Ajuste de curva no Scipy com dados e parâmetros 3d
Eu estou trabalhando em encaixar uma função de distribuição 3D no scipy. Eu tenho um array numpy com contagens em x e y-bins e estou tentando encaixar isso para uma função de distribuição 3-d bastante complicada. Os dados são ajustados a 26 (!) Parâmetros, que descrevem a forma de suas duas populações constituintes.
Eu aprendi aqui que tenho que passar minhas coordenadas xey como 'args' quando eu chamo de leastsq. O código apresentado pelo unutbu funciona como escrito para mim, mas quando tento aplicá-lo ao meu caso específico, recebo o erro "TypeError: leastsq () tem vários valores para o argumento de palavra-chave 'args'"
Aqui está o meu código (desculpe pelo comprimento):
import numpy as np
import matplotlib.pyplot as plt
import scipy.optimize as spopt
from textwrap import wrap
import collections
cl = 0.5
ch = 3.5
rl = -23.5
rh = -18.5
mbins = 10
cbins = 10
def hist_data(mixed_data, mbins, cbins):
import numpy as np
H, xedges, yedges = np.histogram2d(mixed_data[:,1], mixed_data[:,2], bins = (mbins, cbins), weights = mixed_data[:,3])
x, y = 0.5 * (xedges[:-1] + xedges[1:]), 0.5 * (yedges[:-1] + yedges[1:])
return H.T, x, y
def gauss(x, s, mu, a):
import numpy as np
return a * np.exp(-((x - mu)**2. / (2. * s**2.)))
def tanhlin(x, p0, p1, q0, q1, q2):
import numpy as np
return p0 + p1 * (x + 20.) + q0 * np.tanh((x - q1)/q2)
def func3d(p, x, y):
import numpy as np
from sys import exit
rsp0, rsp1, rsq0, rsq1, rsq2, rmp0, rmp1, rmq0, rmq1, rmq2, rs, rm, ra, bsp0, bsp1, bsq0, bsq1, bsq2, bmp0, bmp1, bmq0, bmq1, bmq2, bs, bm, ba = p
x, y = np.meshgrid(coords[0], coords[1])
rs = tanhlin(x, rsp0, rsp1, rsq0, rsq1, rsq2)
rm = tanhlin(x, rmp0, rmp1, rmq0, rmq1, rmq2)
ra = schechter(x, rap, raa, ram) # unused
bs = tanhlin(x, bsp0, bsp1, bsq0, bsq1, bsq2)
bm = tanhlin(x, bmp0, bmp1, bmq0, bmq1, bmq2)
ba = schechter(x, bap, baa, bam) # unused
red_dist = ra / (rs * np.sqrt(2 * np.pi)) * gauss(y, rs, rm, ra)
blue_dist = ba / (bs * np.sqrt(2 * np.pi)) * gauss(y, bs, bm, ba)
result = red_dist + blue_dist
return result
def residual(p, coords, data):
import numpy as np
model = func3d(p, coords)
res = (model.flatten() - data.flatten())
# can put parameter restrictions in here
return res
def poiss_err(data):
import numpy as np
return np.where(np.sqrt(H) > 0., np.sqrt(H), 2.)
# =====
H, x, y = hist_data(mixed_data, mbins, cbins)
data = H
coords = x, y
# x and y will be the projected coordinates of the data H onto the plane z = 0
# x has bins of width 0.5, with centers at -23.25, -22.75, ... , -19.25, -18.75
# y has bins of width 0.3, with centers at 0.65, 0.95, ... , 3.05, 3.35
Param = collections.namedtuple('Param', 'rsp0 rsp1 rsq0 rsq1 rsq2 rmp0 rmp1 rmq0 rmq1 rmq2 rs rm ra bsp0 bsp1 bsq0 bsq1 bsq2 bmp0 bmp1 bmq0 bmq1 bmq2 bs bm ba')
p_guess = Param(rsp0 = 0.152, rsp1 = 0.008, rsq0 = 0.044, rsq1 = -19.91, rsq2 = 0.94, rmp0 = 2.279, rmp1 = -0.037, rmq0 = -0.108, rmq1 = -19.81, rmq2 = 0.96, rs = 1., rm = -20.5, ra = 10000., bsp0 = 0.298, bsp1 = 0.014, bsq0 = -0.067, bsq1 = -19.90, bsq2 = 0.58, bmp0 = 1.790, bmp1 = -0.053, bmq0 = -0.363, bmq1 = -20.75, bmq2 = 1.12, bs = 1., bm = -20., ba = 2000.)
opt, cov, infodict, mesg, ier = spopt.leastsq(residual, p_guess, poiss_err(H), args = coords, maxfev = 100000, full_output = True)
Aqui estão os meus dados, apenas com menos caixas:
[[ 1.00000000e+01 1.10000000e+01 2.10000000e+01 1.90000000e+01
1.70000000e+01 2.10000000e+01 2.40000000e+01 1.90000000e+01
2.80000000e+01 1.90000000e+01]
[ 1.40000000e+01 4.50000000e+01 6.00000000e+01 6.80000000e+01
1.34000000e+02 1.97000000e+02 2.23000000e+02 2.90000000e+02
3.23000000e+02 3.03000000e+02]
[ 3.00000000e+01 1.17000000e+02 3.78000000e+02 9.74000000e+02
1.71900000e+03 2.27700000e+03 2.39000000e+03 2.25500000e+03
1.85600000e+03 1.31000000e+03]
[ 1.52000000e+02 9.32000000e+02 2.89000000e+03 5.23800000e+03
6.66200000e+03 6.19100000e+03 4.54900000e+03 3.14600000e+03
2.09000000e+03 1.33800000e+03]
[ 5.39000000e+02 2.58100000e+03 6.51300000e+03 8.89900000e+03
8.52900000e+03 6.22900000e+03 3.55000000e+03 2.14300000e+03
1.19000000e+03 6.92000000e+02]
[ 1.49600000e+03 4.49200000e+03 8.77200000e+03 1.07610000e+04
9.76700000e+03 7.04900000e+03 4.23200000e+03 2.47200000e+03
1.41500000e+03 7.02000000e+02]
[ 2.31800000e+03 7.01500000e+03 1.28870000e+04 1.50840000e+04
1.35590000e+04 8.55600000e+03 4.15600000e+03 1.77100000e+03
6.57000000e+02 2.55000000e+02]
[ 1.57500000e+03 3.79300000e+03 5.20900000e+03 4.77800000e+03
3.26600000e+03 1.44700000e+03 5.31000000e+02 1.85000000e+02
9.30000000e+01 4.90000000e+01]
[ 7.01000000e+02 1.21600000e+03 1.17600000e+03 7.93000000e+02
4.79000000e+02 2.02000000e+02 8.80000000e+01 3.90000000e+01
2.30000000e+01 1.90000000e+01]
[ 2.93000000e+02 3.93000000e+02 2.90000000e+02 1.97000000e+02
1.18000000e+02 6.40000000e+01 4.10000000e+01 1.20000000e+01
1.10000000e+01 4.00000000e+00]]
Muito obrigado!