Complex Ops

Reduce¤

sum ¤

sum(
    axis: Optional[Union[int, Sequence[int]]] = None,
    keepdim=False,
    acc_dtype: Optional[DTypeLike] = None,
)

Returns the sum of the elements of the tensor along the specified axis or axes.

You can pass in axis and keepdim keyword arguments to control the axis along which the maximum is computed and whether the reduced dimensions are retained.

You can pass in acc_dtype keyword argument to control the data type of the accumulation. If not specified, the accumulation data type is chosen based on the input tensor's data type.

t = Tensor.arange(6).reshape(2, 3)
print(t.numpy())

[[0 1 2]
 [3 4 5]]

print(t.sum().numpy())

print(t.sum(axis=0).numpy())

[3 5 7]

print(t.sum(axis=1).numpy())

[ 3 12]

Source code in tinygrad/tensor.py

def sum(self, axis:Optional[Union[int, Sequence[int]]]=None, keepdim=False, acc_dtype:Optional[DTypeLike]=None):
  """
  Returns the sum of the elements of the tensor along the specified axis or axes.

  You can pass in `axis` and `keepdim` keyword arguments to control the axis along
  which the maximum is computed and whether the reduced dimensions are retained.

  You can pass in `acc_dtype` keyword argument to control the data type of the accumulation.
  If not specified, the accumulation data type is chosen based on the input tensor's data type.

  ```python exec="true" source="above" session="tensor" result="python"
  t = Tensor.arange(6).reshape(2, 3)
  print(t.numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.sum().numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.sum(axis=0).numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.sum(axis=1).numpy())
  ```
  """
  ret = self.cast(acc_dtype or sum_acc_dtype(self.dtype))._reduce(F.Sum, axis, keepdim)
  return ret.cast(self.dtype) if acc_dtype is None and self.dtype in (dtypes.float16, dtypes.bfloat16) else ret

prod ¤

prod(
    axis: Optional[Union[int, Sequence[int]]] = None,
    keepdim=False,
    acc_dtype: Optional[DTypeLike] = None,
)

Returns the product of the elements of the tensor along the specified axis or axes.

You can pass in axis and keepdim keyword arguments to control the axis along which the maximum is computed and whether the reduced dimensions are retained.

You can pass in acc_dtype keyword argument to control the data type of the accumulation. If not specified, the accumulation data type is chosen based on the input tensor's data type.

t = Tensor([-1, -2, -3, 1, 2, 3]).reshape(2, 3)
print(t.numpy())

[[-1 -2 -3]
 [ 1  2  3]]

print(t.prod().numpy())

-36

print(t.prod(axis=0).numpy())

[-1 -4 -9]

print(t.prod(axis=1).numpy())

[-6  6]

Source code in tinygrad/tensor.py

def prod(self, axis:Optional[Union[int, Sequence[int]]]=None, keepdim=False, acc_dtype:Optional[DTypeLike]=None):
  """
  Returns the product of the elements of the tensor along the specified axis or axes.

  You can pass in `axis` and `keepdim` keyword arguments to control the axis along
  which the maximum is computed and whether the reduced dimensions are retained.

  You can pass in `acc_dtype` keyword argument to control the data type of the accumulation.
  If not specified, the accumulation data type is chosen based on the input tensor's data type.

  ```python exec="true" source="above" session="tensor" result="python"
  t = Tensor([-1, -2, -3, 1, 2, 3]).reshape(2, 3)
  print(t.numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.prod().numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.prod(axis=0).numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.prod(axis=1).numpy())
  ```
  """
  return self.cast(acc_dtype or self.dtype)._reduce(F.Prod, axis, keepdim)

max ¤

max(
    axis: Optional[Union[int, Sequence[int]]] = None,
    keepdim=False,
)

Returns the maximum value of the tensor along the specified axis or axes.

You can pass in axis and keepdim keyword arguments to control the axis along which the maximum is computed and whether the reduced dimensions are retained.

t = Tensor([[1, 0, 2], [5, 4, 3]])
print(t.numpy())

[[1 0 2]
 [5 4 3]]

print(t.max().numpy())

print(t.max(axis=0).numpy())

[5 4 3]

print(t.max(axis=1, keepdim=True).numpy())

[[2]
 [5]]

Source code in tinygrad/tensor.py

def max(self, axis:Optional[Union[int, Sequence[int]]]=None, keepdim=False):
  """
  Returns the maximum value of the tensor along the specified axis or axes.

  You can pass in `axis` and `keepdim` keyword arguments to control the axis along
  which the maximum is computed and whether the reduced dimensions are retained.

  ```python exec="true" source="above" session="tensor" result="python"
  t = Tensor([[1, 0, 2], [5, 4, 3]])
  print(t.numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.max().numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.max(axis=0).numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.max(axis=1, keepdim=True).numpy())
  ```
  """
  return self._reduce(F.Max, axis, keepdim)

min ¤

min(
    axis: Optional[Union[int, Sequence[int]]] = None,
    keepdim=False,
)

Returns the minimum value of the tensor along the specified axis or axes.

You can pass in axis and keepdim keyword arguments to control the axis along which the minimum is computed and whether the reduced dimensions are retained.

t = Tensor([[1, 0, 2], [5, 4, 3]])
print(t.numpy())

[[1 0 2]
 [5 4 3]]

print(t.min().numpy())

print(t.min(axis=0).numpy())

[1 0 2]

print(t.min(axis=1, keepdim=True).numpy())

[[0]
 [3]]

Source code in tinygrad/tensor.py

def min(self, axis:Optional[Union[int, Sequence[int]]]=None, keepdim=False):
  """
  Returns the minimum value of the tensor along the specified axis or axes.

  You can pass in `axis` and `keepdim` keyword arguments to control the axis along
  which the minimum is computed and whether the reduced dimensions are retained.

  ```python exec="true" source="above" session="tensor" result="python"
  t = Tensor([[1, 0, 2], [5, 4, 3]])
  print(t.numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.min().numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.min(axis=0).numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.min(axis=1, keepdim=True).numpy())
  ```
  """
  return -((-self).max(axis=axis, keepdim=keepdim))

any ¤

any(
    axis: Optional[Union[int, Sequence[int]]] = None,
    keepdim=False,
)

Tests if any element evaluates to True along the specified axis or axes.

You can pass in axis and keepdim keyword arguments to control the reduce axis and whether the reduced dimensions are retained.

t = Tensor([[True, True], [True, False], [False, False]])
print(t.numpy())

[[ True  True]
 [ True False]
 [False False]]

print(t.any().numpy())

True

print(t.any(axis=0).numpy())

[ True  True]

print(t.any(axis=1, keepdim=True).numpy())

[[ True]
 [ True]
 [False]]

Source code in tinygrad/tensor.py

def any(self, axis:Optional[Union[int, Sequence[int]]]=None, keepdim=False):
  """
  Tests if any element evaluates to `True` along the specified axis or axes.

  You can pass in `axis` and `keepdim` keyword arguments to control the reduce axis and whether the reduced dimensions are retained.

  ```python exec="true" source="above" session="tensor" result="python"
  t = Tensor([[True, True], [True, False], [False, False]])
  print(t.numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.any().numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.any(axis=0).numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.any(axis=1, keepdim=True).numpy())
  ```
  """
  return self.bool().max(axis, keepdim)

all ¤

all(
    axis: Optional[Union[int, Sequence[int]]] = None,
    keepdim=False,
)

Tests if all element evaluates to True along the specified axis or axes.

You can pass in axis and keepdim keyword arguments to control the reduce axis and whether the reduced dimensions are retained.

t = Tensor([[True, True], [True, False], [False, False]])
print(t.numpy())

[[ True  True]
 [ True False]
 [False False]]

print(t.all().numpy())

False

print(t.all(axis=0).numpy())

[False False]

print(t.all(axis=1, keepdim=True).numpy())

[[ True]
 [False]
 [False]]

Source code in tinygrad/tensor.py

def all(self, axis:Optional[Union[int, Sequence[int]]]=None, keepdim=False):
  """
  Tests if all element evaluates to `True` along the specified axis or axes.

  You can pass in `axis` and `keepdim` keyword arguments to control the reduce axis and whether the reduced dimensions are retained.

  ```python exec="true" source="above" session="tensor" result="python"
  t = Tensor([[True, True], [True, False], [False, False]])
  print(t.numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.all().numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.all(axis=0).numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.all(axis=1, keepdim=True).numpy())
  ```
  """
  return self.logical_not().any(axis, keepdim).logical_not()

mean ¤

mean(
    axis: Optional[Union[int, Sequence[int]]] = None,
    keepdim=False,
)

Returns the mean value of the tensor along the specified axis or axes.

