I have the following expression and want to group it by powers of the variable e:
from sympy import symbols
e = symbols('e')
expr = (
0.363635891123757*e
+ 1.27444227529689*(0.006290933064*e + 0.526290933064)*(0.12408152*e + 0.12408152)
+ 2.76494336639746*(0.0483917928*e + 1.0483917928)*(0.12408152*e + 0.12408152)
+ 1.27444227529689*(0.12408152*e + 0.12408152)*(
0.012581866128*e
+ 0.39*(0.006290933064*e + 0.526290933064)*(0.12408152*e + 0.12408152)
+ 0.922581866128
)
+ 2.76494336639746*(0.12408152*e + 0.12408152)*(
0.0967835856*e
+ 0.39*(0.0483917928*e + 1.0483917928)*(0.12408152*e + 0.12408152)
+ 1.0967835856
)
+ 1.63807816642065
)
From their descriptions both powsimp and collect should work, however they return the expression unmodified. When I apply simplify then the expression gets simplified as expected. So I'm wondering what other type of transformation gets applied during the call to simplify?
from sympy.simplify import simplify, powsimp, collect
print(f'{powsimp(expr) = }')
print(f'{collect(expr, e) = }')
print(f'{simplify(expr) = }')
This produces the following output:
powsimp(expr) = 0.363635891123757*e + (0.0080174310478246*e + 0.670727414202207)*(0.12408152*e + 0.12408152) + (0.12408152*e + 0.12408152)*(0.13380056649044*e + 2.8987439328879) + (0.158134734671097*e + 0.158134734671097)*(0.012581866128*e + (0.00245346389496*e + 0.20525346389496)*(0.12408152*e + 0.12408152) + 0.922581866128) + (0.343078375616514*e + 0.343078375616514)*(0.0967835856*e + (0.018872799192*e + 0.408872799192)*(0.12408152*e + 0.12408152) + 1.0967835856) + 1.63807816642065
collect(expr, e) = 0.363635891123757*e + (0.0080174310478246*e + 0.670727414202207)*(0.12408152*e + 0.12408152) + (0.12408152*e + 0.12408152)*(0.13380056649044*e + 2.8987439328879) + (0.158134734671097*e + 0.158134734671097)*(0.012581866128*e + (0.00245346389496*e + 0.20525346389496)*(0.12408152*e + 0.12408152) + 0.922581866128) + (0.343078375616514*e + 0.343078375616514)*(0.0967835856*e + (0.018872799192*e + 0.408872799192)*(0.12408152*e + 0.12408152) + 1.0967835856) + 1.63807816642065
simplify(expr) = 0.000851550024540092*e**3 + 0.0759270659579648*e**2 + 1.42522479477876*e + 2.62459155414223
P.S.: For my use case, this expression is part of a larger expression which I cannot transform via simplify because I get the error described here.
$ conda list | grep sympy
sympy 1.8 py39hf3d152e_0 conda-forge
In general you need to use expand before collect although in this case expand is enough:
In [7]: expr.expand()
Out[7]:
3 2
0.000851550024540092⋅e + 0.0759270659579648⋅e + 1.42522479477876⋅e + 2.62459155414223
I'm working on a piece of code that calculates surface wave velocities. When I run this as a single-shot in my Jupyter notebook it works fine, however when I try to start looping over the phi1 angle, I end up with the 'numpy.ndarray is not callable error' after the zero iteration of the loop.
It seems to be focused on the lambda (g) I am using, but I am not sure the best way to go about debugging it. Any help/review would be greatly appreciated as Google searches aren't helping too much.
I do apologize for the novel of code, but this is trimmed down to where it should be easily reproducible.
## This code is an implementation of the framework described by M. Cherry et al. in
## Cherry, Matthew R., Shamachary Sathish, and Ramana Grandhi. "A numerical method for predicting Rayleigh surface wave
## velocity in anisotropic crystals." Journal of Computational Physics 351 (2017): 108-120.
## The logic of this code is as follows.
## (1) It then calculates R, T, and Qv (which is the velocity independent Q, needed to determine the velocity range
## over which to search.
## (2) It then iterates to determine the velocity range by changing a variable called 'angle'.
## (3) It then finds a minimum vL, and solves for Q (with velocity as a term), N, A, B, and Z matrices.
## (4) It stores the three Euler angles (p1, P, p2) and RSW_vel
## This does not deal with pseudowaves yet.
import matplotlib.pyplot as plt
import numpy as np
import scipy as sp
import scipy.optimize as spo
import scipy.linalg as la
from scipy.linalg import eig, eigvals
import math
from decimal import *
import time
ts1 = time.time()
# Setup material properties
# Setup the Cij matrix of Ni (units in Pa)
C11 = C22 = C33 = 2.41e11
C12 = C13 = C23 = C21 = C31 = C32 = 1.47e11
C14 = C15 = C16 = C24 = C25 = C26 = C34 = C35 = C36 = C41 = C42 = C43 = C51 = C52 = C53 = C61 = C62 = C63 = 0
C44 = C55 = C66 = 1.26e11
C45 = C46 = C56 = C54 = C64 = C65 = 0
Cij_list = np.array([C11,C12,C13,C14,C15,C16,C21,C22,C23,C24,C25,C26,C31,C32,C33,C34,C35,C36,C41,C42,C43,C44,C45,C46,C51,C52,C53,C54,C55,C56,C61,C62,C63,C64,C65,C66])
Cij=Cij_list.reshape(6,6)
print('Cij =')
print(Cij)
# Setup density of Ni (units are in kg/m3)
rho = 8910
RSW_matrix = np.array([0,0,0,0])
