├── Screenshot from 2024-09-12 14-25-22.png ├── Screenshot from 2024-09-12 14-26-29.png ├── Non-Linear Optimization [Python] ├── docs │ ├── error.png │ ├── gradient.png │ └── results └── src │ ├── steepest_descent.py │ ├── newton.py │ ├── conjugate_gradient.py │ ├── quasi_newton.py │ ├── line_search.py │ └── rosenbrock.py ├── QuadraticEstimationMethod.py ├── GradientDecentMethod.m ├── ExhaustiveSearchMethod.py ├── GoldenSectionSearchMethod.py ├── QuadraticEstimationMethod.m ├── IntervalHalvingMethod.py ├── FibonacciSearchMethod.py ├── BisectionMethod.py ├── NewtonRaphsonMethod.py ├── SecantMethod.py ├── ExhaustiveSearchMethod.m ├── GoldenSectionSearchMethod.m ├── BisectionMethod.m ├── BoundingPhaseMethod.py ├── IntervalHalvingMethod.m ├── NewtonRaphsonMethod.m ├── SuccessiveQuadraticEstimationMethod.py ├── fibonacci_search_method.m ├── SuccessiveQuadraticEstimationMethod.m ├── BoundingPhaseMethod.m ├── CubicSearchMethod.py ├── CubicSearchMethod.m ├── README.md ├── LICENSE └── KKT_optimization ├── infill-dphi-focus.ipynb └── .ipynb_checkpoints └── infill-dphi-focus-checkpoint.ipynb /Screenshot from 2024-09-12 14-25-22.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/Soumyabrata111/Optimization-Techniques/HEAD/Screenshot from 2024-09-12 14-25-22.png -------------------------------------------------------------------------------- /Screenshot from 2024-09-12 14-26-29.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/Soumyabrata111/Optimization-Techniques/HEAD/Screenshot from 2024-09-12 14-26-29.png -------------------------------------------------------------------------------- /Non-Linear Optimization [Python]/docs/error.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/Soumyabrata111/Optimization-Techniques/HEAD/Non-Linear Optimization [Python]/docs/error.png -------------------------------------------------------------------------------- /Non-Linear Optimization [Python]/docs/gradient.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/Soumyabrata111/Optimization-Techniques/HEAD/Non-Linear Optimization [Python]/docs/gradient.png -------------------------------------------------------------------------------- /Non-Linear Optimization [Python]/docs/results: -------------------------------------------------------------------------------- 1 | Method Iterations Result 2 | CG 11 (0.9995053, 0.9990086) 3 | Newton 14 (1.0000000, 1.0000000) 4 | Quasi Newton 21 (1.0000000, 1.0000000) 5 | 6 | -------------------------------------------------------------------------------- /QuadraticEstimationMethod.py: -------------------------------------------------------------------------------- 1 | # Quadratic Estimation Method 2 | 3 | import matplotlib.pyplot as plt 4 | import numpy as np 5 | 6 | a=1 #Lower bound 7 | b=5 #Upper bound 8 | c=(a+b)/2 # Mid point of the search space 9 | 10 | # Equation to be minimized 11 | def f(x): 12 | return 2*x**2+16/x 13 | 14 | x=np.linspace(a,b,1000) 15 | 16 | a0=f(a) 17 | a1=(f(b)-f(a))/(b-a) 18 | a2=(1/(c-b))*(((f(c)-f(a))/(c-a))-((f(b)-f(a))/(b-a))) 19 | 20 | # Approximate point for minimum function value 21 | x_bar=(a+b)/2-(a1/(2*a2)) 22 | 23 | # Approximate minimum function value 24 | f_bar=f(x_bar) 25 | 26 | print(f"The approximate minimum function value is {f_bar}, and it is located at {x_bar}") 27 | 28 | # Plot the function 29 | plt.plot(x,f(x)) 30 | plt.xlabel("x",fontweight='bold') 31 | plt.ylabel("f(x)",fontweight='bold') 32 | plt.grid(which='major',axis='both',linestyle='dashed') 33 | plt.title('Exhaustive Search Method',fontweight='bold') 34 | plt.scatter(x_bar,f_bar, color='red', label='Approximate Minimum Point') 35 | plt.legend() 36 | plt.savefig('Quadratic Estimation Method.png',dpi=300) 37 | plt.show() -------------------------------------------------------------------------------- /Non-Linear Optimization [Python]/src/steepest_descent.py: -------------------------------------------------------------------------------- 1 | ''' 2 | This program is free software: you can redistribute it and/or modify 3 | it under the terms of the GNU General Public License as published by 4 | the Free Software Foundation, either version 3 of the License, or 5 | (at your option) any later version. 6 | 7 | This program is distributed in the hope that it will be useful, 8 | but WITHOUT ANY WARRANTY; without even the implied warranty of 9 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 10 | GNU General Public License for more details. 11 | 12 | You should have received a copy of the GNU General Public License 13 | along with this program. If not, see . 14 | ''' 15 | from numpy import * 16 | from line_search import find_step_length 17 | 18 | def steepest_descent(f, fd, x, max_iterations, precision, callback): 19 | for i in range(0, max_iterations): 20 | direction = - fd(x) 21 | alpha = find_step_length(f, fd, x, 1.0, direction, c2=0.9) 22 | x = x + alpha*direction 23 | callback(i, direction, alpha, x) 24 | if linalg.norm(direction) < precision: 25 | break 26 | return x 27 | -------------------------------------------------------------------------------- /GradientDecentMethod.m: -------------------------------------------------------------------------------- 1 | % Gradient (Steepest) DEcent Method as Explained in https://www.youtube.com/watch?v=x7YMV5xcMc8 2 | % Matlab version R2018b 3 | % Date: 22nd October, 2018 4 | clc 5 | clear 6 | %% Taking thefunction as input from user 7 | sc = inputdlg('Type an expression that is a function of x & y ' ); % Taking the equation as input from the user 8 | s = sc{:}; % Function String 9 | f = str2func(['@(x,y) ' s]) 10 | x = input ('Enter the initial guess of x: '); 11 | y = input ('Enter the initial guess of y: '); 12 | a = input ('Enter the learning rate: '); 13 | %% Starting the algorithm 14 | for i=1:100000 15 | z = feval (f,x,y); 16 | x1 = x + .000001 * x; 17 | y1 = y + .000001 * y; 18 | zx = feval (f,x1,y); 19 | zy = feval(f,x,y1); 20 | del_fx = (zx-z)/(.000001*x); % The partial derivative w.r.t x at the chosen point of the user 21 | del_fy = (zy-z)/(.000001*y); % The partial derivative w.r.t y at the chosen point of the user 22 | x_new = x - a*del_fx; 23 | y_new = y - a*del_fy; 24 | x = x_new; 25 | y = y_new; 26 | end 27 | fprintf('The minimum values of the variables x & y are respectively: %f & %f \n',x,y); 28 | -------------------------------------------------------------------------------- /ExhaustiveSearchMethod.py: -------------------------------------------------------------------------------- 1 | # Exhaustive Search Method 2 | 3 | import matplotlib.pyplot as plt 4 | import numpy as np 5 | 6 | a=0.1 #Lower bound 7 | b=14 #Upper bound 8 | n = 1000 #Number of divisions 9 | dx=(b-a)/n #Length of each division 10 | 11 | # Equation to be minimized 12 | def f(x): 13 | return x**2+54/x 14 | 15 | # Initialization 16 | x1=a 17 | x2=x1+dx 18 | x3=x2+dx 19 | x_min=x2 20 | f_min =f(x_min) 21 | 22 | while x3<=b: 23 | if f(x2)<=f(x1) and f(x2)<=f(x3): 24 | print('The approx minimum point is: '+str(x2)) 25 | print('The approx minimum function value is: '+str(f(x2))) 26 | x_min=x2 27 | f_min=f(x_min) 28 | 29 | x1=x2 30 | x2=x1+dx 31 | x3=x2+dx 32 | 33 | # Store the points to where the function is to be evaluated 34 | x = np.linspace(a,b,n) 35 | 36 | # Plot the function 37 | plt.plot(x,f(x)) 38 | plt.xlabel("x",fontweight='bold') 39 | plt.ylabel("f(x)",fontweight='bold') 40 | plt.grid(which='major',axis='both',linestyle='dashed') 41 | plt.title('Exhaustive Search Method',fontweight='bold') 42 | plt.scatter(x_min,f_min, color='red', label='Minimum Point') 43 | plt.legend() 44 | plt.savefig('Exhaustive Search Method.png',dpi=300) 45 | plt.show() -------------------------------------------------------------------------------- /GoldenSectionSearchMethod.py: -------------------------------------------------------------------------------- 1 | # Golden Section Search Method 2 | 3 | import matplotlib.pyplot as plt 4 | import numpy as np 5 | a = 0.1 # Lower bound 6 | b = 14 # Upper bound 7 | eps = 1e-8 # Desired accuracy 8 | gr = (1 + 5 ** 0.5) / 2 # Golden Ratio 9 | 10 | def f(x): 11 | return x ** 2 + 54 / x 12 | 13 | x = np.linspace(a,b,1000) 14 | 15 | # Initialization 16 | x1 = a + (b - a) / gr 17 | x2 = b - (b - a) / gr 18 | 19 | while abs(b - a) > eps: 20 | f1 = f(x1) 21 | f2 = f(x2) 22 | if f1 > f2: 23 | b = x2 24 | x2 = x1 25 | x1 = a + (b - a) / gr 26 | else: 27 | a = x1 28 | x1 = x2 29 | x2 = b - (b - a) / gr 30 | x_min = (a+b)/2 31 | f_min = f(x_min) 32 | print (f"The approximate minimum point and the value respectively are: {x_min} and {f_min}") 33 | 34 | 35 | # Plot the function 36 | plt.plot(x,f(x)) 37 | plt.xlabel("x",fontweight='bold') 38 | plt.ylabel("f(x)",fontweight='bold') 39 | plt.grid(which='major',axis='both',linestyle='dashed') 40 | plt.title('Golden Section Search Method',fontweight='bold') 41 | plt.scatter(x_min,f_min, color='red', label='Minimum Point') 42 | plt.legend() 43 | plt.savefig('Golden Section Search Method.png',dpi=300) 44 | plt.show() 45 | -------------------------------------------------------------------------------- /QuadraticEstimationMethod.m: -------------------------------------------------------------------------------- 1 | % Quadratic Estimation Method 2 | 3 | clear all 4 | clc 5 | 6 | a = 1; % Lower bound 7 | b = 5; % Upper bound 8 | c=(a+b)/2; % Mid point of the search space 9 | 10 | % Function to be minimized 11 | f = @(x) 2*x.^2 + 16./x; 12 | 13 | x_values=linspace(a,b,1000); 14 | y_values=f(x_values); 15 | 16 | a0=f(a); 17 | a1=(f(b)-f(a))/(b-a); 18 | a2=(1/(c-b))*(((f(c)-f(a))/(c-a))-((f(b)-f(a))/(b-a))); 19 | 20 | % Approximate point for minimum function value 21 | x_bar=(a+b)/2-(a1/(2*a2)); 22 | 23 | % Approximate minimum function value 24 | f_bar=f(x_bar); 25 | 26 | fprintf("The approximate minimum function value is %f, and it is located at %f",f_bar,x_bar) 27 | 28 | % Plot the function 29 | figure; 30 | plot(x_values, y_values); 31 | xlabel('x', 'fontweight', 'bold'); 32 | ylabel('f(x)', 'fontweight', 'bold'); 33 | grid on; 34 | title('Quadratic Estimation Method', 'fontweight', 'bold'); 35 | hold on; 36 | scatter(x_bar, f_bar, 'red', 'filled'); 37 | legend(func2str(f), 'Approximate Minimum Point'); 38 | 39 | % Set x-axis ticks to be whole numbers 40 | xticks(a:b); 41 | 42 | % Adjust x-axis limits 43 | ax = gca; 44 | ax.XLim = [a b]; % Update here 45 | 46 | saveas(gcf, 'Quadratic_Estimation_Method.png', 'png'); 47 | -------------------------------------------------------------------------------- /IntervalHalvingMethod.py: -------------------------------------------------------------------------------- 1 | # Interval Halving Method 2 | 3 | import matplotlib.pyplot as plt 4 | import numpy as np 5 | a = 0.1 # Lower bound 6 | b = 14 # Upper bound 7 | eps = 1e-5 # Desired accuracy 8 | 9 | # Function to minimize 10 | def f(x): 11 | return x**2+54/x 12 | 13 | # Initialization 14 | xm = (a+b)/2 # Mid point 15 | L = b - a # Length of search space 16 | x1 = a + L/4 # Left intermediary point 17 | x2 = b - L/4 # Right intermediary point 18 | 19 | f1 = f(x1) 20 | f2 = f(x2) 21 | fm = f(xm) 22 | x = np.linspace(a,b,1000) 23 | 24 | 25 | while abs(L)>eps: 26 | if f1. 14 | ''' 15 | from numpy import * 16 | from line_search import find_step_length 17 | 18 | def newton(f, fd, fdd, x, max_iterations, precision, callback): 19 | for i in range(1, max_iterations): 20 | gradient = fd(x) 21 | hessian = fdd(x) 22 | 23 | direction = -linalg.solve(hessian, gradient) 24 | alpha = find_step_length(f, fd, x, 1.0, direction, c2=0.9) 25 | x_prev = x 26 | x = x + alpha*direction 27 | 28 | callback(i, direction, alpha, x) 29 | 30 | if linalg.norm(x - x_prev) < precision: 31 | break 32 | return x 33 | -------------------------------------------------------------------------------- /FibonacciSearchMethod.py: -------------------------------------------------------------------------------- 1 | # Fibonacci Search Method 2 | 3 | import matplotlib.pyplot as plt 4 | import numpy as np 5 | 6 | a=0.1 #Lower bound 7 | b=14 #Upper bound 8 | n = 2000 #Number of times function is to be evaluated 9 | 10 | # Function to calculate n-th Fibonacci number 11 | def F(n): 12 | fi = [] 13 | fi.append(0) 14 | fi.append(1) 15 | 16 | for i in range(2, n+1): 17 | fi.append(fi[i-1] + fi[i-2]) 18 | return fi[n] 19 | 20 | # Function to be minimized 21 | def f(x): 22 | return x**2+54/x 23 | 24 | # Initialization 25 | k=2 26 | L=b-a # Length of search space 27 | L_ks=(F(n-k+1)/F(n+1))*L 28 | x1=a+L_ks 29 | x2=b-L_ks 30 | f1=f(x1) 31 | f2=f(x2) 32 | x=np.linspace(a,b,1000) 33 | 34 | while k<=n: 35 | if f20.01: 19 | return 0.01*abs(x) 20 | else: 21 | return 0.0001 22 | 23 | # Function to calculate first derivative of the function 24 | def fdx(x): 25 | return ((f(x+dx(x))-f(x-dx(x)))/(2*dx(x))) 26 | 27 | x1=a # Beginning of search space 28 | x2=b # End of search space 29 | z=0.5*(x1+x2) # Mid-point of the search space 30 | 31 | # Initialization 32 | fx1=f(x1) 33 | fx2=f(x2) 34 | fz=f(z) 35 | fdz=fdx(z) 36 | 37 | while abs(fdz)>eps: 38 | if fdz<0: 39 | x1=z 40 | elif fdz>0: 41 | x2=z 42 | z=0.5*(x1+x2) 43 | fx1=f(x1) 44 | fx2=f(x2) 45 | fz=f(z) 46 | fdz=fdx(z) 47 | 48 | print (f"The approximate minimum point and the value respectively are: {z} and {fz}") 49 | 50 | # Plot the function 51 | plt.plot(x_p,f(x_p)) 52 | plt.xlabel("x",fontweight='bold') 53 | plt.ylabel("f(x)",fontweight='bold') 54 | plt.grid(which='major',axis='both',linestyle='dashed') 55 | plt.title('Bisection Method',fontweight='bold') 56 | plt.scatter(z,fz, color='red', label='Approximate Minimum Point') 57 | plt.legend() 58 | plt.savefig('Bisection Method.png',dpi=300) 59 | plt.show() -------------------------------------------------------------------------------- /NewtonRaphsonMethod.py: -------------------------------------------------------------------------------- 1 | # Newton-Raphson Method 2 | 3 | import numpy as np 4 | import matplotlib.pyplot as plt 5 | 6 | a = 0.1 # Lower bound 7 | b = 15 # Upper bound 8 | 9 | x_p = np.linspace(a,b,1000) # points for plotting the function 10 | 11 | # Function to minimize 12 | def f(x): 13 | return x**2+54/x 14 | 15 | # Function to determine the value of 'dx' 16 | def dx(x): 17 | if abs(x)>0.01: 18 | return 0.01*abs(x) 19 | else: 20 | return 0.0001 21 | 22 | # Function to calculate first derivative of the function 23 | def fdx(x): 24 | return ((f(x+dx(x))-f(x-dx(x)))/(2*dx(x))) 25 | 26 | # Function to calculate second derivative of the function 27 | def fddx(x): 28 | return ((f(x+dx(x))-2*f(x)+f(x-dx(x)))/((dx(x))**2)) 29 | 30 | # Initialization 31 | x=a # Initial guess 32 | eps=1e-5 # Small number to check convergency 33 | k=1 # Counter 34 | max_iterations = 1000 # Maximum number of iterations 35 | 36 | xn = x-(fdx(x)/fddx(x)) 37 | fn = f(xn) 38 | 39 | while fn>eps and k <= max_iterations: 40 | k=k+1 41 | x = xn 42 | xn = x-(fdx(x)/fddx(x)) 43 | fn = f(xn) 44 | print (f"The approximate minimum point and the value respectively are: {xn} and {fn}") 45 | 46 | # Plot the function 47 | plt.plot(x_p,f(x_p)) 48 | plt.xlabel("x",fontweight='bold') 49 | plt.ylabel("f(x)",fontweight='bold') 50 | plt.grid(which='major',axis='both',linestyle='dashed') 51 | plt.title('Newton-Raphson Method',fontweight='bold') 52 | plt.scatter(xn,fn, color='red', label='Approximate Minimum Point') 53 | plt.legend() 54 | plt.savefig('Newton-Raphson Method.png',dpi=300) 55 | plt.show() -------------------------------------------------------------------------------- /Non-Linear Optimization [Python]/src/conjugate_gradient.py: -------------------------------------------------------------------------------- 1 | ''' 2 | This program is free software: you can redistribute it and/or modify 3 | it under the terms of the GNU General Public License as published by 4 | the Free Software Foundation, either version 3 of the License, or 5 | (at your option) any later version. 6 | 7 | This program is distributed in the hope that it will be useful, 8 | but WITHOUT ANY WARRANTY; without even the implied warranty of 9 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 10 | GNU General Public License for more details. 11 | 12 | You should have received a copy of the GNU General Public License 13 | along with this program. If not, see . 14 | ''' 15 | from numpy import * 16 | from line_search import find_step_length 17 | 18 | def conjugate_gradient(f, fd, x, max_iterations, precision, callback): 19 | direction = -fd(x) 20 | gradient = None 21 | gradient_next = matrix(fd(x)).T 22 | x_prev = None 23 | 24 | for i in range(1, max_iterations): 25 | alpha = find_step_length(f, fd, x, 1.0, direction, c2=0.1) 26 | x_prev = x 27 | x = x + alpha*direction 28 | 29 | callback(i, direction, alpha, x) 30 | 31 | gradient = gradient_next 32 | gradient_next = matrix(fd(x)).T 33 | 34 | if linalg.norm(x - x_prev) < precision: 35 | break 36 | 37 | BFR = (gradient_next.T * gradient_next) / (gradient.T * gradient) 38 | BFR = squeeze(asarray(BFR)) 39 | 40 | direction = -squeeze(asarray(gradient_next)) + BFR*direction 41 | return x 42 | -------------------------------------------------------------------------------- /Non-Linear Optimization [Python]/src/quasi_newton.py: -------------------------------------------------------------------------------- 1 | ''' 2 | This program is free software: you can redistribute it and/or modify 3 | it under the terms of the GNU General Public License as published by 4 | the Free Software Foundation, either version 3 of the License, or 5 | (at your option) any later version. 6 | 7 | This program is distributed in the hope that it will be useful, 8 | but WITHOUT ANY WARRANTY; without even the implied warranty of 9 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 10 | GNU General Public License for more details. 11 | 12 | You should have received a copy of the GNU General Public License 13 | along with this program. If not, see . 