python复现：PCA-based spatially adaptive denoising of CFA images for single-sensor digital cameras
2024-05-09 12:46:10
PCA-based spatially adaptive denoising of CFA images for single-sensor digital cameras
是2009年一篇基于PCA的图像降噪方法，应用在raw图上，下面的代码和
官方 matlab的结果是一致的（因为是逐句翻译的、、、），但是效率很低，优化空间很大，比如取patch的时候重复计算了很多次。
import cv2
import matplotlib.pyplot as plt
import numpy as np
import scipy
import scipy.signal# 各通道噪声方差
from colour_demosaicing import demosaicing_CFA_Bayer_bilinear
%matplotlib inline
file = r'kodak_fence.tif'
im = cv2.imread(file)
im = im[..., :3]
im = im[..., ::-1]
print(im[100:110,100:110,-1])
[[124 126 128 123 121 121 114 117 122 115][127 128 127 123 121 119 119 120 117 117][127 127 124 124 121 121 120 118 118 112][124 123 119 123 120 121 118 116 117 115][120 115 116 119 121 119 116 114 113 111][119 120 120 122 120 118 111 113 114 113][123 120 121 122 116 115 109 111 118 114][125 123 120 119 117 113 114 113 116 114][117 119 121 119 120 114 115 113 117 116][118 119 120 121 119 118 114 113 118 116]]
im2 = cv2.imread('noise.png')[...,::-1]
im_noise=im2.copy()
print(im2[100:110,100:110,-1])
[[129 127 104 134 132 116 108 108 107 119][146 130 134 122 127 128 116 117 123 119][118 139 125 128 120 113 125 120 138 121][128 133 125 122 116 116 109 114 101 103][110 117 115 116 125 121 124 109 118 117][118 101 130 126 105 118 122 118 108 104][115 116 129 98 119 87 107 106 115 117][124 123 114 109 129 111 120 132 114 97][121 112 134 102 99 130 124 130 130 102][121 112 112 127 106 125 118 98 135 135]]
im.shape
im_clean=im.copy()
bb=1
psnr_noise = 10 * np.log10(255 ** 2 / np.mean((im[bb:-bb,bb:-bb] - im_noise[bb:-bb,bb:-bb]) ** 2, axis=(0,1)))
print(psnr_noise)
[ 29.57315911 29.71359964 30.30441583]
def black_sub(filename, height=800, width=800):raw_image = np.fromfile(filename, dtype=np.uint16)print(len(raw_image))raw_image = raw_image.reshape([height, width])# black levelblack_level = 16white_level = 1023normalized_image = raw_image.astype(np.float32) - black_level# if some values were smaller than black levelnormalized_image[normalized_image < 0] = 0normalized_image = normalized_image / (white_level - black_level)print(normalized_image.min(), normalized_image.max())normalized_image = normalized_image * 255normalized_image2 = np.clip(normalized_image, 0, 255).astype(np.uint8)return normalized_image2
# filename = r'D:\dataset\dang_yingxiangzhiliangceshi\raw\cap_frame_3641.raw'
# tI = black_sub(filename, height=800, width=800)# mI=cv2.blur(tI, (30,30))
n, m, ch = im.shapemI=np.zeros([n, m])
tI=np.zeros([n, m])# noise grgb
mI[0:n,0:m] = im2[:,:,1]
mI[0:n:2,1:m:2] = im2[0:n:2,1:m:2, 0]
mI[1:n:2,0:m:2] = im2[1:n:2,0:m:2, 2]tI[0:n,0:m] = im[:,:,1]
tI[0:n:2,1:m:2] = im[0:n:2,1:m:2, 0]
tI[1:n:2,0:m:2] = im[1:n:2,0:m:2, 2]
psnr = 10 * np.log10(255 ** 2 / np.mean(((mI - tI) ** 2)))
print(psnr)
26.7146060444
2. decomposition
def get_gauss(sigma, len):x = np.arange(-len,len+1)y = np.arange(-len,len+1)xx, yy = np.meshgrid(x,y)z = np.exp(-(xx*xx+yy*yy)/2/(sigma*sigma)) / (2 * np.pi * sigma*sigma)return zw = 10
f = get_gauss(3, w)
