//20100224追加
Integer DAESolver::get_status_code()
{
Integer status_code(0);
Real minimum_occurrence_time(INF);
const RealMatrix::size_type a_taylor_size(3);
RealVector tmp_min;
tmp_min.resize(0);
for (StatusEventArray::size_type i(0); i < the_status_event_.size(); ++i)
{
Integer index = the_status_event_[i].variable_index;
Integer flag = the_status_event_[i].variable_flag;
Real threshold = the_status_event_[i].threshold;
Integer code = the_status_event_[i].status_code;
Real a[a_taylor_size + 1];
if (flag == 0)
{
a[0] = the_value_differential_[index] - threshold;
a[1] = the_taylor_series_[0][index];
Real power = 1.0;
for (Integer j(0); j < a_taylor_size - 1; ++j)
{
power = power * the_tolerable_step_interval_;
a[j + 2] = the_taylor_series_[j + 1][index] / power;
}
}
else
{
a[0] = the_value_algebraic_[index] - threshold;
a[1] = the_taylor_series_[0][
index + the_function_differential_size_];
Real power = 1.0;
for (Integer j(0); j < a_taylor_size - 1; ++j)
{
power = power * the_tolerable_step_interval_;
a[j + 2] = the_taylor_series_[j + 1][
index + the_function_differential_size_] / power;
}
}
Real z[2 * a_taylor_size];
gsl_poly_complex_workspace * w
= gsl_poly_complex_workspace_alloc(a_taylor_size + 1);
gsl_poly_complex_solve(a, a_taylor_size + 1, w, z);
gsl_poly_complex_workspace_free(w);
for (Integer k(0); k < a_taylor_size; k++)
{
const Real solution(z[2 * k]);
if (z[2 * k + 1] == 0.0 && solution >= 0. &&
solution < the_next_time_ - the_current_time_)
{
if (solution < minimum_occurrence_time)
{
minimum_occurrence_time = solution;
status_code = code;
tmp_min.push_back(minimum_occurrence_time);
}
}
}
}
Integer count = 0;
for (Integer n(0); n < tmp_min.size(); n++)
{
if (tmp_min[n] == minimum_occurrence_time) count++;
}
if (count > 1)
{
throw "Some status events occurred at the same time.";
}
return status_code;
}
int
main (void)
{
const double eps = 100.0 * GSL_DBL_EPSILON;
gsl_ieee_env_setup ();
{
double x, y;
double c[3] = { 1.0, 0.5, 0.3 };
x = 0.5;
y = gsl_poly_eval (c, 3, x);
gsl_test_rel (y, 1 + 0.5 * x + 0.3 * x * x, eps,
"gsl_poly_eval({1, 0.5, 0.3}, 0.5)");
}
{
double x, y;
double d[11] = { 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1 };
x = 1.0;
y = gsl_poly_eval (d, 11, x);
gsl_test_rel (y, 1.0, eps,
"gsl_poly_eval({1,-1, 1, -1, 1, -1, 1, -1, 1, -1, 1}, 1.0)");
}
/* Quadratic */
{
double x0, x1;
int n = gsl_poly_solve_quadratic (4.0, -20.0, 26.0, &x0, &x1);
gsl_test (n != 0, "gsl_poly_solve_quadratic, no roots, (2x - 5)^2 = -1");
}
{
double x0, x1;
int n = gsl_poly_solve_quadratic (4.0, -20.0, 25.0, &x0, &x1);
