numpy Fourier级数中的Tensor

gxwragnw 于 2023-05-22 发布在其他

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我正在尝试制作一个傅立叶级数函数，它将Tensor作为机器学习主题的y值。我得到了浮点数的代码，但还没有完成TensorflowTensor的代码。你可以重写这段代码，这样就可以使用y值了：

BATCH_SIZE = 16
MAX_LENGTH = 50
D_MODEL = 32

input_tensor_1 = tf.random.normal((BATCH_SIZE, MAX_LENGTH, D_MODEL))
input_tensor_2 = tf.random.normal((BATCH_SIZE, MAX_LENGTH, D_MODEL))

y = [input_tensor_1, input_tensor_2]
x = tf.range(len(y), dtype=tf.float32)

适用于浮点数的傅立叶级数，将被重写为Tensor：

import tensorflow as tf
import numpy as np

def construct_periodic_function(x, y, num_coefficients):
    sorted_indices = tf.argsort(x)
    x_sorted = tf.gather(x, sorted_indices)
    y_sorted = tf.gather(y, sorted_indices)

    n = tf.shape(x_sorted)[0]
    T = x_sorted[-1] - x_sorted[0]  # Total period
    omega = 2 * np.pi / T  # Angular frequency

    a0 = tf.reduce_mean(y_sorted)
    an = []
    bn = []
    for i in range(1, num_coefficients + 1):
        an_i = 2 * tf.reduce_mean(y_sorted * tf.cos(i * omega * x_sorted))  # Cosine coefficients
        bn_i = 2 * tf.reduce_mean(y_sorted * tf.sin(i * omega * x_sorted))  # Sine coefficients
        an.append(an_i)
        bn.append(bn_i)

    an = tf.stack(an)
    bn = tf.stack(bn)

    def f(x_new):
        y_new = tf.zeros_like(x_new, dtype=tf.float32)
        y_new += a0
        for i in range(1, num_coefficients + 1):
            y_new += an[i-1] * tf.cos(i * omega * x_new)
            y_new += bn[i-1] * tf.sin(i * omega * x_new)
        return y_new

    return f

x = tf.linspace(0.0, 2 * np.pi, 50)
y = tf.sin(x)

num_coefficients = 10

f = construct_periodic_function(x, y, num_coefficients)

x_range = tf.linspace(0.0, 2 * np.pi, 1000)
y_range = f(x_range)

numpy

来源：https://stackoverflow.com/questions/76300767/tensors-in-fourier-series

1条答案

按热度按时间

cxfofazt1#

我做了一个低效的变通方案，那就是一个接一个地遍历Tensor的每个元素，对所有Tensor进行傅里叶级数。这是令人难以置信的低效，甚至可能无法产生预期的结果;我不能保证它完全执行，但下面是代码：

def construct_from_tensor(x, y, num_coefficients):
    batch_list = []
    for i in range(y[0].shape[0]):
        length_list = []
        for j in range(y[0].shape[1]):
            d_model_list = []
            for k in range(y[0].shape[2]):
                d_model_list.append(construct_periodic_function(x, tf.constant([y[l][i,j,k].numpy() for l in range(len(y))]), num_coefficients))
            length_list.append(d_model_list)
        batch_list.append(length_list)

    return batch_list

BATCH_SIZE = 1
MAX_LENGTH = 50
D_MODEL = 1

input_tensors_1 = tf.random.normal((BATCH_SIZE, MAX_LENGTH, D_MODEL))
input_tensors_2 = tf.random.normal((BATCH_SIZE, MAX_LENGTH, D_MODEL))
input_tensors_3 = tf.random.normal((BATCH_SIZE, MAX_LENGTH, D_MODEL))
input_tensors_4 = tf.random.normal((BATCH_SIZE, MAX_LENGTH, D_MODEL))
input_tensors_5 = tf.random.normal((BATCH_SIZE, MAX_LENGTH, D_MODEL))

y = [input_tensors_1, input_tensors_2, input_tensors_3, input_tensors_4, input_tensors_5]
x = tf.constant(tf.range(len(y), dtype=tf.float32).numpy())

num_coefficients = 10  # Number of Fourier coefficients to use

f = construct_from_tensor(x, y, num_coefficients)

y_range = []
for i in range(len(f)):
    y_temp = []
    for j in range(len(f[i])):
        y_temp_2 = []
        for k in range(len(f[i][j])):
            y_temp_2.append(f[i][j][k](x))
        y_temp.append(y_temp_2)
    y_range.append(y_temp)

傅里叶级数函数的其余部分保持不变。

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numpy Fourier级数中的Tensor

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