You can pass in axis and keepdim keyword arguments to control the axis along which the mean is computed and whether the reduced dimensions are retained.

Tensor.manual_seed(42)
t = Tensor.normal(2, 3, mean=2.5, std=0.5)
print(t.numpy())

[[2.0979 1.9493 2.0452]
 [3.1401 1.3559 2.8539]]

print(t.mean().numpy())

2.2403831

print(t.mean(axis=0).numpy())

[2.619  1.6526 2.4496]

print(t.mean(axis=1).numpy())

[2.0308 2.4499]

Source code in tinygrad/tensor.py

def mean(self, axis:Optional[Union[int, Sequence[int]]]=None, keepdim=False):
  """
  Returns the mean value of the tensor along the specified axis or axes.

  You can pass in `axis` and `keepdim` keyword arguments to control the axis along
  which the mean is computed and whether the reduced dimensions are retained.

  ```python exec="true" source="above" session="tensor" result="python"
  Tensor.manual_seed(42)
  t = Tensor.normal(2, 3, mean=2.5, std=0.5)
  print(t.numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.mean().numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.mean(axis=0).numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.mean(axis=1).numpy())
  ```
  """
  output_dtype = self.dtype if dtypes.is_float(self.dtype) else dtypes.float32
  numerator = self.cast(sum_acc_dtype(self.dtype)).sum(axis=axis, keepdim=keepdim)
  return numerator.div(prod([si for si, so in zip(self.shape, self.sum(axis=axis, keepdim=True).shape) if si != so])).cast(output_dtype)

var ¤

var(
    axis: Optional[Union[int, Sequence[int]]] = None,
    keepdim=False,
    correction=1,
)

Returns the variance of the tensor along the specified axis or axes.

You can pass in axis, keepdim, and correction keyword arguments to control the axis along which the variance is computed, whether the reduced dimensions are retained, and the Bessel's correction applied.

Tensor.manual_seed(42)
t = Tensor.normal(2, 3, mean=2.5, std=0.5)
print(t.numpy())

[[2.0979 1.9493 2.0452]
 [3.1401 1.3559 2.8539]]

print(t.var().numpy())

0.4222705

print(t.var(axis=0).numpy())

[0.5431 0.1761 0.327 ]

print(t.var(axis=1).numpy())

[0.0057 0.9183]

Source code in tinygrad/tensor.py

def var(self, axis:Optional[Union[int, Sequence[int]]]=None, keepdim=False, correction=1):
  """
  Returns the variance of the tensor along the specified axis or axes.

  You can pass in `axis`, `keepdim`, and `correction` keyword arguments to control the axis along
  which the variance is computed, whether the reduced dimensions are retained, and the Bessel's correction applied.

  ```python exec="true" source="above" session="tensor" result="python"
  Tensor.manual_seed(42)
  t = Tensor.normal(2, 3, mean=2.5, std=0.5)
  print(t.numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.var().numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.var(axis=0).numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.var(axis=1).numpy())
  ```
  """
  squares = (self - self.mean(axis=axis, keepdim=True)).square()
  n = prod([si for si, so in zip(self.shape, squares.sum(axis=axis, keepdim=True).shape) if si != so])
  return squares.sum(axis=axis, keepdim=keepdim).div(max(0, n-correction))

std ¤

std(
    axis: Optional[Union[int, Sequence[int]]] = None,
    keepdim=False,
    correction=1,
)

Returns the standard deviation of the tensor along the specified axis or axes.

You can pass in axis, keepdim, and correction keyword arguments to control the axis along which the standard deviation is computed, whether the reduced dimensions are retained, and the Bessel's correction applied.

Tensor.manual_seed(42)
t = Tensor.normal(2, 3, mean=2.5, std=0.5)
print(t.numpy())

[[2.0979 1.9493 2.0452]
 [3.1401 1.3559 2.8539]]

print(t.std().numpy())

0.6498234

print(t.std(axis=0).numpy())

[0.7369 0.4197 0.5718]

print(t.std(axis=1).numpy())

[0.0753 0.9583]

Source code in tinygrad/tensor.py

def std(self, axis:Optional[Union[int, Sequence[int]]]=None, keepdim=False, correction=1):
  """
  Returns the standard deviation of the tensor along the specified axis or axes.

  You can pass in `axis`, `keepdim`, and `correction` keyword arguments to control the axis along
  which the standard deviation is computed, whether the reduced dimensions are retained, and the Bessel's correction applied.

  ```python exec="true" source="above" session="tensor" result="python"
  Tensor.manual_seed(42)
  t = Tensor.normal(2, 3, mean=2.5, std=0.5)
  print(t.numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.std().numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.std(axis=0).numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.std(axis=1).numpy())
  ```
  """
  return self.var(axis, keepdim, correction).sqrt()

std_mean ¤

std_mean(
    axis: Optional[Union[int, Sequence[int]]] = None,
    keepdim=False,
    correction=1,
)

Calculates the standard deviation and mean over the dimensions specified by dim. Syntactic sugar around Tensor.std and Tensor.mean to match torch.std_mean.

Tensor.manual_seed(42)
t = Tensor.normal(2, 3, mean=2.5, std=0.5)
print(t.numpy())

[[2.0979 1.9493 2.0452]
 [3.1401 1.3559 2.8539]]

std, mean = t.std_mean()
print(std.numpy(), mean.numpy())

0.6498234 2.2403831

Source code in tinygrad/tensor.py

def std_mean(self, axis:Optional[Union[int, Sequence[int]]]=None, keepdim=False, correction=1):
  """
  Calculates the standard deviation and mean over the dimensions specified by dim.
  Syntactic sugar around `Tensor.std` and `Tensor.mean` to match `torch.std_mean`.

  ```python exec="true" source="above" session="tensor" result="python"
  Tensor.manual_seed(42)
  t = Tensor.normal(2, 3, mean=2.5, std=0.5)
  print(t.numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  std, mean = t.std_mean()
  print(std.numpy(), mean.numpy())
  ```
  """
  return self.std(axis, keepdim, correction), self.mean(axis, keepdim)

softmax ¤

softmax(axis=-1)

Applies the softmax function to the tensor along the specified axis.

Rescales the elements of the tensor such that they lie in the range [0, 1] and sum to 1.

You can pass in the axis keyword argument to control the axis along which the softmax is computed.

Tensor.manual_seed(42)
t = Tensor.randn(2, 3)
print(t.numpy())

[[-0.8042 -1.1013 -0.9095]
 [ 1.2802 -2.2883  0.7078]]

print(t.softmax().numpy())

[[0.3784 0.2811 0.3405]
 [0.628  0.0177 0.3543]]

print(t.softmax(axis=0).numpy())

[[0.1106 0.7662 0.1656]
 [0.8894 0.2338 0.8344]]

Source code in tinygrad/tensor.py

def softmax(self, axis=-1):
  """
  Applies the softmax function to the tensor along the specified axis.

  Rescales the elements of the tensor such that they lie in the range [0, 1] and sum to 1.

  You can pass in the `axis` keyword argument to control the axis along which the softmax is computed.

  ```python exec="true" source="above" session="tensor" result="python"
  Tensor.manual_seed(42)
  t = Tensor.randn(2, 3)
  print(t.numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.softmax().numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.softmax(axis=0).numpy())
  ```
  """
  _, e, ss = self._softmax(axis)
  return e.div(ss)

log_softmax ¤

log_softmax(axis=-1)

Applies the log-softmax function to the tensor along the specified axis.

The log-softmax function is a numerically stable alternative to the softmax function in log space.

You can pass in the axis keyword argument to control the axis along which the log-softmax is computed.

Tensor.manual_seed(42)
t = Tensor.randn(2, 3)
print(t.numpy())

[[-0.8042 -1.1013 -0.9095]
 [ 1.2802 -2.2883  0.7078]]

print(t.log_softmax().numpy())

[[-0.9719 -1.269  -1.0772]
 [-0.4652 -4.0337 -1.0376]]

print(t.log_softmax(axis=0).numpy())

[[-2.2016 -0.2663 -1.7984]
 [-0.1172 -1.4533 -0.181 ]]

Source code in tinygrad/tensor.py

def log_softmax(self, axis=-1):
  """
  Applies the log-softmax function to the tensor along the specified axis.

