Yarynara Sebrio. S

Biografi

Nama  : Yarynara Sebrio Suharyadi

TTL  : Jakarta,23 September 1999

NPM  : 1706070816

Jurusan : Teknik Mesin Paralel Universitas Indonesia

Hobi  : Bermain Tenis lapangan

Hasil Belajar Python

Di bagian pemograman python ini saya mempelajari cara mengerjakan operasi matematika yang sering digunakan untuk membuat simulasi di berbagai sistem seperti fisika,kimia,biologi , cara menyelesaikan matematika tersebut cukup sulit diperoleh karena persamaan disamping yang tidak efisien

UTS

1.A import numpy as np class GEPP():

   def __init__(self, A, b, doPricing=True):
       #super(GEPP, self).__init__()
       self.A = A                      # input: A is an n x n numpy matrix
       self.b = b                      # b is an n x 1 numpy array
       self.doPricing = doPricing

       self.n = None                   # n is the length of A
       self.x = None                   # x is the solution of Ax=b

       self._validate_input()          # method that validates input
       self._elimination()             # method that conducts elimination
       self._backsub()                 # method that conducts back-substitution

   def _validate_input(self):
       self.n = len(self.A)
       if self.b.size != self.n:
           raise ValueError("Invalid argument: incompatible sizes between" +
                            "A & b.", self.b.size, self.n)

   def _elimination(self):
       """
       k represents the current pivot row. Since GE traverses the matrix in the
       upper right triangle, we also use k for indicating the k-th diagonal
       column index.
       :return
       """
       # Elimination
       for k in range(self.n - 1):
           if self.doPricing:
               # Pivot
               maxindex = abs(self.A[k:, k]).argmax() + k
               if self.A[maxindex, k] == 0:
                   raise ValueError("Matrix is singular.")
               # Swap
               if maxindex != k:
                   self.Ak, maxindex = self.Amaxindex, k
                   self.bk, maxindex = self.bmaxindex, k
           else:
               if self.A[k, k] == 0:
                   raise ValueError("Pivot element is zero. Try setting doPricing to True.")
           # Eliminate
           for row in range(k + 1, self.n):
               multiplier = self.A[row, k] / self.A[k, k]
               self.A[row, k:] = self.A[row, k:] - multiplier * self.A[k, k:]
               self.b[row] = self.b[row] - multiplier * self.b[k]

   def _backsub(self):
       # Back Substitution
       self.x = np.zeros(self.n)
       for k in range(self.n - 1, -1, -1):
           self.x[k] = (self.b[k] - np.dot(self.A[k, k + 1:], self.x[k + 1:])) / self.A[k, k]

def main():

   A = np.array([[1., 0., 0., 0.],
                 [-1., 1., 0., 0.],
                 [0., 0., -1., 1.],
                 [0., 0., 0., 1.]])
   b = np.array([[50.],
                 [20.],
                 [5.],
                 [10.]])
   GaussElimPiv = GEPP(np.copy(A), np.copy(b), doPricing=False)
   print(GaussElimPiv.x)
   print(GaussElimPiv.A)
   print(GaussElimPiv.b)
   GaussElimPiv = GEPP(A, b)
   print(GaussElimPiv.x)

if __name__ == "__main__":

   main()

1.B

1. masukan plugin numpy

   import numpy as np 
   def diff_y (x,y): 
      fungsi = x**2 - 4*y
      return (fungsi)
   #definisikan syarat perhitungan
   x=0 
   y=1
   h=0.7
   j=5
   step_size = 0.5
   step_size = -np.arange (0,0.5,h) 
   for t in step_size: 
      k1 = diff_y (x,y)
      k2 = diff_y ((x+0.5*h),(y+0.05*k1*h))
   #simulasi hasil
   w1 = y + 1/3*(k1+2*k2)
   #cek kecepatan pada saat 0,7 detik
   print ('maka x(0.7) sama dengan', w1)

Quiz

Quiz nomor 1.

import numpy as np

class GEPP():

   def __init__(self, A, b, doPricing=True):

