restart:# POWER METHOD ALGORITHM 9.1## To approximate the dominant eigenvalue and an associated# eigenvector of the n by n matrix A given a nonzero vector x:## INPUT: Dimension n: matrix A: vector x: tolerance TOL: maximum# number of iterations N.## OUTPUT: Approximate eigenvalue MU: approximate eigenvector x# or a message that the maximum number of iterations was# exceeded. print(`This is the Power Method.\134n`):OK := FALSE:print(`Choice of input method`):print(`1. input from keyboard - not recommended for large matrices`):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), A(2,1), A(2,2), ..., A(2,N)`): print(`..., A(N,1), A(N,2), ..., A(N,N)\134n`): print(`Place as many entries as desired on each line, but separate `): print(`entries with`): print(`at least one blank.\134n`): print(`The initial approximation should follow in same format.\134n`): 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): 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): OK := FALSE: while OK = FALSE do print(`Input the dimension n - 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 do A[I1-1,J-1] := fscanf(INP, `%f`)[1]: od: od: for I1 from 1 to N do X[I1-1] := fscanf(INP, `%f`)[1]: od: OK := TRUE: fclose(INP): else print(`The number must be a positive integer.\134n`): 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 dimension n - an integer.`): N := scanf(`%d`)[1]: print(`N= `): print(N): if N > 0 then print(`Input Matrix `): for I1 from 1 to N do for J from 1 to N 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: print(`Input initial approximation vector `): for I1 from 1 to N do print(`input entry in position `,I1): X[I1-1] := scanf(`%f`)[1]:print(`Data is `):print(X[I1-1]): od: OK := TRUE: else print(`The number must be a positive integer.\134n`): fi: od: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 positive number.\134n`): fi: od: OK := FALSE: while OK = FALSE do print(`Input maximum number of iterations `): print(`- integer.\134n`): NN := scanf(`%d`)[1]:print(`Maximum number of iterations = `):print(NN):# Use NN in place of N if NN > 0 then OK := TRUE: else print(`Number must be positive integer.\134n`): fi: od:fi:if OK = TRUE then OUP := default: fprintf(OUP, `The original matrix - output by rows:\134n`): for I1 from 1 to N do for J from 1 to N do fprintf(OUP, ` %11.8f`, A[I1-1,J-1]): od: fprintf(OUP, `\134n`): od: fprintf(OUP, `The initial approximation vector is :\134n`): for I1 from 1 to N do fprintf(OUP, ` %11.8f`, X[I1-1]): od: fprintf(OUP, `\134n`):fi:if OK = TRUE then print(`Choice of output method:`): print(`1. Output to screen`): print(`2. Output to text file`): print(`Please enter 1 or 2.`): FLAG := scanf(`%d`)[1]: print(`Input = `):print(FLAG): if FLAG = 2 then print(`Input the file name in the form - drive:\134\134name.ext`): print(`for example A:\134\134OUTPUT.DTA`): NAME := scanf(`%s`)[1]:print(`Output = `):print(NAME): OUP := fopen(NAME,WRITE,TEXT): else OUP := default: fi: fprint(OUP, `POWER METHOD\134n\134n`): fprintf(OUP, `Iter Aapprox Approx eigenvector\134n`): fprintf(OUP, ` eigenvalue\134n`):# Step 1 K := 1:# Step 2 LP := 1: AMAX := abs(X[0]): for I1 from 2 to N do if abs(X[I1-1]) > AMAX then AMAX := abs(X[I1-1]): LP := I1: fi: od:# Step 3 for I1 from 1 to N do X[I1-1] := X[I1-1]/AMAX: od:# Step 4 while K <= NN and OK = TRUE do# Step 5 for I1 from 1 to N do Y[I1-1] := 0: for J from 1 to N do Y[I1-1] := Y[I1-1] + A[I1-1,J-1] * X[J-1]: od: od:# Step 6 YMU := Y[LP-1]:# Step 7 LP := 1: AMAX := abs(Y[0]): for I1 from 2 to N do if abs(Y[I1-1]) > AMAX then AMAX := abs(Y[I1-1]): LP := I1: fi: od:# Step 8 if AMAX <= 0 then print(`0 eigenvalue - select another `): print(`initial vector and begin again\134n`): OK := FALSE: else# Step 9 ERR := 0: for I1 from 1 to N do T := Y[I1-1]/Y[LP-1]: if abs(X[I1-1]-T) > ERR then ERR := abs(X[I1-1]-T): fi: X[I1-1] := T: od: fprintf(OUP, `%d %12.8f`, K, YMU):# Step 10 for I1 from 1 to N do fprintf(OUP, ` %11.8f`, X[I1-1]): od: fprintf(OUP, `\134n`): if ERR <= TOL then fprintf(OUP, `\134n\134nThe eigenvalue = %12.8f`,YMU): fprintf(OUP, ` to tolerance = %.10e\134n`, TOL): fprintf(OUP, `obtained on iteration number = %d\134n\134n`, K): fprintf(OUP, `Unit eigenvector is :\134n\134n`): for I1 from 1 to N do fprintf(OUP, ` %11.8f`, X[I1-1]): od: fprintf(OUP, `\134n`): OK := FALSE: fi:# Step 11 K := K+1: fi:# Step 12 od: if K > NN then print(`Method did not converge within `,NN,` iterations`): fi: if OUP <> default then fclose(OUP): print(`Output file `,NAME,` created successfully`): fi:fi:JSFH