TensorFlow.js 张量运算 #

运算概览 #

TensorFlow.js 提供丰富的张量运算，涵盖数学运算、逻辑运算、归约操作等。

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┌─────────────────────────────────────────────────────────────┐
│                    张量运算分类                               │
├─────────────────────────────────────────────────────────────┤
│                                                             │
│  ┌─────────────┐  ┌─────────────┐  ┌─────────────┐         │
│  │  数学运算    │  │  逻辑运算    │  │  归约操作    │         │
│  │  + - * /    │  │  && || !    │  │  sum mean   │         │
│  └─────────────┘  └─────────────┘  └─────────────┘         │
│  ┌─────────────┐  ┌─────────────┐  ┌─────────────┐         │
│  │  形状操作    │  │  切片索引    │  │  神经网络    │         │
│  │  reshape    │  │  slice      │  │  conv pool  │         │
│  └─────────────┘  └─────────────┘  └─────────────┘         │
│                                                             │
└─────────────────────────────────────────────────────────────┘

基本数学运算 #

加法 #

javascript

const a = tf.tensor([1, 2, 3]);
const b = tf.tensor([4, 5, 6]);

const sum1 = a.add(b);
sum1.print();

const sum2 = tf.add(a, b);
sum2.print();

const sum3 = a.add(10);
sum3.print();

减法 #

javascript

const a = tf.tensor([10, 20, 30]);
const b = tf.tensor([1, 2, 3]);

const diff1 = a.sub(b);
diff1.print();

const diff2 = a.sub(5);
diff2.print();

乘法 #

javascript

const a = tf.tensor([1, 2, 3]);
const b = tf.tensor([4, 5, 6]);

const product1 = a.mul(b);
product1.print();

const product2 = a.mul(2);
product2.print();

除法 #

javascript

const a = tf.tensor([10, 20, 30]);
const b = tf.tensor([2, 5, 10]);

const quotient1 = a.div(b);
quotient1.print();

const quotient2 = a.div(2);
quotient2.print();

整除与取余 #

javascript

const a = tf.tensor([7, 8, 9]);
const b = tf.tensor([2, 3, 4]);

const floorDiv = a.floorDiv(b);
floorDiv.print();

const mod = a.mod(b);
mod.print();

幂运算 #

javascript

const a = tf.tensor([2, 3, 4]);

const pow = a.pow(2);
pow.print();

const square = a.square();
square.print();

const sqrt = tf.tensor([4, 9, 16]).sqrt();
sqrt.print();

指数与对数 #

指数函数 #

javascript

const a = tf.tensor([0, 1, 2]);

const exp = a.exp();
exp.print();

const expm1 = a.expm1();
expm1.print();

对数函数 #

javascript

const a = tf.tensor([1, 2.718, 7.389]);

const log = a.log();
log.print();

const log1p = tf.tensor([0, 1, 2]).log1p();
log1p.print();

const log2 = tf.tensor([2, 4, 8]).log(2);
log2.print();

三角函数 #

基本三角函数 #

javascript

const angles = tf.tensor([0, Math.PI / 4, Math.PI / 2]);

const sin = angles.sin();
sin.print();

const cos = angles.cos();
cos.print();

const tan = angles.tan();
tan.print();

反三角函数 #

javascript

const values = tf.tensor([0, 0.5, 1]);

const asin = values.asin();
asin.print();

const acos = values.acos();
acos.print();

const atan = values.atan();
atan.print();

双曲函数 #

javascript

const values = tf.tensor([0, 1, 2]);

const sinh = values.sinh();
sinh.print();

const cosh = values.cosh();
cosh.print();

const tanh = values.tanh();
tanh.print();

符号与绝对值 #

abs #

javascript

const a = tf.tensor([-1, 2, -3, 4]);
const abs = a.abs();
abs.print();

sign #

javascript

const a = tf.tensor([-5, 0, 5]);
const sign = a.sign();
sign.print();

neg #

javascript

const a = tf.tensor([1, -2, 3]);
const neg = a.neg();
neg.print();

取整函数 #

floor #

javascript

const a = tf.tensor([1.2, 2.7, 3.5]);
const floor = a.floor();
floor.print();

ceil #

javascript

const a = tf.tensor([1.2, 2.7, 3.5]);
const ceil = a.ceil();
ceil.print();

round #

javascript

const a = tf.tensor([1.2, 1.8, 2.5]);
const round = a.round();
round.print();