## This is where the setting up of the loop for p1, P, and p2 should be.
# Setup Euler Angles in Bunge's active notation (one time only - demo, will need to be iterated over), angles in degrees. p1 = phi1, P = Phi, p2 = phi2
#p1 = 15
P = 45
p2 = 8
for rotation in range(0, 180):
## Below this point, everything must be done for every Euler calculation.
p1_rad = np.radians(rotation)
P_rad = np.radians(P)
p2_rad = np.radians(p2)
Eul_Ang_deg = np.array([p1,P,p2])
Eul_Ang_rad = np.array([p1_rad,P_rad,p2_rad])
c1 = np.cos(p1_rad)
c2 = np.cos(P_rad)
c3 = np.cos(p2_rad)
s1 = np.sin(p1_rad)
s2 = np.sin(P_rad)
s3 = np.sin(p2_rad)
# Solve Rotation Matrix from Bunge's active notation, and m and n (m is wave propagation vector, n is plane normal)
Rot_mat = np.array([[c1*c3-c2*s1*s3,-c1*s3-c2*c3*s1,s1*s2],
[c3*s1+c1*c2*s3,c1*c2*c3-s1*s3,-c1*s2],
[s2*s3,c3*s2,c2]]) #- could fill in the rest here and just extract col 1 and col 3
print('Rotation Matrix =')
print(Rot_mat)
m_vec = Rot_mat[[0],:]
m1 = Rot_mat[[0],[0]]
m2 = Rot_mat[[0],[1]]
m3 = Rot_mat[[0],[2]]
n_vec = Rot_mat[[2],:]
n1 = Rot_mat[[2],[0]]
n2 = Rot_mat[[2],[1]]
n3 = Rot_mat[[2],[2]]
# Below, we calculate R, T and Q matrices
# CORRECT R matrix calculations
Rij = np.ndarray(shape=(3,3))
Rij[0,0] = C11*m1*n1 + C61*m2*n1 + C51*m3*n1 + C16*m1*n2 + C66*m2*n2 + C56*m3*n2 + C15*m1*n3 + C65*m2*n3 + C55*m3*n3
Rij[0,1] = C16*m1*n1 + C66*m2*n1 + C56*m3*n1 + C12*m1*n2 + C62*m2*n2 + C52*m3*n2 + C14*m1*n3 + C64*m2*n3 + C54*m3*n3
Rij[0,2] = C15*m1*n1 + C65*m2*n1 + C55*m3*n1 + C14*m1*n2 + C64*m2*n2 + C54*m3*n2 + C13*m1*n3 + C63*m2*n3 + C53*m3*n3
Rij[1,0] = C61*m1*n1 + C21*m2*n1 + C41*m3*n1 + C66*m1*n2 + C26*m2*n2 + C46*m3*n2 + C65*m1*n3 + C25*m2*n3 + C45*m3*n3
Rij[1,1] = C66*m1*n1 + C26*m2*n1 + C46*m3*n1 + C62*m1*n2 + C22*m2*n2 + C42*m3*n2 + C64*m1*n3 + C24*m2*n3 + C44*m3*n3
Rij[1,2] = C65*m1*n1 + C25*m2*n1 + C45*m3*n1 + C64*m1*n2 + C24*m2*n2 + C44*m3*n2 + C63*m1*n3 + C23*m2*n3 + C43*m3*n3
Rij[2,0] = C51*m1*n1 + C41*m2*n1 + C31*m3*n1 + C56*m1*n2 + C46*m2*n2 + C36*m3*n2 + C55*m1*n3 + C45*m2*n3 + C35*m3*n3
Rij[2,1] = C56*m1*n1 + C46*m2*n1 + C36*m3*n1 + C52*m1*n2 + C42*m2*n2 + C32*m3*n2 + C54*m1*n3 + C44*m2*n3 + C34*m3*n3
Rij[2,2] = C55*m1*n1 + C45*m2*n1 + C35*m3*n1 + C54*m1*n2 + C44*m2*n2 + C34*m3*n2 + C53*m1*n3 + C43*m2*n3 + C33*m3*n3
Rij_trans = np.transpose(Rij)
Rij_inv = np.linalg.inv(Rij)
# CORRECT T matrix calculations
Tij = np.ndarray(shape=(3,3))
Tij[0,0] = C11*n1*n1 + C16*n2*n1 + C51*n3*n1 + C16*n1*n2 + C66*n2*n2 + C56*n3*n2 + C15*n1*n3 + C65*n2*n3 + C55*n3*n3
Tij[0,1] = C16*n1*n1 + C66*n2*n1 + C56*n3*n1 + C12*n1*n2 + C62*n2*n2 + C52*n3*n2 + C14*n1*n3 + C64*n2*n3 + C54*n3*n3
Tij[0,2] = C15*n1*n1 + C65*n2*n1 + C55*n3*n1 + C14*n1*n2 + C64*n2*n2 + C54*n3*n2 + C13*n1*n3 + C63*n2*n3 + C53*n3*n3
Tij[1,0] = C61*n1*n1 + C21*n2*n1 + C41*n3*n1 + C66*n1*n2 + C26*n2*n2 + C46*n3*n2 + C65*n1*n3 + C25*n2*n3 + C45*n3*n3
Tij[1,1] = C66*n1*n1 + C26*n2*n1 + C46*n3*n1 + C62*n1*n2 + C22*n2*n2 + C42*n3*n2 + C64*n1*n3 + C24*n2*n3 + C44*n3*n3
Tij[1,2] = C65*n1*n1 + C25*n2*n1 + C45*n3*n1 + C64*n1*n2 + C24*n2*n2 + C44*n3*n2 + C63*n1*n3 + C23*n2*n3 + C43*n3*n3
Tij[2,0] = C51*n1*n1 + C41*n2*n1 + C31*n3*n1 + C56*n1*n2 + C46*n2*n2 + C36*n3*n2 + C55*n1*n3 + C45*n2*n3 + C35*n3*n3