  The log-softmax function is a numerically stable alternative to the softmax function in log space.

  You can pass in the `axis` keyword argument to control the axis along which the log-softmax is computed.

  ```python exec="true" source="above" session="tensor" result="python"
  Tensor.manual_seed(42)
  t = Tensor.randn(2, 3)
  print(t.numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.log_softmax().numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.log_softmax(axis=0).numpy())
  ```
  """
  m, _, ss = self._softmax(axis)
  return m - ss.log()

logsumexp ¤

logsumexp(axis=None, keepdim=False)

Computes the log-sum-exp of the tensor along the specified axis or axes.

The log-sum-exp function is a numerically stable way to compute the logarithm of the sum of exponentials.

You can pass in axis and keepdim keyword arguments to control the axis along which the log-sum-exp is computed and whether the reduced dimensions are retained.

Tensor.manual_seed(42)
t = Tensor.randn(2, 3)
print(t.numpy())

[[-0.8042 -1.1013 -0.9095]
 [ 1.2802 -2.2883  0.7078]]

print(t.logsumexp().numpy())

1.9330813

print(t.logsumexp(axis=0).numpy())

[ 1.3974 -0.835   0.8888]

print(t.logsumexp(axis=1).numpy())

[0.1677 1.7454]

Source code in tinygrad/tensor.py

def logsumexp(self, axis=None, keepdim=False):
  """
  Computes the log-sum-exp of the tensor along the specified axis or axes.

  The log-sum-exp function is a numerically stable way to compute the logarithm of the sum of exponentials.

  You can pass in `axis` and `keepdim` keyword arguments to control the axis along
  which the log-sum-exp is computed and whether the reduced dimensions are retained.

  ```python exec="true" source="above" session="tensor" result="python"
  Tensor.manual_seed(42)
  t = Tensor.randn(2, 3)
  print(t.numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.logsumexp().numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.logsumexp(axis=0).numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.logsumexp(axis=1).numpy())
  ```
  """
  m = self.max(axis=axis, keepdim=True)
  return (self - m).exp().sum(axis=axis, keepdim=keepdim).log() + m.squeeze(axis)

argmax ¤

argmax(axis=None, keepdim=False)

Returns the indices of the maximum value of the tensor along the specified axis.

You can pass in axis and keepdim keyword arguments to control the axis along which the maximum is computed and whether the reduced dimensions are retained.

t = Tensor([[1, 0, 2], [5, 4, 3]])
print(t.numpy())

[[1 0 2]
 [5 4 3]]

print(t.argmax().numpy()) # Returns the index of the maximum value in the flattened tensor.

print(t.argmax(axis=0).numpy()) # Returns the indices of the maximum values along axis 0.

[1 1 1]

print(t.argmax(axis=1).numpy()) # Returns the indices of the maximum values along axis 1.

[2 0]

Source code in tinygrad/tensor.py

def argmax(self, axis=None, keepdim=False):
  """
  Returns the indices of the maximum value of the tensor along the specified axis.

  You can pass in `axis` and `keepdim` keyword arguments to control the axis along
  which the maximum is computed and whether the reduced dimensions are retained.

  ```python exec="true" source="above" session="tensor" result="python"
  t = Tensor([[1, 0, 2], [5, 4, 3]])
  print(t.numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.argmax().numpy()) # Returns the index of the maximum value in the flattened tensor.
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.argmax(axis=0).numpy()) # Returns the indices of the maximum values along axis 0.
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.argmax(axis=1).numpy()) # Returns the indices of the maximum values along axis 1.
  ```
  """
  if axis is None: return self.flatten().argmax(0)
  axis = self._resolve_dim(axis)
  m = self == self.max(axis=axis, keepdim=True)
  idx = m * Tensor.arange(self.shape[axis]-1,-1,-1, requires_grad=False, device=self.device).reshape(self.shape[axis], *[1]*(self.ndim-axis-1))
  return (self.shape[axis]-idx.max(axis=axis, keepdim=keepdim)-1).cast(dtypes.int32)

argmin ¤

argmin(axis=None, keepdim=False)

Returns the indices of the minimum value of the tensor along the specified axis.

You can pass in axis and keepdim keyword arguments to control the axis along which the minimum is computed and whether the reduced dimensions are retained.

t = Tensor([[1, 0, 2], [5, 4, 3]])
print(t.numpy())

[[1 0 2]
 [5 4 3]]

print(t.argmin().numpy()) # Returns the index of the minimum value in the flattened tensor.

print(t.argmin(axis=0).numpy()) # Returns the indices of the minimum values along axis 0.

[0 0 0]

print(t.argmin(axis=1).numpy()) # Returns the indices of the minimum values along axis 1.

[1 2]

Source code in tinygrad/tensor.py

def argmin(self, axis=None, keepdim=False):
  """
  Returns the indices of the minimum value of the tensor along the specified axis.

  You can pass in `axis` and `keepdim` keyword arguments to control the axis along
  which the minimum is computed and whether the reduced dimensions are retained.

  ```python exec="true" source="above" session="tensor" result="python"
  t = Tensor([[1, 0, 2], [5, 4, 3]])
  print(t.numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.argmin().numpy()) # Returns the index of the minimum value in the flattened tensor.
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.argmin(axis=0).numpy()) # Returns the indices of the minimum values along axis 0.
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.argmin(axis=1).numpy()) # Returns the indices of the minimum values along axis 1.
  ```
  """
  return (-self).argmax(axis=axis, keepdim=keepdim)

Processing¤

avg_pool2d ¤

avg_pool2d(
    kernel_size=(2, 2),
    stride=None,
    dilation=1,
    padding=0,
    count_include_pad=True,
)

Applies average pooling over a tensor.

Note

unlike PyTorch, this implementation is not limited to only 2d pooling and instead works for any number of dimensions.

See: https://paperswithcode.com/method/average-pooling

t = Tensor.arange(25).reshape(1, 1, 5, 5)
print(t.avg_pool2d().numpy())

[[[[ 3.  5.]
   [13. 15.]]]]

print(t.avg_pool2d(padding=1).numpy())

[[[[ 0.    0.75  1.75]
   [ 3.75  9.   11.  ]
   [ 8.75 19.   21.  ]]]]

Source code in tinygrad/tensor.py

def avg_pool2d(self, kernel_size=(2,2), stride=None, dilation=1, padding=0, count_include_pad=True):
  """
  Applies average pooling over a tensor.

  NOTE: unlike PyTorch, this implementation is not limited to only 2d pooling and instead works for any number of dimensions.

  See: https://paperswithcode.com/method/average-pooling

  ```python exec="true" source="above" session="tensor" result="python"
  t = Tensor.arange(25).reshape(1, 1, 5, 5)
  print(t.avg_pool2d().numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.avg_pool2d(padding=1).numpy())
  ```
  """
  padding_, axis = self._padding2d(padding, len(k_ := make_pair(kernel_size))), tuple(range(-len(k_), 0))
  def pool(x:Tensor) -> Tensor: return x.pad2d(padding_)._pool(k_, stride if stride is not None else k_, dilation)
  return pool(self).mean(axis=axis) if count_include_pad else pool(self).sum(axis=axis) / pool(self.ones_like()).sum(axis=axis)

max_pool2d ¤

max_pool2d(
    kernel_size=(2, 2), stride=None, dilation=1, padding=0
)

Applies max pooling over a tensor.

Note

unlike PyTorch, this implementation is not limited to only 2d pooling and instead works for any number of dimensions.

See: https://paperswithcode.com/method/max-pooling

t = Tensor.arange(25).reshape(1, 1, 5, 5)
print(t.max_pool2d().numpy())

[[[[ 6  8]
   [16 18]]]]

print(t.max_pool2d(padding=1).numpy())

[[[[ 0.  2.  4.]
   [10. 12. 14.]
   [20. 22. 24.]]]]

Source code in tinygrad/tensor.py

def max_pool2d(self, kernel_size=(2,2), stride=None, dilation=1, padding=0):
  """
  Applies max pooling over a tensor.

  NOTE: unlike PyTorch, this implementation is not limited to only 2d pooling and instead works for any number of dimensions.