gsl_test (n != 2, "gsl_poly_solve_quadratic, one root, (2x - 5)^2 = 0");
gsl_test_rel (x0, 2.5, 1e-9, "x0, (2x - 5)^2 = 0");
gsl_test_rel (x1, 2.5, 1e-9, "x1, (2x - 5)^2 = 0");
gsl_test (x0 != x1, "x0 == x1, (2x - 5)^2 = 0");
}
{
double x0, x1;
int n = gsl_poly_solve_quadratic (4.0, -20.0, 21.0, &x0, &x1);
gsl_test (n != 2, "gsl_poly_solve_quadratic, two roots, (2x - 5)^2 = 4");
gsl_test_rel (x0, 1.5, 1e-9, "x0, (2x - 5)^2 = 4");
gsl_test_rel (x1, 3.5, 1e-9, "x1, (2x - 5)^2 = 4");
}
{
double x0, x1;
int n = gsl_poly_solve_quadratic (4.0, 7.0, 0.0, &x0, &x1);
gsl_test (n != 2, "gsl_poly_solve_quadratic, two roots, x(4x + 7) = 0");
gsl_test_rel (x0, -1.75, 1e-9, "x0, x(4x + 7) = 0");
gsl_test_rel (x1, 0.0, 1e-9, "x1, x(4x + 7) = 0");
}
{
double x0, x1;
int n = gsl_poly_solve_quadratic (5.0, 0.0, -20.0, &x0, &x1);
gsl_test (n != 2,
"gsl_poly_solve_quadratic, two roots b = 0, 5 x^2 = 20");
gsl_test_rel (x0, -2.0, 1e-9, "x0, 5 x^2 = 20");
gsl_test_rel (x1, 2.0, 1e-9, "x1, 5 x^2 = 20");
}
/* Cubic */
{
double x0, x1, x2;
int n = gsl_poly_solve_cubic (0.0, 0.0, -27.0, &x0, &x1, &x2);
gsl_test (n != 1, "gsl_poly_solve_cubic, one root, x^3 = 27");
gsl_test_rel (x0, 3.0, 1e-9, "x0, x^3 = 27");
}
{
double x0, x1, x2;
int n = gsl_poly_solve_cubic (-51.0, 867.0, -4913.0, &x0, &x1, &x2);
gsl_test (n != 3, "gsl_poly_solve_cubic, three roots, (x-17)^3=0");
gsl_test_rel (x0, 17.0, 1e-9, "x0, (x-17)^3=0");
gsl_test_rel (x1, 17.0, 1e-9, "x1, (x-17)^3=0");
gsl_test_rel (x2, 17.0, 1e-9, "x2, (x-17)^3=0");
}
{
double x0, x1, x2;
int n = gsl_poly_solve_cubic (-57.0, 1071.0, -6647.0, &x0, &x1, &x2);
gsl_test (n != 3,
"gsl_poly_solve_cubic, three roots, (x-17)(x-17)(x-23)=0");
gsl_test_rel (x0, 17.0, 1e-9, "x0, (x-17)(x-17)(x-23)=0");
gsl_test_rel (x1, 17.0, 1e-9, "x1, (x-17)(x-17)(x-23)=0");
gsl_test_rel (x2, 23.0, 1e-9, "x2, (x-17)(x-17)(x-23)=0");
}
{
double x0, x1, x2;
int n = gsl_poly_solve_cubic (-11.0, -493.0, +6647.0, &x0, &x1, &x2);
gsl_test (n != 3,
"gsl_poly_solve_cubic, three roots, (x+23)(x-17)(x-17)=0");
gsl_test_rel (x0, -23.0, 1e-9, "x0, (x+23)(x-17)(x-17)=0");
gsl_test_rel (x1, 17.0, 1e-9, "x1, (x+23)(x-17)(x-17)=0");
gsl_test_rel (x2, 17.0, 1e-9, "x2, (x+23)(x-17)(x-17)=0");
}
{
double x0, x1, x2;
int n = gsl_poly_solve_cubic (-143.0, 5087.0, -50065.0, &x0, &x1, &x2);
gsl_test (n != 3,
"gsl_poly_solve_cubic, three roots, (x-17)(x-31)(x-95)=0");
gsl_test_rel (x0, 17.0, 1e-9, "x0, (x-17)(x-31)(x-95)=0");
gsl_test_rel (x1, 31.0, 1e-9, "x1, (x-17)(x-31)(x-95)=0");
gsl_test_rel (x2, 95.0, 1e-9, "x2, (x-17)(x-31)(x-95)=0");
