hypergeometric function

hypergeometric function

[Stefan Koch]

Hello,

I'm a new user of the gsl-library. Everything works well. But when I tried
to look at the hypergeometric function, I recognized a discontinuity (jump)
in the graphic-drawing of the function. I think this should not be so. I
used the following code segment:

void Test(void)
{
	double AktVal, x;
	int n, p, LoopX, MidX, MidY, CalcSize, gsl_error;
	CSize sizeTotal;
	gsl_sf_result result;

	sizeTotal = GetTotalSize();
	MidX = sizeTotal.cx/2.0;
	MidY = sizeTotal.cy/2.0;

	n = 3;
	p= 8;

	CalcSize = 1000;

	x = 0;
	gsl_error = gsl_sf_hyperg_1F1_int_e(-n, p+1, x, &result) ;
	if(gsl_error)	AfxMessageBox(gsl_strerror (gsl_error));
	AktVal = result.val;
	pDC->MoveTo(0, MidY - AktVal);
	for(LoopX = 0; LoopX < CalcSize; LoopX++ )
	{
		x += 0.1;
		gsl_error = gsl_sf_hyperg_1F1_int_e(-n, p+1, x, &result);
		if(gsl_error)	AfxMessageBox(gsl_strerror (gsl_error));
		AktVal = 100.0*result.val;
		pDC->LineTo( LoopX, MidY - AktVal);
	}
}

(Visual C++ 6.0, NT 4.0)

Can anybody tell me if there's something wrong with my code or with the
function? No error message occured.

Thanks for your help.

Best regards
Stefan Koch

mailto:s.koch@seh-zuelpich.de

hypergeometric function

[Stefan Koch]

Hello,

I'm a new user of the gsl-library. Everything works well. But when I tried
to look at the hypergeometric function, I recognized a discontinuity (jump)
in the graphic-drawing of the function. I think this should not be so. I
used the following code segment:

void Test(void)
{
	double AktVal, x;
	int n, p, LoopX, MidX, MidY, CalcSize, gsl_error;
	CSize sizeTotal;
	gsl_sf_result result;

	sizeTotal = GetTotalSize();
	MidX = sizeTotal.cx/2.0;
	MidY = sizeTotal.cy/2.0;

	n = 3;
	p= 8;

	CalcSize = 1000;

	x = 0;
	gsl_error = gsl_sf_hyperg_1F1_int_e(-n, p+1, x, &result) ;
	if(gsl_error)	AfxMessageBox(gsl_strerror (gsl_error));
	AktVal = result.val;
	pDC->MoveTo(0, MidY - AktVal);
	for(LoopX = 0; LoopX < CalcSize; LoopX++ )
	{
		x += 0.1;
		gsl_error = gsl_sf_hyperg_1F1_int_e(-n, p+1, x, &result);
		if(gsl_error)	AfxMessageBox(gsl_strerror (gsl_error));
		AktVal = 100.0*result.val;
		pDC->LineTo( LoopX, MidY - AktVal);
	}
}

(Visual C++ 6.0, NT 4.0)

Can anybody tell me if there's something wrong with my code or with the
function? No error message occured.

Thanks for your help.

Best regards
Stefan Koch

mailto:s.koch@seh-zuelpich.de

Re: hypergeometric function

[Brian Gough]

Stefan Koch writes:
 > I'm a new user of the gsl-library. Everything works well. But when
 > I tried to look at the hypergeometric function, I recognized a
 > discontinuity (jump) in the graphic-drawing of the function. I
 > think this should not be so. I used the following code segment:
 > (Visual C++ 6.0, NT 4.0)
 >  Can anybody tell me if there's something wrong with my code or
 > with the function? No error message occured.

Hi,
I don't see the discontinuity either.

What version of GSL are you using? -- did you compile it yourself or
use a precompiled version.

regards
Brian Gough

Re: hypergeometric function

[Brian Gough]

Stefan Koch writes:
 > I'm a new user of the gsl-library. Everything works well. But when
 > I tried to look at the hypergeometric function, I recognized a
 > discontinuity (jump) in the graphic-drawing of the function. I
 > think this should not be so. I used the following code segment:
 > (Visual C++ 6.0, NT 4.0)
 >  Can anybody tell me if there's something wrong with my code or
 > with the function? No error message occured.

Hi,
I don't see the discontinuity either.

What version of GSL are you using? -- did you compile it yourself or
use a precompiled version.

regards
Brian Gough

Re: AW: hypergeometric function

[Brian Gough]

Stefan Koch writes:
 > With the following function I produced the output shown in the attached file
 > Hyper.jpg. You can see the discontinuity clearly. Please note that I
 > multiply the output of the hypergeometric function by a factor of 100.
 > I used gsl 1.0 from GnuWin32, the precompiled version (dll). I got the
 > dicontinuity with the free download version from Network Theory Ltd. too.

Ok, I see it now at x=13..14.  I didn't see it on the original scale.

Thanks for the bug report.  I've found the problem, so a revised
version will be available in the next release or you can apply the
patch below and rebuild from source to fix it.

regards
Brian Gough

Index: specfunc/hyperg_1F1.c
===================================================================
RCS file: /cvs/gsl/gsl/specfunc/hyperg_1F1.c,v
retrieving revision 1.67
retrieving revision 1.69
diff -u -r1.67 -r1.69
--- hyperg_1F1.c	2001/11/19 22:32:10	1.67
+++ hyperg_1F1.c	2001/12/05 19:34:41	1.69
@@ -1084,13 +1084,28 @@
 	Ma0p1b = (b*(a0+x)*Ma0b + x*(a0-b)*Ma0bp1)/(a0*b);
       }
 
-      Mnm1 = Ma0b;
-      Mn   = Ma0p1b;
-      for(n=a0+1; n<a; n++) {
-    	Mnp1 = ((b-n)*Mnm1 + (2*n-b+x)*Mn)/n;
-    	Mnm1 = Mn;
-    	Mn   = Mnp1;
-      }
+      /* Initialise the recurrence correctly BJG */
+
+      if (a0 >= a)
+        { 
+          Mn = Ma0b;
+        }
+      else if (a0 + 1>= a)
+        {
+          Mn = Ma0p1b;
+        }
+      else
+        {
+          Mnm1 = Ma0b;
+          Mn   = Ma0p1b;
+
+          for(n=a0+1; n<a; n++) {
+            Mnp1 = ((b-n)*Mnm1 + (2*n-b+x)*Mn)/n;
+            Mnm1 = Mn;
+            Mn   = Mnp1;
+          }
+        }
+
       result->val  = Mn;
       result->err  = (fabs(x) + 1.0) * GSL_DBL_EPSILON *  fabs(Mn);
       result->err *= fabs(b-a)+1.0;

Re: AW: hypergeometric function

[Brian Gough]

Stefan Koch writes:
 > With the following function I produced the output shown in the attached file
 > Hyper.jpg. You can see the discontinuity clearly. Please note that I
 > multiply the output of the hypergeometric function by a factor of 100.
 > I used gsl 1.0 from GnuWin32, the precompiled version (dll). I got the
 > dicontinuity with the free download version from Network Theory Ltd. too.

Ok, I see it now at x=13..14.  I didn't see it on the original scale.

Thanks for the bug report.  I've found the problem, so a revised
version will be available in the next release or you can apply the
patch below and rebuild from source to fix it.

regards
Brian Gough

Index: specfunc/hyperg_1F1.c
===================================================================
RCS file: /cvs/gsl/gsl/specfunc/hyperg_1F1.c,v
retrieving revision 1.67
retrieving revision 1.69
diff -u -r1.67 -r1.69
--- hyperg_1F1.c	2001/11/19 22:32:10	1.67
+++ hyperg_1F1.c	2001/12/05 19:34:41	1.69
@@ -1084,13 +1084,28 @@
 	Ma0p1b = (b*(a0+x)*Ma0b + x*(a0-b)*Ma0bp1)/(a0*b);
       }
 
-      Mnm1 = Ma0b;
-      Mn   = Ma0p1b;
-      for(n=a0+1; n<a; n++) {
-    	Mnp1 = ((b-n)*Mnm1 + (2*n-b+x)*Mn)/n;
-    	Mnm1 = Mn;
-    	Mn   = Mnp1;
-      }
+      /* Initialise the recurrence correctly BJG */
+
+      if (a0 >= a)
+        { 
+          Mn = Ma0b;
+        }
+      else if (a0 + 1>= a)
+        {
+          Mn = Ma0p1b;
+        }
+      else
+        {
+          Mnm1 = Ma0b;
+          Mn   = Ma0p1b;
+
+          for(n=a0+1; n<a; n++) {
+            Mnp1 = ((b-n)*Mnm1 + (2*n-b+x)*Mn)/n;
+            Mnm1 = Mn;
+            Mn   = Mnp1;
+          }
+        }
+
       result->val  = Mn;
       result->err  = (fabs(x) + 1.0) * GSL_DBL_EPSILON *  fabs(Mn);
       result->err *= fabs(b-a)+1.0;

RE: AW: hypergeometric function

[J.J. Gomez Cadenas]

Hi all,
I get the problem below when trying to link a test program for a C++ complex
class that wraps gsl complex. The program compiles fine AND compiles, links
and executes no problem in Linux. I have just downloaded version v1 of GSL
for windows. Any ideas?

Note: I have searched in the sources for "HUGE" and I only find the work in
gsl_nan.h
However, I cannot see the word __HUGE there...

thanks, jj

This is the error....


Done Searching Libraries
libgsld.lib(invhyp.obj) : error LNK2001: unresolved external symbol __HUGE
../Win32Debug/test_complex.exe : fatal error LNK1120: 1 unresolved externals
Error executing link.exe.

RE: AW: hypergeometric function

[J.J. Gomez Cadenas]

Hi all,
I get the problem below when trying to link a test program for a C++ complex
class that wraps gsl complex. The program compiles fine AND compiles, links
and executes no problem in Linux. I have just downloaded version v1 of GSL
for windows. Any ideas?

Note: I have searched in the sources for "HUGE" and I only find the work in
gsl_nan.h
However, I cannot see the word __HUGE there...

thanks, jj

This is the error....


Done Searching Libraries
libgsld.lib(invhyp.obj) : error LNK2001: unresolved external symbol __HUGE
../Win32Debug/test_complex.exe : fatal error LNK1120: 1 unresolved externals
Error executing link.exe.

RE: AW: hypergeometric function

[J.J. Gomez Cadenas]

Hi all,
I get the problem below when trying to link a test program for a C++ complex
class that wraps gsl complex. The program compiles fine AND compiles, links
and executes no problem in Linux. I have just downloaded version v1 of GSL
for windows. Any ideas?

