#coding:utf-8
from scipy.optimize import curve_fit
import numpy as np
from math import pi
import matplotlib.pyplot as plt
import math
from scipy import fftpack
from sklearn import preprocessing
import neurolab as nl
# 使用非线性最小二乘法拟合

# 码元数
size = 10
sampling_t = 0.01

t = np.arange(0, size, sampling_t)

#随机生成信号序列
a = np.random.randint(0, 2, size)   #产生随机整数序列

m = np.zeros(len(t), dtype=np.float32)    #产生一个给定形状和类型的用0填充的数组
for i in range(len(t)):
    m[i] = a[int(math.floor(t[i]))]


def awgn(y, snr):      #snr为信噪比dB值
    snr = 10 ** (snr / 10.0)
    xpower = np.sum(y ** 2) / len(y)
    npower = xpower / snr
    return np.random.randn(len(y)) * np.sqrt(npower) + y

def feature_rj(y):         #[feature1, f2, f3] = rj(noise_bpsk, fs)
    global R,J
    global r,j
    h = fftpack.hilbert(y)   # hilbert变换
    z = np.sqrt(y**2 + h**2)   # 包络
    m2 = np.mean(z**2)     # 包络的二阶矩
    m4 = np.mean(z**4)     # 包络的四阶矩
    r = abs((m4-m2**2)/m2**2)
    Ps = np.mean(y**2)/2
    j = abs((m4-2*m2**2)/(4*Ps**2))
    return (r,j)

def feature_Bispectrum(y):
    global w,Z
    ly = size  # 行数10
    nrecs = np.int64(1 / sampling_t)  # 列数100
    nlag = 20
    nsamp = nrecs  # 每段样本数100
    nrecord = size
    nfft = 128
    Bspec = np.zeros((nfft, nfft), dtype=np.float32)
    y = y.reshape(ly, nrecs)
    c3 = np.zeros((nlag + 1, nlag + 1), dtype=np.float32)
    ind = np.arange(nsamp)

    for k in range(nrecord):
        x = y[k][ind]
        x = x - np.mean(x)
        for j in range(nlag + 1):
            z = np.multiply(x[np.arange(nsamp - j)], x[np.arange(j, nsamp)])
            for i in range(j, nlag + 1):
                sum = np.mat(z[np.arange(nsamp - i)]) * np.mat(x[np.arange(i, nsamp)]).T
                sum = sum / nsamp
                c3[i][j] = c3[i][j] + sum  # i,j顺序
    c3 = c3 / nrecord

    c3 = c3 + np.mat(np.tril(c3, -1)).T  # 取对角线以下三角,c3为矩阵
    c31 = c3[1:, 1:]
    c32 = np.mat(np.zeros((nlag, nlag), dtype=np.float32))
    c33 = np.mat(np.zeros((nlag, nlag), dtype=np.float32))  # 不可以直接3者相等
    c34 = np.mat(np.zeros((nlag, nlag), dtype=np.float32))
    for i in range(nlag):
        x = c31[i:, i]
        c32[nlag - 1 - i, 0:nlag - i] = x.T
        c34[0:nlag - i, nlag - 1 - i] = x
        if i < (nlag - 1):
            x = np.flipud(x[1:, 0])  # 上下翻转,翻转后依然为矩阵
            c33 = c33 + np.diag(np.array(x)[:, 0], i + 1) + np.diag(np.array(x)[:, 0], -(i + 1))
    c33 = c33 + np.diag(np.array(c3)[0, :0:-1])
    cmat = np.vstack((np.hstack((c33, c32, np.zeros((nlag, 1), dtype=np.float32))),
                      np.hstack((np.vstack((c34, np.zeros((1, nlag), dtype=np.float32))), c3))))          #41*41
    Bspec = fftpack.fft2(cmat, [nfft, nfft])      #2维傅里叶变换
    Bspec = np.fft.fftshift(Bspec)                #128*128

    waxis = np.arange(-nfft / 2, nfft / 2) / nfft
    X, Y = np.meshgrid(waxis, waxis)
    plt.contourf(X, Y, abs(Bspec))
    plt.contour(X, Y, abs(Bspec))
    Z.append(np.mean(abs(Bspec)))
    #w_content = './w频率改变/'
    #plt.savefig(w_content.decode("utf-8").encode("gbk") +  str(w) + '.jpg')
    return Bspec


def features(s):
#    for mc in range(2):
        snr = np.random.uniform(0, 20)       #从一个均匀分布集合中随机采样，左闭右开--[low,high)
        #s = awgn(s,snr)            #在原始信号的基础上增加SNR信噪比的噪音
        rj = np.array(feature_rj(s))               #计算R,J特征
        z = feature_Bispectrum(s)                  #计算双谱特征，并画图像
        xx = np.int64(np.sqrt(np.size(z))/2)
        z = np.array(z[:xx,xx:])
        z = np.tril(z).real               #取复数z的实部
        bis = np.zeros((1, xx),dtype=np.float32)    #零组
        for i in range(xx):
            for j in range(xx-i):
                bis[0][i] = bis[0][i]+z[xx-1-j][i+j]
        m = bis[0].reshape(1,xx)
        normalized = preprocessing.normalize(m)[0,:]    #样本各个特征值除以各个特征值的平方之和
        features = np.hstack((rj,normalized))           #合并数组r,j和normalized
        return features

        
R = []
J = []
ts1 = np.arange(0, (np.int64(1/sampling_t) * size))/(10*(m+1))
W = []
Z = []
for i in range(0,40,1):
    W.append(i / (2 * pi))

for w in W:
    global r,j
    fsk = np.cos(np.dot(w, ts1) + pi / 4)
    features(fsk)
    R.append(r)
    J.append(j)

def func(x,a,b,c):
    return a * np.power(x,3) + b * np.power(x,2) + c * np.power(x,1)
    
popt, pcov = curve_fit(func, W, R,[1,1,1])
a=popt[0] # popt里面是拟合系数，读者可以自己help其用法
b=popt[1]
c=popt[2]
yvals=func(W,a,b,c)
print(popt)
plot1=plt.plot(W, R, '*',label='original values')
plot2=plt.plot(W, yvals, 'r',label='curve_fit values')
plt.xlabel('W axis')
plt.ylabel('R axis')
plt.legend(loc=4) # 指定legend的位置,读者可以自己help它的用法
plt.title('curve_fit')
plt.show()

popt2, pcov2 = curve_fit(func, W, J,[1,1,1])
a2=popt2[0] # popt里面是拟合系数，读者可以自己help其用法
b2=popt2[1]
c2=popt[2]
yvals2=func(W,a2,b2,c2)
print(popt2)
plot1=plt.plot(W, J, '*',label='original values')
plot2=plt.plot(W, yvals2, 'r',label='curve_fit values')
plt.xlabel('W axis')
plt.ylabel('J axis')
plt.legend(loc=4) # 指定legend的位置,读者可以自己help它的用法
plt.title('curve_fit')
plt.show()