> restart:
> # CHOLESKI'S ALGORITHM 6.6
> #
> # To factor the positive definite n by n matrix A into LL**T,
> # where L is lower triangular.
> #
> # INPUT:   the dimension n: entries A(I,J), 1<=I, J<=n of A.
> #
> # OUTPUT:  the entries L(I,J), 1<=J<=I, 1<=I<=n of L.
> #
> print(`This is Choleski Factorization Method.\n`):
> print(`This is the LDL^t Method for Positive Definite Matrices.\n`):
> 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)\n`):
> print(`Place as many entries as desired on each line, but separate `):
> print(`entries with`):
> print(`at least one blank.`):
> 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:\\name.ext`):
> print(`for example:   A:\\DATA.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:
> 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 dimension n - 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 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:
> 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 matrix - output by rows:\n`):
> 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, `\n`):
> od:
> fi:
> if OK = TRUE then
> # Step 1
> A[0,0] := sqrt(A[0,0]):
> # Step 2
> for J from 2 to N do
> A[J-1,0] := A[J-1,0]/A[0,0]:
> od:
> # Step 3
> NN := N-1:
> for I1 from 2 to NN do
> # Step 4
> KK := I1-1:
> S := 0:
> for K from 1 to KK do
> S := S-A[I1-1,K-1]*A[I1-1,K-1]:
> od:
> A[I1-1,I1-1] := sqrt(A[I1-1,I1-1]+S):
> # Step 5
> JJ := I1+1:
> for J from JJ to N do
> S := 0:
> KK := I1-1:
> for K from 1 to KK do
> S := S - A[J-1,K-1]*A[I1-1,K-1]:
> od:
> A[J-1,I1-1] := (A[J-1,I1-1]+S)/A[I1-1,I1-1]:
> od:
> od:
> # Step 6
> S := 0:
> for K from 1 to NN do
> S := S-A[N-1,K-1]*A[N-1,K-1]:
> od:
> A[N-1,N-1] := sqrt(A[N-1,N-1]+S):
> # Step 7
> 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, `CHOLESKI FACTORIZATION\n\n`):
> fprintf(OUP, `The matrix L output by rows:\n`):
> for I1 from 1 to N do
> for J from 1 to I1 do
> fprintf(OUP, `  %12.8f`, A[I1-1,J-1]):
> od:
> fprintf(OUP, `\n`):
> od:
> if OUP <> default then
> fclose(OUP):
> print(`Output file `,NAME,` created successfully`,NAME):
> fi:
> fi: