double *a123 ( ); double a123_determinant ( ); double *a123_eigen_left ( ); double *a123_eigen_right ( ); double *a123_eigenvalues ( ); double *a123_inverse ( ); double *a123_null_left ( ); double *a123_null_right ( ); void a123_plu ( double p[], double l[], double u[] ); void a123_qr ( double q[], double r[] ); double *a123_rhs ( ); double *a123_solution ( ); void a123_svd ( double u[], double s[], double v[] ); double *aegerter ( int n ); double aegerter_condition ( int n ); double aegerter_determinant ( int n ); double *aegerter_eigenvalues ( int n ); double *aegerter_inverse ( int n ); double *anticirculant ( int m, int n, double x[] ); double anticirculant_determinant ( int n, double x[] ); double *antihadamard ( int n ); double antihadamard_determinant ( int n ); double *antisymm_random ( int n, int key ); double *archimedes ( ); double *archimedes_null_right ( ); double *bab ( int n, double alpha, double beta ); double bab_condition ( int n, double alpha, double beta ); double bab_determinant ( int n, double alpha, double beta ); double *bab_eigen_right ( int n, double alpha, double beta ); double *bab_eigenvalues ( int n, double alpha, double beta ); double *bab_inverse ( int n, double alpha, double beta ); double *bauer ( ); double bauer_condition ( ); double bauer_determinant ( ); double *bauer_inverse ( ); double *bernstein ( int n ); double bernstein_determinant ( int n ); double *bernstein_inverse ( int n ); double *bernstein_poly_01 ( int n, double x ); double *bernstein_vandermonde ( int n ); double *bimarkov_random ( int n, int key ); double *bis ( double alpha, double beta, int m, int n ); double bis_condition ( double alpha, double beta, int n ); double bis_determinant ( double alpha, double beta, int n ); double *bis_eigenvalues ( double alpha, double beta, int n ); double *bis_inverse ( double alpha, double beta, int n ); double *biw ( int n ); double biw_condition ( int n ); double biw_determinant ( int n ); double *biw_inverse ( int n ); double *bodewig ( ); double *bodewig ( ); double bodewig_condition ( ); double bodewig_determinant ( ); double *bodewig_eigen_right ( ); double *bodewig_eigenvalues ( ); double *bodewig_inverse ( ); void bodewig_plu ( double p[], double l[], double u[] ); double *bodewig_rhs ( ); double *bodewig_solution ( ); double *boothroyd ( int n ); double boothroyd_condition ( int n ); double boothroyd_determinant ( int n ); double *boothroyd_inverse ( int n ); double *borderband ( int n ); double borderband_determinant ( int n ); double *borderband_inverse ( int n ); void borderband_plu ( int n, double p[], double l[], double u[] ); void bvec_next_grlex ( int n, int bvec[] ); double c8_abs ( complex x ); complex c8_i ( ); bool c8_le_l2 ( complex x, complex y ); complex c8_normal_01 ( int &seed ); complex c8_one ( ); void c8_swap ( complex *x, complex *y ); complex c8_uniform_01 ( int &seed ); complex c8_zero ( ); complex *c8mat_copy_new ( int m, int n, complex a[] ); complex *c8mat_identity ( int n ); complex *c8mat_mm_new ( int n1, int n2, int n3, complex a[], complex b[] ); double c8mat_norm_fro ( 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 ); complex *c8mat_uniform_01 ( int m, int n, int &seed ); complex *c8mat_zero_new ( int m, int n ); complex *c8vec_copy_new ( int n, complex a[] ); double c8vec_norm_l2 ( int n, complex a[] ); void c8vec_print ( int n, complex a[], string title ); complex *c8vec_uniform_01 ( int n, int &seed ); complex *c8vec_unity ( int n ); double *carry ( int n, int alpha ); double carry_determinant ( int n, int alpha ); double *carry_eigen_left ( int n, int alpha ); double *carry_eigen_right ( int n, int alpha ); double *carry_eigenvalues ( int n, int alpha ); double *carry_inverse ( int n, int alpha ); double *cauchy ( int n, double x[], double y[] ); double cauchy_determinant ( int n, double x[], double y[] ); double *cauchy_inverse ( int n, double x[], double y[] ); double *cheby_diff1 ( int n ); double *cheby_diff1_null_left ( int m, int n ); double *cheby_diff1_null_right ( int m, int n ); double *cheby_t ( int n ); double cheby_t_determinant ( int n ); double *cheby_t_inverse ( int n ); double *cheby_u ( int n ); double cheby_u_determinant ( int n ); double *cheby_u_inverse ( int n ); double *cheby_u_polynomial ( int n, double x ); double *cheby_van1 ( int m, double x1, double x2, int n, double x[] ); double *cheby_van2 ( int n ); double cheby_van2_determinant ( int n ); double *cheby_van2_inverse ( int n ); double *cheby_van3 ( int n ); double cheby_van3_determinant ( int n ); double *cheby_van3_inverse ( int n ); double *chow ( double alpha, double beta, int m, int n ); double chow_determinant ( double alpha, double beta, int n ); double *chow_eigen_left ( double alpha, double beta, int n ); double *chow_eigen_right ( double alpha, double beta, int