void daxpy ( int n, double da, double dx[], int incx, double dy[], int incy ); double ddot ( int n, double dx[], int incx, double dy[], int incy ); double dnrm2 ( int n, double x[], int incx ); void drot ( int n, double x[], int incx, double y[], int incy, double c, double s ); void drotg ( double *sa, double *sb, double *c, double *s ); void dscal ( int n, double sa, double x[], int incx ); int dsvdc ( double a[], int lda, int m, int n, double s[], double e[], double u[], int ldu, double v[], int ldv, double work[], int job ); void dswap ( int n, double x[], int incx, double y[], int incy ); int i4_max ( int i1, int i2 ); int i4_min ( int i1, int i2 ); string i4_to_string ( int i4, string format ); int i4_uniform_ab ( int a, int b, int &seed ); int i4vec_max ( int n, int a[] ); void imtqlx ( int n, double d[], double e[], double z[] ); 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 ); double r8_sign ( double x ); double r8_uniform_ab ( double a, double b, int &seed ); double *r8mat_copy_new ( int m, int n, double a1[] ); double *r8mat_mm_new ( int n1, int n2, int n3, double a[], double b[] ); double *r8mat_mtv_new ( int m, int n, double a[], double x[] ); double *r8mat_mv_new ( int m, int n, double a[], double x[] ); void r8mat_print ( int m, int n, double a[], string title ); void r8mat_print_some ( int m, int n, double a[], int ilo, int jlo, int ihi, int jhi, string title ); void r8poly_print ( int n, double a[], string title ); double r8vec_dot_product ( int n, double a1[], double a2[] ); bool r8vec_in_ab ( int n, double x[], double a, double b ); double *r8vec_linspace_new ( int n, double a_first, double a_last ); double r8vec_max ( int n, double r8vec[] ); void r8vec_print ( int n, double a[], string title ); double *r8vec_uniform_01_new ( int n, int &seed ); double *r8vec_uniform_ab_new ( int n, double b, double c, int &seed ); void r8vec2_print ( int n, double a1[], double a2[], string title ); double *svd_solve ( int m, int n, double a[], double b[] ); double *t_mass_matrix ( int n ); double t_moment ( int e ); double *t_polynomial ( int m, int n, double x[] ); void t_polynomial_01_values ( int &n_data, int &n, double &x, double &fx ); double *t_polynomial_ab ( double a, double b, int m, int n, double x[] ); double t_polynomial_ab_value ( double a, double b, int n, double x ); double *t_polynomial_coefficients ( int n ); void t_polynomial_plot ( int n_num, int n_val[], string output_filename ); double t_polynomial_value ( int n, double x ); void t_polynomial_values ( int &n_data, int &n, double &x, double &fx ); double *t_polynomial_zeros ( int n ); double *t_project_coefficients ( int n, double f ( double x ) ); double *t_project_coefficients_ab ( int n, double f ( double x ), double a, double b ); double *t_project_coefficients_data ( double a, double b, int m, int n, double x[], double d[] ); double *t_project_value ( int m, int n, double x[], double c[] ); double *t_project_value_ab ( int m, int n, double x[], double c[], double a, double b ); void t_quadrature_rule ( int n, double t[], double w[] ); double tt_product ( int i, int j, double x ); double tt_product_integral ( int i, int j ); double ttt_product_integral ( int i, int j, int k ); double tu_product ( int i, int j, double x ); void timestamp ( ); double *u_mass_matrix ( int n ); double u_moment ( int e ); double *u_polynomial ( int m, int n, double x[] ); void u_polynomial_01_values ( int &n_data, int &n, double &x, double &fx ); double *u_polynomial_ab ( double a, double b, int m, int n, double x[] ); double u_polynomial_ab_value ( double a, double b, int n, double x ); double *u_polynomial_coefficients ( int n ); void u_polynomial_plot ( int n_num, int n_val[], string output_filename ); double u_polynomial_value ( int n, double x ); void u_polynomial_values ( int &n_data, int &n, double &x, double &fx ); double *u_polynomial_zeros ( int n ); void u_quadrature_rule ( int n, double t[], double w[] ); double uu_product ( int i, int j, double x ); double uu_product_integral ( int i, int j ); double *v_mass_matrix ( int n ); double v_moment ( int e ); double *v_polynomial ( int m, int n, double x[] ); void v_polynomial_01_values ( int &n_data, int &n, double &x, double &fx ); double *v_polynomial_ab ( double a, double b, int m, int n, double x[] ); double v_polynomial_ab_value ( double a, double b, int n, double x ); double *v_polynomial_coefficients ( int n ); void v_polynomial_plot ( int n_num, int n_val[], string output_filename ); double v_polynomial_value ( int n, double x ); void v_polynomial_values ( int &n_data, int &n, double &x, double &fx ); double *v_polynomial_zeros ( int n ); void v_quadrature_rule ( int n, double t[], double w[] ); double vv_product_integral ( int i, int j ); double *w_mass_matrix ( int n ); double w_moment ( int e ); double *w_polynomial ( int m, int n, double x[] ); void w_polynomial_01_values ( int &n_data, int &n, double &x, double &fx ); double *w_polynomial_ab ( double a, double b, int m, int n, double x[] ); double w_polynomial_ab_value ( double a, double b, int n, double x ); double *w_polynomial_coefficients ( int n ); void w_polynomial_plot ( int n_num, int n_val[], string output_filename ); double w_polynomial_value ( int n, double x ); void w_polynomial_values ( int &n_data, int &n, double &x, double &fx ); double *w_polynomial_zeros ( int n ); void w_quadrature_rule ( int n, double t[], double w[] ); double ww_product_integral ( int i, int j );