  See: https://paperswithcode.com/method/max-pooling

  ```python exec="true" source="above" session="tensor" result="python"
  t = Tensor.arange(25).reshape(1, 1, 5, 5)
  print(t.max_pool2d().numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.max_pool2d(padding=1).numpy())
  ```
  """
  padding_ = self._padding2d(padding, len(k_ := make_pair(kernel_size)))
  return self.pad2d(padding_, value=float('-inf'))._pool(k_, stride if stride is not None else k_, dilation).max(axis=tuple(range(-len(k_), 0)))

conv2d ¤

conv2d(
    weight: Tensor,
    bias: Tensor | None = None,
    groups=1,
    stride=1,
    dilation=1,
    padding=0,
    acc_dtype: DTypeLike | None = None,
) -> Tensor

Applies a convolution over a tensor with a given weight and optional bias.

Note

unlike PyTorch, this implementation is not limited to only 2d convolutions and instead works for any number of dimensions.

See: https://pytorch.org/docs/stable/generated/torch.nn.Conv2d.html

t = Tensor.arange(9).reshape(1, 1, 3, 3)
w = Tensor.ones(1, 1, 2, 2)
print(t.conv2d(w).numpy())

[[[[ 8. 12.]
   [20. 24.]]]]

Source code in tinygrad/tensor.py

def conv2d(self, weight:Tensor, bias:Tensor|None=None, groups=1, stride=1, dilation=1, padding=0, acc_dtype:DTypeLike|None=None) -> Tensor:
  """
  Applies a convolution over a tensor with a given `weight` and optional `bias`.

  NOTE: unlike PyTorch, this implementation is not limited to only 2d convolutions and instead works for any number of dimensions.

  See: https://pytorch.org/docs/stable/generated/torch.nn.Conv2d.html

  ```python exec="true" source="above" session="tensor" result="python"
  t = Tensor.arange(9).reshape(1, 1, 3, 3)
  w = Tensor.ones(1, 1, 2, 2)
  print(t.conv2d(w).numpy())
  ```
  """
  (bs,cin_), (cout,cin), HW = self.shape[:2], weight.shape[:2], weight.shape[2:]
  assert groups*cin == cin_ and len(self.shape) == len(weight.shape), f"Input Tensor shape {self.shape} does not match the shape of the weights {weight.shape}. ({groups*cin} vs. {cin_})"  # noqa: E501
  if isinstance(padding, (tuple,list)): assert len(padding) == 2*len(HW) or len(padding) == len(HW), f"Expected padding of length {2*len(HW)} or {len(HW)}, but got {len(padding)} for tensor of shape {self.shape}"  # noqa: E501
  padding_ = self._padding2d(padding, len(HW))

  # conv2d is a pooling op (with padding)
  x = self.pad2d(padding_)._pool(HW, stride, dilation)   # (bs, groups*cin, oy, ox, H, W)
  rcout, oyx = cout//groups, x.shape[2:-len(HW)]
  if not all(x == 3 for x in HW) or stride != 1 or dilation != 1 or not WINO:
    # normal conv
    x = x.reshape(bs, groups, cin, 1, *oyx, *HW).expand(bs, groups, cin, rcout, *oyx, *HW).permute(0,1,3,*[4+i for i in range(len(oyx))],2,*[4+len(oyx)+i for i in range(len(HW))])  # noqa: E501

    # conv! broadcasted to (bs, groups, rcout, *oyx, cin, *HW)
    ret = (x * weight.reshape(1, groups, rcout, *[1] * len(oyx), cin, *HW)).sum([-1-i for i in range(1+len(oyx))], keepdim=True, acc_dtype=acc_dtype).reshape(bs, cout, *oyx)  # noqa: E501
    return ret if bias is None else ret.add(bias.reshape(1, -1, *[1] * len(HW)))

  HWI, HWO = (6,) * len(HW), (4,) * len(HW)  # F(4x4,3x3) winograd tiles
  winograd_G = [[1/4, 0, 0], [-1/6, -1/6, -1/6], [-1/6, 1/6, -1/6], [1/24, 1/12, 1/6], [1/24, -1/12, 1/6], [0, 0, 1]]
  winograd_Bt = [[4, 0, -5, 0, 1, 0], [0, -4, -4, 1, 1, 0], [0, 4, -4, -1, 1, 0], [0, -2, -1, 2, 1, 0], [0, 2, -1, -2, 1, 0], [0, 4, 0, -5, 0, 1]]
  winograd_At = [[1, 1, 1, 1, 1, 0], [0, 1, -1, 2, -2, 0], [0, 1, 1, 4, 4, 0], [0, 1, -1, 8, -8, 1]] # applying At in pre-order doubles compile time

  # todo: stride == dilation
  # use padding to round up to 4x4 output tiles
  # (bs, cin_, tyx, HWI)
  d = self.pad2d(sum([[padding_[i*2], padding_[i*2+1] + (-(dim + sum(padding_[i * 2:(i + 1) * 2]) - 2) % 4)] for i, dim in enumerate(self.shape[-len(HW):])], []))._pool(HWI, HWO)  # noqa: E501
  # move HW to the front: # (HWI, bs, cin_, tyx)
  d = d.permute(*range(len(d.shape)-len(HW),len(d.shape)), *range(len(d.shape)-len(HW)))
  tyx = d.shape[-len(HWI):]  # dim of tiling

  g = weight.permute(*range(len(weight.shape)-len(HW),len(weight.shape)), *range(len(weight.shape)-len(HW)))  # move HW to the front

  # compute 6x6 winograd tiles: GgGt, BtdB
  # (HWI, groups * rcout, cin) -> (HWI, bs=1, groups, rcout, cin, tyx=(1,1))
  gfactors = _apply_winograd_matrix(winograd_G, g, len(HW)).reshape(*HWI, 1, groups, rcout, cin, *([1]*len(tyx)))
  # (HWI, bs, cin_, tyx) -> (HWI, bs, groups, 1 ,cin, *tyx)
  dfactors = _apply_winograd_matrix(winograd_Bt, d, len(HW)).reshape(*HWI, bs, groups, 1, cin, *tyx)

  # matmul; sum across cin: (HWI, bs, groups, rcout, *tyx); then HWI -> HWO: (HWO, bs, groups, rcout, *tyx)
  ret = _apply_winograd_matrix(winograd_At, (gfactors * dfactors).sum(axis=-1-len(HW), acc_dtype=acc_dtype), len(HW))

  # interleave tyx and HWO: (bs, groups, rcout, oy, HO, ox, WO)
  ret = ret.permute([*range(len(HW), len(ret.shape)-len(HW)), *[i+o for i in range(len(HW)) for o in [len(ret.shape)-len(HW),0]]])
  # merge groups and rcout, tyx and HWO: (bs, groups, cout, *yx), shrink to final
  ret = ret.reshape(bs, cout, *[c * HWO[i] for i, c in enumerate(tyx)]).shrink(tuple((0, s) for s in [bs, cout, *oyx]))

  return (ret if bias is None else ret.add(bias.reshape(1, -1, *[1 for _ in range(len(HW))]))).contiguous().contiguous_backward()

conv_transpose2d ¤

conv_transpose2d(
    weight: Tensor,
    bias: Optional[Tensor] = None,
    groups=1,
    stride=1,
    dilation=1,
    padding=0,
    output_padding=0,
) -> Tensor

Applies a transposed convolution over a tensor with a given weight and optional bias.

Note

unlike PyTorch, this implementation is not limited to only 2d transposed convolutions and instead works for any number of dimensions.

See: https://pytorch.org/docs/stable/generated/torch.nn.ConvTranspose2d.html

t = Tensor.arange(9).reshape(1, 1, 3, 3)
w = Tensor.ones(1, 1, 2, 2)
print(t.conv_transpose2d(w).numpy())

[[[[ 0.  1.  3.  2.]
   [ 3.  8. 12.  7.]
   [ 9. 20. 24. 13.]
   [ 6. 13. 15.  8.]]]]

Source code in tinygrad/tensor.py

def conv_transpose2d(self, weight:Tensor, bias:Optional[Tensor]=None, groups=1, stride=1, dilation=1, padding=0, output_padding=0) -> Tensor:
  """
  Applies a transposed convolution over a tensor with a given `weight` and optional `bias`.

  NOTE: unlike PyTorch, this implementation is not limited to only 2d transposed convolutions and instead works for any number of dimensions.

