Dichotomy
Functions are shown in rres, This code makes the algorithm run twice
def asdf(x):
rres=8*x**3-2*x**2-7*x+3
return rres
i=2
left=0
right=1
while i>0 :
i = i-1
ans = 0.1
mid1 = (left + right + ans) / 2
mid2 = (left + right - ans) / 2
a=asdf(mid1)
c=asdf(mid2)
if a > c :
right = mid1
else :
left = mid2
b=(left+right) / 2
print(" Left limit =%s, Right limit =%s, Minimum x=%s"%(left,right,b))Left limit =0.45, Right limit =0.775, Minimum x=0.6125
Harvest ：
This is my first implementation code . After learning the algorithm , The logical framework basically has , The rest that needs to be clear is the corresponding python Language . So I started looking for “ How to define a function ”（ See mofan Youku ）,“ The loop body ” and “if Conditional statements ” The format of （https://blog.csdn.net/qq_39407518/article/details/79822498）“ Mathematical symbols ”（ See mofan Youku ）, as well as print Use
1.def yes python The middle finger defines , Generally used to define functions , If you need deep learning, building a network can be used to define the network . It's worth noting that
return You must add another line after the function .
I don't know why , But if you don't add it , That function formula is a vase , It's like a result can't be lost .
2. The worst thing is logic . At first, the logic was not clear , Or there are omissions in the code , Cause I will left and right Put it in the circulation body , The result is predictable . But it's also because of this mistake , That's true. pycharm Medium debug How to use it? , Pretty simple , Baidu came out at once .
3. I don't know why , Don't bother watching the video print There is no way to output multiple variables together in my pycharm Used in , The result is strange . Maybe it's because I'm win10 No ios Well .print If multiple variables are output together, it must be print(" name ：%s, name 2：%s"%(a,b)) The result output is the name ：a , name 2：b
return It means to output this def The value of any variable in it is displayed as the result . In general , Is the name of the relational expression of the output function , So when you call this function , The function value corresponding to the variable can be displayed , Otherwise, only run without results , It won't work .
Lattice method —— Three point bisection
import numpy as np
def qwer(x):
third = np.exp(x) - 5*x
return third
left = 1
right = 2
mid1 =float(left+right) / 2
mid2 = (left+mid1) / 2
mid3 = (mid1+right) /2
a = qwer(mid1)
b = qwer(mid2)
c = qwer(mid3)
i = 5
while i > 0:
i=i-1
if a > b:
if c > b :
#b
right = mid1
mid1 = mid2
a=b
mid2 = (left + mid1) / 2
mid3 = (mid1 + right) / 2
b = qwer(mid2)
c = qwer(mid3)
else:#b>c
#c
left = mid1
mid1 = mid3
a = c
mid2 = (left + mid1) / 2
mid3 = (mid1 + right) / 2
b = qwer(mid2)
c = qwer(mid3)
else:#b>a
if a > c:
#C
left = mid1
mid1 = mid3
a = c
mid2 = (left + mid1) / 2
mid3 = (mid1 + right) / 2
b = qwer(mid2)
c = qwer(mid3)
else:#b>a&c>a
# a
left = mid2
right = mid3
mid2 = (left + mid1) / 2
mid3 = (mid1 + right) / 2
b = qwer(mid2)
c = qwer(mid3)
print(" minimum value =%s"%mid1)
print(" Function value =%s"%a)minimum value =1.609375 Function value =-3.047189552275773
About python Data variables in . The result of the first run is obviously wrong , So I adopted debug. Results found ,mid1 The place has always been 1 instead of 1.5, So I began to understand the data variables . At first I guessed python All variables are integer by default , But according to the result of dichotomy, I realize that this guess is wrong , So change the whole file The variable format is not necessary . So I was there mid1 A is added to the formula float, The result is 1.5 了 . But if I use the whole equation （） Cover up , Add in front float, The results are 1. I don't quite understand why . But I know python The data format of is determined according to the amount of input , In other words, if your input is an integer , Then the calculation output directly related to it must be integer , And it's still an integer without carry . I didn't use +float/+.0 Before these two methods ,mid1~3 All integers .
left = 1.0 right = 2.0 mid1 =(left+right) / 2
Or no more mid1 Add in front float, Just click a point after the input quantity
I really want to make complaints about it. print, It's so troublesome. I have to get one every time %s, And sometimes it can't be put together ！！！！
Fibonacci Law
def fibonacci(n):
i=0
a = 0
b = 1
for i in range(n):
i=i+1
c = a+b
a = b
b = c
return c
def bn(x):
ert = x**2 - 6*x + 2
return ert
z = 2
p = 0
left = 0.00000
right = 10.00000
L1 = right - left
while z < 100:
m = fibonacci(z)
l = L1/m
k = 1.000/m
if k < 0.03:
print("n=%s,Fn=%s"%(z,m))
L2 = l*fibonacci(z-1)
t = left + L2
r = right -L2
while p < 3:
p = p + 1
l3 = t - r
e= bn(t)
o = bn(r)
if e>o :
right = t
t = r
r = left + l3
else:#o>e
left = r
r = t
t = right - l3
break
else:
z = z + 1
okk=(left+right)/2
okky=bn(okk)
print(left)
print(right)
print(" Minimum x=",okk)
print(" Minimum y=",okky)Don't ask what I have mastered , Ask me how much I love after writing this code now python The precision of the expression :-) I decided that as long as I write the code of mathematical formula in the future, I will fill a lot of small mathematical points after the input amount 0
fibonacci Function definition , Every time debug My hands are shaking after O(∩_∩)O~
The golden section
def gold(x):
gg= x**2 - 6*x + 9
return gg
left = 1
right = 7
ans = 0.4
a = left + 0.618 * (right - left)
b = left + 0.382*(right - left)
gga = gold(a)
ggb = gold(b)
i = 0
while i < 7:
print("i=%s" % i)
print("left=%s,right=%s" % (left, right))
print("x Left =%s,x Right =%s" % (a, b))
print("y Left =%s,y Right =%s" % (ggb, gga))
c = right - left
if c > 0.4:
i = i + 1
if gga > ggb:
right = a
a = b
b = left + 0.382*(right - left)
gga = ggb
ggb = gold(b)
else:#gga<ggb
left = b
b = a
a = left + 0.618 * (right - left)
ggb = gga
gga = gold(a)
else:
breakI don't know when I have OCD , As long as there is “~” I have to eliminate . Smile to cry . This is very simple , The first four except Fibonacci , All very simple. .
def yy(x):
y=x**4-4*x**3-6*x**2-16*x+4
return y
def xing(xm1,xm2,xm3,fm1,fm2,fm3):
yxxx=0.5000*((xm2**2-xm3**2)*fm1+(xm3**2-xm1**2)*fm2+(xm1**2-xm2**2)*fm3)/((xm2-xm3)*fm1+(xm3-xm1)*fm2+(xm1-xm2)*fm3)
return yxxx
x1 = -1.0000
f1 = yy(x1)
x3 = 6
f3 = yy(x3)
x2 = 0.50000*(x1+x3)
f2 = yy(x2)
xp = xing(x1,x2,x3,f1,f2,f3)
fp = yy(xp)
a = abs(xp-x2)
while abs(xp-x2) > 0.05000:
a = abs(xp - x2)
if xp > x2:
if fp > f2:
x3=xp
f3=fp
xp = xing(x1, x2, x3, f1, f2, f3)
fp = yy(xp)
print("ans=%s" % a)
print("left=%s,right=%s" % (x1, x3))
print("x*=%s,fp*=%s" % (xp, fp))
print("x2=%s,f2=%s" % (x2, f2))
print("******************")
else:#f2>fp
x1 = x2
f1 = f2
x2 = xp
f2 = fp
xp = xing(x1, x2, x3, f1, f2, f3)
fp = yy(xp)
print("ans=%s" % a)
print("left=%s,right=%s" % (x1, x3))
print("x*=%s,fp*=%s" % (xp, fp))
print("x2=%s,f2=%s" % (x2, f2))
print("******************")
else:#xp<x2
if fp > f2:
x1 = xp
f1 = fp
xp = xing(x1, x2, x3, f1, f2, f3)
fp = yy(xp)
print("ans=%s" % a)
print("left=%s,right=%s" % (x1, x3))
print("x*=%s,fp*=%s" % (xp, fp))
print("x2=%s,f2=%s" % (x2, f2))
print("******************")
else:
x3 = x2
f3 = f2
x2 = xp
f2 = fp
xp = xing(x1, x2, x3, f1, f2, f3)
fp = yy(xp)
print("ans=%s" % a)
print("left=%s,right=%s" % (x1, x3))
print("x*=%s,fp*=%s" % (xp, fp))
print("x2=%s,f2=%s" % (x2, f2))
print("******************")This formula looks troublesome , Be more careful when writing . Last time I put that 2 Put it under the semicolon , The result is great , So it's still converted to 0.5 Better （PS： Don't forget the long river 0）.
