restart:# SOR ALGORITHM 7.3## 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 SOR 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)\134n`): 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:\134\134name.ext`): print(`for example: A:\134\134DATA.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 fi: od: else print(`The program will end so the input file can be created.\134n`): 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 fi: od:fi:if OK = TRUE then OUP := default: fprintf(OUP, `The original system - output by rows:\134n`): 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, `\134n`): od: fprintf(OUP, `The initial approximation:\134n`): for I1 from 1 to N do fprintf(OUP, ` %11.8f`, X1[I1-1]): od: fprintf(OUP, `\134n`):fi:if OK = TRUE then OK := FALSE: while OK = FALSE do print(`Input the tolerance.\134n`): TOL := scanf(`%f`)[1]:print(`Tolerance = `):print(TOL): if TOL > 0 then OK := TRUE: else print(`Tolerance must be a positive number.\134n`): fi: od:fi:if OK = TRUE then OK := FALSE: while OK = FALSE do print(`Input maximum number of iterations.\134n`): 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.\134n`): fi: od:fi:if OK = TRUE thenprint(`Input parameter w (omega)`);W := scanf(`%f`)[1]; print(`Omega = `):print(W):# Use W in place of omegafi;if OK = TRUE thenfprintf(OUP,`Iter# Vector\134n`):# 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 := W*(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 for I1 from 1 to N do fprintf(OUP, ` %11.8f`, X1[I1-1]): od: fprintf(OUP, `\134n`): fi: od:# Step 7# Process is completed unsuccessfully. if OK = FALSE then print(`Maximum Number of Iterations Exceeded.\134n`): else print(`Choice of output method:\134n`): print(`1. Output to screen\134n`): print(`2. Output to text file\134n`): print(`Please enter 1 or 2.\134n`): FLAG := scanf(`%d`)[1]:print(`Your input is `):print(FLAG): if FLAG = 2 then print(`Input the file name in the form - drive:\134\134name.ext\134n`): print(`for example: A:\134\134OUTPUT.DTA\134n`): NAME := scanf(`%s`)[1]:print(`Output file is `):print(NAME): OUP := fopen(NAME,WRITE,TEXT): else OUP := default: fi: fprintf(OUP, `SOR ITERATIVE METHOD FOR LINEAR SYSTEMS\134n\134n`); fprintf(OUP, `The solution vector is :\134n`): for I1 from 1 to N do fprintf(OUP, ` %11.8f`, X1[I1-1]): od: fprintf(OUP, `\134nusing %d iterations\134n`, K): fprintf(OUP, `with Tolerance %.10e in infinity-norm\134n`, TOL): fprintf(OUP, `with Parameter %.10e\134n`, W); if OUP <> default then fclose(OUP): print(`Output file `,NAME,` created successfully`): fi: fi:fi:JSFH