v?Erfc

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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v?Erfc

Computes the complementary error function value of vector elements.

Syntax

call vserfc( n, a, y )

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

call vmserfc( n, a, y, mode )

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

call vderfc( n, a, y )

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

call vmderfc( n, a, y, mode )

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

Include Files

mkl_vml.f90

Input Parameters

Name	Type	Description
`n`	INTEGER, INTENT(IN)	Specifies the number of elements to be calculated.
`a`	DOUBLE PRECISION for vderfc, vmderfc REAL, INTENT(IN) for vserfc, vmserfc DOUBLE PRECISION, INTENT(IN) for vderfc, vmderfc	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 for possible values and their description.

Output Parameters

Name	Type	Description
`y`	DOUBLE PRECISION for vderfc, vmderfc REAL, INTENT(OUT) for vserfc, vmserfc DOUBLE PRECISION, INTENT(OUT) for vderfc, vmderfc	Array that specifies the output vector y.

Name

Type

Description

y

DOUBLE PRECISION for vderfc, vmderfc

REAL, INTENT(OUT) for vserfc, vmserfc

DOUBLE PRECISION, INTENT(OUT) for vderfc, vmderfc

Array that specifies the output vector y.

Description

The Erfc function computes the complementary error function values for elements of the input vector a and writes them to the output vector y.

The complementary error function is defined as follows:

Useful relations:

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.

See also Figure "Erf Family Functions Relationship" in Erf function description for Erfc function relationship with the other functions of Erf family.

Special Values for Real Function v?Erfc(x)
Argument	Result	VM Error Status	Exception
X > underflow	+0	VML_STATUS_UNDERFLOW	UNDERFLOW
+∞	+0
-∞	+2
QNAN	QNAN
SNAN	QNAN		INVALID

Parent topic: Special Functions

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v?Erfc

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