> restart:
> # GAUSSIAN ELIMINATION WITH BACKWARD SUBSTITUTION ALGOTITHM 6.1
> #
> # To solve the n by n linear system
> #
> # E1:  A[1,1] X[1] + A[1,2] X[2] +...+ A[1,n] X[n] = A[1,n+1]
> # E2:  A[2,1] X[1] + A[2,2] X[2] +...+ A[2,n] X[n] = A[2,n+1]
> # :
> # .
> # EN:  A[n,1] X[1] + A[n,2] X[2] +...+ A[n,n] X[n] = A[n,n+1]
> #
> # INPUT:   number of unknowns and equations n: augmented
> #          matrix A = (A(I,J)) where 1<=I<=n and 1<=J<=n+1.
> #
> # OUTPUT:  solution x(1), x(2),...,x(n) or a message that the
> #          linear system has no unique solution.
> print(`This is Gaussian Elimination to solve a linear system.`):
> 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(`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 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:
> 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:
> 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:
> # Step 1
> NN := N-1:
> M := N+1:
> ICHG := 0:
> I1 := 1:
> while OK = TRUE and I1 <= NN do
> # Step 2
> # Use IP in place of P
> IP := I1:
> while abs(A[IP-1,I1-1]) <= 1.0e-20 and IP <= N do
> IP := IP+1:
> od:
> if IP = M then
> OK := FALSE:
> else
> # Step 3
> if IP <> I1 then
> for JJ from 1 to M do
> C := A[I1-1,JJ-1]:
> A[I1-1,JJ-1] := A[IP-1,JJ-1]:
> A[IP-1,JJ-1] := C:
> od:
> ICHG := ICHG+1:
> fi:
> # Step 4
> JJ := I1+1:
> for J from JJ to N do
> # Step 5
> # XM is used in place of m(J,I)
> XM := A[J-1,I1-1]/A[I1-1,I1-1]:
> # Step 6
> for K from JJ to M do
> A[J-1,K-1] := A[J-1,K-1] - XM * A[I1-1,K-1]:
> od:
> # Multiplier XM could be saved in A[J,I]
> A[J-1,I1-1] := 0:
> od:
> fi:
> I1 := I1+1:
> od:
> if OK = TRUE
> then
> # Step 7
> if abs(A[N-1,N-1]) <= 1.0e-20 then
> OK := FALSE:
> else
> # Step 8
> # Start backward substitution
> X[N-1] := A[N-1,M-1] / A[N-1,N-1]:
> # Step 9
> for K from 1 to NN do
> I1 := NN-K+1:
> JJ := I1+1:
> SUM := 0:
> for KK from JJ to N do
> SUM := SUM - A[I1-1,KK-1] * X[KK-1]:
> od:
> X[I1-1] := (A[I1-1,M-1]+SUM) / A[I1-1,I1-1]:
> od:
> # Step 10
> # Process is complete
> 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(`Your input is`): print(FLAG):
> if FLAG = 2 then
> print(`Input the file name in the form - drive:\\name.ext`):
> print(`for example:  A:\\OUTPUT.DTA`):
> NAME := scanf(`%s`)[1]: print(`The output file is`): print(NAME):
> OUP := fopen(NAME, WRITE,TEXT):
> else
> OUP := default:
> fi:
> fprintf(OUP, `GAUSSIAN ELIMINATION\n\n`):
> fprintf(OUP, `The reduced system - output by rows:\n`):
> for I1 from 1 to N do
> for J from 1 to M do
> fprintf(OUP, ` %11.8f`, A[I1-1,J-1]):
> od:
> fprintf(OUP, `\n`):
> od:
> fprintf(OUP, `\n\nHas solution vector:\n`):
> for I1 from 1 to N do
> fprintf(OUP, `  %12.8f`, X[I1-1]):
> od:
> fprintf (OUP, `\n\nwith %d row interchange(s)\n`, ICHG):
> if OUP <> default then
> fclose(OUP):
> print(`Output file `,NAME,` created successfully`):
> fi:
> fi:
> fi:
> if OK = FALSE then
> print(`System has no unique solution\n`):
> fi:
> fi: