Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

ID 766686
Date 7/13/2023
Public

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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

INTEGER, INTENT(IN)

Specifies the number of elements to be calculated.

a

DOUBLE PRECISION for vderfinv, vmderfinv

REAL, INTENT(IN) for vserfinv, vmserfinv

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 for possible values and their description.

Output Parameters

Name

Type

Description

y

DOUBLE PRECISION for vderfinv, vmderfinv

REAL, INTENT(OUT) for vserfinv, vmserfinv

DOUBLE PRECISION, INTENT(OUT) for vderfinv, vmderfinv

Array that specifies 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:

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.

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


Sparse Matrices That Can be Solved With PARDISO

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

See Also