ValueError：操作數無法與形狀一起廣播 (3,5) (3,)

Question

我有 15 個 ode 方程需要同時求解，我想使用 solve_ivp 求解它們。

T、co2 和 q 各有 5 個狀態。 初始條件為 T=20, co2 = 0, q=0

我試圖將它們分成 3 個列表，一個用於 T，一個用於 co2，一個用於 q。

我不知道如何解決這個錯誤並且已經研究了幾個小時。 非常感謝您的幫助！

import math
from scipy.integrate import solve_ivp
from bokeh.core.property.instance import Instance
from bokeh.io import save
from bokeh.layouts import column
from bokeh.model import Model
from bokeh.models import CustomJS, Slider, Callback
from bokeh.plotting import ColumnDataSource, figure, show
import numpy as np

# three plots , co2 as y and z as x

###############    User generated - Slider initial value   ############### 
V= 100.0 # volume
r = 5.0
T = 20.0
c_co2_0 = 5.0 # concentration
episl_r = 0.3 # void
v0 = 2.0 # initial vilocity

###############  ---          Static Parameters        ---  ############### 
b0 = 93.0 * (10**(-5))
deltH_0 = 95.3 # calculate b
Tw = -5.0 # room temperature
T0 = 353.15 # temeperature 
t0 = .37 # heterogeneity constant, in paper is denoted as t_h0
alpha = 0.33
chi = 0.0 
q_s0 = 3.40
R = 8.314
kT = 3.5*(10**3) #calculate rA
ρs = 880.0
deltH_co2 = 75.0 # calculate temeprature change 

# ------------------ For Equation 4 : Enegergy Ballance  --------------
ρg = 1.87 # ?
h = 13.8
Cp_g = 37.55 # J/molK
Cp_s = 1580.0 # J/molK

###############   -----  Parameters depend on input  -----  ############### 
L = V / (math.pi * r**2)
deltZ = L / 5.0 # 5 boxes in total
p_co2 = R * T * c_co2_0
a_s = deltZ / r
theta = (1-episl_r) * ρs * Cp_s +  episl_r * ρg * Cp_g

# Equations are calclulated in order 
def b(T):
    b = ( b0 ** ( (deltH_0/ (R * T0) ) * (T0/T - 1) ) )
    return b

def t_h(T):
    return ( t0 + alpha * (1 - T0 / T) )

def q_s(T):
    return ( q_s0 ** ( chi * (1 - T / T0)) )

# Calculate rco2_n (not ode)
# change it to q
def R_co2(T, c_co2, q): 
    b_var = b(T)
    t_var = t_h(T)
    qs_var = q_s(T)
    # print(qs_var)
    r_co2 =  kT * ( R * T * c_co2 * ( (1- ( (q / qs_var)**t_var) )**(1/t_var) ) - q / (b_var*qs_var) ) 
    # print(r_co2)
    return r_co2
# ODE Part 
# Repetitive shortcut

# Equation 2
ener_balan_part1 = v0  * ρg* Cp_g 
def ener_balan(theta, deltZ): # replace v0  * ρg* Cp_g / (theta * deltZ) 
    return(ener_balan_part1/ (theta*deltZ) )
def ener_balan2(episl_r):
    return( (1-episl_r) * ρs * deltH_co2)
def ener_balan3(a_s, Tw, T0):
    return (a_s * h *(Tw-T0))

# Equation 1 Mass Balance : find co2_n

def mass_balan(episl_r, deltZ):
    return ( v0/ (episl_r * deltZ) )
def masss_balan2(episl_r, ρs):
    return( (1-episl_r ) * ρs )
def deriv(t, y):
    T_n, co2_n, q_n = y
    # rco2_ first, rate of generation 
    T1 = -ener_balan(theta, deltZ) * T_n + ener_balan(theta, deltZ) * T0 + ener_balan2(episl_r)* (R_co2(T_n, co2_n, q_n))+ ener_balan3(a_s, Tw, T0)
    co2_1 = -mass_balan(episl_r, deltZ) * co2_n + mass_balan(episl_r, deltZ) * c_co2_0 - (R_co2(T_n, co2_n, q_n)) * masss_balan2(episl_r, ρs)
    q_1 = R_co2(T_n, co2_n, q_n)

    T2 = -ener_balan(theta, deltZ) * T_n + ener_balan(theta, deltZ) * T0 + ener_balan2(episl_r)* (R_co2(T_n, co2_n, q_n))+ ener_balan3(a_s, Tw, T0)
    co2_2 = -mass_balan(episl_r, deltZ) * co2_n + mass_balan(episl_r, deltZ) * c_co2_0 - (R_co2(T_n, co2_n, q_n)) * masss_balan2(episl_r, ρs)
    q_2 = R_co2(T_n, co2_n, q_n)

    T3 = -ener_balan(theta, deltZ) * T_n + ener_balan(theta, deltZ) * T0 + ener_balan2(episl_r)* (R_co2(T_n, co2_n, q_n))+ ener_balan3(a_s, Tw, T0)
    co2_3 = -mass_balan(episl_r, deltZ) * co2_n + mass_balan(episl_r, deltZ) * c_co2_0 - (R_co2(T_n, co2_n, q_n)) * masss_balan2(episl_r, ρs)
    q_3 = R_co2(T_n, co2_n, q_n)

