Re: Complex polynomial evaluation

[Frank Reininghaus <frank78ac@googlemail.com>]

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Hi,

I've written some documentation for my complex polynomial evaluation 
functions and some test cases to be checked by 'make check'. I've 
created patches containing all my modifications to the current CVS 
version with

diff gsl/poly/ [my directory with new version of 'poly'] > patch-poly
diff gsl/doc/ [my directory with new version of 'doc'] > patch-doc

Let me know if there is a way I could create patch files that are more 
convenient to you.

patch-doc also contains a correction for a typo in the macro @inlinefns 
in doc/gsl-ref.texi. I think it should be "Inline versions of these 
*functions* are used...", not "Inline versions of these *function* are 
used..."

Regards,
Frank


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Common subdirectories: gsl/doc/CVS and /home/frank/tmp/doc-with-complex-polynomials/CVS
Common subdirectories: gsl/doc/examples and /home/frank/tmp/doc-with-complex-polynomials/examples
diff gsl/doc/gsl-ref.texi /home/frank/tmp/doc-with-complex-polynomials/gsl-ref.texi
127c127
< Inline versions of these function are used when @code{HAVE_INLINE} is defined.
---
> Inline versions of these functions are used when @code{HAVE_INLINE} is defined.
diff gsl/doc/poly.texi /home/frank/tmp/doc-with-complex-polynomials/poly.texi
25,26c25
< @deftypefun double gsl_poly_eval (const double @var{c}[], const int @var{len}, const double @var{x})
< This function evaluates the polynomial 
---
> The functions described here evaluate the polynomial 
29c28,39
< Horner's method for stability.  @inlinefn{}
---
> Horner's method for stability. @inlinefns{}
> 
> @deftypefun double gsl_poly_eval (const double @var{c}[], const int @var{len}, const double @var{x})
> This function evaluates a polynomial with real coefficients for the real variable @var{x}.
> @end deftypefun
> 
> @deftypefun gsl_complex gsl_poly_complex_eval (const double @var{c}[], const int @var{len}, const gsl_complex @var{x})
> This function evaluates a polynomial with real coefficients for the complex variable @var{x}.
> @end deftypefun
> 
> @deftypefun gsl_complex gsl_complex_poly_complex_eval (const gsl_complex @var{c}[], const int @var{len}, const gsl_complex @var{x})
> This function evaluates a polynomial with complex coefficients for the complex variable @var{x}.

