gnuplot/src/amos_airy.c at master · gnuplot/gnuplot · GitHub

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* Bessel functions and related special functions.

* The routines in this file are wrappers for implementations in an

* external library detected at configuration/build time.

* AMOS - A Portable Package for Bessel Functions of a Complex Argument

* and Nonnegative Order

* D. E. Amos, Sandia National Laboratories, SAND85-1018 (1985)

* The amos routines have been packaged by various projects in slightly

* different ways.

* The zairy_() routine (note Fortran naming and parameter passing conventions)

* is found, for example, in libopenspecfun. We use it to calculate Ai(z).

* Similarly zbiry_() is used to calcualte Bi(z).

* The cexint_() routine is also from the AMOS collection, but is not part

* of the Bessel function subset and not included in libopenspecfun.

* I could not find source for a version of the source that splits the

* real and imaginary parts of the arguments as with the zxxxx.f Bessel

* routines; this one accepts and returns a CMPLX argument rather than separate

* real and imaginary parts.

* D. E. Amos, ALGORITHM 683 A Portable FORTRAN Subroutine

* for Exponential Integrals of a Complex Argument

* ACM Trans. Math. Software 16:178-182 (1990)

* IERR codes from libamos Bessel functions

* 0 no error

* 1 input error, no computation

* 2 overflow predicted from input value

* 3 overflow from computation

* 4 input value out of range, no computation

* 5 other error

* IERR codes from cexint

* 2 underflow

* 4-5 argument reduction caused loss of significance

* 6 failed to converge

* Ethan A Merritt - March 2020

#include "eval.h"

#include "stdfn.h" /* for not_a_number() */

#ifdef HAVE_AMOS

extern void zairy_( double *zr, double *zi, int32_t *id, int32_t *kode,

double *air, double *aii, int32_t *underflow, int32_t *ierr );

extern void zbiry_( double *zr, double *zi, int32_t *id, int32_t *kode,

double *air, double *aii, int32_t *ierr );

extern void zbesh_( double *zr, double *zi, double *nu, int32_t *kode,

int32_t *kind, int32_t *length,

double *zbr, double *zbi, int32_t *underflow, int32_t *ierr);

extern void zbesi_( double *zr, double *zi, double *nu, int32_t *kode, int32_t *length,

double *zbr, double *zbi, int32_t *underflow, int32_t *ierr);

extern void zbesj_( double *zr, double *zi, double *nu, int32_t *kode, int32_t *length,

double *zbr, double *zbi, int32_t *underflow, int32_t *ierr);

extern void zbesk_( double *zr, double *zi, double *nu, int32_t *kode, int32_t *length,

double *zbr, double *zbi, int32_t *underflow, int32_t *ierr);

extern void zbesy_( double *zr, double *zi, double *nu, int32_t *kode, int32_t *length,

double *zbr, double *zbi, int32_t *underflow,

double *wr, double *wi, int32_t *ierr);

#if defined(HAVE_CEXINT) && defined(HAVE_COMPLEX_H)

#include <complex.h>

#include <util.h> /* for int_error() */

extern void cexint_( double complex *z, int32_t *norder, int32_t *kode,

double *tol, int32_t *length,

double complex *cy, int32_t *ierr);

#endif

void

f_amos_Ai(union argument *arg)

{

struct value a;

struct cmplx z, ai;

int32_t id, kode, underflow, ierr;

(void) arg; /* avoid -Wunused warning */

pop(&a);

id = 0; /* 0 = Ai 1 = delAi/delZ */

kode = 1; /* 1 = unscaled 2 = scaled */

if (a.type == INTGR) {

z.real = a.v.int_val;

z.imag = 0;

} else {

z.real = a.v.cmplx_val.real;

z.imag = a.v.cmplx_val.imag;

}

/* Fortran calling conventions! */

zairy_( &z.real, &z.imag, &id, &kode, &ai.real, &ai.imag, &underflow, &ierr );

if (underflow != 0 || ierr != 0) {

FPRINTF((stderr,"zairy( {%.3f, %.3f} ): underflow = %d ierr = %d\n",

z.real, z.imag, underflow, ierr));

undefined = TRUE;

Gcomplex(&a, not_a_number(), 0.0);

} else {

Gcomplex(&a, ai.real, ai.imag);

}

push(&a);

}

void

f_amos_Bi(union argument *arg)

{

struct value a;

struct cmplx z, bi;

int32_t id, kode, ierr;

(void) arg; /* avoid -Wunused warning */

pop(&a);

id = 0; /* 0 = Bi 1 = delBi/delZ */

kode = 1; /* 1 = unscaled 2 = scaled */

if (a.type == INTGR) {

z.real = a.v.int_val;

z.imag = 0;

} else {

z.real = a.v.cmplx_val.real;

z.imag = a.v.cmplx_val.imag;

}

/* Fortran calling conventions! */

zbiry_( &z.real, &z.imag, &id, &kode, &bi.real, &bi.imag, &ierr );

if (ierr != 0) {

FPRINTF((stderr,"zbiry( {%.3f, %.3f} ): ierr = %d\n",

z.real, z.imag, ierr));

undefined = TRUE;

Gcomplex(&a, not_a_number(), 0.0);

} else {

Gcomplex(&a, bi.real, bi.imag);

}

push(&a);

}

* Modified Bessel function of the second kind K_nu(z)

* val = BesselK( nu, z )

* The underlying libamos routine besk fills in an array of values

* val[j] corresponding to a sequence functions BesselK( nu+j, z )

* but we ask for only the j=0 case.