}
{
double x0, x1, x2;
int n = gsl_poly_solve_cubic (-109.0, 803.0, 50065.0, &x0, &x1, &x2);
gsl_test (n != 3,
"gsl_poly_solve_cubic, three roots, (x+17)(x-31)(x-95)=0");
gsl_test_rel (x0, -17.0, 1e-9, "x0, (x+17)(x-31)(x-95)=0");
gsl_test_rel (x1, 31.0, 1e-9, "x1, (x+17)(x-31)(x-95)=0");
gsl_test_rel (x2, 95.0, 1e-9, "x2, (x+17)(x-31)(x-95)=0");
}
/* Quadratic with complex roots */
{
gsl_complex z0, z1;
int n = gsl_poly_complex_solve_quadratic (4.0, -20.0, 26.0, &z0, &z1);
gsl_test (n != 2,
"gsl_poly_complex_solve_quadratic, 2 roots (2x - 5)^2 = -1");
gsl_test_rel (GSL_REAL (z0), 2.5, 1e-9, "z0.real, (2x - 5)^2 = -1");
gsl_test_rel (GSL_IMAG (z0), -0.5, 1e-9, "z0.imag, (2x - 5)^2 = -1");
gsl_test_rel (GSL_REAL (z1), 2.5, 1e-9, "z1.real, (2x - 5)^2 = -1");
gsl_test_rel (GSL_IMAG (z1), 0.5, 1e-9, "z1.imag, (2x - 5)^2 = -1");
}
{
gsl_complex z0, z1;
int n = gsl_poly_complex_solve_quadratic (4.0, -20.0, 25.0, &z0, &z1);
gsl_test (n != 2,
"gsl_poly_complex_solve_quadratic, one root, (2x - 5)^2 = 0");
gsl_test_rel (GSL_REAL (z0), 2.5, 1e-9, "z0.real, (2x - 5)^2 = 0");
gsl_test_rel (GSL_IMAG (z0), 0.0, 1e-9, "z0.imag (2x - 5)^2 = 0");
gsl_test_rel (GSL_REAL (z1), 2.5, 1e-9, "z1.real, (2x - 5)^2 = 0");
gsl_test_rel (GSL_IMAG (z1), 0.0, 1e-9, "z1.imag (2x - 5)^2 = 0");
gsl_test (GSL_REAL (z0) != GSL_REAL (z1),
"z0.real == z1.real, (2x - 5)^2 = 0");
gsl_test (GSL_IMAG (z0) != GSL_IMAG (z1),
"z0.imag == z1.imag, (2x - 5)^2 = 0");
}
{
gsl_complex z0, z1;
int n = gsl_poly_complex_solve_quadratic (4.0, -20.0, 21.0, &z0, &z1);
gsl_test (n != 2,
"gsl_poly_complex_solve_quadratic, two roots, (2x - 5)^2 = 4");
gsl_test_rel (GSL_REAL (z0), 1.5, 1e-9, "z0.real, (2x - 5)^2 = 4");
gsl_test_rel (GSL_IMAG (z0), 0.0, 1e-9, "z0.imag, (2x - 5)^2 = 4");
gsl_test_rel (GSL_REAL (z1), 3.5, 1e-9, "z1.real, (2x - 5)^2 = 4");
gsl_test_rel (GSL_IMAG (z1), 0.0, 1e-9, "z1.imag, (2x - 5)^2 = 4");
}
{
gsl_complex z0, z1;
int n = gsl_poly_complex_solve_quadratic (4.0, 7.0, 0.0, &z0, &z1);
gsl_test (n != 2,
"gsl_poly_complex_solve_quadratic, two roots, x(4x + 7) = 0");
gsl_test_rel (GSL_REAL (z0), -1.75, 1e-9, "z0.real, x(4x + 7) = 0");
gsl_test_rel (GSL_IMAG (z0), 0.0, 1e-9, "z0.imag, x(4x + 7) = 0");
gsl_test_rel (GSL_REAL (z1), 0.0, 1e-9, "z1.real, x(4x + 7) = 0");
gsl_test_rel (GSL_IMAG (z1), 0.0, 1e-9, "z1.imag, x(4x + 7) = 0");
}
{
gsl_complex z0, z1;
int n = gsl_poly_complex_solve_quadratic (5.0, 0.0, -20.0, &z0, &z1);
gsl_test (n != 2,
"gsl_poly_complex_solve_quadratic, two roots b = 0, 5 x^2 = 20");
