adj = adj + adj.T.multiply(adj.T > adj) - adj.multiply(adj.T > adj)
时间: 2024-04-17 13:29:01 浏览: 28
您在代码中使用了一些操作来计算`adj`的新值。让我解释一下这段代码的作用。
首先,`adj.T`表示矩阵`adj`的转置。接下来,`adj.T > adj`会生成一个布尔矩阵,其中元素为True表示`adj.T`中对应位置的值大于`adj`中对应位置的值,否则为False。
接着,`adj.T.multiply(adj.T > adj)`将`adj.T`中大于对应位置的`adj`的值的元素保留下来,其他元素设为0。这样我们得到了一个新的矩阵。
然后,`adj.multiply(adj.T > adj)`将`adj`中大于对应位置的`adj.T`的值的元素保留下来,其他元素设为0。同样地,我们得到了另一个新的矩阵。
最后,通过将先前计算得到的两个矩阵相加,我们得到了一个包含了两个操作结果的新矩阵。这个操作会将`adj`中较大的值保留下来。
请注意,这段代码假设`adj`是一个稀疏矩阵,并且使用了稀疏矩阵的乘法操作符(multiply)和逐元素的大于操作符(>)。
相关问题
计算邻接矩阵A的k(k<n)次幂,A^k的第i行第j列元素为vi到vj长度为k的路径的条数。C语言实现
可以使用动态规划来求解。定义一个二维数组dp[i][j]表示节点i到节点j的长度为k的路径的数量。那么状态转移方程为:
dp[i][j] = Σ dp[i][u] * A[u][j]
其中,u是节点i和节点j之间的任意一个中间节点。初始状态为dp[i][j] = A[i][j] (当i和j之间有边相连时)和dp[i][j] = 0 (当i和j之间没有边相连时)。
根据状态转移方程,我们可以使用邻接矩阵来实现动态规划。具体实现代码如下:
```c
#include <stdio.h>
#include <stdlib.h>
#define MAXN 100
int n; //节点数
int k; //路径长度
int adj[MAXN][MAXN]; //邻接矩阵
int dp[MAXN][MAXN]; //动态规划数组
void matrix_multiply(int a[][MAXN], int b[][MAXN], int c[][MAXN]) {
//矩阵乘法c=a*b
int tmp[MAXN][MAXN];
for (int i = 1; i <= n; i++) {
for (int j = 1; j <= n; j++) {
tmp[i][j] = 0;
for (int k = 1; k <= n; k++) {
tmp[i][j] += a[i][k] * b[k][j];
}
}
}
for (int i = 1; i <= n; i++) {
for (int j = 1; j <= n; j++) {
c[i][j] = tmp[i][j];
}
}
}
void matrix_pow(int a[][MAXN], int k, int c[][MAXN]) {
//矩阵a的k次幂,结果存放在c中
if (k == 0) {
//矩阵的0次幂为单位矩阵
for (int i = 1; i <= n; i++) {
for (int j = 1; j <= n; j++) {
if (i == j) {
c[i][j] = 1;
} else {
c[i][j] = 0;
}
}
}
} else if (k % 2 == 1) {
//k为奇数,先计算a^(k-1)的结果,然后再乘上a
int tmp[MAXN][MAXN];
matrix_pow(a, k - 1, tmp);
matrix_multiply(a, tmp, c);
} else {
//k为偶数,计算a^(k/2)的结果,然后再平方
int tmp[MAXN][MAXN];
matrix_pow(a, k / 2, tmp);
matrix_multiply(tmp, tmp, c);
}
}
int main()
{
//读入图的信息
scanf("%d%d", &n, &k);
for (int i = 1; i <= n; i++) {
for (int j = 1; j <= n; j++) {
scanf("%d", &adj[i][j]);
}
}
//初始化dp数组
for (int i = 1; i <= n; i++) {
for (int j = 1; j <= n; j++) {
if (adj[i][j]) {
dp[i][j] = 1; //i和j之间有边相连,路径长度为1
} else {
dp[i][j] = 0; //i和j之间没有边相连,路径长度为0
}
}
}
//动态规划求解
int tmp[MAXN][MAXN];
matrix_pow(adj, k, tmp); //计算邻接矩阵的k次幂
for (int s = 2; s <= k; s++) { //路径长度从2到k
matrix_multiply(dp, adj, tmp); //计算dp*adj
for (int i = 1; i <= n; i++) {
for (int j = 1; j <= n; j++) {
dp[i][j] = tmp[i][j];
}
}
}
//输出结果
for (int i = 1; i <= n; i++) {
for (int j = 1; j <= n; j++) {
printf("%d ", dp[i][j]);
}
printf("\n");
}
return 0;
}
```
gcn-lstm tensorflow
GCN-LSTM是一种结合了图卷积网络(GCN)和长短时记忆网络(LSTM)的模型,用于处理图数据的时间序列预测问题。下面是使用TensorFlow实现GCN-LSTM的基本步骤:
1.导入必要的库和模块:
```python
import tensorflow as tf
from tensorflow.keras.layers import Input, Dense, LSTM, Dropout, GRU, Bidirectional, Conv1D, MaxPooling1D, Flatten, Reshape, Lambda, Concatenate, Multiply, Add
