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59 lines
1.9 KiB
Python
59 lines
1.9 KiB
Python
# !!!
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import numpy as np
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from QR import QR_fact
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# !!!
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def R3SVD_LiYu(A, t, delta_t, npow, err_thr, maxit):
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# !!!
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# build initial QB decomposition
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# !!!
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n = A.shape[1]
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G = np.random.randn(n, t) # n x t Gaussian random matrix
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normA = np.linalg.norm(A, ord='fro')**2
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i_it = 0
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rank = 0
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Y = np.dot(A,G)
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# The power scheme
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for j in range(npow):
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Q = QR_fact(Y)
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Q = QR_fact( np.dot(A.T,Q) )
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Y = np.dot(A,Q)
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# orthogonalization process
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Q_old = QR_fact(Y)
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B = np.dot(Q_old.T,A)
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normB = np.linalg.norm(B, ord='fro')**2
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# error percentage
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errpr = abs( normA - normB ) / normA
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rank += t
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i_it += 1
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print("iteration = {}, rank = {}, error = {}".format(i_it, rank, errpr))
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# !!!
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# incrementally build up QB decomposition
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# !!!
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while ( (errpr>err_thr) and (i_it<maxit) and (rank<=min(A.shape)-delta_t) ): #
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G = np.random.randn(n, delta_t) # n x delta_t Gaussian random matrix
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Y = np.dot(A,G)
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Y = Y - np.dot(Q_old, np.dot(Q_old.T,Y) ) # orthogonalization with Q
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# power scheme
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for j in range(npow):
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Q = QR_fact(Y)
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Q = QR_fact( np.dot(A.T,Q) )
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Y = np.dot(A,Q)
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Y = Y - np.dot(Q_old, np.dot(Q_old.T,Y) ) # orthogonalization with Q
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Q_new = QR_fact(Y)
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B_new = np.dot(Q_new.T,A)
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# build up approximate basis
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Q_old = np.append(Q_new, Q_old, axis=1)
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B = np.append(B_new, B, axis=0)
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rank += delta_t
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i_it += 1
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normB += np.linalg.norm(B_new, ord='fro')**2
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errpr = abs( normA - normB ) / normA
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print("iteration = {}, rank = {}, error = {}".format(i_it, rank, errpr))
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# !!!
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print("iteration = {}, rank = {}, error = {}".format(i_it, rank, errpr))
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UL, SL, VLT = np.linalg.svd(B, full_matrices=0)
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UL = np.dot(Q_old,UL)
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# !!!
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return UL, SL, VLT
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# !!!
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