  See: https://pytorch.org/docs/stable/generated/torch.nn.ConvTranspose2d.html

  ```python exec="true" source="above" session="tensor" result="python"
  t = Tensor.arange(9).reshape(1, 1, 3, 3)
  w = Tensor.ones(1, 1, 2, 2)
  print(t.conv_transpose2d(w).numpy())
  ```
  """
  x, w = self, weight.unflatten(0, (groups, -1)).transpose(1, 2).flip(*range(3, len(weight.shape)+1))
  HW = weight.shape[2:]
  stride, dilation, padding, output_padding = [make_pair(x, len(HW)) for x in (stride, dilation, padding, output_padding)]
  if any(s>1 for s in stride):
    # handle strides: (k) -> reshape -> (k,1) -> pad -> (k,s) -> reshape -> (k*s) -> shrink (k-(s-1))
    x = x.reshape(None, None, *flatten((k,1) for k in x.shape[2:]))
    x = x.pad((None, None, *flatten((None,(0,s-1)) for s in stride)))
    x = x.reshape(None, None, *[k*s for k,s in zip(x.shape[2::2], stride)])
    x = x.shrink((None, None, *[(0,k-(s-1)) for k,s in zip(x.shape[2:], stride)]))
  padding = flatten((((k-1)*d-p,(k-1)*d-p+op) for k,d,p,op in reversed(list(zip(HW, dilation, padding, output_padding)))))
  return x.conv2d(w.flatten(end_dim=1), groups=groups, bias=bias, dilation=dilation, padding=padding)

dot ¤

dot(
    w: Tensor, acc_dtype: Optional[DTypeLike] = None
) -> Tensor

Performs dot product between two tensors.

You can pass in the optional acc_dtype keyword argument to control the data type of the accumulation.

a = Tensor([[1, 2], [3, 4]])
b = Tensor([[5, 6], [7, 8]])
print(a.dot(b).numpy())

[[19 22]
 [43 50]]

Source code in tinygrad/tensor.py

def dot(self, w:Tensor, acc_dtype:Optional[DTypeLike]=None) -> Tensor:
  """
  Performs dot product between two tensors.

  You can pass in the optional `acc_dtype` keyword argument to control the data type of the accumulation.

  ```python exec="true" source="above" session="tensor" result="python"
  a = Tensor([[1, 2], [3, 4]])
  b = Tensor([[5, 6], [7, 8]])
  print(a.dot(b).numpy())
  ```
  """
  n1, n2 = len(self.shape), len(w.shape)
  assert n1 != 0 and n2 != 0, f"both arguments to matmul need to be at least 1D, but they are {n1}D and {n2}D"
  if (L:=self.shape[-1]) != (R:=w.shape[-min(n2, 2)]): raise AssertionError(f"shapes {self.shape} and {w.shape} cannot be multiplied ({L} != {R})")
  x = self.reshape(*self.shape[0:-1], *[1]*min(n1-1, n2-1, 1), self.shape[-1])
  w = w.reshape(*w.shape[0:-2], *[1]*min(n1-1, n2-1, 1), *w.shape[-min(n2, 2):]).transpose(-1, -min(n2, 2))
  return (x*w).sum(-1, acc_dtype=acc_dtype).cast(least_upper_dtype(x.dtype, w.dtype) if acc_dtype is None else acc_dtype)

matmul ¤

matmul(
    x: Tensor,
    reverse=False,
    acc_dtype: Optional[DTypeLike] = None,
) -> Tensor

Performs matrix multiplication between two tensors.

You can pass in the reverse keyword argument to control the order of the matrix multiplication. You can pass in the optional acc_dtype keyword argument to control the data type of the accumulation.

a = Tensor([[1, 2], [3, 4]])
b = Tensor([[5, 6], [7, 8]])
print(a.matmul(b).numpy())

[[19 22]
 [43 50]]

Source code in tinygrad/tensor.py

def matmul(self, x:Tensor, reverse=False, acc_dtype:Optional[DTypeLike]=None) -> Tensor:
  """
  Performs matrix multiplication between two tensors.

  You can pass in the `reverse` keyword argument to control the order of the matrix multiplication.
  You can pass in the optional `acc_dtype` keyword argument to control the data type of the accumulation.

  ```python exec="true" source="above" session="tensor" result="python"
  a = Tensor([[1, 2], [3, 4]])
  b = Tensor([[5, 6], [7, 8]])
  print(a.matmul(b).numpy())
  ```
  """
  return x.dot(self, acc_dtype=acc_dtype) if reverse else self.dot(x, acc_dtype=acc_dtype)

einsum `staticmethod` ¤

einsum(
    formula: str,
    *raw_xs,
    acc_dtype: Optional[DTypeLike] = None
) -> Tensor

Sums the product of the elements of the input tensors according to a formula based on the Einstein summation convention.

See: https://pytorch.org/docs/stable/generated/torch.einsum.html

x = Tensor([[1, 2], [3, 4]])
y = Tensor([[5, 6], [7, 8]])
print(Tensor.einsum("ij,ij->", x, y).numpy())

Source code in tinygrad/tensor.py

@staticmethod
def einsum(formula:str, *raw_xs, acc_dtype:Optional[DTypeLike]=None) -> Tensor:
  """
  Sums the product of the elements of the input tensors according to a formula based on the Einstein summation convention.

  See: https://pytorch.org/docs/stable/generated/torch.einsum.html

  ```python exec="true" source="above" session="tensor" result="python"
  x = Tensor([[1, 2], [3, 4]])
  y = Tensor([[5, 6], [7, 8]])
  print(Tensor.einsum("ij,ij->", x, y).numpy())
  ```
  """
  def parse_formula(formula: str, *operands: Tensor):
    if "." in formula:
      ell_chars, ell_longest = "".join(set(string.ascii_letters) - set(formula)), 0
      for i, inp in enumerate(filter(lambda x: "..." in x, inputs := formula.split("->")[0].split(","))):
        if (ell_count := max(operands[i].ndim, 1) - (len(inp) - 3)) > ell_longest: ell_longest = ell_count
        inputs[i] = inp.replace("...", "" if ell_count == 0 else ell_chars[-ell_count:])
      inputs_str, out_ellipse = ",".join(inputs), "" if ell_longest == 0 else ell_chars[-ell_longest:]
      return (inputs_str, formula.split("->")[1].replace("...", out_ellipse)) if "->" in formula else (inputs_str, \
          out_ellipse + ''.join(sorted(c for c in inputs_str if inputs_str.count(c) == 1 and c.isalpha() and c not in out_ellipse)))
    return formula.split("->") if "->" in formula else (formula, ''.join(c for c in sorted(formula) if formula.count(c) == 1 and c.isalpha()))

  xs:Tuple[Tensor, ...] = argfix(*raw_xs)
  inputs_str, output = parse_formula(formula.replace(" ", ""), *xs)
  inputs = inputs_str.split(",")
  assert len(xs) == len(inputs), f"number of inputs doesn't match number of operands in formula, expected {len(inputs)}, got {len(xs)}"

  # map the value of each letter in the formula
  letter_val = sorted(merge_dicts([dict(zip(letters, tensor.shape)) for letters, tensor in zip(inputs, xs)]).items())

  xs_:List[Tensor] = []
  lhs = [sorted(enumerate(s), key=lambda e:e[1]) for s in inputs]
  for x,(order,letters) in zip(xs, [list(zip(*l)) for l in lhs]):
    # permute to the sorted letter order, then reshape/expand to create dimensions for the missing letters
    xs_.append(x.permute(order).reshape([val if letter in letters else 1 for letter,val in letter_val]).expand([val for _,val in letter_val]))

  # determine the inverse permutation to revert back to original order
  rhs_letter_order = argsort(list(output))
  rhs_order = argsort(rhs_letter_order)

  # sum over all axes that's not in the output, then permute to the output order
  return functools.reduce(lambda a,b:a*b, xs_) \
    .sum(axis=[axis for axis,(letter,_) in enumerate(letter_val) if letter not in output],acc_dtype=acc_dtype).permute(rhs_order)

cumsum ¤

cumsum(axis: int = 0) -> Tensor

Computes the cumulative sum of the tensor along the specified axis.

You can pass in the axis keyword argument to control the axis along which the cumulative sum is computed.

t = Tensor.ones(2, 3)
print(t.numpy())

[[1. 1. 1.]
 [1. 1. 1.]]

print(t.cumsum(1).numpy())

[[1. 2. 3.]
 [1. 2. 3.]]

Source code in tinygrad/tensor.py

def cumsum(self, axis:int=0) -> Tensor:
  """
  Computes the cumulative sum of the tensor along the specified axis.