Note: I have searched in the sources for "HUGE" and I only find the work in
gsl_nan.h
However, I cannot see the word __HUGE there...

thanks, jj

This is the error....


Done Searching Libraries
libgsld.lib(invhyp.obj) : error LNK2001: unresolved external symbol __HUGE
../Win32Debug/test_complex.exe : fatal error LNK1120: 1 unresolved externals
Error executing link.exe.

RE: AW: hypergeometric function

[Brian Gough]

J.J. Gomez Cadenas writes:
 > I get the problem below when trying to link a test program for a
 > C++ complex class that wraps gsl complex. The program compiles fine
 > AND compiles, links and executes no problem in Linux. I have just
 > downloaded version v1 of GSL for windows. Any ideas?
 >  Note: I have searched in the sources for "HUGE" and I only find
 > the work in gsl_nan.h However, I cannot see the word __HUGE
 > there...
 >  This is the error....
 >
 >  Done Searching Libraries libgsld.lib(invhyp.obj) : error LNK2001:
 > unresolved external symbol __HUGE ../Win32Debug/test_complex.exe :
 > fatal error LNK1120: 1 unresolved externals Error executing
 > link.exe.

Haven't ever seen that.  You'll need to send the program to the list I
think.

Brian

RE: AW: hypergeometric function

[Brian Gough]

J.J. Gomez Cadenas writes:
 > I get the problem below when trying to link a test program for a
 > C++ complex class that wraps gsl complex. The program compiles fine
 > AND compiles, links and executes no problem in Linux. I have just
 > downloaded version v1 of GSL for windows. Any ideas?
 >  Note: I have searched in the sources for "HUGE" and I only find
 > the work in gsl_nan.h However, I cannot see the word __HUGE
 > there...
 >  This is the error....
 >
 >  Done Searching Libraries libgsld.lib(invhyp.obj) : error LNK2001:
 > unresolved external symbol __HUGE ../Win32Debug/test_complex.exe :
 > fatal error LNK1120: 1 unresolved externals Error executing
 > link.exe.

Haven't ever seen that.  You'll need to send the program to the list I
think.

Brian

RE: AW: hypergeometric function

[J.J. Gomez Cadenas]

This is the test program.

#include "GslPP/DataTypes/Complex.h"
#include <iostream>
#include <fstream>


int main() {
  double re,im;
  cout << " Enter the real and imaginary part of a complex number\n";
  cout << " >>enter real part "; cin >> re;
  cout << " >>enter imaginary part "; cin >> im;

  cout.width(10);
  cout.precision(12);

  Complex z1 = Complex (re, im);
  cout << " z1 = " << z1 << endl
       << " real part = " << z1.real ()
       << " imag part = " << z1.imag ()
       << " arg = " << z1.arg ()
       << " abs = " << z1.abs ()
       << endl
       << " z**2 = " << z1.abs2 ()
       << " log |z| = " << z1.logAbs ()
       << endl;

  double r, theta;
  cout << " Enter a complex number in polar coordinates\n";
  cout << " >>enter radius "; cin >> r;
  cout << " >>enter polar angle "; cin >> theta;

  Complex z2 = Complex ();
  z2.setPolar (r, theta);

  cout << " z2 = " << z2 << endl
       << " real part = " << z2.real ()
       << " imag part = " << z2.imag ()
       << " arg = " << z2.arg ()
       << " abs = " << z2.abs ()
       << endl
       << " z**2 = " << z2.abs2 ()
       << " log |z| = " << z2.logAbs ()
       << endl;

    /* Assignement operators */

  Complex z3 = z1;     //Complex& operator = (const Complex& z);
  Complex z4;
  z4= 10.0;  //Complex& operator = (double d);

  cout << " z3 must be = z1, z3 = " << z3 << endl;
  cout << " z4 must be = (10,0), z4 = " << z4 << endl;


  //    Complex& operator += (const Complex& z);
  z1 += z2;
  cout << " z1 += z2 = " <<  z1 << endl;
  z1 = z3;

  //    Complex& operator -= (const Complex& z);
  z1 -= z2;
  cout << " z1 -= z2 = " <<  z1 << endl;
  z1 = z3;

  //    Complex& operator *= (const Complex& z);
  z1 *= z2;
  cout << " z1 *= z2 = " << z1 << endl;
  z1 = z3;

  // Complex& operator *= (double d);
  z1 *= 10.;
  cout << " z1 *= 10.  = " << z1 << endl;
  z1 = z3;

  //    Complex& operator /= (const Complex& z);
  z1 /= z2;
  cout << " z1 /= z2  = " << z1 << endl;
  z1 = z3;

  //    Complex& operator /= (double d);

  z1 /= 10.;
  cout << " z1 /= 10.  = " <<  z1 << endl;
  z1 = z3;

    /*
     * Operations with complex numbers
     */
  //    friend Complex operator - (const Complex& z);

  //Complex operator + (const Complex& z1, const Complex& z2);
  cout << " z1 + z2 = " << z1 + z2 << endl;
  z1 = z3;

  //    Complex operator - (const Complex& z1, const Complex& z2);
  cout << " z1 - z2 = " << z1 - z2 << endl;
  z1 = z3;

  //Complex operator * (const Complex& z1, const Complex& z2);
  cout << " z1 * z2 = " << z1 * z2 << endl;
  z1 = z3;

  // Complex operator / (const Complex& z1, const Complex& z2);
  cout << " z1 / z2 = " << z1 / z2 << endl;
  z1 = z3;

  /*
     Complex operator + (double a, const Complex& z);
     Complex operator - (double a, const Complex& z);
     Complex operator * (double a, const Complex& z);
     Complex operator / (double a, const Complex& z);
  */
  cout << " 10 + z1   = " << 10. + z1 << endl;
  z1 = z3;

  cout << " 10 - z1 = " << 10. - z1 << endl;
  z1 = z3;

  cout << " 10 * z2 = " << 10. * z1 << endl;
  z1 = z3;

  cout << " 10 / z1 = " << 10. / z1 << endl;
  z1 = z3;

  /*
     Complex operator + (const Complex& z, double a);
     Complex operator - (const Complex& z, double a);
     Complex operator * (const Complex& z, double a);
     Complex operator / (const Complex& z, double a);
  */
  cout << " z1 + 10    = " << z1 + 10.  << endl;
  z1 = z3;

  cout << " z1 - 10  = " << z1 - 10.  << endl;
  z1 = z3;

  cout << " z1 * 10  = " << z1 * 10.  << endl;
  z1 = z3;

  cout << " z1/10  = " << z1/10.  << endl;
  z1 = z3;


    /*
     * Complex functions.
     */

  cout << " Elementary functions "
       << endl
       << " abs (z1) = " <<abs (z1)
       <<endl
       << " conj (z1) = " <<conj (z1)
       <<endl
       << " inverse (z1) = " <<inverse (z1)
       <<endl
       << " sqrt (z1) = " <<sqrt (z1)
       <<endl
       << " Csqrt (10.) = " <<Csqrt (10.)
       <<endl
       << " pow (z1,z2) = " <<pow(z1,z2)
       <<endl
       << " pow (z1,10.) = " <<pow(z1,10.)
       <<endl
       << " exp (z1) = " <<exp(z1)
       <<endl
       << " log (z1) = " <<log(z1)
       <<endl
       << " log10 (z1) = " <<log10(z1)
       <<endl;

  cout << " Trigonometric functions "
       << endl
       << " sin (z1) = " <<sin (z1)
       <<endl
       << " cos (z1) = " <<cos (z1)
       <<endl
       << " tan (z1) = " <<tan (z1)
       <<endl
       << " sec (z1) = " <<sec (z1)
       <<endl
       << " csc (z1) = " <<csc (z1)
       <<endl
       << " cot (z1) = " <<cot (z1)
       <<endl;


  cout << " Inverse Trigonometric functions "
       << endl
       << " asin (z1) = " <<asin (z1)
       <<endl
       << " acos (z1) = " <<acos (z1)
       <<endl
       << " atan (z1) = " <<atan (z1)
       <<endl
       << " asec (z1) = " <<asec (z1)
       <<endl
       << " acsc (z1) = " <<acsc (z1)
       <<endl
       << " acot (z1) = " <<acot (z1)
       <<endl;

  cout << " Hyperbolic functions "
       << endl
       << " sinh (z1) = " <<sinh (z1)
       <<endl
       << " cosh (z1) = " <<cosh (z1)
       <<endl
       << " tanh (z1) = " <<tanh (z1)
       <<endl
       << " sech (z1) = " <<sech (z1)
       <<endl
       << " csch (z1) = " <<csch (z1)
       <<endl
       << " coth (z1) = " <<coth (z1)
       <<endl;

  cout << " Inverse hyperbolic functions "
       << endl
       << " asinh (z1) = " <<asinh (z1)
       <<endl
       << " acosh (z1) = " <<acosh (z1)
       <<endl
       << " atanh (z1) = " <<atanh (z1)
       <<endl
       << " asech (z1) = " <<asech (z1)
       <<endl
       << " acsch (z1) = " <<acsch (z1)
       <<endl
       << " acoth (z1) = " <<acoth (z1)
       <<endl;

return 0;
}

This is the header Complex.h

/* -*- mode: c++ -*- */
/*
 * Complex.h
 * This is a wrapper around the complex type defined in the GSL
 *
 * This code is part of the
 * Gsl++library, a C++ wrapper around the GNU Scientific Library (GNU)
 *
 * Copyright for this wrapper (C) 2001,2002
 * J. Burguet, J.J. Gomez-Cadenas, J.A. Hernando
 *
 * For the GSL library
 * Copyright (C) 1996, 1997, 1998, 1999, 2000 Brian Gough and others,
 * see documentation of the GSL library
 *
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2 of the License, or (at
 * your option) any later version.
 *
 * This program is distributed in the hope that it will be useful, but
 * WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
 */

#ifndef _COMPLEX_
#define _COMPLEX_

#include <iostream>    // to overload ostream& <<

#include <gsl/gsl_complex.h>
#include <gsl/gsl_complex_math.h>

using namespace std;   //needed by gcc 3.2 and MVC++

/**
 * Complex numbers
 *
 * This is a wrapper class around the complex numbers defined by the GSL
 *
 * A gsl complex is a structure defined as:
 *
 *   typedef struct
 *   {
 *     double dat[2]
 *   } gsl_complex;
 *
 * See gsl manual chapter 5
 */

class Complex;

Complex operator - (const Complex& z);
Complex operator + (const Complex& z1, const Complex& z2); ///< z1+z2
Complex operator - (const Complex& z1, const Complex& z2); ///< z1-z2
Complex operator * (const Complex& z1, const Complex& z2); ///< z1*z2
Complex operator / (const Complex& z1, const Complex& z2); ///< z1/z2

