.. SPDX-FileCopyrightText: 2019-2020 Intel Corporation .. .. SPDX-License-Identifier: CC-BY-4.0 .. _onemkl_vm_erfcinv: erfcinv ======= .. container:: Computes the inverse complementary error function value of vector elements. .. container:: section .. rubric:: Syntax :class: sectiontitle Buffer API: .. code-block:: cpp namespace oneapi::mkl::vm { sycl::event erfcinv( sycl::queue& exec_queue, std::int64_t n, sycl::buffer& a, sycl::buffer& y, oneapi::mkl::vm::mode mode = oneapi::mkl::vm::mode::not_defined, oneapi::mkl::vm::error_handler errhandler = {}); } // namespace oneapi::mkl::vm USM API: .. code-block:: cpp namespace oneapi::mkl::vm { sycl::event erfcinv( sycl::queue& exec_queue, std::int64_t n, const T *a, T* y, std::vector const & depends = {}, oneapi::mkl::vm::mode mode = oneapi::mkl::vm::mode::not_defined, oneapi::mkl::vm::error_handler errhandler = {}); } // namespace oneapi::mkl::vm ``erfcinv`` supports the following precisions. .. list-table:: :header-rows: 1 * - T * - ``float`` * - ``double`` .. container:: section .. rubric:: Description :class: sectiontitle The erfcinv(a) function computes the inverse complimentary error function values for elements of the input vector ``a`` and writes them to the output vector ``y``. The inverse complementary error function is defined as given by: .. math:: \operatorname{erfcinv}(x) = \operatorname{erfinv}(1 - x) Useful relations for these functions: .. math:: \operatorname{erfcinv}(x) = \operatorname{erfinv}(1 - x) .. math:: \operatorname{cdfnorminv}(x) &= \sqrt{2} \operatorname{erfinv}(2x - 1) \\ &= \sqrt{2} \operatorname{erfcinv}(2 - 2x) .. math:: \operatorname{erfinv}(x) = \operatorname{erf}^{-1}(x) .. math:: \operatorname{erf}(x) = \frac{2}{\sqrt{\pi}} \int_0^x e^{-t^2} \operatorname{d \!} t where :math:`\operatorname{erf}(x)` denotes the error function and :math:`\operatorname{erfinv}(x)` denotes the inverse error function. The following figure illustrates the relationships among erfinv family functions (erfinv, erfcinv, cdfnorminv). .. container:: figtop erfcinv Family Functions Relationship | .. container:: imagecenter |image0| .. container:: tablenoborder .. list-table:: :header-rows: 1 * - Argument - Result - Status code * - +1 - +0 -   * - +2 - -∞ - ``oneapi::mkl::vm::status::sing`` * - -0 - +∞ - ``oneapi::mkl::vm::status::sing`` * - +0 - +∞ - ``oneapi::mkl::vm::status::sing`` * - a < -0 - QNAN - ``oneapi::mkl::vm::status::errdom`` * - a > +2 - QNAN - ``oneapi::mkl::vm::status::errdom`` * - +∞ - QNAN - ``oneapi::mkl::vm::status::errdom`` * - -∞ - QNAN - ``oneapi::mkl::vm::status::errdom`` * - QNAN - QNAN -   * - SNAN - QNAN -   .. container:: section .. rubric:: Input Parameters :class: sectiontitle 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 :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 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 :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. .. container:: section .. rubric:: Output Parameters :class: sectiontitle 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). .. container:: section .. rubric:: Exceptions :class: sectiontitle For list of generated exceptions please refer to  :ref:`onemkl_vm_exceptions` .. container:: familylinks .. container:: parentlink **Parent topic:** :ref:`onemkl_vm_mathematical_functions` .. |image0| image:: ../equations/inverse_error_functions_plot.jpg