ວິທີການພິມຮູບພາບທີ່ມີ API SVD ແລະ TensorFlow Core

ການທົບທວນຄືນ Content ລະຫັດ QR ລະຫັດ QR ລະຫັດ QR ການເກັບຮັກສາລະດັບຕ່ໍາກັບ SVD ຮູບພາບ ສໍາ ລັບ Loading ລະຫັດ QR ການທົບທວນຄືນ approximations ປະເພດ: Compression Factor vs Rank ຊື່ຫຍໍ້ຂອງ : Cumulative sum of singular values ລະຫັດ QR ພາສາລາວ ລະຫັດ QR ການຝຶກອົບຮົມ ITS (SVD) ແລະການນໍາໃຊ້ຂອງຕົນສໍາລັບບັນຫາການປະມານຕ່ໍາ. SVD ໄດ້ຖືກນໍາໃຊ້ເພື່ອ factorize matrix ທີ່ແທ້ຈິງຫຼືທີ່ສົມບູນແບບແລະມີປະເພດຕ່າງໆຂອງການນໍາໃຊ້ໃນວິທະຍາສາດຂໍ້ມູນ, ເຊັ່ນ compression ຮູບພາບ. ຮູບພາບສໍາລັບການຝຶກອົບຮົມນີ້ມາຈາກ Google Brain ຂອງ ໂຄງການ ລະຫັດ QR ຮູບພາບ ລະຫັດ QR import matplotlib from matplotlib.image import imread from matplotlib import pyplot as plt import requests # Preset Matplotlib figure sizes. matplotlib.rcParams['figure.figsize'] = [16, 9] import tensorflow as tf print(tf.__version__) 2024-08-15 02:40:31.007111: E external/local_xla/xla/stream_executor/cuda/cuda_fft.cc:485] Unable to register cuFFT factory: Attempting to register factory for plugin cuFFT when one has already been registered 2024-08-15 02:40:31.028202: E external/local_xla/xla/stream_executor/cuda/cuda_dnn.cc:8454] Unable to register cuDNN factory: Attempting to register factory for plugin cuDNN when one has already been registered 2024-08-15 02:40:31.034794: E external/local_xla/xla/stream_executor/cuda/cuda_blas.cc:1452] Unable to register cuBLAS factory: Attempting to register factory for plugin cuBLAS when one has already been registered 2.17.0 ລະຫັດ QR ຄຸນນະສົມບັດຂອງ matrix, A, ໄດ້ຖືກຄັດເລືອກໂດຍ factorization ຕໍ່ໄປນີ້: ລະຫັດ QR ວິທີການ Am×n: matrix ການເຂົ້າເຖິງທີ່ m≥n Um×n: matrix orthogonal, UTU=I, ມີລັກສະນະທັງ ຫມົດ, ui, ທີ່ສະແດງໃຫ້ເຫັນ vector singular ຂອງ A Σn×n: matrix diagonal ມີແຕ່ລະອຽດ diagonal, σi, ສະແດງໃຫ້ເຫັນຄຸນນະພາບ singular ຂອງ A VTn×n: matrix orthogonal, VTV=I, ມີແຕ່ລະຊຸດ, vi, ທີ່ສະແດງໃຫ້ເຫັນ vector singular ທີ່ຄົງຂອງ A ໃນເວລາທີ່ m<n, U ແລະ Σ ມີຂະຫນາດ (m×m) ແລະ VT ມີຂະຫນາດ (m×n). ການບັນທຶກ Algebra Linear ຂອງ TensorFlow ມີ Function, , ເຊິ່ງສາມາດຖືກນໍາໃຊ້ເພື່ອຄອມພິວເຕີຂະບວນການຄຸນນະພາບ singular ຂອງຫນຶ່ງຫຼືຫຼາຍ matrix. Start by defining a simple matrix and calculating its SVD factorization. tf.linalg.svd A = tf.random.uniform(shape=[40,30]) # Compute the SVD factorization s, U, V = tf.linalg.svd(A) # Define Sigma and V Transpose S = tf.linalg.diag(s) V_T = tf.transpose(V) # Reconstruct the original matrix A_svd = U@S@V_T # Visualize plt.bar(range(len(s)), s); plt.xlabel("Singular value rank") plt.ylabel("Singular value") plt.title("Bar graph of singular values"); WARNING: All log messages before absl::InitializeLog() is called are written to STDERR I0000 00:00:1723689633.424919 126589 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723689633.428762 126589 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723689633.432420 126589 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723689633.437707 126589 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723689633.449819 126589 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723689633.453529 126589 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723689633.457079 126589 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723689633.460600 126589 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723689633.464019 126589 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723689633.467451 126589 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723689633.470857 126589 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723689633.474376 126589 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723689634.696864 126589 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723689634.698995 126589 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723689634.701043 126589 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723689634.703182 126589 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723689634.705235 126589 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723689634.707223 126589 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723689634.709163 126589 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723689634.711162 126589 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723689634.713114 126589 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723689634.715090 126589 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723689634.717036 126589 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723689634.719041 126589 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723689634.757916 126589 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723689634.759983 126589 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723689634.761969 126589 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723689634.764105 126589 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723689634.766234 126589 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723689634.768229 126589 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723689634.770180 126589 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723689634.772176 126589 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723689634.774158 126589 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723689634.776614 126589 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723689634.779022 126589 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723689634.781451 126589 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 ການ Function ສາມາດຖືກນໍາໃຊ້ເພື່ອຄອມພິວເຕີ matrix reconstruction ຈາກ outputs ຂອງ . tf.einsum tf.linalg.svd A_svd = tf.einsum('s,us,vs -> uv',s,U,V) print('\nReconstructed Matrix, A_svd', A_svd) Reconstructed Matrix, A_svd tf.Tensor( [[0.819255 0.95082176 0.30085772 ... 