解释一下这段程序：yn=1; yn1=0; while 1, yn2=yn1; yn1=yn; yn=1.97*yn1-yn2; end。并画出该表达式的图形、写出代码

这段程序是一个计算差分方程的迭代计算过程，其差分方程为：yn = 1.97 * yn-1 - yn-2，其中y0 = 0，y1 = 1。

具体解释如下：

- 首先定义yn=1和yn1=0作为y0和y1的初始值。
- 进入while循环，计算yn2，yn1和yn的值，并将yn1和yn2的值更新为当前的yn和yn1。
- 不断迭代计算，直到满足while循环条件为止（在这里while 1表示一直循环下去）。

该差分方程的图形为一个振荡的曲线，随着迭代次数的增加，曲线逐渐趋近于稳定状态。以下是该表达式的代码和图形：

yn=1; 
yn1=0; 

for i=1:1000
    yn2=yn1;
    yn1=yn;
    yn=1.97*yn1-yn2; 
end

plot(1:1000, yn)
xlabel('Iteration')
ylabel('yn')


相关问题

while True: yn = input('Continue(y/n): ') if yn in ['n', 'N']: break print('running...')

As an AI language model, I can explain how the above code works.

This is a Python code that uses a while loop with a True condition, which means the loop will keep running until a break statement is encountered.

The first line inside the loop prompts the user to input 'y' or 'n' to continue or break the loop respectively.

The next line checks if the input is 'n' or 'N', in which case the loop is terminated using the break statement.

If the input is anything other than 'n' or 'N', the next line of code is executed, which prints the message 'running...' to the console.

The loop then goes back to the first line and prompts the user to input 'y' or 'n' again.

This code can be used to create a simple program that keeps running until the user decides to exit by entering 'n' or 'N' when prompted.

import pygame from pygame.mixer import music import random class Ball(pygame.sprite.Sprite): def __init__(self,image_file,location,speed): pygame.sprite.Sprite.__init__(self) self.image = pygame.image.load(image_file) self.rect = self.image.get_rect() self.rect.left,self.rect.top = location self.speed = speed def move(self): self.rect = self.rect.move(self.speed) if self.rect.left < 0 or self.rect.right > width: self.speed[0] = -self.speed[0] if self.rect.top < 0 and (self.rect.left < 240 or self.rect.right > 400) : self.speed[1] = -self.speed[1] pygame.init() pygame.mixer.init() # 初始化混音器 clock = pygame.time.Clock() pygame.key.set_repeat(500,50) size = width,height = 640,480 screen = pygame.display.set_mode(size) screen.fill([255,255,255]) ball = Ball("desk_ball.png",[320,240],[10,8]) def new_func(Ball): bat = Ball("bat.png",[320,460],[0,0]) return bat bat = new_func(Ball) goal = Ball("goal.png",[240,0],[0,0]) screen.blit(ball.image,ball.rect) pygame.display.set_caption('乒乓球小游戏') #游戏标题 pygame.display.update() score = 0 lives = 5#总共有5个球 music.load("bg.mp3") # 加载背景音乐 music.play(-1) # 循环播放背景音乐，直到程序退出 done = False running = True while running: for event in pygame.event.get(): if event.type == pygame.QUIT: running = False if event.type == pygame.MOUSEMOTION: bat.rect.centerx = event.pos[0] if event.type == pygame.KEYDOWN: if event.key == pygame.K_y and lives == 0: lives = 5 done = False elif event.key == pygame.K_n and lives == 0: running = False if not done: ball.move() if pygame.sprite.collide_rect(ball,bat): ball.speed[1] = -10 if pygame.sprite.collide_rect(ball,goal): score += 1 ball.speed[1] = 10 screen.blit(ball.image,ball.rect) screen.blit(bat.image,bat.rect) for num in range(lives-1): screen.blit(ball.image,[600-num*40,0]) if ball.rect.bottom > height: lives -= 1 ball.rect.left,ball.rect.top = 320,240 if lives == 0: done = True else: over_font = pygame.font.Font(None,50) over_surf = over_font.render("Game over",1,[255,0,0]) screen.blit(over_surf,[240,240]) yn_font = pygame.font.Font(None,40) yn_surf = yn_font.render("Y:continue N:quit",1,[255,0,0]) screen.blit(yn_surf,[210,280]) score_font = pygame.font.Font(None,40) score_surf = score_font.render("score:"+str(score),1,[255,0,0]) screen.blit(score_surf,[0,0]) screen.blit(goal.image,goal.rect) pygame.display.update() clock.tick(20) screen.fill([255,255,255]) pygame.quit()基于这些代码补充在游戏界面加一条分割线

