deter_bas

8/10/2019 deter_bas

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'*****************************************************'* Calculate the determinant of a real square matrix *'* A(n,n) by Gauss method with full pivoting. *'* ------------------------------------------------- *'* Ref.: "Algebre - Algorithmes et programmes en *'* Pascal By Jean-Louis Jardrin, Dunod - *'* Bordas Paris, 1988 p. 76-79" [BIBLI 10]. *'* ------------------------------------------------- *'* SAMPLE RUN: *'* (Calculate the determinant of matrix: *'* 10 18 1 14 22 *'* 4 12 25 8 16 *'* 23 6 19 2 15 *'* 17 5 13 21 9 *'* 11 24 7 20 3 ) *'* *'* Input size of square real matrix: 5 *'* Input desired precision: 1e-10 *'* *'* Line 1 *'* Element 1: 10 *'* Element 2: 18 *'* Element 3: 1 *'* Element 4: 14 *

'* Element 5: 22 *'* *'* Line 2 *'* Element 1: 4 *'* Element 2: 12 *'* Element 3: 25 *'* Element 4: 8 *'* Element 5: 16 *'* *'* Line 3 *'* Element 1: 23 *'* Element 2: 6 *'* Element 3: 19 *

'* Element 4: 2 *'* Element 5: 15 *'* *'* Line 4 *'* Element 1: 17 *'* Element 2: 5 *'* Element 3: 13 *'* Element 4: 21 *'* Element 5: 9 *'* *'* Line 5 *'* Element 1: 11 *'* Element 2: 24 *

'* Element 3: 7 *'* Element 4: 20 *'* Element 5: 3 *'* *'* Determinant = -4680000 *'* *'* *'* Basic version by Jean-Pierre Moreau, Paris. *'* (www.jpmoreau.fr) *'*****************************************************

8/10/2019 deter_bas


'PROGRAM Calculate_deterdefint i-ndefdbl a-h,o-z

MAXSIZE=25

'integer n size of matrix Adim A(MAXSIZE,MAXSIZE) 'pointer to input matrix'real d0 determinant of matrix A'real eps desired precision

cls print print " Calculate the determinant of a real square matrix" print " by Gauss method with full pivoting." print input " Input size of square real matrix: ", n' read precision input " Input desired precision: ", eps' read matrix A(n,n) print for i=1 to n print " Line "; i for j=1 to n

print " Element "; j; ": "; input "", A(i,j) next j print next i

gosub 2000 'd0=DMGT(eps,n,A)

print print " Determinant = "; d0 print print

END

'The subroutine TSRGT applies to input real square matrix A(n,n) the upper'triangularization algorithm of Gauss method with full pivoting and keeps'trace of successive transformations done in integer vectors KP and LP.'-----------------------------------------------------------------------------' Input parameters:' eps precision (real*8)' n size of A matrix (integer)' A pointer to input real square matrix (real*8)' Output parameters:' it flag=1 if A matrix ok, =0 if A matrix is singular (integer)

' C pointer to table storing main diagonal elements and supra-' diagonal elements of upper triangular matrix and the multi-' plying coefficients used during triangularization process' KP table storing informations concerning the column exchanges' during process (integer)' LP table storing informations concerning the line exchanges' during process (integer)'-----------------------------------------------------------------------------'The table C is first initialized to A matrix, then receives at each step k'of the triangularization process, usefull elements of A matrix at step k for

8/10/2019 deter_bas


'k=1,2,...n.'The variables po(real*8), lo and ko(integer) store respectively pivot at step k,'its line number and its column number.'------------------------------------------------------------------------------1000 'Subroutine TSRGT(eps, n, A, it, C, Kp, Lp)dim C(MAXSIZE,MAXSIZE), Kp(MAXSIZE),Lp(MAXSIZE)' set C to A for i=1 to n for j=1 to n C(i,j)=A(i,j) next j next i it=1: k=11010 po=C(k,k): lo=k: ko=k for i=k to n for j=k to n if abs(C(i,j))>abs(po) then po=C(i,j): lo=i: ko=j end if next j next i Lp(k)=lo: Kp(k)=ko if abs(po)<eps then

it=0 else if lo <> k then for j=k to n t0=C(k,j): C(k,j)=C(lo,j): C(lo,j)=t0 next j end if if ko <> k then for i=1 to n t0=C(i,k): C(i,k)=C(i,ko): C(i,ko)=t0 next i end if for i=k+1 to n

C(i,k)=C(i,k)/po for j=k+1 to n C(i,j)=C(i,j)-C(i,k)*C(k,j) next j next i k=k+1 end if if it=1 and k<n then goto 1010 if it=1 and abs(C(n,n))<eps then it=0return 'TSRGT

'The function DMGT returns the determinant of a real square matrix'A(n,n) by Gauss method with full pivoting.

'----------------------------------------------------------------------------' Input parameters:' eps precision (real*8)' n size of A matrix (integer)' A pointer to input real square matrix' Output parameters:' None'-----------------------------------------------------------------------------'The procedure TSRGT is used to reduce A matrix to an upper triangular matrix.'Output variables are it(integer), C(n,n), Kp(n) and Lp(n).

8/10/2019 deter_bas


'If it=0, matrix A is singular, if it=1, matrix A is regular. Table C contains'at location i,j (j>=i) the corresponding element of the upper triangular matrix.'Tables Lp and Kp contain informations relative to exchanges of line or column'that occured during the process. For instance, the element number k of Lp is'an integer <> k if an exchange of line has been made at step k (k=1,2,...,n).'The number of exchanges of lines and columns is stored in integer L. the'determinant of A matrix is stored in d0 (real*8).'-----------------------------------------------------------------------------2000 'd0=DMGT(eps, n, A)

gosub 1000 'call TSRGT(eps,n,A,it,C,Kp,Lp) if it=0 then d0=0# 'matrix singular, det=0 else 'matrix regular, det<>0 d0=1# for k=1 to n

d0=d0*C(k,k) next k l=0 for k=1 to n-1 if Lp(k) <> k then l=l+1 if Kp(k) <> k then l=l+1 next k

if l MOD 2 <> 0 then d0=-d0 'l is odd end ifreturn

'End of file deter.bas

deter_bas

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