Wavelet decomposition and reconstruction

Wavelet decomposition and reconstruction

function H=SE(WS)
load("650837_20161013152521.mat")
WS=double(WS);
vx=WS(1,:);
vy=WS(2,:);
vz=WS(3,:);

N=length(vx);
%用db3小波进行5层分解
[c1,l1]=wavedec(vx,5,'db3');

[c2,l2]=wavedec(vy,5,'db3');

[c3,l3]=wavedec(vz,5,'db3');

%构造第1-5层高频系数 matlab388
dx5=wrcoef('d',c1,l1,'db3',5);
dx4=wrcoef('d',c1,l1,'db3',4);
dx3=wrcoef('d',c1,l1,'db3',3);
dx2=wrcoef('d',c1,l1,'db3',2);
dx1=wrcoef('d',c1,l1,'db3',1);

dy5=wrcoef('d',c2,l2,'db3',5);
dy4=wrcoef('d',c2,l2,'db3',4);
dy3=wrcoef('d',c2,l2,'db3',3);
dy2=wrcoef('d',c2,l2,'db3',2);
dy1=wrcoef('d',c2,l2,'db3',1);

dz5=wrcoef('d',c3,l3,'db3',5);
dz4=wrcoef('d',c3,l3,'db3',4);
dz3=wrcoef('d',c3,l3,'db3',3);
dz2=wrcoef('d',c3,l3,'db3',2);
dz1=wrcoef('d',c3,l3,'db3',1);

%构造第5层高频细节系数 
ax5=wrcoef('a',c1,l1,'db3',5);
ay5=wrcoef('a',c2,l2,'db3',5);
az5=wrcoef('a',c3,l3,'db3',5);

% %合并为一个矩阵
A=[ dx1' dx2' dx3' dx4' dx5' ax5' ];
B=[ dy1' dy2' dy3' dy4' dy5' ay5' ];
C=[ dz1' dz2' dz3' dz4' dz5' az5' ];
for t=1:6
    for s=1:N
     Tx(s)=A(s,t)^2 ;
     Ty(s)=B(s,t)^2 ;
     Tz(s)=C(s,t)^2 ;
    end
   ex(t)= sum(Tx); 
   ey(t)= sum(Ty);
   ez(t)= sum(Tz);
end
%小波熵
Ex=sum(ex);
Ey=sum(ey);
Ez=sum(ez);
px=ex/Ex;
py=ey/Ey;
pz=ez/Ez;
for i=1:6
hx(i)=px(i)*log(px(i));
hy(i)=py(i)*log(py(i));
hz(i)=pz(i)*log(pz(i));
end
Hx=-sum(hx);
Hy=-sum(hy);
Hz=-sum(hz);
H = [Hx,Hy,Hz]
end

from numpy import *
import numpy as np
from wrcoef_1 import wrcoef,wavedec
import pandas as pd
from pandas import DataFrame, Series
import pywt


def get_matrix(x1):
    # WS = np.array(x1)
    signal = x1
    #用db3小波进行5层分解
    C, L1 = wavedec(signal, wavelet='db3', level=5)
    c = pywt.wavedec(signal, 'db3', level=5)
    #构造第5层高频细节系数
    a, details = c[0], c[1:]
    L = [d.size for d in details[1:]] + [signal.size, ]
    for n in range(5):
        a = pywt.upcoef('a', a, 'db3', level=1, take=L[n])
    #构造第1-5层高频系数
    dx5 = wrcoef(C, L1, wavelet='db3', level=5)
    dx4 = wrcoef(C, L1, wavelet='db3', level=4)
    dx3 = wrcoef(C, L1, wavelet='db3', level=3)
    dx2 = wrcoef(C, L1, wavelet='db3', level=2)
    dx1 = wrcoef(C, L1, wavelet='db3', level=1)
    #拼接矩阵并转置
    A = np.vstack((dx1, dx2, dx3, dx4, dx5, a))
    A = np.transpose(A)
    return A


def SE(a1):
    x1 = a1[0]
    x2 = a1[1]
    x3 = a1[2]
    N = len(x1)
    A = get_matrix(x1)
    B = get_matrix(x2)
    C = get_matrix(x3)

    Tx, Ty, Tz = np.zeros((1, 2307)), np.zeros((1, 2307)), np.zeros((1, 2307))
    ex, ey, ez = np.zeros(6), np.zeros(6), np.zeros(6)
    for t in range(6):
        for s in range(N):
            Tx[0, s] = A[s][t] * A[s][t]
            Ty[0, s] = B[s][t] * B[s][t]
            Tz[0, s] = C[s][t] * C[s][t]
        ex[t] = sum(Tx)
        ey[t] = sum(Ty)
        ez[t] = sum(Tz)
    #小波熵
    Ex = sum(ex)
    Ey = sum(ey)
    Ez = sum(ez)

    px = ex / Ex
    py = ey / Ey
    pz = ez / Ez

    hx, hy, hz = np.zeros(6), np.zeros(6), np.zeros(6)
    for i in range(6):
        hx[i] = px[i] * log(px[i])
        hy[i] = py[i] * log(py[i])
        hz[i] = pz[i] * log(pz[i])