Although the code is very long , But mainly because print Too much . I was going to start with print, The final result will miss the last part . Too lazy to think of another way , Just do it
indirect method —— Newton method
def fd(x):
y = 4*x**3-12*x**2-12*x-16
return y
def fdd(x):
ys = 12*x**2-24*x-12
return ys
i = 1
x0 = 3.00000
ans = 0.001
while i < 7:
fd0 = fd(x0)
fdd0 = fdd(x0)
if abs(fd0) > ans:
x1 = x0 - (fd0/fdd0)
x0 = x1
print(" frequency ：%s, The value obtained x:%s"%(i,x1))
i = i + 1
else:#fd0<0.001
print("$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$")
print("Bingo! Smooth customs clearance ！ I wish you a happy start to school ！")
print("Boss X=%s"%x0)
breakIn limine while Inside < It has been written. >, Lead to run Don't come out . then ,debug It doesn't work . Check it online to find out “ No networking ”+“ No breakpoint selected ”. Finally, I want to try to else Output the content inside , Results found run Later I was swiped . So I changed it to i<7 Not in the future , So I thought of adding one break Out of the loop , It worked .
Then just by debug For a moment , It turned out to be i+1 stay if Inside , Because there's no way +1, therefore i=6 Always exist , It's going to keep cycling . Because plus break Good ,i+1 Good , Fine .
This is the first group I realized by myself python Code , It's a mathematical formula python Language assembled . At the beginning, I know what needs to be reflected in the language , But I'm not sure . So I found some dichotomy on the Internet , They are all different , But the framework is similar , But if you want to use our formula, you need to change a lot . Then I began to analyze our problem , I found that it generally needs two parts , Part of the function definition , Part of the circulatory body . But I don't know how to define functions , How to write mathematical formulas , How to make variables , In other words, some small points are not very good at , So I choose Baidu directly . Because I know my reading ability is good , Compared with extracting features from video , I'm better at getting points through reading . Find knowledge purposefully , Grasp more firmly .
So I started the first —— Preparation of dichotomy . I find , I have made a lot of mistakes, and many places are very basic . But I still didn't choose video , But find these problems directly on Baidu , Because after the video, maybe you didn't find something . Of course , This is a step-by-step process , Instead of just putting the program on it , Change little by little .
With the success of the first two , I found myself confident in these codes , Seems to see through their disguise , Grasp the essence . besides , I also realized that since 8 After the month , Learning ability seems to have improved a lot , And there are more effective learning methods . There has been a certain awakening in all aspects . Except for the first one who found a few wrong codes , Others are written according to their own logic , When the logic comes down , If you don't know how to translate a part of the corresponding language, go to Baidu , In fact, these routines are the same, or the routines of mathematical formula transformation are the same .
I also realized , Assembly is actually the most difficult language , What I have learned so far , Because many need to define themselves , Go to hell , Need to remember a lot of flexible and inflexible instructions . But others just need to write down some corresponding .python It's really easy . and , I find myself opening the door to a new world today , I fell in love with this spiritual thing , Full of rigorous beauty , And the unknown change , I found that I seem to be in love with code . It may not be limited to python, These languages are full of challenges . I think when you're confused , You need to trust your intuition , At least I found it accurate
