英文:
Constructing vandermonde matrix using for loop
问题
I am trying to create a matrix using a for loop. The goal of the for loop is to construct a Vandermonde matrix using the years 2010 up until 2022.
x = np.arange(2010, 2022, 1)
y = np.array([143335, 141079, 136607, 132865, 129394, 125637, 122645, 121102, 116426, 110234, 97208, 96123])
vandermonde = np.zeros((12, 12))
for i in range(12):
for j in range(12):
vandermonde[i,j] = x[i]**j
print(vandermonde)
print(x[i]**j)
print("end j=", j)
The problem is that at x[0]**3 my loop is giving me -469333592.
The correct answer should be 2010^3 = 8120601000. I think my loop is running correctly since it is filling in the correct spots in the right order, but I can't figure out what is causing this problem.
Any help is greatly appreciated.
Additionally, I made sure that my thinking was correct with the following:
power2010 = np.zeros((12,1))
for i in range(12):
power2010 = 2010**i
print(power2010)
I tried to look at each run through of the nested for loop to see if there were any errors with the way the matrix was being written, but I didn't find any errors. I think I have the correct method of coding as I tested a for loop for a single value, 2010, and calculated exponents 2010^0 up until 2010^11.
英文:
I am trying to create a matrix using a for loop. The goal of the for loop is to construct a Vandermonde matrix using the years 2010 up until 2022.
x = np.arange(2010, 2022, 1)
y = np.array([143335, 141079, 136607, 132865, 129394, 125637, 122645, 121102, 116426, 110234, 97208, 96123])
vandermonde = np.zeros((12, 12))
for i in range(12):
for j in range(12):
vandermonde[i,j] = x[i]**j
print(vandermonde)
print(x[i]**j)
print("end j=", j)
The problem is that at x[0]**3 my loop is giving me -469333592.
The correct answer should be 2010^3 = 8120601000. I think my loop is running correctly since it is filling in the correct spots in the right order, but I can't figure out what is causing this problem.
Any help is greatly appreciated.
Additionally, I made sure that my thinking was correct with the following:
power2010 = np.zeros((12,1))
for i in range(12):
power2010 = 2010**i
print(power2010)
I tried to look at each run through of the nested for loop to see if there were any errors with the way the matrix was being written, but I didn't find any errors. I think I have the correct method of coding as I tested a for loop for a single value, 2010, and calculated exponents 2010^0 up until 2010^11.
答案1
得分: 2
由于溢出，您得到了负数，您可以将数组更改为np.float64：
x = np.arange(2010, 2022, 1, dtype=np.float64) # 将其更改为 np.float64
# 百万吨纸张消耗量
y = np.array([143335, 141079, 136607, 132865, 129394, 125637, 122645, 121102, 116426, 110234, 97208, 96123])
# 初始化范德蒙矩阵
vandermonde = np.zeros((12, 12))
# i 控制行
for i in range(12):
# j 控制列
for j in range(12):
vandermonde[i,j] = x[i]**j
print(vandermonde)
print(x[i]**j)
print("end j=", j)
# 我的代码结束
# 输出
1.0
end j= 0
2010.0
end j= 1
4040100.0
end j= 2
8120601000.0
end j= 3
16322408010000.0
end j= 4
3.28080401001e+16
end j= 5
6.5944160601201e+19
end j= 6
1.3254776280841401e+23
end j= 7
2.6642100324491215e+26
end j= 8
5.3550621652227346e+29
end j= 9
1.0763674952097696e+33
end j= 10
2.163498665371637e+36
end j= 11
1.0
end j= 0
