Developer Reference for Intel® oneAPI Math Kernel Library for Fortran
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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:

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).

Useful relations for these functions:

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 |