在代码中添加以下代码可以在游戏界面上添加一条分割线：

# 画一条分割线
pygame.draw.line(screen, [0, 0, 0], [0, 240], [640, 240], 5)

将其添加在`screen.fill([255,255,255])`之后，完整代码如下：

import pygame
from pygame.mixer import music
import random

class Ball(pygame.sprite.Sprite):
    def __init__(self,image_file,location,speed):
        pygame.sprite.Sprite.__init__(self)
        self.image = pygame.image.load(image_file)
        self.rect = self.image.get_rect()
        self.rect.left,self.rect.top = location
        self.speed = speed

    def move(self):
        self.rect = self.rect.move(self.speed)
        if self.rect.left < 0 or self.rect.right > width:
            self.speed[0] = -self.speed[0]
        if self.rect.top < 0 and (self.rect.left < 240 or self.rect.right > 400) :
            self.speed[1] = -self.speed[1]

pygame.init()
pygame.mixer.init() # 初始化混音器
clock = pygame.time.Clock()
pygame.key.set_repeat(500,50)

size = width,height = 640,480
screen = pygame.display.set_mode(size)
screen.fill([255,255,255])

ball = Ball("desk_ball.png",[320,240],[10,8])

def new_func(Ball):
    bat = Ball("bat.png",[320,460],[0,0])
    return bat

bat = new_func(Ball)
goal = Ball("goal.png",[240,0],[0,0])

screen.blit(ball.image,ball.rect)
pygame.display.set_caption('乒乓球小游戏') #游戏标题
pygame.display.update()

score = 0
lives = 5#总共有5个球

music.load("bg.mp3") # 加载背景音乐
music.play(-1) # 循环播放背景音乐，直到程序退出

done = False
running = True
while running:
    for event in pygame.event.get():
        if event.type == pygame.QUIT:
            running = False
        if event.type == pygame.MOUSEMOTION:
            bat.rect.centerx = event.pos[0]
        if event.type == pygame.KEYDOWN:
            if event.key == pygame.K_y and lives == 0:
                lives = 5
                done = False
            elif event.key == pygame.K_n and lives == 0:
                running = False

    if not done:
        ball.move()

        if pygame.sprite.collide_rect(ball,bat):
            ball.speed[1] = -10
        if pygame.sprite.collide_rect(ball,goal):
            score += 1
            ball.speed[1] = 10

        screen.blit(ball.image,ball.rect)
        screen.blit(bat.image,bat.rect)

        for num in range(lives-1):
            screen.blit(ball.image,[600-num*40,0])

        if ball.rect.bottom > height:
            lives -= 1
            ball.rect.left,ball.rect.top = 320,240

        if lives == 0:
            done = True
        else:
            over_font = pygame.font.Font(None,50)
            over_surf = over_font.render("Game over",1,[255,0,0])
            screen.blit(over_surf,[240,240])
            yn_font = pygame.font.Font(None,40)
            yn_surf = yn_font.render("Y:continue N:quit",1,[255,0,0])
            screen.blit(yn_surf,[210,280])
        
        score_font = pygame.font.Font(None,40)
        score_surf = score_font.render("score:"+str(score),1,[255,0,0])
        screen.blit(score_surf,[0,0])

        # 画一条分割线
        pygame.draw.line(screen, [0, 0, 0], [0, 240], [640, 240], 5)

        screen.blit(goal.image,goal.rect)
        pygame.display.update()

        clock.tick(20)
        screen.fill([255,255,255])

pygame.quit()