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Common subdirectories: gsl/poly/CVS and /home/frank/tmp/poly-with-complex-evaluation/CVS
diff gsl/poly/eval.c /home/frank/tmp/poly-with-complex-evaluation/eval.c
35a36,68
> 
> gsl_complex
> gsl_poly_complex_eval(const double c[], const int len, const gsl_complex x)
> {
>   int i;
>   gsl_complex ans;
>   GSL_SET_COMPLEX (&ans, c[len-1], 0.0);
>   for(i=len-1; i>0; i--) {
>     /* The following three lines are equivalent to
>        ans = gsl_complex_add_real (gsl_complex_mul (x, ans), c[i-1]); 
>        but faster */
>     double tmp = c[i-1] + GSL_REAL (x) * GSL_REAL (ans) - GSL_IMAG (x) * GSL_IMAG (ans);
>     GSL_SET_IMAG (&ans, GSL_IMAG (x) * GSL_REAL (ans) + GSL_REAL (x) * GSL_IMAG (ans));
>     GSL_SET_REAL (&ans, tmp);
>   } 
>   return ans;
> }
> 
> gsl_complex
> gsl_complex_poly_complex_eval(const gsl_complex c[], const int len, const gsl_complex x)
> {
>   int i;
>   gsl_complex ans = c[len-1];
>   for(i=len-1; i>0; i--) {
>     /* The following three lines are equivalent to
>        ans = gsl_complex_add (c[i-1], gsl_complex_mul (x, ans));
>        but faster */
>     double tmp = GSL_REAL (c[i-1]) + GSL_REAL (x) * GSL_REAL (ans) - GSL_IMAG (x) * GSL_IMAG (ans);
>     GSL_SET_IMAG (&ans, GSL_IMAG (c[i-1]) + GSL_IMAG (x) * GSL_REAL (ans) + GSL_REAL (x) * GSL_IMAG (ans));
>     GSL_SET_REAL (&ans, tmp);
>   }
>   return ans;
> }
diff gsl/poly/gsl_poly.h /home/frank/tmp/poly-with-complex-evaluation/gsl_poly.h
44a45,46
> 
> /* real polynomial, real x */
46a49,54
> /* real polynomial, complex x */
> gsl_complex gsl_poly_complex_eval (const double c [], const int len, const gsl_complex x);
> 
> /* complex polynomial, complex x */
> gsl_complex gsl_complex_poly_complex_eval (const gsl_complex c [], const int len, const gsl_complex x);
> 
57a66,100
> 
> extern inline
> gsl_complex
> gsl_poly_complex_eval(const double c[], const int len, const gsl_complex x)
> {
>   int i;
>   gsl_complex ans;
>   GSL_SET_COMPLEX (&ans, c[len-1], 0.0);
>   for(i=len-1; i>0; i--) {
>     /* The following three lines are equivalent to
>        ans = gsl_complex_add_real (gsl_complex_mul (x, ans), c[i-1]); 
>        but faster */
>     double tmp = c[i-1] + GSL_REAL (x) * GSL_REAL (ans) - GSL_IMAG (x) * GSL_IMAG (ans);
>     GSL_SET_IMAG (&ans, GSL_IMAG (x) * GSL_REAL (ans) + GSL_REAL (x) * GSL_IMAG (ans));
>     GSL_SET_REAL (&ans, tmp);
>   } 
>   return ans;
> }
> 
> extern inline
> gsl_complex
> gsl_complex_poly_complex_eval(const gsl_complex c[], const int len, const gsl_complex x)
> {
>   int i;
>   gsl_complex ans = c[len-1];
>   for(i=len-1; i>0; i--) {
>     /* The following three lines are equivalent to
>        ans = gsl_complex_add (c[i-1], gsl_complex_mul (x, ans));
>        but faster */
>     double tmp = GSL_REAL (c[i-1]) + GSL_REAL (x) * GSL_REAL (ans) - GSL_IMAG (x) * GSL_IMAG (ans);
>     GSL_SET_IMAG (&ans, GSL_IMAG (c[i-1]) + GSL_IMAG (x) * GSL_REAL (ans) + GSL_REAL (x) * GSL_IMAG (ans));
>     GSL_SET_REAL (&ans, tmp);
>   }
>   return ans;
> }
diff gsl/poly/test.c /home/frank/tmp/poly-with-complex-evaluation/test.c
33a34,35
>   /* Polynomial evaluation */
> 
52a55,108
>   {
>     gsl_complex x, y;
>     double c[1] = {0.3};
>     GSL_SET_REAL (&x, 0.75);
>     GSL_SET_IMAG (&x, 1.2);
>     y = gsl_poly_complex_eval (c, 1, x);
> 
>     gsl_test_rel (GSL_REAL (y), 0.3, eps, "y.real, gsl_poly_complex_eval ({0.3}, 0.75 + 1.2i)");
>     gsl_test_rel (GSL_IMAG (y), 0.0, eps, "y.imag, gsl_poly_complex_eval ({0.3}, 0.75 + 1.2i)");
>   }
> 
>   {
>     gsl_complex x, y;
>     double c[4] = {2.1, -1.34, 0.76, 0.45};
>     GSL_SET_REAL (&x, 0.49);
>     GSL_SET_IMAG (&x, 0.95);
>     y = gsl_poly_complex_eval (c, 4, x);
> 
>     gsl_test_rel (GSL_REAL (y), 0.3959143, eps, "y.real, gsl_poly_complex_eval ({2.1, -1.34, 0.76, 0.45}, 0.49 + 0.95i)");
>     gsl_test_rel (GSL_IMAG (y), -0.6433305, eps, "y.imag, gsl_poly_complex_eval ({2.1, -1.34, 0.76, 0.45}, 0.49 + 0.95i)");
>   }
> 
>   {
>     gsl_complex x, y;
>     gsl_complex c[1];
>     GSL_SET_REAL (&c[0], 0.674);
>     GSL_SET_IMAG (&c[0], -1.423);
>     GSL_SET_REAL (&x, -1.44);
>     GSL_SET_IMAG (&x, 9.55);
>     y = gsl_complex_poly_complex_eval (c, 1, x);
> 
>     gsl_test_rel (GSL_REAL (y), 0.674, eps, "y.real, gsl_complex_poly_complex_eval ({0.674 - 1.423i}, -1.44 + 9.55i)");
>     gsl_test_rel (GSL_IMAG (y), -1.423, eps, "y.imag, gsl_complex_poly_complex_eval ({0.674 - 1.423i}, -1.44 + 9.55i)");
>   }
> 
>   {
>     gsl_complex x, y;
>     gsl_complex c[4];
>     GSL_SET_REAL (&c[0], -2.31);
>     GSL_SET_IMAG (&c[0], 0.44);
>     GSL_SET_REAL (&c[1], 4.21);
>     GSL_SET_IMAG (&c[1], -3.19);
>     GSL_SET_REAL (&c[2], 0.93);
>     GSL_SET_IMAG (&c[2], 1.04);
>     GSL_SET_REAL (&c[3], -0.42);
>     GSL_SET_IMAG (&c[3], 0.68);
>     GSL_SET_REAL (&x, 0.49);
>     GSL_SET_IMAG (&x, 0.95);
>     y = gsl_complex_poly_complex_eval (c, 4, x);
> 
>     gsl_test_rel (GSL_REAL (y), 1.82462012, eps, "y.real, gsl_complex_poly_complex_eval ({-2.31 + 0.44i, 4.21 - 3.19i, 0.93 + 1.04i, -0.42 + 0.68i}, 0.49 + 0.95i)");
>     gsl_test_rel (GSL_IMAG (y), 2.30389412, eps, "y.imag, gsl_complex_poly_complex_eval ({-2.31 + 0.44i, 4.21 - 3.19i, 0.93 + 1.04i, -0.42 + 0.68i}, 0.49 + 0.95i)");
>   }
>