14 | ''' 15 | from numpy import * 16 | from line_search import find_step_length 17 | 18 | def quasi_newton(f, fd, x, max_iterations, precision, callback): 19 | I = identity(x.size) 20 | H = I 21 | x_prev = x 22 | f_prev = f 23 | fd_prev = fd 24 | 25 | for i in range(1, max_iterations): 26 | gradient = fd(x) 27 | direction = -H * matrix(gradient).T 28 | direction = squeeze(asarray(direction)) 29 | 30 | alpha = find_step_length(f, fd, x, 1.0, direction, c2=0.9) 31 | x_prev = x 32 | x = x + alpha*direction 33 | 34 | callback(i, direction, alpha, x) 35 | 36 | if linalg.norm(x - x_prev) < precision: 37 | break 38 | 39 | s = matrix(x - x_prev).T 40 | y = matrix(fd(x) - fd(x_prev)).T 41 | rho = float(1 / (y.T*s)) 42 | H = (I - rho*s*y.T)*H*(I - rho*y*s.T) + rho*s*s.T 43 | return x 44 | -------------------------------------------------------------------------------- /SecantMethod.py: -------------------------------------------------------------------------------- 1 | # Secant Method 2 | 3 | import numpy as np 4 | import matplotlib.pyplot as plt 5 | 6 | a = 0.1 # Lower bound 7 | b = 15 # Upper bound 8 | eps=1e-3 # Small number 9 | 10 | x_p = np.linspace(a,b,1000) # points for plotting the function 11 | 12 | # Function to minimize 13 | def f(x): 14 | return x**2+54/x 15 | 16 | # Function to determine the value of 'dx' 17 | def dx(x): 18 | if abs(x)>0.01: 19 | return 0.01*abs(x) 20 | else: 21 | return 0.0001 22 | 23 | # Function to calculate first derivative of the function 24 | def fdx(x): 25 | return ((f(x+dx(x))-f(x-dx(x)))/(2*dx(x))) 26 | 27 | x1=a # Beginning of search space 28 | x2=b # End of search space 29 | z=x2-(fdx(x2))/((fdx(x2)-fdx(x1))/(x2-x1)) # Mid-point of the search space 30 | 31 | # Initialization 32 | fx1=f(x1) 33 | fx2=f(x2) 34 | fz=f(z) 35 | fdz=fdx(z) 36 | 37 | while abs(fdz)>eps: 38 | if fdz<0: 39 | x1=z 40 | elif fdz>0: 41 | x2=z 42 | z=z=x2-(fdx(x2))/((fdx(x2)-fdx(x1))/(x2-x1)) 43 | fx1=f(x1) 44 | fx2=f(x2) 45 | fz=f(z) 46 | fdz=fdx(z) 47 | 48 | print (f"The approximate minimum point and the value respectively are: {z} and {fz}") 49 | 50 | # Plot the function 51 | plt.plot(x_p,f(x_p)) 52 | plt.xlabel("x",fontweight='bold') 53 | plt.ylabel("f(x)",fontweight='bold') 54 | plt.grid(which='major',axis='both',linestyle='dashed') 55 | plt.title('Secant Method',fontweight='bold') 56 | plt.scatter(z,fz, color='red', label='Approximate Minimum Point') 57 | plt.legend() 58 | plt.savefig('Secant Method.png',dpi=300) 59 | plt.show() -------------------------------------------------------------------------------- /ExhaustiveSearchMethod.m: -------------------------------------------------------------------------------- 1 | % Exhaustive Search Method as Explained in the book 2 | %"Optimization of Engineering Design: Algorithms and Examples" by Prof. Kalyanmoy Deb 3 | % Code developed by Sri. Soumyabrata Bhattacharjee 4 | % Matlab version R2022b 5 | % Date: 14th October, 2018 6 | % Date: 25th October, 2023 (Updated) 7 | % Date: 27th October, 2023 (Updated) 8 | 9 | clear all 10 | clc 11 | a=0.1; %Lower bound 12 | b=14; % Upper bound 13 | n = 1000; %Number of divisions 14 | dx=(b-a)/n; %Length of each division 15 | 16 | % Equation to be minimized 17 | f=@(x) x.^2+54./x; 18 | 19 | % Initialization 20 | x1=a; 21 | x2=x1+dx; 22 | x3=x2+dx; 23 | x_min=x2; 24 | f_min=f(x_min); 25 | 26 | while x3<=b 27 | if f(x2)<=f(x1) && f(x2)<=f(x3) 28 | disp(['The approx minimum point is: ' num2str(x2)]) 29 | disp(['The approx minimum function value is: ' num2str(f(x2))]) 30 | x_min=x2; 31 | f_min=f(x_min); 32 | end 33 | x1=x2; 34 | x2=x1+dx; 35 | x3=x2+dx; 36 | 37 | end 38 | 39 | 40 | % Plotting 41 | x = linspace(a,b,n); 42 | plot(x,f(x),'LineWidth',2,'DisplayName',func2str(f)); 43 | xlabel('x',FontWeight='bold'); 44 | ylabel('f(x)','FontWeight','bold') 45 | grid on; 46 | title('Exhaustive Search Method','FontWeight','bold'); 47 | 48 | hold on; 49 | 50 | % Scatter plot for the minimum point 51 | scatter(x_min, f_min, 100, 'red', 'filled', 'DisplayName', 'Minimum Point'); 52 | 53 | % Adding Legend 54 | legend('Location','best') 55 | legend('show') 56 | 57 | % Save the figure as a PNG file 58 | saveas(gcf, 'Exhaustive Search Method.png'); 59 | 60 | % Display the plot 61 | hold off; 62 | -------------------------------------------------------------------------------- /GoldenSectionSearchMethod.m: -------------------------------------------------------------------------------- 1 | % Exhaustive Search Method as Explained in the book 2 | %"Optimization of Engineering Design: Algorithms and Examples" by Prof. Kalyanmoy Deb 3 | % Code developed by Sri. Soumyabrata Bhattacharjee 4 | % Matlab version R2022b 5 | % Date: 14th October, 2018 6 | % Date: 27th October, 2023 (Updated) 7 | 8 | clear all 9 | clc 10 | a = 0.1; % Lower bound 11 | b = 14 ; % Upper bound 12 | eps = 1e-8; % Desired accuracy 13 | gr = (1 + 5^0.5) / 2; % Golden Ratio 14 | 15 | f=@(x) x.^2+54./x; 16 | 17 | x = linspace(a,b,1000); 18 | 19 | % Initialization 20 | x1 = a + (b - a) / gr; 21 | x2 = b - (b - a) / gr; 22 | 23 | while abs(b - a) > eps 24 | f1 = f(x1); 25 | f2 = f(x2); 26 | if f1 > f2 27 | b = x2; 28 | x2 = x1; 29 | x1 = a + (b - a) / gr; 30 | else 31 | a = x1; 32 | x1 = x2; 33 | x2 = b - (b - a) / gr; 34 | end 35 | end 36 | x_min = (a+b)/2; 37 | f_min = f(x_min); 38 | disp(['The approx minimum point is: ',num2str(x_min)]) 39 | disp(['The approx minimum function value is: ',num2str(f_min)]) 40 | 41 | % Plotting 42 | plot(x,f(x),'LineWidth',2,'DisplayName',func2str(f)); 43 | xlabel('x',FontWeight='bold'); 44 | ylabel('f(x)','FontWeight','bold') 45 | grid on; 46 | title('Golden Section Search Method','FontWeight','bold'); 47 | 48 | hold on; 49 | 50 | % Scatter plot for the minimum point 51 | scatter(x_min, f_min, 100, 'red', 'filled', 'DisplayName', 'Minimum Point'); 52 | 53 | % Adding Legend 54 | legend('Location','best') 55 | legend('show') 56 | 57 | % Save the figure as a PNG file 58 | saveas(gcf, 'Golden Section Search Method.png'); 59 | 60 | % Display the plot 61 | hold off; 62 | -------------------------------------------------------------------------------- /BisectionMethod.m: -------------------------------------------------------------------------------- 1 | % Bisection Method 2 | % Matlab version R2018b and R2022a 3 | % Date: 27th October, 2018 4 | % Date: 5th November, 2023 5 | clc 6 | clear 7 | % Bisection Method 8 | 9 | a = 0.1; % Lower bound 10 | b = 15; % Upper bound 11 | eps = 1e-3; % Small number 12 | 13 | x_p = linspace(a, b, 1000); % points for plotting the function 14 | 15 | % Function to minimize 16 | f = @(x) x.^2 + 54./x; 17 | 18 | % Function to determine the value of 'dx' 19 | dx = @(x) abs(x) > 0.01 .* 0.01 .* abs(x) + (abs(x) <= 0.01) .* 0.0001; 20 | 21 | % Function to calculate first derivative of the function 22 | fdx = @(x) (f(x + dx(x)) - f(x - dx(x))) ./ (2 .* dx(x)); 23 | 24 | x1 = a; % Beginning of search space 25 | x2 = b; % End of search space 26 | z = 0.5 .* (x1 + x2); % Mid-point of the search space 27 | 28 | % Initialization 29 | fx1 = f(x1); 30 | fx2 = f(x2); 31 | fz = f(z); 32 | fdz = fdx(z); 33 | 34 | while abs(fdz) > eps 35 | if fdz < 0 36 | x1 = z; 37 | elseif fdz > 0 38 | x2 = z; 39 | end 40 | z = 0.5 .* (x1 + x2); 41 | fx1 = f(x1); 42 | fx2 = f(x2); 43 | fz = f(z); 44 | fdz = fdx(z); 45 | end 46 | 47 | fprintf('The approximate minimum point and the value respectively are: %f and %f\n', z, fz); 48 | 49 | % Plot the function 50 | figure; 51 | plot(x_p, f(x_p), 'b', 'LineWidth', 1.5,'DisplayName', func2str (f)); 52 | xlabel('x', 'FontWeight', 'bold'); 53 | ylabel('f(x)', 'FontWeight', 'bold'); 54 | grid on; 55 | title('Bisection Method', 'FontWeight', 'bold'); 56 | hold on; 57 | scatter(z, fz, 50, 'red', 'filled', 'DisplayName', 'Approximate Minimum Point'); 58 | legend('Location', 'Best'); 59 | saveas(gcf, 'Bisection_Method.png', 'png'); 60 | -------------------------------------------------------------------------------- /BoundingPhaseMethod.py: -------------------------------------------------------------------------------- 1 | # Bounding Phase Method 2 | 3 | import matplotlib.pyplot as plt 4 | import numpy as np 5 | a = 0.1 # Lower bound 6 | b = 14 # Upper bound 7 | dx=1e-5 # Step-size parameter 8 | 9 | # Function to be minimized 10 | def f(x): 11 | return x ** 2 + 54 / x 12 | 13 | # Initialization 14 | x_mid=a+dx*(b-a) # Initial guess 15 | x_lb=x_mid-dx # Current lower bound 16 | x_ub=x_mid+dx # Current upper bound 17 | f_mid = f(x_mid) 18 | f_lb=f(x_lb) 19 | f_ub=f(x_ub) 20 | k=0 # Value will be iterated 21 | x = np.linspace(a,b,1000) 22 | 23 | # Check whether the function is unimodal 24 | 25 | while x_ub<=b and x_lb >=a: 26 | if f_mid>=f_lb and f_mid>=f_ub: 27 | print(f_lb,f_mid,f_ub) 28 | print("The function is not unimodal") 29 | elif f_lb>=f_mid and f_mid>=f_ub: 30 | dx=abs(dx) 31 | print(f"dx: {dx}") 32 | else: 33 | dx=-abs(dx) 34 | print(f"dx: {dx}") 35 | k=k+1 36 | x_mid_new = x_mid + 2**k*dx 37 | f_mid_new = f(x_mid_new) 38 | if f_mid_new > f_mid: 39 | break 40 | x_mid = x_mid_new 41 | x_lb=x_mid-dx 42 | x_ub=x_mid+dx 43 | f_mid = f_mid_new 44 | f_lb=f(x_lb) 45 | f_ub=f(x_ub) 46 | print(f"k={k},x_mid={x_mid},x_lb={x_lb},x_ub={x_ub}") 47 | print (f"The approximate minimum point and the value respectively are: {x_mid} and {f_mid}") 48 | 49 | # Plot the function 50 | plt.plot(x,f(x)) 51 | plt.xlabel("x",fontweight='bold') 52 | plt.ylabel("f(x)",fontweight='bold') 53 | plt.grid(which='major',axis='both',linestyle='dashed') 54 | plt.title('Bounding Phase Method',fontweight='bold') 55 | plt.scatter(x_mid,f_mid, color='red', label='Minimum Point') 56 | plt.legend() 57 | plt.savefig('Bounding Phase Method.png',dpi=300) 58 | plt.show() 59 | -------------------------------------------------------------------------------- /IntervalHalvingMethod.m: -------------------------------------------------------------------------------- 1 | % Interval Halving Method as Explained in the book 2 | %"Optimization of Engineering Design: Algorithms and Examples" by Prof. Kalyanmoy Deb 3 | % Code developed by Sri. Soumyabrata Bhattacharjee 4 | % Matlab version R2022a 5 | % Date: 16th October, 2018 6 | % Date: 31st October, 2023 (updated) 7 | clc 8 | clear 9 | % Interval Halving Method 10 | 11 | a = 0.1; % Lower bound 12 | b = 14; % Upper bound 13 | eps = 1e-5; % Desired accuracy 14 | 15 | % Function to minimize 16 | f = @(x) x.^2 + 54./x; 17 | 18 | % Initialization 19 | xm = (a + b) / 2; % Mid point 20 | L = b - a; % Length of search space 21 | x1 = a + L / 4; % Left intermediary point 22 | x2 = b - L / 4; % Right intermediary point 23 | 24 | f1 = f(x1); 25 | f2 = f(x2); 26 | fm = f(xm); 27 | x_vals = linspace(a, b, 1000); 28 | y_vals = f(x_vals); 29 | 30 | while abs(L) > eps 31 | if f1 < fm 32 | b = xm; 33 | xm = x1; 34 | elseif f2 < fm 35 | a = xm; 36 | xm = x2; 37 | else 38 | a = x1; 39 | b = x2; 40 | end 41 | 42 | L = b - a; 43 | x1 = a + L / 4; 44 | x2 = b - L / 4; 45 | f1 = f(x1); 46 | f2 = f(x2); 47 | fm = f(xm); 48 | end 49 | 50 | fprintf('The minimum point lies between %.8f and %.8f\n', x1, x2); 51 | 52 | % Plot the function 53 | plot(x_vals, y_vals); 54 | xlabel('x', 'FontWeight', 'bold'); 55 | ylabel('f(x)', 'FontWeight', 'bold'); 56 | grid on; 57 | title('Interval Halving Method', 'FontWeight', 'bold'); 58 | 59 | hold on; 60 | scatter(xm, fm, 100, 'red', 'filled', 'MarkerEdgeColor', 'black', 'LineWidth', 1.5, 'DisplayName', 'Approximate Minimum Point'); 61 | legend('show'); 62 | hold off; 63 | 64 | saveas(gcf, 'Interval_Halving_Method.png', 'png'); 65 | -------------------------------------------------------------------------------- /NewtonRaphsonMethod.m: -------------------------------------------------------------------------------- 1 | % Newton-Raphson Method as Explained in the book 2 | %"Optimization of Engineering Design: Algorithms and Examples" by Prof. Kalyanmoy Deb 3 | % Code developed by Sri. Soumyabrata Bhattacharjee 4 | % Matlab version R2022a 5 | % Date: 16th October, 2018 6 | % Date: 4th November, 2023 7 | clc 8 | clear 9 | % Newton-Raphson Method 10 | 11 | a = 0.1; % Lower bound 12 | b = 15; % Upper bound 13 | 14 | x_p = linspace(a, b, 1000); % points for plotting the function 15 | 16 | % Function to minimize 17 | f = @(x) x^2 + 54/x; 18 | 19 | % Function to determine the value of 'dx' 20 | dx = @(x) 0.01 * abs(x); 21 | dx = @(x) max(dx(x), 0.0001); 22 | 23 | % Function to calculate first derivative of the function 24 | fdx = @(x) (f(x + dx(x)) - f(x - dx(x))) / (2 * dx(x)); 25 | 26 | % Function to calculate second derivative of the function 27 | fddx = @(x) (f(x + dx(x)) - 2 * f(x) + f(x - dx(x))) / (dx(x)^2); 28 | 29 | % Initialization 30 | x = a; % Initial guess 31 | eps = 1e-5; % Small number to check convergency 32 | max_iterations = 1000; % Maximum number of iterations 33 | 34 | xn = x - (fdx(x) / fddx(x)); 35 | fn = f(xn); 36 | 37 | k = 1; % Counter 38 | 39 | while fn > eps && k <= max_iterations 40 | k = k + 1; 41 | x = xn; 42 | xn = x - (fdx(x) / fddx(x)); 43 | fn = f(xn); 44 | end 45 | 46 | fprintf('The approximate minimum point and the value respectively are: %.4f and %.4f\n', xn, fn); 47 | 48 | % Plot the function 49 | figure; 50 | plot(x_p, arrayfun(f, x_p),'DisplayName', func2str (f)); 51 | xlabel('x', 'FontWeight', 'bold'); 52 | ylabel('f(x)', 'FontWeight', 'bold'); 53 | grid on; 54 | title('Newton-Raphson Method', 'FontWeight', 'bold'); 55 | hold on; 56 | scatter(xn, fn, 'r', 'filled', 'DisplayName', 'Approximate Minimum Point'); 57 | legend('Location', 'Best'); 58 | saveas(gcf, 'NewtonRaphsonMethod.png', 'png'); 59 | -------------------------------------------------------------------------------- /Non-Linear Optimization [Python]/src/line_search.py: -------------------------------------------------------------------------------- 1 | ''' 2 | This program is free software: you can redistribute it and/or modify 3 | it under the terms of the GNU General Public License as published by 4 | the Free Software Foundation, either version 3 of the License, or 5 | (at your option) any later version. 6 | 7 | This program is distributed in the hope that it will be useful, 8 | but WITHOUT ANY WARRANTY; without even the implied warranty of 9 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 10 | GNU General Public License for more details. 11 | 12 | You should have received a copy of the GNU General Public License 13 | along with this program. If not, see . 14 | ''' 15 | import numpy 16 | 17 | def find_step_length(f, fd, x, alpha, direction, c2): 18 | g = lambda alpha: f(x+alpha*direction) 19 | gd = lambda alpha: numpy.dot(fd(x + alpha*direction), direction) 20 | return interpolation(g, gd, alpha, c2) 21 | 22 | def wolf1(f, fd, alpha): 23 | c1 = 1e-4 24 | return f(alpha) <= f(0) + c1*alpha*fd(alpha) 25 | 26 | def wolf_strong(f, fd, alpha, c2): 27 | return abs(fd(alpha)) <= -c2*fd(0) 28 | 29 | def simple_backtracking(f, fd, alpha, c2): 30 | rate = 0.5 31 | while not (wolf1(f, fd, alpha) or wolf_strong(f, fd, alpha, c2)): 32 | alpha = rate*alpha 33 | return alpha 34 | 35 | def interpolation(f, fd, alpha, c2): 36 | lo = 0.0 37 | hi = 1.0 38 | 39 | for i in range(0, 20): 40 | if wolf1(f, fd, alpha): 41 | if wolf_strong(f, fd, alpha, c2): 42 | return alpha 43 | 44 | half = (lo+hi)/2.0 45 | alpha = - (fd(lo)*hi*hi) / (2*(f(hi)-f(lo)-fd(lo)*hi)) 46 | 47 | if alpha < lo or alpha > hi: # quadratic interpolation failed. reduce by half instead 48 | alpha = half 49 | if fd(alpha) > 0: 50 | hi = alpha 51 | elif fd(alpha) <= 0: 52 | lo = alpha 53 | return alpha 54 | -------------------------------------------------------------------------------- /SuccessiveQuadraticEstimationMethod.py: -------------------------------------------------------------------------------- 1 | # Successive Quadratic Estimation Method 2 | 3 | import matplotlib.pyplot as plt 4 | import numpy as np 5 | 6 | a=0.1 #Lower bound 7 | b=14 #Upper bound 8 | dx=1e-5 # Step size 9 | fcp=1e-8 # Convergence parameter for function evaluation 10 | 11 | # Equation to be minimized 12 | def f(x): 13 | # return 2*x**2+16/x 14 | return x**2+54/x 15 | 16 | x=np.linspace(a,b,1000) 17 | 18 | #Initialization 19 | 20 | x1=a 21 | x2=x1+dx 22 | f1=f(x1) 23 | f2=f(x2) 24 | 25 | if f1>f2: 26 | x3=x1+2*dx 27 | elif f1<=f2: 28 | x3=x1-dx 29 | f3=f(x3) 30 | 31 | # Detemine minimum function value for the initial step 32 | f_min=min({f1,f2,f3}) 33 | 34 | # Determine x-value corresponding to minimum funtion value 35 | if f_min==f1: 36 | x_min=x1 37 | elif f_min==f2: 38 | x_min=x2 39 | elif f_min==f3: 40 | x_min=x3 41 | 42 | # Determine x_bar 43 | a1=(f2-f1)/(x2-x1) 44 | 45 | a2=(1/(x3-x2))*(((f3-f1)/(x3-x1))-((f2-f1)/(x2-x1))) 46 | x_bar=0.5*((x1+x2)-(a1/a2)) 47 | 48 | f_bar=f(x_bar) 49 | 50 | while abs(f_min-f_bar)>fcp: 51 | x2=(x_min+x_bar)/2 52 | x1=x2-dx 53 | x3=x1+2*dx 54 | f1=f(x1) 55 | f2=f(x2) 56 | f3=f(x3) 57 | f_min=min({f1,f2,f3}) 58 | if f_min==f1: 59 | x_min=x1 60 | elif f_min==f2: 61 | x_min=x2 62 | elif f_min==f3: 63 | x_min=x3 64 | a1=(f2-f1)/(x2-x1) 65 | a2=(1/(x3-x2))*(((f3-f1)/(x3-x1))-((f2-f1)/(x2-x1))) 66 | x_bar=0.5*((x1+x2)-(a1/a2)) 67 | f_bar=f(x_bar) 68 | 69 | print(f'The approximate minimum function value is {f_min}, at {x_min}') 70 | 71 | # Plot the function 72 | plt.plot(x,f(x)) 73 | plt.xlabel("x",fontweight='bold') 74 | plt.ylabel("f(x)",fontweight='bold') 75 | plt.grid(which='major',axis='both',linestyle='dashed') 76 | plt.title('Exhaustive Search Method',fontweight='bold') 77 | plt.scatter(x_min,f_min, color='red', label='Approximate Minimum Point') 78 | plt.legend() 79 | plt.savefig('Successive Quadratic Estimation Method.png',dpi=300) 80 | plt.show() 81 | -------------------------------------------------------------------------------- /fibonacci_search_method.m: -------------------------------------------------------------------------------- 1 | % Fibonacci Search Method 2 | % Matlab version R2018b 3 | % Date: 10th February, 2019 (started) 4 | % Date: 2nd November, 2023 (updated) 5 | 6 | clc 7 | clear 8 | a = 0.1; % Lower bound 9 | b = 14; % Upper bound 10 | n = 1000; % Number of times function is to be evaluated 11 | b_p=b; 12 | a_p=a; 13 | 14 | % Function to be minimized 15 | f = @(x) x.^2 + 54./x; 16 | 17 | % Initialization 18 | k = 2; 19 | L = b - a; % Length of search space 20 | L_ks = (F(n-k+1)/F(n+1)) * L; 21 | x1 = a + L_ks; 22 | x2 = b - L_ks; 23 | f1 = f(x1); 24 | f2 = f(x2); 25 | 26 | while k <= n 27 | if f2 < f1 28 | a = x1; 29 | else 30 | b = x2; 31 | end 32 | L = b - a; 33 | L_ks = (F(n - k + 1) / F(n + 1)) * L; % Recalculate L_ks 34 | x1 = a + L_ks; 35 | x2 = b - L_ks; 36 | f1 = f(x1); 37 | f2 = f(x2); 38 | k = k + 1; 39 | end 40 | 41 | x_min = (x1 + x2) / 2; 42 | f_min = f((x1 + x2) / 2); 43 | 44 | fprintf('The approximate minimum point and the value respectively are: %f and %f\n', x_min, f_min); 45 | 46 | % Plot the function 47 | x_values = linspace(0, b_p, 1000); % Update here 48 | y_values = f(x_values); 49 | figure; 50 | plot(x_values, y_values); 51 | xlabel('x', 'fontweight', 'bold'); 52 | ylabel('f(x)', 'fontweight', 'bold'); 53 | grid on; 54 | title('Fibonacci Search Method', 'fontweight', 'bold'); 55 | hold on; 56 | scatter(x_min, f_min, 'red', 'filled'); 57 | legend(func2str(f), 'Approximate Minimum Point'); 58 | 59 | % Set x-axis ticks to be whole numbers 60 | xticks(a_p:b_p); 61 | 62 | % Adjust x-axis limits 63 | ax = gca; 64 | ax.XLim = [a_p b_p]; % Update here 65 | 66 | saveas(gcf, 'Fibonacci_Search_Method.png', 'png'); 67 | 68 | % Function to generate n-th Fibonacci number 69 | function result = F(n) 70 | fi = zeros(1, n+1); 71 | fi(1) = 0; 72 | fi(2) = 1; 73 | 74 | for i = 3:n+1 75 | fi(i) = fi(i-1) + fi(i-2); 76 | end 77 | 78 | result = fi(n+1); 79 | end 80 | -------------------------------------------------------------------------------- /SuccessiveQuadraticEstimationMethod.m: -------------------------------------------------------------------------------- 1 | % Successive Quadratic Estimation Method 2 | 3 | a = 0.1; % Lower bound 4 | b = 14; % Upper bound 5 | dx = 1e-5; % Step size 6 | fcp = 1e-8; % Convergence parameter for function evaluation 7 | 8 | % Equation to be minimized 9 | f = @(x) x^2 + 54/x; 10 | 11 | x = linspace(a, b, 1000); 12 | 13 | % Initialization 14 | x1 = a; 15 | x2 = x1 + dx; 16 | f1 = f(x1); 17 | f2 = f(x2); 18 | 19 | if f1 > f2 20 | x3 = x1 + 2*dx; 21 | elseif f1 <= f2 22 | x3 = x1 - dx; 23 | end 24 | f3 = f(x3); 25 | 26 | % Determine minimum function value for the initial step 27 | f_min = min([f1, f2, f3]); 28 | 29 | % Determine x-value corresponding to minimum function value 30 | if f_min == f1 31 | x_min = x1; 32 | elseif f_min == f2 33 | x_min = x2; 34 | elseif f_min == f3 35 | x_min = x3; 36 | end 37 | 38 | % Determine x_bar 39 | a1 = (f2 - f1) / (x2 - x1); 40 | a2 = (1 / (x3 - x2)) * (((f3 - f1) / (x3 - x1)) - ((f2 - f1) / (x2 - x1))); 41 | x_bar = 0.5 * ((x1 + x2) - (a1 / a2)); 42 | f_bar = f(x_bar); 43 | 44 | while abs(f_min - f_bar) > fcp 45 | x2 = (x_min + x_bar) / 2; 46 | x1 = x2 - dx; 47 | x3 = x1 + 2*dx; 48 | f1 = f(x1); 49 | f2 = f(x2); 50 | f3 = f(x3); 51 | f_min = min([f1, f2, f3]); 52 | if f_min == f1 53 | x_min = x1; 54 | elseif f_min == f2 55 | x_min = x2; 56 | elseif f_min == f3 57 | x_min = x3; 58 | end 59 | a1 = (f2 - f1) / (x2 - x1); 60 | a2 = (1 / (x3 - x2)) * (((f3 - f1) / (x3 - x1)) - ((f2 - f1) / (x2 - x1))); 61 | x_bar = 0.5 * ((x1 + x2) - (a1 / a2)); 62 | f_bar = f(x_bar); 63 | end 64 | 65 | fprintf('The approximate minimum function value is %.8f, at %.8f\n', f_min, x_min); 66 | 67 | % Plot the function 68 | x_values = linspace(a, b, 1000); 69 | y_values = arrayfun(f, x_values); 70 | 71 | figure; 72 | plot(x_values, y_values,'DisplayName', func2str (f)); 73 | xlabel('x', 'FontWeight', 'bold'); 74 | ylabel('f(x)', 'FontWeight', 'bold'); 75 | grid on; 76 | title('Successive Quadratic Estimation Method', 'FontWeight', 'bold'); 77 | hold on; 78 | scatter(x_min, f_min, 'red', 'filled', 'DisplayName', 'Approximate Minimum Point'); 79 | legend('Location', 'Best'); 80 | saveas(gcf, 'Successive_Quadratic_Estimation_Method.png'); 81 | -------------------------------------------------------------------------------- /BoundingPhaseMethod.m: -------------------------------------------------------------------------------- 1 | % Bounding Phase Method as Explained in the book 2 | %"ENGINEERING OPTIMIZATION Methods and Applications" SECOND EDITION by A. Ravindran, K. M. Ragsdell and G. V. Reklaitis 3 | % Code developed by Sri. Soumyabrata Bhattacharjee 4 | % Matlab version R2022a 5 | % Date: 15th October, 2018 6 | % Date: 30th October, 2023 (updated) 7 | 8 | clc 9 | clear all 10 | % Bounding Phase Method 11 | 12 | a = 0.1; % Lower bound 13 | b = 14; % Upper bound 14 | dx = 1e-5; % Step-size parameter 15 | 16 | % Function to be minimized 17 | f = @(x) x.