Complex operator + (double a, const Complex& z);    ///< a + z
Complex operator - (double a, const Complex& z);    ///< a - z
Complex operator * (double a, const Complex& z);    ///< a * z
Complex operator / (double a, const Complex& z);    ///< a / z

Complex operator + (const Complex& z, double a);    ///< z + a
Complex operator - (const Complex& z, double a);    ///< z - a
Complex operator * (const Complex& z, double a);    ///< z * a
Complex operator / (const Complex& z, double a);    ///< z / ac

    /*
     * Complex functions.
     */
    // Elementary functions
     double fabs(const Complex& z);    ///< absolute value, |z|
     double abs(const Complex& z);     ///< absolute value, |z|

Complex conj(const Complex& z);      ///< complex conjugate
Complex inverse(const Complex& z);   ///< 1/z
Complex sqrt(const Complex& z);      ///< complex square root
Complex Csqrt(double a);             ///<  complex sqrt of a real
Complex pow(const Complex& z1, const Complex& z2);  ///< z1**z2
Complex pow(const Complex& z, double a);            ///< z**a
Complex exp(const Complex& z);    ///< exponential function, exp(z)
Complex log(const Complex& z);    ///< natural logarithm, log(z)
Complex log10(const Complex& z);  ///< logarithm in base 10, log10(z)

    // Trigonometric
Complex sin(const Complex& z);    ///< sinus, sin(z)
Complex cos(const Complex& z);    ///< cosinus, cos(z)
Complex tan(const Complex& z);    ///< tangent, tan(z)
Complex sec(const Complex& z);    ///< secant, sec(z) = 1/cos(z)
Complex csc(const Complex& z);    ///< cosecant, cosec(z) = 1/sin(z)
Complex cot(const Complex& z);    ///< cotangent, cotan(z) = 1/cot(z)

    // Inverse trigonometric
Complex asin(const Complex& z);   ///< arcsin(z)
Complex acos(const Complex& z);   ///< arccos(z)
Complex atan(const Complex& z);   ///< arctan(z)
Complex asec(const Complex& z);   ///< arcsec(z)
Complex acsc(const Complex& z);   ///< arccosec(z)
Complex acot(const Complex& z);   ///< arccotg(z)

    // Hyperbolic
Complex sinh(const Complex& z);   ///< sinh(z)
Complex cosh(const Complex& z);   ///< cosh(z)
Complex tanh(const Complex& z);   ///< tanh(z)
Complex sech(const Complex& z);   ///< sech(z) = 1/cosh(z)
Complex csch(const Complex& z);   ///< cosech(z) = 1/sinh(z)
Complex coth(const Complex& z);   ///< cotanh(z) = 1/coth(z)

    // Inverse hyperbolic
Complex asinh(const Complex& z);  ///< arcsinh(z)
Complex acosh(const Complex& z);  ///< arccosh(z)
Complex atanh(const Complex& z);  ///< arctan(z)
Complex asech(const Complex& z);  ///< arcsec(z)
Complex acsch(const Complex& z);  ///< arccosec(z)
Complex acoth(const Complex& z);  ///< arccotg(z)
class Complex {
  private:
    gsl_complex m_gslComplex;   ///< a gsl complex number

  public:
    Complex();
    Complex(double x, double y);
    Complex(const Complex& z);
    ~Complex();

    /* Reading functions  */
    double real() const;   ///< real part, Re(z)
    double imag() const;   ///< imaginary part, Im(z)
    double arg() const;    ///< argument,  -pi < arg(z) < pi
    double abs() const;    ///< absolute value, |z|
    double abs2() const;   ///< squared absolute value, |z|**2

    double logAbs() const; ///< log|z|. It allows accurate evaluation near
|z|=1

    /* Setting functions */
    void setRectangular(double x, double y);
    void setPolar(double r, double theta);

    /* Assignement operators */
    Complex& operator = (const Complex& z);
    Complex& operator = (double d);
    Complex& operator += (const Complex& z);
    Complex& operator -= (const Complex& z);
    Complex& operator *= (const Complex& z);
    Complex& operator *= (double d);
    Complex& operator /= (const Complex& z);
    Complex& operator /= (double d);

    /*
     * Friend functions
     */

    /*
     * Operations with complex numbers
     */
    friend Complex operator - (const Complex& z);

    friend Complex operator + (const Complex& z1, const Complex& z2); ///<
z1+z2
    friend Complex operator - (const Complex& z1, const Complex& z2); ///<
z1-z2
    friend Complex operator * (const Complex& z1, const Complex& z2); ///<
z1*z2
    friend Complex operator / (const Complex& z1, const Complex& z2); ///<
z1/z2

    friend Complex operator + (double a, const Complex& z);    ///< a + z
    friend Complex operator - (double a, const Complex& z);    ///< a - z
    friend Complex operator * (double a, const Complex& z);    ///< a * z
    friend Complex operator / (double a, const Complex& z);    ///< a / z

    friend Complex operator + (const Complex& z, double a);    ///< z + a
    friend Complex operator - (const Complex& z, double a);    ///< z - a
    friend Complex operator * (const Complex& z, double a);    ///< z * a
    friend Complex operator / (const Complex& z, double a);    ///< z / ac

    /*
     * Complex functions.
     */
    // Elementary functions
    friend double fabs(const Complex& z);    ///< absolute value, |z|
    friend double abs(const Complex& z);     ///< absolute value, |z|

    friend Complex conj(const Complex& z);      ///< complex conjugate
    friend Complex inverse(const Complex& z);   ///< 1/z
    friend Complex sqrt(const Complex& z);      ///< complex square root
    friend Complex Csqrt(double a);             ///<  complex sqrt of a real
    friend Complex pow(const Complex& z1, const Complex& z2);  ///< z1**z2
    friend Complex pow(const Complex& z, double a);            ///< z**a
    friend Complex exp(const Complex& z);    ///< exponential function,
exp(z)
    friend Complex log(const Complex& z);    ///< natural logarithm, log(z)
    friend Complex log10(const Complex& z);  ///< logarithm in base 10,
log10(z)

    // Trigonometric
    friend Complex sin(const Complex& z);    ///< sinus, sin(z)
    friend Complex cos(const Complex& z);    ///< cosinus, cos(z)
    friend Complex tan(const Complex& z);    ///< tangent, tan(z)
    friend Complex sec(const Complex& z);    ///< secant, sec(z) = 1/cos(z)
    friend Complex csc(const Complex& z);    ///< cosecant, cosec(z) =
1/sin(z)
    friend Complex cot(const Complex& z);    ///< cotangent, cotan(z) =
1/cot(z)

    // Inverse trigonometric
    friend Complex asin(const Complex& z);   ///< arcsin(z)
    friend Complex acos(const Complex& z);   ///< arccos(z)
    friend Complex atan(const Complex& z);   ///< arctan(z)
    friend Complex asec(const Complex& z);   ///< arcsec(z)
    friend Complex acsc(const Complex& z);   ///< arccosec(z)
    friend Complex acot(const Complex& z);   ///< arccotg(z)

    // Hyperbolic
    friend Complex sinh(const Complex& z);   ///< sinh(z)
    friend Complex cosh(const Complex& z);   ///< cosh(z)
    friend Complex tanh(const Complex& z);   ///< tanh(z)
    friend Complex sech(const Complex& z);   ///< sech(z) = 1/cosh(z)
    friend Complex csch(const Complex& z);   ///< cosech(z) = 1/sinh(z)
    friend Complex coth(const Complex& z);   ///< cotanh(z) = 1/coth(z)

    // Inverse hyperbolic
    friend Complex asinh(const Complex& z);  ///< arcsinh(z)
    friend Complex acosh(const Complex& z);  ///< arccosh(z)
    friend Complex atanh(const Complex& z);  ///< arctan(z)
    friend Complex asech(const Complex& z);  ///< arcsec(z)
    friend Complex acsch(const Complex& z);  ///< arccosec(z)
    friend Complex acoth(const Complex& z);  ///< arccotg(z)
};


ostream& operator << (ostream& s, const Complex& z);


#endif  /* _COMPLEX_ */

And this is the .cpp, all straight forward!

**
 * Complex numbers and complex functions.
 *
 * The class Complex is a wrapper around gsl_complex.
 *
 * @version  v1
 * @author   JJ Gomez Cadenas, JBC
 * @date     17/08/2001
 */

#include <gsl/gsl_errno.h>

#include "GslPP/DataTypes/Complex.h"


/**
 * Default constructor, z = 0.
 */
Complex::Complex() {
	m_gslComplex = gsl_complex_rect(0.0, 0.0);
}


/**
 * Create a complex number z = x + iy
 */
Complex::Complex(double x, double y) {
	m_gslComplex = gsl_complex_rect(x, y);
}


/**
 * Copy constructor
 */
Complex::Complex(const Complex& z) {
	m_gslComplex = gsl_complex_rect(z.real(), z.imag());
}

/**
 * Destructor
 */
Complex::~Complex() {
}


/*
 * Reading functions.
 */

/// Real part
double Complex::real() const {
    return GSL_REAL(m_gslComplex);
}

/// Imaginary part
double Complex::imag() const {
    return GSL_IMAG(m_gslComplex);
}

/// Argument, -pi < arg < pi
double Complex::arg() const {
    return gsl_complex_arg(m_gslComplex);
}

/// Modulus
double Complex::abs() const {
    return gsl_complex_abs(m_gslComplex);
}

/// Modulus squared
double Complex::abs2() const {
    return gsl_complex_abs2(m_gslComplex);
}


double Complex::logAbs() const {
    return gsl_complex_logabs(m_gslComplex);
}


/*
 * Setting functions
 */

void Complex::setRectangular(double x, double y) {
	m_gslComplex = gsl_complex_rect(x, y);
}

void Complex::setPolar(double r, double theta) {
	m_gslComplex = gsl_complex_polar(r, theta);
}


/*
 * Assignement operators.
 */
Complex& Complex::operator = (const Complex& z) {
	m_gslComplex = gsl_complex_rect(z.real(), z.imag());
    return *this;
}


Complex& Complex::operator = (double d) {
	m_gslComplex = gsl_complex_rect(d, 0.0);
    return *this;
}


Complex& Complex::operator += (const Complex& z)

	m_gslComplex = gsl_complex_add(m_gslComplex, z.m_gslComplex);
    return *this;
}


Complex& Complex::operator -= (const Complex& z) {
	m_gslComplex = gsl_complex_sub(m_gslComplex, z.m_gslComplex);
    return *this;
}


Complex& Complex::operator *= (const Complex& z) {
	m_gslComplex = gsl_complex_mul(m_gslComplex, z.m_gslComplex);
    return *this;
}


