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 ( int a, int b, int &seed );
void imtqlx ( int n, double d[], double e[], double z[] );
int r4_nint ( float x );
double r8_choose ( int n, int k );
double r8_epsilon ( );
double r8_max ( double x, double y );
double r8_sign ( double x );
double *r8mat_copy_new ( int m, int n, double a1[] );
double *r8mat_mtv_new ( int m, int n, double a[], double x[] );
double *r8mat_mv_new ( int m, int n, double a[], double x[] );
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_new ( int n, double b, double c, int *seed );
double *r8vec_uniform_01_new ( int n, 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_double_product_integral ( int i, int j );
double t_integral ( int e );
double *t_polynomial ( int m, int n, double x[] );
double *t_polynomial_ab ( double a, double b, int m, int n, double x[] );
double *t_polynomial_coefficients ( int n );
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 t_triple_product_integral ( int i, int j, int k );
void timestamp ( );
double u_double_product_integral ( int i, int j );
double u_integral ( int e );
double *u_polynomial ( int m, int n, double x[] );
double *u_polynomial_coefficients ( int n );
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 v_double_product_integral ( int i, int j );
double *v_polynomial ( int m, int n, double x[] );
void v_polynomial_values ( int &n_data, int &n, double &x, double &fx );
double *v_polynomial_zeros ( int n );
double w_double_product_integral ( int i, int j );
double *w_polynomial ( int m, int n, double x[] );
void w_polynomial_values ( int &n_data, int &n, double &x, double &fx );
double *w_polynomial_zeros ( int n );