0.34306473 0.9112067 0.45277762] [0.71988434 0.20786765 0.3098724 ... 0.82478774 0.82917416 0.19994356] [0.23278469 0.17072585 0.10488278 ... 0.60508984 0.8121238 0.10594818] ... [0.10953172 0.72077066 0.30288345 ... 0.5790409 0.15389094 0.11265922] [0.44894537 0.04313891 0.6947845 ... 0.41589245 0.6668094 0.53494996] [0.79140556 0.47814542 0.24980234 ... 0.32851136 0.86007696 0.32692394]], shape=(40, 30), dtype=float32) ການເກັບຮັກສາລະດັບຕ່ໍາກັບ SVD ປະເພດຂອງ matrix, A, ໄດ້ຖືກຄັດເລືອກໂດຍຂະຫນາດຂອງສະຖານທີ່ vector ທີ່ຖືກກວດສອບໂດຍແຜ່ນຂອງຕົນ. SVD ສາມາດຖືກນໍາໃຊ້ເພື່ອປະມານ matrix ມີປະເພດຕ່ໍາ, ເຊິ່ງຫຼັງຈາກນັ້ນຫຼຸດຜ່ອນ dimensionality ຂອງຂໍ້ມູນທີ່ຈໍາເປັນຕ້ອງສໍາລັບການເກັບຮັກສາຂໍ້ມູນທີ່ສະຫນັບສະຫນູນໂດຍ matrix. ການເກັບຮັກສາ rang-r ຂອງ A ໃນຖານະເປັນ SVD ໄດ້ຖືກຄັດເລືອກໂດຍຮູບເງົາ: Ar=UrΣrVrT ວິທີການ Urm×r: matrix ທີ່ປະກອບດ້ວຍຊັ້ນທໍາອິດ r ຂອງ U Σrr×r: matrix diagonal consisting of the first r singular values in Σ Vrr×nT: matrix ທີ່ປະກອບດ້ວຍເສັ້ນທໍາອິດ r ຂອງ VT ຂ້າພະເຈົ້າສືບຕໍ່ໄດ້ຮັບການປະທັບໃຈ ສໍາ ລັບຜູ້ຊ່ຽວຊານໃນການຄົ້ນຄວ້າແລະການປິ່ນປົວຂອງພວກເຮົາ. ຂ້າພະເຈົ້າສືບຕໍ່ໄດ້ຮັບການປະທັບໃຈ ສໍາ ລັບຜູ້ຊ່ຽວຊານໃນການຄົ້ນຄວ້າແລະການປິ່ນປົວຂອງພວກເຮົາ, ຂ້າພະເຈົ້າສືບຕໍ່ໄດ້ຮັບການປະທັບໃຈ ສໍາ ລັບຜູ້ຊ່ຽວຊານຂອງພວກເຮົາ. def rank_r_approx(s, U, V, r, verbose=False): # Compute the matrices necessary for a rank-r approximation s_r, U_r, V_r = s[..., :r], U[..., :, :r], V[..., :, :r] # ... implies any number of extra batch axes # Compute the low-rank approximation and its size A_r = tf.einsum('...s,...us,...vs->...uv',s_r,U_r,V_r) A_r_size = tf.size(U_r) + tf.size(s_r) + tf.size(V_r) if verbose: print(f"Approximation Size: {A_r_size}") return A_r, A_r_size def viz_approx(A, A_r): # Plot A, A_r, and A - A_r vmin, vmax = 0, tf.reduce_max(A) fig, ax = plt.subplots(1,3) mats = [A, A_r, abs(A - A_r)] titles = ['Original A', 'Approximated A_r', 'Error |A - A_r|'] for i, (mat, title) in enumerate(zip(mats, titles)): ax[i].pcolormesh(mat, vmin=vmin, vmax=vmax) ax[i].set_title(title) ax[i].axis('off') print(f"Original Size of A: {tf.size(A)}") s, U, V = tf.linalg.svd(A) Original Size of A: 1200 # Rank-15 approximation A_15, A_15_size = rank_r_approx(s, U, V, 15, verbose = True) viz_approx(A, A_15) Approximation Size: 1065 # Rank-3 approximation A_3, A_3_size = rank_r_approx(s, U, V, 3, verbose = True) viz_approx(A, A_3) Approximation Size: 213 ຂ້າພະເຈົ້າສືບຕໍ່ໄດ້ຮັບການປະທັບໃຈ ສໍາ ລັບຂ້າພະເຈົ້າສືບຕໍ່ໄດ້ຮັບການປະທັບໃຈ ສໍາ ລັບຂ້າພະເຈົ້າ. ຂ້າພະເຈົ້າສືບຕໍ່ໄດ້ຮັບການປະທັບໃຈ ສໍາ ລັບຂ້າພະເຈົ້າສືບຕໍ່ໄດ້ຮັບການປະທັບໃຈ ສໍາ ລັບຂ້າພະເຈົ້າ. ຂ້າພະເຈົ້າສືບຕໍ່ໄດ້ຮັບການປະທັບໃຈ ສໍາ ລັບຂ້າພະເຈົ້າ ຮູບພາບ ສໍາ ລັບ Loading ຮູບພາບທີ່ຜ່ານມາແມ່ນມີຢູ່ໃນ ຫນ້າທໍາອິດ. Imagen ເປັນຮູບແບບການສົ່ງເສີມ text-to-image ທີ່ຖືກພັດທະນາໂດຍກຸ່ມ Brain ຂອງ Google Research. AI ໄດ້ສ້າງຮູບພາບນີ້ໂດຍລວມທັງຄໍາແນະນໍາ: "ຮູບພາບຂອງຮ່າງກາຍ Corgi ທີ່ຂັບລົດໃນ Times Square. ມັນມີແສງຕາເວັນອອກແລະລັງສືແສງຕາເວັນອອກ." ຂໍຂອບໃຈຫຼາຍ! ທ່ານຍັງສາມາດປ່ຽນ URL ນີ້ພາຍໃຕ້ກັບການເຊື່ອມຕໍ່ .jpg ທັງຫມົດເພື່ອດາວໂຫລດຮູບພາບ custom ຂອງການເລືອກ. ຮູບພາບ ຫຼັງຈາກການອ່ານເອກະສານ JPEG, Matplotlib ສະຫນອງ matrix, I, ຂອງຮູບພາບ (m×n×3) ທີ່ສະແດງໃຫ້ເຫັນຮູບພາບ 2-dimensional ມີ 3 ລະບົບສີສໍາລັບສີຂາວ, ສີຂາວແລະສີຂາວ. img_link = "https://imagen.research.google/main_gallery_images/a-photo-of-a-corgi-dog-riding-a-bike-in-times-square.jpg" img_path = requests.get(img_link, stream=True).raw I = imread(img_path, 0) print("Input Image Shape:", I.shape) Input Image Shape: (1024, 1024, 3) def show_img(I): # Display the image in matplotlib img = plt.imshow(I) plt.axis('off') return show_img(I) ລະຫັດ QR ໃນປັດຈຸບັນ, ການນໍາໃຊ້ SVD ເພື່ອຄອມພິວເຕີການປະມວນຜົນປະມວນຜົນປະມວນຜົນປະມວນຜົນປະມວນຜົນປະມວນຜົນປະມວນຜົນປະມວນຜົນປະມວນຜົນປະມວນຜົນປະມວນຜົນປະມວນຜົນປະມວນຜົນປະມວນຜົນປະມວນຜົນປະມວນຜົນປະມວນຜົນປະມວນຜົນປະມວນຜົນປະມວນຜົນປະມວນຜົນປະມວນຜົນປະມວນຜົນປະມວນຜົນປະມວນຜົນປະມວນຜົນປະມວນຜົນປະມວນຜົນປະມວນຜົນປະມວນຜົນປະມວນຜົນປະມວນຜົນປະມວນຜົນປະມວນຜົນປະມວນຜົນປະມວນຜົນປະມວນຜົນປະມວນຜົນປະມວນຜົນປະມວນຜົນປະມວນຜົນປະມວນຜົນປະມວນຜົນປະມວນຜົນປະມວນຜົນປະ ການເຮັດວຽກທີ່ດີສໍາລັບການນີ້. tf.clip_by_value def compress_image(I, r, verbose=False): # Compress an image with the SVD given a rank I_size = tf.size(I) print(f"Original size of image: {I_size}") # Compute SVD of image I = tf.convert_to_tensor(I)/255 I_batched = tf.transpose(I, [2, 0, 1]) # einops.rearrange(I, 'h w c -> c h w') s, U, V = tf.linalg.svd(I_batched) # Compute low-rank approximation of image across each RGB channel I_r, I_r_size = rank_r_approx(s, U, V, r) I_r = tf.transpose(I_r, [1, 2, 0]) # einops.rearrange(I_r, 'c h w -> h w c') I_r_prop = (I_r_size / I_size) if verbose: # Display compressed image and attributes print(f"Number of singular values used in compression: {r}") print(f"Compressed image size: {I_r_size}") print(f"Proportion of original size: {I_r_prop:.3f}") ax_1 = plt.subplot(1,2,1) show_img(tf.clip_by_value(I_r,0.,1.)) ax_1.set_title("Approximated image") ax_2 = plt.subplot(1,2,2) show_img(tf.clip_by_value(0.5+abs(I-I_r),0.,1.)) ax_2.set_title("Error") return I_r, I_r_prop ໃນປັດຈຸບັນ, calculate rank-r approximations for the following ranks : 100, 50, 10 I_100, I_100_prop = compress_image(I, 100, verbose=True) Original size of image: 3145728 Number of singular values used in compression: 100 Compressed image size: 614700 Proportion of original size: 0.195 I_50, I_50_prop = compress_image(I, 50, verbose=True) Original size of image: 3145728 Number of singular values used in compression: 50 Compressed image size: 307350 Proportion of original size: 0.098 I_10, I_10_prop = compress_image(I, 10, verbose=True) Original size of image: 3145728 Number of singular values used in compression: 