restart:

# CROUT FACTORIZATION FOR TRIDIAGONAL LINEAR SYSTEMS ALGORITHM 6.7

# To solve the n x n linear system

# E1: A[1,1] X[1] + A[1,2] X[2] = A[1,n+1]

# E2: A[2,1] X[1] + A[2,2] X[2] + A[2,3] X[3] = A[2,n+1]

# :

# .

# E(n): A[n,n-1] X[n-1] + A[n,n] X[n] = A[n,n+1]

# INPUT: the dimension n: the entries of A.

# OUTPUT: the solution X(1), ..., X(N).

print(`This is Crout Method for tridiagonal linear systems.\134n`):

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:\134n`):

print(`diagonal entries, lower sub-diagonal entries,\134n`):

print(`upper sub-diagonal entries, inhomogeneous term.\134n\134n`):

print(`Place as many entries as desired on each line, but separate `):

print(`entries \134n`):

print(`with at least one blank.\134n\134n\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 number of equations - an integer.`):

N := scanf(`%d`)[1]: print(`N is`): print(N):

if N > 0 then

# A(I,I) is stored in A(I), 1 <= I <= n

for I1 from 1 to N do

A[I1-1] := fscanf(INP, `%f`)[1]:

od:

# the lower sub-diagonal A(I,I-1) is stored

#in B(I), 2 <= I <= n

for I1 from 2 to N do

B[I1-1] := fscanf(INP, `%f`)[1]:

od:

# the upper sub-diagonal A(I,I+1) is stored

#in C(I), 1 <= I <= n-1

NN := N-1:

for I1 from 1 to NN do

C[I1-1] := fscanf(INP, `%f`)[1]:

od:

# A(I,N+1) is stored in BB(I), 1 <= I <= n

for I1 from 1 to N do

BB[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 number of equations - an integer.`):

N := scanf(`%d`)[1]: print(`N= `): print(N):

if N > 0 then

# A(I,I) is stored in A(I), 1 <= I <= n

for I1 from 1 to N do

print(`Input the diagonal entry in row = `):print(I1):

A[I1-1] := scanf( `%f`)[1]:print(`Entry = `,A[I1-1]):

od:

# the lower sub-diagonal A(I,I-1) is stored

#in B(I), 2 <= I <= n

for I1 from 2 to N do

print(`Input the lower sub-diagonal diagonal entry in row = `):print(I1):print(` and column = `):print(I1-1):

B[I1-1] := scanf(`%f`)[1]:print(`Entry = `,B[I1-1]):

od:

# the upper sub-diagonal A(I,I+1) is stored

#in C(I), 1 <= I <= n-1

NN := N-1:

for I1 from 1 to NN do

print(`Input the upper sub-diagonal diagonal entry in row = `):print(I1):print(` and column = `):print(I1+1):

C[I1-1] := scanf(`%f`)[1]:print(`Entry = `,C[I1-1]):

od:

# A(I,N+1) is stored in BB(I), 1 <= I <= n

for I1 from 1 to N do

print(`Input the entry on the right-hand side of equation = `):print(I1):

BB[I1-1] := scanf(`%f`)[1]:print(`Entry = `,BB[I1-1]):

od:

OK:=TRUE:

else print(`The number must be a positive integer.\134n`):

fi:

od:

fi:

if OK = TRUE then

OUP := default:

fprintf(OUP, `The original system \134n`):

fprintf(OUP,`Diagonal Entries`):

for I1 from 1 to N do

fprintf(OUP, ` %11.8f`, A[I1-1]):

od:

fprintf(OUP, `\134n`):

fprintf(OUP,`Lower Sub-Diagonal Entries`):

for I1 from 2 to N do

fprintf(OUP, ` %11.8f`, B[I1-1]):

od:

fprintf(OUP, `\134n`):

fprintf(OUP,`Upper Sub-Diagonal Entries`):

for I1 from 1 to NN do

fprintf(OUP, ` %11.8f`, C[I1-1]):

od:

fprintf(OUP, `\134n`):

fprintf(OUP,`Inhomogeneous Entries`):

for I1 from 1 to N do

fprintf(OUP, ` %11.8f`, BB[I1-1]):

od:

fprintf(OUP, `\134n`):

if OK = TRUE then

# Steps 1 - 3 set up and solve Lz = 0

# Step 1

# The entries of U overwrite C and the entries of L overwrite A

C[0] := C[0]/A[0]:

