代数方程式ライブラリ 使用例

［ 簡単な説明 ］

代数方程式ライブラリの使用例です。
プログラム・ソース（"test10.c"） 　　　　　　　　　　top （先頭に戻る） 
/*		test10.c			*/
#include	<stdio.h>
#include	"sslib.h"

/*	_f(x) should be defined by user	*/

double _f(double x)
{
	return exp(x) - 2.;
}

int main(void)
{
	Complex a, b, c, x[20];
	double d[20], eps, xe, xs, h, xr;
	int i, iter, n;

	a = tocomplex( 1., 0.);
	b = tocomplex(-3., 0.);
	c = tocomplex( 2., 0.);
	qurt(a, b, c, x);
	printf("  (%4.1f , %4.1f) * x ^ 2\n", a.r, a.i);
	printf("+ (%4.1f , %4.1f) * x\n", b.r, b.i);
	printf("+ (%4.1f , %4.1f) = 0\n", c.r, c.i);
	printf("     x1 = ( %22.15e , %22.15e )\n", x[0].r, x[0].i);
	printf("     x2 = ( %22.15e , %22.15e )\n", x[1].r, x[1].i);
	a = tocomplex( 1., 0.);
	b = tocomplex(-2., 0.);
	c = tocomplex( 1., 0.);
	qurt(a, b, c, x);
	printf("  (%4.1f , %4.1f) * x ^ 2\n", a.r, a.i);
	printf("+ (%4.1f , %4.1f) * x\n", b.r, b.i);
	printf("+ (%4.1f , %4.1f) = 0\n", c.r, c.i);
	printf("     x1 = ( %22.15e , %22.15e )\n", x[0].r, x[0].i);
	printf("     x2 = ( %22.15e , %22.15e )\n", x[1].r, x[1].i);
	a = tocomplex( 1., 0.);
	b = tocomplex(-4., 0.);
	c = tocomplex( 8., 0.);
	qurt(a, b, c, x);
	printf("  (%4.1f , %4.1f) * x ^ 2\n", a.r, a.i);
	printf("+ (%4.1f , %4.1f) * x\n", b.r, b.i);
	printf("+ (%4.1f , %4.1f) = 0\n", c.r, c.i);
	printf("     x1 = ( %22.15e , %22.15e )\n", x[0].r, x[0].i);
	printf("     x2 = ( %22.15e , %22.15e )\n", x[1].r, x[1].i);

	d[0] = 0.1;
	d[1] = -0.5;
	d[2] = 0.8;
	d[3] = 1.4;
	carda(d, x);
	for(i = 0; i <= 3; i++)	printf("   %4.1f * x ^ %d\n", d[i], 3 - i);
	for (i = 0; i < 3; i++)	printf("     x%d = ( %22.15e, %22.15e )\n", i + 1, x[i].r, x[i].i);

	d[0] = 0.1;
	d[1] = -0.5;
	d[2] = 0.8;
	d[3] = 1.4;
	n = 3;
	eps = 1.e-6;
	iter = 100;
	xr = newton(d, n, eps, iter);
	for(i = 0; i <= n; i++)	printf("   %4.1f * x ^ %d\n", d[i], n - i);
	printf("     x = %22.15e\n", xr);

	d[0] = 1.;
	d[1] = -10.;
	d[2] = 55.;
	d[3] = -140.;
	d[4] = 174.;
	d[5] = -100.;
	n = 5;
	eps = 1.e-6;
	iter = 100;
	bairs(d, n, eps, iter, x);
	for(i = 0; i <= n; i++)	printf("   %6.1f * x ^ %d\n", d[i], n - i);
	for (i = 0; i < n; i++)	printf("     x%d = ( %22.15e, %22.15e )\n", i + 1, x[i].r, x[i].i);

	xs = 0.;
	xe = 1.;
	h = 0.1;
	eps = 1.e-6;
	iter = 1000;
	printf("   exp(x) - 2 = 0\n");
	printf("       x = %22.15e\n", regula(xs, xe, h, eps, iter));