  You can pass in the `axis` keyword argument to control the axis along which the cumulative sum is computed.

  ```python exec="true" source="above" session="tensor" result="python"
  t = Tensor.ones(2, 3)
  print(t.numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.cumsum(1).numpy())
  ```
  """
  axis = self._resolve_dim(axis)
  if self.ndim == 0 or 0 in self.shape: return self
  # TODO: someday the optimizer will find this on it's own
  # for now this is a two stage cumsum
  SPLIT = 256
  if self.shape[axis] <= SPLIT*2: return self._cumsum(axis)
  ret = self.transpose(axis,-1).pad2d((round_up(self.shape[axis], SPLIT)-self.shape[axis], 0))
  ret = ret.unflatten(-1, (-1, SPLIT))._cumsum(-1)
  base_add = ret[..., -1]._cumsum(-1, _first_zero=True)
  base_add = base_add.unsqueeze(-1).expand(*base_add.shape, ret.shape[-1])
  def fix(x:Tensor): return x.flatten(start_dim=-2)[..., -self.shape[axis]:].transpose(axis,-1)
  return fix(ret) + fix(base_add)

triu ¤

triu(diagonal: int = 0) -> Tensor

Returns the upper triangular part of the tensor, the other elements are set to 0.

The argument diagonal determines which diagonal is on the boundary. diagonal = 0 means the main diagonal. Positive diagonal means above the main diagonal, and negative diagonal means below the main diagonal.

t = Tensor([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]])
print(t.numpy())

[[ 1  2  3  4]
 [ 5  6  7  8]
 [ 9 10 11 12]]

print(t.triu(diagonal=0).numpy())

[[ 1  2  3  4]
 [ 0  6  7  8]
 [ 0  0 11 12]]

print(t.triu(diagonal=1).numpy())

[[ 0  2  3  4]
 [ 0  0  7  8]
 [ 0  0  0 12]]

print(t.triu(diagonal=-1).numpy())

[[ 1  2  3  4]
 [ 5  6  7  8]
 [ 0 10 11 12]]

Source code in tinygrad/tensor.py

def triu(self, diagonal:int=0) -> Tensor:
  """
  Returns the upper triangular part of the tensor, the other elements are set to 0.

  The argument `diagonal` determines which diagonal is on the boundary. `diagonal = 0` means the main diagonal.
  Positive `diagonal` means above the main diagonal, and negative `diagonal` means below the main diagonal.

  ```python exec="true" source="above" session="tensor" result="python"
  t = Tensor([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]])
  print(t.numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.triu(diagonal=0).numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.triu(diagonal=1).numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.triu(diagonal=-1).numpy())
  ```
  """
  return Tensor._tri(self.shape[-2], self.shape[-1], diagonal=diagonal, device=self.device, dtype=dtypes.bool).where(self, 0).cast(self.dtype)

tril ¤

tril(diagonal: int = 0) -> Tensor

Returns the lower triangular part of the tensor, the other elements are set to 0.

The argument diagonal determines which diagonal is on the boundary. diagonal = 0 means the main diagonal. Positive diagonal means above the main diagonal, and negative diagonal means below the main diagonal.

t = Tensor([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]])
print(t.numpy())

[[ 1  2  3  4]
 [ 5  6  7  8]
 [ 9 10 11 12]]

print(t.tril(diagonal=0).numpy())

[[ 1  0  0  0]
 [ 5  6  0  0]
 [ 9 10 11  0]]

print(t.tril(diagonal=1).numpy())

[[ 1  2  0  0]
 [ 5  6  7  0]
 [ 9 10 11 12]]

print(t.tril(diagonal=-1).numpy())

[[ 0  0  0  0]
 [ 5  0  0  0]
 [ 9 10  0  0]]

Source code in tinygrad/tensor.py

def tril(self, diagonal:int=0) -> Tensor:
  """
  Returns the lower triangular part of the tensor, the other elements are set to 0.

  The argument `diagonal` determines which diagonal is on the boundary. `diagonal = 0` means the main diagonal.
  Positive `diagonal` means above the main diagonal, and negative `diagonal` means below the main diagonal.

  ```python exec="true" source="above" session="tensor" result="python"
  t = Tensor([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]])
  print(t.numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.tril(diagonal=0).numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.tril(diagonal=1).numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.tril(diagonal=-1).numpy())
  ```
  """
  return Tensor._tri(self.shape[-2], self.shape[-1], diagonal=diagonal+1, device=self.device, dtype=dtypes.bool).where(0, self).cast(self.dtype)

interpolate ¤

interpolate(
    size: Tuple[int, ...],
    mode: str = "linear",
    align_corners: bool = False,
) -> Tensor

Downsamples or Upsamples to the input size, accepts 0 to N batch dimensions.

The interpolation algorithm is selected with mode which currently only supports linear, nearest and nearest-exact. To run bilinear or trilinear, pass in a 2D or 3D size.

t = Tensor([[1, 2, 3, 4], [21, 22, 23, 24], [41, 42, 43, 44]])
print(t.numpy())

[[ 1  2  3  4]
 [21 22 23 24]
 [41 42 43 44]]

print(t.interpolate(size=(2,3), mode="linear").numpy())

[[ 6  7  8]
 [36 37 38]]

Source code in tinygrad/tensor.py

def interpolate(self, size:Tuple[int, ...], mode:str="linear", align_corners:bool=False) -> Tensor:
  """
  Downsamples or Upsamples to the input `size`, accepts 0 to N batch dimensions.

  The interpolation algorithm is selected with `mode` which currently only supports `linear`, `nearest` and `nearest-exact`.
  To run `bilinear` or `trilinear`, pass in a 2D or 3D size.

  ```python exec="true" source="above" session="tensor" result="python"
  t = Tensor([[1, 2, 3, 4], [21, 22, 23, 24], [41, 42, 43, 44]])
  print(t.numpy())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  print(t.interpolate(size=(2,3), mode="linear").numpy())
  ```
  """
  assert isinstance(size, (tuple,list)) and all_int(size) and 0 < len(size) <= self.ndim, f"invalid {size=}"
  assert mode in ("linear", "nearest", "nearest-exact"), "only supports linear, nearest or nearest-exact interpolate"
  assert not (align_corners and mode != "linear"), "align_corners option can only be set with the interpolating mode linear"
  x, expand = self, list(self.shape)
  for i in range(-1,-len(size)-1,-1):
    scale = (self.shape[i] - int(align_corners)) / (size[i] - int(align_corners))
    arr, reshape = Tensor.arange(size[i], dtype=dtypes.float32, device=self.device), [1] * self.ndim
    reshape[i] = expand[i] = size[i]
    if mode == "linear":
      index = (scale*arr if align_corners else (scale*(arr+0.5))-0.5).clip(0, self.shape[i]-1)
      low, high, perc = [y.reshape(reshape).expand(expand) for y in (index.floor(), index.ceil(), index - index.floor())]
      x = x.gather(i, low).lerp(x.gather(i, high), perc)
    else:
      index = (scale*(arr+0.5) if mode=="nearest-exact" else scale*arr).cast(dtypes.int32).reshape(reshape).expand(expand)
      x = x.gather(i, index)
  return x.cast(self.dtype)

Neural Network (functional)¤

linear ¤

linear(weight: Tensor, bias: Optional[Tensor] = None)

Applies a linear transformation to self using weight and bias.

See: https://pytorch.org/docs/stable/generated/torch.nn.Linear.html

t = Tensor([[1, 2], [3, 4]])
weight = Tensor([[1, 2], [3, 4]])
bias = Tensor([1, 2])
print(t.linear(weight, bias).numpy())

[[ 8 12]
 [16 24]]

Source code in tinygrad/tensor.py

def linear(self, weight:Tensor, bias:Optional[Tensor]=None):
  """
  Applies a linear transformation to `self` using `weight` and `bias`.

  See: https://pytorch.org/docs/stable/generated/torch.nn.Linear.html

  ```python exec="true" source="above" session="tensor" result="python"
  t = Tensor([[1, 2], [3, 4]])
  weight = Tensor([[1, 2], [3, 4]])
  bias = Tensor([1, 2])
  print(t.linear(weight, bias).numpy())
  ```
  """
  x = self.mul(weight) if len(weight.shape) == 1 else self.dot(weight)
  return x.add(bias) if bias is not None else x

sequential ¤

sequential(ll: List[Callable[[Tensor], Tensor]])

Applies a sequence of functions to self chaining the output of each function to the input of the next.

t = Tensor([1, 2, 3])
print(t.sequential([lambda x: x * 2, lambda x: x + 1]).numpy())

[3 5 7]

Source code in tinygrad/tensor.py

def sequential(self, ll:List[Callable[[Tensor], Tensor]]):
  """
  Applies a sequence of functions to `self` chaining the output of each function to the input of the next.

  ```python exec="true" source="above" session="tensor" result="python"
  t = Tensor([1, 2, 3])
  print(t.sequential([lambda x: x * 2, lambda x: x + 1]).numpy())
  ```
  """
  return functools.reduce(lambda x,f: f(x), ll, self)

layernorm ¤

layernorm(axis=-1, eps: float = 1e-05) -> Tensor

Applies Layer Normalization over a mini-batch of inputs.