Complex& Complex::operator *= (double a) {
	m_gslComplex = gsl_complex_mul_real(m_gslComplex, a);
    return *this;
}


Complex& Complex::operator /= (const Complex& z) {
	m_gslComplex = gsl_complex_div(z.m_gslComplex, m_gslComplex);
    return *this;
}


Complex& Complex::operator /= (double a) {
	m_gslComplex = gsl_complex_div_real(m_gslComplex, a);
    return *this;
}



/*
 * Operations with complex numbers.
 */

Complex operator - (const Complex& z) {
    return Complex(-GSL_REAL(z.m_gslComplex), -GSL_IMAG(z.m_gslComplex));
}


Complex operator + (const Complex& z1, const Complex& z2) {
	gsl_complex gz = gsl_complex_add(z1.m_gslComplex, z2.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex operator - (const Complex& z1, const Complex& z2) {
    gsl_complex gz = gsl_complex_sub(z1.m_gslComplex, z2.m_gslComplex);
    return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex operator * (const Complex& z1, const Complex& z2) {
    gsl_complex gz = gsl_complex_mul(z1.m_gslComplex, z2.m_gslComplex);
    return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex operator / (const Complex& z1, const Complex& z2) {
    gsl_complex gz = gsl_complex_div(z1.m_gslComplex, z2.m_gslComplex);
    return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex operator + (double a, const Complex& z) {
    gsl_complex gz = gsl_complex_add_real(z.m_gslComplex, a);
    return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex operator - (double a, const Complex& z) {
    gsl_complex gz = gsl_complex_sub_real(z.m_gslComplex, a);
    return Complex(-GSL_REAL(gz), -GSL_IMAG(gz));
}


Complex operator * (double a, const Complex& z) {
    gsl_complex gz = gsl_complex_mul_real(z.m_gslComplex, a);
    return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex operator / (double a, const Complex& z) {
    gsl_complex ac = gsl_complex_rect(a, 0);   // complexization of a
    gsl_complex gz = gsl_complex_div(ac, z.m_gslComplex);
    return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex operator + (const Complex& z, double a) {
    gsl_complex gz = gsl_complex_add_real(z.m_gslComplex, a);
    return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex operator - (const Complex& z, double a) {
    gsl_complex gz = gsl_complex_sub_real(z.m_gslComplex, a);
    return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex operator * (const Complex& z, double a) {
    gsl_complex gz = gsl_complex_mul_real(z.m_gslComplex, a);
    return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex operator / (const Complex& z, double a) {
    gsl_complex gz = gsl_complex_div_real(z.m_gslComplex, a);
    return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


/*
 * Complex functions.
 */

// Elementary functions
double fabs(const Complex& z)  {
	return gsl_complex_abs(z.m_gslComplex);
}


double abs(const Complex& z)  {
	return gsl_complex_abs(z.m_gslComplex);
}


Complex conj(const Complex& z) {
	gsl_complex gz = gsl_complex_conjugate(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex inverse(const Complex& z) {
	gsl_complex gz = gsl_complex_inverse(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex sqrt(const Complex& z) {
	gsl_complex gz = gsl_complex_sqrt(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex Csqrt(double a) {
	gsl_complex gz = gsl_complex_sqrt_real(a);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex pow(const Complex& z1, const Complex& z2) {
	gsl_complex gz = gsl_complex_pow(z1.m_gslComplex, z2.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex pow(const Complex& z, double a) {
	gsl_complex gz = gsl_complex_pow_real(z.m_gslComplex, a);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex exp(const Complex& z) {
	gsl_complex gz = gsl_complex_exp(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex log(const Complex& z) {
	gsl_complex gz = gsl_complex_log(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex log10(const Complex& z) {
	gsl_complex gz = gsl_complex_log10(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


// Trigonometric
Complex sin(const Complex& z) {
	gsl_complex gz = gsl_complex_sin(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex cos(const Complex& z) {
	gsl_complex gz = gsl_complex_cos(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex tan(const Complex& z) {
	gsl_complex gz = gsl_complex_tan(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex sec(const Complex& z) {
	gsl_complex gz = gsl_complex_sec(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex csc(const Complex& z) {
	gsl_complex gz = gsl_complex_csc(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex cot(const Complex& z) {
	gsl_complex gz = gsl_complex_cot(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


// Inverse trigonometric
Complex asin(const Complex& z) {
	gsl_complex gz = gsl_complex_arcsin(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex acos(const Complex& z) {
	gsl_complex gz = gsl_complex_arccos(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex atan(const Complex& z) {
	gsl_complex gz = gsl_complex_arctan(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex asec(const Complex& z) {
	gsl_complex gz = gsl_complex_arcsec(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex acsc(const Complex& z) {
	gsl_complex gz = gsl_complex_arccsc(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex acot(const Complex& z) {
	gsl_complex gz = gsl_complex_arccot(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


// Hyperbolic
Complex sinh(const Complex& z) {
	gsl_complex gz = gsl_complex_sinh(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex cosh(const Complex& z) {
	gsl_complex gz = gsl_complex_cosh(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex tanh(const Complex& z) {
	gsl_complex gz = gsl_complex_tanh(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex sech(const Complex& z) {
	gsl_complex gz = gsl_complex_sech(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex csch(const Complex& z) {
	gsl_complex gz = gsl_complex_csch(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex coth(const Complex& z) {
	gsl_complex gz = gsl_complex_coth(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


// Inverse hyperbolic
Complex asinh(const Complex& z) {
	gsl_complex gz = gsl_complex_arcsinh(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex acosh(const Complex& z) {
	gsl_complex gz = gsl_complex_arccosh(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex atanh(const Complex& z) {
	gsl_complex gz = gsl_complex_arctanh(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex asech(const Complex& z) {
	gsl_complex gz = gsl_complex_arcsech(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex acsch(const Complex& z) {
	gsl_complex gz = gsl_complex_arccsch(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex acoth(const Complex& z) {
	gsl_complex gz = gsl_complex_arccoth(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


/**
 * Write complex number to a stream (for visual output)
 */
ostream& operator << (ostream& s, const Complex& z) {
    s << "( " << z.real() << ", " << z.imag() << " )";
    return s;
}

Finally, this is the error

Linking...
Searching Libraries
    Searching C:\Archivos de programa\Microsoft Visual
Studio\VC98\LIB\kernel32.lib:
    Searching C:\Archivos de programa\Microsoft Visual
Studio\VC98\LIB\ws2_32.lib:
    Searching C:\Archivos de programa\Microsoft Visual
Studio\VC98\LIB\advapi32.lib:
    Searching C:\Archivos de programa\Microsoft Visual
Studio\VC98\LIB\msvcrt.lib:
    Searching C:\Archivos de programa\Microsoft Visual
Studio\VC98\LIB\msvcprt.lib:
    Searching C:\Archivos de programa\Microsoft Visual
Studio\VC98\LIB\msvcirt.lib:
    Searching C:\Archivos de programa\Microsoft Visual
Studio\VC98\LIB\oldnames.lib:
    Searching C:\cygwin\jj\GSL++\GslPP\v0r1\Win32Debug\libGslPP.lib:
    Searching C:\ARCHIV~1\GSL\lib\libgsld.lib:
    Searching C:\ARCHIV~1\GSL\lib\libgslcblasd.lib:
    Searching C:\Archivos de programa\Microsoft Visual
Studio\VC98\LIB\kernel32.lib:
    Searching C:\Archivos de programa\Microsoft Visual
Studio\VC98\LIB\ws2_32.lib:
    Searching C:\Archivos de programa\Microsoft Visual
Studio\VC98\LIB\advapi32.lib:
    Searching C:\Archivos de programa\Microsoft Visual
Studio\VC98\LIB\msvcrt.lib:
    Searching C:\Archivos de programa\Microsoft Visual
Studio\VC98\LIB\msvcprt.lib:
    Searching C:\Archivos de programa\Microsoft Visual
Studio\VC98\LIB\msvcirt.lib:
    Searching C:\Archivos de programa\Microsoft Visual
Studio\VC98\LIB\oldnames.lib:
    Searching C:\cygwin\jj\GSL++\GslPP\v0r1\Win32Debug\libGslPP.lib:
    Searching C:\ARCHIV~1\GSL\lib\libgsld.lib:
    Searching C:\ARCHIV~1\GSL\lib\libgslcblasd.lib:
    Searching C:\Archivos de programa\Microsoft Visual
Studio\VC98\LIB\kernel32.lib:
    Searching C:\Archivos de programa\Microsoft Visual
Studio\VC98\LIB\ws2_32.lib:
    Searching C:\Archivos de programa\Microsoft Visual
Studio\VC98\LIB\advapi32.lib:
Done Searching Libraries
libgsld.lib(invhyp.obj) : error LNK2001: unresolved external symbol __HUGE
../Win32Debug/test_complex.exe : fatal error LNK1120: 1 unresolved externals
Error executing link.exe.

test_complex.exe - 2 error(s), 0 warning(s)

Notice that the missing symbol is in a module of libgsld.lib. I downloaded
v1 only a few days ago

Incidentally, I also use cygwin in windows. I compiled the library without
problems and the test example runs flawlessly. It also runs in Linux.
jj

RE: AW: hypergeometric function

[J.J. Gomez Cadenas]

This is the test program.

#include "GslPP/DataTypes/Complex.h"
#include <iostream>
#include <fstream>


int main() {
  double re,im;
  cout << " Enter the real and imaginary part of a complex number\n";
  cout << " >>enter real part "; cin >> re;
  cout << " >>enter imaginary part "; cin >> im;

  cout.width(10);
  cout.precision(12);

  Complex z1 = Complex (re, im);
  cout << " z1 = " << z1 << endl
       << " real part = " << z1.real ()
       << " imag part = " << z1.imag ()
       << " arg = " << z1.arg ()
       << " abs = " << z1.abs ()
       << endl
       << " z**2 = " << z1.abs2 ()
       << " log |z| = " << z1.logAbs ()
       << endl;

  double r, theta;
  cout << " Enter a complex number in polar coordinates\n";
  cout << " >>enter radius "; cin >> r;
  cout << " >>enter polar angle "; cin >> theta;

  Complex z2 = Complex ();
  z2.setPolar (r, theta);

  cout << " z2 = " << z2 << endl
       << " real part = " << z2.real ()
       << " imag part = " << z2.imag ()
       << " arg = " << z2.arg ()
       << " abs = " << z2.abs ()
       << endl
       << " z**2 = " << z2.abs2 ()
       << " log |z| = " << z2.logAbs ()
       << endl;

    /* Assignement operators */

  Complex z3 = z1;     //Complex& operator = (const Complex& z);
  Complex z4;
  z4= 10.0;  //Complex& operator = (double d);

  cout << " z3 must be = z1, z3 = " << z3 << endl;
  cout << " z4 must be = (10,0), z4 = " << z4 << endl;


  //    Complex& operator += (const Complex& z);
  z1 += z2;
  cout << " z1 += z2 = " <<  z1 << endl;
  z1 = z3;

  //    Complex& operator -= (const Complex& z);
  z1 -= z2;
  cout << " z1 -= z2 = " <<  z1 << endl;
  z1 = z3;

  //    Complex& operator *= (const Complex& z);
  z1 *= z2;
  cout << " z1 *= z2 = " << z1 << endl;
  z1 = z3;

  // Complex& operator *= (double d);
  z1 *= 10.;
  cout << " z1 *= 10.  = " << z1 << endl;
  z1 = z3;

  //    Complex& operator /= (const Complex& z);
  z1 /= z2;
  cout << " z1 /= z2  = " << z1 << endl;
  z1 = z3;

  //    Complex& operator /= (double d);

  z1 /= 10.;
  cout << " z1 /= 10.  = " <<  z1 << endl;
  z1 = z3;

    /*
     * Operations with complex numbers
     */
  //    friend Complex operator - (const Complex& z);

  //Complex operator + (const Complex& z1, const Complex& z2);
  cout << " z1 + z2 = " << z1 + z2 << endl;
  z1 = z3;

  //    Complex operator - (const Complex& z1, const Complex& z2);
  cout << " z1 - z2 = " << z1 - z2 << endl;
  z1 = z3;

  //Complex operator * (const Complex& z1, const Complex& z2);
  cout << " z1 * z2 = " << z1 * z2 << endl;
  z1 = z3;

  // Complex operator / (const Complex& z1, const Complex& z2);
  cout << " z1 / z2 = " << z1 / z2 << endl;
  z1 = z3;

  /*
     Complex operator + (double a, const Complex& z);
     Complex operator - (double a, const Complex& z);
     Complex operator * (double a, const Complex& z);
     Complex operator / (double a, const Complex& z);
  */
  cout << " 10 + z1   = " << 10. + z1 << endl;
  z1 = z3;

  cout << " 10 - z1 = " << 10. - z1 << endl;
  z1 = z3;

  cout << " 10 * z2 = " << 10. * z1 << endl;
  z1 = z3;

  cout << " 10 / z1 = " << 10. / z1 << endl;
  z1 = z3;

  /*
     Complex operator + (const Complex& z, double a);
     Complex operator - (const Complex& z, double a);
     Complex operator * (const Complex& z, double a);
     Complex operator / (const Complex& z, double a);
  */
  cout << " z1 + 10    = " << z1 + 10.  << endl;
  z1 = z3;

  cout << " z1 - 10  = " << z1 - 10.  << endl;
  z1 = z3;

  cout << " z1 * 10  = " << z1 * 10.  << endl;
  z1 = z3;

  cout << " z1/10  = " << z1/10.  << endl;
  z1 = z3;


    /*
     * Complex functions.
     */

  cout << " Elementary functions "
       << endl
       << " abs (z1) = " <<abs (z1)
       <<endl
       << " conj (z1) = " <<conj (z1)
       <<endl
       << " inverse (z1) = " <<inverse (z1)
       <<endl
       << " sqrt (z1) = " <<sqrt (z1)
       <<endl
       << " Csqrt (10.) = " <<Csqrt (10.)
       <<endl
       << " pow (z1,z2) = " <<pow(z1,z2)
       <<endl
       << " pow (z1,10.) = " <<pow(z1,10.)
       <<endl
       << " exp (z1) = " <<exp(z1)
       <<endl
       << " log (z1) = " <<log(z1)
       <<endl
       << " log10 (z1) = " <<log10(z1)
       <<endl;

  cout << " Trigonometric functions "
       << endl
       << " sin (z1) = " <<sin (z1)
       <<endl
       << " cos (z1) = " <<cos (z1)
       <<endl
       << " tan (z1) = " <<tan (z1)
       <<endl
       << " sec (z1) = " <<sec (z1)
       <<endl
       << " csc (z1) = " <<csc (z1)
       <<endl
       << " cot (z1) = " <<cot (z1)
       <<endl;


  cout << " Inverse Trigonometric functions "
       << endl
       << " asin (z1) = " <<asin (z1)
       <<endl
       << " acos (z1) = " <<acos (z1)
       <<endl
       << " atan (z1) = " <<atan (z1)
       <<endl
       << " asec (z1) = " <<asec (z1)
       <<endl
       << " acsc (z1) = " <<acsc (z1)
       <<endl
       << " acot (z1) = " <<acot (z1)
       <<endl;

  cout << " Hyperbolic functions "
       << endl
       << " sinh (z1) = " <<sinh (z1)
       <<endl
       << " cosh (z1) = " <<cosh (z1)
       <<endl
       << " tanh (z1) = " <<tanh (z1)
       <<endl
       << " sech (z1) = " <<sech (z1)
       <<endl
       << " csch (z1) = " <<csch (z1)
       <<endl
       << " coth (z1) = " <<coth (z1)
       <<endl;

  cout << " Inverse hyperbolic functions "
       << endl
       << " asinh (z1) = " <<asinh (z1)
       <<endl
       << " acosh (z1) = " <<acosh (z1)
       <<endl
       << " atanh (z1) = " <<atanh (z1)
       <<endl
       << " asech (z1) = " <<asech (z1)
       <<endl
       << " acsch (z1) = " <<acsch (z1)
       <<endl
       << " acoth (z1) = " <<acoth (z1)
       <<endl;

return 0;
}

This is the header Complex.h

/* -*- mode: c++ -*- */
/*
 * Complex.h
 * This is a wrapper around the complex type defined in the GSL
 *
 * This code is part of the
 * Gsl++library, a C++ wrapper around the GNU Scientific Library (GNU)
 *
 * Copyright for this wrapper (C) 2001,2002
 * J. Burguet, J.J. Gomez-Cadenas, J.A. Hernando
 *
 * For the GSL library
 * Copyright (C) 1996, 1997, 1998, 1999, 2000 Brian Gough and others,
 * see documentation of the GSL library
 *
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2 of the License, or (at
 * your option) any later version.
 *
 * This program is distributed in the hope that it will be useful, but
 * WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
 */

#ifndef _COMPLEX_
#define _COMPLEX_

#include <iostream>    // to overload ostream& <<

#include <gsl/gsl_complex.h>
#include <gsl/gsl_complex_math.h>

using namespace std;   //needed by gcc 3.2 and MVC++

/**
 * Complex numbers
 *
 * This is a wrapper class around the complex numbers defined by the GSL
 *
 * A gsl complex is a structure defined as:
 *
 *   typedef struct
 *   {
 *     double dat[2]
 *   } gsl_complex;
 *
 * See gsl manual chapter 5
 */

class Complex;

Complex operator - (const Complex& z);
Complex operator + (const Complex& z1, const Complex& z2); ///< z1+z2
Complex operator - (const Complex& z1, const Complex& z2); ///< z1-z2
Complex operator * (const Complex& z1, const Complex& z2); ///< z1*z2
Complex operator / (const Complex& z1, const Complex& z2); ///< z1/z2

Complex operator + (double a, const Complex& z);    ///< a + z
Complex operator - (double a, const Complex& z);    ///< a - z
Complex operator * (double a, const Complex& z);    ///< a * z
Complex operator / (double a, const Complex& z);    ///< a / z

Complex operator + (const Complex& z, double a);    ///< z + a
Complex operator - (const Complex& z, double a);    ///< z - a
Complex operator * (const Complex& z, double a);    ///< z * a
Complex operator / (const Complex& z, double a);    ///< z / ac

    /*
     * Complex functions.
     */
    // Elementary functions
     double fabs(const Complex& z);    ///< absolute value, |z|
     double abs(const Complex& z);     ///< absolute value, |z|

Complex conj(const Complex& z);      ///< complex conjugate
Complex inverse(const Complex& z);   ///< 1/z
Complex sqrt(const Complex& z);      ///< complex square root
Complex Csqrt(double a);             ///<  complex sqrt of a real
Complex pow(const Complex& z1, const Complex& z2);  ///< z1**z2
Complex pow(const Complex& z, double a);            ///< z**a
Complex exp(const Complex& z);    ///< exponential function, exp(z)
Complex log(const Complex& z);    ///< natural logarithm, log(z)
Complex log10(const Complex& z);  ///< logarithm in base 10, log10(z)

    // Trigonometric
Complex sin(const Complex& z);    ///< sinus, sin(z)
Complex cos(const Complex& z);    ///< cosinus, cos(z)
Complex tan(const Complex& z);    ///< tangent, tan(z)
Complex sec(const Complex& z);    ///< secant, sec(z) = 1/cos(z)
Complex csc(const Complex& z);    ///< cosecant, cosec(z) = 1/sin(z)
Complex cot(const Complex& z);    ///< cotangent, cotan(z) = 1/cot(z)

    // Inverse trigonometric
Complex asin(const Complex& z);   ///< arcsin(z)
Complex acos(const Complex& z);   ///< arccos(z)
Complex atan(const Complex& z);   ///< arctan(z)
Complex asec(const Complex& z);   ///< arcsec(z)
Complex acsc(const Complex& z);   ///< arccosec(z)
Complex acot(const Complex& z);   ///< arccotg(z)

    // Hyperbolic
Complex sinh(const Complex& z);   ///< sinh(z)
Complex cosh(const Complex& z);   ///< cosh(z)
Complex tanh(const Complex& z);   ///< tanh(z)
Complex sech(const Complex& z);   ///< sech(z) = 1/cosh(z)
Complex csch(const Complex& z);   ///< cosech(z) = 1/sinh(z)
Complex coth(const Complex& z);   ///< cotanh(z) = 1/coth(z)

    // Inverse hyperbolic
Complex asinh(const Complex& z);  ///< arcsinh(z)
Complex acosh(const Complex& z);  ///< arccosh(z)
Complex atanh(const Complex& z);  ///< arctan(z)
Complex asech(const Complex& z);  ///< arcsec(z)
Complex acsch(const Complex& z);  ///< arccosec(z)
Complex acoth(const Complex& z);  ///< arccotg(z)
class Complex {
  private:
    gsl_complex m_gslComplex;   ///< a gsl complex number

  public:
    Complex();
    Complex(double x, double y);
    Complex(const Complex& z);
    ~Complex();

    /* Reading functions  */
    double real() const;   ///< real part, Re(z)
    double imag() const;   ///< imaginary part, Im(z)
    double arg() const;    ///< argument,  -pi < arg(z) < pi
    double abs() const;    ///< absolute value, |z|
    double abs2() const;   ///< squared absolute value, |z|**2

    double logAbs() const; ///< log|z|. It allows accurate evaluation near
|z|=1

    /* Setting functions */
    void setRectangular(double x, double y);
    void setPolar(double r, double theta);