       #super(GEPP, self).__init__()

       self.A = A                      # input: A is an n x n numpy matrix

       self.b = b                      # b is an n x 1 numpy array

       self.doPricing = doPricing

       self.n = None                   # n is the length of A

       self.x = None                   # x is the solution of Ax=b

       self._validate_input()          # method that validates input

       self._elimination()             # method that conducts elimination

       self._backsub()                 # method that conducts back-substitution

   def _validate_input(self):

       self.n = len(self.A)

       if self.b.size != self.n:

           raise ValueError("Invalid argument: incompatible sizes between" +

                            "A & b.", self.b.size, self.n)

   def _elimination(self):

       # Elimination

       for k in range(self.n - 1):

           if self.doPricing:

               # Pivot

               maxindex = abs(self.A[k:, k]).argmax() + k

               if self.A[maxindex, k] == 0:

                   raise ValueError("Matrix is singular.")

               # Swap

               if maxindex != k:

                   self.Ak, maxindex = self.Amaxindex, k

                   self.bk, maxindex = self.bmaxindex, k

           else:

               if self.A[k, k] == 0:

                   raise ValueError("Pivot element is zero. Try setting doPricing to True.")

           # Eliminate

           for row in range(k + 1, self.n):

               multiplier = self.A[row, k] / self.A[k, k]

               self.A[row, k:] = self.A[row, k:] - multiplier * self.A[k, k:]

               self.b[row] = self.b[row] - multiplier * self.b[k]

   def _backsub(self):

       # Back Substitution

       self.x = np.zeros(self.n)

       for k in range(self.n - 1, -1, -1):

           self.x[k] = (self.b[k] - np.dot(self.A[k, k + 1:], self.x[k + 1:])) / self.A[k, k]

def main():

   A = np.array([[1., 2., 0., -2., 0.],

                 [0., 1., 0., 2., -1.],

                 [0., 0., 2., 1., 2.],

                 [0., 0., 0., -1., 1.],

                 [0., 1., -1., 1., -1.]])

   b = np.array([[-4.],

                 [1.],

                 [1.],

                 [-2.],

                 [-1.]])

   GaussElimPiv = GEPP(np.copy(A), np.copy(b), doPricing=False)

   print(GaussElimPiv.x)

   print(GaussElimPiv.A)

   print(GaussElimPiv.b)

   GaussElimPiv = GEPP(A, b)

   print(GaussElimPiv.x)

if __name__ == "__main__":

   main()

Quiz no.2

import numpy as np

def diff_y (x,y):

   fungsi = x**2 - 4*y

   returm (fungsi)

x=0

y=1

h=0,01

step_size=np.arrange (0,0,03,h)

for t in step_size:

   k1=diff_y (x,y)

   k2=diff_y ((x+0.5*h), (y+0,5*kl*h))

   y=y+kl*h

print ('make y(0.03) adalah ',y)

Tugas 1

x1 = 0

dx1 = ('0.1')

dx = float (dx1)

x2 = x1+dx

Fx_1 = ((x2**2)-1) / (x1-1)

n = 1 error = 0

print ("n x F(x) error")

print (n," ",x1," ",Fx_1," ",error)

while x2<1 :

Fx_2 = ((x2**2)-1) / (x2-1)

error = ((Fx_2-Fx_1) / Fx_1)

Fx_1 = Fx_2

n = n+1

print (n," ",x1," ",Fx_1," ",error)

x2=x2+dx

Tugas 2

---

---

Tugas 3

Soal ini dikerjakan dengan menggunakan Hukum Kontinuitas Massa Definisi : massa yang masuk ke dalam sistem akan sama dengan massa yang keluar dari sistem

Rumus Q*p=Q*p

Karena terdapat 4 variabel, maka terdapat 4 persamaan

6C1 - 4C2 = 50

-2C1 - 1C3 + 4C4 = 50

7C2 - 3C3 - 4C4 = 0

-4C1 + 4C3 = 0

6C1 - 4C2 + 0C3 + 0C4 = 50

-2C1 + 0C2 - 1C3 + 4C4 = 50

0C1 + 7C2 - 3C3 - 4C4 = 0

-4C1 + 0C2 + 4C3 + 0C4 = 0

Dari model python akan didapatkan nilai

C1 = 275/9

C2 = 100/3

C3 = 275/9

C4 = 425/12

• python segera menyusul