Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

ID 766686
Date 7/13/2023
Public

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Document Table of Contents

v?Erf

Computes the error function value of vector elements.

Syntax

call vserf( n, a, y )

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

call vmserf( n, a, y, mode )

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

call vderf( n, a, y )

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

call vmderf( n, a, y, mode )

call vmderfi(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 vderf, vmderf

REAL, INTENT(IN) for vserf, vmserf

DOUBLE PRECISION, INTENT(IN) for vderf, vmderf

Array, 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 vderf, vmderf

REAL, INTENT(OUT) for vserf, vmserf

DOUBLE PRECISION, INTENT(OUT) for vderf, vmderf

Array, specifies the output vector y.

Description

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

The error function is defined as given by:

Equation

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.

The following figure illustrates the relationships among Erf family functions (Erf, Erfc, CdfNorm).

Erf Family Functions Relationship


Sparse Matrices That Can be Solved With PARDISO

Useful relations for these functions:

Equation


Sparse Matrices That Can be Solved With PARDISO

Special Values for Real Function v?Erf(x)
Argument Result Exception
+ +1  
- -1  
QNAN QNAN  
SNAN QNAN INVALID

See Also