> restart:
> # GAUSS-SEIDEL ITERATIVE TECHNIQUE ALGORITHM 7.2
> #
> # To solve Ax = b given an initial approximation x(0).
> #
> # INPUT:   the number of equations and unknowns n: the entries
> #          A(I,J), 1<=I, J<=n, of the matrix A: the entries
> #          B(I), 1<=I<=n, of the inhomogeneous term b: the
> #          entries XO(I), 1<=I<=n, of x(0): tolerance TOL:
> #          maximum number of iterations N.
> #
> #  OUTPUT: the approximate solution X(1),...,X(n) or a message
> #          that the number of iterations was exceeded.
> print(`This is the Gauss-Seidel Method for Linear Systems.`);
> print(`Choice of input method`):
> print(`1. input from keyboard - not recommended for large systems`):
> print(`2. input from a text file`):
> print(`Please enter 1 or 2.`):
> FLAG := scanf(`%d`)[1]: print(`Your input is`): print(FLAG):
> if FLAG = 2 then
>    print(`The array will be input from a text file in the order`):
>    print(`A(1,1), A(1,2), ..., A(1,N+1), A(2,1), A(2,2), ..., 
>    A(2,N+1)`):
>    print(`..., A(N,1), A(N,2), ..., A(N,N+1)\n`):
>    print(`Place as many entries as desired on each line, but separate `):
>    print(`entries with`):
>    print(`at least one blank.`):
>    print(`The initial approximation should follow in same format`):
>    print(`Has the input file been created? - enter 1 for yes or 2 for no.`):
>    AA := scanf(`%d`)[1]: print(`Your response is`): print(AA): OK:=FALSE:
>    if AA = 1 then
>       print(`Input the file name in the form - drive:\\name.ext`):
>       print(`for example:   A:\\DATA.DTA`):
>       NAME := scanf(`%s`)[1]: print(`The file name is`): print(NAME):
>       INP := fopen(NAME,READ,TEXT):
>       while OK = FALSE do
>          print(`Input the number of equations - an integer.`):
>          N := scanf(`%d`)[1]: print(`N is`): print(N):
>          if N > 0 then
>             for I1 from 1 to N do
>             for J from 1 to N+1 do
>             A[I1-1,J-1] := fscanf(INP, `%f`)[1]:
>             od:
>             od:
>             for I1 from 1 to N do
>             X1[I1-1] := fscanf(INP, `%f`)[1]:
>             od:
>             OK := TRUE:
>             fclose(INP):
>          else 
              print(`The number must be a positive integer.\n`):
>          fi:
>       od:
>    else 
>       print(`The program will end so the input file can be created.\n`):
>    fi:
> else
>    OK := FALSE:
>    while OK = FALSE do
>       print(`Input the number of equations - an integer.`):
>       N := scanf(`%d`)[1]: print(`N= `): print(N):
>       if N > 0 then
>          for I1 from 1 to N do
>          for J from 1 to N+1 do
>          print(`input entry in position `,I1,J): 
>          A[I1-1,J-1] := scanf(`%f`)[1]:print(`Data is `):print(A[I1-1,J-1]):
>          od:
>          od:
>          for I1 from 1 to N do
>          print(`input initial approximation entry in position `,I1): 
>          X1[I1-1] := scanf(`%f`)[1]:print(`Data is `):print(X1[I1-1]):
>          od:
>          OK := TRUE:
>       else 
           print(`The number must be a positive integer.\n`):
>       fi:
>    od:
> fi:
> if OK = TRUE then
>    OUP := default:
>    fprintf(OUP, `The original system - output by rows:\n`):
>    for I1 from 1 to N do
>    for J from 1 to N+1 do
>    fprintf(OUP, ` %11.8f`, A[I1-1,J-1]):
>    od:
>    fprintf(OUP, `\n`):
>    od:
>    fprintf(OUP, `The initial approximation:\n`):
>    for I1 from 1 to N do
>    fprintf(OUP, ` %11.8f`, X1[I1-1]):
>    od:
>    fprintf(OUP, `\n`):
> fi:
> if OK = TRUE then
>    OK := FALSE:
>    while OK = FALSE do
>       print(`Input the tolerance.\n`):
>       TOL := scanf(`%f`)[1]:print(`Tolerance = `):print(TOL):
>       if TOL > 0 then
>          OK := TRUE:
>       else
>          print(`Tolerance must be a positive number.\n`):
>       fi:
>    od:
> fi:
> if OK = TRUE then
>    OK := FALSE:
>    while OK = FALSE do
>       print(`Input maximum number of iterations.\n`):
>       NN := scanf(`%d`)[1]:print(`Maximum number of iterations = `):print(NN):
>       if NN > 0 then
>          OK := TRUE:
>       else
>          print(`Number must be a positive integer.\n`):
>       fi:
>    od:
> fi:
> if OK = TRUE then
> fprintf(OUP,`Iter#  Vector\n`):
> # Step 1
>    K := 1:
>    OK := FALSE:
> # Step 2
>    while OK = FALSE and K <= NN do
> # ERR is used to test accuracy - it measures the infinity norm
>       ERR := 0:
> # Step 3
>       for I1 from 1 to N do
>          S := 0:
>          for J from 1 to N do
>             S := S-A[I1-1,J-1]*X1[J-1]:
>          od:
>          S := (S+A[I1-1,N])/A[I1-1,I1-1]:
>          if abs(S) > ERR then
>            ERR := abs(S):
>          fi:
>           X1[I1-1] := X1[I1-1] + S;
>       od:
> # Step 4
>       if ERR <= TOL then
> # Process is completed successfully.
>          OK := TRUE:
>       else
> # Step 5
>          fprintf(OUP, ` %d `, K):
>          K := K+1:
> # Step 6 is not used since only one vector is needed.
>          for I1 from 1 to N do
>          fprintf(OUP, ` %11.8f`, X1[I1-1]):
>          od:
>          fprintf(OUP, `\n`):
>       fi:
>    od:
> # Step 7
> # Process is completed unsuccessfully.
>    if OK = FALSE then
>       print(`Maximum Number of Iterations Exceeded.\n`):
>    else
>       print(`Choice of output method:\n`):
>       print(`1. Output to screen\n`):
>       print(`2. Output to text file\n`):
>       print(`Please enter 1 or 2.\n`):
>       FLAG := scanf(`%d`)[1]:print(`Your input is `):print(FLAG):
>       if FLAG = 2 then
>          print(`Input the file name in the form - drive:\\name.ext\n`):
>          print(`for example:   A:\\OUTPUT.DTA\n`):
>          NAME := scanf(`%s`)[1]:print(`Output file is `):print(NAME):
>          OUP := fopen(NAME,WRITE,TEXT):
>       else
>          OUP := default:
>       fi:
>       fprintf(OUP, `Gauss-Seidel Method FOR LINEAR SYSTEMS\n\n`):
>       fprintf(OUP, `The solution vector is :\n`):
>       for I1 from 1 to N do
>          fprintf(OUP, ` %11.8f`, X1[I1-1]):
>       od:
>       fprintf(OUP, `\nusing %d iterations\n`, K):
>       fprintf(OUP, `with Tolerance  %.10e in infinity-norm\n`, TOL):
>       if OUP <> default then
>          fclose(OUP):
>          print(`Output file `,NAME,` created successfully`):
>       fi:
>    fi:
> fi: