IndexError: index out of bounds

Question

我是 Python 的新手，感谢任何建设性的反馈。我的任务是使用 ODEINT 求解 PDE，其中我的空间网格定义如下：

L = [8.0, 4.0, 8.0]   # Lenght of spatial zones 
dN = 1.0e2            # Number of grid points
N = [int(l*dN) for l in L] # Gives number of grid points over each spatial zone

通过使用 ODEINT 函数，我相信我必须为我的解决方案定义一个零数组和一个时间点数组。我正在努力找出如何为数组编写正确的大小。我试过：

dydt = np.zeros(shape=N) # For solution
t = np.linspace(0, 2, 2000) # for time

但这给了我错误信息：

IndexError Traceback（最后一次调用）在（） 70 t = np.linspace(0, 2, lN) 71 ---> 72 U = odeint(数字, y0, t, args=(h, D1, D2, N)) 73 74 退出 = U/Np

/Users/severinlangeberg/anaconda/lib/python3.5/site-packages/scipy/integrate/odepack.py in odeint(func, y0, t, args, Dfun, col_deriv, full_output, ml, mu, rtol , atol, tcrit, h0, hmax, hmin, ixpr, mxstep, mxhnil, mxordn, mxords, printmessg) 213 输出 = _odepack.odeint(func, y0, t, args, Dfun, col_deriv, ml, mu, 214 full_output、rtol、atol、tcrit、h0、hmax、hmin、 --> 215 ixpr、mxstep、mxhnil、mxordn、mxords） 216 如果输出 [-1] < 0: 217 warning_msg = _msgs[output[-1]] + " 运行 with full_output = 1 得到量化信息。"

in numeric(y, t, h, D1, D2, N) 39 40 for i in [N[0] + 1]: # 800 = special 2, 必须从 N[1] 开始 ---> 41 dydt[i] = D2 * (-3*y[i] + 4*y[i + 1] - y[i + 2] / h**2) # pluss 42 43 for i in range (N[0] + 2, N[0] + N[1] - 2): # 从 801 到 1197，或者 2 到 397

IndexError：索引 801 超出尺寸为 800 的轴 0 的范围

Which seems to come from my loops:
# ODE setup
def numeric(y, t, h, D1, D2, N):

    dydt = np.zeros((N))

    # End grid points
    dydt[0] = 0
    dydt[-1] = 0


    # Inner grid points
    for i in range (1, N[0] - 2): # 1 to 797
        dydt[i] = D1 * (y[i - 1] - 2*y[i]+ y[i + 1]) / h**2 # range i = j - 1

    for i in [N[0] - 2]: # 798 = special 1
        dydt[i] =  D1 * (-3*y[i] - 4*y[i - 1] + y[i - 2]) / h**2 # minus

    for i in [N[0] - 1]: # 799 = unknown, and last index in N[0]
        dydt[i] = ((D1*(-3*y[i] + 4*y[i + 1] - y[i + 2])) - (D2*(-3*y[i] - 4*y[i - 1] + y[i - 2])))

    for i in [N[0] + 1]: # 800 = special 2, must be from begining of N[1]
        dydt[i] = D2 * (-3*y[i] + 4*y[i + 1] - y[i + 2] / h**2) # pluss

    for i in range (N[0] + 2, N[0] + N[1] - 2): # from 801 to 1197, or 2 to 397
        dydt[i] = D2 * (y[i - 1] - 2*y[i] + y[i + 1]) / h**2 # range

    for i in [N[0] + N[1] - 1]: # at 1198, or 398 = special 3
        dydt[i] = D2 * (-3*y[i] - 4*y[i - 1] + y[i - 2]) / h**2 # range

    for i in [N[0] + N[1]]: # 1199, or 399 = unknown
        dydt[i] = ((D1*(-3*y[i] + 4*y[i + 1] - y[i + 2])) - (D2*(-3*y[i] - 4*y[i - 1] + y[i - 2])))