print(f[:10,:10])
[[ 2.64291611e-07 7.59460747e-07 1.95286554e-06 4.49349653e-069.25212596e-06 1.70468335e-05 2.81054770e-05 4.14651518e-055.47419944e-05 6.46700251e-05][ 7.59460747e-07 2.18236448e-06 5.61169806e-06 1.29123819e-052.65866421e-05 4.89852888e-05 8.07630877e-05 1.19153063e-041.57305015e-04 1.85833918e-04][ 1.95286554e-06 5.61169806e-06 1.44298331e-05 3.32026980e-056.83644778e-05 1.25960009e-04 2.07672947e-04 3.06388333e-044.04491667e-04 4.77850443e-04][ 4.49349653e-06 1.29123819e-05 3.32026980e-05 7.63986075e-051.57305015e-04 2.89830945e-04 4.77850443e-04 7.04992167e-049.30725575e-04 1.09952235e-03][ 9.25212596e-06 2.65866421e-05 6.83644778e-05 1.57305015e-043.23891607e-04 5.96762985e-04 9.83895828e-04 1.45158148e-031.91636740e-03 2.26392058e-03][ 1.70468335e-05 4.89852888e-05 1.25960009e-04 2.89830945e-045.96762985e-04 1.09952235e-03 1.81280588e-03 2.67450615e-033.53086373e-03 4.17122264e-03][ 2.81054770e-05 8.07630877e-05 2.07672947e-04 4.77850443e-049.83895828e-04 1.81280588e-03 2.98881162e-03 4.40951518e-035.82141014e-03 6.87718348e-03][ 4.14651518e-05 1.19153063e-04 3.06388333e-04 7.04992167e-041.45158148e-03 2.67450615e-03 4.40951518e-03 6.50553684e-038.58856282e-03 1.01461881e-02][ 5.47419944e-05 1.57305015e-04 4.04491667e-04 9.30725575e-041.91636740e-03 3.53086373e-03 5.82141014e-03 8.58856282e-031.13385587e-02 1.33949244e-02][ 6.46700251e-05 1.85833918e-04 4.77850443e-04 1.09952235e-032.26392058e-03 4.17122264e-03 6.87718348e-03 1.01461881e-021.33949244e-02 1.58242334e-02]]
w = 10fmI = cv2.GaussianBlur(mI,(2*w+1,2*w+1),3)
print(fmI[100:110,100:110])
[[ 121.93832694 120.80475462 119.34427302 117.70715601 116.06921131114.58486129 113.35933285 112.43633939 111.81440447 111.46699312][ 121.52631498 120.47457756 119.06497391 117.42939834 115.73886432114.16113306 112.82476593 111.80118861 111.11348537 110.74756437][ 120.87684224 119.92483971 118.59186934 116.98478683 115.2656273113.61417197 112.18455321 111.07980339 110.35132867 109.99891044][ 120.06088905 119.22871398 118.0002417 116.45487617 114.74288424113.05241178 111.56081857 110.40168771 109.65525121 109.33631585][ 119.17015693 118.48072734 117.38722186 115.94233693 114.28226138112.59720486 111.08110038 109.89275087 109.13933657 108.8525714 ][ 118.2985367 117.77233662 116.84362262 115.54084722 113.98304615112.35314865 110.851063 109.65205922 108.88682568 108.60707037][ 117.48539156 117.12919512 116.38418959 115.25858743 113.85106686112.32643485 110.8775763 109.68491146 108.89737908 108.58942516][ 116.73276808 116.52954776 115.9655374 115.0346916 113.81328909112.43786173 111.08081869 109.91515716 109.10092106 108.73597896][ 115.98315995 115.88488868 115.46792689 114.72136547 113.70067514112.5076856 111.28264307 110.17813221 109.35522429 108.93094655][ 115.16712536 115.10319425 114.77481649 114.17840339 113.35413192112.36733278 111.31740348 110.32423396 109.53731509 109.08319369]]
smI = mI - fmI
print(smI[100:110,100:110])
[[ 29.06167306 12.19524538 -14.34427302 -16.70715601 -10.0692113117.41513871 -5.35933285 17.56366061 -5.81440447 -5.46699312][ 24.47368502 27.52542244 14.93502609 -13.42939834 11.26113568-14.16113306 3.17523407 0.19881139 11.88651463 -1.74756437][ 6.12315776 -2.92483971 21.40813066 13.01521317 9.73437277.38582803 -11.18455321 -13.07980339 -13.35132867 14.00108956][ 7.93911095 -17.22871398 6.9997583 -5.45487617 1.25711576-10.05241178 -2.56081857 -4.40168771 -8.65525121 -14.33631585][-14.17015693 -1.48072734 2.61277814 -15.94233693 -4.28226138-3.59720486 9.91889962 2.10724913 -10.13933657 21.1474286 ][ -0.2985367 12.22766338 13.15637738 29.45915278 -8.98304615-7.35314865 11.148937 -20.65205922 -0.88682568 17.39292963][ 4.51460844 0.87080488 -0.38418959 1.74141257 -25.85106686-25.32643485 -21.8775763 -37.68491146 4.10262092 -36.58942516][ 7.26723192 -3.52954776 -1.9655374 6.9653084 15.18671091-1.43786173 8.91918131 -13.91515716 4.89907894 9.26402104][-11.98315995 14.11511132 9.53207311 23.27863453 -7.7006751417.4923144 10.71735693 8.82186779 5.64477571 -3.93094655][ 5.83287464 -5.10319425 -2.77481649 14.82159661 -7.3541319229.63266722 6.68259652 -22.32423396 25.46268491 -3.08319369]]
plt.figure()
plt.subplot(131)
plt.imshow(mI, cmap='gray')
plt.title("noise")
plt.subplot(132)
plt.imshow(fmI, cmap='gray')
plt.title("filter")
plt.subplot(133)
plt.imshow(np.abs(smI), cmap='gray')
plt.title("detail")
plt.show()
denoiseing
dI=smI.copy();
s=6;#default variable block size
k=34;# training block size,(k-s)/2 should be an even integer%%%%%%%%%
k2=k//2;#Bayer Pattern: G R; B G
v=12;
vr=13/12;
vb=10/12;
vg=1;# noise pattern, GRBG的6*6，每个通道的噪声方差乘上一个 1.21倍
c=1.1
D = np.zeros([s,s], dtype=np.float32)
D[:,:] = c*vg*v
D[0:s:2, 1:s:2] = c*vr*v # r
D[1:s:2, 0:s:2] = c*vb*v # b
D=D**2
print(D)
[[ 174.23999 204.49 174.23999 204.49 174.23999 204.49 ][ 121. 174.23999 121. 174.23999 121. 174.23999][ 174.23999 204.49 174.23999 204.49 174.23999 204.49 ][ 121. 174.23999 121. 174.23999 121. 174.23999][ 174.23999 204.49 174.23999 204.49 174.23999 204.49 ][ 121. 174.23999 121. 174.23999 121. 174.23999]]
def get_pca(X, D):"""X : 36 * 100 , fetures * n_samplesD : 36, 每个feature的噪声方差"""D = D.reshape(-1)h, n = X.shapemx = np.mean(X, 1).reshape(-1, 1)X = X - mxconvX = X @ X.T / (n-1)DD = np.diag( D)convX = convX - DDconvX[convX < 0] = 0.0001[eig_val, eig_vec] = np.linalg.eigh(convX) # convX * eig_vec = eig_val.reshape(1, -1) * eig_vec# eig_val是特征值， eig_vec是对应的特征向量，col形式的。#print('eig_val : ', eig_val,eig_vec, eig_val.shape, eig_vec.shape)# print(np.sum(convX @ eig_vec - eig_val.reshape(1, -1) * eig_vec <0.01))# print(eig_vec @ X == X @eig_vec.T)ind = np.argsort(eig_val)ind = ind[::-1]eig_vec = eig_vec[:,ind].Teig_val = eig_val[ind]Y = eig_vec @ X #print('ind:\n',ind, eig_val,eig_vec ,Y)return Y, eig_vec, eig_val, mx
tttt=0def pca_cfa(block, D, s):global tttt"""block : 34*34 block, k = 34D:s:6 or 8"""h, w = block.shapeH = (h-s) // 2 + 1 # 15W = (w-s) // 2 + 1L = H*WX = np.zeros([s*s, L]) # 36*225 : 34*34的block, 6*6的patch, step为2, 一共15*15=225个patchDN = np.zeros([1, s*s])k = 0for i in np.arange(0, s):for j in np.arange(0, s):X[k, :] = block[i:(h-s+i+1):2, j:(w-s+j+1):2].reshape([1, L])DN[0, k] = D[i, j]k = k + 1# X是 6*6 * 225# DN 是 6*6个值,每个值对应的该像素的标准差# 中间的一个值q = L // 2 # 112Xc = X[:, q].reshape(-1, 1) # 36XC = np.tile(Xc, [1, L]) # 36 * 225# print(DN, k, X.shape, XC.shape)E = np.abs(X-XC)mE = np.mean(E, axis=0) # 每列的均值，相当于求每个patch与中心patch的均值ind = np.argsort(mE)num = 100X = X[:, ind[:num]]# print('X:',X[:10,:10], DN)# 到这里选出了100个相似的patch, 从225个里面Y, P, V, mx = get_pca(X, DN)#print(Y[:10,:10])Y1 = np.zeros(Y.shape)# inverse transform\# （设置10个为0）for i in np.arange(0,s*s-8):y = Y[i,:]p = P[i,:]p = p*pnv = np.sum(p*DN) # p*DN 噪声方差经过 pca转置, P是单位矩阵，类似求均值了，所以sumif 0==tttt:print(p.shape, DN.shape, (p*DN).shape,nv.shape)py = np.mean(y*y) + 0.01t = max(0, py-nv)if 0==tttt:print(py.shape,py, t)tttt = 1c = t / py# print(c) #基本上很小的数，0-0.3之间Y1[i, :] = 1* Y[i, :]B = P.T @ Y1 + mxB = B[:, 0]B = np.reshape(B, [s, s])#B = B.Treturn B
step = 2
print(n-k,m-k)
for i in np.arange(0, n - k, step):for j in np.arange(0, m - k, step):#if i== 50 and j==50:Block = smI[i:i+k, j:j+k].copy()db = pca_cfa(Block, D, s)dI[i+k2-1:i+k2+1, j+k2-1:j+k2+1] = db[2:4, 2:4]#print(Block[:10,:10])#print(db)#print(x[:10.:10])#print(y[:10.:10])734 478
(36,) (1, 36) (1, 36) ()
() 167.639940721 0
i
a = n-k
b=i+k-1
c=i+k2-1
db
t = dI[99:110,99:110]
print(i,a,b,c,db,t)732 734 765 748 [[-25.80532161 11.18396885 21.5562875 15.1691311 15.4840011229.98028105][-26.3432829 21.56501168 -43.50587703 4.79103188 -4.43557792-7.3855937 ][ 17.00578207 57.53942483 28.85620708 29.88176839 15.8410509313.18102019][-25.43627059 22.4839088 16.93029056 14.54577497 -20.64510537-5.64869904][ 0.15234094 -5.87031587 9.84325354 21.98484204 -6.7842256230.82852626][ -2.9422656 -5.54282893 -14.33997315 -2.43183229 -39.3673716814.82723805]] [[ 2.39425621 -7.50795736 10.1263103 -1.00761166 -14.142967234.27147071 9.48992787 -17.40794547 8.14357609 -0.593323691.87093838][ -5.92387084 31.39388273 14.87143502 -12.58273904 -11.87516387-2.60759948 8.9776016 -4.55399497 11.75790601 -5.73767096-6.51739886][ 6.10456174 22.48420321 21.68501677 15.79794982 -15.8848247211.86451625 -9.66591387 3.03897717 2.02633336 12.97475621.73978256][ -7.54473426 10.60003328 4.92408636 18.46661195 8.991615386.65299865 5.16234318 -15.96123275 -7.76966259 -13.200319742.27381012][-16.26497218 2.37717583 -22.06340946 0.59562629 -5.183137074.26679605 -17.48835341 2.85138918 -4.56904362 -9.51967616-15.8008651 ][ 0.70260208 1.76680755 2.85435522 -2.78418131 -7.97310004-2.99846244 -3.51906016 9.60667614 3.02749668 3.4188040322.40951242][ 2.06235778 -0.97282281 8.61112305 18.59272929 28.4612208-7.33356166 -5.07142281 11.37647051 -22.11546397 -7.403685963.12237772][ -6.29088137 2.36391139 -7.30272654 0.05294837 4.31963347-22.88124845 -27.44595565 -21.358552 -36.03650032 12.40441245-30.47078166][ 6.96705517 4.26531585 3.541887 1.30659318 3.0370303715.66634705 -2.43022019 6.90065626 -13.58299795 5.8628310310.24549084][ 8.18625562 -4.30581833 7.32269359 9.17154543 21.27121419-2.85394241 19.95621912 7.63124297 3.05477624 4.34158611-9.33247657][ -4.23236535 10.92552271 -9.23752909 -0.75844497 16.45297477-4.0952441 29.42888478 7.88977393 -17.74546651 23.72911602-0.42439872]]
