sqrt_op

Structs

Struct: Sqrt

Fields

Methods


fwd(arg0: Array) -> Array

Computes the square root of the input array element-wise.

Args

arg0: Array The input array.

Returns

Array - An array containing the square root of each element in the input array.

Examples:


a = Array([[1, 2], [3, 4]])
result = sqrt(a)
print(result)

Note: This function supports:

Automatic differentiation (forward and reverse modes).
Complex valued arguments.


jvp(primals: List[Array], tangents: List[Array]) -> Array

Computes the Jacobian-vector product for the square root function.

Args

primals: List[Array] A list containing the primal input array.
tangents: List[Array] A list containing the tangent vector.

Returns

Array - The Jacobian-vector product for the square root function.

Implements forward-mode automatic differentiation for the square root function.

Note: The Jacobian-vector product for the square root is computed as dx / (2 * sqrt(x)), where x is the primal input and dx is the tangent vector.


vjp(primals: List[Array], grad: Array, out: Array) -> List[Array]

Computes the vector-Jacobian product for the square root function.

Args

primals: List[Array] A list containing the primal input array.
grad: Array The gradient of the output with respect to some scalar function.
out: Array The output of the forward pass (unused in this function).

Returns

List[Array] - A list containing the gradient with respect to the input.

Implements reverse-mode automatic differentiation for the square root function.

Note: The vector-Jacobian product for the square root is computed as grad / (2 * sqrt(x)), where x is the primal input and grad is the incoming gradient.


unary_simd_op(arg0_real: SIMD[float32, nelts[::DType]().__mul__(2).__floordiv__(2)], arg0_imag: SIMD[float32, nelts[::DType]().__mul__(2).__floordiv__(2)]) -> Tuple[SIMD[float32, nelts[::DType]().__mul__(2).__floordiv__(2)], SIMD[float32, nelts[::DType]().__mul__(2).__floordiv__(2)]]

Low-level function to compute the square root of a complex number represented as SIMD vectors.

Args

arg0_real: SIMD[float32, nelts[::DType]().__mul__(2).__floordiv__(2)] The real part of the complex number.
arg0_imag: SIMD[float32, nelts[::DType]().__mul__(2).__floordiv__(2)] The imaginary part of the complex number.

Returns

Tuple[SIMD[float32, nelts[::DType]().__mul__(2).__floordiv__(2)], SIMD[float32, nelts[::DType]().__mul__(2).__floordiv__(2)]] - The real and imaginary parts of the square root of the complex number as a tuple.


__call__(mut curr: Array, args: List[Array])

Performs the forward pass for element-wise square root computation of an array.

Args

curr: Array The current array to store the result (modified in-place).
args: List[Array] A list containing the input array.

Computes the square root of each element in the input array and stores the result in the current array. Initializes the current array if not already set up.

Note: This function assumes that the shape and data of the args are already set up. If the current array (curr) is not initialized, it computes the shape based on the input array and sets up the data accordingly.

Functions

sqrt


sqrt(arg0: Array) -> Array

Computes the square root of the input array element-wise.

Args

arg0: Array The input array.

Returns

Array - An array containing the square root of each element in the input array.

Examples:


a = Array([[1, 2], [3, 4]])
result = sqrt(a)
print(result)

Note: This function supports:

Automatic differentiation (forward and reverse modes).
Complex valued arguments.