    /* Assignement operators */
    Complex& operator = (const Complex& z);
    Complex& operator = (double d);
    Complex& operator += (const Complex& z);
    Complex& operator -= (const Complex& z);
    Complex& operator *= (const Complex& z);
    Complex& operator *= (double d);
    Complex& operator /= (const Complex& z);
    Complex& operator /= (double d);

    /*
     * Friend functions
     */

    /*
     * Operations with complex numbers
     */
    friend Complex operator - (const Complex& z);

    friend Complex operator + (const Complex& z1, const Complex& z2); ///<
z1+z2
    friend Complex operator - (const Complex& z1, const Complex& z2); ///<
z1-z2
    friend Complex operator * (const Complex& z1, const Complex& z2); ///<
z1*z2
    friend Complex operator / (const Complex& z1, const Complex& z2); ///<
z1/z2

    friend Complex operator + (double a, const Complex& z);    ///< a + z
    friend Complex operator - (double a, const Complex& z);    ///< a - z
    friend Complex operator * (double a, const Complex& z);    ///< a * z
    friend Complex operator / (double a, const Complex& z);    ///< a / z

    friend Complex operator + (const Complex& z, double a);    ///< z + a
    friend Complex operator - (const Complex& z, double a);    ///< z - a
    friend Complex operator * (const Complex& z, double a);    ///< z * a
    friend Complex operator / (const Complex& z, double a);    ///< z / ac

    /*
     * Complex functions.
     */
    // Elementary functions
    friend double fabs(const Complex& z);    ///< absolute value, |z|
    friend double abs(const Complex& z);     ///< absolute value, |z|

    friend Complex conj(const Complex& z);      ///< complex conjugate
    friend Complex inverse(const Complex& z);   ///< 1/z
    friend Complex sqrt(const Complex& z);      ///< complex square root
    friend Complex Csqrt(double a);             ///<  complex sqrt of a real
    friend Complex pow(const Complex& z1, const Complex& z2);  ///< z1**z2
    friend Complex pow(const Complex& z, double a);            ///< z**a
    friend Complex exp(const Complex& z);    ///< exponential function,
exp(z)
    friend Complex log(const Complex& z);    ///< natural logarithm, log(z)
    friend Complex log10(const Complex& z);  ///< logarithm in base 10,
log10(z)

    // Trigonometric
    friend Complex sin(const Complex& z);    ///< sinus, sin(z)
    friend Complex cos(const Complex& z);    ///< cosinus, cos(z)
    friend Complex tan(const Complex& z);    ///< tangent, tan(z)
    friend Complex sec(const Complex& z);    ///< secant, sec(z) = 1/cos(z)
    friend Complex csc(const Complex& z);    ///< cosecant, cosec(z) =
1/sin(z)
    friend Complex cot(const Complex& z);    ///< cotangent, cotan(z) =
1/cot(z)

    // Inverse trigonometric
    friend Complex asin(const Complex& z);   ///< arcsin(z)
    friend Complex acos(const Complex& z);   ///< arccos(z)
    friend Complex atan(const Complex& z);   ///< arctan(z)
    friend Complex asec(const Complex& z);   ///< arcsec(z)
    friend Complex acsc(const Complex& z);   ///< arccosec(z)
    friend Complex acot(const Complex& z);   ///< arccotg(z)

    // Hyperbolic
    friend Complex sinh(const Complex& z);   ///< sinh(z)
    friend Complex cosh(const Complex& z);   ///< cosh(z)
    friend Complex tanh(const Complex& z);   ///< tanh(z)
    friend Complex sech(const Complex& z);   ///< sech(z) = 1/cosh(z)
    friend Complex csch(const Complex& z);   ///< cosech(z) = 1/sinh(z)
    friend Complex coth(const Complex& z);   ///< cotanh(z) = 1/coth(z)

    // Inverse hyperbolic
    friend Complex asinh(const Complex& z);  ///< arcsinh(z)
    friend Complex acosh(const Complex& z);  ///< arccosh(z)
    friend Complex atanh(const Complex& z);  ///< arctan(z)
    friend Complex asech(const Complex& z);  ///< arcsec(z)
    friend Complex acsch(const Complex& z);  ///< arccosec(z)
    friend Complex acoth(const Complex& z);  ///< arccotg(z)
};


ostream& operator << (ostream& s, const Complex& z);


#endif  /* _COMPLEX_ */

And this is the .cpp, all straight forward!

**
 * Complex numbers and complex functions.
 *
 * The class Complex is a wrapper around gsl_complex.
 *
 * @version  v1
 * @author   JJ Gomez Cadenas, JBC
 * @date     17/08/2001
 */

#include <gsl/gsl_errno.h>

#include "GslPP/DataTypes/Complex.h"


/**
 * Default constructor, z = 0.
 */
Complex::Complex() {
	m_gslComplex = gsl_complex_rect(0.0, 0.0);
}


/**
 * Create a complex number z = x + iy
 */
Complex::Complex(double x, double y) {
	m_gslComplex = gsl_complex_rect(x, y);
}


/**
 * Copy constructor
 */
Complex::Complex(const Complex& z) {
	m_gslComplex = gsl_complex_rect(z.real(), z.imag());
}

/**
 * Destructor
 */
Complex::~Complex() {
}


/*
 * Reading functions.
 */

/// Real part
double Complex::real() const {
    return GSL_REAL(m_gslComplex);
}

/// Imaginary part
double Complex::imag() const {
    return GSL_IMAG(m_gslComplex);
}

/// Argument, -pi < arg < pi
double Complex::arg() const {
    return gsl_complex_arg(m_gslComplex);
}

/// Modulus
double Complex::abs() const {
    return gsl_complex_abs(m_gslComplex);
}

/// Modulus squared
double Complex::abs2() const {
    return gsl_complex_abs2(m_gslComplex);
}


double Complex::logAbs() const {
    return gsl_complex_logabs(m_gslComplex);
}


/*
 * Setting functions
 */

void Complex::setRectangular(double x, double y) {
	m_gslComplex = gsl_complex_rect(x, y);
}

void Complex::setPolar(double r, double theta) {
	m_gslComplex = gsl_complex_polar(r, theta);
}


/*
 * Assignement operators.
 */
Complex& Complex::operator = (const Complex& z) {
	m_gslComplex = gsl_complex_rect(z.real(), z.imag());
    return *this;
}


Complex& Complex::operator = (double d) {
	m_gslComplex = gsl_complex_rect(d, 0.0);
    return *this;
}


Complex& Complex::operator += (const Complex& z)

	m_gslComplex = gsl_complex_add(m_gslComplex, z.m_gslComplex);
    return *this;
}


Complex& Complex::operator -= (const Complex& z) {
	m_gslComplex = gsl_complex_sub(m_gslComplex, z.m_gslComplex);
    return *this;
}


Complex& Complex::operator *= (const Complex& z) {
	m_gslComplex = gsl_complex_mul(m_gslComplex, z.m_gslComplex);
    return *this;
}


Complex& Complex::operator *= (double a) {
	m_gslComplex = gsl_complex_mul_real(m_gslComplex, a);
    return *this;
}


Complex& Complex::operator /= (const Complex& z) {
	m_gslComplex = gsl_complex_div(z.m_gslComplex, m_gslComplex);
    return *this;
}


Complex& Complex::operator /= (double a) {
	m_gslComplex = gsl_complex_div_real(m_gslComplex, a);
    return *this;
}



/*
 * Operations with complex numbers.
 */

Complex operator - (const Complex& z) {
    return Complex(-GSL_REAL(z.m_gslComplex), -GSL_IMAG(z.m_gslComplex));
}


Complex operator + (const Complex& z1, const Complex& z2) {
	gsl_complex gz = gsl_complex_add(z1.m_gslComplex, z2.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex operator - (const Complex& z1, const Complex& z2) {
    gsl_complex gz = gsl_complex_sub(z1.m_gslComplex, z2.m_gslComplex);
    return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex operator * (const Complex& z1, const Complex& z2) {
    gsl_complex gz = gsl_complex_mul(z1.m_gslComplex, z2.m_gslComplex);
    return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex operator / (const Complex& z1, const Complex& z2) {
    gsl_complex gz = gsl_complex_div(z1.m_gslComplex, z2.m_gslComplex);
    return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex operator + (double a, const Complex& z) {
    gsl_complex gz = gsl_complex_add_real(z.m_gslComplex, a);
    return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex operator - (double a, const Complex& z) {
    gsl_complex gz = gsl_complex_sub_real(z.m_gslComplex, a);
    return Complex(-GSL_REAL(gz), -GSL_IMAG(gz));
}


Complex operator * (double a, const Complex& z) {
    gsl_complex gz = gsl_complex_mul_real(z.m_gslComplex, a);
    return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex operator / (double a, const Complex& z) {
    gsl_complex ac = gsl_complex_rect(a, 0);   // complexization of a
    gsl_complex gz = gsl_complex_div(ac, z.m_gslComplex);
    return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex operator + (const Complex& z, double a) {
    gsl_complex gz = gsl_complex_add_real(z.m_gslComplex, a);
    return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex operator - (const Complex& z, double a) {
    gsl_complex gz = gsl_complex_sub_real(z.m_gslComplex, a);
    return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex operator * (const Complex& z, double a) {
    gsl_complex gz = gsl_complex_mul_real(z.m_gslComplex, a);
    return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex operator / (const Complex& z, double a) {
    gsl_complex gz = gsl_complex_div_real(z.m_gslComplex, a);
    return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


/*
 * Complex functions.
 */

// Elementary functions
double fabs(const Complex& z)  {
	return gsl_complex_abs(z.m_gslComplex);
}


double abs(const Complex& z)  {
	return gsl_complex_abs(z.m_gslComplex);
}


Complex conj(const Complex& z) {
	gsl_complex gz = gsl_complex_conjugate(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex inverse(const Complex& z) {
	gsl_complex gz = gsl_complex_inverse(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex sqrt(const Complex& z) {
	gsl_complex gz = gsl_complex_sqrt(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex Csqrt(double a) {
	gsl_complex gz = gsl_complex_sqrt_real(a);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex pow(const Complex& z1, const Complex& z2) {
	gsl_complex gz = gsl_complex_pow(z1.m_gslComplex, z2.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex pow(const Complex& z, double a) {
	gsl_complex gz = gsl_complex_pow_real(z.m_gslComplex, a);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex exp(const Complex& z) {
	gsl_complex gz = gsl_complex_exp(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex log(const Complex& z) {
	gsl_complex gz = gsl_complex_log(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex log10(const Complex& z) {
	gsl_complex gz = gsl_complex_log10(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


