From 23293eb5037abc1fc99a82bdc4184be8681af697 Mon Sep 17 00:00:00 2001 From: tsb1995 <47466105+tsb1995@users.noreply.github.com> Date: Thu, 26 Dec 2019 12:13:31 -0800 Subject: [PATCH] restructured maxmin route and function. Updated optimized.html to work with new variable names. Redid graph of maxmin route. Fixed maxmin route so that it properly discounts values outside of bounds given. --- __pycache__/app.cpython-37.pyc | Bin 6348 -> 6434 bytes app.py | 79 +++++++++++++++++---------------- static/img/aprox_plot.png | Bin 29825 -> 33025 bytes static/img/maxmin_plot.png | Bin 15526 -> 20583 bytes templates/optimized.html | 18 ++++---- 5 files changed, 50 insertions(+), 47 deletions(-) diff --git a/__pycache__/app.cpython-37.pyc b/__pycache__/app.cpython-37.pyc index 396a0e9b3f5847e5e09e1c2f791c6de576e29087..4843a522f0d67ee16aeb6bbbf546ecc6e0cf7818 100644 GIT binary patch delta 1800 zcmY*a&5smC6tC*;>FJs2>79?Bk7ZdIIS6CKRWKyNin@S&2&e(W?g(sp>E5N6>7Ln| z8rU7HGYNCh#1Kj9U`UMF<>FPtU*O#X9*m~_2jHafV7zF2uV+N*q<;0@uikt0s_Iqs z_pd%UXf5RPSpwhB<*Q_zk>>j{Mr zPS&YQZz}f`)|FSXcZS^H8A06aNR3oMwzE95LnDpngvK)?B}%Q4NEcKnYf6+Bs-PnZ zsEjD+#^za(Izg^3L>ZxPo4{vAbca#`_8E<+p%k>>erOBg$Jnnc+|o0@1jUJ%BJMkX&NeO@Sn)=6Z6M+uV?mYcK5jv7tz^18iU zaZQ|rm$$283euW_v=mA<@9>(N=XH@D(UAg)cca3PPm8oDOp_62Wx3W2iHdyJm=nc1 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candidates.append(solution) - candidates.append(lb) - candidates.append(ub) - - # Fill values list with solutions - values = list() - for candidate in candidates: - temp = round(f.subs(x, candidate), 3) - values.append(temp) - - # Find max/min of values - maximum = max(values) - newvar = min(values) - - # Create Graph lam_f = lambdify(x, f, 'numpy') - X = np.linspace(lb, ub, (ub-lb)*10) - y = lam_f(X) + # Calculate max/min and store values + fprime = f.diff(x) + extremaX = solve(fprime, x) + extremaY = [] + candidatesX = [lb, ub] + candidatesY = [lam_f(lb), lam_f(ub)] + for extrema in extremaX: + extremaY.append(lam_f(extrema)) + if (lb < extrema < ub): + candidatesX.append(extrema) + candidatesY.append(lam_f(extrema)) + + max_input = candidatesX[np.argmax(candidatesY)] + min_input = candidatesX[np.argmin(candidatesY)] + + max_output = max(candidatesY) + min_output = min(candidatesY) + + # Plot and save figure + dist = ub-lb + X = np.linspace(lb, ub, (dist)*100) plt.style.use('seaborn-whitegrid') - plt.scatter(X, y, c='g', marker='.', ) - max_idx = np.argmax(values) - min_idx = np.argmin(values) - plt.plot(candidates[max_idx], values[max_idx], c='r', marker='o', ms=10, label='max') - plt.plot(candidates[min_idx], values[min_idx], c='b', marker='o', ms=10, label='min') + plt.plot(X, lam_f(X)) + for i in range(2, len(candidatesX)): + print(candidatesX[i]) + epsilon = dist/6 + templb = int(candidatesX[i] - epsilon) + tempub = int(candidatesX[i] + epsilon) + tempX = np.linspace(templb, tempub, epsilon*100) + line = np.ones(tempX.shape) + line = line * candidatesY[i] + plt.plot(tempX, line) + plt.plot(max_input, max_output, c='r', marker='o', label='Maximum') + plt.plot(min_input, min_output, c='b', marker='o', label='Minimum') plt.legend() plt.savefig('static/img/maxmin_plot.png') plt.close() # Turn all into latex - value = latex(f) + f = latex(f) fprime = latex(fprime) - for i, solution in enumerate(solutions): - solutions[i] = latex(solution) - return render_template("optimized.html", value=value, fprime=fprime, solutions=solutions, lb=lb, ub=ub, - candidates=candidates, newvar=newvar, values=values, maximum=maximum, - url='static/img/maxmin_plot.png') + return render_template("optimized.html", ub=ub, lb=lb, max_input=max_input, + max_output=max_output, min_input=min_input, min_output=min_output, + url='static/img/maxmin_plot.png', candidatesX=candidatesX, + candidatesY=candidatesY, f=f, fprime=fprime, extremaX=extremaX) else: return render_template("maxmin.html") @@ -214,10 +215,11 @@ def aprox(): dist = abs(a - h) X = np.linspace(a-dist-100, a + dist+100, (dist)*1000) + # Lambdify so we can apply the function to a linspace lam_f = lambdify(x, f, 'numpy') lam_fprime = lambdify(x, fprime, 'numpy') + X = np.linspace(a-dist-15, a + dist+15, (dist)*1000) - y = lam_f(X) tan_line = fprimea * (X - a) + fa lam_tan_line = lambdify(x, tan_line, "numpy") @@ -239,6 +241,7 @@ def aprox(): return render_template("aproxd.html", 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-

Your function is $f(x) = {{ value }}$

-

Your maximum value is ${{ maximum }}$ and your minimum value is ${{ newvar }}$

+

Your function is $f(x) = {{ f }}$

+

Your maximum value is ${{ max_output }}$ and your minimum value is ${{ min_output }}$

@@ -36,20 +36,20 @@ Step 3 Solve for $x$: - {% for solution in solutions %} + {% for extrema in extremaX %} - $x = {{ solution }}$ + $x = {{ extrema }}$ {% endfor %} Step 4 - Plug solutions and endpoints into $f(x)$: + Plug VALID solutions and endpoints into $f(x)$: - {% for candidate in candidates %} + {% for candidate in candidatesX %} - $f({{ candidate }}) = {{values[loop.index - 1]}}$ + $f({{ candidate }}) = {{candidatesY[loop.index - 1]}}$ {% endfor %} @@ -58,11 +58,11 @@ - Your maximum value is ${{ maximum }}$ + Your maximum value is ${{ max_output }}$ - Your minimum value is ${{ newvar }}$ + Your minimum value is ${{ min_output }}$