erfinv#

Computes inverse error function value of vector elements.

Syntax

Buffer API:

namespace oneapi::math::vm {

sycl::event erfinv(
        sycl::queue& exec_queue,
        std::int64_t n,
        sycl::buffer<T,1>& a,
        sycl::buffer<T,1>& y,
        oneapi::math::vm::mode mode = oneapi::math::vm::mode::not_defined,
        oneapi::math::vm::error_handler<T> errhandler = {});

} // namespace oneapi::math::vm

USM API:

namespace oneapi::math::vm {

sycl::event erfinv(
        sycl::queue& exec_queue,
        std::int64_t n,
        const T *a,
        T* y,
        std::vector<sycl::event> const & depends = {},
        oneapi::math::vm::mode mode = oneapi::math::vm::mode::not_defined,
        oneapi::math::vm::error_handler<T> errhandler = {});

} // namespace oneapi::math::vm

erfinv supports the following precisions.

T
`float`
`double`

Description

The erfinv(a) function computes the inverse error function values for elements of the input vector a and writes them to the output vector y.

\[y_i = \operatorname{erf}^{-1}(a)\]

where \(\operatorname{erf}(x)\) is the error function defined as given by:

\[\operatorname{erf}(x) = \frac{2}{\sqrt{\pi}} \int_0^x e^{-t^2} \operatorname{d \!} t\]

Useful relations for these functions:

\[\operatorname{erfcinv}(x) = \operatorname{erfinv}(1 - x)\]

\[\begin{split}\operatorname{cdfnorminv}(x) &= \sqrt{2} \operatorname{erfinv}(2x - 1) \\ &= \sqrt{2} \operatorname{erfcinv}(2 - 2x)\end{split}\]

\[\operatorname{erf}^{-1}(x) = \operatorname{erfc}^{-1}(1 - x)\]

where \(\operatorname{erfc}\) is the complementary error function.

\[\Phi(x) = \frac{1}{2} \left( 1 + \operatorname{erf}\left(x / \sqrt{2}\right) \right)\]

where

\[\Phi(x) = \frac{1}{\sqrt{2\pi}} \int_0^x \exp(-t^2/2) \operatorname{d \!} t\]

is the cumulative normal distribution function.

\[\Phi^{-1}(x) = \sqrt{2} \operatorname{erf}^{-1}(2x - 1)\]

where \(\Phi^{-1}(x)\) and \(\operatorname{erf}^{-1}(x)\) are the inverses to \(\Phi(x)\) and \(\operatorname{erf}(x)\), respectively.

The following figure illustrates the relationships among erfinv family functions (erfinv, erfcinv, cdfnorminv).

erfinv Family Functions Relationship |

Argument	Result	Status code
+0	+0
-0	-0
+1	+∞	`oneapi::math::vm::status::sing`
-1	-∞	`oneapi::math::vm::status::sing`
\|a\| > 1	QNAN	`oneapi::math::vm::status::errdom`
+∞	QNAN	`oneapi::math::vm::status::errdom`
-∞	QNAN	`oneapi::math::vm::status::errdom`
QNAN	QNAN
SNAN	QNAN

Input Parameters

Buffer API:

exec_queue: The queue where the routine should be executed.
n: Specifies the number of elements to be calculated.
a: The buffer a containing input vector of size n.
mode: Overrides the global VM mode setting for this function call. See set_mode function for possible values and their description. This is an optional parameter. The default value is oneapi::math::vm::mode::not_defined.
errhandler: Sets local error handling mode for this function call. See the create_error_handler function for arguments and their descriptions. This is an optional parameter. The local error handler is disabled by default.

USM API:

exec_queue: The queue where the routine should be executed.
n: Specifies the number of elements to be calculated.
a: Pointer a to the input vector of size n.
depends: Vector of dependent events (to wait for input data to be ready).
mode: Overrides the global VM mode setting for this function call. See the set_mode function for possible values and their description. This is an optional parameter. The default value is oneapi::math::vm::mode::not_defined.
errhandler: Sets local error handling mode for this function call. See the create_error_handler function for arguments and their descriptions. This is an optional parameter. The local error handler is disabled by default.

Output Parameters

Buffer API:

y: The buffer y containing the output vector of size n.

USM API:

y: Pointer y to the output vector of size n.
return value (event): Event, signifying availability of computed output and status code(s).

Exceptions

For list of generated exceptions please refer to Exceptions

Parent topic: VM Mathematical Functions