最值与比较 #

最大值 #

javascript

const a = tf.tensor([1, 5, 3]);
const b = tf.tensor([2, 4, 6]);

const max = a.maximum(b);
max.print();

const maxVal = a.max();
maxVal.print();

最小值 #

javascript

const a = tf.tensor([1, 5, 3]);
const b = tf.tensor([2, 4, 6]);

const min = a.minimum(b);
min.print();

const minVal = a.min();
minVal.print();

比较运算 #

javascript

const a = tf.tensor([1, 2, 3, 4, 5]);
const b = tf.tensor([2, 2, 2, 2, 2]);

const greater = a.greater(b);
greater.print();

const less = a.less(b);
less.print();

const equal = a.equal(b);
equal.print();

const greaterEqual = a.greaterEqual(b);
greaterEqual.print();

const lessEqual = a.lessEqual(b);
lessEqual.print();

where 条件选择 #

javascript

const condition = tf.tensor([true, false, true]);
const a = tf.tensor([1, 2, 3]);
const b = tf.tensor([4, 5, 6]);

const result = tf.where(condition, a, b);
result.print();

归约操作 #

求和 #

javascript

const t = tf.tensor([[1, 2, 3], [4, 5, 6]]);

const sum = t.sum();
sum.print();

const sumAxis0 = t.sum(0);
sumAxis0.print();

const sumAxis1 = t.sum(1);
sumAxis1.print();

平均值 #

javascript

const t = tf.tensor([[1, 2, 3], [4, 5, 6]]);

const mean = t.mean();
mean.print();

const meanAxis0 = t.mean(0);
meanAxis0.print();

最大值与最小值 #

javascript

const t = tf.tensor([[1, 2, 3], [4, 5, 6]]);

const max = t.max();
max.print();

const min = t.min();
min.print();

const argMax = t.argMax();
argMax.print();

const argMin = t.argMin();
argMin.print();

乘积 #

javascript

const t = tf.tensor([[1, 2, 3], [4, 5, 6]]);

const prod = t.prod();
prod.print();

const prodAxis0 = t.prod(0);
prodAxis0.print();

范数 #

javascript

const t = tf.tensor([3, 4]);

const norm1 = t.norm(1);
norm1.print();

const norm2 = t.norm(2);
norm2.print();

const normInf = t.norm('euclidean');
normInf.print();

方差与标准差 #

javascript

const t = tf.tensor([1, 2, 3, 4, 5]);

const variance = t.variance();
variance.print();

const std = t.std();
std.print();

any 与 all #

javascript

const t = tf.tensor([true, false, true]);

const any = t.any();
any.print();

const all = t.all();
all.print();

广播机制 #

广播允许不同形状的张量进行运算。

广播规则 #

text

┌─────────────────────────────────────────────────────────────┐
│                      广播规则                                │
├─────────────────────────────────────────────────────────────┤
│                                                             │
│  1. 从右向左比较形状                                        │
│  2. 维度相等或其中一个为 1 时可以广播                        │
│  3. 缺失的维度视为 1                                        │
│                                                             │
│  示例：                                                     │
│  [3, 1] + [1, 4] = [3, 4]                                  │
│  [3, 4] + [4]    = [3, 4]                                  │
│  [3, 4] + [3, 1] = [3, 4]                                  │
│                                                             │
└─────────────────────────────────────────────────────────────┘

广播示例 #

javascript

const a = tf.tensor([[1], [2], [3]]);
const b = tf.tensor([[10, 20, 30]]);

const result = a.add(b);
result.print();

javascript

const a = tf.tensor([[1, 2, 3], [4, 5, 6]]);
const b = tf.tensor([10, 20, 30]);

const result = a.add(b);
result.print();

javascript

const a = tf.tensor([[1, 2, 3], [4, 5, 6]]);
const b = tf.tensor([[10], [20]]);

const result = a.add(b);
result.print();

矩阵运算 #

矩阵乘法 #

javascript

const a = tf.tensor([[1, 2], [3, 4]]);
const b = tf.tensor([[5, 6], [7, 8]]);

const matMul = a.matMul(b);
matMul.print();

const dot = a.dot(b);
dot.print();

