heat.exponential

Exponential and logarithmic operations module.

Module Contents

exp(x: heat.core.dndarray.DNDarray, out: heat.core.dndarray.DNDarray | None = None) → heat.core.dndarray.DNDarray

Calculate the exponential of all elements in the input array. Result is a DNDarray of the same shape as x.

Parameters:

• x (DNDarray) – The array for which to compute the exponential.

• out (DNDarray, optional) – A location in which to store the results. If provided, it must have a broadcastable shape. If not provided or set to None, a fresh array is allocated.

Examples

>>> ht.exp(ht.arange(5))
DNDarray([ 1.0000,  2.7183,  7.3891, 20.0855, 54.5981], dtype=ht.float32, device=cpu:0, split=None)

expm1(x: heat.core.dndarray.DNDarray, out: heat.core.dndarray.DNDarray | None = None) → heat.core.dndarray.DNDarray

Calculate \(exp(x) - 1\) for all elements in the array. Result is a DNDarray of the same shape as x.

Parameters:

• x (DNDarray) – The array for which to compute the exponential.

• out (DNDarray, optional) – A location in which to store the results. If provided, it must have a broadcastable shape. If not provided or set to None, a fresh array is allocated.

Examples

>>> ht.expm1(ht.arange(5)) + 1.0
DNDarray([ 1.0000,  2.7183,  7.3891, 20.0855, 54.5981], dtype=ht.float64, device=cpu:0, split=None)

exp2(x: heat.core.dndarray.DNDarray, out: heat.core.dndarray.DNDarray | None = None) → heat.core.dndarray.DNDarray

Calculate the exponential of two of all elements in the input array (\(2^x\)). Result is a DNDarray of the same shape as x.

Parameters:

• x (DNDarray) – The array for which to compute the exponential of two.

• out (DNDarray, optional) – A location in which to store the results. If provided, it must have a broadcastable shape. If not provided or set to None, a fresh array is allocated.

Examples

>>> ht.exp2(ht.arange(5))
DNDarray([ 1.,  2.,  4.,  8., 16.], dtype=ht.float32, device=cpu:0, split=None)

log(x: heat.core.dndarray.DNDarray, out: heat.core.dndarray.DNDarray | None = None) → heat.core.dndarray.DNDarray

Natural logarithm, element-wise. The natural logarithm is the inverse of the exponential function, so that \(log(exp(x)) = x\). The natural logarithm is logarithm in base e. Result is a DNDarray of the same shape as x. Negative input elements are returned as NaN.

Parameters:

• x (DNDarray) – The array for which to compute the logarithm.

• out (DNDarray, optional) – A location in which to store the results. If provided, it must have a broadcastable shape. If not provided or set to None, a fresh array is allocated.

Examples

>>> ht.log(ht.arange(5))
DNDarray([  -inf, 0.0000, 0.6931, 1.0986, 1.3863], dtype=ht.float32, device=cpu:0, split=None)

log2(x: heat.core.dndarray.DNDarray, out: heat.core.dndarray.DNDarray | None = None) → heat.core.dndarray.DNDarray

Compute the logarithm to the base 2 (\(log_2(x)\)), element-wise. Result is a DNDarray of the same shape as x. Negative input elements are returned as NaN.

Parameters:

• x (DNDarray) – The array for which to compute the logarithm.

• out (DNDarray, optional) – A location in which to store the results. If provided, it must have a broadcastable shape. If not provided or set to None, a fresh array is allocated.

Examples

>>> ht.log2(ht.arange(5))
DNDarray([  -inf, 0.0000, 1.0000, 1.5850, 2.0000], dtype=ht.float32, device=cpu:0, split=None)

log10(x: heat.core.dndarray.DNDarray, out: heat.core.dndarray.DNDarray | None = None) → heat.core.dndarray.DNDarray

Compute the logarithm to the base 10 (\(log_{10}(x)\)), element-wise. Result is a DNDarray of the same shape as x. Negative input elements are returned as NaN.

Parameters:

• x (DNDarray) – The array for which to compute the logarithm.

• out (DNDarray, optional) – A location in which to store the results. If provided, it must have a broadcastable shape. If not provided or set to None, a fresh array is allocated.

Examples

>>> ht.log10(ht.arange(5))
DNDarray([  -inf, 0.0000, 0.3010, 0.4771, 0.6021], dtype=ht.float32, device=cpu:0, split=None)

log1p(x: heat.core.dndarray.DNDarray, out: heat.core.dndarray.DNDarray | None = None) → heat.core.dndarray.DNDarray

Return the natural logarithm of one plus the input array, element-wise. Result is a DNDarray of the same shape as x. Negative input elements are returned as NaN.