2011.0
end j= 1
4044121.0
end j= 2
8132727331.0
end j= 3
16354914662641.0
end j= 4
3.2889733386571052e+16
end j= 5
6.614125384039439e+19
end j= 6
1.3301006147303311e+23
end j= 7
2.6748323362226958e+26
end j= 8
5.379087828143841e+29
end j= 9
1.0817345622397264e+33
end j= 10
2.1753682046640898e+36
end j= 11
1.0
end j= 0
2012.0
end j= 1
4048144.0
end j= 2
8144865728.0
end j= 3
16387469844736.0
end j= 4
3.297158932760883e+16
end j= 5
6.6338837727148966e+19
end j= 6
1.3347374150702373e+23
end j= 7
2.6854916791213173e+26
end j= 8
5.4032092583920904e+29
end j= 9
1.0871257027884886e+33
end j= 10
2.1872969140104392e+36
end j= 11
1.0
end j= 0
2013.0
end j= 1
4052169.0
end j= 2
8157016197.0
end j= 3
16420073604561.0
end j= 4
3.3053608165981292e+16
end j= 5
6.653691323812034e+19
end j= 6
1.3393880634833625e+23
end j= 7
2.696188171792009e+26
end j= 8
5.427426789817313e+29
end j= 9
1.0925410127902252e+33
end j= 10
2.1992850587467235e+36
end j= 11
1.0
end j= 0
2014.0
end j= 1
4056196.0
end j= 2
8169178744.0
end j= 3
16452725990416.0
end j= 4
3.3135790144697824e+16
end j= 5
6.673548135142142e+19
end j= 6
1.3440525944176274e+23
end j= 7
2.7069219251571014e+26
end j= 8
5.4517407572664026e+29
end j= 9
1.0979805885134534e+33
end j= 10
2.2113329052660953e+36
end j= 11
1.0
end j= 0
2015.0
end j= 1
4060225.0
end j= 2
8181353375.0
end j= 3
16485427050625.0
end j= 4
3.3218135507009376e+16
end j= 5
6.693454304662389e+19
end j= 6
1.3487310423894714e+23
end j= 7
2.717693050414785e+26
end j= 8
5.476151496585791e+29
end j= 9
1.103444526562037e+33
end j= 10
2.2234407210225044e+36
end j= 11
1.0
end j= 0
2016.0
end j= 1
4064256.0
end j= 2
8193540096.0
end j= 3
16518176833536.0
end j= 4
3.3300644496408576e+16
end j= 5
6.713409930475969e+19
end j= 6
1.3534234419839553e+23
end j= 7
2.728501659039654e+26
end j= 8
5.500659344623943e+29
end j= 9
1.1089329238761868e+33
end j= 10
2.2356087745343927e+36
end j= 11
1.0
end j= 0
2017.0
end j= 1
406
<details>
<summary>英文:</summary>
You are getting negative numbers because of the overflow; you can make your array `np.float64`:
x = np.arange(2010, 2022, 1, dtype=np.float64) # change it to np.float64
#million metric tons of paper consumed
y = np.array([143335, 141079, 136607, 132865, 129394, 125637, 122645, 121102, 116426, 110234, 97208, 96123])
#initializing vandermonde matrix
vandermonde = np.zeros((12, 12))
#i controls rows
for i in range(12):
#j controls columns
for j in range(12):
vandermonde[i,j] = x[i]**j
print(vandermonde)
print(x[i]**j)
print("end j=", j)
#end of my code
#output
1.0
end j= 0
2010.0
end j= 1
4040100.0
end j= 2
8120601000.0
end j= 3
16322408010000.0
end j= 4
3.28080401001e+16
end j= 5
6.5944160601201e+19
end j= 6
1.3254776280841401e+23
end j= 7
2.6642100324491215e+26
end j= 8
5.3550621652227346e+29
end j= 9
1.0763674952097696e+33
end j= 10
2.163498665371637e+36
end j= 11
1.0
end j= 0
2011.0
end j= 1
4044121.0
end j= 2
8132727331.0
end j= 3
16354914662641.0
end j= 4
3.2889733386571052e+16
end j= 5
6.614125384039439e+19
end j= 6
1.3301006147303311e+23
end j= 7
2.6748323362226958e+26
end j= 8
5.379087828143841e+29
end j= 9
1.0817345622397264e+33
end j= 10
2.1753682046640898e+36
end j= 11
1.0
end j= 0
2012.0
end j= 1
4048144.0