n ); double *chow_eigenvalues ( double alpha, double beta, int n ); double *chow_inverse ( double alpha, double beta, int n ); double *circulant ( int m, int n, double x[] ); double circulant_determinant ( int n, double x[] ); complex *circulant_eigenvalues ( int n, double x[] ); double *circulant_inverse ( int n, double x[] ); double *circulant2 ( int n ); double circulant2_determinant ( int n ); complex *circulant2_eigenvalues ( int n ); double *circulant2_inverse ( int n ); double *clement1 ( int n ); double clement1_determinant ( int n ); double *clement1_eigenvalues ( int n ); double *clement1_inverse ( int n ); double *clement2 ( int n, double x[], double y[] ); double clement2_determinant ( int n, double x[], double y[] ); double *clement2_inverse ( int n, double x[], double y[] ); double *colleague ( int n, double c[] ); double *combin ( double alpha, double beta, int n ); double combin_condition ( double alpha, double beta, int n ); double combin_determinant ( double alpha, double beta, int n ); double *combin_eigen_right ( double alpha, double beta, int n ); double *combin_eigenvalues ( double alpha, double beta, int n ); double *combin_inverse ( double alpha, double beta, int n ); double *companion ( int n, double x[] ); double companion_condition ( int n, double x[] ); double companion_determinant ( int n, double x[] ); double *companion_inverse ( int n, double x[] ); double complete_symmetric_poly ( int n, int r, double x[] ); complex *complex3 ( ); complex *complex3_inverse ( ); double *complex_i ( ); double complex_i_determinant ( ); double *complex_i_inverse ( ); double *conex1 ( double alpha ); double conex1_condition ( double alpha ); double conex1_determinant ( double alpha ); double *conex1_inverse ( double alpha ); double *conex2 ( double alpha ); double conex2_condition ( double alpha ); double conex2_determinant ( double alpha ); double *conex2_inverse ( double alpha ); double *conex3 ( int n ); double conex3_condition ( int n ); double conex3_determinant ( int n ); double *conex3_inverse ( int n ); double *conex4 ( ); double conex4_condition ( ); double conex4_determinant ( ); double *conex4_inverse ( ); double *conference ( int n ); double conference_determinant ( int n ); double *conference_inverse ( int n ); double *creation ( int m, int n ); double creation_determinant ( int n ); double *creation_null_left ( int m, int n ); double *creation_null_right ( int m, int n ); double *cycol_random ( int m, int n, int k, int key ); double *daub2 ( int n ); double daub2_condition ( int n ); double daub2_determinant ( int n ); double *daub2_inverse ( int n ); double *daub4 ( int n ); double daub4_condition ( int n ); double daub4_determinant ( int n ); double *daub4_inverse ( int n ); double *daub6 ( int n ); double daub6_condition ( int n ); double daub6_determinant ( int n ); double *daub6_inverse ( int n ); double *daub8 ( int n ); double daub8_condition ( int n ); double daub8_determinant ( int n ); double *daub8_inverse ( int n ); double *daub10 ( int n ); double daub10_condition ( int n ); double daub10_determinant ( int n ); double *daub10_inverse ( int n ); double *daub12 ( int n ); double daub12_condition ( int n ); double daub12_determinant ( int n ); double *daub12_inverse ( int n ); double *diagonal ( int m, int n, double x[] ); double diagonal_condition ( int n, double x[] ); double diagonal_determinant ( int n, double x[] ); double *diagonal_eigen_left ( int n, double d[] ); double *diagonal_eigen_right ( int n, double d[] ); double *diagonal_eigenvalues ( int n, double x[] ); double *diagonal_inverse ( int n, double x[] ); double *dif1 ( int m, int n ); double dif1_determinant ( int n ); complex *dif1_eigenvalues ( int n ); double *dif1_inverse ( int n ); double *dif1_null_left ( int m, int n ); double *dif1_null_right ( int m, int n ); double *dif1cyclic ( int n ); double dif1cyclic_determinant ( int n ); double *dif1cyclic_null_left ( int m, int n ); double *dif1cyclic_null_right ( int m, int n ); double *dif2 ( int m, int n ); double dif2_condition ( int n ); double dif2_determinant ( int n ); double *dif2_eigen_right ( int n ); double *dif2_eigenvalues ( int n ); double *dif2_inverse ( int n ); double *dif2_llt ( int n ); void dif2_plu ( int n, double p[], double l[], double u[] ); double *dif2_rhs ( int m, int k ); double *dif2_rtr ( int n ); double *dif2_solution ( int n, int k ); double *dif2cyclic ( int n ); double dif2cyclic_determinant ( int n ); double *dif2cyclic_null_left ( int m, int n ); double *dif2cyclic_null_right ( int m, int n ); double *dorr ( double alpha, int n ); double dorr_determinant ( double alpha, int n ); double *dorr_inverse ( double alpha, int n ); double *downshift ( int n ); double downshift_condition ( int n ); double downshift_determinant ( int n ); complex *downshift_eigenvalues ( int n ); double *downshift_inverse ( int n ); double *eberlein ( double alpha, int n ); double eberlein_determinant ( double alpha, int n ); double *eberlein_eigenvalues ( double alpha, int n ); double *eberlein_null_left ( int m, int n ); double *eulerian ( int m, int n ); double eulerian_determinant ( int n ); double *eulerian_inverse ( int n ); double *exchange ( int m, int n ); double exchange_condition ( int n ); double exchange_determinant ( int n ); double *exchange_eigen_right ( int n ); double *exchange_eigenvalues ( int n ); double *exchange_inverse ( int n ); double *fibonacci1 ( int n, double f1, double f2 ); double fibonacci1_determinant ( int n, double f1, double f2 ); double *fibonacci1_null_left ( int m, int n, double f1, double f2 ); double *fibonacci1_null_right ( int m, int n, double f1, double f2 ); double *fibonacci2 ( int n ); double fibonacci2_condition ( int n ); double fibonacci2_determinant ( int n ); double *fibonacci2_eigenvalues ( int n ); double *fibonacci2_inverse ( int n ); double *fibonacci3 ( int n ); double fibonacci3_determinant ( int n ); complex *fibonacci3_eigenvalues ( int n ); double *fibonacci3_inverse ( int n ); double *fiedler ( int m, int n, double x[] ); double fiedler_determinant ( int n, double x[] ); double *fiedler_inverse ( int n, double x[] ); double *forsythe ( double alpha, double beta, int n ); double forsythe_determinant ( double alpha, double beta, int n ); complex *forsythe_eigenvalues ( double alpha, double beta, int n ); double *forsythe_inverse ( double alpha, double beta, int n ); complex *fourier ( int n ); complex fourier_determinant ( int n ); complex *fourier_eigenvalues ( int n ); complex *fourier_inverse ( int n ); double *fourier_cosine ( int n ); double fourier_cosine_determinant ( int n ); double *fourier_cosine_inverse ( int n ); double *fourier_sine ( int n ); double fourier_sine_determinant ( int n ); double *fourier_sine_inverse ( int n ); double *frank ( int n ); double frank_determinant ( int n ); double *frank_eigenvalues ( int n ); double *frank_inverse ( int n ); double *frank_rhs ( int m, int k ); double *frank_solution ( int n, int k ); double *gear ( int ii, int jj, int n ); double gear_determinant ( int ii, int jj, int n ); double *gear_eigenvalues ( int ii, int jj, int n ); double *gfpp ( int n, double alpha ); double gfpp_condition ( int n, double alpha ); double gfpp_determinant ( int n, double alpha ); double *gfpp_inverse ( int n, double alpha ); void gfpp_plu ( int n, double alpha, double p[], double l[], double u[] ); double *givens ( int m, int n ); double givens_condition ( int n ); double givens_determinant ( int n ); double *givens_eigenvalues ( int n ); double *givens_inverse ( int n ); double *givens_llt ( int n ); void givens_plu ( int n, double p[], double l[], double u[] ); double *gk316 ( int n ); double gk316_determinant ( int n ); double *gk316_eigenvalues ( int n ); double *gk316_inverse ( int n ); double *gk323 ( int m, int n ); double gk323_determinant ( int n ); double *gk323_inverse ( int n ); double *gk324 ( int m, int n, double x[] ); double gk324_determinant ( int n, double x[] ); double *gk324_inverse ( int n, double x[] ); double *grcar ( int m, int n, int k ); double *hadamard ( int m, int n ); double *hamming ( int m, int n ); double *hamming_null_right ( int m, int n ); double *hankel ( int n, double x[] ); double *hankel_n ( int n ); double hankel_n_condition ( int n ); double hankel_n_determinant ( int n ); double *hankel_n_inverse ( int n ); double *hanowa ( double alpha, int n ); double hanowa_determinant ( double alpha, int n ); complex *hanowa_eigenvalues ( double alpha, int n ); double *hanowa_inverse ( double alpha, int n ); double *harman ( ); double harman_condition ( ); double harman_determinant ( ); double *harman_eigenvalues ( ); double *harman_inverse ( ); double *hartley ( int n ); double hartley_condition ( int n ); double hartley_determinant ( int n ); double *hartley_inverse ( int n ); double *helmert ( int n ); double helmert_determinant ( int n ); double *helmert_inverse ( int n ); double *helmert2 ( int n, double x[] ); double *helmert2_inverse ( int n, double x[] ); double *hermite ( int n ); double hermite_determinant ( int n ); double *hermite_inverse ( int n ); double *hermite_roots ( int order ); double *herndon ( int n ); double herndon_determinant ( int n ); double *herndon_eigenvalues ( int n ); double *herndon_inverse ( int n ); complex *hess4 ( ); complex hess4_determinant ( ); complex *hess4_eigen_right ( ); complex *hess4_eigenvalues ( ); complex *hess4_inverse ( ); double *hess5 ( ); double hess5_determinant ( ); complex *hess5_eigen_right ( ); complex *hess5_eigenvalues ( ); double *hess5_inverse ( ); double *hilbert ( int m, int n ); double hilbert_determinant ( int n ); double *hilbert_inverse ( int n ); double *hoffman ( double omega ); double *hoffman_rhs ( ); double *hoffman_optimum ( ); double *householder ( int n, double x[] ); double householder_determinant ( int n, double x[] ); double *householder_eigenvalues ( int n, double x[] ); double *householder_inverse ( int n, double x[] ); void i4_factor ( int n, int maxfactor, int &nfactor, int factor[], int exponent[], int &nleft ); int i4_huge ( ); bool i4_is_even ( int i ); bool i4_is_odd ( int i ); bool i4_is_prime ( int n ); int i4_log_10 ( int i ); int i4_max ( int i1, int i2 ); int i4_min ( int i1, int i2 ); int i4_modp ( int i, int j ); int i4_power ( int i, int j ); int i4_rise ( int i, int n ); int i4_sign ( int i ); int i4_uniform_ab ( int a, int b, int &seed ); int i4_wrap ( int ival, int ilo, int ihi ); void i4mat_print ( int m, int n, int a[], string title ); void i4mat_print_some ( int m, int n, int a[], int ilo, int jlo, int ihi, int jhi, string title ); int i4vec_index ( int n, int a[], int aval ); int *i4vec_indicator_new ( int n ); void i4vec_print ( int n, int a[], string title ); double *idem_random ( int n, int rank, int key ); double idem_random_determinant ( int n, int rank, int key ); double *idem_random_eigen_right ( int n, int rank, int key ); double *idem_random_eigenvalues ( int n, int rank, int key ); double *identity ( int m, int n ); double identity_condition ( int n ); double identity_determinant ( int n ); double *identity_eigen_left ( int n ); double *identity_eigen_right ( int n ); double *identity_eigenvalues ( int n ); double *identity_inverse ( int n ); double *ijfact1 ( int n ); double ijfact1_determinant ( int n ); double *ijfact2 ( int n ); double ijfact2_determinant ( int n ); double *ill3 ( ); double ill3_condition ( ); double ill3_determinant ( ); double *ill3_eigen_right ( ); double *ill3_eigenvalues ( ); double *ill3_inverse ( ); double *indicator ( int m, int n ); double *integration ( double alpha, int n ); double integration_determinant ( double alpha, int n ); double *integration_eigenvalues ( double alpha, int n ); double *integration_inverse ( double alpha, int n ); double *invol ( int n ); double invol_determinant ( int n ); double *invol_eigenvalues ( int n ); double *invol_inverse ( int n ); double *invol_random ( int n, int rank, int key ); double *jacobi ( int m, int n ); double jacobi_determinant ( int n ); double *jacobi_eigenvalues ( int n ); double *jacobi_inverse ( int n ); void jacobi_iterate ( int n, double a[], double lambda[], double x[] ); int jacobi_symbol ( int q, int p ); double *jordan ( int m, int n, double alpha ); double jordan_condition ( int n, double alpha ); double jordan_determinant ( int n, double alpha ); double *jordan_eigenvalues ( int n, double alpha ); double *jordan_inverse ( int n, double alpha ); double *kahan ( double alpha, int m, int n ); double kahan_determinant ( double alpha, int n ); double *kahan_inverse ( double alpha, int n ); double *kershaw ( ); double kershaw_condition ( ); double kershaw_determinant ( ); double *kershaw_eigen_right ( ); double *kershaw_eigenvalues ( ); double *kershaw_inverse ( ); double *kershaw_llt ( ); double *kershawtri ( int n, double x[] ); double kershawtri_determinant ( int n, double x[] ); double *kershawtri_inverse ( int n, double x[] ); double *kms ( double alpha, int m, int n ); double kms_determinant ( double alpha, int n ); double *kms_eigen_right ( double alpha, int n ); double *kms_eigenvalues ( double alpha, int n ); double *kms_eigenvalues_theta ( double alpha, int n ); double kms_eigenvalues_theta_f ( double alpha, int n, double t ); double *kms_inverse ( double alpha, int n ); void kms_ldl ( double alpha, int n, double **l, double **d ); void kms_plu ( double alpha, int n, double p[], double l[], double u[] ); double *krylov ( int n, double b[], double x[] ); double *laguerre ( int n ); double laguerre_determinant ( int n ); double *laguerre_inverse ( int n ); double *lauchli ( double alpha, int m, int n ); double *lauchli_null_left ( double alpha, int m, int n ); double *legendre ( int n ); double legendre_determinant ( int n ); double *legendre_inverse ( int n ); int legendre_symbol ( int q, int p ); double *legendre_van ( int m, int n, double x[] ); double *legendre_zeros ( int n ); double *lehmer ( int m, int n ); double lehmer_determinant ( int n ); double *lehmer_inverse ( int n ); double *lehmer_llt ( int n ); void lehmer_plu ( int n, double p[], double l[], double u[] ); double *leslie ( double b, double di, double da ); double leslie_determinant ( double b, double di, double da ); double *lesp ( int m, int n ); double lesp_determinant ( int n ); double *lesp_inverse ( int n ); double *lietzke ( int n ); double lietzke_condition ( int n ); double lietzke_determinant ( int n ); double *lietzke_inverse ( int n ); double *line_adj ( int n ); double line_adj_determinant ( int n ); double *line_adj_eigen_right ( int n ); double *line_adj_eigenvalues ( int n ); double *line_adj_inverse ( int n ); double *line_adj_null_left ( int m, int n ); double *line_adj_null_right ( int m, int n ); double *line_loop_adj ( int n ); double line_loop_adj_determinant ( int n ); double *line_loop_adj_eigen_right ( int n ); double *line_loop_adj_eigenvalues ( int n ); double *loewner ( double w[], double x[], double y[], double z[], int n ); double *lotkin ( int m, int n ); double lotkin_determinant ( int n ); double *lotkin_inverse ( int n ); double *markov_random ( int n, int key ); double *maxij ( int m, int n ); double maxij_condition ( int n ); double maxij_determinant ( int n ); double *maxij_inverse ( int n ); void maxij_plu ( int n, double p[], double l[], double u[] ); int mertens ( int n ); void mertens_values ( int &n_data, int &n, int &c ); double *milnes ( int m, int n, double x[] ); double milnes_determinant ( int n, double x[] ); double *milnes_inverse ( int n, double x[] ); double *minij ( int m, int n ); double minij_condition ( int n ); double minij_determinant ( int n ); double *minij_eigenvalues ( int n ); double *minij_inverse ( int n ); double *minij_llt ( int n ); void minij_plu ( int n, double p[], double l[], double u[] ); int moebius ( int n ); void moebius_values ( int &n_data, int &n, int &c ); double *moler1 ( double alpha, int m, int n ); double moler1_determinant ( double alpha, int n ); double *moler1_inverse ( double alpha, int n ); double *moler1_llt ( double alpha, int ); void moler1_plu ( double alpha, int n, double p[], double l[], double u[] ); double *moler2 ( ); double moler2_determinant ( ); double *moler2_eigenvalues ( ); double *moler2_null_left ( ); double *moler2_null_right ( ); double *moler3 ( int m, int n ); double moler3_determinant ( int n ); double *moler3_inverse ( int n ); double *moler3_llt ( int n ); void moler3_plu ( int n, double p[], double l[], double u[] ); double *moler4 ( ); double moler4_condition ( ); double moler4_determinant ( ); double *moler4_eigenvalues ( ); double *moler4_inverse ( ); double *neumann ( int nrow, int ncol ); double neumann_determinant ( int n ); double *neumann_null_right ( int nrow, int ncol ); double *one ( int m, int n ); double one_determinant ( int n ); double *one_eigen_right ( int n ); double *one_eigenvalues ( int n ); double *one_null_left ( int m, int n ); double *one_null_right ( int m, int n ); double *ortega ( int n, double u[], double v[], double d[] ); double ortega_determinant ( int n, double u[], double v[], double d[] ); double *ortega_eigen_right ( int n, double u[], double v[], double d[] ); double *ortega_eigenvalues ( int n, double u[], double v[], double d[] ); double *ortega_inverse ( int n, double u[], double v[], double d[] ); double *orth_random ( int n, int key ); double orth_random_determinant ( int n, int key ); double *orth_random_inverse ( int n, int key ); double *orth_symm ( int n ); double orth_symm_condition ( int n ); double orth_symm_determinant ( int n ); double *orth_symm_eigenvalues ( int n ); double *orth_symm_inverse ( int n ); double *oto ( int m, int n ); double oto_condition ( int n ); double oto_determinant ( int n ); double *oto_eigen_right ( int n ); double *oto_eigenvalues ( int n ); double *oto_inverse ( int n ); double *oto_llt ( int n ); void oto_plu ( int n, double p[], double l[], double u[] ); double *parlett ( ); double *parlett_eigenvalues ( ); double *parter ( int m, int n ); double parter_determinant ( int n ); double *parter_inverse ( int n ); double *pascal1 ( int n ); double pascal1_condition ( int n ); double pascal1_determinant ( int n ); double *pascal1_eigenvalues ( int n ); double *pascal1_inverse ( int n ); double *pascal2 ( int n ); double pascal2_determinant ( int n ); double *pascal2_inverse ( int n ); double *pascal2_llt ( int n ); void pascal2_plu ( int n, double p[], double l[], double u[] ); double *pascal3 ( int n, double alpha ); double pascal3_condition ( int n, double alpha ); double pascal3_determinant ( int n, double alpha ); double *pascal3_inverse ( int n, double alpha ); double *pds_random ( int n, int key ); double pds_random_determinant ( int n, int key ); double *pds_random_eigen_right ( int n, int key ); double *pds_random_eigenvalues ( int n, int key ); double *pds_random_inverse ( int n, int key ); double *pei ( double alpha, int n ); double pei_condition ( double alpha, int n ); double pei_determinant ( double alpha, int n ); double *pei_eigen_right ( double alpha, int n ); double *pei_eigenvalues ( double alpha, int n ); double *pei_inverse ( double alpha, int n ); bool perm_check ( int n, int p[] ); void perm_inverse ( int n, int p[] ); int *perm_mat_to_vec ( int n, double