Tij[2,1] = C56*n1*n1 + C46*n2*n1 + C36*n3*n1 + C52*n1*n2 + C42*n2*n2 + C32*n3*n2 + C54*n1*n3 + C44*n2*n3 + C34*n3*n3
Tij[2,2] = C55*n1*n1 + C45*n2*n1 + C35*n3*n1 + C54*n1*n2 + C44*n2*n2 + C34*n3*n2 + C53*n1*n3 + C43*n2*n3 + C33*n3*n3
Tij_trans = np.transpose(Tij)
Tij_inv = np.linalg.inv(Tij)
## R and T defined as above. Q needs to be new - and not remove the rv2. Thus, we introduce Qv for "Q to determine
## critical velocity"
Qv = np.ndarray(shape=(3,3))
Qv[0,0] = C11*m1*m1 + C61*m2*m1 + C51*m3*m1 + C16*m1*m2 + C66*m2*m2 + C56*m3*m2 + C15*m1*m3 + C65*m2*m3 + C55*m3*m3
Qv[0,1] = C16*m1*m1 + C66*m2*m1 + C56*m3*m1 + C12*m1*m2 + C62*m2*m2 + C52*m3*m2 + C14*m1*m3 + C64*m2*m3 + C54*m3*m3
Qv[0,2] = C15*m1*m1 + C65*m2*m1 + C55*m3*m1 + C14*m1*m2 + C64*m2*m2 + C54*m3*m2 + C13*m1*m3 + C63*m2*m3 + C53*m3*m3
Qv[1,0] = C61*m1*m1 + C21*m2*m1 + C41*m3*m1 + C66*m1*m2 + C26*m2*m2 + C46*m3*m2 + C65*m1*m3 + C25*m2*m3 + C45*m3*m3
Qv[1,1] = C66*m1*m1 + C26*m2*m1 + C46*m3*m1 + C62*m1*m2 + C22*m2*m2 + C42*m3*m2 + C64*m1*m3 + C24*m2*m3 + C44*m3*m3
Qv[1,2] = C65*m1*m1 + C25*m2*m1 + C45*m3*m1 + C64*m1*m2 + C24*m2*m2 + C44*m3*m2 + C63*m1*m3 + C23*m2*m3 + C43*m3*m3
Qv[2,0] = C51*m1*m1 + C41*m2*m1 + C31*m3*m1 + C56*m1*m2 + C46*m2*m2 + C36*m3*m2 + C55*m1*m3 + C45*m2*m3 + C35*m3*m3
Qv[2,1] = C56*m1*m1 + C46*m2*m1 + C36*m3*m1 + C52*m1*m2 + C42*m2*m2 + C32*m3*m2 + C54*m1*m3 + C44*m2*m3 + C34*m3*m3
Qv[2,2] = C55*m1*m1 + C45*m2*m1 + C35*m3*m1 + C54*m1*m2 + C44*m2*m2 + C34*m3*m2 + C53*m1*m3 + C43*m2*m3 + C33*m3*m3
res = []
res = spo.minimize_scalar(lambda x: ((min(eigvals(Qv * np.cos(np.radians(x)) * np.cos(np.radians(x)) + (Rij + Rij_trans) * np.cos(np.radians(x)) * np.sin(np.radians(x)) + Tij * np.sin(np.radians(x)) * np.sin(np.radians(x)))) / rho)**(0.5))*(1/(np.abs(np.cos(np.radians(x))))), bracket=(-90,0,90), method='Golden')
vel_L = res.fun.real
vel_L_int = int(vel_L)
print('velocity limit')
print(vel_L)
print(vel_L_int)
Det_B_try = 1
Qij = np.zeros(shape=(3,3))
Qij[0,1] = C16*m1*m1 + C66*m2*m1 + C56*m3*m1 + C12*m1*m2 + C62*m2*m2 + C52*m3*m2 + C14*m1*m3 + C64*m2*m3 + C54*m3*m3
Qij[0,2] = C15*m1*m1 + C65*m2*m1 + C55*m3*m1 + C14*m1*m2 + C64*m2*m2 + C54*m3*m2 + C13*m1*m3 + C63*m2*m3 + C53*m3*m3
Qij[1,0] = C61*m1*m1 + C21*m2*m1 + C41*m3*m1 + C66*m1*m2 + C26*m2*m2 + C46*m3*m2 + C65*m1*m3 + C25*m2*m3 + C45*m3*m3
Qij[1,2] = C65*m1*m1 + C25*m2*m1 + C45*m3*m1 + C64*m1*m2 + C24*m2*m2 + C44*m3*m2 + C63*m1*m3 + C23*m2*m3 + C43*m3*m3
Qij[2,0] = C51*m1*m1 + C41*m2*m1 + C31*m3*m1 + C56*m1*m2 + C46*m2*m2 + C36*m3*m2 + C55*m1*m3 + C45*m2*m3 + C35*m3*m3
Qij[2,1] = C56*m1*m1 + C46*m2*m1 + C36*m3*m1 + C52*m1*m2 + C42*m2*m2 + C32*m3*m2 + C54*m1*m3 + C44*m2*m3 + C34*m3*m3
for v in range(1, vel_L_int):
# Calculate rho vel-squared
rv2 = rho * v ** 2
# CORRECT Q matrix calculations
Qij[0,0] = C11*m1*m1 + C61*m2*m1 + C51*m3*m1 + C16*m1*m2 + C66*m2*m2 + C56*m3*m2 + C15*m1*m3 + C65*m2*m3 + C55*m3*m3 - rv2
Qij[1,1] = C66*m1*m1 + C26*m2*m1 + C46*m3*m1 + C62*m1*m2 + C22*m2*m2 + C42*m3*m2 + C64*m1*m3 + C24*m2*m3 + C44*m3*m3 - rv2
Qij[2,2] = C55*m1*m1 + C45*m2*m1 + C35*m3*m1 + C54*m1*m2 + C44*m2*m2 + C34*m3*m2 + C53*m1*m3 + C43*m2*m3 + C33*m3*m3 - rv2
