#ifndef rn_H
#define rn_H

/* Operations on points and vectors of R^n */
/* Last edited on 2005-01-16 15:01:31 by stolfi */
/* Copyright © 2005 Jorge Stolfi, UNICAMP. See note at end of file. */

/* Based on VectorN.mg, created 95-02-27 by J. Stolfi. */

#include <stdio.h>

void rn_zero (int n, double *r);
  /* Sets {r} to the zero vector. */
  
void rn_all (int n, double x, double *r);
  /* Sets all coordinates of {r} to the value {x}. */
  
void rn_axis (int n, int i, double *r);
  /* Sets {r} to the {i}th vector of the canonical basis. */

void rn_add (int n, double *a, double *b, double *r);
  /* Sets {r = a + b}. */

void rn_sub (int n, double *a, double *b, double *r);
  /* Sets {r = a - b}. */

void rn_neg (int n, double *a, double *r);
  /* Sets {r} to {-a}. */

void rn_scale (int n, double s, double *a, double *r);
  /* Sets {r := s * a}. */

void rn_mix (int n, double s, double *a, double t, double *b, double *r);
  /* Sets {r := s * a + t * b}. */

void rn_mix_in (int n, double s, double *a, double *r);
  /* Sets {r := r + s * a}. */

void rn_weigh (int n, double *a, double *w, double *r);
  /* Sets {r[i] := a[i] * w[i]}. */

double rn_norm (int n, double *a);
  /* Returns the Euclidean length of {a}. */

double rn_norm_sqr (int n, double *a);
  /* Returns the square of the Euclidean length of {a}. */

double rn_L_inf_norm (int n, double *a);
  /* Returns the L-infinity norm of {a} (max absolute coordinate). */

double rn_dist (int n, double *a, double *b);
  /* Returns the Euclidean distance between {a} and {b}. */

double rn_dist_sqr (int n, double *a, double *b);
  /* Returns the square of the Euclidean distance between {a} and {b}. */

double rn_L_inf_dist (int n, double *a, double *b);
  /* Returns the L-infinity distance between {a} and {b} 
    (max absolute diff). */
 
double rn_dir (int n, double *a, double *r);
  /* Sets {r} to {a} normalized to unit Euclidean length; 
    returns the original length. */

double rn_L_inf_dir (int n, double *a, double *r);
  /* Sets {r} to the vector {a/rn_L_inf_norm(a)}; 
    returns the original norm. */

double rn_dot (int n, double *a, double *b);
  /* Dot product of vectors {a} and {b}. */

double rn_cos (int n, double *a, double *b);
  /* Cosine of angle between vectors {a} and {b}. */

double rn_sin (int n, double *a, double *b);
  /* Absolute sine of angle between vectors {a} and {b}. */

void rn_cross (int n, double **a, double *r);
  /* Sets {r} to the `cross product' of the {n-1} given {n}-vectors
    {a[0..n-2]}; namely, a vector perpendicular to {a[0..n-2]}, whose
    length is the {n}-dimensional measure of the parallelotope defined
    by those vectors. */
  
double rn_det (int n, double **a);
  /* Returns the determinant of the {n} x {n} matrix whose rows 
    are tne {n}-vectors {a[0..n-1]}. */

double rn_decomp (int n, double *a, double *u, double *para, double *perp);
  /* Sets {para} and {perp} (when not NULL) to the components of 
    {a} that are parallel and perpendicular to to {u}, respectively.
    Namely, {para = c*u} and {perp = a - c*u}, where 
    {c = rn_dot(n,a,u)/rn_dot(n,u,u)}. Also returns {c}. */

void rn_throw_cube (int n, double *r);
  /* Sets {r} to a uniformly random point of the {n}-cube {[-1 .. +1]^n}. */
 
void rn_throw_ball (int n, double *r);
  /* Sets {r} to a uniformly random point of the unit {n}-ball. */

void rn_throw_normal (int n, double *r);
  /* Sets each coordinate {r[i]} to an independent Gaussian random
    number with zero mean and unit standard deviation. */

void rn_print (FILE *f, int n, double *a);
  /* Prints {a} on file {f}, with some default format. */

void rn_gen_print
  ( FILE *f, int n, double *a, 
    char *fmt, 
    char *lp, char *sep, char *rp
  );
  /* Prints {a} on file {f}, formatting each coordinate with {fmt}. 
    The strings {lp}, {sep}, and {rp} are printed respectively before,
    between, and after all the coordinates of {a}.  When NULL, they default 
    to "%16.8e", "(", " ", and ")", respectively. */

/* HEAP ALLOCATION */

double *rn_alloc(int n);
  /* Allocates {n} {double}s on the heap; bombs out if no mem. */

#endif
/* COPYRIGHT AND AUTHORSHIP NOTICE

  Copyright © 2005 Jorge Stolfi, Universidade Estadual de Campinas (UNICAMP).
  Created by Jorge Stolfi in 1992--2005.
  
  This source file can be freely distributed, used, and modified,
  provided that this copyright and authorship notice is preserved in
  all copies, and that any modified versions of this file are clearly
  marked as such.
  
  This software has NO WARRANTY of correctness or applicability for
  any purpose. Neither the author nor his employers shall be held
  responsible for any losses or damages that may result from its use.

  END OF NOTICE */