a[] ); int perm_sign ( int n, int p[] ); double *perm_vec_to_mat ( int n, int p[] ); double permutation_determinant ( int n, double a[] ); double *permutation_random ( int n, int key ); double permutation_random_determinant ( int n, int key ); double *permutation_random_inverse ( int n, int key ); complex *pick ( int n, complex w[], complex z[] ); double *plu ( int n, int pivot[] ); double plu_determinant ( int n, int pivot[] ); double *plu_inverse ( int n, int pivot[] ); void plu_plu ( int n, int pivot[], double p[], double l[], double u[] ); double *poisson ( int nrow, int ncol ); double poisson_determinant ( int nrow, int ncol ); double *poisson_eigenvalues ( int nrow, int ncol ); double *poisson_rhs ( int nrow, int ncol ); double *poisson_solution ( int nrow, int ncol ); int prime ( int n ); double *prolate ( double alpha, int n ); double *quaternion_i ( ); double *quaternion_j ( ); double *quaternion_k ( ); double r8_choose ( int n, int k ); double r8_epsilon ( ); double r8_factorial ( int n ); double r8_huge ( ); double r8_max ( double x, double y ); double r8_mop ( int i ); int r8_nint ( double x ); double r8_normal_01 ( int &seed ); double r8_sign ( double x ); double r8_uniform_ab ( double b, double c, int &seed ); double r8_uniform_01 ( int &seed ); void r8col_swap ( int m, int n, double a[], int j1, int j2 ); double *r8col_to_r8vec ( int m, int n, double a[] ); void r8mat_copy ( int m, int n, double a1[], double a2[] ); double *r8mat_copy_new ( int m, int n, double a1[] ); double r8mat_determinant ( int n, double a[] ); double *r8mat_diag_get_vector ( int n, double a[] ); double r8mat_gedet ( double a[], int n, int pivot[] ); int r8mat_gefa ( double a[], int n, int pivot[] ); void r8mat_geinverse ( double a[], int n, int pivot[] ); void r8mat_house_axh ( int n, double a[], double v[] ); double *r8mat_house_axh_new ( int n, double a[], double v[] ); double *r8mat_house_form ( int n, double v[] ); double *r8mat_identity ( int n ); double *r8mat_inverse ( int n, double a[] ); int r8mat_is_adjacency ( int m, int n, double a[] ); int r8mat_is_anticirculant ( int m, int n, double a[] ); double r8mat_is_antipersymmetric ( int m, int n, double a[] ); double r8mat_is_antisymmetric ( int m, int n, double a[] ); int r8mat_is_diagonally_dominant ( int n, double a[] ); int r8mat_is_diagonally_dominant_column ( int m, int n, double a[] ); int r8mat_is_diagonally_dominant_row ( int m, int n, double a[] ); double r8mat_is_eigen_left ( int n, int k, double a[], double x[], double lambda[] ); double r8mat_is_eigen_right ( int n, int k, double a[], double x[], double lambda[] ); double r8mat_is_identity ( int n, double a[] ); double r8mat_is_integer ( int m, int n, double a[] ); double r8mat_is_inverse ( int n, double a[], double b[] ); double r8mat_is_inverse_left ( int m, int n, double a[], double b[] ); double r8mat_is_inverse_right ( int m, int n, double a[], double b[] ); double r8mat_is_llt ( int m, int n, double a[], double l[] ); double r8mat_is_null_left ( int m, int n, double a[], double x[] ); double r8mat_is_null_right ( int m, int n, double a[], double x[] ); double r8mat_is_orthogonal ( int m, int n, double a[] ); double r8mat_is_orthogonal_column ( int m, int n, double a[] ); double r8mat_is_orthogonal_row ( int m, int n, double a[] ); int r8mat_is_permutation ( int m, int n, double a[] ); double r8mat_is_plu ( int m, int n, double a[], double p[], double l[], double u[] ); double r8mat_is_solution ( int m, int n, int k, double a[], double x[], double b[] ); bool r8mat_is_square ( int m, int n, double a[] ); double r8mat_is_symmetric ( int m, int n, double a[] ); double r8mat_is_transition ( int m, int n, double a[] ); void r8mat_is_triangular ( int m, int n, double a[], int &ival, int &jval ); int r8mat_is_zero_one ( int m, int n, double a[] ); double *r8mat_mm_new ( int n1, int n2, int n3, double a[], double b[] ); double *r8mat_mmt_new ( int n1, int n2, int n3, double a[], double b[] ); double *r8mat_mtm_new ( int n1, int n2, int n3, double a[], double b[] ); double r8mat_norm_eis ( int m, int n, double a[] ); double r8mat_norm_fro ( int m, int n, double a[] ); double r8mat_norm_l1 ( int m, int n, double a[] ); double r8mat_norm_l2 ( int m, int n, double a[] ); double r8mat_norm_li ( int m, int n, double a[] ); void r8mat_plot ( int m, int n, double a[], string title ); char r8mat_plot_symbol ( double r ); double *r8mat_poly_char ( int n, double a[] ); 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 r8mat_symm_jacobi ( int n, double a[] ); double r8mat_trace ( int n, double a[] ); double *r8mat_transpose_new ( int m, int n, double a[] ); void r8mat_transpose_in_place ( int n, double a[] ); double *r8mat_uniform_01_new ( int m, int n, int &seed ); double *r8mat_uniform_ab_new ( int m, int n, double b, double c, int &seed ); double *r8mat_zero_new ( int m, int n ); int r8poly_degree ( int na, double a[] ); void r8poly_print ( int n, double a[], string title ); void r8row_swap ( int m, int n, double a[], int irow1, int irow2 ); double *r8row_to_r8vec ( int m, int n, double a[] ); double r8vec_amax ( int n, double r8vec[] ); double r8vec_amin ( int n, double r8vec[] ); double r8vec_asum ( int n, double a[] ); void r8vec_copy ( int n, double a1[], double a2[] ); double *r8vec_copy_new ( int n, double a1[] ); double r8vec_dot_product ( int n, double a1[], double a2[] ); double *r8vec_house_column ( int n, double a[], int k ); double *r8vec_indicator_new ( int n ); double *r8vec_linspace_new ( int n, double a_first, double a_last ); double r8vec_max ( int n, double r8vec[] ); double r8vec_norm_l2 ( int n, double a[] ); void r8vec_print ( int n, double a[], string title ); double r8vec_product ( int n, double a[] ); void r8vec_sort_bubble_a ( int n, double a[] ); double r8vec_sum ( int n, double a[] ); double *r8vec_uniform_01_new ( int n, int &seed ); double *r8vec_uniform_ab_new ( int n, double b, double c, int &seed ); void r8vec_zero ( int n, double a[] ); double *r8vec_zero_new ( int n ); void r8vec2_print ( int n, double a1[], double a2[], string title ); double rayleigh ( int n, double a[], double x[] ); double rayleigh2 ( int n, double a[], double x[], double y[] ); double rectangle_adj_determinant ( int row_num, int col_num ); double *redheffer ( int n ); double redheffer_determinant ( int n ); double *ref_random ( int m, int n, double prob, int key ); double ref_random_determinant ( int n, double prob, int key ); double *riemann ( int m, int n ); double *ring_adj ( int n ); double ring_adj_determinant ( int n ); double *ring_adj_null_left ( int m, int n ); double *ring_adj_null_right ( int m, int n ); double *ris ( int n ); double ris_determinant ( int n ); double *ris_inverse ( int n ); double *rodman ( int m, int n, double alpha ); double rodman_condition ( int n, double alpha ); double rodman_determinant ( int n, double alpha ); double *rodman_eigen_right ( int n, double alpha ); double *rodman_eigenvalues ( int n, double alpha ); double *rodman_inverse ( int n, double alpha ); double *rosser1 ( ); double rosser1_determinant ( ); double *rosser1_eigen_left ( ); double *rosser1_eigen_right ( ); double *rosser1_eigenvalues ( ); double *rosser1_null_left ( ); double *rosser1_null_right ( ); double *routh ( int n, double x[] ); double routh_determinant ( int n, double x[] ); double *rowcolsum_matrix ( int row_num, int col_num, int &m, int &n ); double *rutis1 ( ); double rutis1_condition ( ); double rutis1_determinant ( ); double *rutis1_eigen_right ( ); double *rutis1_eigenvalues ( ); double *rutis1_inverse ( ); double *rutis2 ( ); double rutis2_condition ( ); double rutis2_determinant ( ); double *rutis2_eigen_right ( ); double *rutis2_eigenvalues ( ); double *rutis2_inverse ( ); double *rutis3 ( ); double rutis3_condition ( ); double rutis3_determinant ( ); complex *rutis3_eigen_left ( ); complex *rutis3_eigen_right ( ); complex *rutis3_eigenvalues ( ); double *rutis3_inverse ( ); double *rutis4 ( int n ); double rutis4_determinant ( int n ); double *rutis4_eigenvalues ( int n ); double *rutis4_inverse ( int n ); double *rutis5 ( ); double rutis5_condition ( ); double rutis5_determinant ( ); double *rutis5_eigen_right ( ); double *rutis5_eigenvalues ( ); double *rutis5_inverse ( ); double *schur_block ( int n, double x[], double y[] ); double schur_block_determinant ( int n, double x[], double y[] ); complex *schur_block_eigenvalues ( int n, double x[], double y[] ); double *schur_block_inverse ( int n, double x[], double y[] ); double *skew_circulant ( int m, int n, double x[] ); double skew_circulant_determinant ( int n, double x[] ); complex *skew_circulant_eigenvalues ( int n, double x[] ); complex *smoke1 ( int n ); double smoke1_determinant ( int n ); complex *smoke1_eigenvalues ( int n ); complex *smoke2 ( int n ); double smoke2_determinant ( int n ); complex *smoke2_eigenvalues ( int n ); double *snakes ( ); void sort_heap_external ( int n, int &indx, int &i, int &j, int isgn ); double *spline ( int n, double x[] ); double spline_determinant ( int n, double x[] ); double *spline_inverse ( int n, double x[] ); double *stirling ( int m, int n ); double stirling_determinant ( int n ); double *stirling_inverse ( int n ); double *stripe ( int n ); void subset_random ( int n, int &seed, int a[] ); double *sudoku_adj ( ); double *summation ( int m, int n ); double summation_condition ( int n ); double summation_determinant ( int n ); double *summation_eigenvalues ( int n ); double *summation_inverse ( int n ); double *sweet1 ( ); double sweet1_condition ( ); double sweet1_determinant ( ); double *sweet1_inverse ( ); double *sweet2 ( ); double