double c8_abs ( complex x ); complex c8_acos ( complex c1 ); complex c8_acosh ( complex c1 ); complex c8_add ( complex c1, complex c2 ); double c8_arg ( complex x ); complex c8_asin ( complex c1 ); complex c8_asinh ( complex c1 ); complex c8_atan ( complex c1 ); complex c8_atanh ( complex c1 ); complex c8_conj ( complex c1 ); void c8_copy ( complex c1, complex c2 ); complex c8_cos ( complex c1 ); complex c8_cosh ( complex c1 ); complex c8_cube_root ( complex x ); complex c8_div ( complex c1, complex c2 ); complex c8_div_r8 ( complex c1, double r ); complex c8_exp ( complex c1 ); complex c8_i ( ); double c8_imag ( complex c ); complex c8_inv ( complex c1 ); bool c8_le_l1 ( complex x, complex y ); bool c8_le_l2 ( complex x, complex y ); bool c8_le_li ( complex x, complex y ); complex c8_log ( complex c1 ); double c8_mag ( complex x ); complex c8_mul ( complex c1, complex c2 ); complex c8_neg ( complex c1 ); complex c8_nint ( complex c1 ); double c8_norm_l1 ( complex x ); double c8_norm_l2 ( complex x ); double c8_norm_li ( complex x ); complex c8_normal_01 ( int &seed ); complex c8_one ( ); void c8_print ( complex a, string title ); double c8_real ( complex c ); complex c8_sin ( complex c1 ); complex c8_sinh ( complex c1 ); complex c8_sqrt ( complex x ); complex c8_sub ( complex c1, complex c2 ); void c8_swap ( complex &x, complex &y ); complex c8_tan ( complex c1 ); complex c8_tanh ( complex c1 ); void c8_to_cartesian ( complex c, double &x, double &y ); void c8_to_polar ( complex c, double &r, double &theta ); complex c8_uniform_01 ( int &seed ); complex c8_zero ( ); void c8mat_add ( int m, int n, complex alpha, complex a[], complex beta, complex b[], complex c[] ); void c8mat_add_r8 ( int m, int n, double alpha, complex a[], double beta, complex b[], complex c[] ); void c8mat_copy ( int m, int n, complex a1[], complex a2[] ); complex *c8mat_copy_new ( int m, int n, complex a1[] ); void c8mat_fss ( int n, complex a[], int nb, complex x[] ); complex *c8mat_fss_new ( int n, complex a[], int nb, complex b[] ); complex *c8mat_identity_new ( int n ); complex *c8mat_indicator_new ( int m, int n ); void c8mat_minvm ( int n1, int n2, complex a[], complex b[], complex e[] ); complex *c8mat_minvm_new ( int n1, int n2, complex a[], complex b[] ); void c8mat_mm ( int n1, int n2, int n3, complex a[], complex b[], complex c[] ); complex *c8mat_mm_new ( int n1, int n2, int n3, complex a[], complex b[] ); void c8mat_nint ( int m, int n, complex a[] ); double c8mat_norm_fro ( int m, int n, complex a[] ); double c8mat_norm_l1 ( int m, int n, complex a[] ); double c8mat_norm_li ( int m, int n, complex a[] ); void c8mat_print ( int m, int n, complex a[], string title ); void c8mat_print_some ( int m, int n, complex a[], int ilo, int jlo, int ihi, int jhi, string title ); void c8mat_scale ( int m, int n, complex alpha, complex a[] ); void c8mat_scale_r8 ( int m, int n, double alpha, complex a[] ); void c8mat_uniform_01 ( int m, int n, int &seed, complex c[] ); complex *c8mat_uniform_01_new ( int m, int n, int &seed ); complex *c8mat_zero_new ( int m, int n ); void c8vec_copy ( int n, complex a1[], complex a2[] ); complex *c8vec_copy_new ( int n, complex a1[] ); complex *c8vec_indicator_new ( int n ); void c8vec_nint ( int n, complex a[] ); double c8vec_norm_l1 ( int n, complex a[] ); double c8vec_norm_l2 ( int n, complex a[] ); double c8vec_norm_li ( int n, complex a[] ); void c8vec_print ( int n, complex a[], string title ); void c8vec_print_part ( int n, complex a[], int max_print, string title ); void c8vec_print_some ( int n, complex a[], int i_lo, int i_hi, string title ); void c8vec_sort_a_l1 ( int n, complex x[] ); void c8vec_sort_a_l2 ( int n, complex x[] ); void c8vec_sort_a_li ( int n, complex x[] ); complex *c8vec_spiral_new ( int n, int m, complex c1, complex c2 ); complex *c8vec_uniform_01_new ( int n, int &seed ); complex *c8vec_unity_new ( int n ); complex cartesian_to_c8 ( double x, double y ); complex polar_to_c8 ( double r, double theta ); double r8_abs ( double x ); double r8_atan ( double y, double x ); complex r8_csqrt ( double x ); double r8_floor ( double x ); double r8_max ( double x, double y ); double r8_sign ( double x ); double r8_uniform_01 ( int &seed ); void r8poly2_root ( double a, double b, double c, complex &r1, complex &r2 ); void r8poly3_root ( double a, double b, double c, double d, complex &r1, complex &r2, complex &r3 ); void r8poly4_root ( double a, double b, double c, double d, double e, complex &r1, complex &r2, complex &r3, complex &r4 ); void sort_heap_external ( int n, int &indx, int &i, int &j, int isgn ); void timestamp ( );