cdfnorm¶

Computes the cumulative normal distribution function values of vector elements.

Syntax

Buffer API:

namespace oneapi::mkl::vm {

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

} // namespace oneapi::mkl::vm

USM API:

namespace oneapi::mkl::vm {

sycl::event cdfnorm(
        sycl::queue& exec_queue,
        std::int64_t n,
        const T *a,
        T* y,
        std::vector<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

cdfnorm supports the following precisions.

T
`float`
`double`

Description

The cdfnorm function computes the cumulative normal distribution function values for elements of the input vector a and writes them to the output vector y.

The cumulative normal distribution function is defined as given by:

\[\operatorname{cdfnorm}(x) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^{x} e^{-\frac{t^2}{2}} \operatorname{d \!} x\]

Useful relations for these functions:

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

\[\begin{split}\operatorname{cdfnorm}(x) &= \frac{1}{2} \left( 1 + \operatorname{erf}\left(\frac{x}{\sqrt{2}}\right) \right) \\ &= 1 - \frac{1}{2} \operatorname{erfc}\left(\frac{x}{\sqrt{2}}\right)\end{split}\]

where \(\operatorname{erf}\) and \(\operatorname{erfc}\) are the error and complementary error functions, respectively.

The following figure illustrates the relationships among the family of error functions (erf, erfc, cdfnorm).

cdfnorm Family Functions Relationship |

Argument	Result	Status code
a < underflow	+0	`oneapi::mkl::vm::status::underflow`
+∞	+1
-∞	+0
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::mkl::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::mkl::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

oneAPI Specification 1.1-rev-1 documentation

cdfnorm¶