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.\134n`):

print(`This is the LDL^t Method for Positive Definite Matrices.\134n`):

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.`):

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:

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

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:

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 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:

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:

# 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:\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, `CHOLESKI FACTORIZATION\134n\134n`):

fprintf(OUP, `The matrix L output by rows:\134n`):

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, `\134n`):

od:

if OUP <> default then

fclose(OUP):

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

fi:

SUhUaGlzfmlzfkNob2xlc2tpfkZhY3Rvcml6YXRpb25+TWV0aG9kLnwrRzYi

SVpUaGlzfmlzfnRoZX5MRExedH5NZXRob2R+Zm9yflBvc2l0aXZlfkRlZmluaXRlfk1hdHJpY2VzLnwrRzYi

STdDaG9pY2V+b2Z+aW5wdXR+bWV0aG9kRzYi

SWZuMS5+aW5wdXR+ZnJvbX5rZXlib2FyZH4tfm5vdH5yZWNvbW1lbmRlZH5mb3J+bGFyZ2V+bWF0cmljZXNHNiI=

SToyLn5pbnB1dH5mcm9tfmF+dGV4dH5maWxlRzYi

STVQbGVhc2V+ZW50ZXJ+MX5vcn4yLkc2Ig==

SS5Zb3VyfmlucHV0fmlzRzYi

IiIi

SURJbnB1dH50aGV+ZGltZW5zaW9ufm5+LX5hbn5pbnRlZ2VyLkc2Ig==

SSROPX5HNiI=

IiIk

NiVJOWlucHV0fmVudHJ5fmlufnBvc2l0aW9ufkc2IiIiIkYl

SSlEYXRhfmlzfkc2Ig==

JCIiJSIiIQ==

NiVJOWlucHV0fmVudHJ5fmlufnBvc2l0aW9ufkc2IiIiIiIiIw==

SSlEYXRhfmlzfkc2Ig==

JCEiIiIiIQ==

NiVJOWlucHV0fmVudHJ5fmlufnBvc2l0aW9ufkc2IiIiIiIiJA==

SSlEYXRhfmlzfkc2Ig==

JCIiIiIiIQ==

NiVJOWlucHV0fmVudHJ5fmlufnBvc2l0aW9ufkc2IiIiIyIiIg==

SSlEYXRhfmlzfkc2Ig==

JCEiIiIiIQ==

NiVJOWlucHV0fmVudHJ5fmlufnBvc2l0aW9ufkc2IiIiI0Yl

SSlEYXRhfmlzfkc2Ig==

JCIkRCUhIiM=

NiVJOWlucHV0fmVudHJ5fmlufnBvc2l0aW9ufkc2IiIiIyIiJA==

SSlEYXRhfmlzfkc2Ig==

JCIkdiMhIiM=

NiVJOWlucHV0fmVudHJ5fmlufnBvc2l0aW9ufkc2IiIiJCIiIg==

SSlEYXRhfmlzfkc2Ig==

JCIiIiIiIQ==

NiVJOWlucHV0fmVudHJ5fmlufnBvc2l0aW9ufkc2IiIiJCIiIw==

SSlEYXRhfmlzfkc2Ig==

JCIkdiMhIiM=

NiVJOWlucHV0fmVudHJ5fmlufnBvc2l0aW9ufkc2IiIiJEYl

SSlEYXRhfmlzfkc2Ig==

JCIjTiEiIg==

The original matrix - output by rows: 4.00000000 -1.00000000 1.00000000 -1.00000000 4.25000000 2.75000000 1.00000000 2.75000000 3.50000000

STpDaG9pY2V+b2Z+b3V0cHV0fm1ldGhvZDp8K0c2Ig==

STUxLn5PdXRwdXR+dG9+c2NyZWVufCtHNiI=

STgyLn5PdXRwdXR+dG9+dGV4dH5maWxlfCtHNiI=

STZQbGVhc2V+ZW50ZXJ+MX5vcn4yLnwrRzYi

SS9Zb3VyfmlucHV0fmlzfkc2Ig==

IiIi

CHOLESKI FACTORIZATION The matrix L output by rows: 2.00000000 -0.50000000 2.00000000 0.50000000 1.50000000 1.00000000

JSFH