double ball_f1_nd ( double func ( int n, double x[] ), int n, double center[], double r ); double ball_f3_nd ( double func ( int n, double x[] ), int n, double center[], double r ); double ball_monomial_nd ( int n, int p[], double r ); double ball_unit_07_3d ( double func ( double x, double y, double z ) ); double ball_unit_14_3d ( double func ( double x, double y, double z ) ); double ball_unit_15_3d ( double func ( double x, double y, double z ) ); double ball_unit_f1_nd ( double func ( int n, double x[] ), int n ); double ball_unit_f3_nd ( double func ( int n, double x[] ), int n ); double ball_unit_volume_3d ( ); double ball_unit_volume_nd ( int n ); double ball_volume_3d ( double r ); double ball_volume_nd ( int n, double r ); double c1_geg_monomial_integral ( double alpha, int expon );; double c1_jac_monomial_integral ( double alpha, double beta, int expon ); double c1_leg_monomial_integral ( int expon ); double circle_annulus ( double func ( double x, double y ), double center[2], double radius1, double radius2, int nr ); double circle_annulus_area_2d ( double radius1, double radius2 ); double circle_annulus_sector ( double func ( double x, double y ), double center[2], double radius1, double radius2, double theta1, double theta2, int nr ); double circle_annulus_sector_area_2d ( double radius1, double radius2, double theta1, double theta2 ); double circle_area_2d ( double r ); double circle_cap_area_2d ( double r, double h ); double circle_cum ( double func ( double x, double y ), double center[2], double radius, int order ); void circle_rt_set ( int rule, int nr, int nt, int nc, double ra[], double rw[], double ta[], double tw[], double *cw ); void circle_rt_size ( int rule, int *nr, int *nt, int *nc ); double circle_rt_sum ( double func ( double x, double y ), double center[2], double radius, int nr, double ra[], double rw[], int nt, double ta[], double tw[], double zw ); double circle_sector ( double func ( double x, double y ), double center[2], double radius, double theta1, double theta2, int nr ); double circle_sector_area_2d ( double r, double theta1, double theta2 ); double circle_triangle_area_2d ( double r, double theta1, double theta2 ); void circle_xy_set ( int rule, int order, double xtab[], double ytab[], double weight[] ); int circle_xy_size ( int rule ); double circle_xy_sum ( double func ( double x, double y ), double center[2], double r, int order, double xtab[], double ytab[], double weight[] ); void cn_geg_00_1 ( int n, double alpha, int o, double x[], double w[] ); int cn_geg_00_1_size ( int n, double alpha ); void cn_geg_01_1 ( int n, double alpha, int o, double x[], double w[] ); int cn_geg_01_1_size ( int n, double alpha ); void cn_geg_02_xiu ( int n, double alpha, int o, double x[], double w[] ); int cn_geg_02_xiu_size ( int n, double alpha ); void cn_geg_03_xiu ( int n, double alpha, int o, double x[], double w[] ); int cn_geg_03_xiu_size ( int n, double alpha ); double cn_geg_monomial_integral ( int n, double alpha, int expon[] ); void cn_jac_00_1 ( int n, double alpha, double beta, int o, double x[], double w[] ); int cn_jac_00_1_size ( int n, double alpha, double beta ); void cn_jac_01_1 ( int n, double alpha, double beta, int o, double x[], double w[] ); int cn_jac_01_1_size ( int n, double alpha, double beta ); double cn_jac_monomial_integral ( int n, double alpha, double beta, int expon[] ); void cn_jac_02_xiu ( int n, double alpha, double beta, int o, double x[], double w[] ); int cn_jac_02_xiu_size ( int n, double alpha, double beta ); void cn_leg_01_1 ( int n, int o, double x[], double w[] ); int cn_leg_01_1_size ( int n ); void cn_leg_02_xiu ( int n, int o, double x[], double w[] ); int cn_leg_02_xiu_size ( int n ); void cn_leg_03_1 ( int n, int o, double x[], double w[] ); int cn_leg_03_1_size ( int n ); void cn_leg_03_xiu ( int n, int o, double x[], double w[] ); int cn_leg_03_xiu_size ( int n ); void cn_leg_05_1 ( int n, int option, int o, double x[], double w[] ); int cn_leg_05_1_size ( int n ); void cn_leg_05_2 ( int n, int o, double x[], double w[] ); int cn_leg_05_2_size ( int n ); double cn_leg_monomial_integral ( int n, int expon[] ); double cone_unit_3d ( double func ( double x, double y, double z ) ); double cone_volume_3d ( double r, double h ); double cube_shell_nd ( double func ( int n, double x[] ), int n, double r1, double r2 ); double cube_shell_volume_nd ( int n, double r1, double r2 ); double