^2 + 54./x; 18 | 19 | % Initialization 20 | x_mid = a + dx*(b-a); % Initial guess 21 | x_lb = x_mid - dx; % Current lower bound 22 | x_ub = x_mid + dx; % Current upper bound 23 | f_mid = f(x_mid); 24 | f_lb = f(x_lb); 25 | f_ub = f(x_ub); 26 | k = 0; % Value will be iterated 27 | x = linspace(a, b, 1000); 28 | 29 | % Check whether the function is unimodal 30 | while x_ub <= b && x_lb >= a 31 | if f_mid >= f_lb && f_mid >= f_ub 32 | disp([f_lb, f_mid, f_ub]); 33 | disp('The function is not unimodal'); 34 | elseif f_lb >= f_mid && f_mid >= f_ub 35 | dx = abs(dx); 36 | disp(['dx: ', num2str(dx)]); 37 | else 38 | dx = -abs(dx); 39 | disp(['dx: ', num2str(dx)]); 40 | end 41 | k = k + 1; 42 | x_mid_new = x_mid + 2^k*dx; 43 | f_mid_new = f(x_mid_new); 44 | if f_mid_new > f_mid 45 | break; 46 | end 47 | x_mid = x_mid_new; 48 | x_lb = x_mid - dx; 49 | x_ub = x_mid + dx; 50 | f_mid = f_mid_new; 51 | f_lb = f(x_lb); 52 | f_ub = f(x_ub); 53 | disp(['k=', num2str(k), ',x_mid=', num2str(x_mid), ',x_lb=', num2str(x_lb), ',x_ub=', num2str(x_ub)]); 54 | disp(['The approximate minimum point and the value respectively are: ', num2str(x_mid), ' and ', num2str(f_mid)]); 55 | end 56 | 57 | % Plot the function 58 | x_values = linspace(a, b, 1000); 59 | f_values = f(x_values); 60 | 61 | figure; 62 | plot(x_values, f_values,'DisplayName', func2str(f)); 63 | xlabel('x', 'FontWeight', 'bold'); 64 | ylabel('f(x)', 'FontWeight', 'bold'); 65 | grid on; 66 | title('Bounding Phase Method', 'FontWeight', 'bold'); 67 | hold on; 68 | scatter(x_mid, f_mid, 100, 'red', 'filled', 'DisplayName', 'Minimum Point'); 69 | legend('show'); 70 | saveas(gcf, 'Bounding_Phase_Method.png'); 71 | -------------------------------------------------------------------------------- /Non-Linear Optimization [Python]/src/rosenbrock.py: -------------------------------------------------------------------------------- 1 | ''' 2 | This program is free software: you can redistribute it and/or modify 3 | it under the terms of the GNU General Public License as published by 4 | the Free Software Foundation, either version 3 of the License, or 5 | (at your option) any later version. 6 | 7 | This program is distributed in the hope that it will be useful, 8 | but WITHOUT ANY WARRANTY; without even the implied warranty of 9 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 10 | GNU General Public License for more details. 11 | 12 | You should have received a copy of the GNU General Public License 13 | along with this program. If not, see . 14 | ''' 15 | from numpy import * 16 | from newton import * 17 | from quasi_newton import * 18 | from steepest_descent import * 19 | from conjugate_gradient import * 20 | 21 | if __name__ == '__main__': 22 | def f(x): return 100 * math.pow(x[1] - math.pow(x[0], 2), 2) + math.pow(1 - x[0], 2) 23 | def df_dx1(x): return 400*math.pow(x[0], 3) - 400*x[0]*x[1] + 2*x[0] - 2 24 | def df_dx2(x): return 200*x[1] - 200*math.pow(x[0], 2) 25 | def fd(x): return array([ df_dx1(x), df_dx2(x) ]) 26 | 27 | def df_dx1_dx1(x): return 1200*math.pow(x[0], 2) - 400*x[1] + 2 28 | def df_dx1_dx2(x): return-400*x[0] 29 | 30 | def fdd(x): 31 | return array([ 32 | [df_dx1_dx1(x), df_dx1_dx2(x)], 33 | [df_dx1_dx2(x), 200]]) 34 | 35 | def print_error(i, direction, alpha, x): 36 | opt = f(array([1,1])) 37 | print("%d, %.20f" % (i, f(x)-opt)) 38 | 39 | def print_gradient(i, direction, alpha, x): 40 | print("%d, %.20f" % (i, linalg.norm(fd(x)))) 41 | 42 | def print_all(i, direction, alpha, x): 43 | print("iteration %d: \t direction: %s \t alpha: %.7f \t x: %s" 44 | % (i, ["%.7f" % _ for _ in direction], alpha, ["%.7f" % _ for _ in x])) 45 | 46 | x = array([0, 0]) 47 | precision = 10e-6 48 | max_iterations = 100 49 | callback = print_all 50 | 51 | print("steepest descent:") 52 | steepest_descent(f, fd, x, max_iterations, precision, callback) 53 | 54 | print("\nnewton:") 55 | newton(f, fd, fdd, x, max_iterations, precision, callback) 56 | 57 | print("\nquasi newton:") 58 | quasi_newton(f, fd, x, max_iterations, precision, callback) 59 | 60 | print("\nconjugate gradient:") 61 | conjugate_gradient(f, fd, x, max_iterations, precision, callback) 62 | 63 | -------------------------------------------------------------------------------- /CubicSearchMethod.py: -------------------------------------------------------------------------------- 1 | # Cubic Search Method 2 | 3 | import numpy as np 4 | import matplotlib.pyplot as plt 5 | 6 | a = 0.1 # Lower bound 7 | b = 14 # Upper bound 8 | 9 | # Function to minimize 10 | def f(x): 11 | return x**2 + 54/x 12 | 13 | # Function to calculate first derivative of the function 14 | def fdx(x): 15 | dx = 1e-6 # Small value for differentiation 16 | return ((f(x+dx) - f(x-dx)) / (2*dx)) 17 | 18 | # Initialize 19 | x0 = 1 20 | dx = 0.06 # Step size 21 | x_bar = 0 22 | x_k = x0 23 | k = 0 24 | x_p=np.linspace(a,b,1000) 25 | 26 | eps1 = 1e-3 27 | eps2 = 1e-3 28 | 29 | prev_f_bar = float('inf') 30 | 31 | while True: 32 | fdx0 = fdx(x_k) 33 | if fdx0 < 0: 34 | dx = abs(dx) 35 | else: 36 | dx = -abs(dx) 37 | 38 | x_k1 = x_k + 2**k*dx 39 | 40 | fdx_k = fdx(x_k) 41 | fdx_k1 = fdx(x_k1) 42 | 43 | if (fdx_k * fdx_k1) > 0: 44 | x_k = x_k + 2**k*dx 45 | else: 46 | x1 = min(x_k, x_k1) 47 | x2 = max(x_k, x_k1) 48 | f1 = f(x1) 49 | f2 = f(x2) 50 | fd1 = fdx(x1) 51 | fd2 = fdx(x2) 52 | z = (3*(f1-f2)/(x2-x1)) + fd1 + fd2 53 | 54 | if x1 < x2: 55 | w = np.sqrt(z**2 - fd1*fd2) 56 | else: 57 | w = -np.sqrt(z**2 - fd1*fd2) 58 | 59 | mu = (fd2 + w - z) / (fd2 + fd1 + 2*w) 60 | 61 | if mu == 0: 62 | x_bar = x2 63 | elif 0 < mu <= 1: 64 | x_bar = x2 - mu * (x2 - x1) 65 | else: 66 | x_bar = x1 67 | 68 | f_bar = f(x_bar) 69 | f1 = f(x1) 70 | 71 | if f_bar > f1: 72 | x_bar = x_bar - (x_bar - x1) / 2 73 | x1 = x1 + 2**k*dx 74 | k = k + 1 75 | f_bar = f(x_bar) 76 | f1 = f(x1) 77 | else: 78 | fdx_bar = fdx(x_bar) 79 | fdx1 = fdx(x1) 80 | 81 | if abs(fdx_bar) <= eps1 and abs((x_bar - x1) / x_bar) <= eps2: 82 | if f_bar < prev_f_bar: # Check if it's an improvement 83 | best_x_bar = x_bar 84 | best_f_bar = f_bar 85 | break 86 | 87 | if fdx_bar * fdx1 < 0: 88 | x2 = x_bar 89 | x1 = x_bar 90 | f1 = f(x1) 91 | f2 = f(x2) 92 | fd1 = fdx(x1) 93 | fd2 = fdx(x2) 94 | z = (3*(f1-f2)/(x2-x1)) + fd1 + fd2 95 | 96 | if x1 < x2: 97 | w = np.sqrt(z**2 - fd1*fd2) 98 | else: 99 | w = -np.sqrt(z**2 - fd1*fd2) 100 | 101 | mu = (fd2 + w - z) / (fd2 + fd1 + 2*w) 102 | 103 | if mu == 0: 104 | x_bar = x2 105 | elif 0 < mu <= 1: 106 | x_bar = x2 - mu * (x2 - x1) 107 | else: 108 | x_bar = x1 109 | 110 | if f_bar < prev_f_bar: # Check if it's an improvement 111 | best_x_bar = x_bar 112 | best_f_bar = f_bar 113 | 114 | if f_bar > prev_f_bar: # If current f_bar is worse, stop 115 | break 116 | 117 | prev_f_bar = f_bar 118 | 119 | k += 1 120 | 121 | 122 | print(f"The approximate minimum function value is {best_f_bar}, and it is located at {best_x_bar}") 123 | 124 | # Plot the function 125 | plt.plot(x_p,f(x_p)) 126 | plt.xlabel("x",fontweight='bold') 127 | plt.ylabel("f(x)",fontweight='bold') 128 | plt.grid(which='major',axis='both',linestyle='dashed') 129 | plt.title('Cubic Search Method',fontweight='bold') 130 | plt.scatter(x_bar,f_bar, color='red', label='Approximate Minimum Point') 131 | plt.legend() 132 | plt.savefig('Cubic Search Method.png',dpi=300) 133 | plt.show() -------------------------------------------------------------------------------- /CubicSearchMethod.m: -------------------------------------------------------------------------------- 1 | % Cubic Search Method as Explained in the book 2 | %"Optimization of Engineering Design: Algorithms and Examples" by Prof. Kalyanmoy Deb 3 | % Code developed by Sri. Soumyabrata Bhattacharjee 4 | % Matlab version R2018b, R2022a 5 | % Date: 3rd November, 2018 6 | % Date: 5th November, 2023 (updated) 7 | 8 | clc 9 | clear 10 | a = 0.1; % Lower bound 11 | b = 14; % Upper bound 12 | 13 | % Function to minimize 14 | f = @(x) x.^2 + 54./x; 15 | 16 | % Function to calculate first derivative of the function 17 | fdx = @(x) (f(x + 1e-6) - f(x - 1e-6)) / (2e-6); 18 | 19 | % Initialize 20 | x0 = 1; 21 | dx = 0.06; % Step size 22 | x_bar = 0; 23 | x_k = x0; 24 | k = 0; 25 | x_p = linspace(a, b, 1000); 26 | 27 | eps1 = 1e-3; 28 | eps2 = 1e-3; 29 | 30 | prev_f_bar = inf; 31 | 32 | while true 33 | fdx0 = fdx(x_k); 34 | if fdx0 < 0 35 | dx = abs(dx); 36 | else 37 | dx = -abs(dx); 38 | end 39 | 40 | x_k1 = x_k + 2^k * dx; 41 | 42 | fdx_k = fdx(x_k); 43 | fdx_k1 = fdx(x_k1); 44 | 45 | if (fdx_k * fdx_k1) > 0 46 | x_k = x_k + 2^k * dx; 47 | else 48 | x1 = min(x_k, x_k1); 49 | x2 = max(x_k, x_k1); 50 | f1 = f(x1); 51 | f2 = f(x2); 52 | fd1 = fdx(x1); 53 | fd2 = fdx(x2); 54 | z = (3*(f1-f2)/(x2-x1)) + fd1 + fd2; 55 | 56 | if x1 < x2 57 | w = sqrt(z^2 - fd1*fd2); 58 | else 59 | w = -sqrt(z^2 - fd1*fd2); 60 | end 61 | 62 | mu = (fd2 + w - z) / (fd2 + fd1 + 2*w); 63 | 64 | if mu == 0 65 | x_bar = x2; 66 | elseif 0 < mu && mu <= 1 67 | x_bar = x2 - mu * (x2 - x1); 68 | else 69 | x_bar = x1; 70 | end 71 | 72 | f_bar = f(x_bar); 73 | f1 = f(x1); 74 | 75 | if f_bar > f1 76 | x_bar = x_bar - (x_bar - x1) / 2; 77 | x1 = x1 + 2^k * dx; 78 | k = k + 1; 79 | f_bar = f(x_bar); 80 | f1 = f(x1); 81 | else 82 | fdx_bar = fdx(x_bar); 83 | fdx1 = fdx(x1); 84 | 85 | if abs(fdx_bar) <= eps1 && abs((x_bar - x1) / x_bar) <= eps2 86 | if f_bar < prev_f_bar % Check if it's an improvement 87 | best_x_bar = x_bar; 88 | best_f_bar = f_bar; 89 | end 90 | break; 91 | end 92 | 93 | if fdx_bar * fdx1 < 0 94 | x2 = x_bar; 95 | x1 = x_bar; 96 | f1 = f(x1); 97 | f2 = f(x2); 98 | fd1 = fdx(x1); 99 | fd2 = fdx(x2); 100 | z = (3*(f1-f2)/(x2-x1)) + fd1 + fd2; 101 | 102 | if x1 < x2 103 | w = sqrt(z^2 - fd1*fd2); 104 | else 105 | w = -sqrt(z^2 - fd1*fd2); 106 | end 107 | 108 | mu = (fd2 + w - z) / (fd2 + fd1 + 2*w); 109 | 110 | if mu == 0 111 | x_bar = x2; 112 | elseif 0 < mu && mu <= 1 113 | x_bar = x2 - mu * (x2 - x1); 114 | else 115 | x_bar = x1; 116 | end 117 | end 118 | end 119 | 120 | if f_bar < prev_f_bar % Check if it's an improvement 121 | best_x_bar = x_bar; 122 | best_f_bar = f_bar; 123 | end 124 | 125 | if f_bar > prev_f_bar % If current f_bar is worse, stop 126 | break; 127 | end 128 | 129 | prev_f_bar = f_bar; 130 | end 131 | 132 | k = k + 1; 133 | end 134 | 135 | fprintf('The approximate minimum function value is %.6f, and it is located at %.6f\n', best_f_bar, best_x_bar); 136 | 137 | % Plot the function 138 | x_p = linspace(a, b, 1000); 139 | figure; 140 | plot(x_p, f(x_p), 'LineWidth', 1.5,'DisplayName',func2str (f)); 141 | hold on; 142 | xlabel('x', 'FontWeight', 'bold'); 143 | ylabel('f(x)', 'FontWeight', 'bold'); 144 | grid on; 145 | title('Cubic Search Method', 'FontWeight', 'bold'); 146 | scatter(best_x_bar, best_f_bar, 100, 'r', 'filled', 'DisplayName', 'Approximate Minimum Point'); 147 | legend('Location', 'Best'); 148 | saveas(gcf, 'Cubic_Search_Method.png', 'png'); 149 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Optimization Techniques 2 | 3 | This repository contains implementations of various optimization techniques outlined in the book "Optimization of Engineering Design: Algorithms and Examples" by Prof. Kalyanmoy Deb. Each technique provides a visual representation by plotting both the function and the approximate minimum point (marked as 'o'). 4 | 5 | ## Techniques Included 6 | 7 | 1. **Exhaustive Search Method** 8 | - Description: The exhaustive search method is a brute-force approach to finding the minimum of a function within a specified range. 9 | - Versions available for both Python and MATLAB: 10 | - [Python Code](https://github.com/Soumyabrata111/Optimization-Techniques/blob/master/ExhaustiveSearchMethod.py) 11 | - [MATLAB Code](https://github.com/Soumyabrata111/Optimization-Techniques/blob/master/ExhaustiveSearchMethod.m) 12 | 13 | 2. **Golden Section Search** 14 | - Description: The Golden Section Search is an iterative method that narrows down the search space to find the minimum of an unimodal function. 15 | - Versions available for both Python and MATLAB: 16 | - [Python Code](https://github.com/Soumyabrata111/Optimization-Techniques/blob/master/GoldenSectionSearchMethod.py) 17 | - [MATLAB Code](https://github.com/Soumyabrata111/Optimization-Techniques/blob/master/GoldenSectionSearchMethod.m) 18 | 19 | 3. **Bounding Phase Method** 20 | - Description: The Bounding Phase Method is an optimization technique that involves narrowing down the search interval to find the minimum of an unimodal function. 21 | - Versions available for both Python and MATLAB: 22 | - [Python Code](https://github.com/Soumyabrata111/Optimization-Techniques/blob/master/BoundingPhaseMethod.py) 23 | - [MATLAB Code](https://github.com/Soumyabrata111/Optimization-Techniques/blob/master/BoundingPhaseMethod.m) 24 | 25 | 4. **Interval Halving Method** 26 | - Description: The Interval Halving Method is an iterative approach for finding the minimum of a function within a specified interval. 27 | - Versions available for both Python and MATLAB: 28 | - [Python Code](https://github.com/Soumyabrata111/Optimization-Techniques/blob/master/IntervalHalvingMethod.py) 29 | - [MATLAB Code](https://github.com/Soumyabrata111/Optimization-Techniques/blob/master/IntervalHalvingMethod.m) 30 | 5. **Fibonacci Search Method** 31 | - Description: The Fibonacci Search Method is another iterative approach for finding the minimum of a function within a specified interval. 32 | - Version available for Python: 33 | - [Python Code](https://github.com/Soumyabrata111/Optimization-Techniques/blob/master/FibonacciSearchMethod.py) 34 | - [MATLAB Code](https://github.com/Soumyabrata111/Optimization-Techniques/blob/master/fibonacci_search_method.m) 35 | 6. **Quadratic Estimation Method** 36 | - Description: The Quadratic Estimation Method is the simplest of all the polynomial interpolation approaches for finding the minimum of a function within a specified interval. 37 | - Version available for Python: 38 | - [Python Code](https://github.com/Soumyabrata111/Optimization-Techniques/blob/master/QuadraticEstimationMethod.py) 39 | - [MATLAB Code](https://github.com/Soumyabrata111/Optimization-Techniques/blob/master/QuadraticEstimationMethod.m) 40 | 7. **Successive Quadratic Estimation Method** 41 | - Description: It is the more refined form of the Quadratic Estimation Method, which iteratively finds the minimum of a function within a specified interval. 42 | - Version available for Python: 43 | - [Python Code](https://github.com/Soumyabrata111/Optimization-Techniques/blob/master/SuccessiveQuadraticEstimationMethod.py) 44 | - [MATLAB Code](https://github.com/Soumyabrata111/Optimization-Techniques/blob/master/SuccessiveQuadraticEstimationMethod.m) 45 | 8. **Newton-Raphson Method** 46 | - Description: It is a very simple gradient-based method, suitable for unconstrained optimization problems. 47 | - Version available for Python: 48 | - [Python Code](https://github.com/Soumyabrata111/Optimization-Techniques/blob/master/NewtonRaphsonMethod.py) 49 | - [MATLAB Code](https://github.com/Soumyabrata111/Optimization-Techniques/blob/master/NewtonRaphsonMethod.m) 50 | 9. **Bisection Method** 51 | - Description: This version of the Bisection Method, does not need the two endpoints, of the search space to have function values of opposite values. Rather, the algorithm is based on the function's first derivative within the search space. The search space reduces with every iteration. 52 | - Version available for Python: 53 | - [Python Code](https://github.com/Soumyabrata111/Optimization-Techniques/blob/master/BisectionMethod.py) 54 | - [MATLAB Code](https://github.com/Soumyabrata111/Optimization-Techniques/blob/master/BisectionMethod.m) 55 | 10. **Secant Method** 56 | - Description: The Secant Method is a modification of the Bisection Method. Here, the point 'z' of the search space is not the mid-point; rather, it depends on the values of the first derivative of the function. 57 | - Version available for Python: 58 | - [Python Code](https://github.com/Soumyabrata111/Optimization-Techniques/blob/master/SecantMethod.py) 59 | 11. **Cubic Search Method** 60 | - Description: The Cubic Search Method is used to find the minimum of an unimodal function iteratively. It is similar to the successive quadratic point estimation method. 61 | - Versions available for both Python and MATLAB: 62 | - [Python Code](https://github.com/Soumyabrata111/Optimization-Techniques/blob/master/CubicSearchMethod.py) 63 | - [MATLAB Code](https://github.com/Soumyabrata111/Optimization-Techniques/blob/master/CubicSearchMethod.m) 64 | 65 | ## About the Author 66 | 67 | I am pursuing my PhD from the Department of Mechanical Engineering, Indian Institute of Technology Indore. I am also available for freelancing in Optimization Algorithms, Machine Learning, and Deep Learning. My current research work is in time series analysis and classification algorithms. A list of my publications is available at [Google Scholar](https://scholar.google.co.in/citations?user=-ZM_QRcAAAAJ&hl=en) 68 | 69 | ## Get the Latest MATLAB Files 70 | 71 | [![View Optimization-Techniques on File Exchange](https://www.mathworks.com/matlabcentral/images/matlab-file-exchange.svg)](https://in.mathworks.com/matlabcentral/fileexchange/69108-optimization-techniques) 72 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | Copyright (C) 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . 675 | -------------------------------------------------------------------------------- /KKT_optimization/infill-dphi-focus.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "code", 5 | "execution_count": 1, 6 | "metadata": { 7 | "collapsed": false 8 | }, 9 | "outputs": [ 10 | { 11 | "name": "stderr", 12 | "output_type": "stream", 13 | "text": [ 14 | "/home/p2admin/anaconda2/lib/python2.7/site-packages/h5py/__init__.py:34: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n", 15 | " from ._conv import register_converters as _register_converters\n" 16 | ] 17 | } 18 | ], 19 | "source": [ 20 | "import numpy as np\n", 21 | "import tensorflow as tf\n", 22 | "import matplotlib.pyplot as plt\n", 23 | "import scipy.io as sio\n", 24 | "from tensorflow.contrib import rnn\n", 25 | "import math\n", 26 | "import time\n", 27 | "import os\n", 28 | "from datetime import datetime\n", 29 | "import dateutil.tz\n", 30 | "# from utils.utils import *\n", 31 | "\n", 32 | "\n", 33 | "def xavier_init(size):\n", 34 | " in_dim = size[0]\n", 35 | " xavier_stddev = 1. / tf.sqrt(in_dim / 2.)\n", 36 | " return tf.random_normal(shape=size, stddev=xavier_stddev)\n", 37 | "\n", 38 | "def creat_dir(network_type):\n", 39 | " \"\"\"code from on InfoGAN\"\"\"\n", 40 | " now = datetime.now(dateutil.tz.tzlocal())\n", 41 | " timestamp = now.strftime('%Y_%m_%d_%H_%M_%S')\n", 42 | " root_log_dir = \"logs/\" + network_type\n", 43 | " exp_name = network_type + \"_%s\" % timestamp\n", 44 | " log_dir = os.path.join(root_log_dir, exp_name)\n", 45 | "\n", 46 | " now = datetime.now(dateutil.tz.tzlocal())\n", 47 | " timestamp = now.strftime('%Y_%m_%d_%H_%M_%S')\n", 48 | " root_model_dir = \"models/\" + network_type\n", 49 | " exp_name = network_type + \"_%s\" % timestamp\n", 50 | " model_dir = os.path.join(root_model_dir, exp_name)\n", 51 | "\n", 52 | " for path in [log_dir, model_dir]:\n", 53 | " if not os.path.exists(path):\n", 54 | " os.makedirs(path)\n", 55 | " return log_dir, model_dir\n", 56 | "\n", 57 | "tic = time.clock()\n", 58 | "\n", 59 | "E0 = 1\n", 60 | "Emin = 1e-9\n", 61 | "nu = 0.3\n", 62 | "batch_size = 3\n", 63 | "\n", 64 | "'Input'\n", 65 | "nelx, nely, alpha, alpha2, gamma, rmin, density_r = 12*4, 4*4, 0.6, 0.6, 3.0, 3.0, 6.0\n", 66 | "\n", 67 | "'Algorithm parameters'\n", 68 | "p, nn, epsilon_al, epsilon_opt = 16,nely * nelx, 1, 1e-3\n", 69 | "\n", 70 | "'Prepare filter'\n", 71 | "r = rmin\n", 72 | "Range = np.arange(-r, r + 1)\n", 73 | "X = np.array([Range] * len(Range))\n", 74 | "Y = np.array([Range] * len(Range)).T\n", 75 | "X_temp = X.T.reshape(len(Range) ** 2, 1)\n", 76 | "Y_temp = Y.T.reshape(len(Range) ** 2, 1)\n", 77 | "neighbor = np.concatenate((X_temp, Y_temp), 1)\n", 78 | "D = np.sum(neighbor ** 2, 1)\n", 79 | "rn = sum(D <= r ** 2) - sum(D == 0)\n", 80 | "\n", 81 | "pattern_index = []\n", 82 | "for i in range(len(D)):\n", 83 | " if D[i] <= r ** 2 and D[i] != 0:\n", 84 | " pattern_index.append(i)\n", 85 | "pattern = neighbor[pattern_index]\n", 86 | "\n", 87 | "locX = np.asarray([np.arange(1, nelx + 1)] * nely)\n", 88 | "locY = np.asarray([np.arange(1, nely + 1)] * nelx).T\n", 89 | "loc = np.asarray([locY.T.reshape(-1), locX.T.reshape(-1)]).T\n", 90 | "\n", 91 | "M = np.zeros([nn, rn])\n", 92 | "for i in range(nn):\n", 93 | " for j in range(rn):\n", 94 | " locc = loc[i, :] + pattern[j, :]\n", 95 | " count_true = 0\n", 96 | " if locc[0] > nely: count_true = count_true + 1\n", 97 | " if locc[1] > nelx: count_true = count_true + 1\n", 98 | "\n", 99 | " if sum(locc < 1) + count_true == 0:\n", 100 | " M[i, j] = locc[0] + (locc[1] - 1) * nely\n", 101 | " else:\n", 102 | " M[i, j] = 'NaN'\n", 103 | "\n", 104 | "iH = np.ones([int(nelx * nely * (2 * (np.ceil(rmin) - 1) + 1) ** 2), 1], dtype=int)\n", 105 | "jH = np.ones(iH.shape, dtype=int)\n", 106 | "sH = np.zeros(iH.shape)\n", 107 | "k = 0\n", 108 | "for i1 in range(nelx):\n", 109 | " for j1 in range(nely):\n", 110 | " e1 = (i1) * nely + (j1 + 1)\n", 111 | " for i2 in np.arange(int(max(i1 + 1 - (np.ceil(rmin) - 1), 1)),\n", 112 | " int(min(i1 + 1 + (np.ceil(rmin) - 1), nelx)) + 1):\n", 113 | " for j2 in np.arange(int(max(j1 + 1 - (np.ceil(rmin) - 1), 1)),\n", 114 | " int(min(j1 + 1 + (np.ceil(rmin) - 1), nely)) + 1):\n", 115 | " e2 = (i2 - 1) * nely + j2\n", 116 | " iH[k] = e1\n", 117 | " jH[k] = e2\n", 118 | " sH[k] = max(0, rmin - np.sqrt((i1 + 1 - i2) ** 2 + (j1 + 1 - j2) ** 2))\n", 119 | " k = k + 1\n", 120 | "\n", 121 | "iH = iH.reshape(-1) - 1\n", 122 | "jH = jH.reshape(-1) - 1\n", 123 | "sH = sH.reshape(-1)\n", 124 | "\n", 125 | "import scipy.sparse as sps\n", 126 | "\n", 127 | "H = sps.csc_matrix((sH, (iH, jH))).toarray()\n", 128 | "Hs = np.sum(H, 1)\n", 129 | "bigM = H > 0\n", 130 | "\n", 131 | "'create neighbourhood index for N'\n", 132 | "r = density_r\n", 133 | "Range = np.arange(-r, r + 1)\n", 134 | "mesh = Range\n", 135 | "X = np.asarray([Range] * len(Range))\n", 136 | "Y = np.asarray([Range] * len(Range)).T\n", 137 | "neighbor = np.array([X.T.reshape(-1), Y.T.reshape(-1)]).T\n", 138 | "D = np.sum(neighbor ** 2, 1)\n", 139 | "rn = np.sum(D <= r ** 2)\n", 140 | "pattern = neighbor[D <= r ** 2, :]\n", 141 | "locX = np.asarray([np.arange(1, nelx + 1)] * nely)\n", 142 | "locY = np.asarray([np.arange(1, nely + 1)] * nelx).T\n", 143 | "loc = np.asarray([locY.T.reshape(-1), locX.T.reshape(-1)]).T\n", 144 | "N = np.zeros([nn, rn])\n", 145 | "for i in range(nn):\n", 146 | " for j in range(rn):\n", 147 | " locc = loc[i, :] + pattern[j, :]\n", 148 | " count_true = 0\n", 149 | " if locc[0] > nely: count_true = count_true + 1\n", 150 | " if locc[1] > nelx: count_true = count_true + 1\n", 151 | "\n", 152 | " if sum(locc < 1) + count_true == 0:\n", 153 | " N[i, j] = locc[0] + (locc[1] - 1) * nely\n", 154 | " else:\n", 155 | " N[i, j] = 'NaN'\n", 156 | "\n", 157 | "idx_temp = (np.array([np.arange(nn)] * rn).T).reshape(-1).reshape(nn * rn, 1)\n", 158 | "N_t = N.T\n", 159 | "idy = []\n", 160 | "idx = []\n", 161 | "import math\n", 162 | "\n", 163 | "k = 0\n", 164 | "for i in range(N_t.shape[1]):\n", 165 | " for j in range(N_t.shape[0]):\n", 166 | " if not math.isnan(N_t[j, i]):\n", 167 | " idy.append(N_t[j, i])\n", 168 | " idx.append(idx_temp[k])\n", 169 | " k = k + 1\n", 170 | "idy = np.asarray(idy).reshape(len(idy), 1) - 1\n", 171 | "idx = np.asarray(idx)\n", 172 | "bigN = sps.coo_matrix((np.ones(len(idx)), (idx.reshape(-1), idy.reshape(-1)))).toarray()\n", 173 | "N_count = np.sum(~np.isnan(N), axis=1)\n", 174 | "\n", 175 | "'Material Properties'\n", 176 | "E0, Emin, nu = 1, 1e-9, 0.3\n", 177 | "\n", 178 | "'PREPARE FINITE ELEMENT ANALYSIS'\n", 179 | "A11 = np.array([[12, 3, -6, -3], [3, 12, 3, 0], [-6, 3, 12, -3], [-3, 0, -3, 12]])\n", 180 | "A12 = np.array([[-6, -3, 0, 3], [-3, -6, -3, -6], [0, -3, -6, 3], [3, -6, 3, -6]])\n", 181 | "B11 = np.array([[-4, 3, -2, 9], [3, -4, -9, 4], [-2, -9, -4, -3], [9, 4, -3, -4]])\n", 182 | "B12 = np.array([[2, -3, 4, -9], [-3, 2, 9, -2], [4, 9, 2, 3], [-9, -2, 3, 2]])\n", 183 | "\n", 184 | "A1 = np.concatenate((A11, A12), axis=1)\n", 185 | "A2 = np.concatenate((A12.T, A11), axis=1)\n", 186 | "A = np.concatenate((A1, A2))\n", 187 | "\n", 188 | "B1 = np.concatenate((B11, B12), axis=1)\n", 189 | "B2 = np.concatenate((B12.T, B11), axis=1)\n", 190 | "B = np.concatenate((B1, B2))\n", 191 | "\n", 192 | "KE = 1 / (1 - nu ** 2) / 24. * (A + nu * B)\n", 193 | "nodenrs = np.arange((1 + nelx) * (1 + nely)).reshape(1 + nelx, 1 + nely).T\n", 194 | "edofVec = (2 * (nodenrs[0:-1, 0:-1] + 1)).reshape(nelx * nely, 1, order='F')\n", 195 | "edofMat = np.asarray([edofVec.reshape(-1)] * 8).T + \\\n", 196 | " np.asarray(([0, 1, 2 * nely + 2, 2 * nely + 3, 2 * nely + 0, 2 * nely + 1, -2, -1]) * nelx * nely).reshape(\n", 197 | " nelx * nely, 8)\n", 198 | "\n", 199 | "iK = np.zeros([edofMat.shape[0] * 8, edofMat.shape[1] * 1])\n", 200 | "for i in range(edofMat.shape[0]):\n", 201 | " for j in range(edofMat.shape[1]):\n", 202 | " iK[i * 8:(i + 1) * 8, j] = np.asarray(edofMat[i, j] * np.ones([8, 1])).reshape(-1)\n", 203 | "iK = (iK.astype(np.int32).T).reshape(64 * nelx * nely, 1, order='F')\n", 204 | "\n", 205 | "jK = np.zeros([edofMat.shape[0] * 1, edofMat.shape[1] * 8])\n", 206 | "for i in range(edofMat.shape[0]):\n", 207 | " for j in range(edofMat.shape[1]):\n", 208 | " jK[i, j * 8:(j + 1) * 8] = np.asarray(edofMat[i, j] * np.ones([1, 8])).reshape(-1)\n", 209 | "jK = (jK.astype(np.int32).T).reshape(64 * nelx * nely, 1, order='F')\n", 210 | "\n", 211 | "'DEFINE LOADS AND SUPPORTS (HALF MBB-BEAM)'\n", 212 | "# F = np.zeros([2 * (nely + 1) * (nelx + 1), 1])\n", 213 | "# F[((nely + 1) * nelx) * 2 + nely + 1, 0] = -1\n", 214 | "F = tf.placeholder(tf.float32, shape=([2*(nely+1)*(nelx+1),batch_size]))\n", 215 | "\n", 216 | "\n", 217 | "# F=sps.coo_matrix(F)\n", 218 | "U = np.zeros([2 * (nely + 1) * (nelx + 1), 1])\n", 219 | "# fixeddofs=(np.arange(0,2*(nely+1),2).tolist());fixeddofs.append(2*(nelx+1)*(nely+1)-1)\n", 220 | "# fixeddofs=np.asarray(fixeddofs).reshape(1,len(fixeddofs))\n", 221 | "# alldofs = np.arange(2*(nely+1)*(nelx+1)).reshape(1,2*(nely+1)*(nelx+1))\n", 222 | "\n", 223 | "fixeddofs = np.asarray(np.arange(0, 2 * (nely + 1), 1).tolist())\n", 224 | "fixeddofs = fixeddofs.reshape(1, len(fixeddofs))\n", 225 | "alldofs = np.arange(2 * (nely + 1) * (nelx + 1)).reshape(1, 2 * (nely + 1) * (nelx + 1))\n", 226 | "\n", 227 | "freedofs = np.setdiff1d(alldofs, fixeddofs)\n", 228 | "\n", 229 | "'prepare some stuff to reduce cost'\n", 230 | "dphi_idphi = (H / sum(H)).T\n", 231 | "\n", 232 | "'Start Iteration'\n", 233 | "# phi = alpha*np.ones([nn,1])\n", 234 | "\n", 235 | "\n", 236 | "\n", 237 | "\n", 238 | "z_dim, h_dim_1, h_dim_2, h_dim_3, h_dim_4, h_dim_5 = 2, 100, 100, 100, 100, 100\n", 239 | "\n", 240 | "# r_lag = tf.placeholder(tf.float32, shape=([batch_size,1]))\n", 241 | "# r_lag2 = tf.placeholder(tf.float32, shape=([batch_size,1]))\n", 242 | "# lamda_lag = tf.placeholder(tf.float32, shape=([batch_size,1]))\n", 243 | "# lamda_lag2 = tf.placeholder(tf.float32, shape=([batch_size,1]))\n", 244 | "\n", 245 | "F_input = tf.placeholder(tf.float32, shape=([batch_size, z_dim]))\n", 246 | "# F = tf.placeholder(tf.float32, shape=([2*(nely+1)*(nelx+1),batch_size]))\n", 247 | "\n", 248 | "W1 = tf.Variable(xavier_init([z_dim, h_dim_1]))\n", 249 | "b1 = tf.Variable(tf.zeros(shape=[h_dim_1]))\n", 250 | "\n", 251 | "W2 = tf.Variable(xavier_init([h_dim_1, h_dim_2]))\n", 252 | "b2 = tf.Variable(tf.zeros(shape=[h_dim_2]))\n", 253 | "\n", 254 | "W3 = tf.Variable(xavier_init([h_dim_2, h_dim_3]))\n", 255 | "b3 = tf.Variable(tf.zeros(shape=[h_dim_3]))\n", 256 | "\n", 257 | "W4 = tf.Variable(xavier_init([h_dim_3, h_dim_4]))\n", 258 | "b4 = tf.Variable(tf.zeros(shape=[h_dim_4]))\n", 259 | "\n", 260 | "W5 = tf.Variable(xavier_init([h_dim_4, nn]))\n", 261 | "b5 = tf.Variable(tf.zeros(shape=[nn]))\n", 262 | "\n", 263 | "# W6 = tf.Variable(xavier_init([h_dim_5, nn]))\n", 264 | "# b6 = tf.Variable(tf.zeros(shape=[nn]))\n", 265 | "\n", 266 | "h1 = tf.contrib.layers.batch_norm(tf.nn.relu(tf.matmul(F_input, W1) + b1),scale=True)\n", 267 | "h2 = tf.contrib.layers.batch_norm(tf.nn.relu(tf.matmul(h1, W2) + b2),scale=True)\n", 268 | "h3 = tf.contrib.layers.batch_norm(tf.nn.relu(tf.matmul(h2, W3) + b3),scale=True)\n", 269 | "h4 = tf.contrib.layers.batch_norm(tf.nn.relu(tf.matmul(h3, W4) + b4),scale=True)\n", 270 | "# h5 = tf.nn.relu(tf.matmul(h4, W5) + b5)\n", 271 | " \n", 272 | "phi_ = tf.sigmoid(tf.matmul(h4, W5) + b5)\n", 273 | "phi = tf.reshape(phi_, [nn, batch_size])\n", 274 | "\n", 275 | "# phi = (tf.Variable(alpha * np.ones([nn, 1]), dtype='float32'))\n", 276 | "\n", 277 | "loop = 0\n", 278 | "# delta = 1.0\n", 279 | "\n", 280 | "# while beta < 1000:\n", 281 | "loop = loop + 1\n", 282 | "loop2 = 0\n", 283 | "'augmented lagrangian parameters'\n", 284 | "# r_lag = 1\n", 285 | "# r_lag2 = 0.001\n", 286 | "# lamda_lag = 0\n", 287 | "# lamda_lag2 = 0\n", 288 | "\n", 289 | "eta = 0.1\n", 290 | "eta2 = 0.1\n", 291 | "epsilon = 1\n", 292 | "dphi = 1e6\n", 293 | "\n", 294 | "r_lag = tf.placeholder(tf.float32, shape=([batch_size,1]))\n", 295 | "r_lag2 = tf.placeholder(tf.float32, shape=([batch_size,1]))\n", 296 | "lamda_lag = tf.placeholder(tf.float32, shape=([batch_size,1]))\n", 297 | "lamda_lag2 = tf.placeholder(tf.float32, shape=([batch_size,1]))\n", 298 | "beta = tf.placeholder(tf.float32, shape=([batch_size,1]))\n", 299 | "################################################################\n", 300 | "'get initial g and c'\n", 301 | "\n", 302 | "import time\n", 303 | "\n", 304 | "W1_fake = tf.Variable(xavier_init([z_dim, h_dim_1]), trainable=False)\n", 305 | "b1_fake = tf.Variable(tf.zeros(shape=[h_dim_1]), trainable=False)\n", 306 | "W1_fake = W1_fake.assign(W1)\n", 307 | "b1_fake = b1_fake.assign(b1)\n", 308 | "\n", 309 | "W2_fake = tf.Variable(xavier_init([h_dim_1, h_dim_2]), trainable=False)\n", 310 | "b2_fake = tf.Variable(tf.zeros(shape=[h_dim_2]), trainable=False)\n", 311 | "W2_fake = W2_fake.assign(W2)\n", 312 | "b2_fake = b2_fake.assign(b2)\n", 313 | "\n", 314 | "W3_fake = tf.Variable(xavier_init([h_dim_2, h_dim_3]), trainable=False)\n", 315 | "b3_fake = tf.Variable(tf.zeros(shape=[h_dim_3]), trainable=False)\n", 316 | "W3_fake = W3_fake.assign(W3)\n", 317 | "b3_fake = b3_fake.assign(b3)\n", 318 | "\n", 319 | "W4_fake = tf.Variable(xavier_init([h_dim_3, h_dim_4]), trainable=False)\n", 320 | "b4_fake = tf.Variable(tf.zeros(shape=[h_dim_4]), trainable=False)\n", 321 | "W4_fake = W4_fake.assign(W4)\n", 322 | "b4_fake = b4_fake.assign(b4)\n", 323 | "\n", 324 | "W5_fake = tf.Variable(xavier_init([h_dim_4, nn]), trainable=False)\n", 325 | "b5_fake = tf.Variable(tf.zeros(shape=[nn]), trainable=False)\n", 326 | "W5_fake = W5_fake.assign(W5)\n", 327 | "b5_fake = b5_fake.assign(b5)\n", 328 | "\n", 329 | "# W6_fake = tf.Variable(xavier_init([h_dim_5, nn]), trainable=False)\n", 330 | "# b6_fake = tf.Variable(tf.zeros(shape=[nn]), trainable=False)\n", 331 | "# W6_fake = W6_fake.assign(W6)\n", 332 | "# b6_fake = b6_fake.assign(b6)\n", 333 | "\n", 334 | "h1_fake = tf.contrib.layers.batch_norm(tf.nn.relu(tf.matmul(F_input, W1_fake) + b1_fake),scale=True,trainable=False)\n", 335 | "h2_fake = tf.contrib.layers.batch_norm(tf.nn.relu(tf.matmul(h1_fake, W2_fake) + b2_fake),scale=True,trainable=False)\n", 336 | "h3_fake = tf.contrib.layers.batch_norm(tf.nn.relu(tf.matmul(h2_fake, W3_fake) + b3_fake),scale=True,trainable=False)\n", 337 | "h4_fake = tf.contrib.layers.batch_norm(tf.nn.relu(tf.matmul(h3_fake, W4_fake) + b4_fake),scale=True,trainable=False)\n", 338 | "# h5_fake = tf.nn.relu(tf.matmul(h4_fake, W5_fake) + b5_fake)\n", 339 | "\n", 340 | "phi_temp_fake = tf.sigmoid(tf.matmul(h4_fake, W5_fake) + b5_fake)\n", 341 | "phi_fake = tf.reshape(phi_temp_fake,[nn,batch_size])\n" 342 | ] 343 | }, 344 | { 345 | "cell_type": "code", 346 | "execution_count": null, 347 | "metadata": { 348 | "collapsed": true 349 | }, 350 | "outputs": [], 351 | "source": [ 352 | "sep_grad_store,error_store,dphi_store,dobj_store=[],[],[],[]\n", 353 | "c,g,global_density=[],[],[]\n", 354 | "c_fake,g_fake,global_density_fake=[],[],[]\n", 355 | "rho,rho_fake=[],[]\n", 356 | "dphi_fake=[]\n", 357 | "\n", 358 | "tic=time.clock()\n", 359 | "\n", 360 | "learning_rate_fake = tf.placeholder(tf.float32,shape=([batch_size,1]))\n", 361 | "g_old = [tf.Variable(0, dtype='float32',trainable=False)]*batch_size\n", 362 | "global_density_old = [tf.Variable([[0]], dtype='float32',trainable=False)]*batch_size\n", 363 | "c_old = [tf.Variable(0, dtype='float32',trainable=False)]*batch_size\n", 364 | "tic=time.clock()\n", 365 | "\n", 366 | "for i in range(batch_size):\n", 367 | " phi_til = tf.matmul(tf.cast(H, tf.float32), phi[:,i:i+1]) / Hs.reshape(nn, 1)\n", 368 | " rho.append((tf.tanh(beta[i][0] / 2.0) + tf.tanh(beta[i][0] * (phi_til - 0.5))) / (2 * tf.tanh(beta[i][0] / 2.0)))\n", 369 | "\n", 370 | " sK_temp = tf.transpose((KE.reshape(KE.shape[0] * KE.shape[1], 1) * \\\n", 371 | " tf.reshape(Emin + tf.reshape(rho[i], [-1]) ** (gamma) * (E0 - Emin), [1, nelx * nely])))\n", 372 | " sK = tf.reshape(sK_temp, [8 * 8 * nelx * nely, 1])\n", 373 | "\n", 374 | " ###################\n", 375 | " indices_m = np.stack((iK.reshape(-1), jK.reshape(-1)), axis=1)\n", 376 | " values_m = tf.reshape(sK, [-1])\n", 377 | "\n", 378 | " linearized_m = tf.matmul(indices_m, [[10000], [1]])\n", 379 | " y_m, idx_m = tf.unique(tf.squeeze(linearized_m))\n", 380 | "\n", 381 | " idx_m_sort, ind_m_sort = tf.nn.top_k(idx_m, k=nelx * nely * 64)\n", 382 | " idx_m_sort = tf.reverse(idx_m_sort, [0])\n", 383 | " ind_m_sort = tf.reverse(ind_m_sort, [0])\n", 384 | "\n", 385 | " # values_m_test = values_m\n", 386 | " values_m = tf.gather(values_m, ind_m_sort)\n", 387 | " values_m = tf.segment_sum(values_m, idx_m_sort)\n", 388 | "\n", 389 | " y_m = tf.expand_dims(y_m, 1)\n", 390 | " indices_m = tf.concat([y_m // 10000, y_m % 10000], axis=1)\n", 391 | " #####################\n", 392 | "\n", 393 | " #####################\n", 394 | " K_sp = tf.SparseTensor(tf.cast(indices_m, tf.int64),\n", 395 | " tf.reshape(tf.cast(values_m, tf.float32), [-1]),\n", 396 | " [(nely + 1) * (nelx + 1) * 2, (nely + 1) * (nelx + 1) * 2])\n", 397 | " K_sp = tf.sparse_add(tf.zeros(((nely + 1) * (nelx + 1) * 2, (nely + 1) * (nelx + 1) * 2)), K_sp)\n", 398 | " K_dense = (K_sp + tf.transpose(K_sp)) / 2\n", 399 | " #####################\n", 400 | "\n", 401 | " K_temp = tf.gather(K_dense, freedofs.astype(np.int32))\n", 402 | " K_free = tf.transpose(tf.gather(tf.transpose(K_temp), freedofs.astype(np.int32)))\n", 403 | " \n", 404 | " F_RHS=tf.cast(tf.gather(tf.reshape(F[:,i:i+1], [(nelx + 1) * (nely + 1) * 2, 1]), freedofs.astype(np.int64)),\n", 405 | " tf.float32)\n", 406 | " chol = tf.cholesky(K_free+np.diag((np.ones([1,(nelx+1)*(nely+1)*2-len(fixeddofs[0])])*1e-8).tolist()[0]))\n", 407 | " U_pre = tf.cholesky_solve(chol,F_RHS)\n", 408 | " \n", 409 | "# U_pre = tf.matmul(tf.matrix_inverse(tf.cast(K_free, tf.float32)),\n", 410 | "# tf.cast(tf.gather(tf.reshape(F[:,i:i+1], [(nelx + 1) * (nely + 1) * 2, 1]), freedofs.astype(np.int64)),\n", 411 | "# tf.float32))\n", 412 | "\n", 413 | " U = tf.sparse_add(tf.zeros(((nelx + 1) * (nely + 1) * 2)),\n", 414 | " tf.SparseTensor(freedofs.reshape((nelx + 1) * (nely + 1) * 2 - (nely + 1) * 2, 1),\n", 415 | " tf.reshape(tf.cast(U_pre, tf.float32), [-1]), [(nelx + 1) * (nely + 1) * 2]))\n", 416 | "\n", 417 | " 'Objective Function and Sensitivity Analysis'\n", 418 | " ce = tf.reduce_sum(tf.multiply(tf.matmul(tf.reshape(tf.gather(U, edofMat.astype(np.int32)), edofMat.shape),\n", 419 | " KE.astype(np.float32)), tf.gather(U, edofMat.astype(np.int32))), axis=1)\n", 420 | " ce = tf.reshape(ce, [nn, 1])\n", 421 | " c.append(tf.reduce_sum(tf.multiply(tf.cast(tf.multiply(rho[i] ** gamma, (E0 - Emin)), tf.float32), ce)))\n", 422 | " rho_bar = tf.divide(tf.matmul(tf.cast(bigN, tf.float32), rho[i]), N_count.reshape(nn, 1))\n", 423 | " g.append((tf.reduce_sum(rho_bar ** p) / nely / nelx) ** (1.0 / p) / alpha - 1.0)\n", 424 | " global_density.append(tf.matmul(tf.transpose(rho[i]), tf.ones([nn, 1])) / nn - alpha2)\n", 425 | " ###################################################################\n", 426 | "\n", 427 | " # if ((max(abs(dphi)))2) or (loo2>100):\n", 428 | "\n", 429 | "\n", 430 | " dc_drho = -gamma * rho[i] ** (gamma - 1) * (E0 - Emin) * ce\n", 431 | " drho_dphi = beta[i][0] * (1 - tf.tanh(beta[i][0] * (phi[:,i:i+1] - 0.5)) ** 2) / 2.0 / tf.tanh(beta[i][0] / 2.)