121 lines
4.0 KiB
Python
121 lines
4.0 KiB
Python
from fractions import Fraction
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import numpy as np
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import scipy as sp
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def solve_equation(eq):
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"""
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配平化学方程式，返回配平后的化学方程式
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:param eq: 化学方程式，
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格式为
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{
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'left': [ {
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'atoms': [ {'元素名称': 元素个数}, {'元素名称': 元素个数}, ... ],
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'coefficient': 系数,
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'pretty_name': 化学式的字符串表示
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}, ... ],
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'right': [ ... ]
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}
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:return: 配平后的化学方程式，与输入格式相同
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若无法配平，则返回 None
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"""
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# 统计所有元素的种类
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elements = set()
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for each in eq['left']:
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for atom in each['atoms']:
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elements.add(list(atom.keys())[0])
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for each in eq['right']:
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for atom in each['atoms']:
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elements.add(list(atom.keys())[0])
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elements = list(elements)
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# 构造系数矩阵
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matrix = []
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constant = []
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for atom in elements:
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# 遍历左边，左侧系数为正
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row = []
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for each in eq['left']:
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for atom_ in each['atoms']:
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if atom in atom_:
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row.append(atom_[atom])
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break
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else:
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row.append(0)
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# 遍历右边，右侧系数为负
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for each in eq['right']:
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for atom_ in each['atoms']:
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if atom in atom_:
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row.append(-atom_[atom])
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break
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else:
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row.append(0)
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# 取出row中的最后一个元素，反转后加入常数项
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constant.append(-row.pop())
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matrix.append(row)
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matrix = np.mat(matrix, int)
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# 求解线性方程组
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try:
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result = np.linalg.solve(matrix, constant).tolist()
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except np.linalg.LinAlgError:
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# 将常数项取负，插入到矩阵的最后一列
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constant = [-x for x in constant]
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matrix = np.insert(matrix, matrix.shape[1], constant, axis=1)
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# 再次尝试求解
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try:
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constant = np.zeros(matrix.shape[0], int)
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result = sp.linalg.solve(matrix, constant).tolist()
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except Exception as e:
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print('无法配平' + str(e))
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return None
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# 将结果写入化学方程式，最后一个生成物的系数需要计算得到
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last_substance = eq['right'][-1]
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last_atom = list(last_substance['atoms'][0].keys())[0]
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# 计算除最后一种生成物外的所有生成物包含last_atom的系数之和
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sum_ = 0
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index = 0
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print(result)
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for each in eq['left']:
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for atom in each['atoms']:
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if last_atom in atom:
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# 该生成物包含last_atom，则获得last_atom的总个数，等于系数*原子个数
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sum_ += result[index] * atom[last_atom]
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break
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index += 1
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for each in eq['right'][:-1]:
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for atom in each['atoms']:
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if last_atom in atom:
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sum_ -= result[index] * atom[last_atom]
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break
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index += 1
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result.append(sum_ / last_substance['atoms'][0][last_atom])
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result = expand_to_int(*result)
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for i, each in enumerate(eq['left']):
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each['coefficient'] = result[i]
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for i, each in enumerate(eq['right']):
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each['coefficient'] = result[i + len(eq['left'])]
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return eq
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def expand_to_int(*args):
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"""
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将一系列小数同时扩大，全部转换为最接近的整数
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:param args: 一系列小数
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:return: 一系列整数
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"""
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# 将所有小数转换为分数
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fractions = []
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for each in args:
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fractions.append(Fraction(each).limit_denominator())
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# 计算所有分数的最小公倍数
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lcm = 1
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for each in fractions:
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lcm = lcm * each.denominator // np.gcd(lcm, each.denominator)
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# 将所有分数扩大为最小公倍数
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result = []
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for each in fractions:
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result.append(each.numerator * lcm // each.denominator)
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return result |