Qij_trans = np.transpose(Qij)
Qij_inv = np.linalg.inv(Qij)
# Create a new Nik matrix
TR_ik = -1*np.matmul(Tij_inv, Rij_trans)
TI_ik = Tij_inv
QRTR_ik = -Qij + np.matmul(np.matmul(Rij, Tij_inv), Rij_trans)
RT_ik = -1*np.matmul(Rij, Tij_inv)
# Nik Creation
Nik_r1to3 = np.concatenate((TR_ik,TI_ik),axis=1)
Nik_r4to6 = np.concatenate((QRTR_ik,RT_ik),axis=1)
Nik_whole = np.concatenate((Nik_r1to3,Nik_r4to6))
# Eigenvalues and Eigenvectors of Nik
eigvals, eigvecs = eig(Nik_whole)
## The following code sorts the eigenvalues for those with negative imaginary numbers, and conducts the matrix
## operations to generate the B, A, and Z matrices from the COLUMNS in Pythons representation of eigenvectors
eigvecsT = np.transpose(eigvecs)
output_ab = output_ab_neg_imag = eigvecsT[eigvals.imag < 0]
output_abT = np.transpose(output_ab)
### This is the B matrix (bottom 3 vectors assumed as b)
B_matrix = output_b = np.delete(output_abT, [0,1,2], axis=0)
B_matrixT = np.transpose(B_matrix)
### This is the A matrix (these are the displacement vectors, and when A is combined with B, the surface impedance (Z) matrix can be found)
A_matrix = output_a = np.delete(output_abT, [3,4,5], axis=0)
det_B = np.linalg.det(B_matrix)
det_cc_B = det_B.conjugate()
det_B_x_det_cc_B = det_B*det_cc_B
v_real = v.real
det_B_x_det_cc_B_real = det_B_x_det_cc_B.real
if det_B_x_det_cc_B_real < Det_B_try:
RSW_vel = v_real
Det_B_try = det_B_x_det_cc_B_real
print('RSW =')
print(RSW_vel)
print('Min |B|x|B|* =')
print(Det_B_try)
col_to_be_added2 = np.array([p1, P, p2, RSW_vel])
RSW_matrix = np.column_stack((RSW_matrix,col_to_be_added2))
print('RSW vel matrix is')
print(RSW_matrix)
Now i m trying to solve 6th order of nonlinear equations.
For solving this problem, 'fsolve' is the best module for my situation.
But i have a problem for using this 'fsolve'.
My Equations below : eq1, eq2, eq3, eq4, eq5, eq6
U = (E*h/32)*(pi**4*K3+8*pi**2*K4+16*J2-pi**4/b*K1**2-8*pi**2/b*K1*J1)+pi**2/2*D*((K1*K2)**0.5+(1-v)*K5-v*K6)+F/(4*b)*pi**2*K1
eq1 = diff(U,b_1)
eq2 = diff(U,b_2)
eq3 = diff(U,b_3)
eq4 = diff(U,b_4)
eq5 = diff(U,b_5)
eq6 = diff(U,b_6)
Now i m gonna try to define functions:
def functions(v):
b_1 = v[0]
b_2 = v[1]
b_3 = v[2]
b_4 = v[3]
b_5 = v[4]
b_6 = v[5]
return eq1,eq2,eq3,eq4,eq5,eq6
Until now, all of code is perfectly completed.
But next, I got a error code for 'fsolve'
x0 = [0.1,0.1,0.1,0.1,0.1,0.1]
solutions = fsolve(functions,x0)
Traceback (most recent call last):
File "C:\Users\user\AppData\Roaming\Python\Python37\site-packages\sympy\core\expr.py", line 327, in __float__
raise TypeError("can't convert expression to float")
TypeError: can't convert expression to float
Traceback (most recent call last):
File "C:\Users\user\Desktop\-----\trial.py", line 97, in <module>
solutions = fsolve(functions,x0)
File "C:\Users\user\anaconda3\lib\site-packages\scipy\optimize\minpack.py", line 147, in fsolve
res = _root_hybr(func, x0, args, jac=fprime, **options)
File "C:\Users\user\anaconda3\lib\site-packages\scipy\optimize\minpack.py", line 225, in _root_hybr
ml, mu, epsfcn, factor, diag)
error: Result from function call is not a proper array of floats.
Actually i don't know exactly meaning about 'array of floats'.
