This function evaluates the inverse error function.

Function Return Value

ERFI — Function value.   (Output)

Required Arguments

X — Argument for which the function value is desired.   (Input)

FORTRAN 90 Interface

Generic:                              ERFI (X)

Specific:                             The specific interface names are S_ERFI and D_ERFI.

FORTRAN 77 Interface

Single:                                ERFI (X)

Double:                              The double precision function name is DERFI.

Description

Function ERFI(X) computes the inverse of the error function erf x, defined in ERF.

The function ERFI(X) is defined for |x| < 1. If xmax< |x| < 1, then the answer will be less accurate than half precision. Very approximately,

where ε = AMACH(4) is the machine precision.

Figure 5- 3 Plot of erf−1(x)

Comments

Informational error

Type           Code

3                   2          Result of ERFI(X) is accurate to less than one-half precision because the absolute value of the argument is too large .

Example

In this example, erf⁻¹(erf(1.0)) is computed and printed.

 

      USE ERFI_INT

      USE ERF_INT

      USE UMACH_INT

 

      IMPLICIT   NONE

!                                 Declare variables

      INTEGER    NOUT

      REAL       VALUE, X

!                                 Compute

      X     = ERF(1.0)

      VALUE = ERFI(X)

!                                 Print the results

      CALL UMACH (2, NOUT)

      WRITE (NOUT,99999) X, VALUE

99999 FORMAT (' ERFI(', F6.3, ') = ', F6.3)

      END

Output

 

ERFI( 0.843) =  1.000

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