Described: https://paperswithcode.com/method/layer-normalization
Paper: https://arxiv.org/abs/1607.06450v1

t = Tensor.randn(8, 10, 16) * 2 + 8
print(t.mean().item(), t.std().item())

8.071012496948242 1.9488691091537476

t = t.layernorm()
print(t.mean().item(), t.std().item())

-9.22094933741846e-09 1.0003890991210938

Source code in tinygrad/tensor.py

def layernorm(self, axis=-1, eps:float=1e-5) -> Tensor:
  """
  Applies Layer Normalization over a mini-batch of inputs.

  - Described: https://paperswithcode.com/method/layer-normalization
  - Paper: https://arxiv.org/abs/1607.06450v1

  ```python exec="true" source="above" session="tensor" result="python"
  t = Tensor.randn(8, 10, 16) * 2 + 8
  print(t.mean().item(), t.std().item())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  t = t.layernorm()
  print(t.mean().item(), t.std().item())
  ```
  """
  y = (self - self.mean(axis, keepdim=True))
  return y.mul((y*y).mean(axis, keepdim=True).add(eps).rsqrt())

batchnorm ¤

batchnorm(
    weight: Optional[Tensor],
    bias: Optional[Tensor],
    mean: Tensor,
    invstd: Tensor,
    axis: Union[int, Tuple[int, ...]] = 1,
) -> Tensor

Applies Batch Normalization over a mini-batch of inputs.

Described: https://paperswithcode.com/method/batch-normalization
Paper: https://arxiv.org/abs/1502.03167

t = Tensor.randn(8, 4, 16, 16) * 2 + 8
print(t.mean().item(), t.std().item())

7.981656551361084 2.002045154571533

t = t.batchnorm(None, None, t.mean(axis=(0,2,3)), t.var(axis=(0,2,3)).add(1e-5).rsqrt())
print(t.mean().item(), t.std().item())

1.3217827188327647e-07 0.9998158812522888

Source code in tinygrad/tensor.py

def batchnorm(self, weight:Optional[Tensor], bias:Optional[Tensor], mean:Tensor, invstd:Tensor, axis:Union[int,Tuple[int,...]]=1) -> Tensor:
  """
  Applies Batch Normalization over a mini-batch of inputs.

  - Described: https://paperswithcode.com/method/batch-normalization
  - Paper: https://arxiv.org/abs/1502.03167

  ```python exec="true" source="above" session="tensor" result="python"
  t = Tensor.randn(8, 4, 16, 16) * 2 + 8
  print(t.mean().item(), t.std().item())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  t = t.batchnorm(None, None, t.mean(axis=(0,2,3)), t.var(axis=(0,2,3)).add(1e-5).rsqrt())
  print(t.mean().item(), t.std().item())
  ```
  """
  axis_ = argfix(axis)
  shape = tuple(s if ax in axis_ else 1 for ax, s in enumerate(self.shape))
  x = self - mean.reshape(shape)
  if weight is not None: x = x * weight.reshape(shape)
  ret = x.mul(invstd.reshape(shape) if len(invstd.shape) == len(axis_) else invstd)
  return (ret + bias.reshape(shape)) if bias is not None else ret

dropout ¤

dropout(p=0.5) -> Tensor

Applies dropout to self.

Note

dropout is only applied when Tensor.training is True.

Described: https://paperswithcode.com/method/dropout
Paper: https://jmlr.org/papers/v15/srivastava14a.html

Tensor.manual_seed(42)
t = Tensor.randn(2, 2)
with Tensor.train():
  print(t.dropout().numpy())

[[-2.6226 -0.    ]
 [-1.3097  0.    ]]

Source code in tinygrad/tensor.py

def dropout(self, p=0.5) -> Tensor:
  """
  Applies dropout to `self`.

  NOTE: dropout is only applied when `Tensor.training` is `True`.

  - Described: https://paperswithcode.com/method/dropout
  - Paper: https://jmlr.org/papers/v15/srivastava14a.html

  ```python exec="true" source="above" session="tensor" result="python"
  Tensor.manual_seed(42)
  t = Tensor.randn(2, 2)
  with Tensor.train():
    print(t.dropout().numpy())
  ```
  """
  if not Tensor.training or p == 0: return self
  return self * (Tensor.rand(*self.shape, requires_grad=False, dtype=dtypes.default_float, device=self.device) >= p) * (1/(1.0 - p))

one_hot ¤

one_hot(num_classes: int = -1) -> Tensor

Converts self to a one-hot tensor.

num_classes defaults to -1, which means num_classes will be inferred as max(self) + 1.

t = Tensor([0, 1, 3, 3, 4])
print(t.one_hot(5).numpy())

[[1 0 0 0 0]
 [0 1 0 0 0]
 [0 0 0 1 0]
 [0 0 0 1 0]
 [0 0 0 0 1]]

Source code in tinygrad/tensor.py

def one_hot(self, num_classes:int=-1) -> Tensor:
  """
  Converts `self` to a one-hot tensor.

  `num_classes` defaults to -1, which means num_classes will be inferred as max(self) + 1.

  ```python exec="true" source="above" session="tensor" result="python"
  t = Tensor([0, 1, 3, 3, 4])
  print(t.one_hot(5).numpy())
  ```
  """
  if num_classes == -1: num_classes = (self.max()+1).item()
  return (self[..., None] == Tensor.arange(num_classes, requires_grad=False, device=self.device)).where(1, 0)

scaled_dot_product_attention ¤

scaled_dot_product_attention(
    key: Tensor,
    value: Tensor,
    attn_mask: Optional[Tensor] = None,
    dropout_p: float = 0.0,
    is_causal: bool = False,
) -> Tensor

Computes scaled dot-product attention. self is the query tensor, key is the key tensor, and value is the value tensor.

Described: https://paperswithcode.com/method/scaled
Paper: https://arxiv.org/abs/1706.03762v7

q = Tensor.randn(2, 4, 8)
k = Tensor.randn(2, 4, 8)
v = Tensor.randn(2, 4, 8)
print(q.scaled_dot_product_attention(k, v).numpy())

[[[ 0.7096 -1.3188 -0.5629  0.6426 -0.025  -0.0636 -0.1879  0.3882]
  [ 0.6264 -0.7172 -0.3801  0.3077 -0.5498 -1.1599 -0.0885  0.3348]
  [ 0.6083 -0.5665 -0.2999  0.2557 -0.1295 -0.5506 -0.3255  0.1949]
  [ 0.7322 -1.4959 -0.6557  0.7118 -0.4007 -0.5873  0.0327  0.5346]]

 [[ 0.1278 -0.3112 -0.4018  0.0586 -0.3478 -0.0718 -0.904  -0.1595]
  [ 0.284  -0.2957 -0.5639 -0.1012 -0.5746 -0.4352 -1.0691 -0.2931]
  [-0.4256 -0.2026  0.4066  0.694   0.2838  0.494  -0.1331 -0.0593]
  [ 0.1401 -0.4061 -0.429   0.0877 -0.3795  0.037  -0.9037 -0.0037]]]

Source code in tinygrad/tensor.py

def scaled_dot_product_attention(self, key:Tensor, value:Tensor, attn_mask:Optional[Tensor]=None,
                                 dropout_p:float=0.0, is_causal:bool=False) -> Tensor:
  """
  Computes scaled dot-product attention.
  `self` is the query tensor, `key` is the key tensor, and `value` is the value tensor.

