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.
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tsb1995
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30abed0c99
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79
app.py
79
app.py
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@ -126,52 +126,53 @@ def maxmin():
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# Setup our symbols for SymPy
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f = setup_symbols(f)
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# Get Derivative, solve for real solutions, update candidates list
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fprime = f.diff(x)
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solutions = list()
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solution = round(f.subs(x,0), 3)
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if lb <= solution <= ub:
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solutions.append(solution)
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candidates = list()
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for solution in solutions:
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candidates.append(solution)
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candidates.append(lb)
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candidates.append(ub)
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# Fill values list with solutions
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values = list()
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for candidate in candidates:
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temp = round(f.subs(x, candidate), 3)
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values.append(temp)
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# Find max/min of values
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maximum = max(values)
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newvar = min(values)
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# Create Graph
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lam_f = lambdify(x, f, 'numpy')
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X = np.linspace(lb, ub, (ub-lb)*10)
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y = lam_f(X)
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# Calculate max/min and store values
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fprime = f.diff(x)
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extremaX = solve(fprime, x)
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extremaY = []
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candidatesX = [lb, ub]
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candidatesY = [lam_f(lb), lam_f(ub)]
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for extrema in extremaX:
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extremaY.append(lam_f(extrema))
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if (lb < extrema < ub):
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candidatesX.append(extrema)
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candidatesY.append(lam_f(extrema))
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max_input = candidatesX[np.argmax(candidatesY)]
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min_input = candidatesX[np.argmin(candidatesY)]
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max_output = max(candidatesY)
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min_output = min(candidatesY)
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# Plot and save figure
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dist = ub-lb
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X = np.linspace(lb, ub, (dist)*100)
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plt.style.use('seaborn-whitegrid')
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plt.scatter(X, y, c='g', marker='.', )
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max_idx = np.argmax(values)
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min_idx = np.argmin(values)
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plt.plot(candidates[max_idx], values[max_idx], c='r', marker='o', ms=10, label='max')
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plt.plot(candidates[min_idx], values[min_idx], c='b', marker='o', ms=10, label='min')
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plt.plot(X, lam_f(X))
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for i in range(2, len(candidatesX)):
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print(candidatesX[i])
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epsilon = dist/6
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templb = int(candidatesX[i] - epsilon)
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tempub = int(candidatesX[i] + epsilon)
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tempX = np.linspace(templb, tempub, epsilon*100)
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line = np.ones(tempX.shape)
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line = line * candidatesY[i]
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plt.plot(tempX, line)
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plt.plot(max_input, max_output, c='r', marker='o', label='Maximum')
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plt.plot(min_input, min_output, c='b', marker='o', label='Minimum')
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plt.legend()
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plt.savefig('static/img/maxmin_plot.png')
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plt.close()
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# Turn all into latex
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value = latex(f)
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f = latex(f)
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fprime = latex(fprime)
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for i, solution in enumerate(solutions):
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solutions[i] = latex(solution)
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return render_template("optimized.html", value=value, fprime=fprime, solutions=solutions, lb=lb, ub=ub,
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candidates=candidates, newvar=newvar, values=values, maximum=maximum,
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url='static/img/maxmin_plot.png')
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return render_template("optimized.html", ub=ub, lb=lb, max_input=max_input,
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max_output=max_output, min_input=min_input, min_output=min_output,
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url='static/img/maxmin_plot.png', candidatesX=candidatesX,
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candidatesY=candidatesY, f=f, fprime=fprime, extremaX=extremaX)
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else:
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return render_template("maxmin.html")
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@ -214,10 +215,11 @@ def aprox():
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dist = abs(a - h)
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X = np.linspace(a-dist-100, a + dist+100, (dist)*1000)
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# Lambdify so we can apply the function to a linspace
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lam_f = lambdify(x, f, 'numpy')
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lam_fprime = lambdify(x, fprime, 'numpy')
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X = np.linspace(a-dist-15, a + dist+15, (dist)*1000)
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y = lam_f(X)
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tan_line = fprimea * (X - a) + fa
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lam_tan_line = lambdify(x, tan_line, "numpy")
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@ -239,6 +241,7 @@ def aprox():
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return render_template("aproxd.html", value=value, fprime=fprime, a=a, h=h, fa=fa, fprimea=fprimea,
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lh=lh, url='static/img/aprox_plot.png')
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else:
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return render_template("aprox.html")
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@ -8,8 +8,8 @@
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<div class="col-sm-12" style="background-color: #0f11175c; padding: 20px">
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<font color="white" size="5">
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<div>
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<p>Your function is $f(x) = {{ value }}$</p>
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<p>Your maximum value is ${{ maximum }}$ and your minimum value is ${{ newvar }}$</p>
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<p>Your function is $f(x) = {{ f }}$</p>
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<p>Your maximum value is ${{ max_output }}$ and your minimum value is ${{ min_output }}$</p>
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</div>
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</font>
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</div>
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@ -36,20 +36,20 @@
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<td>Step 3</td>
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<td>Solve for $x$:</td>
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</tr>
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{% for solution in solutions %}
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{% for extrema in extremaX %}
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<tr class="table-secondary">
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<td></td>
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<td>$x = {{ solution }}$</td>
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<td>$x = {{ extrema }}$</td>
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</tr>
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{% endfor %}
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<tr class="bg-dark text-white">
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<td>Step 4</td>
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<td>Plug solutions and endpoints into $f(x)$:</td>
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<td>Plug VALID solutions and endpoints into $f(x)$:</td>
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</tr>
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{% for candidate in candidates %}
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{% for candidate in candidatesX %}
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<tr class="table-secondary">
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<td></td>
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<td>$f({{ candidate }}) = {{values[loop.index - 1]}}$</td>
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<td>$f({{ candidate }}) = {{candidatesY[loop.index - 1]}}$</td>
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</tr>
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{% endfor %}
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<tr class="bg-dark text-white">
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@ -58,11 +58,11 @@
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</tr>
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<tr class="table-secondary">
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<td></td>
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<td>Your maximum value is ${{ maximum }}$</td>
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<td>Your maximum value is ${{ max_output }}$</td>
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</tr>
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<tr class="table-secondary">
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<td></td>
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<td>Your minimum value is ${{ newvar }}$</td>
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<td>Your minimum value is ${{ min_output }}$</td>
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</tr>
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</tbody>
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</table>
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