問題描述

我似乎在使用浮點(diǎn)數(shù)時失去了很多精度.

I seem to be losing a lot of precision with floats.

例如我需要求解一個矩陣:

For example I need to solve a matrix:

4.0x -2.0y 1.0z =11.0
1.0x +5.0y -3.0z =-6.0
2.0x +2.0y +5.0z =7.0

這是我用來從文本文件中導(dǎo)入矩陣的代碼:

This is the code I use to import the matrix from a text file:

f = open('gauss.dat')
lines =  f.readlines()
f.close()

j=0
for line in lines:
    bits = string.split(line, ',')
    s=[]
    for i in range(len(bits)):
        if (i!= len(bits)-1):
            s.append(float(bits[i]))
            #print s[i]
    b.append(s)
    y.append(float(bits[len(bits)-1]))

我需要使用 gauss-seidel 求解，所以我需要重新排列 x、y 和 z 的方程:

I need to solve using gauss-seidel so I need to rearrange the equations for x, y, and z:

x=(11+2y-1z)/4
y=(-6-x+3z)/5
z=(7-2x-2y)/7

這是我用來重新排列方程式的代碼.b 是系數(shù)矩陣，y 是答案向量:

Here is the code I use to rearrange the equations. b is a matrix of coefficients and y is the answer vector:

def equations(b,y):
    i=0
    eqn=[]
    row=[]
    while(i<len(b)):
        j=0
        row=[]
        while(j<len(b)):
            if(i==j):
                row.append(y[i]/b[i][i])
            else:
                row.append(-b[i][j]/b[i][i])
            j=j+1
        eqn.append(row)
        i=i+1
    return eqn

但是我得到的答案并不精確到小數(shù)位.

However the answers I get back aren't precise to the decimal place.

例如，從上面重新排列第二個等式后，我應(yīng)該得到:

For example, upon rearranging the second equation from above, I should get:

y=-1.2-.2x+.6z

我得到的是:

y=-1.2-0.20000000000000001x+0.59999999999999998z

這似乎不是一個大問題，但是當(dāng)您將數(shù)字提高到非常高的冪時，錯誤會非常大.有沒有解決的辦法?我嘗試了 Decimal 類，但它不適用于冪(即 Decimal(x)**2).

This might not seem like a big issue but when you raise the number to a very high power the error is quite large. Is there a way around this? I tried the Decimal class but it does not work well with powers (i.e, Decimal(x)**2).

有什么想法嗎?

推薦答案

我對 Decimal 類不夠熟悉，無法幫助您解決問題，但您的問題是由于小數(shù)通常無法準(zhǔn)確表示二進(jìn)制，所以你看到的是最接近的近似值；如果不使用特殊類(可能是 Decimal)，就無法避免這個問題.

I'm not familiar enough with the Decimal class to help you out, but your problem is due to the fact that decimal fractions can often not be accurate represented in binary, so what you're seeing is the closest possible approximation; there's no way to avoid this problem without using a special class (like Decimal, probably).

那么小數(shù)類不能正常工作怎么辦?只要我從字符串而不是浮點(diǎn)數(shù)開始，power 似乎就可以正常工作.

What about the decimal class isn't working properly for you? As long as I start with a string, rather than a float, powers seem to work fine.

>>> import decimal
>>> print(decimal.Decimal("1.2") ** 2)
1.44

模塊文檔解釋了 decimal.Decimal 的必要性和用法很清楚，如果你還沒有，你應(yīng)該檢查一下.

The module documentation explains the need for and usage of decimal.Decimal pretty clearly, you should check it out if you haven't yet.

這篇關(guān)于浮點(diǎn)數(shù)和小數(shù)點(diǎn)的小數(shù)位問題.十進(jìn)制的文章就介紹到這了，希望我們推薦的答案對大家有所幫助，也希望大家多多支持html5模板網(wǎng)！