import??pandas?as?pd
import?numpy?as?np
import?matplotlib.pyplot?as?plt
import?matplotlib?as?mpl
from?scipy?import?linalg


class?ran_subsid（）:
????def?__init__（selftdata）:
????????self.tdata=tdata
????def?subsid（self）:
????????print（self.tdata.shape）
????????（TimePointNum?MesNodeTotalNum）?=?self.tdata.shape
????????MesNodeTotalNum?=?MesNodeTotalNum?-?1
????????TimePointNum?=?TimePointNum
????????N?=?2?*?n
????????M?=?100??#?將字符串轉化為數值
????????j?=?TimePointNum?-?2?*?M??#?Hankel矩陣最后一個矩陣塊對應坐標為（2?*?i，j）?即2?*?i?+?j需?<=?TimePointNum
????????Hankel?=?np.zeros（（（2?*?M?+?1）?*?MesNodeTotalNum?j））
????????for?col?in?range（0?j）:
????????????m?=?0
????????????for?row?in?range（0?（2?*?M?+?1））:
????????????????km?=?col?+?row
????????????????m?=?m?+?1
????????????????Hankel[row?col]?=?self.tdata[km?1]
????????print（Hankel.shape）
????????Yp?=?Hankel[0:M?*?MesNodeTotalNum?:]
????????Yf?=?Hankel[M?*?MesNodeTotalNum:2?*?M?*?MesNodeTotalNum?:]
????????Yf2?=?Hankel[（M?+?1）?*?MesNodeTotalNum:（2?*?M?+?1）?*?MesNodeTotalNum?:]
????????#?print（Yp.shape?Yf.shape?Yf2.shape）
????????Teop1?=?np.dot（Yf?np.transpose（Yp））?/?j
????????#?組成第二個Toeplitz矩陣
????????Teop2?=?np.dot（Yf2?np.transpose（Yp））?/?j
????????#?print（‘Teop1:‘?Teop1.shape）
????????#?#?組成第一個Toeplitz矩陣
????????[U?S?V]?=?np.linalg.svd（Teop1）
????????S1?=?np.diag（S）
????????#?print（‘S1:‘S1.shape）
????????plt.plot（S?‘k*‘）??#?S1Y用黑色的星號表示
????????plt.ylabel（‘Singular?value‘）
????????plt.xlabel（‘Order?of?system‘）
????????plt.title（‘Singular?value?decomposition?results?‘）
????????plt.show（）
????????#?#?