ddI = dI.copy()ddI = ddI + fmIplt.figure(figsize=(20,15))
plt.subplot(131)
plt.imshow(mI,cmap='gray')
plt.subplot(132)
plt.imshow(tI,cmap='gray')
plt.subplot(133)
plt.imshow(ddI,cmap='gray')
plt.show()
bb = 20
psnr = 10 * np.log10(255 ** 2 / np.mean(((ddI[bb:-bb,bb:-bb] - tI[bb:-bb,bb:-bb]) ** 2)))
print(psnr)
psnr = 10 * np.log10(255 ** 2 / np.mean(((mI[bb:-bb,bb:-bb] - tI[bb:-bb,bb:-bb]) ** 2)))
print(psnr)
27.4094591896
26.7145989939
print(ddI.min(),ddI.max(),ddI.mean())
#
im_noise_bayer2rgb = demosaicing_CFA_Bayer_bilinear(mI, "GRBG")
im_noise_bayer2rgb2 = np.clip(im_noise_bayer2rgb,0,255).astype(np.uint8)
rgb = demosaicing_CFA_Bayer_bilinear(ddI, "GRBG")
rgb2 = np.clip(rgb,0,255).astype(np.uint8)
print(rgb2.max(),rgb2.min())
plt.figure(figsize=(20,15))
plt.subplot(131)
plt.imshow(im_noise_bayer2rgb2)
plt.subplot(132)
plt.imshow(im2)
plt.subplot(133)
plt.imshow(rgb2)
plt.show()bb = 1
psnr = 10 * np.log10(255 ** 2 / np.mean(((im[bb:-bb,bb:-bb] - rgb2[bb:-bb,bb:-bb]) ** 2)))
print(psnr)psnr_noise = 10 * np.log10(255 ** 2 / np.mean(((im[bb:-bb,bb:-bb] - im2[bb:-bb,bb:-bb]) ** 2)))
print(psnr_noise)bb = 1
psnr = 10 * np.log10(255 ** 2 / np.mean(((im[bb:-bb,bb:-bb] - rgb2[bb:-bb,bb:-bb]) ** 2), axis=(0,1)))
print(psnr)psnr_noise = 10 * np.log10(255 ** 2 / np.mean(((im[bb:-bb,bb:-bb] - im_noise[bb:-bb,bb:-bb]) ** 2), axis=(0,1)))
print(psnr_noise)
-13.911260205 273.354212873 112.224014452
255 030.3929142051
29.8523440731
[ 30.19659709 30.45414954 30.53523719]
[ 29.57315911 29.71359964 30.30441583]
bayer_diff_noise = np.abs(im_noise_bayer2rgb-im2)
bayer_diff_noise2 = np.clip(bayer_diff_noise,0,255).astype(np.uint8)+40
plt.figure(figsize=(20,15))
plt.imshow(bayer_diff_noise2)
plt.show()bayer_diff_denoise = np.abs(im_noise_bayer2rgb-rgb2)
bayer_diff_denoise2 = np.clip(bayer_diff_noise,0,255).astype(np.uint8)+40
plt.figure(figsize=(20,15))
plt.imshow(bayer_diff_denoise2)
plt.show()
q = np.random.randn(18,6)
conv = q.T@q
[eig_val, eig_vec] = np.linalg.eigh(conv)
# convX * eig_vec = eig_val.reshape(1, -1) * eig_vec
# eig_val是特征值， eig_vec是对应的特征向量，col形式的。
print('eig_val : ', eig_val,eig_vec, eig_val.shape, eig_vec.shape)
print(np.sum(conv @ eig_vec - eig_val.reshape(1, -1) * eig_vec <0.01))
print(eig_vec @ conv - (conv @eig_vec.T).T)
print(q @ eig_vec.T , (eig_vec.T @ q.T).T)
print(eig_vec @ conv)
eig_val : [ 3.00685873 6.20435828 11.58297164 13.42519523 17.6300857243.47319024] [[ 0.08787425 -0.32322719 0.68824544 -0.17445992 0.61739305 -0.05010059][ 0.20655283 -0.32032156 -0.31217256 -0.10821841 0.05036977 -0.86199187][-0.39190487 -0.22314618 -0.36999561 -0.7642356 0.15395569 0.22794997][-0.02485003 0.34875418 -0.446504 0.2923101 0.76925841 0.03440172][-0.34883424 -0.73228301 -0.1652491 0.53024788 0.01514715 0.18269308][-0.82080556 0.29198661 0.25553213 0.08478473 -0.0244625 -0.40980303]] (6,) (6, 6)
36
[[ 0. 0. 0. 0. 0. 0.][ 0. 0. 0. 0. 0. 0.][ 0. 0. 0. 0. 0. 0.][ 0. 0. 0. 0. 0. 0.][ 0. 0. 0. 0. 0. 0.][ 0. 0. 0. 0. 0. 0.]]