gsl_test_rel (GSL_REAL (z0), -2.0, 1e-9, "z0.real, 5 x^2 = 20");
gsl_test_rel (GSL_IMAG (z0), 0.0, 1e-9, "z0.imag, 5 x^2 = 20");
gsl_test_rel (GSL_REAL (z1), 2.0, 1e-9, "z1.real, 5 x^2 = 20");
gsl_test_rel (GSL_IMAG (z1), 0.0, 1e-9, "z1.imag, 5 x^2 = 20");
}
{
gsl_complex z0, z1;
int n = gsl_poly_complex_solve_quadratic (5.0, 0.0, 20.0, &z0, &z1);
gsl_test (n != 2,
"gsl_poly_complex_solve_quadratic, two roots b = 0, 5 x^2 = -20");
gsl_test_rel (GSL_REAL (z0), 0.0, 1e-9, "z0.real, 5 x^2 = -20");
gsl_test_rel (GSL_IMAG (z0), -2.0, 1e-9, "z0.imag, 5 x^2 = -20");
gsl_test_rel (GSL_REAL (z1), 0.0, 1e-9, "z1.real, 5 x^2 = -20");
gsl_test_rel (GSL_IMAG (z1), 2.0, 1e-9, "z1.imag, 5 x^2 = -20");
}
/* Cubic with complex roots */
{
gsl_complex z0, z1, z2;
int n = gsl_poly_complex_solve_cubic (0.0, 0.0, -27.0, &z0, &z1, &z2);
gsl_test (n != 3, "gsl_poly_complex_solve_cubic, three root, x^3 = 27");
gsl_test_rel (GSL_REAL (z0), -1.5, 1e-9, "z0.real, x^3 = 27");
gsl_test_rel (GSL_IMAG (z0), -1.5 * sqrt (3.0), 1e-9,
"z0.imag, x^3 = 27");
gsl_test_rel (GSL_REAL (z1), -1.5, 1e-9, "z1.real, x^3 = 27");
gsl_test_rel (GSL_IMAG (z1), 1.5 * sqrt (3.0), 1e-9, "z1.imag, x^3 = 27");
gsl_test_rel (GSL_REAL (z2), 3.0, 1e-9, "z2.real, x^3 = 27");
gsl_test_rel (GSL_IMAG (z2), 0.0, 1e-9, "z2.imag, x^3 = 27");
}
{
gsl_complex z0, z1, z2;
int n = gsl_poly_complex_solve_cubic (-1.0, 1.0, 39.0, &z0, &z1, &z2);
gsl_test (n != 3,
"gsl_poly_complex_solve_cubic, three root, (x+3)(x^2-4x+13) = 0");
gsl_test_rel (GSL_REAL (z0), -3.0, 1e-9, "z0.real, (x+3)(x^2+1) = 0");
gsl_test_rel (GSL_IMAG (z0), 0.0, 1e-9, "z0.imag, (x+3)(x^2+1) = 0");
gsl_test_rel (GSL_REAL (z1), 2.0, 1e-9, "z1.real, (x+3)(x^2+1) = 0");
gsl_test_rel (GSL_IMAG (z1), -3.0, 1e-9, "z1.imag, (x+3)(x^2+1) = 0");
gsl_test_rel (GSL_REAL (z2), 2.0, 1e-9, "z2.real, (x+3)(x^2+1) = 0");
gsl_test_rel (GSL_IMAG (z2), 3.0, 1e-9, "z2.imag, (x+3)(x^2+1) = 0");
}
{
gsl_complex z0, z1, z2;
int n =
gsl_poly_complex_solve_cubic (-51.0, 867.0, -4913.0, &z0, &z1, &z2);
gsl_test (n != 3,
"gsl_poly_complex_solve_cubic, three roots, (x-17)^3=0");
gsl_test_rel (GSL_REAL (z0), 17.0, 1e-9, "z0.real, (x-17)^3=0");
gsl_test_rel (GSL_IMAG (z0), 0.0, 1e-9, "z0.imag, (x-17)^3=0");
gsl_test_rel (GSL_REAL (z1), 17.0, 1e-9, "z1.real, (x-17)^3=0");
gsl_test_rel (GSL_IMAG (z1), 0.0, 1e-9, "z1.imag, (x-17)^3=0");
gsl_test_rel (GSL_REAL (z2), 17.0, 1e-9, "z2.real, (x-17)^3=0");
gsl_test_rel (GSL_IMAG (z2), 0.0, 1e-9, "z2.imag, (x-17)^3=0");
}
{
gsl_complex z0, z1, z2;
int n =
gsl_poly_complex_solve_cubic (-57.0, 1071.0, -6647.0, &z0, &z1, &z2);