    for i in [N[0] + N[1] + 1]: # at 1200, or 1 = special 4
        dydt[i] =  D1 * (-3*y[i + 1] + 4*y[i + 2] - y[i + 3] / h**2)  # pluss

    for i in range (N[0] + N[1] + 2, N[0] + N[1] + N[2] - 1): # 1202 to 1999
        dydt[i] = D1 * (y[i - 1] - 2*y[i]+ y[i + 1]) / h**2 # range

    return dydt

Answer 1

乍一看，问题似乎出在 for 循环上，而不是使用 for i in [N[0]]，您确定不是 for i in range(N[0]) 吗？

for i in [N[0]] 相当多余，因为列表只包含一个元素，即。 N[0]，因此当您尝试查找 dydt[800] <-- 最大索引为 799 时，大小为 800 的列表将超出索引。

像这样：

In [9]: N
Out[9]: [800, 400, 800]

In [10]: for i in [N[0]]:  # ie. i == N[0] == 800
   ....:     dydt[i] = 0
   ....:     
---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
<ipython-input-10-04daa45ec403> in <module>()
      1 for i in [N[0]]:  # ie. i == N[0] == 800
----> 2     dydt[i] = 0
      3 

IndexError: index 800 is out of bounds for axis 0 with size 800

In [11]: for i in range(N[0]):
   ....:     dydt[i] = 0
   ....:

Answer 2

L = [8.0, 4.0, 8.0] 
dN = 1.0e2 
N = [int(l*dN) for l in L] # create array [800, 400, 800] 

dydt = np.zeros(shape=N) # create 3 dimensional matrix 
                         # 1d has size 800 (from 0 to 799 including)
                         # 2d has size 400 (from 0 to 399 including)
                         # 3d same as 1st

在此代码中：

for i in[N[0]]: 
    dydt[i] = 0 # Unknown point

我总是 800 所以它实际上与 dydt[ 800 ] = 0 相同。大于 799.

看来你使用 numpy 数组的方式不对。

是的，在低级别它们表示为连续的整数或浮点数数组。但是在 python 级别 np.array 表示为数组数组。（即 python 中作为 3d 矩阵 mtx = np.zeros(shape=[800,400,800] 的第一个元素将是 mtx[0][0][0]））。

因此 for i in[N[0]]: 之后的所有代码都将无效。它试图访问超出矩阵边界的子数组。

更新：

例如你有 3d 矩阵 (3x3x3)

 mtx=np.zero(shape=[3,3,3])
 print(mtx) 
 #[ [ [ 0.  0.  0.]
 #    [ 0.  0.  0.]
 #    [ 0.  0.  0.] ]

 #  [ [ 0.  0.  0.]
 #    [ 0.  0.  0.]
 #    [ 0.  0.  0.] ]

 #  [ [ 0.  0.  0.]
 #    [ 0.  0.  0.]
 #    [ 0.  0.  0.] ] ]

 mtx[0] = 1 
 print( mtx )
 #[ [ [ 1.  1.  1.]
 #    [ 1.  1.  1.]
 #    [ 1.  1.  1.] ]

 #  [ [ 0.  0.  0.]
 #    [ 0.  0.  0.]
 #    [ 0.  0.  0.] ]

 #  [ [ 0.  0.  0.]
 #    [ 0.  0.  0.]
 #    [ 0.  0.  0.] ] ]

 mtx[0][1] = 2
 #[ [ [ 1.  1.  1.]
 #    [ 2.  2.  2.]
 #    [ 1.  1.  1.] ]

 # others are zeros

 mtx[0][1][2] = 3
 #[ [ [ 1.  1.  1.]
 #    [ 2.  2.  3.]
 #    [ 1.  1.  1.] ]

 # others are zeros

IndexError: index out of bounds

IndexError: index out of bounds

python

arrays

syntax-error

pde

odeint

但这给了我错误信息：