    T4 = -ener_balan(theta, deltZ) * T_n + ener_balan(theta, deltZ) * T0 + ener_balan2(episl_r)* (R_co2(T_n, co2_n, q_n))+ ener_balan3(a_s, Tw, T0)
    co2_4 = -mass_balan(episl_r, deltZ) * co2_n + mass_balan(episl_r, deltZ) * c_co2_0 - (R_co2(T_n, co2_n, q_n)) * masss_balan2(episl_r, ρs)
    q_4 = R_co2(T_n, co2_n, q_n)

    T5 = -ener_balan(theta, deltZ) * T_n + ener_balan(theta, deltZ) * T0 + ener_balan2(episl_r)* (R_co2(T_n, co2_n, q_n))+ ener_balan3(a_s, Tw, T0)
    co2_5 = -mass_balan(episl_r, deltZ) * co2_n + mass_balan(episl_r, deltZ) * c_co2_0 - (R_co2(T_n, co2_n, q_n)) * masss_balan2(episl_r, ρs)
    q_5 = R_co2(T_n, co2_n, q_n)

    T_ls = np.array([T1, T2, T3, T4, T5])
    co2_ls = np.array([co2_1, co2_2, co2_3, co2_4, co2_5])
    q_ls = np.array([q_1, q_2, q_3, q_4, q_5])

    return T_ls, co2_ls, q_ls
    
t0, tf = 0, 10
############# initial condition 
T_initial = 20
c_co2_0 = 0
q0 = 0
init_cond = np.array([20, 0, 0])
N=5
soln = solve_ivp(deriv, (t0, tf), init_cond)

這是錯誤消息

helper.py:293: RuntimeWarning: divide by zero encountered in double_scalars
  r_co2 =  kT * ( R * T * c_co2 * ( (1- ( (q / qs_var)**t_var) )**(1/t_var) ) - q / (b_var*qs_var) )
Traceback (most recent call last):
  File "helper.py", line 350, in <module>
    soln = solve_ivp(deriv, (t0, tf), init_cond)
  File "/Users/cocochen/.local/share/virtualenvs/py-HkKPxrQC/lib/python3.8/site-packages/scipy/integrate/_ivp/ivp.py", line 546, in solve_ivp
    solver = method(fun, t0, y0, tf, vectorized=vectorized, **options)
  File "/Users/cocochen/.local/share/virtualenvs/py-HkKPxrQC/lib/python3.8/site-packages/scipy/integrate/_ivp/rk.py", line 96, in __init__
    self.h_abs = select_initial_step(
  File "/Users/cocochen/.local/share/virtualenvs/py-HkKPxrQC/lib/python3.8/site-packages/scipy/integrate/_ivp/common.py", line 104, in select_initial_step
    d1 = norm(f0 / scale)
ValueError: operands could not be broadcast together with shapes (3,5) (3,) 

Answer 1

當我重新創建確切的錯誤消息時，我給出了一個基於示例的答案。 所以這里的問題是你沒有遵循Numpy 廣播規則。 這基本上說如果數組的尺寸相同或等於 1 ，則可以廣播數組（給定某些操作）。

讓我們看一個帶有錯誤和解決方案的示例：

 import numpy as np array_1 = np.arange(15).reshape(3,5) array_2 = np.arange(3)

array_1的形狀為(3, 5) array_2的形狀為(3,)

如果您嘗試使用以下代碼添加它們（在內部將被廣播）

array_1 + array_2

這將是錯誤

ValueError: operands could not be broadcast together with shapes (3,5) (3,) 

由於我們沒有遵循上述規則。 為了解決這個問題，我們需要像這樣重塑 array_2

array_2 = array_2.reshape(-1,1)

現在，如果您檢查，array_2 形狀是

(3, 1)

現在如果我們嘗試添加兩個數組

array_1 + array_2

它將起作用，因為現在滿足兩個規則，兩個數組都具有維度或維度值為 1（array_2 形狀（3,1））

Answer 2

https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.solve_ivp.html

solve_ivp的fun參數指定為

The calling signature is fun(t, y). Here t is a scalar, and there are two options for the ndarray y: 
It can either have shape (n,); then fun must return array_like with shape (n,).

y是init_cond = np.array([20, 0, 0]) ，形狀 (3,)

這意味着deriv必須返回 (3,) 結果。 什么是

 deriv(0, init_cond)

我不會下載並運行你的代碼，但deriv的結尾是

T_ls = np.array([T1, T2, T3, T4, T5])
co2_ls = np.array([co2_1, co2_2, co2_3, co2_4, co2_5])
q_ls = np.array([q_1, q_2, q_3, q_4, q_5])
return T_ls, co2_ls, q_ls

這將創建 3 個形狀 (5,) 數組，並將它們作為元組返回。 這形成了一個 (3,5) 數組。

我的猜測是錯誤點

norm(f0 / scale)

f0來自試驗func運行，因此是 (3,5)，而scale是 (3,) 從init_cond派生的。

未能閱讀或遵循規范是這些scipy求解功能（也是優化和集成）出現問題的常見原因。