The eq1~eq6 is really complicated expressions. For example (eq1):
519749583.393768*b_1**3 + 519749583.393768*b_1**2*b_2 + 311849750.036261*b_1**2*b_3 + 222749821.454472*b_1**2*b_4 + 173249861.131256*b_1**2*b_5 + 141749886.380119*b_1**2*b_6 + 589049527.846271*b_1*b_2**2 + 920699262.011818*b_1*b_2*b_3 + 742499404.84824*b_1*b_2*b_4 + 619499503.439037*b_1*b_2*b_5 + 530653420.807624*b_1*b_2*b_6 + 395009683.379264*b_1*b_3**2 + 672299461.117134*b_1*b_3*b_4 + 581053380.409443*b_1*b_3*b_5 + 510299590.968427*b_1*b_3*b_6 + 296183828.527375*b_1*b_4**2 + 524699579.42609*b_1*b_4*b_5 + 469323153.224931*b_1*b_4*b_6 + 236661575.009363*b_1*b_5**2 + 429394392.660243*b_1*b_5*b_6 + 196977114.839905*b_1*b_6**2 + 39642.9110110422*b_1 + 193049845.260542*b_2**3 + 482129613.548124*b_2**2*b_3 + 406949673.808743*b_2**2*b_4 + 350618949.729969*b_2**2*b_5 + 307488215.070719*b_2**2*b_6 + 420149663.228267*b_2*b_3**2 + 732095017.5835*b_2*b_3*b_4 + 645437944.186494*b_2*b_3*b_5 + 575987321.121736*b_2*b_3*b_6 + 326318969.207663*b_2*b_4**2 + 585464236.60242*b_2*b_4*b_5 + 529609601.687166*b_2*b_4*b_6 + 266189415.118358*b_2*b_5**2 + 486862510.0121*b_2*b_5*b_6 + 224616040.694387*b_2*b_6**2 - 29192.3833775011*b_2 + 125272976.510293*b_3**3 + 334349732.001359*b_3**2*b_4 + 299655189.675087*b_3**2*b_5 + 270932940.727941*b_3**2*b_6 + 302393649.018531*b_3*b_4**2 + 549176644.826696*b_3*b_4*b_5 + 501838635.183477*b_3*b_4*b_6 + 252001834.206563*b_3*b_5**2 + 464613445.578031*b_3*b_5*b_6 + 215729827.081362*b_3*b_6**2 - 28558.195613361*b_3 + 92286363.2746599*b_4**3 + 253972873.350655*b_4**2*b_5 + 234063996.922265*b_4**2*b_6 + 234970783.525745*b_4*b_5**2 + 436229928.976872*b_4*b_5*b_6 + 203716223.26551*b_4*b_6**2 - 24903.5955817128*b_4 + 72968765.0411644*b_5**3 + 204424758.743579*b_5**2*b_6 + 191897759.069662*b_5*b_6**2 - 21706.6337724143*b_5 + 60314467.7838601*b_6**3 - 19178.52782655*b_6 + 52.9828871992195*((35.720610813872*b_2**2 + 142.882443255488*b_2*b_3 + 214.323664883232*b_2*b_4 + 285.764886510976*b_2*b_5 + 357.20610813872*b_2*b_6 + 257.188397859878*b_3**2 + 918.529992356708*b_3*b_4 + 1333.56947038455*b_3*b_5 + 1753.55725813553*b_3*b_6 + 893.0152703468*b_4**2 + 2727.7557348775*b_4*b_5 + 3709.44804605594*b_4*b_6 + 2154.22760600582*b_5**2 + 6001.0626167305*b_5*b_6 + 4254.9551116524*b_6**2)*(0.482*b_1**2 + 0.321333333333333*b_1*b_2 + 0.1928*b_1*b_3 + 0.137714285714286*b_1*b_4 + 0.107111111111111*b_1*b_5 + 0.0876363636363637*b_1*b_6 + 0.0964*b_2**2 + 0.137714285714286*b_2*b_3 + 0.107111111111111*b_2*b_4 + 0.0876363636363637*b_2*b_5 + 0.0741538461538462*b_2*b_6 + 0.0535555555555556*b_3**2 + 0.0876363636363637*b_3*b_4 + 0.0741538461538462*b_3*b_5 + 0.0642666666666667*b_3*b_6 + 0.0370769230769231*b_4**2 + 0.0642666666666667*b_4*b_5 + 0.0567058823529412*b_4*b_6 + 0.0283529411764706*b_5**2 + 0.0507368421052632*b_5*b_6 + 0.022952380952381*b_6**2))**0.5*(0.964*b_1 + 0.321333333333333*b_2 + 0.1928*b_3 + 0.137714285714286*b_4 + 0.107111111111111*b_5 + 0.0876363636363637*b_6)/(0.482*b_1**2 + 0.321333333333333*b_1*b_2 + 0.1928*b_1*b_3 + 0.137714285714286*b_1*b_4 + 0.107111111111111*b_1*b_5 + 0.0876363636363637*b_1*b_6 + 0.0964*b_2**2 + 0.137714285714286*b_2*b_3 + 0.107111111111111*b_2*b_4 + 0.0876363636363637*b_2*b_5 + 0.0741538461538462*b_2*b_6 + 0.0535555555555556*b_3**2 + 0.0876363636363637*b_3*b_4 + 0.0741538461538462*b_3*b_5 + 0.0642666666666667*b_3*b_6 + 0.0370769230769231*b_4**2 + 0.0642666666666667*b_4*b_5 + 0.0567058823529412*b_4*b_6 + 0.0283529411764706*b_5**2 + 0.0507368421052632*b_5*b_6 + 0.022952380952381*b_6**2) + (-1.28102213260338e-7*b_2 - 3.20255533150846e-8*b_3 - 3.20255533150846e-8*b_4 - 1.60127766575423e-8*b_6)*(0.482*b_1**2 + 0.321333333333333*b_1*b_2 + 0.1928*b_1*b_3 + 