java.lang.Object

netlib.specfun.Caljy1

public class Caljy1
extends java.lang.Object

First-order Bessel functions of the first and second kind (J1 and Y1).

Changes:

Original Version (netlib.org/specfun), November 10, 1987, W. J. Cody.
2011, S. Reiser: ported to Java.
2020-08-24, S. Reiser: rearranged calculations for X > 8. Let functions sin(x), cos(x) handle the argument reduction. To calculate sin(x+const), cos(x+const) use the identities
```
   sin(x+y) = sin(x)cos(y) + cos(x)sin(y),
   cos(x+y) = cos(x)cos(y) - sin(x)sin(y).
```
2020-08-29, Reiser: One of the values
u := sin(x)-cos(x) and
v := sin(x)+cos(x)
will be less accurate than the other. Use cos(2*x) and the identity
cos(2*x) = cos(x)^2 - sin(x)^2
to calculate the less accurate one by means of the other (technique taken from netlib/fdlibm, file "e_j0.c").

  Produced by f2java.  f2java is part of the Fortran-
  -to-Java project at the University of Tennessee Netlib
  numerical software repository.

  Original authorship for the BLAS and LAPACK numerical
  routines may be found in the Fortran source, available at
  http://www.netlib.org.

  Fortran input file: j1y1.f
  f2java version: 0.8.1

 C---------------------------------------------------------------------
 C
 C This packet computes first-order Bessel functions of the first and
 C   second kind (J1 and Y1), for real arguments X, where 0 < X <= XMAX
 C   for Y1, and |X| <= XMAX for J1.  It contains two function-type
 C   subprograms,  BESJ1  and  BESY1,  and one subroutine-type
 C   subprogram,  CALJY1.  The calling statements for the primary
 C   entries are:
 C
 C           Y = BESJ1(X)
 C   and
 C           Y = BESY1(X),
 C
 C   where the entry points correspond to the functions J1(X) and Y1(X),
 C   respectively.  The routine  CALJY1  is intended for internal packet
 C   use only, all computations within the packet being concentrated in
 C   this one routine.  The function subprograms invoke  CALJY1  with
 C   the statement
 C           CALL CALJY1(ARG,RESULT,JINT),
 C   where the parameter usage is as follows:
 C
 C      Function                  Parameters for CALJY1
 C       call              ARG             RESULT          JINT
 C
 C     BESJ1(ARG)     |ARG| .LE. XMAX       J1(ARG)          0
 C     BESY1(ARG)   0 .LT. ARG .LE. XMAX    Y1(ARG)          1
 C
 C   The main computation uses unpublished minimax rational
 C   approximations for X .LE. 8.0, and an approximation from the
 C   book  Computer Approximations  by Hart, et. al., Wiley and Sons,
 C   New York, 1968, for arguments larger than 8.0   Part of this
 C   transportable packet is patterned after the machine-dependent
 C   FUNPACK program BESJ1(X), but cannot match that version for
 C   efficiency or accuracy.  This version uses rational functions
 C   that are theoretically accurate to at least 18 significant decimal
 C   digits for X <= 8, and at least 18 decimal places for X > 8.  The
 C   accuracy achieved depends on the arithmetic system, the compiler,
 C   the intrinsic functions, and proper selection of the machine-
 C   dependent constants.
 C
 C*******************************************************************
 C
 C Explanation of machine-dependent constants
 C
 C   XINF   = largest positive machine number
 C   XMAX   = largest acceptable argument.  The functions AINT, SIN
 C            and COS must perform properly for  ABS(X) .LE. XMAX.
 C            We recommend that XMAX be a small integer multiple of
 C            sqrt(1/eps), where eps is the smallest positive number
 C            such that  1+eps > 1.
 C   XSMALL = positive argument such that  1.0-(1/2)(X/2)**2 = 1.0
 C            to machine precision for all  ABS(X) .LE. XSMALL.
 C            We recommend that  XSMALL < sqrt(eps)/beta, where beta
 C            is the floating-point radix (usually 2 or 16).
 C
 C     Approximate values for some important machines are
 C
 C                          eps      XMAX     XSMALL      XINF
 C
 C  CDC 7600      (S.P.)  7.11E-15  1.34E+08  2.98E-08  1.26E+322
 C  CRAY-1        (S.P.)  7.11E-15  1.34E+08  2.98E-08  5.45E+2465
 C  IBM PC (8087) (S.P.)  5.96E-08  8.19E+03  1.22E-04  3.40E+38
 C  IBM PC (8087) (D.P.)  1.11D-16  2.68D+08  3.72D-09  1.79D+308
 C  IBM 195       (D.P.)  2.22D-16  6.87D+09  9.09D-13  7.23D+75
 C  UNIVAC 1108   (D.P.)  1.73D-18  4.30D+09  2.33D-10  8.98D+307
 C  VAX 11/780    (D.P.)  1.39D-17  1.07D+09  9.31D-10  1.70D+38
 C
 C*******************************************************************
 C*******************************************************************
 C
 C Error Returns
 C
 C  The program returns the value zero for  X .GT. XMAX, and returns
 C    -XINF when BESLY1 is called with a negative or zero argument.
 C
 C
 C Intrinsic functions required are:
 C
 C     ABS, AINT, COS, LOG, SIN, SQRT
 C
 C
 C  Author: W. J. Cody
 C          Mathematics and Computer Science Division
 C          Argonne National Laboratory
 C          Argonne, IL 60439
 C
 C  Latest modification: November 10, 1987
 C
 C--------------------------------------------------------------------

Method Summary

Modifier and Type Method Description

static void caljy1(double arg, doubleW result, int jint)

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Details
- caljy1
  
  public static void caljy1(double arg, doubleW result, int jint)

Class Caljy1

Method Summary

Methods inherited from class java.lang.Object

Method Details

caljy1