Python实现矩阵基尼系数计算器
最编程
2024-01-19 11:26:40
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为什么要实现矩阵计算器？
答：因为可以带来便利，相当于把matlib中对矩阵的基本操作抽离出来，降低操作门槛，同时也更加灵活*，代码可以自己控制，功能可以自己添加修改。
–参考了pyqt5的example中的calculator。有关矩阵的库主要使用了sympy,参考了大佬的博客：sympy矩阵操作。
计算器样子，丑媳妇早晚要见大大们， 后续我学好了qss和style 再优化它~/滑稽/逃：
言归正传，输入，输出格式举例（转置）：
一些想法：
1.实现计算器之前可以先在https://www.draw.io/上绘制模型，这样布局的时候会更有底气，如：
2.如果想要把他变成exe，先
pip install pyinstaller然后：
pyinstaller -F -w -p /d/software/python3.7.4/lib calc.py-F是生产单个文件，-w是图像界面显示（注意：需要在windows下），-p指出python lib的位置
之后运行会报错，没事不慌，
打开生产的 calc.spec，在第二、三行插入
import sys
sys.setrecursionlimit(5000)最后：
pyinstaller calc.spec就在dist文件夹下生产了calc.exe
矩阵计算器代码：
#!/usr/bin/python3
# -*- encoding_utf-8 -*-
import sys
sys.setrecursionlimit(5000) #为了用pyinstaller生产exe添加
if hasattr(sys, 'frozen'): #为了生产exe添加
os.environ['PATH'] = sys._MEIPASS + ";" + os.environ['PATH']
from PyQt5.QtWidgets import (QToolButton, QFrame, QVBoxLayout, QHBoxLayout, QGridLayout,
QApplication, QTextEdit, QSizePolicy, QLineEdit)
from PyQt5.QtGui import QIntValidator, QTextOption, QTextCursor
from sympy import symbols, Matrix, solve, diff, eye
class Button(QToolButton):
def __init__(self, text, parent=None):
super(Button, self).__init__(parent)
self.setSizePolicy(QSizePolicy.Expanding, QSizePolicy.Preferred)
self.setText(text)
def sizeHint(self):
size = super(Button, self).sizeHint()
size.setHeight(size.height() + 50)
size.setWidth(max(size.width(), size.height()))
return size
class Calc(QFrame):
NumDigitButtons = 10
def __init__(self):
super().__init__()
self.initData()
self.initUI()
self.initConnect()
def initData(self):
pass
def initUI(self):
self.layout = QVBoxLayout()
self.createDisplayBox()
self.createInputBox()
self.setLayout(self.layout)
self.show()
def initConnect(self):
self.input.textChanged.connect(self.cursorChange)
def cursorChange(self):
print('cursorChange')
cursor = self.input.textCursor()
cursor.movePosition(QTextCursor.End)
self.input.setTextCursor(cursor)
def createDisplayBox(self):
layout = QHBoxLayout()
self.input = QTextEdit()
self.output = QTextEdit()
self.output.setReadOnly(True)
self.output.setWordWrapMode(QTextOption.NoWrap)
layout.addWidget(self.input)
layout.addWidget(self.output)
layout.setStretch(1.5, 1)
self.layout.addLayout(layout)
def createInputBox(self):
layout = QGridLayout()
self.digitButtons = []
for i in range(Calc.NumDigitButtons):
self.digitButtons.append(self.createButton(str(i),
self.digitClicked))
self.reverseButton = self.createButton("求逆",
self.reverseOperateClicked)
self.powButton = self.createButton("次方:",
self.powOperatorClicked)
self.powLineEdit = QLineEdit()
self.powLineEdit.setValidator(QIntValidator())
self.transposeButton = self.createButton("转置",
self.transposeOperatorClicked)
self.eigenvectButton = self.createButton("特征向量",
self.eigenvectOperatorClicked)
self.eigenvalButton = self.createButton("特征值",
self.eigenvalOperatorClicked)
self.rankButton = self.createButton("秩",
self.rankOperatorClicked)
self.detButton = self.createButton("行列式",
self.detOperatorClicked)
self.rrefButton = self.createButton("最简型",
self.rrefOperatorClicked)
self.blankSpaceButton = self.createButton(" ",
self.balnkOperatorClicked)
self.EnterButton = self.createButton("Enter",
self.EnterOperatorClicked)
self.clearButton = self.createButton("Clear",
self.clearOperatorClicked)
self.minusButton = self.createButton("-",
self.minuxOperatorClicked)
for i in range(1, Calc.NumDigitButtons):
row = ((9 - i) / 3) + 2
column = ((i - 1) % 3) + 1
layout.addWidget(self.digitButtons[i], row, column)
layout.addWidget(self.digitButtons[0], 5, 1)
layout.addWidget(self.reverseButton, 2, 4)
layout.addWidget(self.powButton, 1, 1)