10 Compressed image size: 61470 Proportion of original size: 0.020 ການທົບທວນຄືນ approximations ມີປະເພດຕ່າງໆຂອງວິທີທີ່ຫນ້າສົນໃຈທີ່ຈະກວດສອບປະສິດທິພາບແລະໄດ້ຮັບການຄວບຄຸມຫຼາຍກ່ວາ matrix approximations. ປະເພດ: Compression Factor vs Rank ສໍາລັບແຕ່ລະປະມານທີ່ຜ່ານມາ, ເບິ່ງວິທີທີ່ຂະຫນາດຂອງຂໍ້ມູນທີ່ແຕກຕ່າງກັນກັບລະດັບ. plt.figure(figsize=(11,6)) plt.plot([100, 50, 10], [I_100_prop, I_50_prop, I_10_prop]) plt.xlabel("Rank") plt.ylabel("Proportion of original image size") plt.title("Compression factor vs rank"); ຂ້າພະເຈົ້າສືບຕໍ່ໄດ້ຮັບການປະທັບໃຈຂອງຂ້າພະເຈົ້າ, ຂ້າພະເຈົ້າສືບຕໍ່ໄດ້ຮັບການປະທັບໃຈຂອງຂ້າພະເຈົ້າ, ຂ້າພະເຈົ້າສືບຕໍ່ໄດ້ຮັບການປະທັບໃຈຂອງຂ້າພະເຈົ້າ. ລະຫັດ QR ລະຫັດ QR ລະຫັດ QR c=xy=r×(m+n+1)m×n ວິທີການ x: ຂະຫນາດຂອງ Air y: ຂະຫນາດ A ລະຫັດ QR R: ປະເພດຂອງ approximation m ແລະ n: ລະດັບແລະຂະຫນາດແຜ່ນຂອງ A ສໍາລັບການຊອກຫາຄຸນນະພາບ, r, ທີ່ຕ້ອງການທີ່ຈະ comprimate ຮູບພາບກັບຄຸນນະພາບທີ່ຕ້ອງການ, c, ຄຸນນະພາບເຫຼົ່ານີ້ສາມາດຖືກປັບປຸງເພື່ອປິ່ນປົວສໍາລັບ r: ລະຫັດ QR ລະຫັດ QR ລະຫັດ QR ການຄົ້ນຄວ້າແລະການປິ່ນປົວຂອງການປິ່ນປົວຂອງການປິ່ນປົວຂອງການປິ່ນປົວຂອງການປິ່ນປົວຂອງການປິ່ນປົວຂອງການປິ່ນປົວຂອງການປິ່ນປົວຂອງການປິ່ນປົວຂອງການປິ່ນປົວຂອງການປິ່ນປົວ def compress_image_with_factor(I, compression_factor, verbose=False): # Returns a compressed image based on a desired compression factor m,n,o = I.shape r = int((compression_factor * m * n)/(m + n + 1)) I_r, I_r_prop = compress_image(I, r, verbose=verbose) return I_r Compress ຮູບພາບ ສໍາ ລັບ 15% ຂອງຂະຫນາດเดิมຂອງຕົນ. compression_factor = 0.15 I_r_img = compress_image_with_factor(I, compression_factor, verbose=True) Original size of image: 3145728 Number of singular values used in compression: 76 Compressed image size: 467172 Proportion of original size: 0.149 ຊື່ຫຍໍ້ຂອງ : Cumulative sum of singular values ການຄຸ້ມຄອງຄຸນນະສົມບັດຂອງຄຸນນະສົມບັດທີ່ແຕກຕ່າງກັນສາມາດເປັນອຸປະກອນທີ່ເຫມາະສົມສໍາລັບຂະຫນາດຂອງພະລັງງານທີ່ໄດ້ຮັບການເກັບຮັກສາໂດຍການຄຸ້ມຄອງຄຸນສົມບັດທີ່ແຕກຕ່າງກັນ. visualize the RGB-average cumulative proportion of singular values in the sample image. ການເຮັດວຽກສາມາດຖືກນໍາໃຊ້ສໍາລັບການນີ້. tf.cumsum def viz_energy(I): # Visualize the energy captured based on rank # Computing SVD I = tf.convert_to_tensor(I)/255 I_batched = tf.transpose(I, [2, 0, 1]) s, U, V = tf.linalg.svd(I_batched) # Plotting average proportion across RGB channels props_rgb = tf.map_fn(lambda x: tf.cumsum(x)/tf.reduce_sum(x), s) props_rgb_mean = tf.reduce_mean(props_rgb, axis=0) plt.figure(figsize=(11,6)) plt.plot(range(len(I)), props_rgb_mean, color='k') plt.xlabel("Rank / singular value number") plt.ylabel("Cumulative proportion of singular values") plt.title("RGB-averaged proportion of energy captured by the first 'r' singular values") viz_energy(I) ມັນຄ້າຍຄືກັນວ່າຫຼາຍກ່ວາ 90% ຂອງພະລັງງານໃນຮູບພາບນີ້ແມ່ນກວດສອບໃນໄລຍະ 100 ນິ້ວເລກທີເລກທີເລກທີເລກທີເລກທີເລກທີເລກທີເລກທີເລກທີເລກທີເລກທີເລກທີເລກທີເລກທີເລກທີເລກທີເລກທີ. def