	return 1;
}
出力結果 1 　　　　　　　　　　top （先頭に戻る） 
  ( 1.0 ,  0.0) * x ^ 2
+ (-3.0 ,  0.0) * x
+ ( 2.0 ,  0.0) = 0
     x1 = (  2.000000000000000e+00 ,  0.000000000000000e+00 )
     x2 = (  1.000000000000000e+00 ,  0.000000000000000e+00 )
  ( 1.0 ,  0.0) * x ^ 2
+ (-2.0 ,  0.0) * x
+ ( 1.0 ,  0.0) = 0
     x1 = (  1.000000000000000e+00 ,  0.000000000000000e+00 )
     x2 = (  1.000000000000000e+00 ,  0.000000000000000e+00 )
  ( 1.0 ,  0.0) * x ^ 2
+ (-4.0 ,  0.0) * x
+ ( 8.0 ,  0.0) = 0
     x1 = (  2.000000000000000e+00 , -2.000000000000000e+00 )
     x2 = (  2.000000000000000e+00 ,  2.000000000000000e+00 )
    0.1 * x ^ 3
   -0.5 * x ^ 2
    0.8 * x ^ 1
    1.4 * x ^ 0
     x1 = ( -9.999999999998614e-01,  0.000000000000000e+00 )
     x2 = (  2.999999999999930e+00,  2.236067977499910e+00 )
     x3 = (  2.999999999999930e+00, -2.236067977499910e+00 )
    0.1 * x ^ 3
   -0.5 * x ^ 2
    0.8 * x ^ 1
    1.4 * x ^ 0
     x = -9.999999999999999e-01
      1.0 * x ^ 5
     -6.0 * x ^ 4
     25.0 * x ^ 3
     -2.0 * x ^ 2
      2.0 * x ^ 1
      0.0 * x ^ 0
     x1 = (  3.000000000000081e+00,  4.000000000000217e+00 )
     x2 = (  3.000000000000081e+00, -4.000000000000217e+00 )
     x3 = (  9.999999999977374e-01,  1.000000000001475e+00 )
     x4 = (  9.999999999977374e-01, -1.000000000001475e+00 )
     x5 = (  2.000000000004364e+00,  0.000000000000000e+00 )
   exp(x) - 2 = 0
       x =  6.931470233921545e-01
プログラム・ソース（"test11.c"） 　　　　　　　　　　top （先頭に戻る） 
/*		test11.c				*/
#include	<stdio.h>
#include	"sslib.h"

double _f(double x){ return x; }

int main(void)
{
	static double ar[4] = { 4., 3., 2., 1.};
	static double ai[4] = { 4., 3., 2., 1.};
	Complex a[4], x[4], y;
	double eps;
	int i, iter, n;

	eps = 1.e-6;
	n = 3;
	iter = 100;
	for(i = 0; i <= n; i++)
	{
		a[i].r = ar[i];
		a[i].i = ai[i];
		printf("( %4.1f , %4.1f ) * x ^ %d\n", ar[i], ai[i], n - i);
	}
	cnewton(a, x, n, eps, iter);
	for(i = 0; i < n; i++)
	{
		y = cfunc(a, n, x[i]);
		printf("func( x(%d) = { %14.7e , %14.7e } ) = { %10.3e, %10.3e }\n", i, x[i].r, x[i].i, y.r, y.i);
	}

	return 1;
}
出力結果 2 　　　　　　　　　　top （先頭に戻る） 
(  4.0 ,  4.0 ) * x ^ 3
(  3.0 ,  3.0 ) * x ^ 2
(  2.0 ,  2.0 ) * x ^ 1
(  1.0 ,  1.0 ) * x ^ 0
func( x(0) = { -7.2085207e-02 ,  6.3832674e-01 } ) = {  6.558e-11, -1.992e-09 }
func( x(1) = { -6.0582959e-01 , -3.3478094e-10 } ) = {  8.680e-10, -9.863e-10 }
func( x(2) = { -7.2085207e-02 , -6.3832674e-01 } ) = {  2.018e-11, -1.854e-11 }
プログラム・ソース（"test12.c"） 　　　　　　　　　　top （先頭に戻る） 
/*		test12.c				*/
#include	<stdio.h>
#include	"sslib.h"

double _f(double x){ return x; }

int main(void)
{
	int i, iter, n;
	Complex c[4], rt[4], w;
	static double ar[4] = { 2., 3., 8., -5.};
	double x, eps;

	n = 3;
	eps = 1.e-6;
	iter = 100;
	for(i = 0; i <= n; i++)
	{
		c[i].r = ar[i];
		c[i].i = 0.;
	}
	dka(c, rt, n, eps, iter);

	printf("* Coefficient\n");
	for(i = 0; i <= n; i++)	printf("  x ^ %2d : %5.1f\n", n - i, ar[i]);
	printf("* Result\n");
	for(i = 1; i <= n; i++)
	{
		printf("   x(%d) = { %22.15e , %22.15e }\n", i, rt[i].r, rt[i].i);
		w = cfunc(c, n, rt[i]);
		printf("         error = { %12.5e , %12.5e }\n", w.r, w.i);
	}

	return 1;
}
出力結果 3 　　　　　　　　　　top （先頭に戻る） 
* Coefficient
  x ^  3 :   2.0
  x ^  2 :   3.0
  x ^  1 :   8.0
  x ^  0 :  -5.0
* Result
   x(1) = {  4.999999999999999e-01 ,  2.904184808559377e-18 }
         error = { -8.88178e-16 ,  3.63023e-17 }
   x(2) = { -1.000000000000000e+00 ,  2.000000000000000e+00 }
         error = {  0.00000e+00 ,  0.00000e+00 }
   x(3) = { -1.000000000000000e+00 , -2.000000000000000e+00 }
         error = {  0.00000e+00 ,  0.00000e+00 }