util.py

import json
import math
import sympy
import sympy.parsing.sympy_parser
from sympy import latex

global X
X = sympy.Symbol('x')


def calcPrecision(ea):
    if ea == 0: return 'Exact'
    if ea >= 0.5: return 0
    return int(-1 * math.log10(2.0 * ea))


def getXCoeff(func, power):
    return func.collect(X).coeff(X ** power)


def mulFunc(func, symbol=None, num=None, func2=None):
    temp = func
    if symbol != None:
        temp = sympy.Mul(temp, sympy.Symbol(symbol))
    if num != None:
        temp = sympy.Mul(temp, sympy.sympify(num))
    if func2 != None:
        temp = sympy.Mul(temp, func2)
    return temp


def addToFunc(func, symbol=None, num=None, func2=None):
    temp = func
    if symbol != None:
        temp = sympy.Add(func, sympy.Symbol(symbol))
    if num != None:
        temp = sympy.Add(func, sympy.sympify(num))
    if func2 != None:
        temp = sympy.Add(temp, func2)
    return temp


def evaluateFunc(f, val):
    return sympy.N(f.subs({X: val}))


def evaluateNthDerivative(f, val, n):
    return sympy.N(sympy.diff(f, X, n).subs({X: val}))


def parseExpr(expr):
    modifiedExpr = ""
    for c in expr.lower().replace('^', '**'):
        if c >= 'a' and c <= 'z':
            if len(modifiedExpr) > 0 and modifiedExpr[-1] >= '0' and modifiedExpr[-1] <= '9':
                modifiedExpr += '*'
            elif len(modifiedExpr) > 0 and (modifiedExpr[-1] == '.' or modifiedExpr[-1] == 'E'):
                modifiedExpr += '*'

            if c == 'e':
                modifiedExpr += "E"
            else:
                modifiedExpr += c
        else:
            modifiedExpr += c

    func = sympy.parsing.sympy_parser.parse_expr(modifiedExpr)
    if len(list(func.free_symbols)) > 1 or (len(list(func.free_symbols)) == 1 and list(func.free_symbols)[0] != X):
        raise ValueError('Invalid variables used in expression')
    return func


def getLineEquation(point1, point2=(), slope=float("nan")):
    if math.isnan(slope):
        slope = (point2[1] - point1[1]) / (point2[0] - point1[0])
    c = point1[1] - slope * point1[0]
    return parseExpr(str(slope) + "x+" + str(c))


def toLatex(equation):
    try:
        return (True, latex(parseExpr(str(equation)), mode='inline'))
    except (SyntaxError, ValueError, UnicodeEncodeError, sympy.parsing.sympy_tokenize.TokenError) as e:
        return (False, equation)


def castJsonToString(data):
    for key in data.keys():
        if type(data[key]) == type({}):
            data[key] = castJsonToString(data[key])
        else:
            data[key] = str(data[key])
    return data


def load(path, mainWindow, optionsWindow):
    with open(path, 'r') as file:
        data = json.load(file)
    data = castJsonToString(data)

    mainWindow.equationField.setText(data['equation'])
    if 'max_iters' in data.keys():
        mainWindow.maxItersField.setText(data['max_iters'])
    if 'eps' in data.keys():
        mainWindow.epsField.setText(data['eps'])

    if 'bisection' in data.keys():
        optionsWindow.bisectionCheckBox.setChecked(True)
        optionsWindow.bisectionXlField.setText(data['bisection']['xl'])
        optionsWindow.bisectionXuField.setText(data['bisection']['xu'])

    if 'false_position' in data.keys():
        optionsWindow.falsePositionCheckBox.setChecked(True)
        optionsWindow.falsePositionXlField.setText(data['false_position']['xl'])
        optionsWindow.falsePositionXlField.setText(data['false_position']['xu'])

    if 'fixed_point' in data.keys():
        optionsWindow.fixedPointCheckBox.setChecked(True)
        optionsWindow.fixedPointX0Field.setText(data['fixed_point']['x0'])

    if 'newton_raphson' in data.keys():
        optionsWindow.newtonRaphsonCheckBox.setChecked(True)
        optionsWindow.newtonRaphsonX0Field.setText(data['newton_raphson']['x0'])

    if 'secant' in data.keys():
        optionsWindow.secantCheckBox.setChecked(True)
        optionsWindow.secantX0Field.setText(data['secant']['x0'])
        optionsWindow.secantX1Field.setText(data['secant']['x1'])

    if 'birge_vieta' in data.keys():
        optionsWindow.birgeVietaCheckBox.setChecked(True)
        optionsWindow.birgeVietaX0Field.setText(data['birge_vieta']['x0'])


def save(path, resultSets):
    data = {}
    for resultSet in resultSets:
        data[resultSet.getTable().getTitle()] = {'Equation': resultSet.getEquation(),
                                                 'Root': resultSet.getRoot(),
                                                 'Number of iterations': resultSet.getNumberOfIterations(),
                                                 'Precision': resultSet.getPrecision(),
                                                 'Execution Time': resultSet.getExecutionTime(),
                                                 'Table': {'Header': resultSet.getTable().getHeader(),
                                                           'Data': resultSet.getTable().getData()}}
    with open(path, 'w') as file:
        json.dump(castJsonToString(data), file, indent=4, sort_keys=True)