Z[0] := BB[0]/A[0]:

# Step 2

for I1 from 2 to NN do

A[I1-1] := A[I1-1]-B[I1-1]*C[I1-2]:

C[I1-1] := C[I1-1]/A[I1-1]:

Z[I1-1] := (BB[I1-1]-B[I1-1]*Z[I1-2])/A[I1-1]:

od:

# Step 3

A[N-1] := A[N-1]-B[N-1]*C[N-2]:

Z[N-1] := (BB[N-1]-B[N-1]*Z[N-2])/A[N-1]:

# Step 4

# Steps 4 and 5 solve Ux = z

X[N-1] := Z[N-1]:

# Step 5

for I2 from 1 to NN do

I1 := NN-I2+1:

X[I1-1] := Z[I1-1]-C[I1-1]*X[I1]:

od:

# Step 6

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 entry 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, `CROUT METHOD FOR TRIDIAGONAL LINEAR SYSTEMS\134n\134n`):

fprintf(OUP, `The solution is\134n`):

for I1 from 1 to N do

fprintf(OUP, ` %12.8f`, X[I1-1]):

od:

fprintf(OUP, `\134n`):

if OUP <> default then

fclose(OUP):

print(`Output file `,NAME,` created successfully`):

fi:

SVZUaGlzfmlzfkNyb3V0fk1ldGhvZH5mb3J+dHJpZGlhZ29uYWx+bGluZWFyfnN5c3RlbXMufCtHNiI=

STdDaG9pY2V+b2Z+aW5wdXR+bWV0aG9kRzYi

SWVuMS5+aW5wdXR+ZnJvbX5rZXlib2FyZH4tfm5vdH5yZWNvbW1lbmRlZH5mb3J+bGFyZ2V+c3lzdGVtc0c2Ig==

SToyLn5pbnB1dH5mcm9tfmF+dGV4dH5maWxlRzYi

STVQbGVhc2V+ZW50ZXJ+MX5vcn4yLkc2Ig==

SS5Zb3VyfmlucHV0fmlzRzYi

IiIi

SUxJbnB1dH50aGV+bnVtYmVyfm9mfmVxdWF0aW9uc34tfmFufmludGVnZXIuRzYi

SSROPX5HNiI=

IiIl

SUNJbnB1dH50aGV+ZGlhZ29uYWx+ZW50cnl+aW5+cm93fj1+RzYi

IiIi

NiRJKUVudHJ5fj1+RzYiJCIiIyIiIQ==

SUNJbnB1dH50aGV+ZGlhZ29uYWx+ZW50cnl+aW5+cm93fj1+RzYi

IiIj

NiRJKUVudHJ5fj1+RzYiJCIiIyIiIQ==

SUNJbnB1dH50aGV+ZGlhZ29uYWx+ZW50cnl+aW5+cm93fj1+RzYi

IiIk

NiRJKUVudHJ5fj1+RzYiJCIiIyIiIQ==

SUNJbnB1dH50aGV+ZGlhZ29uYWx+ZW50cnl+aW5+cm93fj1+RzYi

IiIl

NiRJKUVudHJ5fj1+RzYiJCIiIyIiIQ==

SVZJbnB1dH50aGV+bG93ZXJ+c3ViLWRpYWdvbmFsfmRpYWdvbmFsfmVudHJ5fmlufnJvd349fkc2Ig==

IiIj

SS9+YW5kfmNvbHVtbn49fkc2Ig==

IiIi