gsl_test (n != 3,
"gsl_poly_complex_solve_cubic, three roots, (x-17)(x-17)(x-23)=0");
gsl_test_rel (GSL_REAL (z0), 17.0, 1e-9, "z0.real, (x-17)(x-17)(x-23)=0");
gsl_test_rel (GSL_IMAG (z0), 0.0, 1e-9, "z0.imag, (x-17)(x-17)(x-23)=0");
gsl_test_rel (GSL_REAL (z1), 17.0, 1e-9, "z1.real, (x-17)(x-17)(x-23)=0");
gsl_test_rel (GSL_IMAG (z1), 0.0, 1e-9, "z1.imag, (x-17)(x-17)(x-23)=0");
gsl_test_rel (GSL_REAL (z2), 23.0, 1e-9, "z2.real, (x-17)(x-17)(x-23)=0");
gsl_test_rel (GSL_IMAG (z2), 0.0, 1e-9, "z2.imag, (x-17)(x-17)(x-23)=0");
}
{
gsl_complex z0, z1, z2;
int n =
gsl_poly_complex_solve_cubic (-11.0, -493.0, +6647.0, &z0, &z1, &z2);
gsl_test (n != 3,
"gsl_poly_complex_solve_cubic, three roots, (x+23)(x-17)(x-17)=0");
gsl_test_rel (GSL_REAL (z0), -23.0, 1e-9,
"z0.real, (x+23)(x-17)(x-17)=0");
gsl_test_rel (GSL_IMAG (z0), 0.0, 1e-9, "z0.imag, (x+23)(x-17)(x-17)=0");
gsl_test_rel (GSL_REAL (z1), 17.0, 1e-9, "z1.real, (x+23)(x-17)(x-17)=0");
gsl_test_rel (GSL_IMAG (z1), 0.0, 1e-9, "z1.imag, (x+23)(x-17)(x-17)=0");
gsl_test_rel (GSL_REAL (z2), 17.0, 1e-9, "z2.real, (x+23)(x-17)(x-17)=0");
gsl_test_rel (GSL_IMAG (z2), 0.0, 1e-9, "z2.imag, (x+23)(x-17)(x-17)=0");
}
{
gsl_complex z0, z1, z2;
int n =
gsl_poly_complex_solve_cubic (-143.0, 5087.0, -50065.0, &z0, &z1, &z2);
gsl_test (n != 3,
"gsl_poly_complex_solve_cubic, three roots, (x-17)(x-31)(x-95)=0");
gsl_test_rel (GSL_REAL (z0), 17.0, 1e-9, "z0.real, (x-17)(x-31)(x-95)=0");
gsl_test_rel (GSL_IMAG (z0), 0.0, 1e-9, "z0.imag, (x-17)(x-31)(x-95)=0");
gsl_test_rel (GSL_REAL (z1), 31.0, 1e-9, "z1.real, (x-17)(x-31)(x-95)=0");
gsl_test_rel (GSL_IMAG (z1), 0.0, 1e-9, "z1.imag, (x-17)(x-31)(x-95)=0");
gsl_test_rel (GSL_REAL (z2), 95.0, 1e-9, "z2.real, (x-17)(x-31)(x-95)=0");
gsl_test_rel (GSL_IMAG (z2), 0.0, 1e-9, "z2.imag, (x-17)(x-31)(x-95)=0");
}
{
/* Wilkinson polynomial: y = (x-1)(x-2)(x-3)(x-4)(x-5) */
double a[6] = { -120, 274, -225, 85, -15, 1 };
double z[6*2];
gsl_poly_complex_workspace *w = gsl_poly_complex_workspace_alloc (6);
int status = gsl_poly_complex_solve (a, 6, w, z);
gsl_poly_complex_workspace_free (w);
gsl_test (status,
"gsl_poly_complex_solve, 5th-order Wilkinson polynomial");
gsl_test_rel (z[0], 1.0, 1e-9, "z0.real, 5th-order polynomial");
gsl_test_rel (z[1], 0.0, 1e-9, "z0.imag, 5th-order polynomial");
gsl_test_rel (z[2], 2.0, 1e-9, "z1.real, 5th-order polynomial");
gsl_test_rel (z[3], 0.0, 1e-9, "z1.imag, 5th-order polynomial");
gsl_test_rel (z[4], 3.0, 1e-9, "z2.real, 5th-order polynomial");
gsl_test_rel (z[5], 0.0, 1e-9, "z2.imag, 5th-order polynomial");
