Bisection methodFor details, see rres. This code causes the algorithm to run twice##Related free learning recommendations: python video tutorial
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("左极限=%s,右极限=%s,极小值x=%s"%(left,right,b))
左极限=0.45,右极限=0.775,极小值x=0.6125
This is the first code I implemented. After learning the algorithm, the logical framework is basically there, and the only thing that needs to be clarified is the corresponding python language. So I started looking for "how to define a function" (see mofan's Youku for details), the format of "loop body" and "if conditional statement" (https://blog.csdn.net/qq_39407518/article/details/79822498) "Mathematical symbols" (see mofan's Youku for details), and the use of print
return must be added on a new line after the function.I don’t know why, but if it is not added, the function formula will be like a vase, just like a result that cannot be output. 2. The most confusing thing is logic. The logic was not clear at first, or there was an omission in the code, which led me to put left and right in the loop body. The result is predictable. But it was also because of this error that I knew how to use debug in pycharm. It was quite simple and Baidu came up with it instantly. 3. I don’t know why, but the print multiple variables outputted together in the video I watched cannot be used in my pycharm, and the result is very strange. Maybe it's because I'm on win10 and not ios. print If multiple variables are output together, it must be print("Name: %s, Name 2: %s" % (a, b)). The result output is name: a, Name 2: b Question: 1. Why add return?
return means to output any variable value in this def as the result. Generally speaking, the relational expression of the output function is named so that when you call this function, the function value corresponding to the variable can be displayed. Otherwise, it will only run without results and will have no effect.Grid method - three-point equal division method
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("最小值=%s"%mid1) print("函数值=%s"%a)
最小值=1.609375 函数值=-3.047189552275773
left = 1.0 right = 2.0 mid1 =(left+right) / 2
I really want to complain about print. It’s so troublesome. I have to get %s every time. And sometimes they can’t be put together! ! ! !
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("极小值x=",okk) print("极小值y=",okky)
fibonacci function definition after the small mathematical points of the input amount. Every time after debugging, my hands are shaking O(∩_∩)O~
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左=%s,x右=%s" % (a, b)) print("y左=%s,y右=%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: break
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("******************")
Although the code is very long, it is mainly because there are too many prints. I planned to print it at the beginning, but the final part would be missed. I'm too lazy to think of other methods, so let's just do this
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("次数:%s,所得的值x:%s"%(i,x1)) i = i + 1 else:#fd0<0.001 print("$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$") print("Bingo!顺利通关!祝您开学愉快!") print("Boss X=%s"%x0) break
Then I just debugged and found out that i 1 is in the if. Because there is no way to 1, i=6 always exists, and it keeps looping. Because it doesn’t matter if you add break or i 1, it’s OK.
This is the first set of python codes I implemented by myself, which are mathematical formulas assembled in python language. When I first started, I knew roughly what needed to be reflected in the language, but it was not clear. So I looked for a few dichotomies on the Internet. They are all different, but the framework is similar. However, if we want to use our formula, we need to change a lot. Then I started to analyze our problem, and I found that it generally requires two parts, one part function definition and one part loop body. But I don’t know how to define functions, how to write mathematical formulas, how to make variables, which means I don’t know how to do some small things, so I chose to go directly to Baidu. Because I know I’m a good reader, and I’m better at getting the key points from reading than from extracting them from a video. Find knowledge points with purpose and have a firmer grasp.
So I started writing the first one - the dichotomy. I found that I made a lot of mistakes and a lot of them were very basic. But I still didn’t choose the video. Instead, I looked for these questions directly on Baidu, because you might not have found the point after the video. Of course, this is a step-by-step process, not just putting the program in place and changing it bit by bit.
With the success of the first two, I found that I have confidence in these codes, and it seems that I have seen through their disguise and grasped the essence. In addition, I also realized that my learning ability seems to have improved a lot since August, and I have more effective learning methods. There has been a certain awakening in all aspects. Except for the first one where I found a few erroneous codes, the others were all written according to my own logic. After the logic was understood, if I didn’t know how to translate a certain part of the language, I would just go to Baidu. In fact, these routines are all the same or The routines for transforming mathematical formulas are the same.
I also realized that assembly is actually the most difficult language. What I have learned so far is because many of them need to be defined and figured out by myself. They need to remember a lot of instructions and cannot be flexible. But for others, you just need to write down some corresponding ones. python is really simple. Moreover, I found that I seemed to have opened the door to a new world today. I fell in love with this thing that is full of spirituality, full of rigorous beauty, and the unknown changes. I found that I seemed to fall in love with code. It may not be limited to python, these languages are full of challenges. I think when you are in doubt, you need to trust your intuition, at least I found it to be very accurate
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