// Trigonometric
Complex sin(const Complex& z) {
	gsl_complex gz = gsl_complex_sin(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex cos(const Complex& z) {
	gsl_complex gz = gsl_complex_cos(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex tan(const Complex& z) {
	gsl_complex gz = gsl_complex_tan(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex sec(const Complex& z) {
	gsl_complex gz = gsl_complex_sec(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex csc(const Complex& z) {
	gsl_complex gz = gsl_complex_csc(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex cot(const Complex& z) {
	gsl_complex gz = gsl_complex_cot(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


// Inverse trigonometric
Complex asin(const Complex& z) {
	gsl_complex gz = gsl_complex_arcsin(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex acos(const Complex& z) {
	gsl_complex gz = gsl_complex_arccos(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex atan(const Complex& z) {
	gsl_complex gz = gsl_complex_arctan(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex asec(const Complex& z) {
	gsl_complex gz = gsl_complex_arcsec(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex acsc(const Complex& z) {
	gsl_complex gz = gsl_complex_arccsc(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex acot(const Complex& z) {
	gsl_complex gz = gsl_complex_arccot(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


// Hyperbolic
Complex sinh(const Complex& z) {
	gsl_complex gz = gsl_complex_sinh(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex cosh(const Complex& z) {
	gsl_complex gz = gsl_complex_cosh(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex tanh(const Complex& z) {
	gsl_complex gz = gsl_complex_tanh(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex sech(const Complex& z) {
	gsl_complex gz = gsl_complex_sech(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex csch(const Complex& z) {
	gsl_complex gz = gsl_complex_csch(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex coth(const Complex& z) {
	gsl_complex gz = gsl_complex_coth(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


// Inverse hyperbolic
Complex asinh(const Complex& z) {
	gsl_complex gz = gsl_complex_arcsinh(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex acosh(const Complex& z) {
	gsl_complex gz = gsl_complex_arccosh(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex atanh(const Complex& z) {
	gsl_complex gz = gsl_complex_arctanh(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex asech(const Complex& z) {
	gsl_complex gz = gsl_complex_arcsech(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex acsch(const Complex& z) {
	gsl_complex gz = gsl_complex_arccsch(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


Complex acoth(const Complex& z) {
	gsl_complex gz = gsl_complex_arccoth(z.m_gslComplex);
	return Complex(GSL_REAL(gz), GSL_IMAG(gz));
}


/**
 * Write complex number to a stream (for visual output)
 */
ostream& operator << (ostream& s, const Complex& z) {
    s << "( " << z.real() << ", " << z.imag() << " )";
    return s;
}

Finally, this is the error

Linking...
Searching Libraries
    Searching C:\Archivos de programa\Microsoft Visual
Studio\VC98\LIB\kernel32.lib:
    Searching C:\Archivos de programa\Microsoft Visual
Studio\VC98\LIB\ws2_32.lib:
    Searching C:\Archivos de programa\Microsoft Visual
Studio\VC98\LIB\advapi32.lib:
    Searching C:\Archivos de programa\Microsoft Visual
Studio\VC98\LIB\msvcrt.lib:
    Searching C:\Archivos de programa\Microsoft Visual
Studio\VC98\LIB\msvcprt.lib:
    Searching C:\Archivos de programa\Microsoft Visual
Studio\VC98\LIB\msvcirt.lib:
    Searching C:\Archivos de programa\Microsoft Visual
Studio\VC98\LIB\oldnames.lib:
    Searching C:\cygwin\jj\GSL++\GslPP\v0r1\Win32Debug\libGslPP.lib:
    Searching C:\ARCHIV~1\GSL\lib\libgsld.lib:
    Searching C:\ARCHIV~1\GSL\lib\libgslcblasd.lib:
    Searching C:\Archivos de programa\Microsoft Visual
Studio\VC98\LIB\kernel32.lib:
    Searching C:\Archivos de programa\Microsoft Visual
Studio\VC98\LIB\ws2_32.lib:
    Searching C:\Archivos de programa\Microsoft Visual
Studio\VC98\LIB\advapi32.lib:
    Searching C:\Archivos de programa\Microsoft Visual
Studio\VC98\LIB\msvcrt.lib:
    Searching C:\Archivos de programa\Microsoft Visual
Studio\VC98\LIB\msvcprt.lib:
    Searching C:\Archivos de programa\Microsoft Visual
Studio\VC98\LIB\msvcirt.lib:
    Searching C:\Archivos de programa\Microsoft Visual
Studio\VC98\LIB\oldnames.lib:
    Searching C:\cygwin\jj\GSL++\GslPP\v0r1\Win32Debug\libGslPP.lib:
    Searching C:\ARCHIV~1\GSL\lib\libgsld.lib:
    Searching C:\ARCHIV~1\GSL\lib\libgslcblasd.lib:
    Searching C:\Archivos de programa\Microsoft Visual
Studio\VC98\LIB\kernel32.lib:
    Searching C:\Archivos de programa\Microsoft Visual
Studio\VC98\LIB\ws2_32.lib:
    Searching C:\Archivos de programa\Microsoft Visual
Studio\VC98\LIB\advapi32.lib:
Done Searching Libraries
libgsld.lib(invhyp.obj) : error LNK2001: unresolved external symbol __HUGE
../Win32Debug/test_complex.exe : fatal error LNK1120: 1 unresolved externals
Error executing link.exe.

test_complex.exe - 2 error(s), 0 warning(s)

Notice that the missing symbol is in a module of libgsld.lib. I downloaded
v1 only a few days ago

Incidentally, I also use cygwin in windows. I compiled the library without
problems and the test example runs flawlessly. It also runs in Linux.
jj

RE: AW: hypergeometric function

[Brian Gough]

J.J. Gomez Cadenas writes:
 > Done Searching Libraries
 > libgsld.lib(invhyp.obj) : error LNK2001: unresolved external symbol __HUGE
 > ../Win32Debug/test_complex.exe : fatal error LNK1120: 1 unresolved externals
 > Error executing link.exe.
 > 
 > test_complex.exe - 2 error(s), 0 warning(s)
 > 
 > Notice that the missing symbol is in a module of libgsld.lib. I downloaded
 > v1 only a few days ago
 > 

Hi,
I couldn't even get that far unfortunately (see below).  

Have you tried recompiling the library yourself using GSL.dsw?

Brian

--------------------Configuration: test - Win32 Debug--------------------
Compiling...
jjtest.c
c:\program files\microsoft visual studio\vc98\include\eh.h(32) : fatal error C1189: #error :  "eh.h is only for C++!"
Error executing cl.exe.

jjtest.obj - 1 error(s), 0 warning(s)

--------------------Configuration: test - Win32 Debug--------------------
Compiling...
GSL_Complex.cpp
c:\program files\microsoft visual studio\vc98\include\utility(81) : error C2146: syntax error : missing ';' before identifier 'iterator_category'
        c:\program files\microsoft visual studio\vc98\include\utility(84) : see reference to class template instantiation 'std::iterator_traits<_It>' being compiled
c:\program files\microsoft visual studio\vc98\include\utility(81) : error C2838: illegal qualified name in member declaration
        c:\program files\microsoft visual studio\vc98\include\utility(84) : see reference to class template instantiation 'std::iterator_traits<_It>' being compiled

 ....

        c:\program files\microsoft visual studio\vc98\include\xstring(292) : see declaration of 'replace'
        c:\program files\microsoft visual studio\vc98\include\xstring(597) : see reference to class template instantiation 'std::basic_string<_E,_Tr,_A>' being compiled
c:\program files\microsoft visual studio\vc98\include\xstring(297) : fatal error C1003: error count exceeds 100; stopping compilation
        c:\program files\microsoft visual studio\vc98\include\xstring(597) : see reference to class template instantiation 'std::basic_string<_E,_Tr,_A>' being compiled
Error executing cl.exe.

GSL_Complex.obj - 102 error(s), 0 warning(s)

RE: AW: hypergeometric function

[Brian Gough]

J.J. Gomez Cadenas writes:
 > Done Searching Libraries
 > libgsld.lib(invhyp.obj) : error LNK2001: unresolved external symbol __HUGE
 > ../Win32Debug/test_complex.exe : fatal error LNK1120: 1 unresolved externals
 > Error executing link.exe.
 > 
 > test_complex.exe - 2 error(s), 0 warning(s)
 > 
 > Notice that the missing symbol is in a module of libgsld.lib. I downloaded
 > v1 only a few days ago
 > 

Hi,
I couldn't even get that far unfortunately (see below).  

Have you tried recompiling the library yourself using GSL.dsw?

Brian

--------------------Configuration: test - Win32 Debug--------------------
Compiling...
jjtest.c
c:\program files\microsoft visual studio\vc98\include\eh.h(32) : fatal error C1189: #error :  "eh.h is only for C++!"
Error executing cl.exe.

jjtest.obj - 1 error(s), 0 warning(s)

--------------------Configuration: test - Win32 Debug--------------------
Compiling...
GSL_Complex.cpp
c:\program files\microsoft visual studio\vc98\include\utility(81) : error C2146: syntax error : missing ';' before identifier 'iterator_category'
        c:\program files\microsoft visual studio\vc98\include\utility(84) : see reference to class template instantiation 'std::iterator_traits<_It>' being compiled
c:\program files\microsoft visual studio\vc98\include\utility(81) : error C2838: illegal qualified name in member declaration
        c:\program files\microsoft visual studio\vc98\include\utility(84) : see reference to class template instantiation 'std::iterator_traits<_It>' being compiled

 ....

        c:\program files\microsoft visual studio\vc98\include\xstring(292) : see declaration of 'replace'
        c:\program files\microsoft visual studio\vc98\include\xstring(597) : see reference to class template instantiation 'std::basic_string<_E,_Tr,_A>' being compiled
c:\program files\microsoft visual studio\vc98\include\xstring(297) : fatal error C1003: error count exceeds 100; stopping compilation
        c:\program files\microsoft visual studio\vc98\include\xstring(597) : see reference to class template instantiation 'std::basic_string<_E,_Tr,_A>' being compiled
Error executing cl.exe.