#define NJ 1

void

f_amos_BesselK(union argument *arg)

{

struct value a;

struct cmplx z;

struct cmplx Bk[NJ];

double nu;

int32_t kode, length, underflow, ierr;

(void) arg; /* avoid -Wunused warning */

/* ... unpack arguments ... */

pop(&a);

if (a.type == INTGR) {

z.real = a.v.int_val;

z.imag = 0;

} else {

z.real = a.v.cmplx_val.real;

z.imag = a.v.cmplx_val.imag;

}

nu = real(pop(&a));

kode = 1; /* 1 = unscaled 2 = scaled */

length = NJ; /* number of members in the returned sequence of functions */

/* Fortran calling conventions! */

zbesk_( &z.real, &z.imag, &nu, &kode, &length,

&Bk[0].real, &Bk[0].imag, &underflow, &ierr );

if (ierr != 0) {

FPRINTF((stderr,"zbesk( {%.3f, %.3f} ): ierr = %d\n",

z.real, z.imag, ierr));

undefined = TRUE;

Gcomplex(&a, not_a_number(), 0.0);

} else {

Gcomplex(&a, Bk[0].real, Bk[0].imag);

}

push(&a);

}

* Hankel functions of the first and second kinds

* val = Hankel1( nu, z ) = Jnu(z) + iYnu(z)

* val = Hankel2( nu, z ) = Jnu(z) - iYnu(z)

* The underlying libamos routine besi fills in an array of values

* val[j] corresponding to a sequence functions Hankel( kind, nu+j, z )

* but we ask for only the j=0 case.

void

f_amos_Hankel(int k, union argument *arg)

{

struct value a;

struct cmplx z;

struct cmplx H[NJ];

double nu;

int32_t kode, kind, length, underflow, ierr;

(void) arg; /* avoid -Wunused warning */

/* ... unpack arguments ... */

pop(&a);

if (a.type == INTGR) {

z.real = a.v.int_val;

z.imag = 0;

} else {

z.real = a.v.cmplx_val.real;

z.imag = a.v.cmplx_val.imag;

}

nu = real(pop(&a));

kode = 1; /* 1 = unscaled 2 = scaled */

kind = k; /* 1 = first kind, 2 = second kind */

length = NJ; /* number of members in the returned sequence of functions */

/* Fortran calling conventions! */

zbesh_( &z.real, &z.imag, &nu, &kode, &kind, &length,

&H[0].real, &H[0].imag, &underflow, &ierr );

if (ierr != 0) {

FPRINTF((stderr,"zbesh( {%.3f, %.3f} ): ierr = %d\n",

z.real, z.imag, ierr));

undefined = TRUE;

Gcomplex(&a, not_a_number(), 0.0);

} else {

Gcomplex(&a, H[0].real, H[0].imag);

}

push(&a);

}

void

f_Hankel1(union argument *arg) { f_amos_Hankel( 1, arg ); }

void

f_Hankel2(union argument *arg) { f_amos_Hankel( 2, arg ); }

* Modified Bessel function of the first kind I_nu(z)

* with complex argument z.

* val = BesselI( nu, z )

* The underlying libamos routine besi fills in an array of values

* val[j] corresponding to a sequence functions BesselI( nu+j, z )

* but we ask for only the j=0 case.

void

f_amos_BesselI(union argument *arg)

{

struct value a;

struct cmplx z;

struct cmplx Bi[NJ];

double nu;

int32_t kode, length, underflow, ierr;

(void) arg; /* avoid -Wunused warning */

/* ... unpack arguments ... */

pop(&a);

if (a.type == INTGR) {

z.real = a.v.int_val;

z.imag = 0;

} else {

z.real = a.v.cmplx_val.real;

z.imag = a.v.cmplx_val.imag;

}

nu = real(pop(&a));

kode = 1; /* 1 = unscaled 2 = scaled */

length = NJ; /* number of members in the returned sequence of functions */

/* Fortran calling conventions! */

zbesi_( &z.real, &z.imag, &nu, &kode, &length,

&Bi[0].real, &Bi[0].imag, &underflow, &ierr );

if (ierr != 0) {

FPRINTF((stderr,"zbesi( {%.3f, %.3f} ): ierr = %d\n",

z.real, z.imag, ierr));

undefined = TRUE;

Gcomplex(&a, not_a_number(), 0.0);

} else {

Gcomplex(&a, Bi[0].real, Bi[0].imag);

}

push(&a);

}

* Modified Bessel function of the first kind J_nu(z)

* with complex argument z.

