用Julia语言写一段绘制抽样函数的代码

好的，以下是用 Julia 语言编写的绘制抽样函数的示例代码：

using Distributions, Plots

# 创建正态分布抽样函数
normal_dist = Normal(0, 1)

# 生成1000个样本
samples = rand(normal_dist, 1000)

# 绘制抽样分布直方图
histogram(samples, bins = 50, label = "Samples Distribution", xlabel = "Values", ylabel = "Frequency", alpha = 0.5)

这段代码使用了 `Distributions` 和 `Plots` 两个 Julia 的常用包，首先创建了一个正态分布抽样函数 `normal_dist`，然后使用 `rand()` 函数从该抽样函数中抽取了 1000 个样本，最后使用 `histogram()` 函数绘制抽样分布的直方图。

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使用Julia语言写一个基于transformer模型的代码

好的，以下是一个基于Transformer模型的Julia代码示例：

using Flux
using Flux.Data: DataLoader
using Flux: onehot, crossentropy, throttle

# 定义超参数
EMBED_SIZE = 256
HIDDEN_SIZE = 512
NUM_HEADS = 8
NUM_LAYERS = 6
DROPOUT = 0.1
BATCH_SIZE = 64

# 定义Transformer模型
struct Transformer
    embedding::Dense
    encoder::Chain
    decoder::Chain
end

function Transformer(vocab_size::Int, max_seq_len::Int; hidden_size=HIDDEN_SIZE, num_heads=NUM_HEADS, num_layers=NUM_LAYERS, dropout=DROPOUT)
    # 定义嵌入层
    embedding = Dense(vocab_size, EMBED_SIZE)
    # 定义编码器
    encoder_layer = TransformerLayer(hidden_size, num_heads, dropout)
    encoder = Chain([encoder_layer for i in 1:num_layers]...)
    # 定义解码器
    decoder_layer = TransformerLayer(hidden_size, num_heads, dropout)
    decoder = Chain([decoder_layer for i in 1:num_layers]...)
    # 返回Transformer模型
    Transformer(embedding, encoder, decoder)
end

# 定义一个Transformer层
struct TransformerLayer
    self_attention::MultiheadAttention
    feed_forward::Chain
    dropout1::Dropout
    dropout2::Dropout
    layer_norm1::LayerNorm
    layer_norm2::LayerNorm
end

function TransformerLayer(hidden_size::Int, num_heads::Int, dropout::Float64)
    # 定义自注意力层
    self_attention = MultiheadAttention(hidden_size, hidden_size, num_heads)
    # 定义前馈网络
    feed_forward = Chain(Dense(hidden_size, hidden_size, relu), Dense(hidden_size, hidden_size))
    # 定义dropout层和layer normalization层
    dropout1 = Dropout(dropout)
    dropout2 = Dropout(dropout)
    layer_norm1 = LayerNorm(hidden_size)
    layer_norm2 = LayerNorm(hidden_size)
    # 返回TransformerLayer
    TransformerLayer(self_attention, feed_forward, dropout1, dropout2, layer_norm1, layer_norm2)
end

# Transformer层的前向传播
function (layer::TransformerLayer)(x, mask)
    # 多头自注意力
    attention_out = layer.self_attention(x, x, x, mask)
    # Add & Norm
    x = layer_norm1(x + layer.dropout1(attention_out))
    # 前馈网络
    ff_out = layer.feed_forward(x)
    # Add & Norm
    x = layer_norm2(x + layer.dropout2(ff_out))
    # 返回Transformer层的输出
    x
end

# Transformer模型的前向传播
function (model::Transformer)(src, tgt)
    # 嵌入源序列和目标序列
    src_emb = model.embedding(src)
    tgt_emb = model.embedding(tgt)
    # 定义掩码
    src_pad_mask = src .== 0
    tgt_pad_mask = tgt .== 0
    tgt_len = size(tgt, 2)
    tgt_sub_mask = Flux.tril!(ones(tgt_len, tgt_len))
    tgt_mask = reshape(tgt_sub_mask, 1, tgt_len, tgt_len, 1) .| reshape(tgt_pad_mask, size(tgt, 1), 1, 1, tgt_len)
    # 编码源序列
    enc_out = model.encoder(src_emb, src_pad_mask)
    # 解码目标序列
    dec_out = model.decoder(tgt_emb, enc_out, tgt_mask, tgt_pad_mask)
    # 返回解码器的输出
    dec_out
end

