*np.exp(r2*t)
+        else:
+            return lambda t: r1*A*np.exp(r1*t)+r2*B*np.exp(r2*t)
+
+    elif sgn == -1:
+        aph = -h/(2*m)
+        bet = np.sqrt(-delta)/(2*m)
+        r1 = aph+bet*1j
+        r2 = aph-bet*1j
+        A = (m*r1*x0+m*v0+h*x0)/(m*(r1-r2))
+        B = (m*r2*x0+m*v0+h*x0)/(m*(r2-r1))
+
+        if not derivative:
+            return lambda t: A*np.exp(r1*t)+B*np.exp(r2*t)
+        else:
+            return lambda t: r1*A*np.exp(r1*t)+r2*B*np.exp(r2*t)
+
+    else:
+        r = -h/(2*m)
+
+        B = (m*r*x0+m*v0+h*v0)/m
+
+        if not derivative:
+            return lambda t: np.exp(r*t)*(x0+B*t)
+        else:
+            return lambda t: np.exp(r*t)*(x0+B+B*r*t)
+
+def tickUnit(data, unit):
+    abs_data = np.abs(data)
+    scale_factors = [(1e24, 'Y'), (1e21, 'Z'), (1e18, 'E'),(1e15,'P'),
+                     (1e12, 'T'), (1e9, 'G'), (1e6, 'M'),(1e3, 'k'),
+                     (1, ''), (1e-3, 'm'),(1e-6, 'μ'), (1e-9, 'n'),
+                     (1e-12, 'p'),(1e-15,'f'),(1e-18,'a'),
+                     (1e-21,'z'),(1e-24,'y')]
+    for factor, prefix in scale_factors:
+        if np.max(abs_data) >= factor:
+            return f'{{:.1e}} {prefix}{unit}{{}}{{}}'
+    return f'{{:.{int(-np.log10(abs_data.min()))+1}f}} {unit}{{}}{{}}'
+
+if __name__ == '__main__':
+    TIME = np.linspace(0,100,400)
+    a = 1
+    b = 1
+    c = 1
+    y0 = 10
+    A = 10
+    w = 1
+    phi = 0
+    func = LAPLACE_SOLVE(a,b,c,y0,A,w,phi)
+    values = np.round(func(TIME),2)
+
+    plt.plot(TIME,A*np.sin(w*TIME+phi),label='Générateur',color='green')
+    plt.plot(TIME,values,label='Partie Réelle (Observée)')
+    plt.plot(TIME,-1j*values, color='red',label='Partie Imaginaire')
+    plt.grid()
+    plt.legend()
+    plt.show()
+    '''TAU_2 = DIFF_SOLVE(1,1,1,1)
+    TAU_1 = DIFF_SOLVE(0.25,1,0.25,1)
+    TAU_0 = DIFF_SOLVE(0.25,1,1,1)
+    print('TAU - 2')
+    for t in TIME:
+        print('TIME:',np.round(t,2),'VALUE:',np.round(TAU_2(t),2))
+    print('TAU - 1')
+    for t in TIME:
+        print('TIME:',np.round(t,2),'VALUE:',np.round(TAU_1(t),2))
+    print('TAU - 0')
+    for t in TIME:
+        print('TIME:',np.round(t,2),'VALUE:',np.round(TAU_0(t),2))'''

build main.bat

@@ -1 +1 @@
-pyinstaller main.py --add-data "C:/Users/x64/AppData/Local/Programs/Python/Python39/Lib/site-packages/customtkinter;customtkinter/" --add-data "./res/case.png;res/"  --add-data "./res/condensateur.png;res/" --add-data "./res/electron.png;res/" --add-data "./res/generateur.png;res/" --add-data "./res/chemsList.txt;res/" --add-data "./res/lucyna.png;res/" --add-data "./res/neutron.png;res/" --add-data "./res/proton.png;res/" --add-data "./res/resistor.png;res/" --add-data "./res/soleil.png;res/" --add-data "./res/terre.png;res/" -n "Suite de Physique" -y
+pyinstaller main.py --upx-dir="C:/UPX" --add-data "C:/Users/x64/AppData/Local/Programs/Python/Python39/Lib/site-packages/customtkinter;customtkinter/" --add-data "./res/case.png;res/"  --add-data "./res/condensateur.png;res/" --add-data "./res/electron.png;res/" --add-data "./res/generateur.png;res/" --add-data "./res/chemsList.txt;res/" --add-data "./res/lucyna.png;res/" --add-data "./res/neutron.png;res/" --add-data "./res/proton.png;res/" --add-data "./res/resistor.png;res/" --add-data "./res/soleil.png;res/" --add-data "./res/terre.png;res/" -n "Suite de Physique" -y

guiWorks.py

@@ -135,7 +135,7 @@ def Zwork(feedback=None):
             elemVal.configure(text=str(currVal)+" électron(s)")
             elemsBox.set("1-Hydrogène")
             print("Hydrogène 1")
-            
+
     def elemsBoxy(elemy):
         #Ztextbox.delete("0.0","end")
         #Ztextbox.insert("0.0",elemy.split("-")[0])
@@ -207,7 +207,7 @@ def circle_dist(cx,cy,N,n1,n2,nd1,nd2,rayon,randy=False):
                 nd1 += 1
             else:
                 nd2 += 1
-
+    Zwork(1)
 
     def updateGraphics():
         global t, dessN, dessZ, currZ, currN, NZ

main.py

@@ -3,6 +3,7 @@
 import rc
 import guiWorks
 import nbodyTk
+import mech
 import guideManager as gum
 #import pyi_splash
 
@@ -26,13 +27,17 @@ def GRAV_PROG():
 def RC_PROG():
     rc.MAIN_RC(app)
 
+def MECH_PROG():
+    mech.MAIN_MECH(app)
 #pyi_splash.close()
 
 ATOM = ctk.CTkButton(app, text="L'atome",command=ATOM_PROG,font=("Arial", 25),width=250,height=30)
-ATOM.place(relx=0.5,rely=0.25,anchor=S)
+ATOM.place(relx=0.5,rely=0.2,anchor=S)
 GRAV = ctk.CTkButton(app, text="Gravitation", command=GRAV_PROG,font=("Arial", 25),width=250,height=30)
-GRAV.place(relx=0.5,rely=0.5,anchor=S)
+GRAV.place(relx=0.5,rely=0.4,anchor=S)
 COND = ctk.CTkButton(app, text="Circuit RC",command=RC_PROG,font=("Arial", 25),width=250,height=30)
-COND.place(relx=0.5,rely=0.75,anchor=S)
+COND.place(relx=0.5,rely=0.6,anchor=S)
+COND = ctk.CTkButton(app, text="Mécanique",command=MECH_PROG,font=("Arial", 25),width=250,height=30)
+COND.place(relx=0.5,rely=0.8,anchor=S)
 
 app.mainloop()