Question

我想找到满足方程式的点（x，y）

A（（x-x0）^ 2）+ 2B（x-x0）（y-y0）+ C（（y-y0）^ 2）= deltachi2

使用python。这是我的代码

import math
deltachi2=2.3 #2.3 for 1-sigma and 6.18 for 2-sigma
A=3.
B=2.
C=1.1
x0=1.5
y0=3.
x_ini=1.
x_fin=2.
y_ini=2.
y_fin=4.
number_of_x_devisions=100
delta_x= float(x_fin-x_ini)/float(number_of_x_devisions)
number_of_y_devisions=100
delta_y= float(math.log10(y_fin)-math.log10(y_ini))/float(number_of_y_devisions)
filename="test.txt"
outfile=open(filename,"w") 

for i in range(number_of_x_devisions+1):
    x_i=x_ini+ i*delta_x

for j in range(number_of_y_devisions+1): 
    y_j=y_ini * pow(10,(delta_y*j))

    XX=A*pow((x_i-x0),2)+2.*B*(x_i-x0)*(y_j-y0)+C*pow((y_j-y0),2)
    if XX==deltachi2:
        outfile.write("%1.12e       %1.12e       %1.12e\n"%(x_i,y_j,XX))


outfile.close()

正如我说的，我需要找到一组点（x，y），它们使等高线图成为1σ和2σ（1-sigam的deltachi2为2.3，而2σ的为6.18）。但是，以上代码给出了空白输出。如何正确找到轮廓？

Answer 1

您的上述代码存在缩进问题； for j循环应嵌套在for i循环内，以扫描两个“维度”。

此外，由于您正在使用浮点数学运算（并且使用朴素网格搜索而不是更好的算法），因此可能找不到确切的解决方案，因此您需要使用epsilon或准确性阈值来找到近似解。

此外，我对您的代码进行了一些重构，以将x_i和y_j值的生成移到生成器函数中，因此问题本身更易于阅读。

import math


def x_gen(x_ini, x_fin, num_div):
    delta_x = float(x_fin - x_ini) / float(num_div)
    for i in range(num_div):
        yield x_ini + i * delta_x


def y_gen(y_ini, y_fin, num_div):
    delta_y = float(math.log10(y_fin) - math.log10(y_ini)) / float(num_div)
    for j in range(num_div + 1):
        yield y_ini * pow(10, (delta_y * j))


EPSILON = .01

deltachi2 = 2.3  # 2.3 for 1-sigma and 6.18 for 2-sigma
A = 3.
B = 2.
C = 1.1
x0 = 1.5
y0 = 3.

for x_i in x_gen(1, 2, 100):
    for y_j in y_gen(2, 4, 100):
        XX = (
            A * pow((x_i - x0), 2)
            + 2. * B * (x_i - x0) * (y_j - y0)
            + C * pow((y_j - y0), 2)
        )
        err = abs(XX - deltachi2)
        if err < EPSILON:
            print((x_i, y_j, XX, err))

此代码打印出了两种可能的解决方案（我也添加了打印错误）：

(1.0, 2.411615655381521, 2.307584439928287, 0.007584439928287168)
(1.01, 2.394957409237857, 2.3088676681935825, 0.008867668193582645)
(1.02, 2.378414230005442, 2.3096504347952513, 0.009650434795251517)
(1.03, 2.3619853228590606, 2.309936594096949, 0.009936594096949136)
(1.04, 2.3456698984637576, 2.309730056780758, 0.009730056780758112)
(1.05, 2.3294671729369116, 2.309034788099698, 0.009034788099698154)
(1.06, 2.3133763678105748, 2.3078548061624873, 0.00785480616248746)
(1.07, 2.29739670999407, 2.3061941802500714, 0.006194180250071568)
(1.08, 2.2815274317368472, 2.3040570291634124, 0.004057029163412551)
(1.09, 2.265767770591597, 2.3014475196020174, 0.0014475196020176107)
(1.1, 2.250116969377619, 2.298369864572757, 0.0016301354272427737)
(1.11, 2.23457427614444, 2.2948283218284615, 0.0051716781715382965)
(1.12, 2.21913894413569, 2.290827192335828, 0.009172807664171945)
(1.18, 2.1140360811227605, 2.304659088270414, 0.00465908827041428)
(1.19, 2.0994333672461347, 2.2971249106473923, 0.002875089352607496)
(1.23, 2.027918959580058, 2.307983227711846, 0.00798322771184612)
(1.24, 2.0139111001134378, 2.2979409062094645, 0.0020590937905353712)
(1.77, 3.9723699817481437, 2.3089132998333692, 0.008913299833369415)
(1.8, 3.9176811903477073, 2.2975700722470327, 0.0024299277529671315)
(1.88, 3.784230586902383, 2.301749866868204, 0.0017498668682041085)
(1.9100000000000001, 3.7321319661472296, 2.2946153619215264, 0.005384638078473447)
(1.99, 3.6050018504433208, 2.3087335898127352, 0.00873358981273542)

如何用两个变量解一个方程

1 个答案: