% CROUT FACTORIZATION FOR TRIDIAGONAL LINEAR SYSTEMS ALGORITHM 6.7
%
% To solve the n x n linear system
%
% E1: A(1,1) X(1) + A(1,2) X(2) = A(1,n+1)
% E2: A(2,1) X(1) + A(2,2) X(2) + A(2,3) X(3) = A(2,n+1)
% :
% .
% E(n): A(n,n-1) X(n-1) + A(n,n) X(n) = A(n,n+1)
%
% INPUT: the dimension n; the entries of A.
%
% OUTPUT: the solution X(1), ..., X(N).
syms('AA', 'OK', 'NAME', 'INP', 'N', 'I', 'A', 'B', 'NN');
syms('C', 'BB', 'Z', 'X', 'II', 'FLAG', 'OUP', 's');
TRUE = 1;
FALSE = 0;
fprintf(1,'This is Crout Method for tridiagonal linear systems.\n');
fprintf(1,'The array will be input from a text file in the order:\n');
fprintf(1,'all diagonal entries, all lower sub-diagonal entries, all ');
fprintf(1,'upper sub-diagonal\n');
fprintf(1,'entries, inhomogeneous term.\n\n');
fprintf(1,'Place as many entries as desired on each line, but separate
');
fprintf(1,'entries with\n');
fprintf(1,'at least one blank.\n\n\n');
fprintf(1,'Has the input file been created? - enter Y or N.\n');
AA = input(' ','s');
OK = FALSE;
if AA == 'Y' | AA == 'y'
fprintf(1,'Input the file name in the form - drive:\\name.ext\n');
fprintf(1,'for example: A:\\DATA.DTA\n');
NAME = input(' ','s');
INP = fopen(NAME,'rt');
OK = FALSE;
while OK == FALSE
fprintf(1,'Input the number of equations - an integer.\n');
N = input(' ');
if N > 0
A = zeros(1,N);
B = zeros(1,N);
C = zeros(1,N);
BB = zeros(1,N);
X = zeros(1,N);
Z = zeros(1,N);
% A(I,I) is stored in A(I), 1 <= I <= n */
for I = 1 : N
A(I) = fscanf(INP, '%f',1);
end;
% the lower sub-diagonal A(I,I-1) is stored
%in B(I), 2 <= I <= n */
for I = 2 : N
B(I) = fscanf(INP, '%f',1);
end;
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