0.137714285714286*b_1*b_4 + 0.107111111111111*b_1*b_5 + 0.0876363636363637*b_1*b_6 + 0.0964*b_2**2 + 0.137714285714286*b_2*b_3 + 0.107111111111111*b_2*b_4 + 0.0876363636363637*b_2*b_5 + 0.0741538461538462*b_2*b_6 + 0.0535555555555556*b_3**2 + 0.0876363636363637*b_3*b_4 + 0.0741538461538462*b_3*b_5 + 0.0642666666666667*b_3*b_6 + 0.0370769230769231*b_4**2 + 0.0642666666666667*b_4*b_5 + 0.0567058823529412*b_4*b_6 + 0.0283529411764706*b_5**2 + 0.0507368421052632*b_5*b_6 + 0.022952380952381*b_6**2) + (1.18477228028269e-9*b_1 + 6.14508444130024e-10*b_2 + 4.60881333097518e-10*b_3 + 1.53627111032506e-10*b_4 + 1.53627111032506e-10*b_5)*(78.9568352087149*b_1**2 + 52.6378901391433*b_1*b_2 + 31.582734083486*b_1*b_3 + 22.5590957739185*b_1*b_4 + 17.5459633797144*b_1*b_5 + 14.3557882197663*b_1*b_6 + 15.791367041743*b_2**2 + 22.5590957739185*b_2*b_3 + 17.5459633797144*b_2*b_4 + 14.3557882197663*b_2*b_5 + 12.1472054167254*b_2*b_6 + 8.77298168985721*b_3**2 + 14.3557882197663*b_3*b_4 + 12.1472054167254*b_3*b_5 + 10.5275780278287*b_3*b_6 + 6.07360270836269*b_4**2 + 10.5275780278287*b_4*b_5 + 9.2890394363194*b_4*b_6 + 4.6445197181597*b_5**2 + 8.31124581144368*b_5*b_6 + 3.75984929565309*b_6**2) + (0.964*b_1 + 0.321333333333333*b_2 + 0.1928*b_3 + 0.137714285714286*b_4 + 0.107111111111111*b_5 + 0.0876363636363637*b_6)*(-1.28102213260338e-7*b_1*b_2 - 3.20255533150846e-8*b_1*b_3 - 3.20255533150846e-8*b_1*b_4 - 1.60127766575423e-8*b_1*b_6 - 1.60127766575423e-8*b_2**2 - 3.20255533150846e-8*b_2*b_3 - 1.60127766575423e-8*b_2*b_5 - 8.00638832877115e-9*b_3**2 + 1.60127766575423e-8*b_3*b_4 - 8.00638832877115e-9*b_3*b_6 - 8.00638832877115e-9*b_4*b_5 + 8.00638832877115e-9*b_4*b_6 + 4.00319416438558e-9*b_5**2 - 8.00638832877115e-9*b_5*b_6 + 4.00319416438558e-9*b_6**2 + 41123.3516712057) - 129937395.848442*(4*b_1 + 1.33333333333333*b_2 + 0.8*b_3 + 0.571428571428572*b_4 + 0.444444444444445*b_5 + 0.363636363636364*b_6)*(b_1**2 + 0.666666666666667*b_1*b_2 + 0.4*b_1*b_3 + 0.285714285714286*b_1*b_4 + 0.222222222222222*b_1*b_5 + 0.181818181818182*b_1*b_6 + 0.2*b_2**2 + 0.285714285714286*b_2*b_3 + 0.222222222222222*b_2*b_4 + 0.181818181818182*b_2*b_5 + 0.153846153846154*b_2*b_6 + 0.111111111111111*b_3**2 + 0.181818181818182*b_3*b_4 + 0.153846153846154*b_3*b_5 + 0.133333333333333*b_3*b_6 + 0.076923076923077*b_4**2 + 0.133333333333333*b_4*b_5 + 0.117647058823529*b_4*b_6 + 0.0588235294117647*b_5**2 + 0.105263157894737*b_5*b_6 + 0.0476190476190477*b_6**2) + (157.91367041743*b_1 + 52.6378901391433*b_2 + 31.582734083486*b_3 + 22.5590957739185*b_4 + 17.5459633797144*b_5 + 14.3557882197663*b_6)*(5.92386140141343e-10*b_1**2 + 6.14508444130024e-10*b_1*b_2 + 4.60881333097518e-10*b_1*b_3 + 1.53627111032506e-10*b_1*b_4 + 1.53627111032506e-10*b_1*b_5 + 2.30440666548759e-10*b_2**2 + 1.53627111032506e-10*b_2*b_3 + 1.53627111032506e-10*b_2*b_4 + 1.53627111032506e-10*b_2*b_6 + 7.6813555516253e-11*b_3**2 - 7.6813555516253e-11*b_3*b_4 + 7.6813555516253e-11*b_3*b_6 + 7.6813555516253e-11*b_4*b_5 + 7.6813555516253e-11*b_4*b_6 + 3.84067777581265e-11*b_5**2 - 251.041666666667)
I must solve such theses 6 equations.
But " Result from function call is not a proper array of floats. " error message comes out.
Is there anyone who help my code?
I'm Python beginning, so Plz understane me
Closed. This question needs details or clarity. It is not currently accepting answers.
Want to improve this question? Add details and clarify the problem by editing this post.
Closed 5 years ago.
Improve this question
i need to take input from user and only that group of words should return to me where the input string occurs. For example if i search for people then only those group of words where people appears should be retrieved as output.
