Xavier and He Weight Initialization

Weights that start too big or too small make deep networks hard to train. Two standard schemes pick the scale from the layer size, where fan_in is the number of inputs and fan_out the number of outputs:

Xavier (Glorot) suits sigmoid and tanh layers; He suits ReLU layers.

Implement init_bound(method, fan_in, fan_out).

Input

method: One of "xavier_uniform", "xavier_normal", "he_uniform" or "he_normal".

fan_in, fan_out: The layer's number of inputs and outputs.

Output

Return the limit or standard deviation as a decimal number.

Constraints

1 ≤ fan_in, fan_out ≤ 100,000

Examples

Input:
fan_in = 3
method = "xavier_uniform"
fan_out = 3

Expected output:
expected = 1.0

Input:
long long fan_in = 3;
std::string method = "xavier_uniform";
long long fan_out = 3;

Expected output:
double expected = 1.0;

Input:
long fan_in = 3;
string method = "xavier_uniform";
long fan_out = 3;

Expected output:
double expected = 1.0;

Input:
fan_in = 50
method = "he_normal"
fan_out = 10

Expected output:
expected = 0.2

Input:
long long fan_in = 50;
std::string method = "he_normal";
long long fan_out = 10;

Expected output:
double expected = 0.2;

Input:
long fan_in = 50;
string method = "he_normal";
long fan_out = 10;

Expected output:
double expected = 0.2;

References

This challenge is adapted for CodeUtility. Follow the statement and constraints above.

• Glorot and Bengio, Understanding the difficulty of training deep feedforward neural networks
• He et al., Delving Deep into Rectifiers