compress_image_with_energy(I, energy_factor, verbose=False): # Returns a compressed image based on a desired energy factor # Computing SVD I_rescaled = tf.convert_to_tensor(I)/255 I_batched = tf.transpose(I_rescaled, [2, 0, 1]) s, U, V = tf.linalg.svd(I_batched) # Extracting singular values props_rgb = tf.map_fn(lambda x: tf.cumsum(x)/tf.reduce_sum(x), s) props_rgb_mean = tf.reduce_mean(props_rgb, axis=0) # Find closest r that corresponds to the energy factor r = tf.argmin(tf.abs(props_rgb_mean - energy_factor)) + 1 actual_ef = props_rgb_mean[r] I_r, I_r_prop = compress_image(I, r, verbose=verbose) print(f"Proportion of energy captured by the first {r} singular values: {actual_ef:.3f}") return I_r Compress ຮູບພາບ ສໍາ ລັບ ການ ປັບ 75% ຂອງ ພະລັງງານຂອງຕົນ. energy_factor = 0.75 I_r_img = compress_image_with_energy(I, energy_factor, verbose=True) Original size of image: 3145728 Number of singular values used in compression: 35 Compressed image size: 215145 Proportion of original size: 0.068 Proportion of energy captured by the first 35 singular values: 0.753 ລະຫັດ QR ມີການເຊື່ອມຕໍ່ທີ່ຫນ້າສົນໃຈລະຫວ່າງຜົນປະໂຫຍດ aproximation ແລະຄຸນນະສົມບັດ singular. ມັນສະແດງໃຫ້ເຫັນວ່າລະດັບ Frobenius Square ຂອງການ aproximation ແມ່ນມີຄຸນນະສົມບັດຂອງສະກຸນນະສົມບັດຂອງຄຸນນະສົມບັດ singular ຂອງຕົນທີ່ບໍ່ມີ: ຂ້າ ພະ ເຈົ້າ ຂ້າ ພະ ເຈົ້າ ຂ້າ ພະ ເຈົ້າ ການທົດສອບການເຊື່ອມຕໍ່ນີ້ທີ່ມີການຄາດຄະເນ-10 ການຄາດຄະເນຂອງ matrix ໃນຕອນເລີ່ມຕົ້ນຂອງ tutorial ນີ້. s, U, V = tf.linalg.svd(A) A_10, A_10_size = rank_r_approx(s, U, V, 10) squared_norm = tf.norm(A - A_10)**2 s_squared_sum = tf.reduce_sum(s[10:]**2) print(f"Squared Frobenius norm: {squared_norm:.3f}") print(f"Sum of squared singular values left out: {s_squared_sum:.3f}") Squared Frobenius norm: 33.021 Sum of squared singular values left out: 33.021 ພາສາລາວ ຊື່ຫຍໍ້ຂອງ : This notebook introduced the process of implementing the singular value decomposition with TensorFlow and applying it to write an image compression algorithm. Here are a few more tips that may help: API ຂອງ TensorFlow Core ສາມາດຖືກນໍາໃຊ້ສໍາລັບປະເພດຕ່າງໆຂອງການນໍາໃຊ້ຄອມພິວເຕີວິທະຍາສາດຄຸນນະພາບສູງ. ຖ້າຫາກວ່າທ່ານກໍາລັງຊອກຫາຂໍ້ມູນເພີ່ມເຕີມກ່ຽວກັບການເຮັດວຽກ Algebra Linear ຂອງ TensorFlow, ກະລຸນາຊອກຫາເອກະສານສໍາລັບ module Linalg. SVD ຍັງສາມາດນໍາໃຊ້ເພື່ອສ້າງລະບົບການແນະນໍາ. ສໍາລັບຕົວຢ່າງເພີ່ມເຕີມຂອງການນໍາໃຊ້ TensorFlow Core API, ດາວນ໌ໂຫລດ ຖ້າຫາກວ່າທ່ານຕ້ອງການຮູ້ເພີ່ມເຕີມກ່ຽວກັບການດາວໂຫລດແລະການ preparing data, ກະລຸນາເບິ່ງ tutorials ຢູ່ ປະເພດ . ຄູ່ມື ຮູບພາບ ສໍາ ລັບ Data Loading ລະຫັດ QR ຫນ້າທໍາອິດທີ່ຜ່ານມາໃນເວັບໄຊທ໌ TensorFlow, ເອກະສານນີ້ສະແດງໃຫ້ເຫັນຢູ່ໃນເວັບໄຊທ໌ນີ້ພາຍໃຕ້ຊື່ໃຫມ່ແລະໄດ້ຮັບອະນຸຍາດໂດຍ CC BY 4.0. ຫນ້າທໍາອິດທີ່ຜ່ານມາໃນເວັບໄຊທ໌ TensorFlow, ເອກະສານນີ້ສະແດງໃຫ້ເຫັນຢູ່ໃນເວັບໄຊທ໌ນີ້ພາຍໃຕ້ຊື່ໃຫມ່ແລະໄດ້ຮັບອະນຸຍາດໂດຍ CC BY 4.0. ປະເພດ TensorFlow ປະເພດ TensorFlow