v?CdfNormInv

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

v?CdfNormInv

Computes the inverse cumulative normal distribution function values of vector elements.

Syntax

call vscdfnorminv ( n , a , y )

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

call vmscdfnorminv ( n , a , y , mode )

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

call vdcdfnorminv ( n , a , y )

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

call vmdcdfnorminv ( n , a , y , mode )

call vmdcdfnorminvi(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 `vdcdfnorminv` , `vmdcdfnorminv`Fortran 90: REAL , INTENT(IN) for `vscdfnorminv` , `vmscdfnorminv`Fortran 90: DOUBLE PRECISION , INTENT(IN) for `vdcdfnorminv` , `vmdcdfnorminv`	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 `vdcdfnorminv` , `vmdcdfnorminv`Fortran 90: REAL , INTENT(OUT) for `vscdfnorminv` , `vmscdfnorminv`Fortran 90: DOUBLE PRECISION , INTENT(OUT) for `vdcdfnorminv` , `vmdcdfnorminv`	Array that specifies the output vector `y` .

Description

vsCdfNormInv vdCdfNormInv vmsCdfNormInv vmdCdfNormInv

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

The inverse cumulative normal distribution function is defined as given by:

where CdfNorm(x) denotes the cumulative normal distribution function.

Useful relations:

Sparse Matrices That Can be Solved With PARDISO

where erfinv(x) denotes the inverse error function and erfcinv(x) denotes the inverse complementary error functions.

See also Figure “ErfInv Family Functions Relationship” in ErfInv function description for CdfNormInv function relationship with the other functions of ErfInv family.

Special Values for Real Function v?CdfNormInv(x)

Argument	Result	VM Error Status	Exception
+0.5	+0
+1	∞	VML_STATUS_SING	ZERODIVIDE
-0	∞	VML_STATUS_SING	ZERODIVIDE
+0	∞	VML_STATUS_SING	ZERODIVIDE
X < -0	QNAN	VML_STATUS_ERRDOM	INVALID
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?CdfNormInv

Syntax

Include Files

Input Parameters

Output Parameters

Description