[[-0.28604411 -1.12444082 -1.99047454 -0.81004248 -1.61292579 -0.66351663][ 0.21973116 0.35220044 0.2430437 -0.22633582 0.70423737 -1.21817532][-0.48757707 0.01916215 0.15872299 -0.52964081 1.14307178 -0.31505747][-1.30867509 -0.36797715 -0.33869114 1.48919373 0.25654388 -0.5580843 ][ 0.95980308 -0.3433002 0.48891304 1.65378029 0.9426408 0.79037999][-0.82253679 -0.4499282 -1.73138871 1.46541122 0.29257894 -0.12554285][-0.57803434 -0.12893755 0.97914154 1.18823126 -1.00594376 0.42347444][ 0.93968361 0.86445293 -1.43869371 -0.24434619 1.03763686 0.05760273][ 0.61635883 1.11112675 -0.07769851 -0.49675303 1.05073505 -0.5592649 ][-2.18383768 -2.01124521 -1.16609084 1.29879153 -1.17353974 -0.45591985][-0.36399424 -0.78391182 0.35930308 -0.19128518 0.26045013 -1.02106562][ 1.32562539 0.37206846 -0.69934282 0.2410139 -0.68051064 -1.20360493][ 0.11779126 -0.12449757 -0.52275902 -0.22211952 -0.61323223 0.22617533][-0.27327115 -0.94221235 -0.99726921 -0.05611817 -0.15930349 1.35568788][ 1.39445607 -0.25021183 -0.63857315 -1.01563787 0.89414256 0.87480807][-0.77712993 -1.08026094 1.29529701 -0.82567868 -0.92267392 0.13429965][ 1.69804121 2.26584728 -0.53652959 -0.75482311 2.53634673 0.09713854][ 0.26171984 0.42264116 -0.62067484 0.33506406 0.45127744 -1.77625057]] [[-0.05136115 -0.16015255 0.20927743 -1.91351599 1.69654497 -1.5473325 ][-0.3466322 0.26303613 1.1393501 0.32727152 0.2967792 0.76149943][-0.13502622 1.21278329 0.34400607 0.27365695 0.02051475 0.51668239][ 0.13371458 0.34012412 0.14721203 1.53336544 0.77306548 -1.20567201][-1.00318087 -0.66462649 -1.21801211 1.50908486 -0.32198251 0.46228868][ 0.13852317 0.15944682 -0.74832478 1.00510857 1.87510392 -0.9973177 ][ 0.35020046 -0.79061303 -0.12505924 0.82516552 -0.98020791 -1.2278269 ][ 0.15218709 0.03377902 -0.56454656 -0.18720029 1.38505245 1.59480662][ 0.15723072 0.22838697 0.54392109 0.14056405 0.34432641 1.66525424][-0.11682554 0.47656554 -0.13409514 0.46727202 1.24691184 -3.37847056][-0.77504359 0.58505138 0.93077875 0.12223913 0.05350184 -0.44269169][-0.36338127 -1.44019124 0.7929206 -0.40871018 1.06776627 0.46103859][ 0.16845739 -0.29130282 -0.26683035 -0.65513962 0.27303937 -0.30167113][-0.06772517 0.39145899 -1.61245105 -0.5986978 0.34968528 -0.76476109][-0.7802866 0.27700291 -1.11717732 -1.04000602 0.21367203 1.39651656][-0.30160065 0.48566603 0.49775838 -0.75119022 -1.49195163 -1.27866865][ 0.31816796 0.38629151 -0.27657952 0.33850528 0.67752998 3.79696451][-0.26735673 -0.18439108 1.29255671 0.50863063 1.35019886 0.49539963]]
[[ -0.40105476 -19.20241152 9.97654104 -0.40928512 6.29898326-10.4763983 ][ 0.50257292 -20.69111949 2.49696061 0.02592651 5.38770129-11.44541867][ -7.98031657 -3.67744296 -5.78579834 -12.84257337 1.561091531.28449002][ -0.2390802 10.52613786 -8.81522432 5.15695706 6.199218554.25763913][ -3.32536728 -22.28929842 1.40108721 6.37097294 5.42142478-8.08483245][-11.00613909 2.56600124 3.68737603 -0.84821884 0.51813781-3.33330161]]
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