v?ErfInv

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

v?ErfInv

Computes inverse error function value of vector elements.

Syntax

call vserfinv ( n , a , y )

call vserfinvi(n, a, inca, y, incy)

call vmserfinv ( n , a , y , mode )

call vmserfinvi(n, a, inca, y, incy, mode)

call vderfinv ( n , a , y )

call vderfinvi(n, a, inca, y, incy)

call vmderfinv ( n , a , y , mode )

call vmderfinvi(n, a, inca, y, incy, mode)

Include Files

mkl_vml.f90

Input Parameters

Name	Type	Description
`n`		Specifies the number of elements to be calculated.
`a`	Fortran 77: DOUBLE PRECISION for `vderfinv` , `vmderfinv`Fortran 90: REAL , INTENT(IN) for `vserfinv` , `vmserfinv`Fortran 90: DOUBLE PRECISION , INTENT(IN) for `vderfinv` , `vmderfinv`	Array that specifies the input vector `a` .
`inca` , `incy`	INTEGER, INTENT(IN)	Specifies increments for the elements of `a` and `y` .
`mode`	INTEGER(KIND=8) , INTENT(IN)	Overrides global VM mode setting for this function call. See vmlSetMode (Sets a new mode for VM functions according to the mode parameter and stores the previous VM mode to oldmode.) for possible values and their description.

Output Parameters

Name	Type	Description
`y`	Fortran 77: DOUBLE PRECISION for `vderfinv` , `vmderfinv`Fortran 90: REAL , INTENT(OUT) for `vserfinv` , `vmserfinv`Fortran 90: DOUBLE PRECISION , INTENT(OUT) for `vderfinv` , `vmderfinv`	Array that specifies the output vector `y` .

Description

vsErfInv vdErfInv vmsErfInv vmdErfInv

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:

where erfc is the complementary error function.

where

is the cumulative normal distribution function.

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:

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

NOTE:

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

v?ErfInv

Syntax

Include Files

Input Parameters

Output Parameters

Description

ErfInv Family Functions Relationship