# 定义多头自注意力层
struct MultiheadAttention
    wq::Dense
    wk::Dense
    wv::Dense
    linear::Dense
    num_heads::Int
end

function MultiheadAttention(hidden_size::Int, key_size::Int, num_heads::Int)
    # 计算每个头的维度
    head_size = div(hidden_size, num_heads)
    # 定义权重矩阵
    wq = Dense(hidden_size, key_size * num_heads)
    wk = Dense(hidden_size, key_size * num_heads)
    wv = Dense(hidden_size, hidden_size * num_heads)
    linear = Dense(hidden_size * num_heads, hidden_size)
    # 返回MultiheadAttention层
    MultiheadAttention(wq, wk, wv, linear, num_heads)
end

# 多头自注意力层的前向传播
function (layer::MultiheadAttention)(xq, xk, xv, mask)
    # 计算batch size和sequence length
    bsz, len_q, _ = size(xq)
    _, len_k, _ = size(xk)
    _, len_v, _ = size(xv)
    # 将输入张量的最后一维分成num_heads个维度
    q = reshape(layer.wq(xq), bsz, len_q, layer.num_heads, :)
    k = reshape(layer.wk(xk), bsz, len_k, layer.num_heads, :)
    v = reshape(layer.wv(xv), bsz, len_v, layer.num_heads, :)
    # 转置第2个和第3个维度
    q = permutedims(q, (1, 3, 2, 4))
    k = permutedims(k, (1, 3, 2, 4))
    v = permutedims(v, (1, 3, 2, 4))
    # 定义掩码
    mask = reshape(mask, bsz, 1, len_q, len_k)
    # 计算注意力分数
    scores = einsum("b h i d, b h j d -> b h i j", q, k) / sqrt(size(q, end))
    # 应用掩码
    if mask != nothing
        scores = mask .* scores .+ (1 .- mask) .* -Inf
    end
    # 计算注意力权重
    attn_weights = softmax(scores, dims=4)
    # Dropout
    attn_weights = dropout(attn_weights, 0.1)
    # 计算上下文张量
    context = einsum("b h i j, b h j d -> b h i d", attn_weights, v)
    # 将上下文张量展开成2维张量
    context = reshape(context, bsz, len_q, layer.num_heads * size(v, end))
    # 线性变换
    linear_out = layer.linear(context)
    # 返回MultiheadAttention层的输出
    linear_out
end

# 加载数据集
train_data, test_data = Flux.Data.MNIST.traindata(Float32)
train_data = DataLoader(train_data, batchsize=BATCH_SIZE, shuffle=true)

# 定义损失函数和优化器
loss(x, y) = crossentropy(model(x, x), y)
opt = ADAM()

# 训练模型
model = Transformer(784, 28, hidden_size=256, num_layers=4)
for epoch in 1:10
    for (x, y) in train_data
        Flux.back!(loss, x, y)
        Flux.update!(opt, params(model))
    end
end

请注意，这只是一个示例代码，并且可能需要根据您的特定用例进行修改。此外，为了使代码更易于理解，省略了某些细节。

用Julia 语言写一个爱心

以下是用Julia语言编写一个简单的爱心图案的代码：

using Cairo, Colors, ColorSchemes

# 创建一个新的画布
surface = Cairo.PDFSurface("heart.pdf", 5inch, 5inch)
ctx = Cairo.CairoContext(surface)

# 设置画笔的颜色和宽度
set_source_rgb(ctx, 0.9, 0.1, 0.4)
set_line_width(ctx, 0.1)

# 绘制爱心
heart(x, y, size) = ((2.5 .* x ./ size).^2 .+ (2.5 .* y ./ size).^2 .- 1).^3 .- (2.5 .* x ./ size).^2 .* (2.5 .* y ./ size).^3
for i in range(-1, stop=1, length=200)
    for j in range(-1, stop=1, length=200)
        if heart(i, j, 1) ≤ 0.01
            line(ctx, i + 2.5, j + 2.5, i + 2.5, j + 2.5)
        end
    end
end

# 填充爱心
set_source(ctx, get(ColorSchemes.RdPu_9.colors, 3))
fill_preserve(ctx)
set_source_rgb(ctx, 0, 0, 0)
stroke(ctx)

# 保存文件并关闭画布
Cairo.finish(ctx)

运行上述代码会生成一个名为"heart.pdf"的文件，其中包含一个爱心图案。