from tensorflow.keras.models import Model
from tensorflow.keras.optimizers import Adam
from tensorflow.keras.callbacks import EarlyStopping, ModelCheckpoint
from tensorflow.keras import backend as K
```
2.定义GCN层:
```python
class GraphConvolution(tf.keras.layers.Layer):
def __init__(self, output_dim, adj_matrix, **kwargs):
self.output_dim = output_dim
self.adj_matrix = adj_matrix
super(GraphConvolution, self).__init__(**kwargs)
def build(self, input_shape):
self.kernel = self.add_weight(name='kernel',
shape=(input_shape[1], self.output_dim),
initializer='glorot_uniform',
trainable=True)
super(GraphConvolution, self).build(input_shape)
def call(self, x):
adj_matrix = tf.cast(self.adj_matrix, dtype=tf.float32)
output = tf.matmul(adj_matrix, x)
output = tf.matmul(output, self.kernel)
return output
def compute_output_shape(self, input_shape):
return (input_shape[0], self.output_dim)
```
3.定义GCN-LSTM模型:
```python
def gcn_lstm_model(adj_matrix, num_nodes, num_features, num_timesteps_input, num_timesteps_output, num_filters, kernel_size, lstm_units, dropout_rate):
# Input layer
input_layer = Input(shape=(num_timesteps_input, num_nodes, num_features))
# GCN layer
gcn_layer = GraphConvolution(num_filters, adj_matrix)(input_layer)
gcn_layer = Lambda(lambda x: K.permute_dimensions(x, (0, 2, 1, 3)))(gcn_layer)
gcn_layer = Reshape((num_nodes, num_timesteps_input * num_filters))(gcn_layer)
# LSTM layer
lstm_layer = LSTM(lstm_units, return_sequences=True)(gcn_layer)
lstm_layer = Dropout(dropout_rate)(lstm_layer)
# Output layer
output_layer = TimeDistributed(Dense(num_timesteps_output))(lstm_layer)
# Model definition
model = Model(inputs=input_layer, outputs=output_layer)
model.compile(loss='mse', optimizer=Adam(lr=0.001))
return model
```
4.训练模型:
```python
# Define model hyperparameters
num_nodes = 10
num_features = 1
num_timesteps_input = 24
num_timesteps_output = 12
num_filters = 32
kernel_size = 3
lstm_units = 64
dropout_rate = 0.2
batch_size = 32
epochs = 100
# Load data
x_train, y_train, x_val, y_val = load_data()
# Define adjacency matrix
adj_matrix = get_adjacency_matrix(num_nodes)
# Define model
model = gcn_lstm_model(adj_matrix, num_nodes, num_features, num_timesteps_input, num_timesteps_output, num_filters, kernel_size, lstm_units, dropout_rate)
# Train model
early_stopping = EarlyStopping(monitor='val_loss', patience=10)
model_checkpoint = ModelCheckpoint('gcn_lstm.h5', save_best_only=True, save_weights_only=True)
history = model.fit(x_train, y_train, batch_size=batch_size, epochs=epochs, validation_data=(x_val, y_val), callbacks=[early_stopping, model_checkpoint])
```
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