Parameters:

• x (DNDarray) – The array for which to compute the logarithm.

• out (DNDarray, optional) – A location in which to store the results. If provided, it must have a broadcastable shape. If not provided or set to None, a fresh array is allocated.

Examples

>>> ht.log1p(ht.arange(5))
DNDarray([0.0000, 0.6931, 1.0986, 1.3863, 1.6094], dtype=ht.float32, device=cpu:0, split=None)

logaddexp(x1: heat.core.dndarray.DNDarray, x2: heat.core.dndarray.DNDarray, out: heat.core.dndarray.DNDarray | None = None) → heat.core.dndarray.DNDarray

Calculates the logarithm of the sum of exponentiations \(log(exp(x1) + exp(x2))\) for each element \({x1}_i\) of the input array x1 with the respective element \({x2}_i\) of the input array x2.

Parameters:

• x1 (DNDarray) – first input array. Should have a floating-point data type.

• x2 (DNDarray) – second input array. Must be compatible with x1. Should have a floating-point data type.

• out (DNDarray, optional) – A location in which to store the results. If provided, it must have a broadcastable shape. If not provided or set to None, a fresh array is allocated.

See also

logaddexp2()

Logarithm of the sum of exponentiations of inputs in base-2.

Examples

>>> ht.logaddexp(ht.array([-1.0]), ht.array([-1.0, -2, -3]))
DNDarray([-0.3069, -0.6867, -0.8731], dtype=ht.float32, device=cpu:0, split=None)

logaddexp2(x1: heat.core.dndarray.DNDarray, x2: heat.core.dndarray.DNDarray, out: heat.core.dndarray.DNDarray | None = None) → heat.core.dndarray.DNDarray

Calculates the logarithm of the sum of exponentiations in base-2 \(log2(exp(x1) + exp(x2))\) for each element \({x1}_i\) of the input array x1 with the respective element \({x2}_i\) of the input array x2.

Parameters:

• x1 (DNDarray) – first input array. Should have a floating-point data type.

• x2 (DNDarray) – second input array. Must be compatible with x1. Should have a floating-point data type.

• out (DNDarray, optional) – A location in which to store the results. If provided, it must have a broadcastable shape. If not provided or set to None, a fresh array is allocated.

See also

logaddexp()

Logarithm of the sum of exponentiations of inputs.

Examples

>>> ht.logaddexp2(ht.array([-1.0]), ht.array([-1.0, -2, -3]))
DNDarray([ 0.0000, -0.4150, -0.6781], dtype=ht.float32, device=cpu:0, split=None)

sqrt(x: heat.core.dndarray.DNDarray, out: heat.core.dndarray.DNDarray | None = None) → heat.core.dndarray.DNDarray

Return the non-negative square-root of a tensor element-wise. Result is a DNDarray of the same shape as x. Negative input elements are returned as NaN.

Parameters:

• x (DNDarray) – The array for which to compute the square-roots.

• out (DNDarray, optional) – A location in which to store the results. If provided, it must have a broadcastable shape. If not provided or set to None, a fresh array is allocated.

Examples

>>> ht.sqrt(ht.arange(5))
DNDarray([0.0000, 1.0000, 1.4142, 1.7321, 2.0000], dtype=ht.float32, device=cpu:0, split=None)
>>> ht.sqrt(ht.arange(-5, 0))
DNDarray([nan, nan, nan, nan, nan], dtype=ht.float32, device=cpu:0, split=None)

square(x: heat.core.dndarray.DNDarray, out: heat.core.dndarray.DNDarray | None = None) → heat.core.dndarray.DNDarray

Return a new tensor with the squares of the elements of input.

Parameters:

• x (DNDarray) – The array for which to compute the squares.

• out (DNDarray, optional) – A location in which to store the results. If provided, it must have a broadcastable shape. If not provided or set to None, a fresh array is allocated.

Examples

>>> a = ht.random.rand(4)
>>> a
DNDarray([0.8654, 0.1432, 0.9164, 0.6179], dtype=ht.float32, device=cpu:0, split=None)
>>> ht.square(a)
DNDarray([0.7488, 0.0205, 0.8397, 0.3818], dtype=ht.float32, device=cpu:0, split=None)