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
\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)
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).
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 sizen
. - mode
- Overrides the global VM mode setting for this function call. See
:ref:`onemkl_vm_setmode`
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 :ref:`onemkl_vm_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 sizen
. - 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 :ref:`onemkl_vm_setmode`
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 :ref:`onemkl_vm_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 sizen
.
USM API:
- y
- Pointer
y
to the output vector of sizen
. - return value (event)
- Event, signifying availability of computed output and status code(s).
Exceptions
For list of generated exceptions please refer to :ref:`onemkl_vm_exceptions`