end j= 2
8144865728.0
end j= 3
16387469844736.0
end j= 4
3.297158932760883e+16
end j= 5
6.6338837727148966e+19
end j= 6
1.3347374150702373e+23
end j= 7
2.6854916791213173e+26
end j= 8
5.4032092583920904e+29
end j= 9
1.0871257027884886e+33
end j= 10
2.1872969140104392e+36
end j= 11
1.0
end j= 0
2013.0
end j= 1
4052169.0
end j= 2
8157016197.0
end j= 3
16420073604561.0
end j= 4
3.3053608165981292e+16
end j= 5
6.653691323812034e+19
end j= 6
1.3393880634833625e+23
end j= 7
2.696188171792009e+26
end j= 8
5.427426789817313e+29
end j= 9
1.0925410127902252e+33
end j= 10
2.1992850587467235e+36
end j= 11
1.0
end j= 0
2014.0
end j= 1
4056196.0
end j= 2
8169178744.0
end j= 3
16452725990416.0
end j= 4
3.3135790144697824e+16
end j= 5
6.673548135142142e+19
end j= 6
1.3440525944176274e+23
end j= 7
2.7069219251571014e+26
end j= 8
5.4517407572664026e+29
end j= 9
1.0979805885134534e+33
end j= 10
2.2113329052660953e+36
end j= 11
1.0
end j= 0
2015.0
end j= 1
4060225.0
end j= 2
8181353375.0
end j= 3
16485427050625.0
end j= 4
3.3218135507009376e+16
end j= 5
6.693454304662389e+19
end j= 6
1.3487310423894714e+23
end j= 7
2.717693050414785e+26
end j= 8
5.476151496585791e+29
end j= 9
1.103444526562037e+33
end j= 10
2.2234407210225044e+36
end j= 11
1.0
end j= 0
2016.0
end j= 1
4064256.0
end j= 2
8193540096.0
end j= 3
16518176833536.0
end j= 4
3.3300644496408576e+16
end j= 5
6.713409930475969e+19
end j= 6
1.3534234419839553e+23
end j= 7
2.728501659039654e+26
end j= 8
5.500659344623943e+29
end j= 9
1.1089329238761868e+33
end j= 10
2.2356087745343927e+36
end j= 11
1.0
end j= 0
2017.0
end j= 1
4068289.0
end j= 2
8205738913.0
end j= 3
16550975387521.0
end j= 4
3.3383317356629856e+16
end j= 5
6.733415110832242e+19
end j= 6
1.3581298278548632e+23
end j= 7
2.7393478627832593e+26
end j= 8
5.5252646392338334e+29
end j= 9
1.1144458777334643e+33
end j= 10
2.2478373353883975e+36
end j= 11
1.0
end j= 0
2018.0
end j= 1
4072324.0
end j= 2
8217949832.0
end j= 3
16583822760976.0
end j= 4
3.346615433164957e+16
end j= 5
6.753469944126883e+19
end j= 6
1.3628502347248049e+23
end j= 7
2.7502317736746564e+26
end j= 8
5.5499677192754564e+29
end j= 9
1.1199834857497871e+33
end j= 10
2.2601266742430705e+36
end j= 11
1.0
end j= 0
2019.0
end j= 1
4076361.0
end j= 2
8230172859.0
end j= 3
16616719002321.0
end j= 4
3.35491556656861e+16
end j= 5
6.7735745289020236e+19
end j= 6
1.3675846973853184e+23
end j= 7
2.7611535040209582e+26
end j= 8
5.5747689246183146e+29
end j= 9
1.1255458458804377e+33
end j= 10
2.2724770628326038e+36
end j= 11
1.0
end j= 0
2020.0
end j= 1
4080400.0
end j= 2
8242408000.0
end j= 3
16649664160000.0
end j= 4
3.36323216032e+16
end j= 5
6.7937289638464e+19
end j= 6
1.3723332506969728e+23
end j= 7
2.772113166407885e+26
end j= 8
5.599668596143928e+29
end j= 9
1.1311330564210734e+33
end j= 10
2.2848887739705682e+36
end j= 11
1.0
end j= 0
2021.0
end j= 1
4084441.0
end j= 2
8254655261.0
end j= 3
16682658282481.0
end j= 4
3.37156523888941e+16
end j= 5
6.813933347795498e+19
end j= 6
1.3770959295894702e+23
end j= 7
2.783110873700319e+26
end j= 8
5.624667075748345e+29
end j= 9
1.1367452160087405e+33
end j= 10
2.2973620815536645e+36
end j= 11
</details>
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