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API Reference

Class ember.Tensor

The core data structure of the Ember library. A Tensor represents a multi-dimensional array of elements, similar to NumPy arrays but optimized for Ember's backend (C/CUDA).

Constructor

__init__(data)

Creates a Tensor from a Python list or compatible data structure.

  • Arguments:
  • data (list | number): The data to initialize the tensor with.
  • Returns: A new Tensor instance.
import ember
t = ember.Tensor([1.0, 2.0, 3.0])

from_np(array)

Creates a Tensor from a NumPy array.

  • Arguments:
  • array (numpy.ndarray): The NumPy array to convert.
  • Returns: A new Tensor instance.

Methods

to_np() -> numpy.ndarray

Converts the tensor back to a NumPy array.

to_cpu() -> list

Converts the tensor data to a Python list.

reshape(new_shape: tuple[int, ...]) -> Tensor

Returns a Tensor with the same data but a different shape.

  • Arguments:
  • new_shape: The new shape. One dimension can be -1, which will be inferred.

Operators

Tensor objects support standard Python operators.

Operator Method Description Formula
+ __add__ Elementwise addition \(c_i = a_i + b_i\)
- __sub__ Elementwise subtraction \(c_i = a_i - b_i\)
* __mul__ Elementwise multiplication \(c_i = a_i \cdot b_i\)
/ __truediv__ Elementwise division \(c_i = \frac{a_i}{b_i}\)
@ __matmul__ Matrix multiplication \(C_{ij} = \sum_k A_{ik} B_{kj}\)
- __neg__ Elementwise negation \(b_i = -a_i\)
> __gt__ Elementwise greater than \(c_i = 1 \text{ if } a_i > b_i \text{ else } 0\)

Functional API

All functional operations are available directly under the ember namespace.

Elementwise Math Operations

Functions that operate on each element of the input tensor independently. For an input tensor \(A\) with elements \(a_i\), the output tensor \(B\) has elements \(b_i\):

\[b_i = f(a_i)\]

Trigonometric

Function Description Equation
ember.sin(x) Sine \(b_i = \sin(a_i)\)
ember.cos(x) Cosine \(b_i = \cos(a_i)\)
ember.tan(x) Tangent \(b_i = \tan(a_i)\)
ember.ctg(x) Cotangent \(b_i = \cot(a_i)\)

Hyperbolic

Function Description Equation
ember.sinh(x) Hyperbolic Sine \(b_i = \sinh(a_i)\)
ember.cosh(x) Hyperbolic Cosine \(b_i = \cosh(a_i)\)
ember.tanh(x) Hyperbolic Tangent \(b_i = \tanh(a_i)\)
ember.ctgh(x) Hyperbolic Cotangent \(b_i = \coth(a_i)\)

Other

Function Description Equation
ember.exp(x) Exponential \(b_i = e^{a_i}\)

Binary Elementwise Operations

Functions that extend elementwise operations to two tensors (or a tensor and a scalar). For inputs \(A, B\), the output \(C\) is:

\[c_i = f(a_i, b_i)\]
Function Description Equation
ember.max(a, b) Elementwise maximum \(c_i = \max(a_i, b_i)\)
ember.min(a, b) Elementwise minimum \(c_i = \min(a_i, b_i)\)

Random Module (ember.random)

Utilities for generating tensors with random or constant values.

ember.random.uniform(low, high, size)

Draws samples from a uniform distribution.

  • Arguments:
  • low (float): Lower boundary of the output interval.
  • high (float): Upper boundary of the output interval.
  • size (tuple[int]): Shape of the output tensor.
  • Equation: \(x_i \sim U(\text{low}, \text{high})\)

ember.random.constant(value, size)

Return a new tensor of given shape and type, filled with value.

  • Arguments:
  • value (float): Fill value.
  • size (tuple[int]): Shape of the output tensor.
  • Equation: \(x_i = \text{value}\)

ember.random.zeros(size)

Returns a new tensor of given shape, filled with zeros.

ember.random.ones(size)

Returns a new tensor of given shape, filled with ones.

Neural Networks (ember.nn)

Components for building neural networks. Note: You may need to import submodules explicitly, e.g., from ember.nn.layers import Linear.

Layers

ember.nn.layers.Linear(in_features, out_features)

Applies a linear transformation to the incoming data.

  • Arguments:
  • in_features (int): Size of each input sample.
  • out_features (int): Size of each output sample.
  • Forward: \(y = x W + b\)
  • Where \(W\) is weight matrix of shape (in_features, out_features) and \(b\) is bias of shape (out_features,).

Methods:

  • reset(): Re-initializes weights and biases.
  • parameters() -> list[Tensor]: Returns [w, b].
  • gradients() -> list[Tensor | None]: Returns [grad_w, grad_b].

Activations

Activation functions applied elementwise.

ember.nn.activations.ReLU

Rectified Linear Unit.

  • Equation: \(f(x) = \max(0, x)\)

ember.nn.activations.Sigmoid

Sigmoid function.

  • Equation: \(f(x) = \frac{1}{1 + e^{-x}}\)

ember.nn.activations.Tanh

Hyperbolic Tangent function.

  • Equation: \(f(x) = \tanh(x)\)

ember.nn.activations.GELU

Gaussian Error Linear Unit (using tanh approximation).

  • Equation: \(f(x) \approx 0.5 x (1 + \tanh(0.8 x))\)