gsl_test_rel (z[6], 4.0, 1e-9, "z3.real, 5th-order polynomial");
gsl_test_rel (z[7], 0.0, 1e-9, "z3.imag, 5th-order polynomial");
gsl_test_rel (z[8], 5.0, 1e-9, "z4.real, 5th-order polynomial");
gsl_test_rel (z[9], 0.0, 1e-9, "z4.imag, 5th-order polynomial");
}
{
/* : 8-th order polynomial y = x^8 + x^4 + 1 */
double a[9] = { 1, 0, 0, 0, 1, 0, 0, 0, 1 };
double z[8*2];
double C = 0.5;
double S = sqrt (3.0) / 2.0;
gsl_poly_complex_workspace *w = gsl_poly_complex_workspace_alloc (9);
int status = gsl_poly_complex_solve (a, 9, w, z);
gsl_poly_complex_workspace_free (w);
gsl_test (status, "gsl_poly_complex_solve, 8th-order polynomial");
gsl_test_rel (z[0], -S, 1e-9, "z0.real, 8th-order polynomial");
gsl_test_rel (z[1], C, 1e-9, "z0.imag, 8th-order polynomial");
gsl_test_rel (z[2], -S, 1e-9, "z1.real, 8th-order polynomial");
gsl_test_rel (z[3], -C, 1e-9, "z1.imag, 8th-order polynomial");
gsl_test_rel (z[4], -C, 1e-9, "z2.real, 8th-order polynomial");
gsl_test_rel (z[5], S, 1e-9, "z2.imag, 8th-order polynomial");
gsl_test_rel (z[6], -C, 1e-9, "z3.real, 8th-order polynomial");
gsl_test_rel (z[7], -S, 1e-9, "z3.imag, 8th-order polynomial");
gsl_test_rel (z[8], C, 1e-9, "z4.real, 8th-order polynomial");
gsl_test_rel (z[9], S, 1e-9, "z4.imag, 8th-order polynomial");
gsl_test_rel (z[10], C, 1e-9, "z5.real, 8th-order polynomial");
gsl_test_rel (z[11], -S, 1e-9, "z5.imag, 8th-order polynomial");
gsl_test_rel (z[12], S, 1e-9, "z6.real, 8th-order polynomial");
gsl_test_rel (z[13], C, 1e-9, "z6.imag, 8th-order polynomial");
gsl_test_rel (z[14], S, 1e-9, "z7.real, 8th-order polynomial");
gsl_test_rel (z[15], -C, 1e-9, "z7.imag, 8th-order polynomial");
}
{
int i;
double xa[7] = {0.16, 0.97, 1.94, 2.74, 3.58, 3.73, 4.70 };
double ya[7] = {0.73, 1.11, 1.49, 1.84, 2.30, 2.41, 3.07 };
double dd_expected[7] = { 7.30000000000000e-01,
4.69135802469136e-01,
-4.34737219941284e-02,
2.68681098870099e-02,
-3.22937056934996e-03,
6.12763259971375e-03,
-6.45402453527083e-03 };
double dd[7], coeff[7], work[7];
gsl_poly_dd_init (dd, xa, ya, 7);
for (i = 0; i < 7; i++)
{
gsl_test_rel (dd[i], dd_expected[i], 1e-10, "divided difference dd[%d]", i);
}
for (i = 0; i < 7; i++)
{
double y = gsl_poly_dd_eval(dd, xa, 7, xa[i]);
gsl_test_rel (y, ya[i], 1e-10, "divided difference y[%d]", i);
}
gsl_poly_dd_taylor (coeff, 1.5, dd, xa, 7, work);
for (i = 0; i < 7; i++)
{
double y = gsl_poly_eval(coeff, 7, xa[i] - 1.5);
gsl_test_rel (y, ya[i], 1e-10, "taylor expansion about 1.5 y[%d]", i);
}
}
/* now summarize the results */
exit (gsl_test_summary ());
}