* val = BesselJ( nu, z )

* The underlying libamos routine besi fills in an array of values

* val[j] corresponding to a sequence functions BesselJ( nu+j, z )

* but we ask for only the j=0 case.

void

f_amos_BesselJ(union argument *arg)

{

struct value a;

struct cmplx z;

struct cmplx Bj[NJ];

double nu;

int32_t kode, length, underflow, ierr;

(void) arg; /* avoid -Wunused warning */

/* ... unpack arguments ... */

pop(&a);

if (a.type == INTGR) {

z.real = a.v.int_val;

z.imag = 0;

} else {

z.real = a.v.cmplx_val.real;

z.imag = a.v.cmplx_val.imag;

}

nu = real(pop(&a));

kode = 1; /* 1 = unscaled 2 = scaled */

length = NJ; /* number of members in the returned sequence of functions */

/* Fortran calling conventions! */

zbesj_( &z.real, &z.imag, &nu, &kode, &length,

&Bj[0].real, &Bj[0].imag, &underflow, &ierr );

if (ierr != 0) {

FPRINTF((stderr,"zbesj( {%.3f, %.3f} ): ierr = %d\n",

z.real, z.imag, ierr));

undefined = TRUE;

Gcomplex(&a, not_a_number(), 0.0);

} else {

Gcomplex(&a, Bj[0].real, Bj[0].imag);

}

push(&a);

}

* Modified Bessel function of the second kind Y_nu(z)

* with complex argument z.

* val = BesselY( nu, z )

* The underlying libamos routine besi fills in an array of values

* val[j] corresponding to a sequence functions BesselJ( nu+j, z )

* but we ask for only the j=0 case.

void

f_amos_BesselY(union argument *arg)

{

struct value a;

struct cmplx z;

struct cmplx By[NJ];

double WorkR[NJ], WorkI[NJ]; /* Scratch space for zbesy_ */

double nu;

int32_t kode, length, underflow, ierr;

(void) arg; /* avoid -Wunused warning */

/* ... unpack arguments ... */

pop(&a);

if (a.type == INTGR) {

z.real = a.v.int_val;

z.imag = 0;

} else {

z.real = a.v.cmplx_val.real;

z.imag = a.v.cmplx_val.imag;

}

nu = real(pop(&a));

kode = 1; /* 1 = unscaled 2 = scaled */

length = NJ; /* number of members in the returned sequence of functions */

/* Fortran calling conventions! */

zbesy_( &z.real, &z.imag, &nu, &kode, &length,

&By[0].real, &By[0].imag, &underflow,

&WorkR[0], &WorkI[0], &ierr );

if (ierr != 0) {

fprintf(stderr,"zbesy( {%.3f, %.3f} ): ierr = %d\n",

z.real, z.imag, ierr);

undefined = TRUE;

Gcomplex(&a, not_a_number(), 0.0);

} else {

Gcomplex(&a, By[0].real, By[0].imag);

}

push(&a);

}

#if defined(HAVE_CEXINT) && defined(HAVE_COMPLEX_H)

void

f_amos_cexint(union argument *arg)

{

struct value a;

double complex z, cy;

double tolerance;

int32_t norder, kode, length, ierr;

(void) arg; /* avoid -Wunused warning */

pop(&a); /* complex z */

kode = 1; /* 1 = unscaled 2 = scaled */

length = NJ; /* number of members in the returned sequence of functions */

tolerance = 1.e-8; /* FIXME: not sure what is reasonable to ask for */

if (a.type == INTGR) {

z = (double)a.v.int_val;

} else {

z = a.v.cmplx_val.real + I * a.v.cmplx_val.imag;

}

if (carg(z) < -M_PI || carg(z) > M_PI)

int_error(NO_CARET, "cexint requires arg(z) in [-pi:pi]");

pop(&a); /* integer norder */

if (a.type == INTGR)

norder = a.v.int_val;

if (a.type != INTGR || norder < 0)

int_error(NO_CARET, "cexint requires integer n >= 0");

/* Special case for n = 0.

* E0(z) = exp(-z)/z by definition, so just return that

if (norder == 0) {

cy = cexp(-z)/z;

push(Gcomplex(&a, creal(cy), cimag(cy)));

return;

}

/* Fortran calling conventions! */

cexint_( &z, &norder, &kode, &tolerance, &length, &cy, &ierr );

/* ierr == 2 means underflow, in which case cy has already been set to 0 */

if (ierr == 1 || ierr > 2) {

FPRINTF((stderr, "f_amos_cexint( %d, {%g, %g} ): ierr = %d\n",

norder, creal(z), cimag(z), ierr));

undefined = TRUE;

Gcomplex(&a, not_a_number(), 0.0);

} else {

Gcomplex(&a, creal(cy), cimag(cy));

}

push(&a);

}

#endif

#undef NJ

#endif /* HAVE_AMOS */

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