  - Described: https://paperswithcode.com/method/scaled
  - Paper: https://arxiv.org/abs/1706.03762v7

  ```python exec="true" source="above" session="tensor" result="python"
  q = Tensor.randn(2, 4, 8)
  k = Tensor.randn(2, 4, 8)
  v = Tensor.randn(2, 4, 8)
  print(q.scaled_dot_product_attention(k, v).numpy())
  ```
  """
  # NOTE: it also works when `key` and `value` have symbolic shape.
  assert all_int(self.shape), f"does not support symbolic shape {self.shape}"
  if is_causal: attn_mask = Tensor.ones(self.shape[-2], key.shape[-2], requires_grad=False, device=self.device).tril(0).cast(dtypes.bool)
  if attn_mask is not None and attn_mask.dtype == dtypes.bool: attn_mask = (attn_mask == 0).where(-float("inf"), 0)
  qk = self.matmul(key.transpose(-2,-1), acc_dtype=least_upper_dtype(self.dtype, key.dtype, dtypes.float32)) / math.sqrt(self.shape[-1])
  return ((qk+attn_mask) if attn_mask is not None else qk).softmax(-1).cast(self.dtype).dropout(dropout_p) @ value

binary_crossentropy ¤

binary_crossentropy(
    Y: Tensor, reduction: ReductionStr = "mean"
) -> Tensor

Computes the binary cross-entropy loss between self and Y.

See: https://pytorch.org/docs/stable/generated/torch.nn.BCELoss.html

t = Tensor([0.1, 0.9, 0.2])
Y = Tensor([0, 1, 0])
print(t.binary_crossentropy(Y).item())

0.14462155103683472

Source code in tinygrad/tensor.py

def binary_crossentropy(self, Y:Tensor, reduction:ReductionStr="mean") -> Tensor:
  """
  Computes the binary cross-entropy loss between `self` and `Y`.

  See: https://pytorch.org/docs/stable/generated/torch.nn.BCELoss.html

  ```python exec="true" source="above" session="tensor" result="python"
  t = Tensor([0.1, 0.9, 0.2])
  Y = Tensor([0, 1, 0])
  print(t.binary_crossentropy(Y).item())
  ```
  """
  return (-Y*self.log() - (1-Y)*(1-self).log())._do_reduction(reduction)

binary_crossentropy_logits ¤

binary_crossentropy_logits(
    Y: Tensor, reduction: ReductionStr = "mean"
) -> Tensor

Computes the binary cross-entropy loss between self and Y where self is logits.

See: https://pytorch.org/docs/stable/generated/torch.nn.BCEWithLogitsLoss.html

t = Tensor([-1, 2, -3])
Y = Tensor([0, 1, 0])
print(t.binary_crossentropy_logits(Y).item())

0.16292566061019897

Source code in tinygrad/tensor.py

def binary_crossentropy_logits(self, Y:Tensor, reduction:ReductionStr="mean") -> Tensor:
  """
  Computes the binary cross-entropy loss between `self` and `Y` where `self` is logits.

  See: https://pytorch.org/docs/stable/generated/torch.nn.BCEWithLogitsLoss.html

  ```python exec="true" source="above" session="tensor" result="python"
  t = Tensor([-1, 2, -3])
  Y = Tensor([0, 1, 0])
  print(t.binary_crossentropy_logits(Y).item())
  ```
  """
  return (self.maximum(0) - Y * self + (1 + self.abs().neg().exp()).log())._do_reduction(reduction)

sparse_categorical_crossentropy ¤

sparse_categorical_crossentropy(
    Y: Tensor,
    ignore_index=-1,
    label_smoothing=0.0,
    reduction: ReductionStr = "mean",
) -> Tensor

Computes the sparse categorical cross-entropy loss between self and Y.

Note

self is logits and Y is the target labels. NOTE: unlike PyTorch, this function expects the class axis to be -1

See: https://pytorch.org/docs/stable/generated/torch.nn.CrossEntropyLoss.html

t = Tensor([[-1, 2, -3], [1, -2, 3]])
Y = Tensor([1, 2])
print(t.sparse_categorical_crossentropy(Y).item())

0.09391524642705917

Source code in tinygrad/tensor.py

def sparse_categorical_crossentropy(self, Y:Tensor, ignore_index=-1, label_smoothing=0.0, reduction:ReductionStr="mean") -> Tensor:
  """
  Computes the sparse categorical cross-entropy loss between `self` and `Y`.

  NOTE: `self` is logits and `Y` is the target labels.
  NOTE: unlike PyTorch, this function expects the class axis to be -1

  See: https://pytorch.org/docs/stable/generated/torch.nn.CrossEntropyLoss.html

  ```python exec="true" source="above" session="tensor" result="python"
  t = Tensor([[-1, 2, -3], [1, -2, 3]])
  Y = Tensor([1, 2])
  print(t.sparse_categorical_crossentropy(Y).item())
  ```
  """
  assert 0.0 <= label_smoothing <= 1.0, "label_smoothing must be in [0.0, 1.0]"
  assert reduction in ("mean", "sum", "none"), "reduction must be one of ['mean', 'sum', 'none']"
  log_probs, loss_mask = self.log_softmax(), (Y != ignore_index)
  y_counter = Tensor.arange(self.shape[-1], requires_grad=False, device=self.device).unsqueeze(0).expand(Y.numel(), self.shape[-1])
  y = ((y_counter == Y.flatten().reshape(-1, 1)) * loss_mask.reshape(-1, 1)).reshape(*Y.shape, self.shape[-1])
  smoothing = label_smoothing * (log_probs.mean(-1) * loss_mask)
  unreduced = ((1 - label_smoothing) * (log_probs * y).sum(-1) + smoothing)
  # NOTE: because of ignore_index, we can't use Tensor.mean (so can't use `_do_reduction` here)
  return -(unreduced.sum() / loss_mask.sum() if reduction == "mean" else (unreduced.sum() if reduction == "sum" else unreduced))

cross_entropy ¤

cross_entropy(
    Y: Tensor,
    reduction: ReductionStr = "mean",
    label_smoothing: float = 0.0,
) -> Tensor

Compute the cross entropy loss between input logits and target.

Note

self are logits and Y are the target labels or class probabilities.

See: https://pytorch.org/docs/stable/generated/torch.nn.functional.cross_entropy.html

t = Tensor([[-1, 2, -3], [1, -2, 3]])
Y = Tensor([1, 2])
print(t.cross_entropy(Y).item())

0.09391524642705917

t = Tensor([[-1, 2, -3], [1, -2, 3]])
Y = Tensor([1, 2])
print(t.cross_entropy(Y, reduction='none').numpy())

[0.055  0.1328]

Source code in tinygrad/tensor.py

def cross_entropy(self, Y:Tensor, reduction:ReductionStr="mean", label_smoothing:float=0.0) -> Tensor:
  """
  Compute the cross entropy loss between input logits and target.

  NOTE: `self` are logits and `Y` are the target labels or class probabilities.

  See: https://pytorch.org/docs/stable/generated/torch.nn.functional.cross_entropy.html

  ```python exec="true" source="above" session="tensor" result="python"
  t = Tensor([[-1, 2, -3], [1, -2, 3]])
  Y = Tensor([1, 2])
  print(t.cross_entropy(Y).item())
  ```
  ```python exec="true" source="above" session="tensor" result="python"
  t = Tensor([[-1, 2, -3], [1, -2, 3]])
  Y = Tensor([1, 2])
  print(t.cross_entropy(Y, reduction='none').numpy())
  ```
  """
  assert 0.0 <= label_smoothing <= 1.0, "label_smoothing must be in [0.0, 1.0]"
  Y = Y.one_hot(num_classes=cast(int, self.shape[1])) if Y.ndim < 2 else Y
  Y = (1 - label_smoothing)*Y + label_smoothing / cast(int, Y.shape[1])
  ret = -self.log_softmax(axis=1).mul(Y).sum(axis=1)
  return ret._do_reduction(reduction)

Complex Ops

Reduce¤

sum ¤

prod ¤

max ¤

min ¤

any ¤

all ¤

mean ¤

var ¤

std ¤

std_mean ¤

softmax ¤

log_softmax ¤

logsumexp ¤

argmax ¤

argmin ¤

Processing¤

avg_pool2d ¤

max_pool2d ¤

conv2d ¤

conv_transpose2d ¤

dot ¤

matmul ¤

einsum staticmethod ¤

cumsum ¤

triu ¤

tril ¤

interpolate ¤

Neural Network (functional)¤

linear ¤

sequential ¤

layernorm ¤

batchnorm ¤

dropout ¤

one_hot ¤

scaled_dot_product_attention ¤

binary_crossentropy ¤

binary_crossentropy_logits ¤

sparse_categorical_crossentropy ¤

cross_entropy ¤

einsum `staticmethod` ¤