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 Aiʹ(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(32) 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(32) 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 )
Published date: 03/19/2020
Last modified date: 03/19/2020