cube_unit_3d ( double func ( double x, double y, double z ) ); void cube_unit_nd ( double func ( int n, double x[] ), double qa[], double qb[], int n, int k ); double cube_unit_volume_nd ( int n ); double ellipse_area_2d ( double r1, double r2 ); double ellipse_circumference_2d ( double r1, double r2 ); double ellipse_eccentricity_2d ( double r1, double r2 ); double ellipsoid_volume_3d ( double r1, double r2, double r3 ); int en_r2_01_1_size ( int n ); void en_r2_01_1 ( int n, int o, double x[], double w[] ); int en_r2_02_xiu_size ( int n ); void en_r2_02_xiu ( int n, int o, double x[], double w[] ); int en_r2_03_1_size ( int n ); void en_r2_03_1 ( int n, int o, double x[], double w[] ); int en_r2_03_2_size ( int n ); void en_r2_03_2 ( int n, int o, double x[], double w[] ); void en_r2_03_xiu ( int n, int o, double x[], double w[] ); int en_r2_03_xiu_size ( int n ); int en_r2_05_1_size ( int n ); void en_r2_05_1 ( int n, int option, int o, double x[], double w[] ); int en_r2_05_2_size ( int n ); void en_r2_05_2 ( int n, int o, double x[], double w[] ); int en_r2_05_3_size ( int n ); void en_r2_05_3 ( int n, int o, double x[], double w[] ); int en_r2_05_4_size ( int n ); void en_r2_05_4 ( int n, int o, double x[], double w[] ); int en_r2_05_5_size ( int n ); void en_r2_05_5 ( int n, int o, double x[], double w[] ); int en_r2_05_6_size ( int n ); void en_r2_05_6 ( int n, int o, double x[], double w[] ); int en_r2_07_1_size ( int n ); void en_r2_07_1 ( int n, int option, int o, double x[], double w[] ); int en_r2_07_2_size ( int n ); void en_r2_07_2 ( int n, int o, double x[], double w[] ); int en_r2_07_3_size ( int n ); void en_r2_07_3 ( int n, int option, int o, double x[], double w[] ); int en_r2_09_1_size ( int n ); void en_r2_09_1 ( int n, int option, int o, double x[], double w[] ); int en_r2_11_1_size ( int n ); void en_r2_11_1 ( int n, int option, int o, double x[], double w[] ); double en_r2_monomial_integral ( int n, int alpha[] ); double ep1_glg_monomial_integral ( int expon, double alpha ); double ep1_lag_monomial_integral ( int expon ); void epn_glg_00_1 ( int n, double alpha, int o, double x[], double w[] ); int epn_glg_00_1_size ( int n, double alpha ); void epn_glg_01_1 ( int n, double alpha, int o, double x[], double w[] ); int epn_glg_01_1_size ( int n, double alpha ); void epn_glg_02_xiu ( int n, double alpha, int o, double x[], double w[] ); int epn_glg_02_xiu_size ( int n, double alpha ); double epn_glg_monomial_integral ( int n, int expon[], double alpha ); void epn_lag_00_1 ( int n, int o, double x[], double w[] ); int epn_lag_00_1_size ( int n ); void epn_lag_01_1 ( int n, int o, double x[], double w[] ); int epn_lag_01_1_size ( int n ); void epn_lag_02_xiu ( int n, int o, double x[], double w[] ); int epn_lag_02_xiu_size ( int n ); double epn_lag_monomial_integral ( int n, int expon[] ); void gw_02_xiu ( int n, int o, double gamma0, double delta0, double c1, double volume_1d, double x[], double w[] ); int gw_02_xiu_size ( int n ); double hexagon_area_2d ( double r ); double hexagon_sum ( double func ( double x, double y ), double center[2], double r, int order, double xtab[], double ytab[], double weight[] ); double hexagon_unit_area_2d ( ); void hexagon_unit_set ( int rule, int order, double xtab[], double ytab[], double weight[] ); int hexagon_unit_size ( int rule ); int i4_factorial ( int n ); int i4_factorial2 ( int n ); int i4_max ( int i1, int i2 ); int i4_min ( int i1, int i2 ); int i4_power ( int i, int j ); int i4vec_sum ( int n, int a[] ); void i4vec_zero ( int n, int a[] ); void ksub_next2 ( int n, int k, int a[], int *in, int *iout ); void legendre_set ( int order, double xtab[], double weight[] ); void legendre_set_x1 ( int order, double xtab[], double weight[] ); void legendre_set_x2 ( int order, double xtab[], double weight[] ); double lens_half_2d ( double func ( double x, double y ), double center[2], double r, double theta1, double theta2, int order ); double lens_half_area_2d ( double r, double theta1, double theta2 ); double lens_half_h_area_2d ( double r, double h ); double lens_half_w_area_2d ( double r, double w ); double *monomial_value ( int dim_num, int point_num, double x[], int expon[] ); double octahedron_unit_nd ( double func ( int n, double x[] ), int n ); double octahedron_unit_volume_nd ( int n ); double parallelipiped_volume_3d ( double x[4], double y[4], double z[4] ); double parallelipiped_volume_nd ( int n, double v[] ); double polygon_1_2d ( int n, double x[], double y[] ); double polygon_x_2d ( int n, double x[], double y[] ); double polygon_xx_2d ( int n, double x[], double y[] ); double polygon_xy_2d ( int n, double x[], double y[] ); double polygon_y_2d ( int n, double x[], double y[] ); double polygon_yy_2d ( int n, double x[], double y[] ); double pyramid_unit_o01_3d ( double func ( double x, double y, double z ) ); double pyramid_unit_o05_3d ( double func ( double x, double y, double z ) ); double pyramid_unit_o06_3d ( double func ( double x, double y, double z ) ); double pyramid_unit_o08_3d ( double func ( double x, double y, double z ) ); double pyramid_unit_o08b_3d ( double func ( double x, double y, double z ) ); double pyramid_unit_o09_3d ( double func ( double x, double y, double z ) ); double pyramid_unit_o13_3d ( double func ( double x, double y, double z ) ); double pyramid_unit_o18_3d ( double func ( double x, double y, double z ) ); double pyramid_unit_o27_3d ( double func ( double x, double y, double z ) ); double pyramid_unit_o48_3d ( double func ( double x, double y, double z ) ); double pyramid_unit_monomial_3d ( int alpha, int beta, int gamma ); double pyramid_unit_volume_3d ( ); double pyramid_volume_3d ( double r, double h ); double qmdpt ( double func ( int n, double x[] ), int n, int nsub ); double qmult_1d ( double func ( double x ), double a, double b ); double qmult_2d ( double func ( double x, double y ), double a, double b, double fup ( double x ), double flo ( double x ) ); double qmult_3d ( double func ( double x, double y, double z ), double a, double b, double fup1 ( double x ), double flo1 ( double x ), double fup2 ( double x, double y ), double flo2 ( double x, double y ) ); double r8_asin ( double s ); double r8_choose ( int n, int k ); double r8_factorial ( int n ); double r8_hyper_2f1 ( double a, double b, double c, double x ); double r8_mop ( int i ); double r8_psi ( double xx ); void r8_swap ( double *x, double *y ); void r8_swap3 ( double *x, double *y, double *z ); double r8_uniform_01 ( int *seed ); double r8ge_det ( int n, double a_lu[], int pivot[] ); int r8ge_fa ( int n, double a[], int pivot[] ); double r8vec_dot_product ( int n, double a1[], double a2[] ); double r8vec_even_select ( int n, double xlo, double xhi, int ival ); bool r8vec_mirror_next ( int n, double a[] ); void r8vec_print ( int n, double a[], string title ); void r8vec_zero ( int n, double a[] ); double rectangle_3d ( double func ( double x, double y, double z ), double a[3], double b[3] ); double rectangle_sub_2d ( double func ( double x, double y ), double xval[2], double yval[2], int nsub[2], int order, double xtab[], double ytab[], double weight[] ); void rule_adjust ( double a, double b, double c, double d, int order, double x[], double w[] ); int s_len_trim ( char *s ); double simplex_nd ( double func ( int n, double x[] ), int n, double v[] ); double simplex_unit_01_nd ( double func ( int n, double x[] ), int n ); double simplex_unit_03_nd ( double func ( int n, double x[] ), int n ); double simplex_unit_05_nd ( double func ( int n, double x[] ), int n ); double simplex_unit_05_2_nd ( double func ( int n, double x[] ), int n ); double simplex_unit_volume_nd ( int n ); double simplex_volume_nd ( int n, double v[] ); double sin_power_int ( double a, double b, int n ); double sphere_05_nd ( double func ( int n, double x[] ), int n, double center[], double r ); double sphere_07_1_nd ( double func ( int n, double x[] ), int n, double center[], double r ); double sphere_area_3d ( double r ); double sphere_area_nd ( int n, double r ); double sphere_cap_area_2d ( double r, double h ); double sphere_cap_area_3d ( double r, double h ); double sphere_cap_area_nd ( int dim_num, double r, double h ); double sphere_cap_volume_2d ( double r, double h ); double sphere_cap_volume_3d ( double r, double h ); double sphere_cap_volume_nd ( int dim_num, double r, double h ); double sphere_k ( int n ); double sphere_monomial_int_nd ( int n, double r, int e[] ); double sphere_shell_03_nd ( double func ( int n, double x[] ), int n, double center[], double r1, double r2 ); double sphere_shell_volume_nd ( int n, double r1, double r2 ); double sphere_unit_03_nd ( double func ( int n, double x[] ), int n ); double sphere_unit_04_nd ( double func ( int n, double x[] ), int n ); double sphere_unit_05_nd ( double func ( int n, double x[] ), int n ); double