\n", 432 | " dc_dphi = tf.reduce_sum(bigM * (dphi_idphi * (dc_drho * drho_dphi)), axis=0)\n", 433 | " dg_drhobar = 1.0 / alpha / nn * (1.0 / nn * tf.reduce_sum(rho_bar ** p)) ** (1.0 / p - 1) * rho_bar ** (p - 1)\n", 434 | " dg_dphi = tf.reduce_sum(bigM * (dphi_idphi * (tf.matmul(tf.cast(bigN, tf.float32),\n", 435 | " (dg_drhobar / N_count.reshape(nn, 1))) * drho_dphi)), axis=0)\n", 436 | "\n", 437 | " dphi = dc_dphi + tf.cast(lamda_lag[i][0] * dg_dphi * tf.reduce_sum(tf.cast(g[i] > 0, tf.float32)), tf.float32) + \\\n", 438 | " tf.cast(2.0 / r_lag[i][0] * g[i] * dg_dphi * tf.reduce_sum(tf.cast(g[i] > 0, tf.float32)), tf.float32) + \\\n", 439 | " lamda_lag2[i][0] * tf.ones(nn, 1) / nn * (tf.reduce_sum(tf.cast(global_density[i] > 0, tf.float32))) + \\\n", 440 | " tf.reshape(2.0 / r_lag2[i][0] * global_density[i] / nn / nn * tf.ones([nn, 1]) * (\n", 441 | " tf.reduce_sum(tf.cast(global_density[i] > 0, tf.float32))), [-1])\n", 442 | " \n", 443 | " dphi_store.append(dphi)\n", 444 | " \n", 445 | "\n", 446 | " \n", 447 | "############################################################################################################\n", 448 | "\n", 449 | " 'get initial g and c'\n", 450 | " phi_til_fake = tf.matmul(tf.cast(H, tf.float32), phi_fake[:,i:i+1]) / Hs.reshape(nn, 1)\n", 451 | " rho_fake.append((tf.tanh(beta[i][0] / 2.0) + tf.tanh(beta[i][0] * (phi_til_fake - 0.5))) / (2 * tf.tanh(beta[i][0] / 2.0)))\n", 452 | "\n", 453 | " sK_temp_fake = tf.transpose((KE.reshape(KE.shape[0] * KE.shape[1], 1) * \\\n", 454 | " tf.reshape(Emin + tf.reshape(rho_fake[i], [-1]) ** (gamma) * (E0 - Emin), [1, nelx * nely])))\n", 455 | " sK_fake = tf.reshape(sK_temp_fake, [8 * 8 * nelx * nely, 1])\n", 456 | "\n", 457 | " ###################\n", 458 | " indices_m = np.stack((iK.reshape(-1), jK.reshape(-1)), axis=1)\n", 459 | " values_m_fake = tf.reshape(sK_fake, [-1])\n", 460 | "\n", 461 | " linearized_m = tf.matmul(indices_m, [[10000], [1]])\n", 462 | " y_m, idx_m = tf.unique(tf.squeeze(linearized_m))\n", 463 | "\n", 464 | " idx_m_sort, ind_m_sort = tf.nn.top_k(idx_m, k=nelx * nely * 64)\n", 465 | " idx_m_sort = tf.reverse(idx_m_sort, [0])\n", 466 | " ind_m_sort = tf.reverse(ind_m_sort, [0])\n", 467 | "\n", 468 | " values_m_fake = tf.gather(values_m_fake, ind_m_sort)\n", 469 | " values_m_fake = tf.segment_sum(values_m_fake, idx_m_sort)\n", 470 | "\n", 471 | " y_m = tf.expand_dims(y_m, 1)\n", 472 | " indices_m = tf.concat([y_m // 10000, y_m % 10000], axis=1)\n", 473 | " #####################\n", 474 | "\n", 475 | " #####################\n", 476 | " K_sp_fake = tf.SparseTensor(tf.cast(indices_m, tf.int64),\n", 477 | " tf.reshape(tf.cast(values_m_fake, tf.float32), [-1]),\n", 478 | " [(nely + 1) * (nelx + 1) * 2, (nely + 1) * (nelx + 1) * 2])\n", 479 | " K_sp_fake = tf.sparse_add(tf.zeros(((nely + 1) * (nelx + 1) * 2, (nely + 1) * (nelx + 1) * 2)), K_sp_fake)\n", 480 | " K_dense_fake = (K_sp_fake + tf.transpose(K_sp_fake)) / 2.0\n", 481 | " #####################\n", 482 | "\n", 483 | " K_temp_fake = tf.gather(K_dense_fake, freedofs.astype(np.int32))\n", 484 | " K_free_fake = tf.transpose(tf.gather(tf.transpose(K_temp_fake), freedofs.astype(np.int32)))\n", 485 | "\n", 486 | " F_RHS_fake=tf.cast(tf.gather(tf.reshape(F[:,i:i+1], [(nelx + 1) * (nely + 1) * 2, 1]), freedofs.astype(np.int64)),\n", 487 | " tf.float32)\n", 488 | " chol_fake = tf.cholesky(K_free_fake+np.diag((np.ones([1,(nelx+1)*(nely+1)*2-len(fixeddofs[0])])*1e-8).tolist()[0]))\n", 489 | " U_pre_fake = tf.cholesky_solve(chol_fake,F_RHS_fake)\n", 490 | " \n", 491 | "# U_pre_fake = tf.matmul(tf.matrix_inverse(tf.cast(K_free_fake, tf.float32)),\n", 492 | "# tf.cast(tf.gather(tf.reshape(F[:,i:i+1], [(nelx + 1) * (nely + 1) * 2, 1]), freedofs.astype(np.int64)),\n", 493 | "# tf.float32))\n", 494 | "\n", 495 | " U_fake = tf.sparse_add(tf.zeros(((nelx + 1) * (nely + 1) * 2)),\n", 496 | " tf.SparseTensor(freedofs.reshape((nelx + 1) * (nely + 1) * 2 - (nely + 1) * 2, 1),\n", 497 | " tf.reshape(tf.cast(U_pre_fake, tf.float32), [-1]),\n", 498 | " [(nelx + 1) * (nely + 1) * 2]))\n", 499 | "\n", 500 | " 'Objective Function and Sensitivity Analysis'\n", 501 | " ce_fake = tf.reduce_sum(tf.multiply(tf.matmul(tf.reshape(tf.gather(U_fake, edofMat.astype(np.int32)), edofMat.shape),\n", 502 | " KE.astype(np.float32)), tf.gather(U_fake, edofMat.astype(np.int32))),\n", 503 | " axis=1)\n", 504 | " ce_fake = tf.reshape(ce_fake, [nn, 1])\n", 505 | " c_fake.append(tf.reduce_sum(tf.multiply(tf.cast(tf.multiply(rho_fake[i] ** gamma, (E0 - Emin)), tf.float32), ce_fake)))\n", 506 | " rho_bar_fake=tf.divide(tf.matmul(tf.cast(bigN, tf.float32), rho_fake[i]), N_count.reshape(nn, 1))\n", 507 | " g_fake.append((tf.reduce_sum(rho_bar_fake ** p) / nely / nelx) ** (1. / p) / alpha - 1.0)\n", 508 | " global_density_fake.append(tf.matmul(tf.transpose(rho_fake[i]), tf.ones([nn, 1])) / nn - alpha2)\n", 509 | " ###################################################################\n", 510 | "\n", 511 | " # if ((max(abs(dphi)))2) or (loo2>100):\n", 512 | "\n", 513 | "\n", 514 | " dc_drho_fake = -gamma * rho_fake[i] ** (gamma - 1) * (E0 - Emin) * ce_fake\n", 515 | " drho_dphi_fake = beta[i][0] * (1 - tf.tanh(beta[i][0] * (phi_fake[:,i:i+1] - 0.5)) ** 2) / 2.0 / tf.tanh(beta[i][0] / 2.)\n", 516 | " dc_dphi_fake = tf.reduce_sum(bigM * (dphi_idphi * (dc_drho_fake * drho_dphi_fake)), axis=0)\n", 517 | " dg_drhobar_fake = 1.0 / alpha / nn * (1.0 / nn * tf.reduce_sum(rho_bar_fake ** p)) ** (1.0 / p - 1) * rho_bar_fake ** (\n", 518 | " p - 1)\n", 519 | " dg_dphi_fake = tf.reduce_sum(bigM * (dphi_idphi * (tf.matmul(tf.cast(bigN, tf.float32),\n", 520 | " (dg_drhobar_fake / N_count.reshape(nn,\n", 521 | " 1))) * drho_dphi_fake)),\n", 522 | " axis=0)\n", 523 | "\n", 524 | " A = dc_dphi_fake + tf.cast(lamda_lag[i][0] * dg_dphi_fake * tf.reduce_sum(tf.cast(g_fake[i] > 0, tf.float32)), tf.float32) + \\\n", 525 | " tf.cast(2.0 / r_lag[i][0] * g_fake[i] * dg_dphi_fake * tf.reduce_sum(tf.cast(g_fake[i] > 0, tf.float32)), tf.float32)\n", 526 | "\n", 527 | " B = lamda_lag2[i][0] * tf.ones(nn, 1) / nn * (tf.reduce_sum(tf.cast(global_density_fake[i] > 0, tf.float32))) + \\\n", 528 | " 2.0 / r_lag2[i][0] * global_density_fake[i] / nn / nn * tf.ones([nn]) * (tf.reduce_sum(tf.cast(global_density_fake[i] > 0, tf.float32)))\n", 529 | "\n", 530 | " dphi_fake.append(A + B)\n", 531 | " \n", 532 | " \n", 533 | " error_sep = tf.reduce_sum(((tf.reshape(dphi_fake[i], [nn, 1]) * phi[:,i:i+1])))\n", 534 | " error_store.append(error_sep)\n", 535 | " \n", 536 | " sep_grad=tf.reduce_sum(tf.abs(tf.gradients((tf.reshape(dphi_fake[i], [nn, 1]) * phi[:,i:i+1]),W1)))\n", 537 | " sep_grad_store.append(sep_grad)\n", 538 | " \n", 539 | "############################################################################################\n", 540 | "# g_old = tf.Variable(0, dtype='float32',trainable=False)\n", 541 | "# global_density_old = tf.Variable([[0]], dtype='float32',trainable=False)\n", 542 | "# c_old = tf.Variable(0, dtype='float32',trainable=False)\n", 543 | "\n", 544 | " g_old[i] = g_old[i].assign(g[i])\n", 545 | " global_density_old[i] = global_density_old[i].assign(global_density[i])\n", 546 | " c_old[i] = c_old[i].assign(c[i])\n", 547 | "\n", 548 | "# assign_g=tf.assign(g_old[i],g[i])\n", 549 | "# assign_gd=tf.assign(global_density_old[i],global_density[i])\n", 550 | "# assign_c=tf.assign(c_old[i],c[i])\n", 551 | "\n", 552 | " 'learning rate adjusting'\n", 553 | " delta = -dphi_fake[i] * learning_rate_fake[i][0]\n", 554 | " phi_temp = phi_fake[:,i:i+1] + tf.reshape(delta, [nn, 1])\n", 555 | "\n", 556 | " # assign_phi = tf.assign(phi,phi_temp)\n", 557 | "\n", 558 | " # phi_temp=tf.Variable(np.ones([nn,1]), dtype='float32')\n", 559 | " # phi_temp=phi_temp.assign(phi)\n", 560 | "\n", 561 | " phi_til_temp = tf.matmul(tf.cast(H, tf.float32), phi_temp) / tf.reshape(tf.cast(Hs, tf.float32), [nn, 1])\n", 562 | " rho_temp = (tf.tanh(beta[i][0] / 2.0) + tf.tanh(beta[i][0] * (phi_til_temp - 0.5))) / (2 * tf.tanh(beta[i][0] / 2.0))\n", 563 | " rho_bar_temp = (tf.matmul(tf.cast(bigN, tf.float32), rho_temp) / tf.reshape(tf.cast(N_count, tf.float32), [nn, 1]))\n", 564 | " g_temp = (tf.reduce_sum(rho_bar_temp ** p) / nn) ** (1.0 / p) / alpha - 1.0\n", 565 | " global_density_temp = tf.matmul(tf.transpose(rho_temp), tf.ones([nn, 1])) / nn - alpha2\n", 566 | "\n", 567 | " sK_temp_fake2 = tf.transpose((KE.reshape(KE.shape[0] * KE.shape[1], 1) * \\\n", 568 | " tf.reshape(Emin + tf.reshape(rho_temp, [-1]) ** (gamma) * (E0 - Emin), [1, nelx * nely])))\n", 569 | " sK_fake2 = tf.reshape(sK_temp_fake2, [8 * 8 * nelx * nely, 1])\n", 570 | "\n", 571 | " ###################\n", 572 | " values_m_fake2 = tf.reshape(sK_fake2, [-1])\n", 573 | " values_m_fake2 = tf.gather(values_m_fake2, ind_m_sort)\n", 574 | " values_m_fake2 = tf.segment_sum(values_m_fake2, idx_m_sort)\n", 575 | " ###################\n", 576 | "\n", 577 | " ###################\n", 578 | " K_sp_fake2 = tf.SparseTensor(tf.cast(indices_m, tf.int64),\n", 579 | " tf.reshape(tf.cast(values_m_fake2, tf.float32), [-1]),\n", 580 | " [(nely + 1) * (nelx + 1) * 2, (nely + 1) * (nelx + 1) * 2])\n", 581 | " K_sp_fake2 = tf.sparse_add(tf.zeros(((nely + 1) * (nelx + 1) * 2, (nely + 1) * (nelx + 1) * 2)), K_sp_fake2)\n", 582 | " K_dense_fake2 = (K_sp_fake2 + tf.transpose(K_sp_fake2)) / 2.0\n", 583 | " ###################\n", 584 | "\n", 585 | " K_temp_fake2 = tf.gather(K_dense_fake2, freedofs.astype(np.int32))\n", 586 | " K_free_fake2 = tf.transpose(tf.gather(tf.transpose(K_temp_fake2), freedofs.astype(np.int32)))\n", 587 | " \n", 588 | " F_RHS_fake2=tf.cast(tf.gather(tf.reshape(F[:,i:i+1], [(nelx + 1) * (nely + 1) * 2, 1]), freedofs.astype(np.int64)),\n", 589 | " tf.float32)\n", 590 | " chol_fake2 = tf.cholesky(K_free_fake2+np.diag((np.ones([1,(nelx+1)*(nely+1)*2-len(fixeddofs[0])])*1e-8).tolist()[0]))\n", 591 | " U_pre_fake2 = tf.cholesky_solve(chol_fake2,F_RHS_fake2)\n", 592 | " \n", 593 | "# U_pre_fake2 = tf.matmul(tf.matrix_inverse(tf.cast(K_free_fake2, tf.float32)+np.diag((np.ones([1,(nelx+1)*(nely+1)*2-len(fixeddofs[0])])*1e-15).tolist()[0])),\n", 594 | "# tf.cast(tf.gather(tf.reshape(F[:,i:i+1], [(nelx + 1) * (nely + 1) * 2, 1]), freedofs.astype(np.int64)),tf.float32))\n", 595 | "\n", 596 | " U_fake2 = tf.sparse_add(tf.zeros(((nelx + 1) * (nely + 1) * 2)),\n", 597 | " tf.SparseTensor(freedofs.reshape((nelx + 1) * (nely + 1) * 2 - (nely + 1) * 2, 1),\n", 598 | " tf.reshape(tf.cast(U_pre_fake2, tf.float32), [-1]),\n", 599 | " [(nelx + 1) * (nely + 1) * 2]))\n", 600 | "\n", 601 | " ce_temp = tf.reduce_sum(tf.multiply(tf.matmul(tf.reshape(tf.gather(U_fake2, edofMat.astype(np.int32)), edofMat.shape),\n", 602 | " KE.astype(np.float32)), tf.gather(U_fake2, edofMat.astype(np.int32))),axis=1)\n", 603 | " \n", 604 | " ce_temp = tf.reshape(ce_temp, [nn, 1])\n", 605 | " c_temp = tf.reduce_sum(tf.multiply(tf.cast(tf.multiply(rho_temp ** gamma, (E0 - Emin)), tf.float32), ce_temp))\n", 606 | "\n", 607 | " A2 = (c_temp + lamda_lag[i][0] * g_temp * (tf.reduce_sum(tf.cast(g_temp > 0, tf.float32))) + 1.0 / r_lag[i][0] * g_temp ** 2 * (\n", 608 | " tf.reduce_sum(tf.cast(g_temp > 0, tf.float32))) + \\\n", 609 | " 1.0 / r_lag2[i][0] * global_density_temp ** 2 * (tf.reduce_sum(tf.cast(global_density_temp > 0, tf.float32))))\n", 610 | "\n", 611 | " B2 = (c_old[i] + lamda_lag[i][0] * g_old[i] * (tf.reduce_sum(tf.cast(g_old[i] > 0, tf.float32))) + 1.0 / r_lag[i][0] * g_old[i] ** 2 * (\n", 612 | " tf.reduce_sum(tf.cast(g_old[i] > 0, tf.float32))) + \\\n", 613 | " 1.0 / r_lag2[i][0] * global_density_old[i] ** 2 * (tf.reduce_sum(tf.cast(global_density_old[i] > 0, tf.float32))))\n", 614 | " dobj = A2 - B2\n", 615 | " dobj_store.append(dobj)\n", 616 | " \n", 617 | "toc=time.clock()\n", 618 | "print(toc-tic)" 619 | ] 620 | }, 621 | { 622 | "cell_type": "code", 623 | "execution_count": null, 624 | "metadata": { 625 | "collapsed": true 626 | }, 627 | "outputs": [], 628 | "source": [ 629 | "global_step = tf.Variable(0, trainable=False)\n", 630 | "starter_learning_rate = 0.001\n", 631 | "learning_rate = tf.train.exponential_decay(starter_learning_rate, global_step,\n", 632 | " 1000, 1.0, staircase=True)\n", 633 | "\n", 634 | "solver0 = tf.train.AdamOptimizer(learning_rate).minimize(error_store[0], global_step=global_step)\n", 635 | "solver1 = tf.train.AdamOptimizer(learning_rate).minimize(error_store[1], global_step=global_step)\n", 636 | "solver2 = tf.train.AdamOptimizer(learning_rate).minimize(error_store[2], global_step=global_step)\n", 637 | "\n", 638 | "sess = tf.Session()\n", 639 | "sess.run(tf.global_variables_initializer())" 640 | ] 641 | }, 642 | { 643 | "cell_type": "code", 644 | "execution_count": null, 645 | "metadata": { 646 | "collapsed": true 647 | }, 648 | "outputs": [], 649 | "source": [ 650 | "force=-1\n", 651 | "F_batch=np.zeros([batch_size,z_dim])\n", 652 | "\n", 653 | "# alpha=1.5\n", 654 | "theta = np.linspace(np.pi*0.,2.0*np.pi/5.,batch_size)\n", 655 | "\n", 656 | "count=0\n", 657 | "for i in range(batch_size-1,-1,-1):\n", 658 | "# theta = 2*(i+1)*np.pi/10.#+i*np.pi/9*alpha\n", 659 | " print theta[i]\n", 660 | "# theta = (i+1)*np.pi/10\n", 661 | " Fx = force*np.sin(theta[i])\n", 662 | " Fy = force*np.cos(theta[i])\n", 663 | " \n", 664 | " # up-right corner\n", 665 | " F_batch[count,0]=Fx\n", 666 | " F_batch[count,1]=Fy\n", 667 | " count=count+1 \n", 668 | "\n", 669 | "count=0\n", 670 | "F_sp=np.zeros([2*(nely+1)*(nelx+1),batch_size])\n", 671 | "for i in range(batch_size-1,-1,-1):\n", 672 | "# theta = 2*(i+1)*np.pi/10.#+i*np.pi/9*alpha\n", 673 | "# theta = (i+1)*np.pi/5\n", 674 | " Fx = force*np.sin(theta[i])\n", 675 | " Fy = force*np.cos(theta[i]) \n", 676 | " F_sp[(nely+1)*2*nelx+nely, count] = Fx\n", 677 | " F_sp[(nely+1)*2*nelx+nely+1, count] = Fy\n", 678 | " count=count+1\n", 679 | "\n", 680 | "print F_batch" 681 | ] 682 | }, 683 | { 684 | "cell_type": "code", 685 | "execution_count": null, 686 | "metadata": { 687 | "collapsed": true 688 | }, 689 | "outputs": [], 690 | "source": [ 691 | "lamda_value = np.zeros([batch_size, 1])\n", 692 | "lamda_value2 = np.zeros([batch_size, 1])\n", 693 | "r_value = np.ones([batch_size, 1]) * 1\n", 694 | "r_value2 = np.ones([batch_size, 1]) * 0.001\n", 695 | "eta = np.ones([batch_size, 1]) * 0.1\n", 696 | "eta2 = np.ones([batch_size, 1]) * 0.1\n", 697 | "j, j2 = 0, 0\n", 698 | "\n", 699 | "k_j = np.ones([batch_size, 1])\n", 700 | "thre_range = 0.02\n", 701 | "agg = 0\n", 702 | "total_E_pre = 1e20\n", 703 | "count_k = 0\n", 704 | "count = 0\n", 705 | "drho=1e6\n", 706 | "it=0\n", 707 | "beta_value=np.ones([batch_size,1])*10\n", 708 | "learning_rate_fake_value=np.ones([batch_size,1])*0.001" 709 | ] 710 | }, 711 | { 712 | "cell_type": "code", 713 | "execution_count": null, 714 | "metadata": { 715 | "collapsed": true 716 | }, 717 | "outputs": [], 718 | "source": [ 719 | "import os\n", 720 | "import time\n", 721 | "timestr = time.strftime(\"%Y%m%d-%H%M%S_bn\")\n", 722 | "if not os.path.exists(timestr):\n", 723 | " os.makedirs(timestr)" 724 | ] 725 | }, 726 | { 727 | "cell_type": "code", 728 | "execution_count": null, 729 | "metadata": { 730 | "collapsed": true 731 | }, 732 | "outputs": [], 733 | "source": [ 734 | "####################\n", 735 | "# logdir,modeldir=creat_dir('infill_var')\n", 736 | "# summary_writer = tf.summary.FileWriter(logdir)\n", 737 | "# summary_op_train = tf.summary.merge([tf.summary.scalar(\"train/error\",error_total)])\n", 738 | "####################\n", 739 | "\n", 740 | "# for it in range(100000):\n", 741 | "it=0\n", 742 | "drho_total_store=[]\n", 743 | "\n", 744 | "while min(beta_value)<11:\n", 745 | " it=it+1\n", 746 | " # sess.run([assign_phi_fake,assign_c,assign_g,assign_gd], feed_dict={learning_rate_fake: starter_learning_rate, lamda_lag: lamda_value,\n", 747 | " # lamda_lag2: lamda_value2,\n", 748 | " # r_lag: r_value,\n", 749 | " # r_lag2: r_value2})\n", 750 | " \n", 751 | "# total_E, g_value, gd, dphi_fake_value, dobj_value, lr, phi_fake_value,rho_value = sess.run([error_store, g,\n", 752 | "# global_density, dphi_fake, dobj_store,\n", 753 | "# learning_rate,phi_fake,rho],\n", 754 | "# feed_dict={learning_rate_fake: learning_rate_fake_value,\n", 755 | "# lamda_lag:lamda_value,\n", 756 | "# lamda_lag2:lamda_value2,\n", 757 | "# r_lag:r_value,\n", 758 | "# r_lag2:r_value2,\n", 759 | "# F_input:F_batch,\n", 760 | "# F:F_sp, \n", 761 | "# learning_rate:starter_learning_rate,beta:beta_value})\n", 762 | "\n", 763 | " \n", 764 | " \n", 765 | " loop2=0\n", 766 | " \n", 767 | " while 1:\n", 768 | "# try:\n", 769 | " g_value_temp,dphi_fake_value,rho_pre = sess.run([g,dphi_fake,rho], \n", 770 | " feed_dict={learning_rate_fake: learning_rate_fake_value,\n", 771 | " lamda_lag:lamda_value,lamda_lag2:lamda_value2,\n", 772 | " r_lag:r_value,r_lag2:r_value2,F_input: F_batch,\n", 773 | " F:F_sp,learning_rate:starter_learning_rate,\n", 774 | " beta:beta_value})\n", 775 | "# except:\n", 776 | "# stop=1\n", 777 | "\n", 778 | " \n", 779 | " dphi_fake_value_max=max(max(abs(np.array(dphi_fake_value[0])).reshape(-1)),\n", 780 | " max(abs(np.array(dphi_fake_value[1])).reshape(-1)),\n", 781 | " max(abs(np.array(dphi_fake_value[2])).reshape(-1)))\n", 782 | " \n", 783 | " \n", 784 | " if (dphi_fake_value_max < 1*batch_size and max(g_value_temp) < 0.01 and loop2 > 0) or (loop2 > 100):\n", 785 | "\n", 786 | "# if (drho < 0.05 and max(g_value_temp) < 0.005 and loop2 > 0) or (loop2 > 100):\n", 787 | " # print('wrong')\n", 788 | " lamda_value = np.zeros([batch_size, 1])\n", 789 | " lamda_value2 = np.zeros([batch_size, 1])\n", 790 | " r_value = np.ones([batch_size, 1]) * 1\n", 791 | " r_value2 = np.ones([batch_size, 1]) * 0.001\n", 792 | " eta = np.ones([batch_size, 1]) * 0.1\n", 793 | " eta2 = np.ones([batch_size, 1]) * 0.1\n", 794 | " dphi_fake_value=np.array([1e6]*batch_size)\n", 795 | " drho=np.array([1e6]*batch_size)\n", 796 | " break\n", 797 | "\n", 798 | " loop2 = loop2 + 1\n", 799 | " j, j2 = 0, 0\n", 800 | " loop3 = np.array([0]*batch_size)\n", 801 | " dphi_fake_value = np.array([1e6]*batch_size)\n", 802 | " drho = np.array([1e6]*batch_size)\n", 803 | " \n", 804 | "\n", 805 | "\n", 806 | " while (max(max(abs(np.array(dphi_fake_value[0])).reshape(-1)),\n", 807 | " max(abs(np.array(dphi_fake_value[1])).reshape(-1)),\n", 808 | " max(abs(np.array(dphi_fake_value[2])).reshape(-1)))) > epsilon and min(loop3) < 1000:\n", 809 | " \n", 810 | "# rho_value_pre = sess.run(rho, feed_dict={learning_rate_fake: learning_rate_fake_value,lamda_lag:lamda_value,lamda_lag2:lamda_value2,r_lag:r_value,r_lag2:r_value2,\n", 811 | "# F_input: F_batch,F:F_sp,learning_rate:starter_learning_rate,beta:beta_value})\n", 812 | "\n", 813 | " \n", 814 | " for i in range(batch_size):\n", 815 | " if count>=4000:\n", 816 | " break\n", 817 | " if loop3[i]>1000:\n", 818 | " continue\n", 819 | "# dphi_fake_value[i] = np.array([1e6])\n", 820 | "# g_value = g_value_temp[i]\n", 821 | "\n", 822 | " starter_learning_rate = 0.001\n", 823 | " learning_rate_fake_value[i]=0.001\n", 824 | " loop3[i] = loop3[i] + 1\n", 825 | " loop4 = np.asarray([0]*batch_size)\n", 826 | "\n", 827 | " tic=time.clock()\n", 828 | " while loop4[i] < 10:\n", 829 | " try:\n", 830 | " dphi_fake_value, dobj_value,rho_value = sess.run([dphi_fake, dobj_store,rho],\n", 831 | " feed_dict={learning_rate_fake: learning_rate_fake_value,lamda_lag:lamda_value,\n", 832 | " lamda_lag2:lamda_value2, r_lag:r_value,\n", 833 | " r_lag2:r_value2,F_input:F_batch,\n", 834 | " F:F_sp,learning_rate:learning_rate_fake_value[i][0],\n", 835 | " beta:beta_value})\n", 836 | " except:\n", 837 | " starter_learning_rate = starter_learning_rate*0.5\n", 838 | " learning_rate_fake_value[i] = learning_rate_fake_value[i]*0.5\n", 839 | " \n", 840 | "\n", 841 | "\n", 842 | " if dobj_value[i] > 0:\n", 843 | " starter_learning_rate = starter_learning_rate * 0.5\n", 844 | " learning_rate_fake_value[i] = learning_rate_fake_value[i]*0.5\n", 845 | " loop4[i] = loop4[i] + 1\n", 846 | " if loop4[i] == 10:\n", 847 | " loop3[i] = 10000\n", 848 | " dphi_fake_value[i] = np.array([0])\n", 849 | " drho[i] = np.array([0])\n", 850 | " # break\n", 851 | " else:\n", 852 | " if i == 0:\n", 853 | " try:\n", 854 | " sess.run([solver0],feed_dict={learning_rate_fake: learning_rate_fake_value,lamda_lag:lamda_value,\n", 855 | " lamda_lag2:lamda_value2,r_lag:r_value,r_lag2:r_value2,\n", 856 | " F_input: F_batch,F:F_sp,learning_rate:learning_rate_fake_value[i][0],beta:beta_value})\n", 857 | "\n", 858 | " except:\n", 859 | " print('jump0')\n", 860 | " \n", 861 | " if i == 1:\n", 862 | " try:\n", 863 | " sess.run([solver1],feed_dict={learning_rate_fake: learning_rate_fake_value,lamda_lag:lamda_value,\n", 864 | " lamda_lag2:lamda_value2,r_lag:r_value,r_lag2:r_value2,\n", 865 | " F_input: F_batch,F:F_sp,learning_rate:learning_rate_fake_value[i][0],beta:beta_value})\n", 866 | "\n", 867 | " except:\n", 868 | " print('jump1')\n", 869 | " \n", 870 | " if i == 2:\n", 871 | " try:\n", 872 | " sess.run([solver2],feed_dict={learning_rate_fake: learning_rate_fake_value,lamda_lag:lamda_value,\n", 873 | " lamda_lag2:lamda_value2,r_lag:r_value,r_lag2:r_value2,\n", 874 | " F_input: F_batch,F:F_sp,learning_rate:learning_rate_fake_value[i][0],beta:beta_value})\n", 875 | " except:\n", 876 | " print('jump2')\n", 877 | " \n", 878 | " break\n", 879 | "\n", 880 | " toc=time.clock()\n", 881 | " count = count + 1\n", 882 | "# try:\n", 883 | " g_value,c_value,sep_grad_value,error_total_value,phi_value,rho_curr=sess.run([g,c,sep_grad_store,error_store,phi,rho], \n", 884 | " feed_dict={learning_rate_fake: learning_rate_fake_value, lamda_lag: lamda_value,\n", 885 | " lamda_lag2: lamda_value2,r_lag: r_value,\n", 886 | " r_lag2: r_value2, F_input: F_batch, F: F_sp, learning_rate: learning_rate_fake_value[i][0],\n", 887 | " beta: beta_value})\n", 888 | "# except:\n", 889 | "# print('jump3')\n", 890 | "\n", 891 | " drho[i]=sum(abs(rho_curr[i]-rho_pre[i]).reshape(-1))\n", 892 | " drho_total=sum(abs(np.array(rho_curr)-np.array(rho_pre)).reshape(-1))\n", 893 | " drho_total_store.append(drho_total)\n", 894 | " print('iteration:{}'.format(it))\n", 895 | " print('updating_case:{}'.format(i))\n", 896 | " print('num_update:{}'.format(count))\n", 897 | " print('total_error:{}'.format(np.sum(np.array(error_total_value))))\n", 898 | " print('g_value:{}'.format(g_value))\n", 899 | " print('c_value:{}'.format(c_value))\n", 900 | " print('log_r:{}'.format(np.log(r_value)))\n", 901 | "# print('max_abs_dphi:{}'.format(max(abs(dphi_fake_value.reshape(-1)))))\n", 902 | " print('gradient_W1:{}'.format(sep_grad_value))\n", 903 | " print('dobj_value:{}'.format(dobj_value))\n", 904 | " # r_lag2:r_value2,F_input: F_batch,F:F_sp,learning_rate:starter_learning_rate,beta:beta_value})))\n", 905 | " print('dphi_fake_value_max:{}'.format((max(abs(dphi_fake_value[i].reshape(-1))))))\n", 906 | "# print('drho_fake_value_max:{}'.format(max(abs(rho_value[i].reshape(-1)-rho_value_pre[i].reshape(-1)))))\n", 907 | " print('drho:{}'.format(drho))\n", 908 | " print('loop3:{}'.format(loop3))\n", 909 | " print\n", 910 | " print('running time:{}'.format(toc-tic))\n", 911 | " print()\n", 912 | " if count%500 == 0:\n", 913 | " sio.savemat('{}/c_value.mat'.format(timestr), mdict={'c': np.array(c_value)})\n", 914 | " sio.savemat('{}/rho.mat'.format(timestr), mdict={'rho': np.array(rho_curr)})\n", 915 | " sio.savemat('{}/drho.mat'.format(timestr), mdict={'drho': np.array(drho_total_store)})\n", 916 | " fig, axs = plt.subplots(2, 5, figsize=(15, 4), facecolor='w', edgecolor='k')\n", 917 | " fig.subplots_adjust(hspace=.1, wspace=.001)\n", 918 | "\n", 919 | " axs = axs.ravel()\n", 920 | "\n", 921 | " for i in range(batch_size):\n", 922 | " axs[i].imshow(1 - rho_curr[i].reshape([nelx, nely]).T, 'gray')\n", 923 | " axs[i].set_title('c={}'.format(c_value[i]))\n", 924 | " plt.savefig('{}/opt_{}.png'.format(timestr, str(count)))\n", 925 | " plt.close()\n", 926 | " if count >= 4000:\n", 927 | " break\n", 928 | "# drho1=max(rho_value_cur[0].reshape(-1)-rho_value_pre[0].reshape(-1))\n", 929 | "# drho2=max(rho_value_cur[1].reshape(-1)-rho_value_pre[1].reshape(-1))\n", 930 | "# drho3=max(rho_value_cur[2].reshape(-1)-rho_value_pre[2].reshape(-1))\n", 931 | "# drho=max(drho1,drho2,drho3)\n", 932 | " \n", 933 | " \n", 934 | "# g_value, gd, rho_value_cur = sess.run([g, global_density,rho], \n", 935 | "# feed_dict={learning_rate_fake: learning_rate_fake_value,lamda_lag:lamda_value,\n", 936 | "# lamda_lag2:lamda_value2,r_lag:r_value,\n", 937 | "# r_lag2:r_value2,F_input: F_batch,F:F_sp,\n", 938 | "# learning_rate:starter_learning_rate,beta:beta_value})\n", 939 | " for i in range(batch_size): \n", 940 | " g_value, gd= sess.run([g, global_density], \n", 941 | " feed_dict={learning_rate_fake: learning_rate_fake_value,lamda_lag:lamda_value,\n", 942 | " lamda_lag2:lamda_value2,r_lag:r_value,\n", 943 | " r_lag2:r_value2,F_input: F_batch,F:F_sp,\n", 944 | " learning_rate:learning_rate_fake_value[i][0],beta:beta_value}) \n", 945 | " if g_value[i] < eta[i]:\n", 946 | " lamda_value[i] = lamda_value[i] + 2 * g_value[i] / r_value[i]\n", 947 | " j = j + 1\n", 948 | " eta[i] = eta[i] * 0.5\n", 949 | " else:\n", 950 | " r_value[i] = r_value[i] * 0.5\n", 951 | " j = 0\n", 952 | "\n", 953 | " if gd[i] < eta2[i]:\n", 954 | " lamda_value2[i] = lamda_value2[i] + 2 * gd[i][0] / r_value2[i]\n", 955 | " j2 = j2 + 1\n", 956 | " eta2[i] = eta2[i] * 0.5\n", 957 | " else:\n", 958 | " r_value2[i] = r_value2[i] * 0.5\n", 959 | " j2 = 0\n", 960 | " \n", 961 | " for i in range(batch_size):\n", 962 | " beta_value[i] = 1.5 * beta_value[i]\n", 963 | "\n", 964 | "phi_value, rho_value = sess.run([phi, rho],feed_dict={learning_rate_fake: learning_rate_fake_value, lamda_lag: lamda_value,lamda_lag2: lamda_value2,r_lag: r_value,\n", 965 | " r_lag2: r_value2, F_input: F_batch, F: F_sp, learning_rate: starter_learning_rate, beta: beta_value})\n", 966 | "\n", 967 | "print('finished')\n", 968 | "# sio.savemat('result/infill_phi_{}.mat'.format(count), mdict={'phi': phi_value})\n", 969 | "# sio.savemat('result/infill_rho_{}.mat'.format(count), mdict={'rho': rho_value})" 970 | ] 971 | }, 972 | { 973 | "cell_type": "code", 974 | "execution_count": null, 975 | "metadata": { 976 | "collapsed": true 977 | }, 978 | "outputs": [], 979 | "source": [ 980 | "# import os\n", 981 | "# import time\n", 982 | "# timestr = time.strftime(\"%Y%m%d-%H%M%S\")\n", 983 | "# if not os.path.exists(timestr):\n", 984 | "# os.makedirs(timestr)\n", 985 | "\n", 986 | "sio.savemat('{}/c_value.mat'.format(timestr), mdict={'c': np.array(c_value)})\n", 987 | "sio.savemat('{}/rho.mat'.format(timestr), mdict={'rho': np.array(rho_curr)})\n", 988 | "sio.savemat('{}/drho.mat'.format(timestr), mdict={'drho': np.array(drho_total_store)})" 989 | ] 990 | }, 991 | { 992 | "cell_type": "code", 993 | "execution_count": null, 994 | "metadata": { 995 | "collapsed": true 996 | }, 997 | "outputs": [], 998 | "source": [ 999 | "phi_value, rho_value = sess.run([phi, rho],feed_dict={learning_rate_fake: learning_rate_fake_value, lamda_lag: lamda_value,lamda_lag2: lamda_value2,r_lag: r_value,\n", 1000 | " r_lag2: r_value2, F_input: F_batch, F: F_sp, learning_rate: starter_learning_rate, beta: beta_value})\n", 1001 | "\n", 1002 | "sio.savemat('result/infill_phi_{}.mat'.format(count), mdict={'phi': phi_value})\n", 1003 | "sio.savemat('result/infill_rho_{}.mat'.format(count), mdict={'rho': rho_value})" 1004 | ] 1005 | }, 1006 | { 1007 | "cell_type": "code", 1008 | "execution_count": null, 1009 | "metadata": { 1010 | "collapsed": true 1011 | }, 1012 | "outputs": [], 1013 | "source": [ 1014 | "'training result'\n", 1015 | "%matplotlib inline\n", 1016 | "fig, axs = plt.subplots(2,5, figsize=(15, 4), facecolor='w', edgecolor='k')\n", 1017 | "fig.subplots_adjust(hspace = .1, wspace=.001)\n", 1018 | "\n", 1019 | "axs = axs.ravel()\n", 1020 | "\n", 1021 | "for i in range(batch_size):\n", 1022 | " axs[i].imshow(1-rho_value[i].reshape([nelx,nely]).T,'gray')\n", 1023 | "# axs[i].set_title(str(250+i))" 1024 | ] 1025 | }, 1026 | { 1027 | "cell_type": "code", 1028 | "execution_count": null, 1029 | "metadata": { 1030 | "collapsed": true 1031 | }, 1032 | "outputs": [], 1033 | "source": [] 1034 | } 1035 | ], 1036 | "metadata": { 1037 | "kernelspec": { 1038 | "display_name": "Python 2", 1039 | "language": "python", 1040 | "name": "python2" 1041 | }, 1042 | "language_info": { 1043 | "codemirror_mode": { 1044 | "name": "ipython", 1045 | "version": 2 1046 | }, 1047 | "file_extension": ".py", 1048 | "mimetype": "text/x-python", 1049 | "name": "python", 1050 | "nbconvert_exporter": "python", 1051 | "pygments_lexer": "ipython2", 1052 | "version": "2.7.13" 1053 | } 1054 | }, 1055 | "nbformat": 4, 1056 | "nbformat_minor": 2 1057 | } 1058 | -------------------------------------------------------------------------------- /KKT_optimization/.ipynb_checkpoints/infill-dphi-focus-checkpoint.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "code", 5 | "execution_count": 1, 6 | "metadata": { 7 | "collapsed": false 8 | }, 9 | "outputs": [ 10 | { 11 | "name": "stderr", 12 | "output_type": "stream", 13 | "text": [ 14 | "/home/p2admin/anaconda2/lib/python2.7/site-packages/h5py/__init__.py:34: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n", 15 | " from ._conv import register_converters as _register_converters\n" 16 | ] 17 | } 18 | ], 19 | "source": [ 20 | "import numpy as np\n", 21 | "import tensorflow as tf\n", 22 | "import matplotlib.pyplot as plt\n", 23 | "import scipy.io as sio\n", 24 | "from tensorflow.contrib import rnn\n", 25 | "import math\n", 26 | "import time\n", 27 | "import os\n", 28 | "from datetime import datetime\n", 29 | "import dateutil.tz\n", 30 | "# from utils.utils import *\n", 31 | "\n", 32 | "\n", 33 | "def xavier_init(size):\n", 34 | " in_dim = size[0]\n", 35 | " xavier_stddev = 1. / tf.sqrt(in_dim / 2.)\n", 36 | " return tf.random_normal(shape=size, stddev=xavier_stddev)\n", 37 | "\n", 38 | "def creat_dir(network_type):\n", 39 | " \"\"\"code from on InfoGAN\"\"\"\n", 40 | " now = datetime.now(dateutil.tz.tzlocal())\n", 41 | " timestamp = now.strftime('%Y_%m_%d_%H_%M_%S')\n", 42 | " root_log_dir = \"logs/\" + network_type\n", 43 | " exp_name = network_type + \"_%s\" % timestamp\n", 44 | " log_dir = os.path.join(root_log_dir, exp_name)\n", 45 | "\n", 46 | " now = datetime.now(dateutil.tz.tzlocal())\n", 47 | " timestamp = now.strftime('%Y_%m_%d_%H_%M_%S')\n", 48 | " root_model_dir = \"models/\" + network_type\n", 49 | " exp_name = network_type + \"_%s\" % timestamp\n", 50 | " model_dir = os.path.join(root_model_dir, exp_name)\n", 51 | "\n", 52 | " for path in [log_dir, model_dir]:\n", 53 | " if not os.path.exists(path):\n", 54 | " os.makedirs(path)\n", 55 | " return log_dir, model_dir\n", 56 | "\n", 57 | "tic = time.clock()\n", 58 | "\n", 59 | "E0 = 1\n", 60 | "Emin = 1e-9\n", 61 | "nu = 0.3\n", 62 | "batch_size = 3\n", 63 | "\n", 64 | "'Input'\n", 65 | "nelx, nely, alpha, alpha2, gamma, rmin, density_r = 12*4, 4*4, 0.6, 0.6, 3.0, 3.0, 6.0\n", 66 | "\n", 67 | "'Algorithm parameters'\n", 68 | "p, nn, epsilon_al, epsilon_opt = 16,nely * nelx, 1, 1e-3\n", 69 | "\n", 70 | "'Prepare filter'\n", 71 | "r = rmin\n", 72 | "Range = np.arange(-r, r + 1)\n", 73 | "X = np.array([Range] * len(Range))\n", 74 | "Y = np.array([Range] * len(Range)).T\n", 75 | "X_temp = X.T.reshape(len(Range) ** 2, 1)\n", 76 | "Y_temp = Y.T.reshape(len(Range) ** 2, 1)\n", 77 | "neighbor = np.concatenate((X_temp, Y_temp), 1)\n", 78 | "D = np.sum(neighbor ** 2, 1)\n", 79 | "rn = sum(D <= r ** 2) - sum(D == 0)\n", 80 | "\n", 81 | "pattern_index = []\n", 82 | "for i in range(len(D)):\n", 83 | " if D[i] <= r ** 2 and D[i] != 0:\n", 84 | " pattern_index.append(i)\n", 85 | "pattern = neighbor[pattern_index]\n", 86 | "\n", 87 | "locX = np.asarray([np.arange(1, nelx + 1)] * nely)\n", 88 | "locY = np.asarray([np.arange(1, nely + 1)] * nelx).T\n", 89 | "loc = np.asarray([locY.T.reshape(-1), locX.T.reshape(-1)]).T\n", 90 | "\n", 91 | "M = np.zeros([nn, rn])\n", 92 | "for i in range(nn):\n", 93 | " for j in range(rn):\n", 94 | " locc = loc[i, :] + pattern[j, :]\n", 95 | " count_true = 0\n", 96 | " if locc[0] > nely: count_true = count_true + 1\n", 97 | " if locc[1] > nelx: count_true = count_true + 1\n", 98 | "\n", 99 | " if sum(locc < 1) + count_true == 0:\n", 100 | " M[i, j] = locc[0] + (locc[1] - 1) * nely\n", 101 | " else:\n", 102 | " M[i, j] = 'NaN'\n", 103 | "\n", 104 | "iH = np.ones([int(nelx * nely * (2 * (np.ceil(rmin) - 1) + 1) ** 2), 1], dtype=int)\n", 105 | "jH = np.ones(iH.shape, dtype=int)\n", 106 | "sH = np.zeros(iH.shape)\n", 107 | "k = 0\n", 108 | "for i1 in range(nelx):\n", 109 | " for j1 in range(nely):\n", 110 | " e1 = (i1) * nely + (j1 + 1)\n", 111 | " for i2 in np.arange(int(max(i1 + 1 - (np.ceil(rmin) - 1), 1)),\n", 112 | " int(min(i1 + 1 + (np.ceil(rmin) - 1), nelx)) + 1):\n", 113 | " for j2 in np.arange(int(max(j1 + 1 - (np.ceil(rmin) - 1), 1)),\n", 114 | " int(min(j1 + 1 + (np.ceil(rmin) - 1), nely)) + 1):\n", 115 | " e2 = (i2 - 1) * nely + j2\n", 116 | " iH[k] = e1\n", 117 | " jH[k] = e2\n", 118 | " sH[k] = max(0, rmin - np.sqrt((i1 + 1 - i2) ** 2 + (j1 + 1 - j2) ** 2))\n", 119 | " k = k + 1\n", 120 | "\n", 121 | "iH = iH.reshape(-1) - 1\n", 122 | "jH = jH.reshape(-1) - 1\n", 123 | "sH = sH.reshape(-1)\n", 124 | "\n", 125 | "import scipy.sparse as sps\n", 126 | "\n", 127 | "H = sps.csc_matrix((sH, (iH, jH))).toarray()\n", 128 | "Hs = np.sum(H, 1)\n", 129 | "bigM = H > 0\n", 130 | "\n", 131 | "'create neighbourhood index for N'\n", 132 | "r = density_r\n", 133 | "Range = np.arange(-r, r + 1)\n", 134 | "mesh = Range\n", 135 | "X = np.asarray([Range] * len(Range))\n", 136 | "Y = np.asarray([Range] * len(Range)).T\n", 137 | "neighbor = np.array([X.T.reshape(-1), Y.T.reshape(-1)]).T\n", 138 | "D = np.sum(neighbor ** 2, 1)\n", 139 | "rn = np.sum(D <= r ** 2)\n", 140 | "pattern = neighbor[D <= r ** 2, :]\n", 141 | "locX = np.asarray([np.arange(1, nelx + 1)] * nely)\n", 142 | "locY = np.asarray([np.arange(1, nely + 1)] * nelx).T\n", 143 | "loc = np.asarray([locY.T.reshape(-1), locX.T.reshape(-1)]).T\n", 144 | "N = np.zeros([nn, rn])\n", 145 | "for i in range(nn):\n", 146 | " for j in range(rn):\n", 147 | " locc = loc[i, :] + pattern[j, :]\n", 148 | " count_true = 0\n", 149 | " if locc[0] > nely: count_true = count_true + 1\n", 150 | " if locc[1] > nelx: count_true = count_true + 1\n", 151 | "\n", 152 | " if sum(locc < 1) + count_true == 0:\n", 153 | " N[i, j] = locc[0] + (locc[1] - 1) * nely\n", 154 | " else:\n", 155 | " N[i, j] = 'NaN'\n", 156 | "\n", 157 | "idx_temp = (np.array([np.arange(nn)] * rn).T).reshape(-1).reshape(nn * rn, 1)\n", 158 | "N_t = N.T\n", 159 | "idy = []\n", 160 | "idx = []\n", 161 | "import math\n", 162 | "\n", 163 | "k = 0\n", 164 | "for i in range(N_t.shape[1]):\n", 165 | " for j in range(N_t.shape[0]):\n", 166 | " if not math.isnan(N_t[j, i]):\n", 167 | " idy.append(N_t[j, i])\n", 168 | " idx.append(idx_temp[k])\n", 169 | " k = k + 1\n", 170 | "idy = np.asarray(idy).reshape(len(idy), 1) - 1\n", 171 | "idx = np.asarray(idx)\n", 172 | "bigN = sps.coo_matrix((np.ones(len(idx)), (idx.reshape(-1), idy.reshape(-1)))).toarray()\n", 173 | "N_count = np.sum(~np.isnan(N), axis=1)\n", 174 | "\n", 175 | "'Material Properties'\n", 176 | "E0, Emin, nu = 1, 1e-9, 0.3\n", 177 | "\n", 178 | "'PREPARE FINITE ELEMENT ANALYSIS'\n", 179 | "A11 = np.array([[12, 3, -6, -3], [3, 12, 3, 0], [-6, 3, 12, -3], [-3, 0, -3, 12]])\n", 180 | "A12 = np.array([[-6, -3, 0, 3], [-3, -6, -3, -6], [0, -3, -6, 3], [3, -6, 3, -6]])\n", 181 | "B11 = np.array([[-4, 3, -2, 9], [3, -4, -9, 4], [-2, -9, -4, -3], [9, 4, -3, -4]])\n", 182 | "B12 = np.array([[2, -3, 4, -9], [-3, 2, 9, -2], [4, 9, 2, 3], [-9, -2, 3, 2]])\n", 183 | "\n", 184 | "A1 = np.concatenate((A11, A12), axis=1)\n", 185 | "A2 = np.concatenate((A12.T, A11), axis=1)\n", 186 | "A = np.concatenate((A1, A2))\n", 187 | "\n", 188 | "B1 = np.concatenate((B11, B12), axis=1)\n", 189 | "B2 = np.concatenate((B12.T, B11), axis=1)\n", 190 | "B = np.concatenate((B1, B2))\n", 191 | "\n", 192 | "KE = 1 / (1 - nu ** 2) / 24. * (A + nu * B)\n", 193 | "nodenrs = np.arange((1 + nelx) * (1 + nely)).reshape(1 + nelx, 1 + nely).T\n", 194 | "edofVec = (2 * (nodenrs[0:-1, 0:-1] + 1)).reshape(nelx * nely, 1, order='F')\n", 195 | "edofMat = np.asarray([edofVec.reshape(-1)] * 8).T + \\\n", 196 | " np.asarray(([0, 1, 2 * nely + 2, 2 * nely + 3, 2 * nely + 0, 2 * nely + 1, -2, -1]) * nelx * nely).reshape(\n", 197 | " nelx * nely, 8)\n", 198 | "\n", 199 | "iK = np.zeros([edofMat.shape[0] * 8, edofMat.shape[1] * 1])\n", 200 | "for i in range(edofMat.shape[0]):\n", 201 | " for j in range(edofMat.shape[1]):\n", 202 | " iK[i * 8:(i + 1) * 8, j] = np.asarray(edofMat[i, j] * np.ones([8, 1])).reshape(-1)\n", 203 | "iK = (iK.astype(np.int32).T).reshape(64 * nelx * nely, 1, order='F')\n", 204 | "\n", 205 | "jK = np.zeros([edofMat.shape[0] * 1, edofMat.shape[1] * 8])\n", 206 | "for i in range(edofMat.shape[0]):\n", 207 | " for j in range(edofMat.shape[1]):\n", 208 | " jK[i, j * 8:(j + 1) * 8] = np.asarray(edofMat[i, j] * np.ones([1, 8])).reshape(-1)\n", 209 | "jK = (jK.astype(np.int32).T).reshape(64 * nelx * nely, 1, order='F')\n", 210 | "\n", 211 | "'DEFINE LOADS AND SUPPORTS (HALF MBB-BEAM)'\n", 212 | "# F = np.zeros([2 * (nely + 1) * (nelx + 1), 1])\n", 213 | "# F[((nely + 1) * nelx) * 2 + nely + 1, 0] = -1\n", 214 | "F = tf.placeholder(tf.float32, shape=([2*(nely+1)*(nelx+1),batch_size]))\n", 215 | "\n", 216 | "\n", 217 | "# F=sps.coo_matrix(F)\n", 218 | "U = np.zeros([2 * (nely + 1) * (nelx + 1), 1])\n", 219 | "# fixeddofs=(np.arange(0,2*(nely+1),2).tolist());fixeddofs.append(2*(nelx+1)*(nely+1)-1)\n", 220 | "# fixeddofs=np.asarray(fixeddofs).reshape(1,len(fixeddofs))\n", 221 | "# alldofs = np.arange(2*(nely+1)*(nelx+1)).reshape(1,2*(nely+1)*(nelx+1))\n", 222 | "\n", 223 | "fixeddofs = np.asarray(np.arange(0, 2 * (nely + 1), 1).tolist())\n", 224 | "fixeddofs = fixeddofs.reshape(1, len(fixeddofs))\n", 225 | "alldofs = np.arange(2 * (nely + 1) * (nelx + 1)).reshape(1, 2 * (nely + 1) * (nelx + 1))\n", 226 | "\n", 227 | "freedofs = np.setdiff1d(alldofs, fixeddofs)\n", 228 | "\n", 229 | "'prepare some stuff to reduce cost'\n", 230 | "dphi_idphi = (H / sum(H)).T\n", 231 | "\n", 232 | "'Start Iteration'\n", 233 | "# phi = alpha*np.ones([nn,1])\n", 234 | "\n", 235 | "\n", 236 | "\n", 237 | "\n", 238 | "z_dim, h_dim_1, h_dim_2, h_dim_3, h_dim_4, h_dim_5 = 2, 100, 100, 100, 100, 100\n", 239 | "\n", 240 | "# r_lag = tf.placeholder(tf.float32, shape=([batch_size,1]))\n", 241 | "# r_lag2 = tf.placeholder(tf.float32, shape=([batch_size,1]))\n", 242 | "# lamda_lag = tf.placeholder(tf.float32, shape=([batch_size,1]))\n", 243 | "# lamda_lag2 = tf.placeholder(tf.float32, shape=([batch_size,1]))\n", 244 | "\n", 245 | "F_input = tf.placeholder(tf.float32, shape=([batch_size, z_dim]))\n", 246 | "# F = tf.placeholder(tf.float32, shape=([2*(nely+1)*(nelx+1),batch_size]))\n", 247 | "\n", 248 | "W1 = tf.Variable(xavier_init([z_dim, h_dim_1]))\n", 249 | "b1 = tf.Variable(tf.zeros(shape=[h_dim_1]))\n", 250 | "\n", 251 | "W2 = tf.Variable(xavier_init([h_dim_1, h_dim_2]))\n", 252 | "b2 = tf.Variable(tf.zeros(shape=[h_dim_2]))\n", 253 | "\n", 254 | "W3 = tf.Variable(xavier_init([h_dim_2, h_dim_3]))\n", 255 | "b3 = tf.Variable(tf.zeros(shape=[h_dim_3]))\n", 256 | "\n", 257 | "W4 = tf.Variable(xavier_init([h_dim_3, h_dim_4]))\n", 258 | "b4 = tf.Variable(tf.zeros(shape=[h_dim_4]))\n", 259 | "\n", 260 | "W5 = tf.Variable(xavier_init([h_dim_4, nn]))\n", 261 | "b5 = tf.Variable(tf.zeros(shape=[nn]))\n", 262 | "\n", 263 | "# W6 = tf.Variable(xavier_init([h_dim_5, nn]))\n", 264 | "# b6 = tf.Variable(tf.zeros(shape=[nn]))\n", 265 | "\n", 266 | "h1 = tf.contrib.layers.batch_norm(tf.nn.relu(tf.matmul(F_input, W1) + b1),scale=True)\n", 267 | "h2 = tf.contrib.layers.batch_norm(tf.nn.relu(tf.matmul(h1, W2) + b2),scale=True)\n", 268 | "h3 = tf.contrib.layers.batch_norm(tf.nn.relu(tf.matmul(h2, W3) + b3),scale=True)\n", 269 | "h4 = tf.contrib.layers.batch_norm(tf.nn.relu(tf.matmul(h3, W4) + b4),scale=True)\n", 270 | "# h5 = tf.nn.relu(tf.matmul(h4, W5) + b5)\n", 271 | " \n", 272 | "phi_ = tf.sigmoid(tf.matmul(h4, W5) + b5)\n", 273 | "phi = tf.reshape(phi_, [nn, batch_size])\n", 274 | "\n", 275 | "# phi = (tf.Variable(alpha * np.ones([nn, 1]), dtype='float32'))\n", 276 | "\n", 277 | "loop = 0\n", 278 | "# delta = 1.0\n", 279 | "\n", 280 | "# while beta < 1000:\n", 281 | "loop = loop + 1\n", 282 | "loop2 = 0\n", 283 | "'augmented lagrangian parameters'\n", 284 | "# r_lag = 1\n", 285 | "# r_lag2 = 0.001\n", 286 | "# lamda_lag = 0\n", 287 | "# lamda_lag2 = 0\n", 288 | "\n", 289 | "eta = 0.1\n", 290 | "eta2 = 0.1\n", 291 | "epsilon = 1\n", 292 | "dphi = 1e6\n", 293 | "\n", 294 | "r_lag = tf.placeholder(tf.float32, shape=([batch_size,1]))\n", 295 | "r_lag2 = tf.placeholder(tf.float32, shape=([batch_size,1]))\n", 296 | "lamda_lag = tf.placeholder(tf.float32, shape=([batch_size,1]))\n", 297 | "lamda_lag2 = tf.placeholder(tf.float32, shape=([batch_size,1]))\n", 298 | "beta = tf.placeholder(tf.float32, shape=([batch_size,1]))\n", 299 | "################################################################\n", 300 | "'get initial g and c'\n", 301 | "\n", 302 | "import time\n", 303 | "\n", 304 | "W1_fake = tf.Variable(xavier_init([z_dim, h_dim_1]), trainable=False)\n", 305 | "b1_fake = tf.Variable(tf.zeros(shape=[h_dim_1]), trainable=False)\n", 306 | "W1_fake = W1_fake.assign(W1)\n", 307 | "b1_fake = b1_fake.assign(b1)\n", 308 | "\n", 309 | "W2_fake = tf.Variable(xavier_init([h_dim_1, h_dim_2]), trainable=False)\n", 310 | "b2_fake = tf.Variable(tf.zeros(shape=[h_dim_2]), trainable=False)\n", 311 | "W2_fake = W2_fake.assign(W2)\n", 312 | "b2_fake = b2_fake.assign(b2)\n", 313 | "\n", 314 | "W3_fake = tf.Variable(xavier_init([h_dim_2, h_dim_3]), trainable=False)\n", 315 | "b3_fake = tf.Variable(tf.zeros(shape=[h_dim_3]), trainable=False)\n", 316 | "W3_fake = W3_fake.assign(W3)\n", 317 | "b3_fake = b3_fake.assign(b3)\n", 318 | "\n", 319 | "W4_fake = tf.Variable(xavier_init([h_dim_3, h_dim_4]), trainable=False)\n", 320 | "b4_fake = tf.Variable(tf.zeros(shape=[h_dim_4]), trainable=False)\n", 321 | "W4_fake = W4_fake.assign(W4)\n", 322 | "b4_fake = b4_fake.assign(b4)\n", 323 | "\n", 324 | "W5_fake = tf.Variable(xavier_init([h_dim_4, nn]), trainable=False)\n", 325 | "b5_fake = tf.Variable(tf.zeros(shape=[nn]), trainable=False)\n", 326 | "W5_fake = W5_fake.assign(W5)\n", 327 | "b5_fake = b5_fake.assign(b5)\n", 328 | "\n", 329 | "# W6_fake = tf.Variable(xavier_init([h_dim_5, nn]), trainable=False)\n", 330 | "# b6_fake = tf.Variable(tf.zeros(shape=[nn]), trainable=False)\n", 331 | "# W6_fake = W6_fake.assign(W6)\n", 332 | "# b6_fake = b6_fake.assign(b6)\n", 333 | "\n", 334 | "h1_fake = tf.contrib.layers.batch_norm(tf.nn.relu(tf.matmul(F_input, W1_fake) + b1_fake),scale=True,trainable=False)\n", 335 | "h2_fake = tf.contrib.layers.batch_norm(tf.nn.relu(tf.matmul(h1_fake, W2_fake) + b2_fake),scale=True,trainable=False)\n", 336 | "h3_fake = tf.contrib.layers.batch_norm(tf.nn.relu(tf.matmul(h2_fake, W3_fake) + b3_fake),scale=True,trainable=False)\n", 337 | "h4_fake = tf.contrib.layers.batch_norm(tf.nn.relu(tf.matmul(h3_fake, W4_fake) + b4_fake),scale=True,trainable=False)\n", 338 | "# h5_fake = tf.nn.relu(tf.matmul(h4_fake, W5_fake) + b5_fake)\n", 339 | "\n", 340 | "phi_temp_fake = tf.sigmoid(tf.matmul(h4_fake, W5_fake) + b5_fake)\n", 341 | "phi_fake = tf.reshape(phi_temp_fake,[nn,batch_size])\n" 342 | ] 343 | }, 344 | { 345 | "cell_type": "code", 346 | "execution_count": null, 347 | "metadata": { 348 | "collapsed": true 349 | }, 350 | "outputs": [], 351 | "source": [ 352 | "sep_grad_store,error_store,dphi_store,dobj_store=[],[],[],[]\n", 353 | "c,g,global_density=[],[],[]\n", 354 | "c_fake,g_fake,global_density_fake=[],[],[]\n", 355 | "rho,rho_fake=[],[]\n", 356 | "dphi_fake=[]\n", 357 | "\n", 358 | "tic=time.clock()\n", 359 | "\n", 360 | "learning_rate_fake = tf.placeholder(tf.float32,shape=([batch_size,1]))\n", 361 | "g_old = [tf.Variable(0, dtype='float32',trainable=False)]*batch_size\n", 362 | "global_density_old = [tf.Variable([[0]], dtype='float32',trainable=False)]*batch_size\n", 363 | "c_old = [tf.Variable(0, dtype='float32',trainable=False)]*batch_size\n", 364 | "tic=time.clock()\n", 365 | "\n", 366 | "for i in range(batch_size):\n", 367 | " phi_til = tf.matmul(tf.cast(H, tf.float32), phi[:,i:i+1]) / Hs.reshape(nn, 1)\n", 368 | " rho.append((tf.tanh(beta[i][0] / 2.0) + tf.tanh(beta[i][0] * (phi_til - 0.5))) / (2 * tf.tanh(beta[i][0] / 2.0)))\n", 369 | "\n", 370 | " sK_temp = tf.transpose((KE.reshape(KE.shape[0] * KE.shape[1], 1) * \\\n", 371 | " tf.reshape(Emin + tf.reshape(rho[i], [-1]) ** (gamma) * (E0 - Emin), [1, nelx * nely])))\n", 372 | " sK = tf.reshape(sK_temp, [8 * 8 * nelx * nely, 1])\n", 373 | "\n", 374 | " ###################\n", 375 | " indices_m = np.stack((iK.reshape(-1), jK.reshape(-1)), axis=1)\n", 376 | " values_m = tf.reshape(sK, [-1])\n", 377 | "\n", 378 | " linearized_m = tf.matmul(indices_m, [[10000], [1]])\n", 379 | " y_m, idx_m = tf.unique(tf.squeeze(linearized_m))\n", 380 | "\n", 381 | " idx_m_sort, ind_m_sort = tf.nn.top_k(idx_m, k=nelx * nely * 64)\n", 382 | " idx_m_sort = tf.reverse(idx_m_sort, [0])\n", 383 | " ind_m_sort = tf.reverse(ind_m_sort, [0])\n", 384 | "\n", 385 | " # values_m_test = values_m\n", 386 | " values_m = tf.gather(values_m, ind_m_sort)\n", 387 | " values_m = tf.segment_sum(values_m, idx_m_sort)\n", 388 | "\n", 389 | " y_m = tf.expand_dims(y_m, 1)\n", 390 | " indices_m = tf.concat([y_m // 10000, y_m % 10000], axis=1)\n", 391 | " #####################\n", 392 | "\n", 393 | " #####################\n", 394 | " K_sp = tf.SparseTensor(tf.cast(indices_m, tf.int64),\n", 395 | " tf.reshape(tf.cast(values_m, tf.float32), [-1]),\n", 396 | " [(nely + 1) * (nelx + 1) * 2, (nely + 1) * (nelx + 1) * 2])\n", 397 | " K_sp = tf.sparse_add(tf.zeros(((nely + 1) * (nelx + 1) * 2, (nely + 1) * (nelx + 1) * 2)), K_sp)\n", 398 | " K_dense = (K_sp + tf.transpose(K_sp)) / 2\n", 399 | " #####################\n", 400 | "\n", 401 | " K_temp = tf.gather(K_dense, freedofs.astype(np.int32))\n", 402 | " K_free = tf.transpose(tf.gather(tf.transpose(K_temp), freedofs.astype(np.int32)))\n", 403 | " \n", 404 | " F_RHS=tf.cast(tf.gather(tf.reshape(F[:,i:i+1], [(nelx + 1) * (nely + 1) * 2, 1]), freedofs.astype(np.int64)),\n", 405 | " tf.float32)\n", 406 | " chol = tf.cholesky(K_free+np.diag((np.ones([1,(nelx+1)*(nely+1)*2-len(fixeddofs[0])])*1e-8).tolist()[0]))\n", 407 | " U_pre = tf.cholesky_solve(chol,F_RHS)\n", 408 | " \n", 409 | "# U_pre = tf.matmul(tf.matrix_inverse(tf.cast(K_free, tf.float32)),\n", 410 | "# tf.cast(tf.gather(tf.reshape(F[:,i:i+1], [(nelx + 1) * (nely + 1) * 2, 1]), freedofs.astype(np.int64)),\n", 411 | "# tf.float32))\n", 412 | "\n", 413 | " U = tf.sparse_add(tf.zeros(((nelx + 1) * (nely + 1) * 2)),\n", 414 | " tf.SparseTensor(freedofs.reshape((nelx + 1) * (nely + 1) * 2 - (nely + 1) * 2, 1),\n", 415 | " tf.reshape(tf.cast(U_pre, tf.float32), [-1]), [(nelx + 1) * (nely + 1) * 2]))\n", 416 | "\n", 417 | " 'Objective Function and Sensitivity Analysis'\n", 418 | " ce = tf.reduce_sum(tf.multiply(tf.matmul(tf.reshape(tf.gather(U, edofMat.astype(np.int32)), edofMat.shape),\n", 419 | " KE.astype(np.float32)), tf.gather(U, edofMat.astype(np.int32))), axis=1)\n", 420 | " ce = tf.reshape(ce, [nn, 1])\n", 421 | " c.append(tf.reduce_sum(tf.multiply(tf.cast(tf.multiply(rho[i] ** gamma, (E0 - Emin)), tf.float32), ce)))\n", 422 | " rho_bar = tf.divide(tf.matmul(tf.cast(bigN, tf.float32), rho[i]), N_count.reshape(nn, 1))\n", 423 | " g.append((tf.reduce_sum(rho_bar ** p) / nely / nelx) ** (1.0 / p) / alpha - 1.0)\n", 424 | " global_density.append(tf.matmul(tf.transpose(rho[i]), tf.ones([nn, 1])) / nn - alpha2)\n", 425 | " ###################################################################\n", 426 | "\n", 427 | " # if ((max(abs(dphi)))2) or (loo2>100):\n", 428 | "\n", 429 | "\n", 430 | " dc_drho = -gamma * rho[i] ** (gamma - 1) * (E0 - Emin) * ce\n", 431 | " drho_dphi = beta[i][0] * (1 - tf.tanh(beta[i][0] * (phi[:,i:i+1] - 0.5)) ** 2) / 2.0 / tf.tanh(beta[i][0] / 2.)\n", 432 | " dc_dphi = tf.reduce_sum(bigM * (dphi_idphi * (dc_drho * drho_dphi)), axis=0)\n", 433 | " dg_drhobar = 1.0 / alpha / nn * (1.0 / nn * tf.reduce_sum(rho_bar ** p)) ** (1.0 / p - 1) * rho_bar ** (p - 1)\n", 434 | " dg_dphi = tf.reduce_sum(bigM * (dphi_idphi * (tf.matmul(tf.cast(bigN, tf.float32),\n", 435 | " (dg_drhobar / N_count.reshape(nn, 1))) * drho_dphi)), axis=0)\n", 436 | "\n", 437 | " dphi = dc_dphi + tf.cast(lamda_lag[i][0] * dg_dphi * tf.reduce_sum(tf.cast(g[i] > 0, tf.float32)), tf.float32) + \\\n", 438 | " tf.cast(2.0 / r_lag[i][0] * g[i] * dg_dphi * tf.reduce_sum(tf.cast(g[i] > 0, tf.float32)), tf.float32) + \\\n", 439 | " lamda_lag2[i][0] * tf.ones(nn, 1) / nn * (tf.reduce_sum(tf.cast(global_density[i] > 0, tf.float32))) + \\\n", 440 | " tf.reshape(2.0 / r_lag2[i][0] * global_density[i] / nn / nn * tf.ones([nn, 1]) * (\n", 441 | " tf.reduce_sum(tf.cast(global_density[i] > 0, tf.float32))), [-1])\n", 442 | " \n", 443 | " dphi_store.append(dphi)\n", 444 | " \n", 445 | "\n", 446 | " \n", 447 | "############################################################################################################\n", 448 | "\n", 449 | " 'get initial g and c'\n", 450 | " phi_til_fake = tf.matmul(tf.cast(H, tf.float32), phi_fake[:,i:i+1]) / Hs.reshape(nn, 1)\n", 451 | " rho_fake.append((tf.tanh(beta[i][0] / 2.0) + tf.tanh(beta[i][0] * (phi_til_fake - 0.5))) / (2 * tf.tanh(beta[i][0] / 2.0)))\n", 452 | "\n", 453 | " sK_temp_fake = tf.transpose((KE.reshape(KE.shape[0] * KE.shape[1], 1) * \\\n", 454 | " tf.reshape(Emin + tf.reshape(rho_fake[i], [-1]) ** (gamma) * (E0 - Emin), [1, nelx * nely])))\n", 455 | " sK_fake = tf.reshape(sK_temp_fake, [8 * 8 * nelx * nely, 1])\n", 456 | "\n", 457 | " ###################\n", 458 | " indices_m = np.stack((iK.reshape(-1), jK.reshape(-1)), axis=1)\n", 459 | " values_m_fake = tf.reshape(sK_fake, [-1])\n", 460 | "\n", 461 | " linearized_m = tf.matmul(indices_m, [[10000], [1]])\n", 462 | " y_m, idx_m = tf.unique(tf.squeeze(linearized_m))\n", 463 | "\n", 464 | " idx_m_sort, ind_m_sort = tf.nn.top_k(idx_m, k=nelx * nely * 64)\n", 465 | " idx_m_sort = tf.reverse(idx_m_sort, [0])\n", 466 | " ind_m_sort = tf.reverse(ind_m_sort, [0])\n", 467 | "\n", 468 | " values_m_fake = tf.gather(values_m_fake, ind_m_sort)\n", 469 | " values_m_fake = tf.segment_sum(values_m_fake, idx_m_sort)\n", 470 | "\n", 471 | " y_m = tf.expand_dims(y_m, 1)\n", 472 | " indices_m = tf.concat([y_m // 10000, y_m % 10000], axis=1)\n", 473 | " #####################\n", 474 | "\n", 475 | " #####################\n", 476 | " K_sp_fake = tf.SparseTensor(tf.cast(indices_m, tf.int64),\n", 477 | " tf.reshape(tf.cast(values_m_fake, tf.float32), [-1]),\n", 478 | " [(nely + 1) * (nelx + 1) * 2, (nely + 1) * (nelx + 1) * 2])\n", 479 | " K_sp_fake = tf.sparse_add(tf.zeros(((nely + 1) * (nelx + 1) * 2, (nely + 1) * (nelx + 1) * 2)), K_sp_fake)\n", 480 | " K_dense_fake = (K_sp_fake + tf.transpose(K_sp_fake)) / 2.0\n", 481 | " #####################\n", 482 | "\n", 483 | " K_temp_fake = tf.gather(K_dense_fake, freedofs.astype(np.int32))\n", 484 | " K_free_fake = tf.transpose(tf.gather(tf.transpose(K_temp_fake), freedofs.astype(np.int32)))\n", 485 | "\n", 486 | " F_RHS_fake=tf.cast(tf.gather(tf.reshape(F[:,i:i+1], [(nelx + 1) * (nely + 1) * 2, 1]), freedofs.astype(np.int64)),\n", 487 | " tf.float32)\n", 488 | " chol_fake = tf.cholesky(K_free_fake+np.diag((np.ones([1,(nelx+1)*(nely+1)*2-len(fixeddofs[0])])*1e-8).tolist()[0]))\n", 489 | " U_pre_fake = tf.cholesky_solve(chol_fake,F_RHS_fake)\n", 490 | " \n", 491 | "# U_pre_fake = tf.matmul(tf.matrix_inverse(tf.cast(K_free_fake, tf.float32)),\n", 492 | "# tf.cast(tf.gather(tf.reshape(F[:,i:i+1], [(nelx + 1) * (nely + 1) * 2, 1]), freedofs.astype(np.int64)),\n", 493 | "# tf.float32))\n", 494 | "\n", 495 | " U_fake = tf.sparse_add(tf.zeros(((nelx + 1) * (nely + 1) * 2)),\n", 496 | " tf.SparseTensor(freedofs.reshape((nelx + 1) * (nely + 1) * 2 - (nely + 1) * 2, 1),\n", 497 | " tf.reshape(tf.cast(U_pre_fake, tf.float32), [-1]),\n", 498 | " [(nelx + 1) * (nely + 1) * 2]))\n", 499 | "\n", 500 | " 'Objective Function and Sensitivity Analysis'\n", 501 | " ce_fake = tf.reduce_sum(tf.multiply(tf.matmul(tf.reshape(tf.gather(U_fake, edofMat.astype(np.int32)), edofMat.shape),\n", 502 | " KE.astype(np.float32)), tf.gather(U_fake, edofMat.astype(np.int32))),\n", 503 | " axis=1)\n", 504 | " ce_fake = tf.reshape(ce_fake, [nn, 1])\n", 505 | " c_fake.append(tf.reduce_sum(tf.multiply(tf.cast(tf.multiply(rho_fake[i] ** gamma, (E0 - Emin)), tf.float32), ce_fake)))\n", 506 | " rho_bar_fake=tf.divide(tf.matmul(tf.cast(bigN, tf.float32), rho_fake[i]), N_count.reshape(nn, 1))\n", 507 | " g_fake.append((tf.reduce_sum(rho_bar_fake ** p) / nely / nelx) ** (1. / p) / alpha - 1.0)\n", 508 | " global_density_fake.append(tf.matmul(tf.transpose(rho_fake[i]), tf.ones([nn, 1])) / nn - alpha2)\n", 509 | " ###################################################################\n", 510 | "\n", 511 | " # if ((max(abs(dphi)))2) or (loo2>100):\n", 512 | "\n", 513 | "\n", 514 | " dc_drho_fake = -gamma * rho_fake[i] ** (gamma - 1) * (E0 - Emin) * ce_fake\n", 515 | " drho_dphi_fake = beta[i][0] * (1 - tf.tanh(beta[i][0] * (phi_fake[:,i:i+1] - 0.5)) ** 2) / 2.0 / tf.tanh(beta[i][0] / 2.)\n", 516 | " dc_dphi_fake = tf.reduce_sum(bigM * (dphi_idphi * (dc_drho_fake * drho_dphi_fake)), axis=0)\n", 517 | " dg_drhobar_fake = 1.0 / alpha / nn * (1.0 / nn * tf.reduce_sum(rho_bar_fake ** p)) ** (1.0 / p - 1) * rho_bar_fake ** (\n", 518 | " p - 1)\n", 519 | " dg_dphi_fake = tf.reduce_sum(bigM * (dphi_idphi * (tf.matmul(tf.cast(bigN, tf.float32),\n", 520 | " (dg_drhobar_fake / N_count.reshape(nn,\n", 521 | " 1))) * drho_dphi_fake)),\n", 522 | " axis=0)\n", 523 | "\n", 524 | " A = dc_dphi_fake + tf.cast(lamda_lag[i][0] * dg_dphi_fake * tf.reduce_sum(tf.cast(g_fake[i] > 0, tf.float32)), tf.float32) + \\\n", 525 | " tf.cast(2.0 / r_lag[i][0] * g_fake[i] * dg_dphi_fake * tf.reduce_sum(tf.cast(g_fake[i] > 0, tf.float32)), tf.float32)\n", 526 | "\n", 527 | " B = lamda_lag2[i][0] * tf.ones(nn, 1) / nn * (tf.reduce_sum(tf.cast(global_density_fake[i] > 0, tf.float32))) + \\\n", 528 | " 2.0 / r_lag2[i][0] * global_density_fake[i] / nn / nn * tf.ones([nn]) * (tf.reduce_sum(tf.cast(global_density_fake[i] > 0, tf.float32)))\n", 529 | "\n", 530 | " dphi_fake.append(A + B)\n", 531 | " \n", 532 | " \n", 533 | " error_sep = tf.reduce_sum(((tf.reshape(dphi_fake[i], [nn, 1]) * phi[:,i:i+1])))\n", 534 | " error_store.append(error_sep)\n", 535 | " \n", 536 | " sep_grad=tf.reduce_sum(tf.abs(tf.gradients((tf.reshape(dphi_fake[i], [nn, 1]) * phi[:,i:i+1]),W1)))\n", 537 | " sep_grad_store.append(sep_grad)\n", 538 | " \n", 539 | "############################################################################################\n", 540 | "# g_old = tf.Variable(0, dtype='float32',trainable=False)\n", 541 | "# global_density_old = tf.Variable([[0]], dtype='float32',trainable=False)\n", 542 | "# c_old = tf.Variable(0, dtype='float32',trainable=False)\n", 543 | "\n", 544 | " g_old[i] = g_old[i].assign(g[i])\n", 545 | " global_density_old[i] = global_density_old[i].assign(global_density[i])\n", 546 | " c_old[i] = c_old[i].assign(c[i])\n", 547 | "\n", 548 | "# assign_g=tf.assign(g_old[i],g[i])\n", 549 | "# assign_gd=tf.assign(global_density_old[i],global_density[i])\n", 550 | "# assign_c=tf.assign(c_old[i],c[i])\n", 551 | "\n", 552 | " 'learning rate adjusting'\n", 553 | " delta = -dphi_fake[i] * learning_rate_fake[i][0]\n", 554 | " phi_temp = phi_fake[:,i:i+1] + tf.reshape(delta, [nn, 1])\n", 555 | "\n", 556 | " # assign_phi = tf.assign(phi,phi_temp)\n", 557 | "\n", 558 | " # phi_temp=tf.Variable(np.ones([nn,1]), dtype='float32')\n", 559 | " # phi_temp=phi_temp.assign(phi)\n", 560 | "\n", 561 | " phi_til_temp = tf.matmul(tf.cast(H, tf.float32), phi_temp) / tf.reshape(tf.cast(Hs, tf.float32), [nn, 1])\n", 562 | " rho_temp = (tf.tanh(beta[i][0] / 2.0) + tf.tanh(beta[i][0] * (phi_til_temp - 0.5))) / (2 * tf.tanh(beta[i][0] / 2.0))\n", 563 | " rho_bar_temp = (tf.matmul(tf.cast(bigN, tf.float32), rho_temp) / tf.reshape(tf.cast(N_count, tf.float32), [nn, 1]))\n", 564 | " g_temp = (tf.reduce_sum(rho_bar_temp ** p) / nn) ** (1.0 / p) / alpha - 1.0\n", 565 | " global_density_temp = tf.matmul(tf.transpose(rho_temp), tf.ones([nn, 1])) / nn - alpha2\n", 566 | "\n", 567 | " sK_temp_fake2 = tf.transpose((KE.reshape(KE.shape[0] * KE.shape[1], 1) * \\\n", 568 | " tf.reshape(Emin + tf.reshape(rho_temp, [-1]) ** (gamma) * (E0 - Emin), [1, nelx * nely])))\n", 569 | " sK_fake2 = tf.reshape(sK_temp_fake2, [8 * 8 * nelx * nely, 1])\n", 570 | "\n", 571 | " ###################\n", 572 | " values_m_fake2 = tf.reshape(sK_fake2, [-1])\n", 573 | " values_m_fake2 = tf.gather(values_m_fake2, ind_m_sort)\n", 574 | " values_m_fake2 = tf.segment_sum(values_m_fake2, idx_m_sort)\n", 575 | " ###################\n", 576 | "\n", 577 | " ###################\n", 578 | " K_sp_fake2 = tf.SparseTensor(tf.cast(indices_m, tf.int64),\n", 579 | " tf.reshape(tf.cast(values_m_fake2, tf.float32), [-1]),\n", 580 | " [(nely + 1) * (nelx + 1) * 2, (nely + 1) * (nelx + 1) * 2])\n", 581 | " K_sp_fake2 = tf.sparse_add(tf.zeros(((nely + 1) * (nelx + 1) * 2, (nely + 1) * (nelx + 1) * 2)), K_sp_fake2)\n", 582 | " K_dense_fake2 = (K_sp_fake2 + tf.transpose(K_sp_fake2)) / 2.0\n", 583 | " ###################\n", 584 | "\n", 585 | " K_temp_fake2 = tf.gather(K_dense_fake2, freedofs.astype(np.int32))\n", 586 | " K_free_fake2 = tf.transpose(tf.gather(tf.transpose(K_temp_fake2), freedofs.astype(np.int32)))\n", 587 | " \n", 588 | " F_RHS_fake2=tf.cast(tf.gather(tf.reshape(F[:,i:i+1], [(nelx + 1) * (nely + 1) * 2, 1]), freedofs.astype(np.int64)),\n", 589 | " tf.float32)\n", 590 | " chol_fake2 = tf.cholesky(K_free_fake2+np.diag((np.ones([1,(nelx+1)*(nely+1)*2-len(fixeddofs[0])])*1e-8).tolist()[0]))\n", 591 | " U_pre_fake2 = tf.cholesky_solve(chol_fake2,F_RHS_fake2)\n", 592 | " \n", 593 | "# U_pre_fake2 = tf.matmul(tf.matrix_inverse(tf.cast(K_free_fake2, tf.float32)+np.diag((np.ones([1,(nelx+1)*(nely+1)*2-len(fixeddofs[0])])*1e-15).tolist()[0])),\n", 594 | "# tf.cast(tf.gather(tf.reshape(F[:,i:i+1], [(nelx + 1) * (nely + 1) * 2, 1]), freedofs.astype(np.int64)),tf.float32))\n", 595 | "\n", 596 | " U_fake2 = tf.sparse_add(tf.zeros(((nelx + 1) * (nely + 1) * 2)),\n", 597 | " tf.SparseTensor(freedofs.reshape((nelx + 1) * (nely + 1) * 2 - (nely + 1) * 2, 1),\n", 598 | " tf.reshape(tf.cast(U_pre_fake2, tf.float32), [-1]),\n", 599 | " [(nelx + 1) * (nely + 1) * 2]))\n", 600 | "\n", 601 | " ce_temp = tf.reduce_sum(tf.multiply(tf.matmul(tf.reshape(tf.gather(U_fake2, edofMat.astype(np.int32)), edofMat.shape),\n", 602 | " KE.astype(np.float32)), tf.gather(U_fake2, edofMat.astype(np.int32))),axis=1)\n", 603 | " \n", 604 | " ce_temp = tf.reshape(ce_temp, [nn, 1])\n", 605 | " c_temp = tf.reduce_sum(tf.multiply(tf.cast(tf.multiply(rho_temp ** gamma, (E0 - Emin)), tf.float32), ce_temp))\n", 606 | "\n", 607 | " A2 = (c_temp + lamda_lag[i][0] * g_temp * (tf.reduce_sum(tf.cast(g_temp > 0, tf.float32))) + 1.0 / r_lag[i][0] * g_temp ** 2 * (\n", 608 | " tf.reduce_sum(tf.cast(g_temp > 0, tf.float32))) + \\\n", 609 | " 1.0 / r_lag2[i][0] * global_density_temp ** 2 * (tf.reduce_sum(tf.cast(global_density_temp > 0, tf.float32))))\n", 610 | "\n", 611 | " B2 = (c_old[i] + lamda_lag[i][0] * g_old[i] * (tf.reduce_sum(tf.cast(g_old[i] > 0, tf.float32))) + 1.0 / r_lag[i][0] * g_old[i] ** 2 * (\n", 612 | " tf.reduce_sum(tf.cast(g_old[i] > 0, tf.float32))) + \\\n", 613 | " 1.0 / r_lag2[i][0] * global_density_old[i] ** 2 * (tf.reduce_sum(tf.cast(global_density_old[i] > 0, tf.float32))))\n", 614 | " dobj = A2 - B2\n", 615 | " dobj_store.append(dobj)\n", 616 | " \n", 617 | "toc=time.clock()\n", 618 | "print(toc-tic)" 619 | ] 620 | }, 621 | { 622 | "cell_type": "code", 623 | "execution_count": null, 624 | "metadata": { 625 | "collapsed": true 626 | }, 627 | "outputs": [], 628 | "source": [ 629 | "global_step = tf.Variable(0, trainable=False)\n", 630 | "starter_learning_rate = 0.001\n", 631 | "learning_rate = tf.train.exponential_decay(starter_learning_rate, global_step,\n", 632 | " 1000, 1.0, staircase=True)\n", 633 | "\n", 634 | "solver0 = tf.train.AdamOptimizer(learning_rate).minimize(error_store[0], global_step=global_step)\n", 635 | "solver1 = tf.train.AdamOptimizer(learning_rate).minimize(error_store[1], global_step=global_step)\n", 636 | "solver2 = tf.train.AdamOptimizer(learning_rate).minimize(error_store[2], global_step=global_step)\n", 637 | "\n", 638 | "sess = tf.Session()\n", 639 | "sess.run(tf.global_variables_initializer())" 640 | ] 641 | }, 642 | { 643 | "cell_type": "code", 644 | "execution_count": null, 645 | "metadata": { 646 | "collapsed": true 647 | }, 648 | "outputs": [], 649 | "source": [ 650 | "force=-1\n", 651 | "F_batch=np.zeros([batch_size,z_dim])\n", 652 | "\n", 653 | "# alpha=1.5\n", 654 | "theta = np.linspace(np.pi*0.,2.0*np.pi/5.,batch_size)\n", 655 | "\n", 656 | "count=0\n", 657 | "for i in range(batch_size-1,-1,-1):\n", 658 | "# theta = 2*(i+1)*np.pi/10.#+i*np.pi/9*alpha\n", 659 | " print theta[i]\n", 660 | "# theta = (i+1)*np.pi/10\n", 661 | " Fx = force*np.sin(theta[i])\n", 662 | " Fy = force*np.cos(theta[i])\n", 663 | " \n", 664 | " # up-right corner\n", 665 | " F_batch[count,0]=Fx\n", 666 | " F_batch[count,1]=Fy\n", 667 | " count=count+1 \n", 668 | "\n", 669 | "count=0\n", 670 | "F_sp=np.zeros([2*(nely+1)*(nelx+1),batch_size])\n", 671 | "for i in range(batch_size-1,-1,-1):\n", 672 | "# theta = 2*(i+1)*np.pi/10.#+i*np.pi/9*alpha\n", 673 | "# theta = (i+1)*np.pi/5\n", 674 | " Fx = force*np.sin(theta[i])\n", 675 | " Fy = force*np.cos(theta[i]) \n", 676 | " F_sp[(nely+1)*2*nelx+nely, count] = Fx\n", 677 | " F_sp[(nely+1)*2*nelx+nely+1, count] = Fy\n", 678 | " count=count+1\n", 679 | "\n", 680 | "print F_batch" 681 | ] 682 | }, 683 | { 684 | "cell_type": "code", 685 | "execution_count": null, 686 | "metadata": { 687 | "collapsed": true 688 | }, 689 | "outputs": [], 690 | "source": [ 691 | "lamda_value = np.zeros([batch_size, 1])\n", 692 | "lamda_value2 = np.zeros([batch_size, 1])\n", 693 | "r_value = np.ones([batch_size, 1]) * 1\n", 694 | "r_value2 = np.ones([batch_size, 1]) * 0.001\n", 695 | "eta = np.ones([batch_size, 1]) * 0.1\n", 696 | "eta2 = np.ones([batch_size, 1]) * 0.1\n", 697 | "j, j2 = 0, 0\n", 698 | "\n", 699 | "k_j = np.ones([batch_size, 1])\n", 700 | "thre_range = 0.02\n", 701 | "agg = 0\n", 702 | "total_E_pre = 1e20\n", 703 | "count_k = 0\n", 704 | "count = 0\n", 705 | "drho=1e6\n", 706 | "it=0\n", 707 | "beta_value=np.ones([batch_size,1])*10\n", 708 | "learning_rate_fake_value=np.ones([batch_size,1])*0.001" 709 | ] 710 | }, 711 | { 712 | "cell_type": "code", 713 | "execution_count": null, 714 | "metadata": { 715 | "collapsed": true 716 | }, 717 | "outputs": [], 718 | "source": [ 719 | "import os\n", 720 | "import time\n", 721 | "timestr = time.strftime(\"%Y%m%d-%H%M%S_bn\")\n", 722 | "if not os.path.exists(timestr):\n", 723 | " os.makedirs(timestr)" 724 | ] 725 | }, 726 | { 727 | "cell_type": "code", 728 | "execution_count": null, 729 | "metadata": { 730 | "collapsed": true 731 | }, 732 | "outputs": [], 733 | "source": [ 734 | "####################\n", 735 | "# logdir,modeldir=creat_dir('infill_var')\n", 736 | "# summary_writer = tf.summary.FileWriter(logdir)\n", 737 | "# summary_op_train = tf.summary.merge([tf.summary.scalar(\"train/error\",error_total)])\n", 738 | "####################\n", 739 | "\n", 740 | "# for it in range(100000):\n", 741 | "it=0\n", 742 | "drho_total_store=[]\n", 743 | "\n", 744 | "while min(beta_value)<11:\n", 745 | " it=it+1\n", 746 | " # sess.run([assign_phi_fake,assign_c,assign_g,assign_gd], feed_dict={learning_rate_fake: starter_learning_rate, lamda_lag: lamda_value,\n", 747 | " # lamda_lag2: lamda_value2,\n", 748 | " # r_lag: r_value,\n", 749 | " # r_lag2: r_value2})\n", 750 | " \n", 751 | "# total_E, g_value, gd, dphi_fake_value, dobj_value, lr, phi_fake_value,rho_value = sess.run([error_store, g,\n", 752 | "# global_density, dphi_fake, dobj_store,\n", 753 | "# learning_rate,phi_fake,rho],\n", 754 | "# feed_dict={learning_rate_fake: learning_rate_fake_value,\n", 755 | "# lamda_lag:lamda_value,\n", 756 | "# lamda_lag2:lamda_value2,\n", 757 | "# r_lag:r_value,\n", 758 | "# r_lag2:r_value2,\n", 759 | "# F_input:F_batch,\n", 760 | "# F:F_sp, \n", 761 | "# learning_rate:starter_learning_rate,beta:beta_value})\n", 762 | "\n", 763 | " \n", 764 | " \n", 765 | " loop2=0\n", 766 | " \n", 767 | " while 1:\n", 768 | "# try:\n", 769 | " g_value_temp,dphi_fake_value,rho_pre = sess.run([g,dphi_fake,rho], \n", 770 | " feed_dict={learning_rate_fake: learning_rate_fake_value,\n", 771 | " lamda_lag:lamda_value,lamda_lag2:lamda_value2,\n", 772 | " r_lag:r_value,r_lag2:r_value2,F_input: F_batch,\n", 773 | " F:F_sp,learning_rate:starter_learning_rate,\n", 774 | " beta:beta_value})\n", 775 | "# except:\n", 776 | "# stop=1\n", 777 | "\n", 778 | " \n", 779 | " dphi_fake_value_max=max(max(abs(np.array(dphi_fake_value[0])).reshape(-1)),\n", 780 | " max(abs(np.array(dphi_fake_value[1])).reshape(-1)),\n", 781 | " max(abs(np.array(dphi_fake_value[2])).reshape(-1)))\n", 782 | " \n", 783 | " \n", 784 | " if (dphi_fake_value_max < 1*batch_size and max(g_value_temp) < 0.01 and loop2 > 0) or (loop2 > 100):\n", 785 | "\n", 786 | "# if (drho < 0.05 and max(g_value_temp) < 0.005 and loop2 > 0) or (loop2 > 100):\n", 787 | " # print('wrong')\n", 788 | " lamda_value = np.zeros([batch_size, 1])\n", 789 | " lamda_value2 = np.zeros([batch_size, 1])\n", 790 | " r_value = np.ones([batch_size, 1]) * 1\n", 791 | " r_value2 = np.ones([batch_size, 1]) * 0.001\n", 792 | " eta = np.ones([batch_size, 1]) * 0.1\n", 793 | " eta2 = np.ones([batch_size, 1]) * 0.1\n", 794 | " dphi_fake_value=np.array([1e6]*batch_size)\n", 795 | " drho=np.array([1e6]*batch_size)\n", 796 | " break\n", 797 | "\n", 798 | " loop2 = loop2 + 1\n", 799 | " j, j2 = 0, 0\n", 800 | " loop3 = np.array([0]*batch_size)\n", 801 | " dphi_fake_value = np.array([1e6]*batch_size)\n", 802 | " drho = np.array([1e6]*batch_size)\n", 803 | " \n", 804 | "\n", 805 | "\n", 806 | " while (max(max(abs(np.array(dphi_fake_value[0])).reshape(-1)),\n", 807 | " max(abs(np.array(dphi_fake_value[1])).reshape(-1)),\n", 808 | " max(abs(np.array(dphi_fake_value[2])).reshape(-1)))) > epsilon and min(loop3) < 1000:\n", 809 | " \n", 810 | "# rho_value_pre = sess.run(rho, feed_dict={learning_rate_fake: learning_rate_fake_value,lamda_lag:lamda_value,lamda_lag2:lamda_value2,r_lag:r_value,r_lag2:r_value2,\n", 811 | "# F_input: F_batch,F:F_sp,learning_rate:starter_learning_rate,beta:beta_value})\n", 812 | "\n", 813 | " \n", 814 | " for i in range(batch_size):\n", 815 | " if count>=4000:\n", 816 | " break\n", 817 | " if loop3[i]>1000:\n", 818 | " continue\n", 819 | "# dphi_fake_value[i] = np.array([1e6])\n", 820 | "# g_value = g_value_temp[i]\n", 821 | "\n", 822 | " starter_learning_rate = 0.001\n", 823 | " learning_rate_fake_value[i]=0.001\n", 824 | " loop3[i] = loop3[i] + 1\n", 825 | " loop4 = np.asarray([0]*batch_size)\n", 826 | "\n", 827 | " tic=time.clock()\n", 828 | " while loop4[i] < 10:\n", 829 | " try:\n", 830 | " dphi_fake_value, dobj_value,rho_value = sess.run([dphi_fake, dobj_store,rho],\n", 831 | " feed_dict={learning_rate_fake: learning_rate_fake_value,lamda_lag:lamda_value,\n", 832 | " lamda_lag2:lamda_value2, r_lag:r_value,\n", 833 | " r_lag2:r_value2,F_input:F_batch,\n", 834 | " F:F_sp,learning_rate:learning_rate_fake_value[i][0],\n", 835 | " beta:beta_value})\n", 836 | " except:\n", 837 | " starter_learning_rate = starter_learning_rate*0.5\n", 838 | " learning_rate_fake_value[i] = learning_rate_fake_value[i]*0.5\n", 839 | " \n", 840 | "\n", 841 | "\n", 842 | " if dobj_value[i] > 0:\n", 843 | " starter_learning_rate = starter_learning_rate * 0.5\n", 844 | " learning_rate_fake_value[i] = learning_rate_fake_value[i]*0.5\n", 845 | " loop4[i] = loop4[i] + 1\n", 846 | " if loop4[i] == 10:\n", 847 | " loop3[i] = 10000\n", 848 | " dphi_fake_value[i] = np.array([0])\n", 849 | " drho[i] = np.array([0])\n", 850 | " # break\n", 851 | " else:\n", 852 | " if i == 0:\n", 853 | " try:\n", 854 | " sess.run([solver0],feed_dict={learning_rate_fake: learning_rate_fake_value,lamda_lag:lamda_value,\n", 855 | " lamda_lag2:lamda_value2,r_lag:r_value,r_lag2:r_value2,\n", 856 | " F_input: F_batch,F:F_sp,learning_rate:learning_rate_fake_value[i][0],beta:beta_value})\n", 857 | "\n", 858 | " except:\n", 859 | " print('jump0')\n", 860 | " \n", 861 | " if i == 1:\n", 862 | " try:\n", 863 | " sess.run([solver1],feed_dict={learning_rate_fake: learning_rate_fake_value,lamda_lag:lamda_value,\n", 864 | " lamda_lag2:lamda_value2,r_lag:r_value,r_lag2:r_value2,\n", 865 | " F_input: F_batch,F:F_sp,learning_rate:learning_rate_fake_value[i][0],beta:beta_value})\n", 866 | "\n", 867 | " except:\n", 868 | " print('jump1')\n", 869 | " \n", 870 | " if i == 2:\n", 871 | " try:\n", 872 | " sess.run([solver2],feed_dict={learning_rate_fake: learning_rate_fake_value,lamda_lag:lamda_value,\n", 873 | " lamda_lag2:lamda_value2,r_lag:r_value,r_lag2:r_value2,\n", 874 | " F_input: F_batch,F:F_sp,learning_rate:learning_rate_fake_value[i][0],beta:beta_value})\n", 875 | " except:\n", 876 | " print('jump2')\n", 877 | " \n", 878 | " break\n", 879 | "\n", 880 | " toc=time.clock()\n", 881 | " count = count + 1\n", 882 | "# try:\n", 883 | " g_value,c_value,sep_grad_value,error_total_value,phi_value,rho_curr=sess.run([g,c,sep_grad_store,error_store,phi,rho], \n", 884 | " feed_dict={learning_rate_fake: learning_rate_fake_value, lamda_lag: lamda_value,\n", 885 | " lamda_lag2: lamda_value2,r_lag: r_value,\n", 886 | " r_lag2: r_value2, F_input: F_batch, F: F_sp, learning_rate: learning_rate_fake_value[i][0],\n", 887 | " beta: beta_value})\n", 888 | "# except:\n", 889 | "# print('jump3')\n", 890 | "\n", 891 | " drho[i]=sum(abs(rho_curr[i]-rho_pre[i]).reshape(-1))\n", 892 | " drho_total=sum(abs(np.array(rho_curr)-np.array(rho_pre)).reshape(-1))\n", 893 | " drho_total_store.append(drho_total)\n", 894 | " print('iteration:{}'.format(it))\n", 895 | " print('updating_case:{}'.format(i))\n", 896 | " print('num_update:{}'.format(count))\n", 897 | " print('total_error:{}'.format(np.sum(np.array(error_total_value))))\n", 898 | " print('g_value:{}'.format(g_value))\n", 899 | " print('c_value:{}'.format(c_value))\n", 900 | " print('log_r:{}'.format(np.log(r_value)))\n", 901 | "# print('max_abs_dphi:{}'.format(max(abs(dphi_fake_value.reshape(-1)))))\n", 902 | " print('gradient_W1:{}'.format(sep_grad_value))\n", 903 | " print('dobj_value:{}'.format(dobj_value))\n", 904 | " # r_lag2:r_value2,F_input: F_batch,F:F_sp,learning_rate:starter_learning_rate,beta:beta_value})))\n", 905 | " print('dphi_fake_value_max:{}'.format((max(abs(dphi_fake_value[i].reshape(-1))))))\n", 906 | "# print('drho_fake_value_max:{}'.format(max(abs(rho_value[i].reshape(-1)-rho_value_pre[i].reshape(-1)))))\n", 907 | " print('drho:{}'.format(drho))\n", 908 | " print('loop3:{}'.format(loop3))\n", 909 | " print\n", 910 | " print('running time:{}'.format(toc-tic))\n", 911 | " print()\n", 912 | " if count%500 == 0:\n", 913 | " sio.savemat('{}/c_value.mat'.format(timestr), mdict={'c': np.array(c_value)})\n", 914 | " sio.savemat('{}/rho.mat'.format(timestr), mdict={'rho': np.array(rho_curr)})\n", 915 | " sio.savemat('{}/drho.mat'.format(timestr), mdict={'drho': np.array(drho_total_store)})\n", 916 | " fig, axs = plt.subplots(2, 5, figsize=(15, 4), facecolor='w', edgecolor='k')\n", 917 | " fig.subplots_adjust(hspace=.1, wspace=.001)\n", 918 | "\n", 919 | " axs = axs.ravel()\n", 920 | "\n", 921 | " for i in range(batch_size):\n", 922 | " axs[i].imshow(1 - rho_curr[i].reshape([nelx, nely]).T, 'gray')\n", 923 | " axs[i].set_title('c={}'.format(c_value[i]))\n", 924 | " plt.savefig('{}/opt_{}.png'.format(timestr, str(count)))\n", 925 | " plt.close()\n", 926 | " if count >= 4000:\n", 927 | " break\n", 928 | "# drho1=max(rho_value_cur[0].reshape(-1)-rho_value_pre[0].reshape(-1))\n", 929 | "# drho2=max(rho_value_cur[1].reshape(-1)-rho_value_pre[1].reshape(-1))\n", 930 | "# drho3=max(rho_value_cur[2].reshape(-1)-rho_value_pre[2].reshape(-1))\n", 931 | "# drho=max(drho1,drho2,drho3)\n", 932 | " \n", 933 | " \n", 934 | "# g_value, gd, rho_value_cur = sess.run([g, global_density,rho], \n", 935 | "# feed_dict={learning_rate_fake: learning_rate_fake_value,lamda_lag:lamda_value,\n", 936 | "# lamda_lag2:lamda_value2,r_lag:r_value,\n", 937 | "# r_lag2:r_value2,F_input: F_batch,F:F_sp,\n", 938 | "# learning_rate:starter_learning_rate,beta:beta_value})\n", 939 | " for i in range(batch_size): \n", 940 | " g_value, gd= sess.run([g, global_density], \n", 941 | " feed_dict={learning_rate_fake: learning_rate_fake_value,lamda_lag:lamda_value,\n", 942 | " lamda_lag2:lamda_value2,r_lag:r_value,\n", 943 | " r_lag2:r_value2,F_input: F_batch,F:F_sp,\n", 944 | " learning_rate:learning_rate_fake_value[i][0],beta:beta_value}) \n", 945 | " if g_value[i] < eta[i]:\n", 946 | " lamda_value[i] = lamda_value[i] + 2 * g_value[i] / r_value[i]\n", 947 | " j = j + 1\n", 948 | " eta[i] = eta[i] * 0.5\n", 949 | " else:\n", 950 | " r_value[i] = r_value[i] * 0.5\n", 951 | " j = 0\n", 952 | "\n", 953 | " if gd[i] < eta2[i]:\n", 954 | " lamda_value2[i] = lamda_value2[i] + 2 * gd[i][0] / r_value2[i]\n", 955 | " j2 = j2 + 1\n", 956 | " eta2[i] = eta2[i] * 0.5\n", 957 | " else:\n", 958 | " r_value2[i] = r_value2[i] * 0.5\n", 959 | " j2 = 0\n", 960 | " \n", 961 | " for i in range(batch_size):\n", 962 | " beta_value[i] = 1.5 * beta_value[i]\n", 963 | "\n", 964 | "phi_value, rho_value = sess.run([phi, rho],feed_dict={learning_rate_fake: learning_rate_fake_value, lamda_lag: lamda_value,lamda_lag2: lamda_value2,r_lag: r_value,\n", 965 | " r_lag2: r_value2, F_input: F_batch, F: F_sp, learning_rate: starter_learning_rate, beta: beta_value})\n", 966 | "\n", 967 | "print('finished')\n", 968 | "# sio.savemat('result/infill_phi_{}.mat'.format(count), mdict={'phi': phi_value})\n", 969 | "# sio.savemat('result/infill_rho_{}.mat'.format(count), mdict={'rho': rho_value})" 970 | ] 971 | }, 972 | { 973 | "cell_type": "code", 974 | "execution_count": null, 975 | "metadata": { 976 | "collapsed": true 977 | }, 978 | "outputs": [], 979 | "source": [ 980 | "# import os\n", 981 | "# import time\n", 982 | "# timestr = time.strftime(\"%Y%m%d-%H%M%S\")\n", 983 | "# if not os.path.exists(timestr):\n", 984 | "# os.makedirs(timestr)\n", 985 | "\n", 986 | "sio.savemat('{}/c_value.mat'.format(timestr), mdict={'c': np.array(c_value)})\n", 987 | "sio.savemat('{}/rho.mat'.format(timestr), mdict={'rho': np.array(rho_curr)})\n", 988 | "sio.savemat('{}/drho.mat'.format(timestr), mdict={'drho': np.array(drho_total_store)})" 989 | ] 990 | }, 991 | { 992 | "cell_type": "code", 993 | "execution_count": null, 994 | "metadata": { 995 | "collapsed": true 996 | }, 997 | "outputs": [], 998 | "source": [ 999 | "phi_value, rho_value = sess.run([phi, rho],feed_dict={learning_rate_fake: learning_rate_fake_value, lamda_lag: lamda_value,lamda_lag2: lamda_value2,r_lag: r_value,\n", 1000 | " r_lag2: r_value2, F_input: F_batch, F: F_sp, learning_rate: starter_learning_rate, beta: beta_value})\n", 1001 | "\n", 1002 | "sio.savemat('result/infill_phi_{}.mat'.format(count), mdict={'phi': phi_value})\n", 1003 | "sio.savemat('result/infill_rho_{}.mat'.format(count), mdict={'rho': rho_value})" 1004 | ] 1005 | }, 1006 | { 1007 | "cell_type": "code", 1008 | "execution_count": null, 1009 | "metadata": { 1010 | "collapsed": true 1011 | }, 1012 | "outputs": [], 1013 | "source": [ 1014 | "'training result'\n", 1015 | "%matplotlib inline\n", 1016 | "fig, axs = plt.subplots(2,5, figsize=(15, 4), facecolor='w', edgecolor='k')\n", 1017 | "fig.subplots_adjust(hspace = .1, wspace=.001)\n", 1018 | "\n", 1019 | "axs = axs.ravel()\n", 1020 | "\n", 1021 | "for i in range(batch_size):\n", 1022 | " axs[i].imshow(1-rho_value[i].reshape([nelx,nely]).T,'gray')\n", 1023 | "# axs[i].set_title(str(250+i))" 1024 | ] 1025 | }, 1026 | { 1027 | "cell_type": "code", 1028 | "execution_count": null, 1029 | "metadata": { 1030 | "collapsed": true 1031 | }, 1032 | "outputs": [], 1033 | "source": [] 1034 | } 1035 | ], 1036 | "metadata": { 1037 | "kernelspec": { 1038 | "display_name": "Python 2", 1039 | "language": "python", 1040 | "name": "python2" 1041 | }, 1042 | "language_info": { 1043 | "codemirror_mode": { 1044 | "name": "ipython", 1045 | "version": 2 1046 | }, 1047 | "file_extension": ".py", 1048 | "mimetype": "text/x-python", 1049 | "name": "python", 1050 | "nbconvert_exporter": "python", 1051 | "pygments_lexer": "ipython2", 1052 | "version": "2.7.13" 1053 | } 1054 | }, 1055 | "nbformat": 4, 1056 | "nbformat_minor": 2 1057 | } 1058 | --------------------------------------------------------------------------------