here is my sample output:
[(0, '0.897*"allah" + 0.120*"indeed" + 0.117*"lord" + 0.110*"said" + 0.101*"people" + 0.093*"upon" + 0.083*"shall" + 0.082*"unto" + 0.072*"believe" + 0.070*"earth"'), (1, '0.495*"lord" + 0.398*"said" + -0.377*"allah" + 0.252*"shall" + 0.241*"people" + 0.236*"unto" + 0.195*"indeed" + 0.131*"upon" + 0.117*"come" + 0.109*"thou"'), (2, '-0.682*"lord" + 0.497*"shall" + 0.350*"unto" + 0.125*"thee" + 0.125*"thou" + -0.098*"indeed" + -0.092*"said" + 0.092*"come" + 0.091*"people" + 0.080*"truth"'), (3, '-0.615*"shall" + 0.520*"people" + -0.395*"lord" + 0.259*"said" + 0.227*"indeed" + 0.103*"would" + 0.081*"sent" + 0.078*"among" + -0.059*"deeds" + -0.053*"good"'), (4, '0.675*"unto" + -0.425*"shall" + -0.335*"indeed" + 0.214*"thou" + 0.180*"thee" + 0.161*"lord" + -0.105*"said" + 0.099*"hath" + -0.075*"upon"'), (5, '-0.760*"said" + 0.356*"indeed" + 0.261*"upon" + 0.157*"would" + -0.130*"shall" + 0.109*"earth" + -0.108*"allah" + 0.105*"lord" + 0.100*"truth" + 0.096*"good"')
Here is my expected output:
[(0, '0.897*"allah" + 0.120*"indeed" + 0.117*"lord" + 0.110*"said" + 0.101*"people" + 0.093*"upon" + 0.083*"shall" + 0.082*"unto" + 0.072*"believe" + 0.070*"earth"'), (1, '0.495*"lord" + 0.398*"said" + -0.377*"allah" + 0.252*"shall" + 0.241*"people" + 0.236*"unto" + 0.195*"indeed" + 0.131*"upon" + 0.117*"come" + 0.109*"thou"'), (2, '-0.682*"lord" + 0.497*"shall" + 0.350*"unto" + 0.125*"thee" + 0.125*"thou" + -0.098*"indeed" + -0.092*"said" + 0.092*"come" + 0.091*"people" + 0.080*"truth"'), (3, '-0.615*"shall" + 0.520*"people" + -0.395*"lord" + 0.259*"said" + 0.227*"indeed" + 0.103*"would" + 0.081*"sent" + 0.078*"among" + -0.059*"deeds" + -0.053*"good"')]
Use a function with two parameter , one is your desired string and
second is your list :
Data is :
data=[(0,
'0.897*"allah" + 0.120*"indeed" + 0.117*"lord" + 0.110*"said" + 0.101*"people" + 0.093*"upon" + 0.083*"shall" + 0.082*"unto" + 0.072*"believe" + 0.070*"earth"'),
(1,
'0.495*"lord" + 0.398*"said" + -0.377*"allah" + 0.252*"shall" + 0.241*"people" + 0.236*"unto" + 0.195*"indeed" + 0.131*"upon" + 0.117*"come" + 0.109*"thou"'),
(2,
'-0.682*"lord" + 0.497*"shall" + 0.350*"unto" + 0.125*"thee" + 0.125*"thou" + -0.098*"indeed" + -0.092*"said" + 0.092*"come" + 0.091*"people" + 0.080*"truth"'),
(3,
'-0.615*"shall" + 0.520*"people" + -0.395*"lord" + 0.259*"said" + 0.227*"indeed" + 0.103*"would" + 0.081*"sent" + 0.078*"among" + -0.059*"deeds" + -0.053*"good"'),
(4,
'0.675*"unto" + -0.425*"shall" + -0.335*"indeed" + 0.214*"thou" + 0.180*"thee" + 0.161*"lord" + -0.105*"said" + 0.099*"hath" + -0.075*"upon"'),
(5,
'-0.760*"said" + 0.356*"indeed" + 0.261*"upon" + 0.157*"would" + -0.130*"shall" + 0.109*"earth" + -0.108*"allah" + 0.105*"lord" + 0.100*"truth" + 0.096*"good"')]
Detailed solution :
def search_strin(stri,list_1):
final_list=[]
for tup in list_1:
for item in tup:
if isinstance(item,str):
if stri in item:
final_list.append(tup)
return final_list
print(search_strin('people',data))
output:
Its returning only those group which have 'people' in string.
[(0, '0.897*"allah" + 0.120*"indeed" + 0.117*"lord" + 0.110*"said" + 0.101*"people" + 0.093*"upon" + 0.083*"shall" + 0.082*"unto" + 0.072*"believe" + 0.070*"earth"'), (1, '0.495*"lord" + 0.398*"said" + -0.377*"allah" + 0.252*"shall" + 0.241*"people" + 0.236*"unto" + 0.195*"indeed" + 0.131*"upon" + 0.117*"come" + 0.109*"thou"'), (2, '-0.682*"lord" + 0.497*"shall" + 0.350*"unto" + 0.125*"thee" + 0.125*"thou" + -0.098*"indeed" + -0.092*"said" + 0.092*"come" + 0.091*"people" + 0.080*"truth"'), (3, '-0.615*"shall" + 0.520*"people" + -0.395*"lord" + 0.259*"said" + 0.227*"indeed" + 0.103*"would" + 0.081*"sent" + 0.078*"among" + -0.059*"deeds" + -0.053*"good"')]
Just for fun one line solution if you want to try:
search='people'
print([tup for tup in data for item in tup if isinstance(item,str) if search in item])
As you commented you are getting empty list , You should check that you are passing correct list. You can check here live running code :
I'm going to find $I_m=\int_0^{2\pi} \prod_{k=1}^m cos(kx){}dx$, where $m=1,2,3\ldots$
Simple SAGE code:
x=var('x')
f = lambda m,x : prod([cos(k*x) for k in range(1,m+1)])
for m in range(1,15+1):
print m, numerical_integral(f(m,x), 0, 2*pi)[0],integrate(f(m,x),x,0,2*pi).n()
Output:
1 -1.47676658757e-16 0.000000000000000
2 -5.27735962315e-16 0.000000000000000
3 1.57079632679 1.57079632679490
4 0.785398163397 0.785398163397448
5 -2.60536121164e-16 0.000000000000000
6 -1.81559273097e-16 0.000000000000000
7 0.392699081699 0.392699081698724
8 0.343611696486 0.147262155637022
9 -1.72448482421e-16 0.294524311274043
10 -1.8747663502e-16 0.196349540849362
11 0.214757310304 0.312932080728671
12 0.190213617698 0.177941771394734
13 -1.30355375996e-16 0.208621387152447
14 -1.25168280013e-16 0.0859029241215959
15 0.138441766107 0.134223318939994
As you can see numerical answer is right, but result of integrate(...) is right for $m=1,2,\ldots,7$ and then there is some bug.
