def backprop(ANFISObj, columnX, columns, theWSum, theW, theLayerFive):
paramGrp = [0]* len(ANFISObj.memFuncs[columnX])
for MF in range(len(ANFISObj.memFuncs[columnX])):
parameters = np.empty(len(ANFISObj.memFuncs[columnX][MF][1]))
timesThru = 0
for alpha in sorted(ANFISObj.memFuncs[columnX][MF][1].keys()):
bucket3 = np.empty(len(ANFISObj.X))
for rowX in range(len(ANFISObj.X)):
varToTest = ANFISObj.X[rowX,columnX]
tmpRow = np.empty(len(ANFISObj.memFuncs))
tmpRow.fill(varToTest)
bucket2 = np.empty(ANFISObj.Y.ndim)
for colY in range(ANFISObj.Y.ndim):
rulesWithAlpha = np.array(np.where(ANFISObj.rules[:,columnX]==MF))[0]
adjCols = np.delete(columns,columnX)
senSit = mfDerivs.partial_dMF(ANFISObj.X[rowX,columnX],ANFISObj.memFuncs[columnX][MF],alpha)
# produces d_ruleOutput/d_parameterWithinMF
dW_dAplha = senSit * np.array([np.prod([ANFISObj.memClass.evaluateMF(tmpRow)[c][ANFISObj.rules[r][c]] for c in adjCols]) for r in rulesWithAlpha])
bucket1 = np.empty(len(ANFISObj.rules[:,0]))
for consequent in range(len(ANFISObj.rules[:,0])):
fConsequent = np.dot(np.append(ANFISObj.X[rowX,:],1.),ANFISObj.consequents[((ANFISObj.X.shape[1] + 1) * consequent):(((ANFISObj.X.shape[1] + 1) * consequent) + (ANFISObj.X.shape[1] + 1)),colY])
acum = 0
if consequent in rulesWithAlpha:
acum = dW_dAplha[np.where(rulesWithAlpha==consequent)] * theWSum[rowX]
acum = acum - theW[consequent,rowX] * np.sum(dW_dAplha)
acum = acum / theWSum[rowX]**2
bucket1[consequent] = fConsequent * acum
sum1 = np.sum(bucket1)
if ANFISObj.Y.ndim == 1:
bucket2[colY] = sum1 * (ANFISObj.Y[rowX]-theLayerFive[rowX,colY])*(-2)
else:
bucket2[colY] = sum1 * (ANFISObj.Y[rowX,colY]-theLayerFive[rowX,colY])*(-2)
sum2 = np.sum(bucket2)
bucket3[rowX] = sum2
sum3 = np.sum(bucket3)
parameters[timesThru] = sum3
timesThru = timesThru + 1
paramGrp[MF] = parameters
return paramGrp
def backprop(ANFISObj, columnX, columns, theWSum, theW, theLayerFive):
paramGrp = [0]* len(ANFISObj.memFuncs[columnX])
for MF in range(len(ANFISObj.memFuncs[columnX])):
parameters = np.empty(len(ANFISObj.memFuncs[columnX][MF][1]))
timesThru = 0
for alpha in sorted(ANFISObj.memFuncs[columnX][MF][1].keys()):
bucket3 = np.empty(len(ANFISObj.X))
for rowX in range(len(ANFISObj.X)):
varToTest = ANFISObj.X[rowX,columnX]
tmpRow = np.empty(len(ANFISObj.memFuncs))
tmpRow.fill(varToTest)
bucket2 = np.empty(ANFISObj.Y.ndim)
for colY in range(ANFISObj.Y.ndim):
rulesWithAlpha = np.array(np.where(ANFISObj.rules[:,columnX]==MF))[0]
adjCols = np.delete(columns,columnX)
senSit = mfDerivs.partial_dMF(ANFISObj.X[rowX,columnX],ANFISObj.memFuncs[columnX][MF],alpha)
# produces d_ruleOutput/d_parameterWithinMF
dW_dAplha = senSit * np.array([np.prod([ANFISObj.memClass.evaluateMF(tmpRow)[c][ANFISObj.rules[r][c]] for c in adjCols]) for r in rulesWithAlpha])
bucket1 = np.empty(len(ANFISObj.rules[:,0]))
for consequent in range(len(ANFISObj.rules[:,0])):
fConsequent = np.dot(np.append(ANFISObj.X[rowX,:],1.),ANFISObj.consequents[((ANFISObj.X.shape[1] + 1) * consequent):(((ANFISObj.X.shape[1] + 1) * consequent) + (ANFISObj.X.shape[1] + 1)),colY])
acum = 0
if consequent in rulesWithAlpha:
acum = dW_dAplha[np.where(rulesWithAlpha==consequent)] * theWSum[rowX]
acum = acum - theW[consequent,rowX] * np.sum(dW_dAplha)
acum = acum / theWSum[rowX]**2
bucket1[consequent] = fConsequent * acum
sum1 = np.sum(bucket1)
if ANFISObj.Y.ndim == 1:
bucket2[colY] = sum1 * (ANFISObj.Y[rowX]-theLayerFive[rowX,colY])*(-2)
else:
bucket2[colY] = sum1 * (ANFISObj.Y[rowX,colY]-theLayerFive[rowX,colY])*(-2)
sum2 = np.sum(bucket2)
bucket3[rowX] = sum2
sum3 = np.sum(bucket3)
parameters[timesThru] = sum3
timesThru = timesThru + 1
paramGrp[MF] = parameters
return paramGrp
def backprop(ANFISObj, columnX, columns, theWSum, theW, theLayerFive):
"""
Parameters
----------
ANFISObj: anfis对象
columnX： 第X个变量id
columns：列表[0, 1, 2,...,len(n)-1]，共n个变量
theWSum：第二层的和
theW： 第二层
theLayerFive：第五层
Returns
-------
paramGrp：bp后的参数Group，[[p1],[p2],[p3],...,[pn]]。共n个mf，[pi]为第i个mf的参数列表。
"""
paramGrp = [0] * len(ANFISObj.memFuncs[columnX])
for MF in range(len(ANFISObj.memFuncs[columnX])):
parameters = np.empty(len(ANFISObj.memFuncs[columnX][MF][1]))
timesThru = 0
# alpha为每个mf的参数。
for alpha in sorted(ANFISObj.memFuncs[columnX][MF][1].keys()):
# bucket3用于存放每个inputcase对当前MF-alpha参数的修正值
bucket3 = np.empty(len(ANFISObj.X))
for rowX in range(len(ANFISObj.X)):
# 这些是错误语句所用到的变量，现已失效
# varToTest = ANFISObj.X[rowX, columnX]
# tmpRow = np.empty(len(ANFISObj.memFuncs))
# tmpRow.fill(varToTest)
# bucket2用于存放当前inputcase（即第rowX个input）下，对应output中每个colY值的MF-alpha参数修正值。
bucket2 = np.empty(ANFISObj.Y.shape[1])
for colY in range(ANFISObj.Y.shape[1]):
# 选出rules中包含MF的那些rule的编号。
rulesWithAlpha = np.array(
np.where(ANFISObj.rules[:, columnX] == MF))[0]
# 删除本列后的其他列的编号
adjCols = np.delete(columns, columnX)
# MF关于alpha的偏导数
# 这相当于第一层的delta
senSit = mfDerivs.partial_dMF(
ANFISObj.X[rowX, columnX],
ANFISObj.memFuncs[columnX][MF], alpha)
# produces d_ruleOutput/d_parameterWithinMF
# 每个rule in rulesWithAlpha为形如(3, 4, 1)的元组（该例为有三个输入变量，该rule由三个输入变量中的第3， 4， 1个
# MF的并组成。所以alpha在该rule对应的偏导dW_dAlpha为senSit(alpha所在的MF的偏导)*其他两个输入变量对应的MF值的积。
# dW_dAlpha其实就是前两层的对应rulesWithAopha的delta
# 一个错误的计算，正确的在下一行
# dW_dAplha = senSit * np.array([np.prod([ANFISObj.memClass.evaluateMF(tmpRow)[c][ANFISObj.rules[r][c]] for c in adjCols]) for r in rulesWithAlpha])
if ANFISObj.and_func == 'T-S':
dW_dAlpha = senSit * np.array([
np.prod([
ANFISObj.memClass.evaluateMF(
ANFISObj.X[rowX])[c][ANFISObj.rules[r][c]]
for c in adjCols
]) for r in rulesWithAlpha
])
else:
dW_dAlpha = senSit * np.array(
[1. for r in rulesWithAlpha])
bucket1 = np.empty(len(ANFISObj.rules[:, 0]))
for consequent in range(len(ANFISObj.rules[:, 0])):
# fConsequent为第4层的delta
# 因为第五层与consequent对应的rule的值L5为：rule*x1*w1 + rule*x2*w2 + ...+ rule*xn*wn, n为x的维数
# = rule*(x1*w1 + x2*w2 + ...+ xn*wn)
# 故第四层delta=(x1*w1 + x2*w2 + ...+ xn*wn)
# 上式中rule为第三层与consequent对应的输出
l4_rule_gap = ANFISObj.X.shape[1] + 1
l4_rule_id = l4_rule_gap * consequent
fConsequent = np.dot(
np.append(ANFISObj.X[rowX, :], 1.),
ANFISObj.consequents[l4_rule_id:l4_rule_id +
l4_rule_gap, colY])
# acum为第三层及之前各层的delta
# 第三层归一化后的rule(L3) = rule(L2)/ Total(rule_l2)
# 后Total(rule_l2)记为Total
# 故在第三层求alpha的偏导为：
# ...................................................
# 记rule共n条，第二层偏导数结果为d_rule(对应程序中的dW_dAlpha)
# 1、若当前rulei与alpha相关：
# d_rule(L3) = (d_rulei * Total - d_Total * rulei) / (Total * Total)
# 其中d_rulei不为0，且d_rulei = dW_dAlpha
# 2、若当前rulei与alpha无关：
# 则上面的d_rulei = 0
acum = 0
if consequent in rulesWithAlpha:
acum = dW_dAlpha[np.where(
rulesWithAlpha == consequent)] * theWSum[rowX]
acum = acum - theW[rowX,
consequent] * np.sum(dW_dAlpha)
acum /= theWSum[rowX]**2
# 该consequent的delta为前四层的delta的积
bucket1[consequent] = fConsequent * acum
# 加总所有consequent的结果
sum1 = np.sum(bucket1)
# sum1*最后一层的误差的delta
bucket2[colY] = sum1 * (ANFISObj.Y[rowX, colY] -
theLayerFive[rowX, colY]) * (-2)
# 加总所有的colY的结果
sum2 = np.sum(bucket2)
# MF-alpha中第rowX个input的参数修正delta
bucket3[rowX] = sum2
# 加总所有的inputcase的结果
sum3 = np.sum(bucket3)
# MF的第timesThru个参数的修正delta
parameters[timesThru] = sum3
# 计算MF的下一个参数
timesThru = timesThru + 1
# MF的参数修正delta
paramGrp[MF] = parameters
return paramGrp