sphere_unit_07_3d ( double func ( double x, double y, double z ) ); double sphere_unit_07_1_nd ( double func ( int n, double x[] ), int n ); double sphere_unit_07_2_nd ( double func ( int n, double x[] ), int n ); double sphere_unit_11_3d ( double func ( double x, double y, double z ) ); double sphere_unit_11_nd ( double func ( int n, double x[] ), int n ); double sphere_unit_14_3d ( double func ( double x, double y, double z ) ); double sphere_unit_15_3d ( double func ( double x, double y, double z ) ); double sphere_unit_area_3d ( ); double sphere_unit_area_nd ( int n ); void sphere_unit_area_values ( int *n_data, int *n, double *area ); double sphere_unit_monomial_nd ( int n, int p[] ); double sphere_unit_volume_nd ( int dim_num ); void sphere_unit_volume_values ( int *n_data, int *n, double *volume ); double sphere_volume_2d ( double r ); double sphere_volume_3d ( double r ); double sphere_volume_nd ( int dim_num, double r ); double square_sum ( double func ( double x, double y ), double center[2], double r, int order, double xtab[], double ytab[], double weight[] ); void square_unit_set ( int rule, int order, double xtab[], double ytab[], double weight[] ); int square_unit_size ( int rule ); double square_unit_sum ( double func ( double x, double y ), int order, double xtab[], double ytab[], double weight[] ); void subset_gray_next ( int n, int a[], bool *more, int *ncard, int *iadd ); double tetra_07 ( double func ( double x, double y, double z ), double x[], double y[], double z[] ); double tetra_sum ( double func ( double x, double y, double z ), double x[4], double y[4], double z[4], int order, double xtab[], double ytab[], double ztab[], double weight[] ); double tetra_tproduct ( double func ( double x, double y, double z ), int order, double x[4], double y[4], double z[4] ); int tetra_unit_size ( int rule ); void tetra_unit_set ( int rule, int order, double xtab[], double ytab[], double ztab[], double weight[] ); double tetra_unit_sum ( double func ( double x, double y, double z ), int order, double xtab[], double ytab[], double ztab[], double weight[] ); double tetra_unit_volume ( ); double tetra_volume ( double x[4], double y[4], double z[4] ); void timestamp ( ); double torus_1 ( double func ( double x, double y, double z ), double r1, double r2, int n ); double torus_14s ( double func ( double x, double y, double z ), double r1, double r2 ); double torus_5s2 ( double func ( double x, double y, double z ), double r1, double r2 ); double torus_6s2 ( double func ( double x, double y, double z ), double r1, double r2 ); double torus_area_3d ( double r1, double r2 ); double torus_square_14c ( double func ( double x, double y, double z ), double r1, double r2 ); double torus_square_5c2 ( double func ( double x, double y, double z ), double r1, double r2 ); double torus_square_area_3d ( double r1, double r2 ); double torus_square_volume_3d ( double r1, double r2 ); double torus_volume_3d ( double r1, double r2 ); void triangle_rule_adjust ( double xval[3], double yval[3], int order, double xtab[], double ytab[], double weight[], double xtab2[], double ytab2[], double weight2[] ); double triangle_sub ( double func ( double x, double y ), double xval[3], double yval[], int nsub, int order, double xtab[], double ytab[], double weight[] ); double triangle_sum ( double func ( double x, double y ), double xval[3], double yval[3], int order, double xtab[], double ytab[], double weight[] ); double triangle_sum_adjusted ( double func ( double x, double y ), int order, double xtab[], double ytab[], double weight[] ); void triangle_unit_product_set ( int rule, int order, double xtab[], double ytab[], double weight[] ); int triangle_unit_product_size ( int rule ); void triangle_unit_set ( int rule, int order, double xtab[], double ytab[], double weight[] ); int triangle_unit_size ( int rule ); double triangle_unit_sum ( double func ( double x, double y ), int order, double xtab[], double ytab[], double weight[] ); double triangle_unit_volume ( ); double triangle_volume ( double x[3], double y[3] ); double *tvec_even ( int nt ); double *tvec_even2 ( int nt ); double *tvec_even3 ( int nt ); double *tvec_even_bracket ( int nt, double theta1, double theta2 ); double *tvec_even_bracket2 ( int nt, double theta1, double theta2 ); double *tvec_even_bracket3 ( int nt, double theta1, double theta2 ); void vec_lex_next ( int dim_num, int base, int a[], bool *more );