CAID
This function evaluates the derivative of the Airy function of the first kind for complex arguments.
Function Return Value
CAID — Complex function value. (Output)
Required Arguments
Z — Complex argument for which the Airy function value is desired. (Input)
Optional Arguments
SCALING — Logical argument specifying whether or not the scaling function will be applied to the Aiʹ(z) function value. (Input)
Default: SCALING = .false.
FORTRAN 90 Interface
Generic: C_CAID (Z)
Specific: The specific interface names are C_CAID and Z_CAID.
Description
The function Ai
ʹ(
z) is defined to be the derivative of the Airy function, Ai(
z) (see
CAI).
An optional argument, SCALING, defines a scaling function s(z) that multiplies the results. This scaling function is
Scaling | Action |
|---|
.false. | |
.true. | |
Comments
Informational Errors
Type | Code | Description |
|---|
2 | 1 | The real part of (2/3) × Z(3∕2) was too large in the region where the function is exponentially small; function values were set to zero to avoid underflow. Try supplying the optional argument SCALING. |
2 | 2 | The real part of (2/3) × Z(3∕2) was too large in the region where the function is exponentially large; function values were set to zero to avoid underflow. Try supplying the optional argument SCALING. |
Example
In this example, Ai (0.49, 0.49) and Aiʹ(0.49, 0.49) are computed and printed.
USE CAID_INT
USE CAI_INT
USE UMACH_INT
IMPLICIT NONE
! Declare variables
INTEGER NOUT
COMPLEX Y, Z, W, Z
! Compute
W = CMPLX(0.49,0.49)
Y = CAI(W)
Z = CAID(W)
! Print the results
CALL UMACH (2, NOUT)
WRITE (NOUT,99998) W, Y
WRITE (NOUT,99997) W, Z
!
99997 FORMAT(12x,"CAID(",F6.3 ", ",F6.3 ") = ( ",F6.3, ", ",F6.3," )" )
99998 FORMAT(12x,"CAI(",F6.3 ", ",F6.3 ") = ( ",F6.3, ", ",F6.3," )" )
End
Output
CAI( 0.490, 0.490) = ( 0.219, -0.113 )
CAID( 0.490, 0.490) = ( -0.240, 0.064 )