    Hx = -sum(hx)
    Hy = -sum(hy)
    Hz = -sum(hz)
    H = [Hx, Hy, Hz]

    return H


def exread(path):  # 读取excel数据存为矩阵格式
    df = pd.read_excel(path)
    data1 = df.iloc[:, 0]
    data2 = df.iloc[:, 1]
    data3 = df.iloc[:, 2]
    a1 = np.vstack((data1, data2, data3))

    return a1


def write_excel_xls(path, Cx, Cy, Cz):
    df = DataFrame(  # 设置保存数据
        {'id': Series(['650837_20161013152530']),
         'num1': Series([Cx]),
         'num2': Series([Cy]),
         'num3': Series([Cz])})
    df.to_excel(path, index=False)  # 保存文件


if __name__ == '__main__':
    # 获取excel中的矩阵
    a1 = exread('650837_20161013152521_11.xls')
    #计算结果
    H = SE(a1)
    # 写入文件
    write_excel_xls('SE.xls', H[0], H[1], H[2])

import math
import numpy as np
import pywt
import pandas as pd


def wavedec(data, wavelet, mode='symmetric', level=1, axis=-1):
    """
    Multiple level 1-D discrete fast wavelet decomposition
    Calling Sequence
    ----------------
    [C, L] = wavedec(data, wavelet, mode, level, axis)
    [C, L] = wavedec(data, wavelet)
    [C, L] = wavedec(data, 'sym3')
    Parameters
    ----------
    data: array_like
        Input data
    wavelet : Wavelet object or name string
        Wavelet to use
    mode : str, optional
        Signal extension mode, see Modes (default: 'symmetric')
    level : int, optional
        Decomposition level (must be >= 0). Default is 1.
    axis: int, optional
        Axis over which to compute the DWT. If not given, the
        last axis is used.
    Returns
    -------
    C: list
        Ordered list of flattened coefficients arrays (N=level):
        C = [app. coef.(N)|det. coef.(N)|... |det. coef.(1)]
    L: list
        Ordered list of individual lengths of coefficients arrays.
        L(1)   = length of app. coef.(N)
        L(i)   = length of det. coef.(N-i+2) for i = 2,...,N+1
        L(N+2) = length(X).
    Description
    -----------
    wavedec can be used for multiple-level 1-D discrete fast wavelet
    decomposition using a specific wavelet name or instance of the
    Wavelet class instance.
    The coefficient vector C contains the approximation coefficient at level N
    and all detail coefficient from level 1 to N
    The first entry of L is the length of the approximation coefficient,
    then the length of the detail coefficients are stored and the last
    value of L is the length of the signal vector.
    The approximation coefficient can be extracted with C(1:L(1)).
    The detail coefficients can be obtained with C(L(1):sum(L(1:2))),
    C(sum(L(1:2)):sum(L(1:3))),.... until C(sum(L(1:length(L)-2)):sum(L(1:length(L)-1)))
    The implementation of the function is based on pywt.wavedec
    with the following minor changes:
        - checking of the axis is dropped out
        - checking of the maximum possible level is dropped out
          (as for Matlab's implementation)
        - returns format is modified to Matlab's internal format:
          two separate lists of details coefficients and
          corresponding lengths
    Examples
    --------
    >>> C, L = wavedec([3, 7, 1, 1, -2, 5, 4, 6], 'sym3', level=2)
    >>> C
    array([  7.38237875   5.36487594   8.83289608   2.21549896  11.10312807
            -0.42770133   3.72423411   0.48210099   1.06367045  -5.0083641
            -2.11206142  -2.64704675  -3.16825651  -0.67715519   0.56811154
             2.70377533])
    >>> L
    array([5, 5, 6, 8])
    """
    data = np.asarray(data)

    if not isinstance(wavelet, pywt.Wavelet):
        wavelet = pywt.Wavelet(wavelet)

    # Initialization
    coefs, lengths = [], []

    # Decomposition
    lengths.append(len(data))
    for i in range(level):
        data, d = pywt.dwt(data, wavelet, mode, axis)

