276 lines
9.8 KiB
Python
276 lines
9.8 KiB
Python
from flask import Flask, render_template, request, redirect, Response
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from sympy import *
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from helpers import apology, setup_symbols, gif_apology
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import numpy as np
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import matplotlib
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from matplotlib.patches import Rectangle
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matplotlib.use('Agg')
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from matplotlib import pyplot as plt
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app = Flask(__name__)
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app.config['SEND_FILE_MAX_AGE_DEFAULT'] = 1
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# Convert our commonly used variables into sympy symbols
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x, y, z, t, X, Y, Z, T = symbols('x y z t X Y Z T')
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@app.route('/')
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def hello():
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return render_template('index.html')
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@app.route('/differentiation', methods=['GET', 'POST'])
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def differentiation():
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if request.method == "POST":
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# Check if inputs were given
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if not request.form.get("function"):
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return gif_apology("must provide a function", 400)
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f = request.form.get("function")
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# Setup our symbols for SymPy
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f = setup_symbols(f)
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# Differentiate and return latex expressions
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fprime = latex(f.diff(x))
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value = latex(f)
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return render_template("differentiated.html", value=value, fprime=fprime)
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else:
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return render_template("differentiation.html")
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@app.route("/integration", methods=["GET", "POST"])
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def integration():
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if request.method == "POST":
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# Check if inputs were given
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if not request.form.get("function"):
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return apology("must provide a function", 400)
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f = request.form.get("function")
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# Setup our symbols for SymPy
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f = setup_symbols(f)
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# Integrate and return latex expressions
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fintegral = latex(f.integrate(x))
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value = latex(f)
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return render_template("integrated.html", value=value, fintegral=fintegral)
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else:
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return render_template("integration.html")
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@app.route("/riemann", methods = ["GET", "POST"])
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def riemann():
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if request.method == "POST":
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# Check if inputs were given
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if not request.form.get("function"):
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return apology("must provide a function", 400)
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if not request.form.get("lowerbound"):
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return apology("must provide a lower bound", 400)
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if not request.form.get("upperbound"):
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return apology("must provide an upper bound", 400)
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if not request.form.get("subintervals"):
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return apology("must provide a number of subintervals", 400)
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if not request.form.get("sumtype"):
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return apology("must choose left or right", 400)
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# Get our info from form
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f = request.form.get("function")
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sumtype = request.form.get("sumtype")
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lb = int(request.form.get("lowerbound"))
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ub = int(request.form.get("upperbound"))
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si = int(request.form.get("subintervals"))
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# Setup our symbols for SymPy
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f = setup_symbols(f)
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lam_f = lambdify(x, f, 'numpy')
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# Run through Riemann Sum algorithm, creatings lists for display
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# of inputs, outputs, and areas (their products)
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value = latex(f)
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dx = round((ub - lb) / si, 3)
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inputs = list()
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if sumtype == "1":
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for i in range(0, si):
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inputs.append(round(lb + dx * (i), 3))
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if sumtype == "2":
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for i in range(0, si):
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inputs.append(round(lb + dx * (i + 1), 3))
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outputs = list()
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for input in inputs:
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temp = f.subs(x, input)
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outputs.append(round(temp, 3))
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rectangles = list()
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for output in outputs:
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temp = output * dx
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rectangles.append(round(temp, 3))
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result = round(sum(rectangles), 3)
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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.plot(X, lam_f(X))
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axes = plt.gca()
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for i in range(si):
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rect = Rectangle((inputs[i], 0), width=dx, height=outputs[i],edgecolor='w')
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axes.add_patch(rect)
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axes.set_xlim(lb-dx, ub+2*dx)
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axes.set_ylim(0)
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plt.savefig('static/img/riemann_plot.png')
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plt.close()
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# Choose template based on left or right sum
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if sumtype == "1":
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return render_template("summed.html", value=value, sumtype=sumtype, lb=lb, ub=ub, si=si, dx=dx,
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inputs=inputs, outputs=outputs, rectangles=rectangles, result=result, url='static/img/riemann_plot.png')
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else:
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return render_template("rightSummed.html", value=value, sumtype=sumtype, lb=lb, ub=ub, si=si, dx=dx,
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inputs=inputs, outputs=outputs, rectangles=rectangles, result=result, url='static/img/riemann_plot.png')
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else:
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return render_template("riemann.html")
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@app.route("/maxmin", methods=["GET", "POST"])
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def maxmin():
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if request.method == "POST":
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# Check if inputs were given
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if not request.form.get("function"):
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return apology("must provide a function", 400)
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if not request.form.get("lowerbound"):
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return apology("must provide a lower bound", 400)
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if not request.form.get("upperbound"):
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return apology("must provide an upper bound", 400)
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# Get input from form
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f = request.form.get("function")
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lb = round(sympify(request.form.get("lowerbound")), 3)
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ub = round(sympify(request.form.get("upperbound")), 3)
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# Setup our symbols for SymPy
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f = setup_symbols(f)
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lam_f = lambdify(x, f, 'numpy')
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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.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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f = latex(f)
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fprime = latex(fprime)
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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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@app.route("/aprox", methods=["GET", "POST"])
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def aprox():
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if request.method == "POST":
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# Check if inputs were given
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if not request.form.get("function"):
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return apology("must provide a function", 400)
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if not request.form.get("easy"):
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return apology("must provide an easy value", 400)
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if not request.form.get("hard"):
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return apology("must provide a difficult value", 400)
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# Get inputs, sympify them, and check to see if valid
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f = request.form.get("function")
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a = request.form.get("easy")
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h = request.form.get("hard")
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# Setup our symbols for SymPy
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f = setup_symbols(f)
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# Make sure a and h are numbers
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a = sympify(a)
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h = sympify(h)
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if not a.is_number:
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return apology("easy value must be a number", 400)
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if not h.is_number:
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return apology("difficult value must be a number", 400)
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a = round(a, 3)
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h = round(h, 3)
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# Run through Linearization algorithm
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fprime = f.diff(x)
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fa = round(f.subs(x, a), 3)
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fprimea = round(fprime.subs(x, a), 3)
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lh = round(fa + fprimea*(float(h)-float(a)), 3)
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# Create and Save Plot
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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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tan_line = fprimea * (X - a) + fa
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lam_tan_line = lambdify(x, tan_line, "numpy")
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plt.style.use('seaborn-whitegrid')
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plt.plot(X, lam_f(X), label='Original f(x)')
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plt.plot(X, lam_tan_line(X), label='Tangent Line')
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plt.plot(a, fa, c='r', marker='o', label='Easy Point a')
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plt.plot(h, lh, c='b', marker='o', label='Approximation of f(h)')
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plt.legend()
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plt.savefig('static/img/aprox_plot.png')
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plt.close()
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# Convert to latex for MathJax reading
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value = latex(f)
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fprime = latex(fprime)
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fa = latex(fa)
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lh = latex(lh)
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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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def errorhandler(e):
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"""Handle error"""
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if not isinstance(e, HTTPException):
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e = InternalServerError()
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return apology(e.name, e.code)
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if __name__ == '__main__':
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app.run()
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