We can print indefinite integral:
for m in range(7,11+1):
print 'm=',m
print 'Indef_I_m=',integrate(f(m,x),x)
And Output:
m = 7
Indef_I_m = 1/16*x + 1/16*sin(2*x) + 1/32*sin(4*x) + 7/384*sin(6*x) +
7/512*sin(8*x) + 3/320*sin(10*x) + 5/768*sin(12*x) + 5/896*sin(14*x) +
1/256*sin(16*x) + 1/384*sin(18*x) + 1/640*sin(20*x) + 1/704*sin(22*x) +
1/1536*sin(24*x) + 1/1664*sin(26*x) + 1/1792*sin(28*x)
m = 8
Indef_I_m = 3/128*x + 5/256*sin(2*x) + 1/32*sin(3*x) + 5/512*sin(4*x) +
5/768*sin(6*x) + 1/256*sin(8*x) + 1/256*sin(10*x) + 1/256*sin(12*x) +
1/256*sin(14*x) + 1/256*sin(16*x) + 7/2304*sin(18*x) + 3/1280*sin(20*x)
+ 5/2816*sin(22*x) + 1/768*sin(24*x) + 3/3328*sin(26*x) +
1/1792*sin(28*x) + 1/1920*sin(30*x) + 1/4096*sin(32*x) +
1/4352*sin(34*x) + 1/4608*sin(36*x) + 3/32*sin(x)
m = 9
Indef_I_m = 3/64*x + 3/128*sin(2*x) + 23/768*sin(3*x) + 3/256*sin(4*x) +
3/640*sin(5*x) + 1/128*sin(6*x) + 5/1792*sin(7*x) + 5/2304*sin(9*x) +
3/2816*sin(11*x) + 1/832*sin(13*x) + 1/1280*sin(15*x) + 3/4352*sin(17*x)
+ 5/4864*sin(19*x) + 1/1344*sin(21*x) + 3/2944*sin(23*x) +
7/6400*sin(25*x) + 1/1152*sin(27*x) + 3/3712*sin(29*x) +
5/7936*sin(31*x) + 1/2112*sin(33*x) + 3/8960*sin(35*x) +
1/4736*sin(37*x) + 1/4992*sin(39*x) + 1/10496*sin(41*x) +
1/11008*sin(43*x) + 1/11520*sin(45*x) + 23/256*sin(x)
m = 10
Indef_I_m = 1/32*x + 1/64*sin(2*x) + 17/512*sin(3*x) + 1/128*sin(4*x) +
7/2560*sin(5*x) + 1/192*sin(6*x) + 3/1792*sin(7*x) + 1/1152*sin(9*x) +
5/5632*sin(11*x) + 3/6656*sin(13*x) + 1/2560*sin(15*x) +
5/8704*sin(17*x) + 3/9728*sin(19*x) + 1/2688*sin(21*x) +
1/2944*sin(23*x) + 1/6400*sin(25*x) + 1/4608*sin(27*x) +
3/14848*sin(29*x) + 3/15872*sin(31*x) + 5/16896*sin(33*x) +
3/8960*sin(35*x) + 3/9472*sin(37*x) + 1/3328*sin(39*x) +
5/20992*sin(41*x) + 1/5504*sin(43*x) + 1/7680*sin(45*x) +
1/12032*sin(47*x) + 1/12544*sin(49*x) + 1/26112*sin(51*x) +
1/27136*sin(53*x) + 1/28160*sin(55*x) + 13/128*sin(x)
m = 11
Indef_I_m = 51/1024*x + 53/2048*sin(2*x) + 13/768*sin(3*x) + 53/4096*sin(4*x) +
13/1536*sin(6*x) + 1/2048*sin(8*x) + 1/2560*sin(10*x) + 1/3072*sin(12*x)
+ 5/14336*sin(14*x) + 1/4096*sin(16*x) + 5/18432*sin(18*x) +
1/4096*sin(20*x) + 1/5632*sin(22*x) + 5/24576*sin(24*x) +
5/26624*sin(26*x) + 5/28672*sin(28*x) + 1/5120*sin(30*x) +
3/16384*sin(32*x) + 5/34816*sin(34*x) + 1/9216*sin(36*x) +
5/38912*sin(38*x) + 1/10240*sin(40*x) + 1/10752*sin(42*x) +
3/22528*sin(44*x) + 3/23552*sin(46*x) + 1/8192*sin(48*x) +
3/25600*sin(50*x) + 5/53248*sin(52*x) + 1/13824*sin(54*x) +
3/57344*sin(56*x) + 1/29696*sin(58*x) + 1/30720*sin(60*x) +
1/63488*sin(62*x) + 1/65536*sin(64*x) + 1/67584*sin(66*x) +
13/256*sin(x)
so for $m=7$ answer is right compare with Indef_I_7 via WolframAlpha
and for $m=8$ answer is incorrect Indef_I_8 via WolframAlpha
There should be Indef_I_8=$\frac{7x}{128}+\ldots$ and no $\sin(x)$, $\sin(3x)$ in summation, only $\sin(2k)$ for $k=1,2,3,\ldots 18$
Sorry for volumetric calculations !
The question is - Am I right that it is the bug in the symbolic integration?
Well, apparently setting algorithm='mathematica_free' solved the issue; this is probably a bug in the default algorithm used bye SAGE ('maxima').
So the answer is - Yes. It is a bug in algorithm='maxima', so use algorithm='mathematica_free' (def new function to find definite integral) or simplify_full() for such product of cos(kx) and than integrate.
f(8,x).simplify_full().integral(x,0,2pi) == 7/64pi and
(7/64*pi).n() == 0.343611696486384 is correct