Arithmetic

7 functions — 7 documented.

add¶

Element-wise addition.

Shapes are broadcast by NumPy rules. Broadcasting is implemented by giving the expanded axes stride 0 rather than by materialising a copy — Shape holds strides in bytes and permits 0, so a broadcast operand re-reads the same element instead of allocating an expanded one.

Parameters

input (Tensor)

The left operand.

other (Tensor)

The right operand, broadcastable against input.

Returns

A tensor of the broadcast shape.

Example

copy>>> a = vkml.tensor(np.array([1.0, 2.0], dtype=np.float32))
>>> b = vkml.tensor(np.array([[10.0], [20.0]], dtype=np.float32))
>>> vkml.add(a, b).numpy()
array([[11., 12.],
       [21., 22.]], dtype=float32)

Implementation

See also sub, mul, maximum

sub¶

Element-wise subtraction, input − other.

Shapes are broadcast by NumPy rules. Broadcasting is implemented by giving the expanded axes stride 0 rather than by materialising a copy — Shape holds strides in bytes and permits 0, so a broadcast operand re-reads the same element instead of allocating an expanded one.

Parameters

input (Tensor)

The left operand.

other (Tensor)

The right operand, broadcastable against input.

Returns

A tensor of the broadcast shape.

Example

copy>>> vkml.sub(vkml.tensor(np.array([5.0, 3.0], dtype=np.float32)),
...           vkml.tensor(np.array([2.0, 1.0], dtype=np.float32))).numpy()
array([3., 2.], dtype=float32)

Implementation

See also add, neg

mul¶

Element-wise multiplication.

Shapes are broadcast by NumPy rules. Broadcasting is implemented by giving the expanded axes stride 0 rather than by materialising a copy — Shape holds strides in bytes and permits 0, so a broadcast operand re-reads the same element instead of allocating an expanded one.

Parameters

input (Tensor)

The left operand.

other (Tensor)

The right operand, broadcastable against input.

Returns

A tensor of the broadcast shape.

Example

copy>>> vkml.mul(vkml.tensor(np.array([2.0, 3.0], dtype=np.float32)),
...           vkml.tensor(np.array([4.0, 5.0], dtype=np.float32))).numpy()
array([ 8., 15.], dtype=float32)

Implementation

See also div, add, square

div¶

Element-wise division, input / other.

IEEE division throughout: x/0 is ±inf and 0/0 is NaN, rather than raising.

Shapes are broadcast by NumPy rules. Broadcasting is implemented by giving the expanded axes stride 0 rather than by materialising a copy — Shape holds strides in bytes and permits 0, so a broadcast operand re-reads the same element instead of allocating an expanded one.

Parameters

input (Tensor)

The left operand.

other (Tensor)

The right operand, broadcastable against input.

Returns

A tensor of the broadcast shape.

Example

copy>>> vkml.div(vkml.tensor(np.array([1.0, 0.0], dtype=np.float32)),
...           vkml.tensor(np.array([2.0, 0.0], dtype=np.float32))).numpy()
array([0.5, nan], dtype=float32)

Implementation

See also mul, reciprocal

pow¶

Element-wise power, input ** other.

Matches std::pow, not GLSL's pow. GLSL leaves pow(x, y) explicitly undefined for x < 0, while std::pow is defined there whenever y is an integer — std::pow(-2, 3) is -8, not NaN. Leaving the built-in to handle it would make the two backends disagree on a case the CPU answers perfectly well, so the shader peels the sign off and reapplies it.

Shapes are broadcast by NumPy rules. Broadcasting is implemented by giving the expanded axes stride 0 rather than by materialising a copy — Shape holds strides in bytes and permits 0, so a broadcast operand re-reads the same element instead of allocating an expanded one.

Parameters

input (Tensor)

The left operand.

other (Tensor)

The right operand, broadcastable against input.

Returns

A tensor of the broadcast shape.

Example

copy>>> vkml.pow(vkml.tensor(np.array([-2.0, 2.0], dtype=np.float32)),
...           vkml.tensor(np.array([3.0, 3.0], dtype=np.float32))).numpy()
array([-8.,  8.], dtype=float32)

In the Vulkan kernel

pow matching std::pow, which the CPU kernel uses.

GLSL's pow(x, y) is explicitly undefined for x < 0, but std::pow is defined there whenever y is an integer -- std::pow(-2, 3) is -8, not NaN. Leaving the built-in to handle it would make the two backends disagree on a case the CPU answers perfectly well, so the sign is peeled off and reapplied.

Implementation

See also square, sqrt, exp

maximum¶

Element-wise maximum of two tensors.

NaN propagates, matching torch.maximum. GLSL's max() is undefined for NaN and std::fmax returns the non-NaN operand, so the shader tests for NaN explicitly and returns a quiet NaN written from its bit pattern — not 0.0/0.0, which the compiler is free to constant-fold or treat as undefined.

This is tested as exact, so the difference is not academic.

Shapes are broadcast by NumPy rules. Broadcasting is implemented by giving the expanded axes stride 0 rather than by materialising a copy — Shape holds strides in bytes and permits 0, so a broadcast operand re-reads the same element instead of allocating an expanded one.

Parameters

input (Tensor)

The left operand.

other (Tensor)

The right operand, broadcastable against input.

Returns

A tensor of the broadcast shape.

Example

copy>>> vkml.maximum(vkml.tensor(np.array([1.0, float('nan')], dtype=np.float32)),
...               vkml.tensor(np.array([2.0, 5.0], dtype=np.float32))).numpy()
array([ 2., nan], dtype=float32)

Implementation

See also minimum, clamp_min, amax, relu

minimum¶

Element-wise minimum of two tensors.

NaN propagates, by the same explicit test as maximum.

Shapes are broadcast by NumPy rules. Broadcasting is implemented by giving the expanded axes stride 0 rather than by materialising a copy — Shape holds strides in bytes and permits 0, so a broadcast operand re-reads the same element instead of allocating an expanded one.

Parameters

input (Tensor)

The left operand.

other (Tensor)

The right operand, broadcastable against input.

Returns

A tensor of the broadcast shape.

Example

copy>>> vkml.minimum(vkml.tensor(np.array([1.0, float('nan')], dtype=np.float32)),
...               vkml.tensor(np.array([2.0, 5.0], dtype=np.float32))).numpy()
array([ 1., nan], dtype=float32)

Implementation

See also maximum, clamp_max, amin