TRIDIAGONAL - Functions to solve tridiagonal systems of equations Tu=r for u.

tridif		Solve a tridiagonal system of equations (float version)
tridid		Solve a tridiagonal system of equations (double version)
tripd		Solve a positive definite, symmetric tridiagonal system
tripp		Solve an unsymmetric tridiagonal system that uses 
		Gaussian elimination with partial pivoting

Function Prototypes:
void tridif (int n, float a[], float b[], float c[], float r[], float u[]);
void tridid (int n, double a[], double b[], double c[], double r[], double u[]);
void tripd (float *d, float *e, float *b, int n);
void tripp(int n, float *d, float *e, float *c, float *b);

tridif, tridid:
Input:
n		dimension of system
a		array[n] of lower sub-diagonal of T (a[0] ignored)
b		array[n] of diagonal of T
c		array[n] of upper super-diagonal of T (c[n-1] ignored)
r		array[n] of right-hand-side column vector

Output:
u		array[n] of solution (left-hand-side) column vector

tripd:
Input:
d	array[n], the diagonal of A 
e	array[n], the superdiagonal of A
b	array[n], the rhs column vector of Ax=b

Output:
b	b is overwritten with the solution to Ax=b
tripp:
Input:
d	diagonal vector of matrix
e       upper-diagonal vector of matrix
c       lower-diagonal vector of matrix
b       right-hand vector
n       dimension of matrix

Output:
b       solution vector

Notes:
For example, a tridiagonal system of dimension 4 is specified as:

    |b[0]    c[0]     0       0  | |u[0]|     |r[0]|
    |a[1]    b[1]    c[1]     0  | |u[1]|  =  |r[1]|
    | 0      a[2]    b[2]    c[2]| |u[2]|     |r[2]|
    | 0       0      a[3]    b[3]| |u[3]|     |r[3]|

The tridiagonal matrix is assumed to be non-singular.

tripd:
Given an n-by-n symmetric, tridiagonal, positive definite matrix A and
 n-vector b, following algorithm overwrites b with the solution to Ax = b

Authors:  tridif, tridid: Dave Hale, Colorado School of Mines, 10/03/89
tripd, tripp: Zhenyue Liu, Colorado School of Mines,  1992-1993