v?ErfInv

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 6/24/2024

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v?ErfInv

Computes inverse error function value of vector elements.

Syntax

vhErfInv( n, a, y );

vhErfInvI(n, a, inca, y, incy);

vmhErfInv( n, a, y, mode );

vmhErfInvI(n, a, inca, y, incy, mode);

vsErfInv( n, a, y );

vsErfInvI(n, a, inca, y, incy);

vmsErfInv( n, a, y, mode );

vmsErfInvI(n, a, inca, y, incy, mode);

vdErfInv( n, a, y );

vdErfInvI(n, a, inca, y, incy);

vmdErfInv( n, a, y, mode );

vmdErfInvI(n, a, inca, y, incy, mode);

Include Files

mkl.h

Input Parameters

Name	Type	Description
`n`	const MKL_INT	Specifies the number of elements to be calculated.
`a`	const _Float16* for vhErfInv, vmhErfInv const float* for vsErfInv, vmsErfInv const double* for vdErfInv, vmdErfInv	Pointer to an array that contains the input vector a.
inca, incy	const MKL_INT	Specifies increments for the elements of `a` and `y`.
mode	const MKL_INT64	Overrides global VM mode setting for this function call. See vmlSetMode for possible values and their description.

Output Parameters

Name	Type	Description
`y`	_Float16* for vhErfInv, vmhErfInv float* for vsErfInv, vmsErfInv double* for vdErfInv, vmdErfInv	Pointer to an array that contains the output vector y.

Name

Type

Description

y

_Float16* for vhErfInv, vmhErfInv

float* for vsErfInv, vmsErfInv

double* for vdErfInv, vmdErfInv

Pointer to an array that contains the output vector y.

Description

The ErfInv 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:

Useful relations:

Equation

where erfc is the complementary error function.

Equation

where

Equation

is the cumulative normal distribution function.

Equation

where Φ^-1(x) and erf^-1(x) are the inverses to Φ(x) and erf(x) respectively.

Figure "ErfInv Family Functions Relationship" illustrates the relationships among ErfInv family functions (ErfInv, ErfcInv, CdfNormInv).

ErfInv Family Functions Relationship

Sparse Matrices That Can be Solved With PARDISO

Useful relations for these functions:

Equation

Special Values for Real Function v?ErfInv(x)
Argument	Result	VM Error Status	Exception
+0	+0
-0	-0
+1	+∞	VML_STATUS_SING	ZERODIVIDE
-1	-∞	VML_STATUS_SING	ZERODIVIDE
\|X\| > 1	QNAN	VML_STATUS_ERRDOM	INVALID
+∞	QNAN	VML_STATUS_ERRDOM	INVALID
-∞	QNAN	VML_STATUS_ERRDOM	INVALID
QNAN	QNAN
SNAN	QNAN		INVALID

Parent topic: Special Functions

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Developer Reference for Intel® oneAPI Math Kernel Library for C

v?ErfInv

Syntax

Include Files

Input Parameters

Output Parameters

Description

See Also