erfinv¶

Computes the element-wise inverse error function of vector elements.

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 = erf-1(a),

where erf(x) is the error function defined as given by:

$\mathrm{erf} (x) = \frac{2}{\sqrt{\pi}} \int_0^x e^{-t^2}dt$

Useful relations:

$\mathrm{erf}^{-1} (x) = \mathrm{erfc}^{-1} (1-x)$

where erfc is the complementary error function.

$\Phi = \frac{1}{2} \mathrm{erf} (\frac{x}{\sqrt{2}})$

where

$\Phi (x) = - \frac{1}{\sqrt{2\pi}} \int_0^x \exp (- frac{t^2}{2}) dt$

is the cumulative normal distribution function.

$\Phi^{-1} (x) = \sqrt{2} \mathrm{erf}^{-1} (2x-1)$

where $\phi-1(x)$ and erf-1(x) are the inverses to $\phi (x)$ and erf(x), respectively.

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

erfinv Family Functions Relationship — `erfinv` Family Functions Relationship¶

Useful relations for these functions:

$\mathrm{erfcinv} (x) = \mathrm{erfinv} (1 - x)$

$\mathrm{cdfnorminv} (x) = \sqrt{2} \mathrm{erfinv} (2x - 1) = \sqrt{2} \mathrm{erfcinv} (2 - 2x)$

Argument	Result	Error Code
+0	+0
-0	-0
+1	+ $\infty$	`status::sing`
-1	- $\infty$	`status::sing`
\|a\| > 1	QNAN	`status::errdom`
+ $\infty$	QNAN	`status::errdom`
- $\infty$	QNAN	`status::errdom`
QNAN	QNAN
SNAN	QNAN

API ¶

Syntax¶

Buffer API

namespace oneapi::mkl::vm {

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

}

namespace oneapi::mkl::vm {

sycl::event erfinv(sycl::queue & exec_queue,
      sycl::buffer<T> & a,
      oneapi::mkl::slice sa,
      sycl::buffer<T> & y,
      oneapi::mkl::slice sy,
      oneapi::mkl::vm::mode mode = oneapi::mkl::vm::mode::not_defined,
      oneapi::mkl::vm::error_handler<T> errhandler = {});
}

USM API

namespace oneapi::mkl::vm {

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

}

namespace oneapi::mkl::vm {

sycl::event erfinv(sycl::queue & exec_queue,
      T const * a,
      oneapi::mkl::slice sa,
      T * y,
      oneapi::mkl::slice sy,
      std::vector<cl::sycl::event> const & depends = {},
      oneapi::mkl::vm::mode mode = oneapi::mkl::vm::mode::not_defined,
      oneapi::mkl::vm::error_handler<T> errhandler = {});

}

erfinv supports the following precisions and devices:

T	Devices supported
`float`	Host, CPU, and GPU
`double`	Host, CPU, and GPU

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 containing the input vector.
sa: Slice selector for a. See Data Types for a description of the oneMKL slice type.
sy: Slice selector for y. See Data Types for a description of the oneMKL slice type.
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 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 to the input vector.
sa: Slice selector for a. See Data Types for a description of the oneMKL slice type.
sy: Slice selector for y. See Data Types for a description of the oneMKL slice type.
depends: Vector of dependent events (to wait for input data to be ready). This is an optional parameter. The default is an empty vector.
mode: Overrides the global VM mode setting for this function call. See the See the set_mode function for possible values and their description. This is an optional parameter. The default value is 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 containing the output vector.
return value (event): Computation end event.

USM API

y: Pointer to the output vector.
return value (event): Computation end event.

Examples ¶

An example of how to use erfinv can be found in the oneMKL installation directory, under:

examples/dpcpp/vml/source/verfinv.cpp

cdfnorm erfcinv

oneAPI Math Kernel Library (oneMKL) documentation

erfinv¶

Description¶

API¶

Syntax¶

Input Parameters¶

Output Parameters¶

Examples¶

Description ¶

API ¶

Examples ¶