GSL_Complex.obj - 102 error(s), 0 warning(s)

RE: AW: hypergeometric function

[J.J. Gomez Cadenas]

Hi Brian,
No, I haven't tried, I just downloaded the .exe program. I may try next
week. MVC++ is a pain in the neck...
jj



-----Mensaje original-----
De: Brian Gough [ mailto:bjg@network-theory.co.uk ]
Enviado el: jueves, 13 de diciembre de 2001 0:36
Para: J.J. Gomez Cadenas
CC: J.J. Gomez Cadenas; gsl-discuss@sources.redhat.com
Asunto: RE: AW: hypergeometric function


J.J. Gomez Cadenas writes:
 > Done Searching Libraries
 > libgsld.lib(invhyp.obj) : error LNK2001: unresolved external symbol
__HUGE
 > ../Win32Debug/test_complex.exe : fatal error LNK1120: 1 unresolved
externals
 > Error executing link.exe.
 >
 > test_complex.exe - 2 error(s), 0 warning(s)
 >
 > Notice that the missing symbol is in a module of libgsld.lib. I
downloaded
 > v1 only a few days ago
 >

Hi,
I couldn't even get that far unfortunately (see below).

Have you tried recompiling the library yourself using GSL.dsw?

Brian

--------------------Configuration: test - Win32 Debug--------------------
Compiling...
jjtest.c
c:\program files\microsoft visual studio\vc98\include\eh.h(32) : fatal error
C1189: #error :  "eh.h is only for C++!"
Error executing cl.exe.

jjtest.obj - 1 error(s), 0 warning(s)

--------------------Configuration: test - Win32 Debug--------------------
Compiling...
GSL_Complex.cpp
c:\program files\microsoft visual studio\vc98\include\utility(81) : error
C2146: syntax error : missing ';' before identifier 'iterator_category'
        c:\program files\microsoft visual studio\vc98\include\utility(84) :
see reference to class template instantiation 'std::iterator_traits<_It>'
being compiled
c:\program files\microsoft visual studio\vc98\include\utility(81) : error
C2838: illegal qualified name in member declaration
        c:\program files\microsoft visual studio\vc98\include\utility(84) :
see reference to class template instantiation 'std::iterator_traits<_It>'
being compiled

 ....

        c:\program files\microsoft visual studio\vc98\include\xstring(292) :
see declaration of 'replace'
        c:\program files\microsoft visual studio\vc98\include\xstring(597) :
see reference to class template instantiation 'std::basic_string<_E,_Tr,_A>'
being compiled
c:\program files\microsoft visual studio\vc98\include\xstring(297) : fatal
error C1003: error count exceeds 100; stopping compilation
        c:\program files\microsoft visual studio\vc98\include\xstring(597) :
see reference to class template instantiation 'std::basic_string<_E,_Tr,_A>'
being compiled
Error executing cl.exe.

GSL_Complex.obj - 102 error(s), 0 warning(s)

RE: AW: hypergeometric function

[J.J. Gomez Cadenas]

Hi Brian,
No, I haven't tried, I just downloaded the .exe program. I may try next
week. MVC++ is a pain in the neck...
jj



-----Mensaje original-----
De: Brian Gough [mailto:bjg@network-theory.co.uk]
Enviado el: jueves, 13 de diciembre de 2001 0:36
Para: J.J. Gomez Cadenas
CC: J.J. Gomez Cadenas; gsl-discuss@sources.redhat.com
Asunto: RE: AW: hypergeometric function


J.J. Gomez Cadenas writes:
 > Done Searching Libraries
 > libgsld.lib(invhyp.obj) : error LNK2001: unresolved external symbol
__HUGE
 > ../Win32Debug/test_complex.exe : fatal error LNK1120: 1 unresolved
externals
 > Error executing link.exe.
 >
 > test_complex.exe - 2 error(s), 0 warning(s)
 >
 > Notice that the missing symbol is in a module of libgsld.lib. I
downloaded
 > v1 only a few days ago
 >

Hi,
I couldn't even get that far unfortunately (see below).

Have you tried recompiling the library yourself using GSL.dsw?

Brian

--------------------Configuration: test - Win32 Debug--------------------
Compiling...
jjtest.c
c:\program files\microsoft visual studio\vc98\include\eh.h(32) : fatal error
C1189: #error :  "eh.h is only for C++!"
Error executing cl.exe.

jjtest.obj - 1 error(s), 0 warning(s)

--------------------Configuration: test - Win32 Debug--------------------
Compiling...
GSL_Complex.cpp
c:\program files\microsoft visual studio\vc98\include\utility(81) : error
C2146: syntax error : missing ';' before identifier 'iterator_category'
        c:\program files\microsoft visual studio\vc98\include\utility(84) :
see reference to class template instantiation 'std::iterator_traits<_It>'
being compiled
c:\program files\microsoft visual studio\vc98\include\utility(81) : error
C2838: illegal qualified name in member declaration
        c:\program files\microsoft visual studio\vc98\include\utility(84) :
see reference to class template instantiation 'std::iterator_traits<_It>'
being compiled

 ....

        c:\program files\microsoft visual studio\vc98\include\xstring(292) :
see declaration of 'replace'
        c:\program files\microsoft visual studio\vc98\include\xstring(597) :
see reference to class template instantiation 'std::basic_string<_E,_Tr,_A>'
being compiled
c:\program files\microsoft visual studio\vc98\include\xstring(297) : fatal
error C1003: error count exceeds 100; stopping compilation
        c:\program files\microsoft visual studio\vc98\include\xstring(597) :
see reference to class template instantiation 'std::basic_string<_E,_Tr,_A>'
being compiled
Error executing cl.exe.

GSL_Complex.obj - 102 error(s), 0 warning(s)

RE: AW: hypergeometric function

[J.J. Gomez Cadenas]

Hi Brian,
No, I haven't tried, I just downloaded the .exe program. I may try next
week. MVC++ is a pain in the neck...
jj



-----Mensaje original-----
De: Brian Gough [mailto:bjg@network-theory.co.uk]
Enviado el: jueves, 13 de diciembre de 2001 0:36
Para: J.J. Gomez Cadenas
CC: J.J. Gomez Cadenas; gsl-discuss@sources.redhat.com
Asunto: RE: AW: hypergeometric function


J.J. Gomez Cadenas writes:
 > Done Searching Libraries
 > libgsld.lib(invhyp.obj) : error LNK2001: unresolved external symbol
__HUGE
 > ../Win32Debug/test_complex.exe : fatal error LNK1120: 1 unresolved
externals
 > Error executing link.exe.
 >
 > test_complex.exe - 2 error(s), 0 warning(s)
 >
 > Notice that the missing symbol is in a module of libgsld.lib. I
downloaded
 > v1 only a few days ago
 >

Hi,
I couldn't even get that far unfortunately (see below).

Have you tried recompiling the library yourself using GSL.dsw?

Brian

--------------------Configuration: test - Win32 Debug--------------------
Compiling...
jjtest.c
c:\program files\microsoft visual studio\vc98\include\eh.h(32) : fatal error
C1189: #error :  "eh.h is only for C++!"
Error executing cl.exe.

jjtest.obj - 1 error(s), 0 warning(s)

--------------------Configuration: test - Win32 Debug--------------------
Compiling...
GSL_Complex.cpp
c:\program files\microsoft visual studio\vc98\include\utility(81) : error
C2146: syntax error : missing ';' before identifier 'iterator_category'
        c:\program files\microsoft visual studio\vc98\include\utility(84) :
see reference to class template instantiation 'std::iterator_traits<_It>'
being compiled
c:\program files\microsoft visual studio\vc98\include\utility(81) : error
C2838: illegal qualified name in member declaration
        c:\program files\microsoft visual studio\vc98\include\utility(84) :
see reference to class template instantiation 'std::iterator_traits<_It>'
being compiled

 ....

        c:\program files\microsoft visual studio\vc98\include\xstring(292) :
see declaration of 'replace'
        c:\program files\microsoft visual studio\vc98\include\xstring(597) :
see reference to class template instantiation 'std::basic_string<_E,_Tr,_A>'
being compiled
c:\program files\microsoft visual studio\vc98\include\xstring(297) : fatal
error C1003: error count exceeds 100; stopping compilation
        c:\program files\microsoft visual studio\vc98\include\xstring(597) :
see reference to class template instantiation 'std::basic_string<_E,_Tr,_A>'
being compiled
Error executing cl.exe.

GSL_Complex.obj - 102 error(s), 0 warning(s)

Re: hypergeometric function

[Dan, Ho-Jin]

[-- Attachment #1: Type: text/plain, Size: 422 bytes --]

Hi,
I couldn't find the discontinuty of the hypergeometry graph.
please, check the file hyperg.gif,

Yours,
Dan, Ho-Jin

Stefan Koch wrote:

>Hello,
>
>I'm a new user of the gsl-library. Everything works well. But when I tried
>to look at the hypergeometric function, I recognized a discontinuity (jump)
>in the graphic-drawing of the function. I think this should not be so. I
>used the following code segment:
>
--snip


[-- Attachment #2: gsl_sf_h1.c --]
[-- Type: text/plain, Size: 240 bytes --]

#include <stdio.h>
#include <gsl/gsl_sf.h>

int main()
{
  int i, m=1000;
  int n=3, p=8;
  double result, x;

  for (i=0; i<m; i++) {
    x = i*0.1;
    result = gsl_sf_hyperg_1F1_int(-n, p+1, x);
    printf("%f %f\n", x, result);
  }
}



[-- Attachment #3: hyperg.gif --]
[-- Type: image/gif, Size: 14044 bytes --]

Re: hypergeometric function

[Dan, Ho-Jin]

[-- Attachment #1: Type: text/plain, Size: 422 bytes --]

Hi,
I couldn't find the discontinuty of the hypergeometry graph.
please, check the file hyperg.gif,

Yours,
Dan, Ho-Jin

Stefan Koch wrote:

>Hello,
>
>I'm a new user of the gsl-library. Everything works well. But when I tried
>to look at the hypergeometric function, I recognized a discontinuity (jump)
>in the graphic-drawing of the function. I think this should not be so. I
>used the following code segment:
>
--snip


[-- Attachment #2: gsl_sf_h1.c --]
[-- Type: text/plain, Size: 240 bytes --]

#include <stdio.h>
#include <gsl/gsl_sf.h>

int main()
{
  int i, m=1000;
  int n=3, p=8;
  double result, x;

  for (i=0; i<m; i++) {
    x = i*0.1;
    result = gsl_sf_hyperg_1F1_int(-n, p+1, x);
    printf("%f %f\n", x, result);
  }
}



[-- Attachment #3: hyperg.gif --]
[-- Type: image/gif, Size: 14044 bytes --]

Re: hypergeometric function

[Dan, Ho-Jin]

Hi,
I couldn't find the discontinuty of the hypergeometry graph.
please, check the file hyperg.gif,

Yours,
Dan, Ho-Jin

Stefan Koch wrote:

>Hello,
>
>I'm a new user of the gsl-library. Everything works well. But when I tried
>to look at the hypergeometric function, I recognized a discontinuity (jump)
>in the graphic-drawing of the function. I think this should not be so. I
>used the following code segment:
>
--snip