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Module tridiagonal_mod

Contact:  Isaac Held ,  Bruce Wyman
Reviewers: 
Change History: WebCVS Log

OVERVIEW

Solves the tridiagonal system of equations.

The following schematic represents the system of equations solved, where X is the solution. 
     | B(1)  A(1)   0     0                .......            0    |  |X(1)|   |D(1)|
     | C(2)  B(2)  A(2)   0                .......            0    |  |X(2)|   |D(2)|
     |  0    C(3)  B(3)  A(3)  0           .......            0    |  | .. |   | .. |
     |  ..........................................                 |  | .. | = | .. |
     |  ..........................................                 |  | .. |   | .. |
     |                                  C(N-2) B(N-2) A(N-2)  0    |  | .. |   | .. |
     |                                    0    C(N-1) B(N-1) A(N-1)|  | .. |   | .. |
     |                                    0      0    C(N)   B(N)  |  |X(N)|   |D(N)|
To solve this system 
   call tri_invert(X,D,A,B,C)

       real, intent(out), dimension(:,:,:) :: X
       real, intent(in),  dimension(:,:,:) :: D
       real, optional,    dimension(:,:,:) :: A,B,C
For simplicity (?), A and C are assumed to be dimensioned the same size as B, D, and X, although any input values for A(N) and C(1) are ignored. (some checks are needed here)

If A is not present, it is assumed that the matrix (A,B.C) has not been changed since the last call to tri_invert.

To release memory, 
    call close_tridiagonal
The following module variables are used to retain the relevant information if one recalls tri_invert without changing (A,B,C)

OTHER MODULES USED










PUBLIC INTERFACE







tri_invert:


   Sets up and solves the tridiagonal system of equations. 



close_tridiagonal:


   Releases memory used by the solver. 












PUBLIC DATA



None.










PUBLIC ROUTINES



    

  1. 


    tri_invert
    

    call tri_invert ( x,d,a,b,c)
    

    

    
DESCRIPTION

    

       Sets up and solves the tridiagonal system of equations. 
    

    

    

    
INPUT

    

    

    

    
d      The right-hand side term, see the schematic above. 
       [real, dimension(:,:,:)]    		

    

    

    

    

    
INPUT/OUTPUT

    

    

    

    
a,b,c      The left-hand-side terms (matrix), see the schematic above.
   If A is not present, it is assumed that the matrix (A,B.C)
   has not been changed since the last call to tri_invert. 
       [real, dimension(:,:,:)]    		

    

    

    

    

    
OUTPUT

    

    

    

    
x      The solution to the tridiagonal system of equations. 
       [real, dimension(:,:,:)]    		

    

    

    

    

    
NOTE

    

       For simplicity, A and C are assumed to be dimensioned the same size
   as B, D, and X, although any input values for A(N) and C(1) are ignored.
   There are no checks to make sure the sizes agree. 
    

       The value of A(N) is modified on output, and B and C are unchanged. 
    

    

    

    

    2. 

  2. 


    close_tridiagonal
    

    call close_tridiagonal 

    

    

    
DESCRIPTION

    

       Releases memory used by the solver. 
    

    

    

    
NOTE

    

       There are no arguments to this routine. 
    

    

    

    

    3. 














DATA SETS


None.













ERROR MESSAGES


None.










REFERENCES




        None.
      








COMPILER SPECIFICS




        None.
      








PRECOMPILER OPTIONS




        None.
      








LOADER OPTIONS



None.










TEST PROGRAM



None.










KNOWN BUGS





   Optional arguments A,B,C have no intent declaration,
   so the default intent is inout. The value of A(N) is modified
   on output, and B and C are unchanged. 










NOTES



   The following private allocatable arrays save the relevant information
   if one recalls tri_invert without changing (A,B,C): 
        allocate ( e  (size(x,1), size(x,2), size(x,3)) )
        allocate ( g  (size(x,1), size(x,2), size(x,3)) )
        allocate ( cc (size(x,1), size(x,2), size(x,3)) )
        allocate ( bb (size(x,1), size(x,2)) )
   This storage is deallocated when close_tridiagonal is called. 








FUTURE PLANS





   Maybe a cleaner version? 










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