math.rst

Mathematical Expressions

DALI allows you to use regular Python arithmetic operations and other mathematical functions in the :meth:`~nvidia.dali.Pipeline.define_graph` method on the values that are returned from invoking other operators.

The expressions that are used will be incorporated into the pipeline without needing to explicitly instantiate operators and will describe the element-wise operations on Tensors.

At least one of the inputs to the arithmetic expression must be returned by other DALI operator - that is a value of :class:`nvidia.dali.pipeline.DataNode` representing a batch of tensors. The other input can be :meth:`nvidia.dali.types.Constant` or regular Python value of type bool, int, or float. As the operations performed are element-wise, the shapes of all operands must match.

Note

If one of the operands is a batch of Tensors that represent scalars, the scalar values are broadcast to the other operand.

For details and examples see :doc:`expressions tutorials <examples/general/expressions/index>`.

Type Promotion Rules

For operations that accept two (or more) arguments, type promotions apply. The resulting type is calculated in accordance to the table below.

Operand Type	Operand Type	Result Type	Additional Conditions
T	T	T
floatX	T	floatX	where T is not a float
floatX	floatY	floatZ	where Z = max(X, Y)
intX	intY	intZ	where Z = max(X, Y)
uintX	uintY	uintZ	where Z = max(X, Y)
intX	uintY	int2Y	if X <= Y
intX	uintY	intX	if X > Y

T stands for any one of the supported numerical types: bool, int8, int16, int32, int64, uint8, uint16, uint32, uint64, float32, and float64.

bool type is considered the smallest unsigned integer type and is treated as uint1 with respect to the table above.

Note

Type promotion is commutative.

For more than two arguments, the resulting type is calculated as a reduction from left to right - first calculating the result of operating on first two arguments, next between that intermediate result and the third argument and so on, until we have only the result type left.

Supported Arithmetic Operations

Currently, DALI supports the following operations:

.. function:: Unary arithmetic operators: +, -

    Unary operators that implement ``__pos__(self)`` and ``__neg__(self)``.
    The result of a unary arithmetic operation always preserves the input type.
    Unary operators accept only TensorList inputs from other operators.

    :rtype: TensorList of the same type

.. function:: Binary arithmetic operations: +, -, *, /, //, **

    Binary operators that implement ``__add__``, ``__sub__``, ``__mul__``, ``__truediv__``,
    ``__floordiv__`` and ``__pow__`` respectively.

    The result of an arithmetic operation between two operands is described
    :ref:`above <type promotions>`, with the exception of ``/``, the ``__truediv__`` operation,
    which always returns ``float32`` or ``float64`` type.

    .. note::
        The only allowed arithmetic operation between two ``bool`` values is multiplication
        ``(*)``.

    :rtype: TensorList of the type that is calculated based on the type promotion rules.

.. function:: Comparison operations: ==, !=, <, <=, >, >=

    Comparison operations.

    :rtype: TensorList of ``bool`` type.

.. function:: Bitwise binary operations: &, |, ^

    The bitwise binary operations follow the same type promotion rules as arithmetic binary
    operations, but their inputs are restricted to integral types (including ``bool``).

    .. note::
        A bitwise operation can be applied to two boolean inputs. Those operations can be used
        to emulate element-wise logical operations on Tensors.

    :rtype: TensorList of the type that is calculated based on the type promotion rules.

Mathematical Functions

Similarly to arithmetic expressions, one can use selected mathematical functions in the Pipeline graph definition. They also accept :class:`nvidia.dali.pipeline.DataNode`, :meth:`nvidia.dali.types.Constant` or regular Python value of type bool, int, or float as arguments. At least one of the inputs must be the output of other DALI Operator.

.. autofunction:: nvidia.dali.math.abs

.. autofunction:: nvidia.dali.math.fabs

.. autofunction:: nvidia.dali.math.floor

.. autofunction:: nvidia.dali.math.ceil

.. autofunction:: nvidia.dali.math.pow

.. autofunction:: nvidia.dali.math.fpow

.. autofunction:: nvidia.dali.math.min

.. autofunction:: nvidia.dali.math.max

.. autofunction:: nvidia.dali.math.clamp

Exponents and logarithms

.. autofunction:: nvidia.dali.math.sqrt

.. autofunction:: nvidia.dali.math.rsqrt

.. autofunction:: nvidia.dali.math.cbrt

.. autofunction:: nvidia.dali.math.exp

.. autofunction:: nvidia.dali.math.log

.. autofunction:: nvidia.dali.math.log2

.. autofunction:: nvidia.dali.math.log10

Trigonometric Functions

.. autofunction:: nvidia.dali.math.sin

.. autofunction:: nvidia.dali.math.cos

.. autofunction:: nvidia.dali.math.tan

.. autofunction:: nvidia.dali.math.asin

.. autofunction:: nvidia.dali.math.acos

.. autofunction:: nvidia.dali.math.atan

.. autofunction:: nvidia.dali.math.atan2

Hyperbolic Functions

.. autofunction:: nvidia.dali.math.sinh

.. autofunction:: nvidia.dali.math.cosh

.. autofunction:: nvidia.dali.math.tanh

.. autofunction:: nvidia.dali.math.asinh

.. autofunction:: nvidia.dali.math.acosh

.. autofunction:: nvidia.dali.math.atanh