转置 #

javascript

const a = tf.tensor([[1, 2, 3], [4, 5, 6]]);
const transposed = a.transpose();
transposed.print();

行列式 #

javascript

const a = tf.tensor([[1, 2], [3, 4]]);
const det = tf.linalg.det(a);
det.print();

逆矩阵 #

javascript

const a = tf.tensor([[1, 2], [3, 4]]);
const inv = tf.linalg.inv(a);
inv.print();

矩阵分解 #

javascript

const a = tf.tensor([[1, 2], [3, 4], [5, 6]]);

const [q, r] = tf.linalg.qr(a);
q.print();
r.print();

逐元素运算 #

clipByValue #

javascript

const t = tf.tensor([1, 5, 10, 15, 20]);
const clipped = t.clipByValue(5, 15);
clipped.print();

relu #

javascript

const t = tf.tensor([-2, -1, 0, 1, 2]);
const relu = t.relu();
relu.print();

sigmoid #

javascript

const t = tf.tensor([-2, -1, 0, 1, 2]);
const sigmoid = t.sigmoid();
sigmoid.print();

softmax #

javascript

const t = tf.tensor([1, 2, 3]);
const softmax = t.softmax();
softmax.print();

elu #

javascript

const t = tf.tensor([-2, -1, 0, 1, 2]);
const elu = t.elu();
elu.print();

selu #

javascript

const t = tf.tensor([-2, -1, 0, 1, 2]);
const selu = t.selu();
selu.print();

leakyRelu #

javascript

const t = tf.tensor([-2, -1, 0, 1, 2]);
const leakyRelu = tf.leakyRelu(t, 0.1);
leakyRelu.print();

归一化 #

batchNorm #

javascript

const x = tf.tensor([[1, 2], [3, 4]]);
const mean = tf.tensor([1, 2]);
const variance = tf.tensor([1, 1]);
const offset = tf.tensor([0, 0]);
const scale = tf.tensor([1, 1]);

const normalized = tf.batchNorm(x, mean, variance, offset, scale);
normalized.print();

layerNorm #

javascript

const t = tf.tensor([[1, 2, 3], [4, 5, 6]]);
const normalized = tf.layers.normalization().apply(t);

梯度运算 #

计算梯度 #

javascript

const x = tf.tensor([1, 2, 3]);

const grad = tf.grad(x => x.square());
const gradient = grad(x);
gradient.print();

计算高阶梯度 #

javascript

const x = tf.tensor([1, 2, 3]);

const f = x => x.square();
const grad1 = tf.grad(f);
const grad2 = tf.grad(grad1);

console.log('一阶导数:');
grad1(x).print();
console.log('二阶导数:');
grad2(x).print();

valueAndGrad #

javascript

const x = tf.tensor([1, 2, 3]);

const f = x => x.square().sum();
const { value, grad } = tf.valueAndGrad(f)(x);

console.log('函数值:');
value.print();
console.log('梯度:');
grad.print();

多变量梯度 #

javascript

const x1 = tf.tensor([1, 2, 3]);
const x2 = tf.tensor([4, 5, 6]);

const f = (x1, x2) => x1.mul(x2).sum();
const grads = tf.grads(f);

const [grad1, grad2] = grads([x1, x2]);
grad1.print();
grad2.print();

自定义操作 #

使用 tf.customGrad #

javascript

const customOp = tf.customGrad((x, save) => {
  save([x]);
  return {
    value: x.square(),
    gradFunc: (dy, saved) => {
      const [x] = saved;
      return dy.mul(x.mul(2));
    }
  };
});

const x = tf.tensor([1, 2, 3]);
const y = customOp(x);
y.print();

运算链式调用 #

javascript

const result = tf.tidy(() => {
  return tf.tensor([1, 2, 3])
    .square()
    .add(1)
    .div(2)
    .sqrt();
});

result.print();

性能优化 #

使用 tf.tidy #

javascript

const result = tf.tidy(() => {
  const a = tf.tensor([1, 2, 3]);
  const b = a.square();
  const c = b.add(1);
  return c;
});

避免不必要的同步 #

javascript

const t = tf.tensor([1, 2, 3]);
const data = t.data();

使用 inplace 操作 #

javascript

const t = tf.tensor([1, 2, 3]);
t.add(1);

下一步 #

现在你已经掌握了张量运算，接下来学习模型构建，了解如何构建神经网络模型！