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rom_stuff_dsamp_burg.py
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import numpy as np
from sklearn import cluster
from scipy import interpolate
import matplotlib.pyplot as plt
from burg import plot_it, locations
#from cfd import plot_it
#from cfd import plot_ind
from util import read_me
def cluster_me(X, k):
ck, ind, _ = cluster.k_means(X.T, k)
Xk = [X[:, ind==i] for i in range(k)]
return ck, Xk, ind
def pod(Xk, ny):
Uk, Sk, Vk = np.linalg.svd(Xk, full_matrices=0, compute_uv=1)
return Uk[:, :min(ny, Uk.shape[1])]
def project(Vk, v):
return np.dot(Vk, np.dot(Vk.T, v))
from rom_stuff import pod, read_me, cluster_me, downsamp_1D, downsamp_cberg, matrix_interp
#def reconstruct(A_downsamp, A_indices)
if __name__ == '__main__':
snaps = read_me('burg/snaps_0p05_0p02_5.dat')
# snaps = read_me('cfd/naca0012ref0p1.snaps.mu0',
# 'cfd/naca0012ref0p1.snaps.mu3',
# 'cfd/naca0012ref0p1.snaps.mu5',
# 'cfd/naca0012ref0p1.snaps.mu7',)
#test with small number of snaps
# snaps = snaps[0:6,0:9]
# Apply k means clustering to samples
nclusti = 6
nclustj = 2
nclust = (nclusti,nclustj)
Xk = []
ck = []
ind = [0]*nclust[0]
ck_col, Xk_col, ind_col = cluster_me(snaps, nclust[0])
## Spatial discretization for entire mesh
lmin, lmax, nel = 0.0, 100.0, snaps.shape[0] #0.0, 100.0, 1000
nodes = np.linspace(lmin, lmax, nel+1)
# Hyper reduction at the chosen points
pvect = 250
pct_tol = 1*10**-7 #1*10**-15 or -11 or -5
tol = pct_tol*(np.max(snaps)-np.min(snaps))
loc = 0.5*(nodes[:-1]+nodes[1:])
A_ind = [downsamp_1D(Xk_col[k], loc, tol)[:-1] for k in range(nclust[0])]
lenA = [len(A_ind[k]) for k in range(nclust[0])]
print(lenA)
Xk_col_down = [Xk_col[k][np.array(A_ind[ind_col[pvect]])] for k in range(nclust[0])]
# Perform POD on column clusters
Vk_col = [pod(Xk_col[k], 10) for k in range(nclust[0])]
# Perform POD on downsampled column clusters
Vk_col_down = [pod(Xk_col_down[k], 10) for k in range(nclust[0])]
# Hyper reduction according to carlberg at the chosen points
A_ind_cberg = [downsamp_cberg(Vk_col[k], 350) for k in range(nclust[0])]
Xk_col_down_cberg = [Xk_col[k][np.array(np.sort(A_ind_cberg[ind_col[pvect]]))] for k in range(nclust[0])]
Vk_col_down_cberg = [Vk_col[k][np.sort(A_ind_cberg[ind_col[pvect]])] for k in range(nclust[0])]
Vk_col_down_cberg = [pod(Xk_col_down_cberg[k], 10) for k in range(nclust[0])]
#
# # Apply k means clustering to deconstruct domain into submatrices
# for i in range(nclust[0]):
# cki, Xki, indi = cluster_me(Xk_col[i].T, nclust[1])
# Xk = Xk + Xki
# ck = list(ck)+list(cki)
# ind[i] = indi
# Vk = [pod(Xk[k].T, 50) for k in range(nclust[0]*nclust[1])]
# Vk2 = [pod(Vk[k].T, 40) for k in range(nclust[0]*nclust[1])]
#
# #Choose a vector for testing
#pvect=1050 #1050 for berg, 20 for CFD
#pvect2 =200
# Construct test vector in downsampled space
downsample = snaps[:, pvect][np.array(A_ind[ind_col[pvect]])]
downlocs = np.array(A_ind[ind_col[pvect]])/10
# downsample2 = snaps[:, [pvect2]][np.array(A_ind[ind_col[pvect2]])]
# downlocs2 = np.array(A_ind[ind_col[pvect2]])/10
# Project Vk matrix onto given test vector in downsampled space
proj = project(Vk_col_down[ind_col[pvect]], downsample)
# Reconstruct vector in original space?
projinterp = np.interp(np.linspace(0.0, 100.0, snaps.shape[0]),downlocs,proj)
# Construct test vector in downsampled CBERG space
Aind = np.sort(A_ind_cberg[ind_col[pvect]])
downsample_cberg = snaps[:, pvect][np.array(Aind)]
downlocs_cberg = np.array(Aind)/10
# downsample2 = snaps[:, [pvect2]][np.array(A_ind[ind_col[pvect2]])]
# downlocs2 = np.array(A_ind[ind_col[pvect2]])/10
# Project Vk matrix onto given test vector in downsampled space
proj_cberg = project(Vk_col_down_cberg[ind_col[pvect]], downsample_cberg)
# Reconstruct vector in original space?
#projinterp_cberg = np.interp(np.linspace(0.0, 100.0, snaps.shape[0]),downlocs_cberg,proj_cberg)
f = interpolate.interp1d(downlocs_cberg, proj_cberg, fill_value = "extrapolate")
projinterp_cberg = f(np.linspace(0.0, 100.0, snaps.shape[0]))
# # Construct test vector in submatrix space
# indvect=ind[ind_col[pvect]]
# snap = snaps[:, [pvect]]
# snapk = [snap[indvect==i] for i in range(nclust[1])]
# # Project Vk submatrces onto given test vector in submatrix space
# Vksub = Vk[ind_col[pvect]*nclust[1]:(ind_col[pvect]+1)*nclust[1]]
# proj = [project(Vksub[i], snapk[i]) for i in range(nclust[1])]
# # Reconsruct vector in original space
# projl = Vkvectl=[list(a) for a in proj]
# projvect = [0]*snaps.shape[0]
# for i in range(snaps.shape[0]):
# projvect[i]=projl[indvect[i]].pop(0)
#
# # Berg Plotting
# # plot 1st 5 modes of 1st basis
# plot_it(Vk[0][:, :5])
# # plot centers
# plot_it(ck_col.T)
# # plot vector and its projection onto nearest basis
# plot_it(np.hstack((snaps[:, [pvect]], projvect)))
# plot original vector
plot_it(snaps[:-1, [pvect]],np.linspace(0.0, 100.0, 1000)[:-1, None])
# # plot downsampled vectors
plot_it(downsample,downlocs)
plot_it(downsample_cberg,downlocs_cberg, [0,100,2,6])
# print(downsample.shape)
#plot_it(downsample2,downlocs2)
# plot projections of downsampled vectors
#plot_it(proj,downlocs)
#plot_it(proj_cberg,downlocs_cberg)
# # plot vector and its projection onto nearest col-only basis
plot_it(np.hstack((snaps[:, [pvect]], project(Vk_col[ind_col[pvect]], snaps[:, [pvect]]))))
# plot both downsampled and un-downsampled vectors
plot_it(np.hstack((snaps[:, [pvect]], projinterp[:,None])))
plot_it(np.hstack((snaps[:, [pvect]], projinterp_cberg[:,None])))
# # plot vector and its projection onto 1st col-only basis
## plot_it(np.hstack((snaps[:, [pvect]], project(Vk_col[0], snaps[:, [pvect]]))))
# Burg Error Calc
# Calculate RMS error between vector and projection
projcolvect = project(Vk_col[ind_col[pvect]], snaps[:, [pvect]])
Mean_Sqrt_Error_colvect = np.sqrt(np.mean(np.square(projcolvect-snaps[:, [pvect]])))
Mean_Sqrt_Error_interp = np.sqrt(np.mean(np.square(projinterp[:,None]-snaps[:, [pvect]])))
Mean_Sqrt_Error_interp_mod = np.sqrt(np.mean(np.square(projinterp_cberg[:,None]-snaps[:, [pvect]])))
print("--- Mean Abs Error is %s---" %round(Mean_Sqrt_Error_colvect,5))
print("--- Mean HROM Orig Sqrt Error is %s---" %round(Mean_Sqrt_Error_interp,5))
print("--- Mean HROM Mod Sqrt Error is %s---" %round(Mean_Sqrt_Error_interp_mod,5))
#
# # CFD Plotting
# # plot centers
## plot_it(ck_col.T[:,0])
# # plot vector
## plot_it(np.hstack((snaps[:, [pvect]])),'uabs')
# # plot vector and its projection onto nearest basis
## plot_it(np.hstack((projvect)),'uabs')
# # plot vector projection onto nearest col-only basis
## plot_it(np.hstack((project(Vk_col[ind_col[pvect]], snaps[:, [pvect]]))),'uabs')
# # plot vector projection onto 1st col-only basis
## plot_it(np.hstack((project(Vk_col[0], snaps[:, [pvect]]))))
# # plot vector and its projection onto nearest basis
## plot_ind(np.hstack((indvect)),'ru',nclust[1])
#
# # Old CFD Plotting
# #Choose vector to plot
## pvect=20
# # plot centers
## plot_it(ck[:,0])
# # plot vector
## plot_it(np.hstack((snaps[:, [pvect]])))
# # plot vector projection onto nearest basis
## plot_it(np.hstack((project(Vk[ind[pvect]], snaps[:, [pvect]]))))
# # plot vector projection onto 1st basis
## plot_it(np.hstack((project(Vk[0], snaps[:, [pvect]]))))
#
# #Discarded:
# # Vkvectl=[list(a) for a in Vk[ind_col[pvect]*nclust[1]:(ind_col[pvect]+1)*nclust[1]]]
## Vkvect = [0]*snaps.shape[0]
## for i in range(snaps.shape[0]):
## Vkvect[i]=Vkvectl[indvect[i]].pop(0)
## Vkvect = np.array(Vkvect)
# # Split Vk for sub-matrix projections