“numpy.float64”对象不能解释为整数，但我无法确定它要求整数的位置

Question

运行以下代码时遇到此错误消息'numpy.float64' object cannot be interpreted as an integer：

from scipy.integrate import nquad
from numpy import sqrt, sin, cos, pi, arcsin, maximum, log, log10, exp
from matplotlib.pyplot import xscale, yscale, plot, show, savefig

#define constants
msun=1500
m1=30*msun
m2=30*msun
M=m1+m2
eta=m1*m2/M**2
mSMBH=4.2*10**6*msun
v=5/10**4
pc=3.09*10**16
r0=1.005*10**21              #nfw parameter#
rho0=1.27/10**49             #nfw parameter#
pmtpy=3*10**8*365*24*3600    #rate from per-meter to per-yr
rhoc=1.35*10**(-53)
cm=2.16

#define functions
def g(x):
    return log(1+x)-x/(1+x)
def y(x):
    return 1.43*10**12*1500/x
def sig(x):
    return 13.216*y(x)**0.41/(1+1.102*y(x)**0.2+6.22*y(x)**0.333)
def c(x):
    return 2.881*(1+(sig(x)/1.257)**1.022)*exp(0.06/sig(x)**2)
def r0(x):
    return (3*x/(800*c(x)**3*rhoc*pi))**(1/3)
def rho0(x):
    return 200*rhoc*c(x)**3/3/g(c(x))
def sigma(x):
    return sqrt(4*pi*rho0(x)*r0(x)**2*g(cm)/cm)
def mSMBH(x):
    return 1500*10**(8.15+4.38*log10(1500*sigma(x)))
def rcap(x):
    return 8*mSMBH(x)

def Rsp(x):
    return 0.122*sqrt(mSMBH(x)/rho0(x)/r0(x))
def rhosp(r,x):
    return 3*rho0(x)*r0(x)*Rsp(x)**(4/3)*(1-rcap(x)/r)**3/r**(7/3)

#x,y,z are to be integrated, and m is the x-axis parameter to be searched through using while loop
def v(z,m):
    return sqrt(mSMBH(m)/z)
def vrel(y,z,m):
    return 2*v(z,m)*sin(y/2)
def vcm(y,z,m):
    return 2*v(z,m)*cos(y/2)
def bmin(y,z,m):
    return 2*M/vrel(y,z,m)
def bmax(y,z,m):
    return maximum(bmin(y,z,m), M*(340*eta/(3*cos(1)*vrel(y,z,m)**9))**(1/7))
def a(x,y,z,m):
    if bmax(y,z,m)>bmin(y,z,m):
        return M/(vrel(y,z,m)**2*((bmax(y,z,m)/x)**7-1))
    else:
        return 0
def rt(x,y,z,m):
    return a(x,y,z,m)*(mSMBH(m)/M)**(1/3)
def rd(x,y,z,m):
    return maximum(rcap(m),rt(x,y,z,m))
def rz(x,y,z,m):
    return rd(x,y,z,m)*(sqrt(1+8*mSMBH(m)/(rd(x,y,z,m)*vcm(y,z,m)**2))-1)/2
def thetal(x,y,z,m):
    if rd(x,y,z,m)<z and rz(x,y,z,m)<z:
        return arcsin(rd(x,y,z,m)*sqrt(2*(vcm(y,z,m)**2/2-mSMBH(m)/z+mSMBH(m)/rd(x,y,z,m)))/(vcm(y,z,m)*z))
    else:
        return pi/2

#prepare looping tools    
m=10**9*msun
M=[]           #x value array
Rate=[]        #result estimation array
RateUp=[]      #result upper bound array
RateDown=[]    #result lower bound array
options={'limit':200}

while m<10**14*msun:
    def zbound():
        return [rcap(m),Rsp(m)]
    def ybound(z_foo):
        return [10**(-10),pi-10**(-10)]
    def xbound(y,z):
        return [bmin(y,z,m)-10**(-6),bmax(y,z,m)-10**(-6)]
    def f(x,y,z):
        return pmtpy*8*pi**2*v(z,m)/m1**2*rhosp(z,m)**2*z**2*sin(y/2)**2*cos(y/2)*x*cos(thetal(x,y,z,m))
    ans=nquad(f, [xbound,ybound,zbound],opts=[options,options,options])   
    M.append(m)
    Rate.append(ans[0])
    RateUp.append(ans[0]+ans[1])
    RateDown.append(ans[0]-ans[1])
    m+=10**15

xscale('log')
yscale('log')
plot(M,Rate,M,RateUp,M,RateDown)
show() 

基本上，我试图计算一个依赖于参数m的三重积分，这个错误具体发生在

    File "C:/Users/user/.spyder-py3/temp.py", line 83, in xbound
        return [bmin(y,z,m)-10**(-6),bmax(y,z,m)-10**(-6)]
    File "C:/Users/user/.spyder-py3/temp.py", line 52, in bmax
        return maximum(bmin(y,z,m), M*(340*eta/(3*cos(1)*vrel(y,z,m)**9))**(1/7))

TypeError: 'numpy.float64' object cannot be interpreted as an integer

但我真的不知道为什么我的代码中的'bmax'中需要整数。知道有什么问题吗？非常感谢你的帮助！