        # Store detail and its length
        coefs.append(d)
        lengths.append(len(d))

    # Add the last approximation
    coefs.append(data)
    lengths.append(len(data))

    # Reverse (since we've appended to the end of list)
    coefs.reverse()
    lengths.reverse()

    return np.concatenate(coefs).ravel(), lengths


def detcoef(coefs, lengths, levels=None):
    """
    1-D detail coefficients extraction
    Calling Sequence
    ----------------
    D = detcoef(C, L)
    D = detcoef(C, L, N)
    D = detcoef(C, L, [1, 2, 3])
    Parameters
    ----------
    coefs: list
        Ordered list of flattened coefficients arrays (N=level):
        C = [app. coef.(N)|det. coef.(N)|... |det. coef.(1)]
    lengths: list
        Ordered list of individual lengths of coefficients arrays.
        L(1)   = length of app. coef.(N)
        L(i)   = length of det. coef.(N-i+2) for i = 2,...,N+1
        L(N+2) = length(X).
    levels : int or list
        restruction level with N<=length(L)-2
    Returns
    ----------
    D : reconstructed detail coefficient
    Description
    -----------
    detcoef is for extraction of detail coefficient at different level
    after a multiple level decomposition. If levels is omitted,
    the detail coefficients will extract at all levels.
    The wavelet coefficients and lengths can be generated using wavedec.
    Examples
    --------
    >>> x = range(100)
    >>> w = pywt.Wavelet('sym3')
    >>> C, L = wavedec(x, wavelet=w, level=5)
    >>> D = detcoef(C, L, levels=len(L)-2)
    """
    if not levels:
        levels = range(len(lengths) - 2)

    if not isinstance(levels, list):
        levels = [levels]

    first = np.cumsum(lengths) + 1
    first = first[-3::-1]
    last = first + lengths[-2:0:-1] - 1

    x = []
    for level in levels:
        d = coefs[first[level - 1] - 1:last[level - 1]]
        x.append(d)

    if len(x) == 1:
        x = x[0]

    return x


def wrcoef(coefs, lengths, wavelet, level):
    """
    Restruction from single branch from multiple level decomposition
    Calling Sequence
    ----------------
    X = wrcoef(C, L, wavelet, level)
    Parameters
    ----------
    # type='a' is not implemented.
    # type : string
    #   approximation or detail, 'a' or 'd'.
    coefs: list
        Ordered list of flattened coefficients arrays (N=level):
        C = [app. coef.(N)|det. coef.(N)|... |det. coef.(1)]
    lengths: list
        Ordered list of individual lengths of coefficients arrays.
        L(1)   = length of app. coef.(N)
        L(i)   = length of det. coef.(N-i+2) for i = 2,...,N+1
        L(N+2) = length(X).
    wavelet : Wavelet object or name string
        Wavelet to use
    level : int
        restruction level with level<=length(L)-2
    Returns
    ----------
    X :
        vector of reconstructed coefficients
    Description
    -----------
    wrcoef is for reconstruction from single branch of multiple level
    decomposition from 1-D wavelet coefficients.
    The wavelet coefficients and lengths can be generated using wavedec.
    Examples
    --------
    >>> x = range(100)
    >>> w = pywt.Wavelet('sym3')
    >>> C, L = wavedec(x, wavelet=w, level=5)
    >>> X = wrcoef(C, L, wavelet=w, level=len(L)-2)
    """
    def upsconv(x, f, s):
        # returns an extended copy of vector x obtained by inserting zeros
        # as even-indexed elements of data: y(2k-1) = data(k), y(2k) = 0.
        y_len = 2 * len(x) + 1
        y = np.zeros(y_len)
        y[1:y_len:2] = x

        # performs the 1-D convolution of the vectors y and f
        y = np.convolve(y, f, 'full')

        # extracts the vector y from the input vector
        sy = len(y)
        d = (sy - s) / 2.0
        y = y[int(math.floor(d)):(sy - int(math.ceil(d)))]

        return y

    if not isinstance(wavelet, pywt.Wavelet):
        wavelet = pywt.Wavelet(wavelet)

    data = detcoef(coefs, lengths, level)

    idx = len(lengths) - level
    data = upsconv(data, wavelet.rec_hi, lengths[idx])
    for k in range(level-1):
        data = upsconv(data, wavelet.rec_lo, lengths[idx + k + 1])

    return data


def exread(path):  # 读取excel数据存为矩阵格式
    df = pd.read_excel(path, header=None)
    data1 = df.iloc[:, 0]
    data2 = df.iloc[:, 1]
    data3 = df.iloc[:, 2]
    a1 = np.vstack((data1, data2, data3))

    return a1


if __name__ == '__main__':
    # Define wavelet parameters
    # Generate input data
    WS = np.array(exread('.\\wsread.xls'))
    X = WS[0]
    signal = X
    print('x=', signal)

    # Define wavelet
    # print([w.dec_lo, w.dec_hi, w.rec_lo, w.rec_hi])

    C, L = wavedec(signal, wavelet='db3', level=5)
    D = wrcoef(C, L, wavelet='db3', level=5)
    print(D)