sweet2_condition ( ); double sweet2_determinant ( ); double *sweet2_inverse ( ); double *sweet3 ( ); double sweet3_condition ( ); double sweet3_determinant ( ); double *sweet3_inverse ( ); double *sweet4 ( ); double sweet4_condition ( ); double sweet4_determinant ( ); double *sweet4_inverse ( ); double *sylvester ( int n, int nx, double x[], int ny, double y[] ); double *sylvester_kac ( int n ); double sylvester_kac_determinant ( int n ); double *sylvester_kac_eigen_right ( int n ); double *sylvester_kac_eigenvalues ( int n ); double *sylvester_kac_inverse ( int n ); double *symm_random ( int n, double d[], int key ); double symm_random_determinant ( int n, double d[], int key ); double *symm_random_eigen_left ( int n, double d[], int key ); double *symm_random_eigen_right ( int n, double d[], int key ); double *symm_random_eigenvalues ( int n, double d[], int key ); double *symm_random_inverse ( int n, double d[], int key ); void timestamp ( ); double *toeplitz ( int n, double x[] ); double *toeplitz_5diag ( int n, double d1, double d2, double d3, double d4, double d5 ); double *toeplitz_5s ( int row_num, int col_num, double alpha, double beta, double gamma, int n ); double toeplitz_5s_determinant ( int row_num, int col_num, double alpha, double beta, double gamma ); double *toeplitz_5s_eigenvalues ( int row_num, int col_num, double alpha, double beta, double gamma ); double *toeplitz_pds ( int m, int n, double x[], double y[] ); double *tournament_random ( int n, int key ); double tournament_random_determinant ( int n, int key ); double *transition_random ( int n, int key ); double *trench ( double alpha, int m, int n ); double *tri_l1_inverse ( int n, double a[] ); double *tri_u_inverse ( int n, double a[] ); double *tri_upper ( double alpha, int n ); double tri_upper_condition ( double alpha, int n ); double tri_upper_determinant ( double alpha, int n ); double *tri_upper_eigenvalues ( int n ); double *tri_upper_inverse ( double alpha, int n ); double tridiagonal_determinant ( int n, double a[] ); double *tris ( int m, int n, double x, double y, double z ); double tris_determinant ( int n, double x, double y, double z ); complex *tris_eigenvalues ( int n, double x, double y, double z ); double *tris_inverse ( int n, double alpha, double beta, double gamma ); double *triv ( int n, double x[], double y[], double z[] ); double triv_determinant ( int n, double x[], double y[], double z[] ); double *triv_inverse ( int n, double x[], double y[], double z[] ); double *triw ( double alpha, int k, int n ); double triw_determinant ( double alpha, int k, int n ); double *triw_eigenvalues ( int n ); double *triw_inverse ( double alpha, int k, int n ); double *upshift ( int n ); double upshift_condition ( int n ); double upshift_determinant ( int n ); complex *upshift_eigenvalues ( int n ); double *upshift_inverse ( int n ); double *vand1 ( int n, double x[] ); double vand1_determinant ( int n, double x[] ); double *vand1_inverse ( int n, double x[] ); void vand1_inverse_ul ( int n, double x[], double u[], double l[] ); double *vand2 ( int n, double x[] ); double vand2_determinant ( int n, double x[] ); double *vand2_inverse ( int n, double x[] ); void vand2_inverse_ul ( int n, double x[], double u[], double l[] ); void vand2_lu ( int n, double x[], double l[], double u[] ); void vand2_plu ( int n, double x[], double p[], double l[], double u[] ); double *wathen ( int nx, int ny, int n ); int wathen_order ( int nx, int ny ); double *wilk03 ( ); double wilk03_condition ( ); double wilk03_determinant ( ); double *wilk03_eigenvalues ( ); double *wilk03_inverse ( ); double *wilk03_rhs ( ); double *wilk03_solution ( ); double *wilk04 ( ); double wilk04_condition ( ); double wilk04_determinant ( ); double *wilk04_eigenvalues ( ); double *wilk04_inverse ( ); double *wilk04_rhs ( ); double *wilk04_solution ( ); double *wilk05 ( ); double wilk05_condition ( ); double wilk05_determinant ( ); double *wilk05_inverse ( ); double *wilk12 ( ); double wilk12_condition ( ); double wilk12_determinant ( ); double *wilk12_eigen_right ( ); double *wilk12_eigenvalues ( ); double *wilk20 ( double alpha ); double *wilk21 ( int n ); double wilk21_determinant ( int n ); double *wilk21_inverse ( int n ); double *wilson ( ); double wilson_condition ( ); double wilson_determinant ( ); double *wilson_eigen_right ( ); double *wilson_eigenvalues ( ); double *wilson_inverse ( ); double *wilson_llt ( ); void wilson_plu ( double p[], double l[], double u[] ); double *wilson_rhs ( ); double *wilson_solution ( ); double *zero ( int m, int n ); double zero_determinant ( int n ); double *zero_eigen_right ( int n ); double *zero_eigenvalues ( int n ); double *zero_null_right ( int m, int n ); double *zero_null_left ( int m, int n ); double *zielke ( int n, double x, double y, double z );