restart:

# LDL^t ALGORITHM 6.5

# To factor the positive definite n by n matrix A into LDL**T,

# where L is a lower triangular matrix with ones along the diagonal

# and D is a diagonal matrix with positive entries on the

# diagonal.

# 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 and D(I),

# 1<=I<=n of D.

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:

# Step 1

for I1 from 1 to N do

# Step 2

for J from 1 to I1-1 do

V[J-1] := A[I1-1,J-1]*D1[J-1]:

od:

# Step 3

D1[I1-1] := A[I1-1,I1-1]:

for J from 1 to I1-1 do

D1[I1-1] := D1[I1-1]-A[I1-1,J-1]*V[J-1]:

od:

# Step 4

for J from I1+1 to N do

for K from 1 to I1-1 do

A[J-1,I1-1] := A[J-1,I1-1]-A[J-1,K-1]*V[K-1]:

od:

A[J-1,I1-1] := A[J-1,I1-1]/D1[I1-1]:

od:

# Step 5

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(`The output file is `):print(NAME):

OUP := fopen(NAME,WRITE,TEXT):

else

OUP := default:

fi:

fprintf(OUP, `LDL^t FACTORIZATION\134n\134n`):

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

for I1 from 1 to N do

for J from 1 to I1-1 do

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

od:

fprintf(OUP, `\134n`):

od:

fprintf(OUP, `The diagonal of D:\134n`):

for I1 from 1 to N do

fprintf(OUP, ` %12.8f`, D1[I1-1]):

od:

fprintf(OUP, `\134n`):

if OUP <> default then

fclose(OUP):

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

fi:

SVpUaGlzfmlzfnRoZX5MRExedH5NZXRob2R+Zm9yflBvc2l0aXZlfkRlZmluaXRlfk1hdHJpY2VzLnwrRzYi

STdDaG9pY2V+b2Z+aW5wdXR+bWV0aG9kRzYi

SWZuMS5+aW5wdXR+ZnJvbX5rZXlib2FyZH4tfm5vdH5yZWNvbW1lbmRlZH5mb3J+bGFyZ2V+bWF0cmljZXNHNiI=

SToyLn5pbnB1dH5mcm9tfmF+dGV4dH5maWxlRzYi

STVQbGVhc2V+ZW50ZXJ+MX5vcn4yLkc2Ig==

SS5Zb3VyfmlucHV0fmlzRzYi

IiIj

SVZUaGV+YXJyYXl+d2lsbH5iZX5pbnB1dH5mcm9tfmF+dGV4dH5maWxlfmlufnRoZX5vcmRlckc2Ig==

SVpBKDEsMSksfkEoMSwyKSx+Li4uLH5BKDEsTiksfkEoMiwxKSx+QSgyLDIpLH4uLi4sfnwrQSgyLE4pRzYi

SUIuLi4sfkEoTiwxKSx+QShOLDIpLH4uLi4sfkEoTixOKXwrRzYi

SWduUGxhY2V+YXN+bWFueX5lbnRyaWVzfmFzfmRlc2lyZWR+b25+ZWFjaH5saW5lLH5idXR+c2VwYXJhdGV+RzYi

SS1lbnRyaWVzfndpdGhHNiI=

STRhdH5sZWFzdH5vbmV+YmxhbmsuRzYi

SWpuSGFzfnRoZX5pbnB1dH5maWxlfmJlZW5+Y3JlYXRlZD9+LX5lbnRlcn4xfmZvcn55ZXN+b3J+Mn5mb3J+bm8uRzYi

STFZb3VyfnJlc3BvbnNlfmlzRzYi

IiIi

SVJJbnB1dH50aGV+ZmlsZX5uYW1lfmlufnRoZX5mb3Jtfi1+ZHJpdmU6XG5hbWUuZXh0RzYi

STtmb3J+ZXhhbXBsZTp+fn5BOlxEQVRBLkRUQUc2Ig==

STFUaGV+ZmlsZX5uYW1lfmlzRzYi

US5FOlxBTEcwNjUuRFRBNiI=

SURJbnB1dH50aGV+ZGltZW5zaW9ufm5+LX5hbn5pbnRlZ2VyLkc2Ig==

SSVOfmlzRzYi

IiIk

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

LDL^t FACTORIZATION The matrix L output by rows: -0.25000000 0.25000000 0.75000000 The diagonal of D: 4.00000000 4.00000000 1.00000000

JSFH