layout.addWidget(self.powLineEdit,1, 2, 1, 2)
layout.addWidget(self.transposeButton, 1, 4)
layout.addWidget(self.eigenvectButton, 3, 5)
layout.addWidget(self.eigenvalButton, 4, 5)
layout.addWidget(self.rankButton, 3, 4)
layout.addWidget(self.detButton, 1, 5)
layout.addWidget(self.rrefButton, 2, 5)
layout.addWidget(self.blankSpaceButton, 5, 2, 1, 2)
layout.addWidget(self.EnterButton, 4, 4)
layout.addWidget(self.clearButton, 5, 5)
layout.addWidget(self.minusButton, 5, 4)
self.layout.addLayout(layout)
def formateInput(self, inputText):
inputText.strip()
print("inputText", inputText, type(inputText))
inputText += ' \n'
listForMat = list()
templist = list()
currentNum = ''
for char in inputText:
print(char)
if char.isalnum():
currentNum += char
if char == '-':
currentNum += char
if char.isspace():
if currentNum.isalnum() or currentNum[1:].isalnum():
templist.append(int(currentNum))
currentNum = ''
if char == '\n' and len(templist) != 0:
listForMat.append(templist)
templist = []
return listForMat
def formatOutput(self, matrix):
output = ''
row, column = matrix.shape
print(column)
count = 0
for i in matrix:
print(count)
if count % column == 0 and count != 0:
output += '\n'
output += str(i) + ' '
count += 1
return output
def reverseOperateClicked(self):
text = self.input.toPlainText()
print('text :', text)
listForMat = self.formateInput(text)
print(listForMat)
A = Matrix(listForMat)
# 不是方阵或者不满秩 无法求逆
if A.shape[0] != A.shape[1] or A.rank() != A.shape[0]:
self.abortOperation()
return
reverse_A = A ** -1
output = self.formatOutput(reverse_A)
self.output.setPlainText(output)
def abortOperation(self):
self.output.setPlainText("####")
def powOperatorClicked(self):
n = self.powLineEdit.text()
if n.isalnum():
text = self.input.toPlainText()
listForMat = self.formateInput(text)
A = Matrix(listForMat)
# 不是方阵没法求次方
if A.shape[0] != A.shape[1]:
self.abortOperation()
return
output = ''
output_forhuman = ''
eigenvalmap = A.eigenvals()
iseigenvals_int = True
for key in eigenvalmap.keys():
if key % 1 != 0:
print('isinstance(key, int):', key)
iseigenvals_int = False
break
if iseigenvals_int and A.rank() > 1:
try:
answer = pow_Matrix(A, int(n))
A = answer[0]
output_forhuman = str(answer[1])
output = output_forhuman + '\n \n'
except Exception:
A = A ** int(n)
else:
A = A ** int(n)
output += self.formatOutput(A)
self.output.setPlainText(output)
def transposeOperatorClicked(self):
text = self.input.toPlainText()
print('text :', text)
listForMat = self.formateInput(text)
print(listForMat)
A = Matrix(listForMat)
print(A)
A = Matrix(A)
transpose_A = A.T
output = self.formatOutput(transpose_A)
self.output.setPlainText(output)
def eigenvectOperatorClicked(self):
text = self.input.toPlainText()
listForMat = self.formateInput(text)
A = Matrix(listForMat)
# 不是方正没法求特征向量
if A.shape[0] != A.shape[1]:
self.abortOperation()
return
eigenvectList = A.eigenvects()
output = ''
for i in range(len(eigenvectList)):
output += '特征值:' + str(eigenvectList[i][0])
output += ' ,数量:' + str(eigenvectList[i][1])
output += ' ,特征向量: \n'
for j in range(len(eigenvectList[i][2])):# 可能有多个特征向量
output += self.formatOutput(eigenvectList[i][2][j]) + ' '
output += '\n \n'
output += '\n'
self.output.setPlainText(output)
def eigenvalOperatorClicked(self):
text = self.input.toPlainText()
listForMat = self.formateInput(text)
A = Matrix(listForMat)
# 不是方正没法求特征值
if A.shape[0] != A.shape[1]:
self.abortOperation()
return
eigenvalmap = A.eigenvals()
output = ''
for val, num in eigenvalmap.items():
for i in range(num):
output += str(val) + ' '
self.output.setPlainText(output)
def rankOperatorClicked(self):
text = self.input.toPlainText()
listForMat = self.formateInput(text)
A = Matrix(listForMat)
rank = A.rank()
output = str(rank)
self.output.setPlainText(output)
def detOperatorClicked(self):
text = self.input.toPlainText()
listForMat = self.formateInput(text)
A = Matrix(listForMat)
# 不是方正没法求行列式
if A.shape[0] != A.shape[1]:
self.abortOperation()
return
det = A.det()
output = str(det)
self.output.setPlainText(output)
def rrefOperatorClicked(self):
text = self.input.toPlainText()
listForMat = self.formateInput(text)
A = Matrix(listForMat)
rrf_matrix = A.rref()[0]
output = self.formatOutput(rrf_matrix)
self.output.setPlainText(output)
def balnkOperatorClicked(self):
text = self.input.toPlainText()
text += ' '
self.input.setPlainText(text)
def EnterOperatorClicked(self):
text = self.input.toPlainText()
text += '\n'
self.input.setPlainText(text)
def minuxOperatorClicked(self):
text = self.input.toPlainText()
text += '-'
self.input.setPlainText(text)
def clearOperatorClicked(self):
self.output.setPlainText('')
self.input.setPlainText('')
self.powLineEdit.setText('')
def createButton(self, text, member):
button = Button(text)
button.clicked.connect(member)
return button
def digitClicked(self):
clickedButton = self.sender()
digitValue = int(clickedButton.text())
self.input.setPlainText(self.input.toPlainText() + str(digitValue))
def getYuExpression(n):
# 确定特征值后获取余数的表达式
# 次数比特征值次数少1,而range默认如取到倒数第二个
symbolsList = ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k']
expression = symbols(symbolsList[0])
for i in range(1, n):
expression += symbols(symbolsList[i]) * symbols("x") ** (i)
print('expression:', expression)
return expression
def findSame(numlist):
'''
输入特征值图
输出最多的重复次数的数字，和最多重复次数
'''
maxSame = 0
for tzz, same_num in numlist.items():
if maxSame < same_num:
maxSame = same_num
maxSameNum = tzz
return maxSameNum, maxSame
def calEquation(A, expression, tzz, same_num, same_nums):
expressionList = list()
for key in tzz.keys():
expressionList.append(expression.subs('x', key))
for i in range(same_nums - 1):
dify = diff(expression, symbols('x'))
expression = dify
print('dify :', dify)
expressionList.append(dify.subs('x', same_num))
print('expressionList: ', expressionList)
# 用sympy.solve 求解方程组
answers = solve(expressionList)
print('answers', answers)
answerList = list()
human_answerList = list()
# 用列表格式化a,b,c..
for key, value in answers.items():
if key == symbols('a'):
human_answerList.append((key, value))
size = A.rank()
value = value * eye(size)
answerList.append((key, value))
else:
answerList.append((key, value))
human_answerList.append((key, value))
# 列表中添加变量x的值为A
answerList.append((symbols('x'), A))
return (answerList, human_answerList)
def pow_Matrix(A, n): # 老师人赛电脑方法的代码实现
tzz = A.eigenvals() # "返回值为一个字典，特征值：根的重数"
rank = A.rank() # 获得矩阵A的秩
yu_expression = getYuExpression(rank) # 获得余数的表达式
same_num, same_nums = findSame(tzz)
print('same_num:', same_num, ' same_nums:', same_nums)
expression = symbols("x") ** n - yu_expression
print(expression)
# 例如 记录了变量 a,b 的值
result = calEquation(A, expression, tzz, same_num, same_nums)
answerList = result[0]
human_answeList = result[1]
print('answerList :', answerList)
answer = yu_expression.subs(answerList)
print('answer: ', answer)
human_answer = yu_expression.subs(human_answeList)
return (answer, human_answer)
if __name__ == '__main__':
app = QApplication(sys.argv)
calc = Calc()
sys.exit(app.exec_())说下代码中pow_Matrix想法的来源：
如何求矩阵A的100次方？矩阵论老师让我们手算，纳尼(⊙o⊙)？，老师：呵呵一笑我这里有更高级的方法，人脑赛电脑哦！
题目如下：
解法：
代码中的pow_Matrix函数的实现完全就是仿照这一步步下来的。（当特征值是整数的时候，才执行了pow_Matrix，因为特征值奇形怪状的话这种方法会比较飙不动。）
用计算器进行计算：（比正常的A**1000计算多了的第一行和上图答案最后一行的解答是对应的）
上一篇： 理解特征向量是什么
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